Keywords: stability, microgrids, renewables, inverter, grid forming Power System Stability Frequency Stability Rotor Angle Stability Voltage Stability Small-Disturbance Angle Stability Transient Stability Large-Disturbance Voltage Stability Small-Disturbance Voltage Stability

This thesis deals with the stability issues introduced by the interconnection of massive renewables into an isolated microgrid. This research aims to identify the problems related to the topic, the indices to help understand the issues, and the strategy to enhance microgrid stability from the power system point of view.

In the first part, a state of the art on the evolution of power stability is addressed. A short history of power system stability since its first identification and how it has evolved is firstly presented. This part also provides a literature review of the power system stability, including its classification, and how it has evolved due to two reasons: the microgrid concept and the trend towards the integration of more inverter-based generation. A review of the practical indices for grid stability assessment is also reported, including the ones that we propose. This part is also useful for analyzing the positioning of this PhD research.

The second part of thesis presents the efforts to enhance the dynamic stability of microgrids characterized by massive renewable penetration. The main challenges and the current efforts are reviewed, which have shown that the current solutions focus on maintaining the philosophy of a classical power grid.

With the advent of more intermittent energy, the current efforts have proven to be costly. Therefore, a new perspective is proposed. Here, the generating elements and the customers are exposed with higher deviations in voltage and frequency, which are necessary so that that the power equilibrium and the stability of the microgrid can be maintained. This perspective is suitable with the microgrid concept to realize the dream of universal electricity.

The concept is then developed into a novel regulation strategy in which the system frequency and voltage are maintained in such a way to keep their ratio essentially constant around 1 (p.u. voltage to p.u. frequency). This strategy can potentially be implemented on all grid forming technologies. The benefits of employing this strategy include assurance that the electrical machinery is not harmed, plug-and-play feature, compatibility with current grid-tied inverter technologies, and no need for fast communication systems.

Finally, this proposed strategy is easy to implement and does not require revolution in terms of power system equipment and control. This implementation of this concept provides a very valuable piece of flexibility: time, which enhances the resilience and stability of a microgrid. However, wider frequency and voltage deviations occur and have to be accepted by all the actors within the microgrid. A validation through computer simulations in Power Factory and real-time hardware in the loop experiments has been carried out with satisfactory results.

First of all, I would like to sincerely express my gratitude towards all external defense committee members: Prof. Corinne Alonso, Prof. Jean-Claude Vannier, Dr. Georges Kariniotakis, Mr Eddie Widiono for your time to evaluate the thesis manuscript and for your constructive comments. From the bottom of my heart, I am also indebted to my excellent supervisors: Prof. Nouredine Hadjsaid, Prof. Ngapuli Sinisuka, Dr.

Lauric Garbuio, Dr. Vincent Debusschere, and Dr. Thi-Thu Ha Pham for your supervision and encouragement which made it possible for me to finish my PhD.

I would not forget to thank my friends and colleagues in Grenoble. Each and every one in Indonesian student association, thank you very much for creating a familiar environment in Grenoble, to make me feel like home when I needed the most. I would like to name some: Andy, Alif, Samuel, Mas Joko, Mbak Sita, Tika, Ditya, Puti, Mas Marwan, Mbak Rini, Mbak Anike, Mbak Inge dan mas Erwin, Tika, Raihan, Adi, Ali, Mbak Dwi, Mbak Isti, and the others that I might have forgotten to mention here, but surely everyone is unforgettable in my mind! I would like to take this wonderful opportunity to thank everyone in SYREL (power system team) group in G2elab: Vannak, Alexander, Felix, Bhargav, Nikolas, Stéphane, Mahana, Audrey, Ali, Pierre, Mamadou, Lalitha, Jonathan, Kim, Rafael, Jesus, Marcos, Anne, Laure, and the OPLAT teams for the warm friendship and fruitful conversations. None of this would have been possible without the help and support of G2elab's technical team, thank you Cedric and Antoine, thank you very much. I wish to express my gratitude to my parents and brothers, to my grandma and to my cousins and my extended family members for your support and encouragement. I am also extremely thankful to Afriana, my other half. Thank you for being you and thank you for staying on this long ride. I would like also to acknowledge the financial support from Indonesia Endowment Fund for Education (LPDP) for financing my PhD in Grenoble, which has made it possible for me to reach this level comfortably and successfully. I would like also to extend my gratitude towards all LPDP staff which is always helpful and responsive. Table 2. 2.5 -Comparison of Today's Grid and Smart Grid [START_REF]The Modern Grid Initiative[END_REF], [START_REF] Momoh | Smart Grid: Fundamentals of Design and Analysis[END_REF] 2.7 -Comparison of supply voltage requirements of microgrids according to some standards [78] Table 2.8 -Characteristics of Energy Storage Systems [START_REF] Mongkoltanatas | Energy Storage for stability of microgrids[END_REF], [START_REF] Vazquez | Energy Storage Systems for Transport and Grid Applications[END_REF] 2.9 -Summary of load modelling [START_REF] Arguence | Modélisation des ilots non-intentionnels et caractérisation des méthodes passives de détection d'ilotage[END_REF], [START_REF] Bokhari | Experimental Determination of the ZIP Coefficients for Modern Residential, Commercial, and Industrial Loads[END_REF]- [START_REF]Bibliography on load models for power flow and dynamic performance simulation[END_REF] 2.12 -General Comparison Among Three Types of Microgrids [START_REF] Hebner | Technical cross-fertilization between terrestrial microgrids and ship power systems[END_REF]- [START_REF] Skjong | The Marine Vessel's Electrical Power System: From its Birth to Present Day[END_REF] .................................. Table 2. [START_REF] Steinmetz | Power Control and Stability of Electric Generating Stations[END_REF] 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6. [START_REF] Martins | Efficient Eigenvalue and Frequency Response Methods Applied to Power System Small-Signal Stability Studies[END_REF] The past few decades has marked rapid evolution in electrical power sector that includes a major shift in significant operational aspects due to several key issues. One of the key issues is the climate change, which has led countries all over the globe to act collectively to slow down the temperature increase by reducing CO2 emissions. This consequently has caused a paradigm shift, especially in the way the electricity is produced. Renewable energy sources have been prioritized ever since. The way to handle their production variability thus has become critical. Technological advancements are catching up therewith.

Natural disasters that happened in the past few years have made engineers pay special attention to resilience in their designs. Resilience is defined as the ability to respond, adapt to, and recover upon a disruptive event. Microgrids are often brought on the table when the resilience is desired. By consensus, microgrid is defined as an integrated energy system consisting of distributed energy resources and multiple electrical loads operating as single autonomous grid. When a macrogrid is composed of a number of microgrids, a total blackout could possibly be better anticipated.

Microgrid is often seen as an important part of smart grids. However, the term "microgrid" itself is not standardized. Although there is a consensus on its main characteristics, the notions of size, technical requirements, and main objectives are often diverse. Some researchers consider a building such as data center or even a house to be a microgrid, thus pushing the advantages of a DC backbone [1], [2], while some others consider a small power system with the capacity of hundreds of kilowatts up to tens of megawatts to be a microgrid [3], [4], which is often constructed based on AC technologies. Another remark is that an intelligent central control system and a rapid communication system are often assumed to be available in the microgrid [5]- [START_REF] Sahoo | Control Techniques in AC, DC, and Hybrid AC-DC Microgrid: A Review[END_REF], thus enabling the execution of complex algorithms and the exchange of measurements and command signals.

Judging from the necessary investment for the installation and operation of the state-of-the-art elements required in the theoretical definition of (smart)-microgrid, it is sometimes difficult to justify the profitability aspect as the cost is high [START_REF] Fittrin | Optimal configuration of PV-Wind turbine-grid-battery in low potency energy resources[END_REF], especially in low human development index (HDI) areas which exhibit low productivity. An island in an emerging country which is inhabited by villagers could be thought of as an example. This means such microgrids most probably do not enjoy much flexibility, computational power and intelligence. However, electricity is still crucial in such areas in order to boost the local economic growth [START_REF] Fittrin | Optimal configuration of PV-Wind turbine-grid-battery in low potency energy resources[END_REF]- [START_REF] Lorde | The importance of electrical energy for economic growth in Barbados[END_REF]. The same situation can be presumed regarding the role of microgrids in post-disaster recovery, as discussed in [START_REF] Kinn | To what Extent is Electricity Central to Resilience and Disaster Management of the Built Environment?[END_REF].

Problem Statement

Transition towards more renewable energy affects electrical power systems in many aspects.

Traditionally, the generation side is dominated by dispatchable generators, meaning that the active power produced can be easily controlled. However, the situation is changing since more variable renewable energy sources (VRES) are integrated into power systems. Consequently, both production and consumption constantly fluctuate, which might worsen the power system stability. The system becomes more prone to disturbance, and may suffer more blackouts.

Power system operation and control strategies were developed based on the classic assumption that the generation side is dispatchable and can be controlled to satisfy the demand at any given time.

Frequency controls (i.e. primary, secondary, tertiary controls) evolved based on this assumption. With the transition in the generation side, which becomes less controllable, this assumption may not hold true anymore. System operators have taken a number of actions to ensure that the assumption is still somewhat acceptable so that the classical controls and protections are still applicable. Such actions include the use of available flexibility, including stand-by fast-response generators, storage capacity, interconnection capacity to adjacent grids, and demand response, in addition to the limitation of VRES penetration level.

Microgrid in the form of small independent power system is often the beginning of a power grid.

It may grow into a larger grid, and eventually become a macrogrid in the future. However, to ensure the reliability and resilience of the grid, engineers and researchers are now thinking of dividing a microgrid into a number of microgrids. Each microgrid has to be capable of functioning when the main macrogrid is down due to disruptive events. Some crucial challenges arise from this vision.

Upon disruptive events, we believe that a microgrid has to survive with minimum computational power and communication. It furthermore has to be able to deal with massive penetration of variable renewables with limited flexibility, thus minimum amount of dispatchable sources. In this regard, we would also like to challenge the renewable limitation strategy, for instance the VRES limit of 30% in France, which has also been in force in a number of French overseas departments and regions.

In order to tackle these challenges, we carried out this PhD research, focusing on standalone AC microgrids, with a peak load ranging from 1 MW to 100 MW. Such characteristics are displayed by either newly-constructed power grids in rural areas and on small islands or microgrids serving as the last resort following disruptive events which strike a macrogrid. Consequently, these microgrids may consist of elements normally available in today's AC grids, such as generators, transformers, batteries, PVs and other non-dispatchable sources, medium voltage distribution lines, and loads.

The main question that we address in this PhD research is how the grid will evolve with new requirements, notably massive variable renewable energy penetration of up to 100%. Important issues are identified and then strategies to preserve power system dynamic stability are rethought.

Considering that evolution is normally better accepted than revolution, the control strategies to preserve power system stability are developed around the classical power system control strategies.

This is done to ensure that the solutions will be easily understood by engineers and researchers accustomed to the classical notion of power system stability.

Principal Contributions

The contributions of this thesis concern a number of key issues in standalone microgrids with limited computational power and communications in the presence of massive penetration of variable renewables. They are presented as follows.

Power System Stability and its Classification

The contributions include:

C.1. State of the art of the evolution of power system stability and its classification

The text-book knowledge on power system stability is based on the behavior of synchronous machine. With the interconnected of more inverter-based generations in power grids, the power system stability needs to depend less on or even independent of synchronous machines. The reviewed topics include general power system stability problem and classification, simulation tools, changes in regulation strategy and grid standards.

C.2. Identification of the challenges in microgrids operating with massive variable renewable energy sources (VRES) connected via inverters and efforts to tackle the issues Microgrids have different behavior compared to large interconnected grids which brings along new challenges. These challenges need to be tackled in order for the microgrid to function reliable as expected. The key challenges and the efforts to accommodate massive VRES in microgrids are discussed.

Indices of microgrid stability

With regard to the development of the indices dealing with microgrid stability, the contributions of this research are as follows:

C.3. State of the art of indices used in power system stability assessment

The definition, approach, and significance of indices such as critical clearing time, renewable energy penetration level, frequency excursion, and indices derived from eigenvalue analysis and PV/QV curves are reviewed.

C.4. Updated definition of critical clearing time

The classical critical clearing time calculation is based on the behavior of synchronous machines. This definition has to be updated with the advent of more inverterbased generators in the grid.

C.5. New indices for preliminary microgrid stability assessment

As the limit of variable renewable penetration varies on a case-per-case basis, new indices are necessary as a guide in the design and operations of microgrids. The new indices are introduced based on practical requirements of maintaining power supply and balance stability. They are useful and practical for microgrid planning and operation purposes.

Strategy to preserve microgrid stability operating with massive VRES

The contributions in the strategies to preserve microgrid stability are listed as follows.

C.6. Novel views on quality of supply of grids functioning with massive VRES

The needs of the society which are served by the means of electric energy evolve over time. As the electric power systems were mostly developed in the 20 th

PART I Power System Stability in Microgrids

Chapter 2 -State of the Art on the Evolution of

Power System Stability

In this chapter, the state of the art on the evolution of power stability is presented. A short history of power system stability since its first identification and how it has evolved is reported. It also provides a literature review of the power system stability, including its classification, and how it has evolved due to two reasons: the microgrid concept and the trend towards the integration of more inverter-based generation.

Introduction

Power system stability was recognized as a problem as early as the 1920s, during which a power system was typically composed of remote power plants supplying electricity to load centers over long distances [START_REF] Kundur | Power System Stability[END_REF]. In 1920, Steinmetz published a paper discussing the stability of a 230 MW power system [START_REF] Steinmetz | Power Control and Stability of Electric Generating Stations[END_REF]. He observed a phenomenon which appeared to be transient angle instability and provided analysis of the issue. In this early period, exciters and short circuit clearance were slow. Engineers put more focus on steady state and transient rotor angle instability, hence synchronizing torque was often studied.

With the technological advancements such as faster exciters and fast fault clearance, in addition to the new challenges such as interconnections and operations close to the thermal limits, the dependence on the controls increased. Generator problems, including the modeling of synchronous machine and its controls, became the new emphasis of stability studies. The assessment was carried out with numerical integration methods. The equations were initially solved manually in a very simplified way with numerical integration or graphical method (equal-area criterion) [START_REF] Pavella | Transient Stability of Power Systems: A Unified Approach to Assessment and Control[END_REF] before 1950s. The development of the computer in 1950s brought much improvement on power system stability studies. It enabled the simulation (notably in time-domain) of complex power systems with detailed element and control models. New categories of power system stability began to emerge, i.e.

frequency stability in 1970s-1980s [START_REF] Elgerd | Optimum Megawatt-Frequency Control of Multiarea Electric Energy Systems[END_REF]- [START_REF] Converti | Long-term stability solution of interconnected power systems[END_REF], small signal stability [START_REF] Martins | Efficient Eigenvalue and Frequency Response Methods Applied to Power System Small-Signal Stability Studies[END_REF]- [START_REF] Semlyen | Sequential computation of the complete eigensystem for the study zone in small signal stability analysis of large power systems[END_REF] and voltage stability in 1980s [START_REF] Kwatny | Loss of steady state stability and voltage collapse in electric power systems[END_REF]- [START_REF] Fischl | A comparison of indices for predicting voltage collapse in power systems[END_REF].

In 2004, IEEE/CIGRE Joint Task Force on Stability Terms and Definitions defined power system stability as the ability of an electric power system, for a given initial operating condition, to regain a state of operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically the entire system remains intact [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF]. This definition is applicable to the interconnected power system as a whole. Instability can be displayed by a run-away or run-down situation, such as a gradual increase in angular separation of generator rotors, or a continuous drop in bus voltages, that may cause an outage in a major portion of the power system.

Anderson and Fouad published the first version of their book devoted to power system control and stability in 1977 [START_REF] Anderson | Power System Control and Stability[END_REF]. The second version came out in 2003 [START_REF] Anderson | Power system control and stability[END_REF]. In the book, it is stated that if the oscillatory response of a power system during the transient period following a disturbance is damped and the system settles in a finite time to a new steady operating condition, the system is stable. The system is considered unstable if it the system does not fulfill the criteria of being stable according to that definition. The stability problems addressed in the book are strongly associated with the behavior of synchronous machines and other parameters affecting the synchronous machines, such as tie lines and line capacitances.

In 1994, Kundur published a book entitled "Power System Stability and Control" [START_REF] Kundur | Power System Stability And Control[END_REF]. This textbook is considered one of the main references in the domain of power system stability. Kundur analyzed the issues of power system stability mostly based on the behavior of synchronous machines, loads, and their associated controls based on time domain or modal analysis. He mentioned that the power system stability problem is essentially how to keep interconnected synchronous machines in synchronism. In a more recent book published in 2007 by Grigsby et al. [START_REF] Grigsby | Power System Stability and Control[END_REF], power system stability issues are also addressed, particularly in the second part of the book titled "Power System Dynamics and Stability". The contributors laid out power system stability based on the behavior of synchronous machines, loads, and their associated controls. In both references, the behavior of synchronous machines and their associated controls is vital to the stability of the whole power network, which is well justified since they dominate the generation side. Power electronics applications are discussed, yet not in an extensive manner. The discussion mostly covers their use in reactive power compensation and HVDC technology.

Over the past few decades, more and more VRES have been integrated into power systems, mostly through inverter technologies, which differ from the synchronous machine technology. More RES are expected to be integrated into power systems in the future. In the context of Indonesian electricity, the data presented in PLN's electrical power business plan for 2018-2027 [START_REF]Electrical Power Provision Business Plan of PT Perusahaan Listrik Negara (Persero) Year 2018-2027[END_REF] regarding the plan of VRES plant construction in Indonesia unveils positive growth of renewable generation, as depicted in Figure 2.1. The document also mentions some efforts in order to comply with the Indonesian National Energy Policy [32], [START_REF]Powering the Nation: Indonesian Power Industry Survey 2017[END_REF] which targets at least 23% of RES in the national energy mix by 2025. Similar trend of VRES growth is observed in other countries, as reported by Ecofys and Digsilent for Ireland power grid [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF] and by International Energy Agency [START_REF]Renewables 2017[END_REF]. From the trend, it makes sense to expect that power system stability problems are evolving.

The motivation of this chapter lies in the identification of the development of power system stability issues and how they will evolve in the future with more interest in microgrids and more inverter-based variable renewables being interconnected. A short historical review has been provided

earlier in this subchapter. The rest of chapter will address the stability classifications and their possible changes, discussions on the ongoing development of power systems, and the microgrid concept.

Classical Stability Classifications

As stated by Kundur in [START_REF] Kundur | Power System Stability[END_REF], [START_REF] Kundur | Power System Stability And Control[END_REF] and reiterated by IEEE/CIGRE joint task force in [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF], power system stability is essentially a single problem. However, for the sake of the analysis of stability problems, which includes identifying essential factors contributing to instability and how to enhance the stable operation, the classification is necessary. The classification is based on (1) the physical nature of the resulting instability related to the main variable in which instability can be observed, (2) the size of the disturbance, which indicates the most appropriate method of calculation, and (3) the devices, processes, and the time span that must be taken into consideration [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF]. Nevertheless, there might be interdependency among the categories. For instance, voltage instability may be observed

Rotor Angle Stability

Rotor angle stability refers to the ability of synchronous machines of an interconnected power system to remain in synchronism after being subjected to a disturbance. Instability occurs in the form of increasing angular swings of some generators, leading to the loss of synchronism. The loss of synchronism may occur between one machine and the rest of the system, or between groups of machines, with synchronism maintained within each group [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF].

This category of power system stability originated from the physical behavior of synchronous machine, known as the swing equation, and the load transfer among generators in a power system is dictated by the power-angle relationship [START_REF] Pavella | Transient Stability of Power Systems: A Unified Approach to Assessment and Control[END_REF], [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF], [START_REF] Anderson | Power system control and stability[END_REF], [START_REF] Kundur | Power System Stability And Control[END_REF], [START_REF] Hadjsaïd | Power Systems and Restructuring[END_REF] . The swing equation governs the rotational dynamics of a synchronous machine [START_REF] Grainger | Power system analysis[END_REF], formulated as follows [START_REF] Hadjsaïd | Power Systems and Restructuring[END_REF]. The latter form of the equation is more preferred since power is more convenient than torque in calculations. The same thing can be said about per unit systems. The equations show that the dynamics of a synchronous machine, or a power system composed primarily by synchronous machines, depend on the equilibrium of power production and consumption and the total inertia. A higher power variation results in a higher frequency variation, especially in systems with a low total inertia. The equation also represents the conservation of energy. Kinetic energy of the rotating mass is converted into electrical energy when there is unbalance between the electric power supplied and the respective mechanical power supplying the synchronous machine.

𝐽

The other important equation is the so-called power-angle equation. This equation describes the transmitted power as a function of rotor angle [START_REF] Hadjsaid | Security Analysis[END_REF]. Considering a simple model of a generator connected to an infinite bus through a reactance as shown in Figure 2.3, the equation can be formulated as follows.

𝑃 𝑒 = 𝐸 ′ 𝐸 𝐵 𝑋 𝑇 𝑠𝑖𝑛 𝛿 = 𝑃 𝑚𝑎𝑥 𝑠𝑖𝑛 𝛿 Eq. 2.3

Figure 2.3 -Simple Model of Generator connected to an infinity bus [38]

This equation governs the power transfer over an inductive transmission line. The transferred power is proportional to the sinus of the angle between the sending bus and the receiving bus.

As this category of stability focuses on the ability to maintain the synchronous operation of synchronous machines, the rotor angle is the main variable to monitor. Rotor angle stability is categorized as short term phenomena and traditionally divided into two categories, transient angle stability and small disturbance angle stability. They are discussed more thoroughly as follows.

Transient Stability

Transient angle stability, also known as large-disturbance rotor angle stability, is the first category of power system stability into which many research efforts were devoted [START_REF] Kundur | Power System Stability[END_REF], [START_REF] Steinmetz | Power Control and Stability of Electric Generating Stations[END_REF]. It is generally scenario-based and is concerned with the ability of the power system to maintain synchronism when subjected to a severe disturbance [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF], such as short circuits, loss of load, or loss of generation. Corresponding equations are normally non-linear and cannot be linearized at certain points due to the large perturbations involved. Instability may occur in a very short time frame (a few seconds), leaving little to no time for operators to intervene.

Transient stability depends on both the initial operating state and the severity of the disturbance.

It may not always occur as first swing instability, although it is normally associated with the first swing problem. Time domain simulation is often used in this analysis, and it takes much computational time. Therefore, direct methods of stability assessment, such as those based on Lyapunov or energy function, are attractive alternatives.

The direct method determines the transient stability without explicitly solving the system differential equations. Such methods are very appealing, although they still possess some challenges, as described below.

 They do not include time stamp of load change.

 They do not account for real-time information on system topology and devices contributing to system changes  They do not inform the decision-maker of real time status of the system stability.

Small Signal Rotor Angle Stability

Small signal rotor angle stability deals with small perturbations. The corresponding equations can therefore be linearized at a specific operation point [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF], [START_REF] Kundur | Power System Stability And Control[END_REF]. This category of stability is dependent on the operating state of the system. Instability may appear in two forms: increase in rotor angle deviation through a non-oscillatory mode due to lack of synchronizing torque, or rotor angle oscillations of increasing amplitude due to insufficient damping torque. The latter is more common in today's interconnected power systems. The time frame of interest is in the order of 10 to 20 seconds after a perturbation [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF].

Local plant modes, inter-area modes, control modes, and torsional mode oscillations fall into this category. The stability depends on the strength of transmission system seen by the power plant, generator excitation control, plant output, and load characteristics.

Tools for small signal rotor angle stability analysis have to able to detect the existence of oscillations and identifying the influencing factors, so as to provide the operators with the information on how to develop mitigation measures. Investigation is often conducted with nonlinear time-domain simulations as an extension to transient stability analysis. However, this method poses some problems, such as the dependency on scenarios, lengthy calculation, and insufficient insight into the nature of the oscillatory problem, which leads to difficulty in developing countermeasures [START_REF] Paserba | Small Signal Stability and Power System Oscillations[END_REF]. A method called modal analysis, otherwise known as Eigen analysis, is well suited for investigating problems concerning oscillations [START_REF] Kundur | Power System Stability And Control[END_REF], [START_REF] Paserba | Small Signal Stability and Power System Oscillations[END_REF]. Here, power system model and its associated controls are linearized at a specific operating point. The stability of each mode and the relationship between the modes, the variables, and parameters of the modes can be identified. Another technique named spectral estimation, which is based on Prony analysis, may be used to analyze time domain responses and return information on the oscillatory modes. All three methods can be employed as a complement to each other.

Frequency Stability

Frequency stability is linked to the ability of a power system to maintain the operating equilibrium following a severe system upset [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF]. Severe perturbations may result in separation of the system into islands. It is more specifically concerned with the ability of a power system to maintain steady frequency following a severe perturbation causing a significant imbalance between generation and load [START_REF] Kundur | Power System Stability[END_REF], [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF]. It is associated with equipment responses, coordination of control and protection, and power reserve management. Frequency stability is typically analyzed with timedomain simulations. The models include controls and protections that might not be taken into account in conventional transient stability studies, such as volts/hertz protection tripping schemes [START_REF] Kundur | Power System Stability[END_REF].

The figure below shows a typical frequency movement at a bus in a power system following sudden trip of a generator. Before the event, the power system is working at the nominal frequency.

Following the generator trip, the power system experiences sudden change, the power production is less than the consumption. The frequency decreases, and the electric power output of the synchronous machines increases, proportional to the rate of change of frequency (ROCOF). The inertia of the synchronous machines limits the ROCOF. After some time, the primary reserve is activated automatically based on the droop control of the machines. The mechanical power of the machines is increased and the frequency climbs up until it reaches the quasi steady state frequency, typically close to system's nominal frequency. After some time, the dispatching of all generators is adjusted, known as secondary and tertiary regulation, to reach the nominal frequency and to prepare for another upcoming contingency. The sensitivity of the frequency to temporary imbalances is inversely proportional to the total system inertia. Shortly after the loss of generation power, the inertia of the rotating machinery releases kinetic energy to help limit the deviation of system frequency, as explained by the swing equation shown in Eq. 2.2. This provides additional instantaneous power output from the synchronous machines which maintains the power balance in the system, prior to the activation of the primary regulation.

Frequency stability is further classified into long term and short term. Short term frequency stability is dealing with severe upsets and fast dynamics, dealing with the responses of elements such as generator controls and protections [START_REF] Kundur | Power System Stability[END_REF]. The study period is within a few seconds. Long term frequency stability deals with slow dynamics, including cascading events, which may eventually result in system-wide blackout. The study period may reach tens of minutes. Discussions on long term frequency stability and some lessons learned from real events are presented in [START_REF] Davidson | Long term dynamic response of power systems: An analysis of major disturbances[END_REF] and [START_REF] Converti | Long-term stability solution of interconnected power systems[END_REF].

Voltage Stability

Voltage stability is linked to the ability of a power system to maintain acceptable voltages at all busbars in the power system under normal operating conditions and following a perturbation [START_REF] Kundur | Power System Stability And Control[END_REF].

Voltage stability is compromised when an upset (e.g. network fault), increase in load, or change of power generation results in a progressive and uncontrollable decline or rise in voltage. The main cause leading to voltage instability is the failure to respond to the demand for reactive power [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF]. In contrast to active power, reactive power cannot be transmitted over long distances, especially in inductive grids. Measures to preserve reactive power balance should be available locally. The driving force for voltage instability is usually the loads [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF], [START_REF] Kundur | Power System Stability And Control[END_REF], [START_REF] Cutsem | Voltage instability: phenomena, countermeasures, and analysis methods[END_REF], [START_REF] Hill | Nonlinear dynamic load models with recovery for voltage stability studies[END_REF]. Following a disturbance, the power consumption tends to be restored by the action of motor slip adjustment, distribution voltage regulators, tap-changing transformers, and thermostats. This builds up the stress on the high voltage network due to the increase of reactive power consumption and consequently causes further voltage reduction which might lead to a voltage collapse. Voltage and transient stability issues are interrelated and the same mitigation measures may be relevant for both cases.

In terms of classification, voltage stability is comprised of short term and long term voltage stability [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF], [START_REF] Kundur | Power System Stability And Control[END_REF]. The short term voltage stability involves dynamics of fast acting load components such as induction motors, electronically controlled loads, and HVDC converters. Study period is in the order of several seconds, and dynamic modeling of loads is often important. On the other hand, the long term voltage stability involves slower acting equipment such as tap-changing transformers, capacitor switching, generator redispatching, load shedding, thermostatically controlled loads, and current limiters. The study period may extend to several minutes.

A brief description about the most popular methods to analyze voltage stability problems is presented below [START_REF] Kundur | Power System Stability And Control[END_REF], [START_REF] Cutsem | Voltage instability: phenomena, countermeasures, and analysis methods[END_REF], [START_REF] Jabri | Voltage stability assessment of a microgrid[END_REF]:

1. P-V and Q-V curves method
The active power versus voltage (PV) and reactive power versus voltage (QV) curves are widely used in assessing voltage stability issues. They mainly predict the point at which the voltage at a certain bus will collapse. In other words, the MW distance and MVAr distance to the critical point is predicted.

Modal Analysis

The idea is to compute the eigenvalues of the buses in the power system network. The smallest eigenvalues extracted from the load flow reduced Jacobian matrix indicate the buses that are likely to have voltage collapse. In addition, a participation factor for the buses for the smallest eigenvalue mode is calculated to have an idea of which one is more contributing to the instability.

Singular value decomposition (SVD)

The idea is to find when the Jacobian matrix is going to be singular. With this technique, it is difficult to find the exact amount of MVAR leading to the singularity of the Jacobian matrix, but on the other hand, it can be approximated in case of availability of the linearity property of the SVD index. The disadvantage is that it requires large amount of calculation time.

Time domain simulation

This is similar to analysis of rotor angle stability. Dynamic modeling of loads is often essential. In contrast to angle stability, short circuits near loads are more important.

It should be noted that methods 1-3 above are the so-called static analyses, while method 4 is known as the dynamic analysis.

The concept of large signal voltage stability and small signal voltage stability is similar to that of transient stability. The difference is that in voltage stability analysis, the load dynamics is emphasized [START_REF] Mansour | Voltage Stability[END_REF], in addition to transformer tap changers and generator field current controls [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF].

Large signal voltage stability deals with large disturbances whereas small signal voltage stability with small ones, hence linearization around the operating point is permissible [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF].

Short term voltage stability involves dynamics of fast acting load components. The period is in the order of several seconds. It is somewhat similar to rotor angle stability analysis. Long-term voltage stability involes slower acting equipment such as tap-changing transformers, the study period may extend to several minutes.

Comments on the Classification

These classifications of power system stability prove to be useful as it is widely used in power system stability analysis these days. However, in 2006 Samuelsson and Lindahl revealed that an instability phenomenon occurred following the operation of two wind farms which are based on induction generators, each rated at 160 MW and 150 MW [START_REF] Samuelsson | Closure of 'Definition and classification of power system stability[END_REF]. With regard to the classification proposed by IEEE/CIGRE in [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF], this case does not fit into any of the categories. Kundur et al.

acknowledged that earlier efforts to define power system stability do not completely reflect current industry needs, experiences, and understanding [START_REF] Kundur | Closure of 'Definition and classification of power system stability[END_REF]. The classifications do not comprehend all practical stability scenarios. Consequently, we can infer from these comments that there is still room for improvement concerning the stability classifications, which will be discussed later in Section 2.5.2.

Simulation Tools

Power System Stability Simulations

In a transient stability analysis, the power system and all its elements are traditionally represented in phasors, with sequence networks. The emphasis is placed on the positive sequence. This calculation strategy is well known as RMS analysis, otherwise known as electromechanical transient analysis (TS). The calculation is initialized with a power flow analysis, which defines the topology, line impedances, connected loads and generations, and pre-disturbance states. Another calculation strategy is the so-called EMT analysis, which stands for electromagnetic transient analysis.

In EMT simulations, the time step is in the order of microsecond [START_REF] Han | Power system electromagnetic transient and electromechanical transient hybrid simulation based on PSCAD[END_REF]. The electrical networks are modeled completely in three phase unbalanced fashion and the modeling of electrical equipment is more detailed. In addition, the equations are solved in time domain, consequently instantaneous voltages and currents can be displayed.

On the other hand, in RMS simulations, the time step is in the order of milisecond. Sequence phasor network is put in action. If an unsymmetrical event is of interest, all positive sequence, negative sequence, and zero sequence are used. Else if a symmetrical event is of interest, only positive sequence is employed. Equipment modeling is less detailed. Consequently, RMS simulation less time consuming compared to the EMT simulations.

Reference [START_REF]Integrating Inverter-Based Resources into Weak Power Systems -Reliability Guideline[END_REF] discusses the limitations that one may encounter when using transient stability (RMS) simulations to evaluate power system stability. When dealing with high penetration of inverter-based resources and weak grid interconnections, the following considerations should be made:

• Validity at certain range of frequency

Transient stability programs use simplified generator models which neglect the dynamics of stator flux. In addition, constant bus admittance matrix is used to model the transmission network. Due to such simplifications, any high frequency oscillations above 5 Hz produced by a transient stability program are not reliable. Harmonic effects due to switching or controls may not be accurately represented.

• Positive sequence RMS based

The effect of DC current components, as well as zero and negative sequence components are often neglected in these calculations. Due to the RMS-based calculations, care should be taken when dealing with protection and control elements which normally use phase quantities.

• Large time step

Power electronic converters contain control loops and algorithms with fast response times, faster than the time steps used in transient stability programs.

• Limited converter electrical representation

Depending on the model, converter electrical representation is simplified. For instance, the DC bus may be assumed to be constant. Controls and interfaces of IBG are often simplified or ignored. These elements can be influential to the converter behavior.

The abovementioned points lead some manufacturers to recommend the use of EMT tools to confirm the equipment behavior or to validate the transient stability results. EMT simulations are also used for analyzing overvoltages in power systems, such as lightning overvoltage, switching overvoltage, and surge arrester influences. However, EMT simulations are sometimes complicated to be conducted as the available models typically represent only large signal performance [START_REF] Etxegarai | Current procedures and practices on grid code compliance verification of renewable power generation[END_REF]. RMS is favored when frequencies below the fundamental frequency are of interest, such as frequency and voltage responses following a line or generator trip, phenomena well known as the transient stability problem.

When the focus is on fast transient behaviors of the whole system, such as in grid-code compliance studies, detailed models of the elements are often not necessary [START_REF] Shuai | Microgrid stability: Classification and a review[END_REF]. Simplified models of elements such as IBGs and electrical machinery may therefore be employed to conduct RMS studies for system dynamic behavior analysis. However, it is also feasible to apply EMT-type programs to study transient stability or small signal stability problems, producing more precise results at the expense of computational speed and data requirements [START_REF] Mahseredjian | Simulation Tools for Electromagnetic Transients in Power Systems: Overview and Challenges[END_REF]. In the newest version of some simulation programs, time domain co-simulation of RMS and EMT models with individual time steps is featured, such as the case of Power Factory 2019 [START_REF]DIgSILENT releases PowerFactory 2019 -DIgSILENT[END_REF]. An example of RMS and EMT simulation results is shown above. More in-depth comparison between RMS and EMT is discussed in [START_REF] Mahseredjian | Simulation Tools for Electromagnetic Transients in Power Systems: Overview and Challenges[END_REF], [START_REF] Lund | Dynamic fault simulation of wind turbines using commercial simulation tools[END_REF], [START_REF] Sørensen | Simulation and verification of transient events in large wind power installations[END_REF]. In general, the components of the power system that influence the electrical and mechanical torques of the machines should be included in the model. These components are as follows [START_REF] Anderson | Power system control and stability[END_REF]:

• The network before, during, and after the transient In addition to the elements listed above, the behavior of inverter-based generations and storage systems along with their controls needs to be modeled for the dynamic analysis.

A typical power system stability study consists of the following steps [START_REF] Kundur | Closure of 'Definition and classification of power system stability[END_REF]:

✓ ✓ ✓ Eurostag X ✓ ✓ Matlab/Simulink ✓ ✓ ✓ Open DSS X ✓ ✓ PSCAD/EMTDC ✓ X X PSD-BPA X ✓ ✓ Siemens PSS/E X ✓ ✓ ETAP ✓ ✓ ✓
Sometimes, repeated simulations are necessary and scripting capability becomes very important.

The possibility to create a custom controller representation is also very crucial, especially when dealing with inverter-based generation (IBG) where the models are not well standardized. The comparison regarding these issues is presented in A popularity study was conducted. 50 research papers were arbitrary chosen for this purpose.

The result is illustrated as follows. In terms of acceptance by system regulators for grid code compliance verification, DigSILENT

Power Factory is chosen as a dynamic simulation program in the UK, and PSS/E in Australia, Ireland, and Spain, as reported in [START_REF] Etxegarai | Current procedures and practices on grid code compliance verification of renewable power generation[END_REF], [START_REF] Bullich-Massagué | Power plant control in large-scale photovoltaic plants: design, implementation and validation in a 9.4 MW photovoltaic plant[END_REF].

In this research, Digsilent Power Factory is used as this program is among the highly requested simulation programs in industrial communities, such as the case for the customers of Schneider Electric.

Power Systems

Introduction

The current electricity grids were established at the end of the 19 th century and are ageing. In order to respond to the challenges of the 21 st century, which include renewable integration, distributed generation, EV integration, and mass-electrification, the network evolves towards a more intelligent grid in order to maintain the reliability, efficiency, and power quality of today's electricity supply.

The trend is moving towards more use of more intelligent components, such as intelligent appliances which are able to decide on when to consume based on a set of criteria, smart power meters which are useful for monitoring and billing purposes, as well as demand response interface, smart substations, distribution automation, and smart generation [START_REF] Morales Jadan | Development of optimal energy management in Galapagos Islands towards Smart Grid[END_REF].

Stability analysis is an integral component of system security and reliability assessment [START_REF] Kundur | Overview on definition and classification of power system stability[END_REF].

Traditionally, power systems are designed to comply with N-1 criterion. This means that a power system is planned such that, with all facilities are in service, it is operating in a secure state, and with one credible contingency event, the system moves to a satisfactory state. This criterion has proven to be the best practice solution in several domains [START_REF]ENTSO-E's supporting document to the submitted Network Code on Load-Frequency Control and Reserves[END_REF], [START_REF] Kundur | Overview on definition and classification of power system stability[END_REF], [START_REF]Supporting Document for the Network Code on Operational Security[END_REF].

ENTSO-E in [START_REF]ENTSO-E's supporting document to the submitted Network Code on Load-Frequency Control and Reserves[END_REF] requires that the frequency containment reserves, defined as the operational reserves activated to contain system frequency after the occurrence of an imbalance, is sized to the reference incident that may cause the biggest active power imbalance with an N-1 failure. The same is also widely practiced in the industry, as discussed in [START_REF] Kundur | Overview on definition and classification of power system stability[END_REF]. However, with more and more shares of variable renewables in power systems, it becomes more difficult to satisfy the N-1 criterion at all times, notably in generation loss cases, i.e. the problem of maintaining the power balance between production and consumption. Classically, generators are operated such that upon any trip of a single unit of generator, the system moves to a new satisfactory state without any load shedding. Thus, it is necessary to have total grid spinning reserve of at least the active power rating of the largest unit of generator in service. In the worst case scenario and with insufficient spinning reserve, an event (e.g. largest generator loss) may cause continuingly decreasing frequency and eventually may result in a blackout.

The spinning reserve problem is relatively simple to deal with when all generators are dispatchable or fully predictable. However, with variable, somewhat unpredictable, and undispatchable nature induced by some types of renewables, power production may decrease at the same time due to sudden weather change. This complicates the calculation of the necessary spinning reserve.

For the sake of variable renewable generations, such as wind farms, it is considered less important to consider the small signal stability, even for islanded systems, as discussed in [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF], [START_REF] Persson | Frequency response by Wind Farms in Islanded Power Systems with High Wind Power Penetration[END_REF], [START_REF] Potamianakis | Modeling and simulation of small hybrid power systems[END_REF]. Frequency stability becomes the focus due to frequent power imbalance occurring in the system.

in [START_REF] Ernst | Solving the fluctuation problems in a land with 100% of renewable energy[END_REF], Ernst discusses how to deal with 100% renewables. He argues that supplying power grids with 100% of renewable energy is possible, albeit complicated due to the intermittent behavior of renewable sources. He analyzed some figures of wind power production and here are some of his important conclusions: (i) rapid changes at a country level are possible within one to several hours, (ii) the larger the area, the smaller the variations. To answer the basic working principle of an electrical network where the power generated must be equal to the power consumed at all times, Ernst proposed three generic solutions: (i) storing energy and releasing it at the right time (ii) controlling the power generated, and (iii) controlling the demand for energy. In his presentation, he also complimented his proposals with examples.

ENTSO-e in [START_REF]Supporting Document for the Network Code on Operational Security[END_REF] states that inertia adequacy will play an important role in order to ensure system stability after major perturbations in the future, when intermittent generation with small inertia is increasing. Studies to identify the necessary minimum amount of inertia in any synchronous area and how to respect the minimum inertia are needed. Additionally, the same document identifies some causes of frequency deviations in today's power systems and some new opportunities. One of the phenomena which can accentuate the frequency deviation is the development of renewable energies.

Technologies such as solar panels or wind turbine provide little or no natural inertial response to the system compared to conventional synchronous generators due to decoupling through power electronic equipment. It is illustrated in the following curve. Lower system inertia is observed especially during off-peak periods because fewer synchronous generations are online. The condition can be more complicated with high penetration of VRES.

Greater penetration of intermittent sources may displace conventional generation and system operators would face more challenges in real-time operations. On the other hand, new opportunities arise, such as the possibility of activating synthetic inertia provider and automatic frequency demand side response.

With more and more electronically coupled renewables installed, inverters will eventually replace synchronous generators and they have to be able to provide the services that synchronous machines were previously responsible for. Several obstacles such as limited overcurrent of inverters, less inertia, and less stored energy in the power conversion process still leave the stability problem of microgrids challenging.

Smart Grid Concept

Hajdsaid et. Al assembled the desired changes in the distribution system towards intelligent systems in [START_REF] Hadjsaïd | Electrical Distribution Network[END_REF]. First of all, the authors pointed out that the future operating modes will be impacted by the future, which depends on the assigned objectives. For the European case, the four elements which can characterize the expected qualities of the future networks are [START_REF] Hadjsaïd | The Electrical Distribution Network: From Heritage to Innovation[END_REF], [START_REF] Hadjsaid | Smart Grids: Motivation, Stakes, and Perspectives[END_REF]:

Hz s  Accessible.
Networks will be capable of connecting all the producers willing to be integrated.

 Economical

Emphasis will be put on making the best use and creating profit. This will allow cost optimization for all users.

 Flexible

Redundancy of the paths will be increased in order to optimize the network reaction to various perturbations.

 Reliable

Networks will have to ensure and increase the quality and security of supply.

There are various views on smart grid concept. However, the main drivers for smart grid development are somewhat similar all over the world, as explained by Hadjsaid et. Al in [START_REF] Hadjsaid | Smart Grids: Motivation, Stakes, and Perspectives[END_REF]. Within the EU, the priorities are the challenge of integrating more renewable energies, energy efficiency, and EU market integration in the framework of a carbon-free economy. In the US, the main drivers are blackouts, peak-load situations, and ageing assets. In China, the priorities are the issues of fast development of the grid, the need of integrating large-scale wind farms in the north and nation-wide interconnection. Some other important issues in China include the development of electric vehicles, PVs, and microgrids.

According to the EU SmartGrids technology platform, the concept is defined as an electricity network which intelligently integrates the actions of generators and consumers connected to it in order to efficiently deliver sustainable, economic, and secure electricity supplies. Whereas the US Department of Energy's definition of smartgrid is a self-healing network, which enables active participation of consumers, operates resiliently against attack and natural disasters, accommodates all generation and storage options, enables introduction of new products, services, and markets, optimizes asset utilization and operates efficiently, and provides power quality for the digital economy [START_REF] Hadjsaid | Smart Grids: Motivation, Stakes, and Perspectives[END_REF].

Present and Future Development

Momoh in his book "Smart Grid" drew a comparison of today's grid and smart grid. The summary is as follows. With regard to the future of electricity systems, Jamasb et.al discussed the topic in their book titled Future Electricity Technologies and Systems [START_REF] Jamasb | Future Electricity Technologies and Systems[END_REF]. Some challenges and possibilities that they identified are summarized as follows:

1. Distributed (renewable) generations More and more distributed generations, mostly based on renewable energies, are integrated into power systems. This is partly stimulated by the framework of the economic incentives for renewable energies [START_REF] Hadjsaïd | The Electrical Distribution Network: From Heritage to Innovation[END_REF]. In addition, RES prices have decreased over the past few years, making them a financially attractive alternative to fossil-based generation [START_REF]Microgrid Stability Definitions, Analysis, and Modeling[END_REF]. However, many experts believe that the future power system will still see centralized and distributed generation coexist [START_REF] Barroso | The Future Power System: Centralized, Distributed, or Just Integrated?[END_REF].

The interconnection interface of DER could be based on either electrical machinery or power electronics. With electrical machinery technologies, they are often operated at high rpm, high frequency. In order to obtain maximum efficiency, they might be operated at variable speed as well. Up until hundreds of kilowatts of power rating, it is feasible to use IGBT-based AC-DC-AC frequency converter.

Types of distributed generations are discussed in detail in [START_REF] Reza | Stability analysis of transmission system with high penetration of distributed generation[END_REF]. They range from conventional fossil based generations to renewable-based distributed generations connected through inverters. From power system point of view, DGs are classified into two major categories, controllable and non-controllable, as shown below. A significant portion of distributed generations is intermittent and interconnected through inverters. They have different limitations and behavior from the classical synchronous machinebased sources. The modeling and control strategies may vary from one manufacturer to the others. However, they also offer more flexibility and faster response which could be the key to the future grid operation. The flexibility includes dynamic variation of control parameters and control algorithms, often under strict limitations of current and temperature.

Many studies considered that frequency variation is a consequence of a step variation of power or production [START_REF] Mongkoltanatas | Energy Storage for stability of microgrids[END_REF]- [START_REF] Delille | Dynamic frequency control support: A virtual inertia provided by distributed energy storage to isolated power systems[END_REF]. However, active power of renewable energy may fluctuate rather slowly, as discussed in [START_REF] Anvari | Short term fluctuations of wind and solar power systems[END_REF].

2. Limitations of semiconductors.

Voltage and current limits are regulated by the maximum allowable temperature. However, due to the small unit scale of power electronics, there is no usable short time rating. As a future perspective, silicon carbide devices will increase the ability of converters to withstand very high currents in the future.

Growth of microgrids

An important difference of a microgrid and a small power system is that microgrids may be dominated by IBGs, therefore the operation and protection must be suited to power electronic technologies.

4. Reactive compensation service from power electronics.

Basic hardware blocks used in all power electronics (PE) technologies are similar to each other. The power processing can use the spare capacity of the inverter that is available when the DG is not running at full power to provide reactive power compensation.

5. Compatibility level and load management [START_REF] Green | The role of power electronics in future power systems[END_REF] Most domestic loads operate at low voltage DC, which normally include internal voltage regulation that can tolerate considerable deviations in the voltage and the frequency supplied by the utility. An increasing number of portable appliances, such as laptop and smartphone are labelled "universal input", indicating a wide range of operation, typically between 40 and 65 Hz and 90 and 250 V. Two issues can be identified: first, an increasing number of loads belong to the constant power type, consequently they consume a fixed power irrespective (within a certain range) of the voltage and the frequency supplied. Constant-power loads deteriorate the damping in a power system and may cause problems for system operators. Secondly, in terms of compatibility, these loads are immune to high degrees of undervoltage and sag.

In systems other than public electricity supply, voltage regulation is treated differently.

Instead of regulating the distributed voltage to maintain tight limits, wide limits are authorized.

Reliance is then placed on the load-side, in the form of load regulation so as to process the distribution voltage into a well-regulated voltage required for final use. The distribution inside a computer system is designed based on this principle. The systems proposed for future automobiles and electric aircraft also feature this philosophy of voltage regulation, and the same philosophy can potentially be adapted for off-grid systems.

Newer standards and regulations show that more flexible voltage and frequency limits are accepted. This is reflected in the evolution and amendment of IEEE 1547 standard. It was first introduced in 2003 [START_REF]IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems[END_REF], and have been amended several times since then. It was originally developed with an assumption of a lower penetration of DER, therefore it was rather specific to grid-connected sources. However, the growth of DER has been very rapid since the inception of the standard and the need for updating the standard is inevitable [START_REF]IEEE 1547 -New Interconnection Requirements for Distributed Energy Resources Fact Sheet[END_REF]. This standard, which will be more thoroughly discussed in Subchapter 2.4.5, displays the acceptance of wider frequency and voltage variations.

Wider range of limits is found in smaller networks, such as ships and islanded grids, as summarized by Czarkowski et. Al. in [78], shown below. In France, the frequency of medium voltage network (referred to as HTA in French) may vary between -6% to +4% for islanded systems, while the frequency limitation is stricter between ±1% for interconnected systems [START_REF] Alvarez-Hérault | Characteristics of Distribution Network[END_REF].

Demand-side actions

Balancing supply and demand is traditionally achieved almost entirely through supply-side action, but power electronics and controllable loads could open up useful possibilities for demand-side action that would allow greater use of intermittent and uncontrolled supply sources.

Distributed generation will benefit a distributed demand-side management. What is sought is responsive loads that can react to network conditions or control signals with a reduction of consumption.

New protection strategies

It is not sensible to require power electronic equipment to mimic the fault response of conventional plant. Instead, fault protection and fault ride through must be rethought. In some circumstances, the less onerous fault current interruption that results might lead to overall cost benefits.

New stability behavior

Traditional synchronous generators suffer a dynamic stability problem that may result in a loss of synchronism following a fault or disturbance. This is a relatively low frequency problem (less than system nominal frequency) governed by the acceleration of the inertia of the generator and prime mover. Inverter-interfaced power sources do not have inertia as such. Synchronization is maintained by a control loop, often through a phase-locked loop. The dynamic stability issue for an inverter is maintaining the stability of control loops governing the current output.

Electricity Storage

A group of experts in the US identified and defined applications for electricity storage in power systems, ranging from power quality improvement (high power storage, in the range of seconds) to the replacement of spinning reserve for grid stability and the need for generation scheduling (in the range of minutes) and to load levelling, peak shaving, and energy management (high energy storage, in the range of hours).

Energy storage consists of various technologies, ranging from mechanical, electrochemical, chemical, electrical, and thermal storages. They are discussed in more detail in [START_REF] Reza | Stability analysis of transmission system with high penetration of distributed generation[END_REF], [START_REF] Mongkoltanatas | Energy Storage for stability of microgrids[END_REF]. The summary is presented in Table 2.8. Certain experts believe that electricity storage technology will reshape the future operation of power systems. Mongkoltanatas in [START_REF] Mongkoltanatas | Energy Storage for stability of microgrids[END_REF] explains that power and energy storage is designed based on various purposes. If energy storage is installed for load leveling purposes, it has to be dimensioned based on the peak load consumption and maximum power production. However, the high penetration of renewables may complicate the calculation. Often, energy storage is sized according to the penetration rate of variable renewables. If all energy production comes from variable renewables, the energy storage may have to be designed according to the capacity of the grid, which causes the project cost to skyrocket.

Despite countless research efforts dedicated into figuring the shape of the power system of the future, it is still not very clear. Some of the possible scenarios identified by NREL from several projects and reports are illustrated in Figure 2.9. In the figure, the names represent the examples in progress and the institutions. It should be anticipated that the power systems will become increasingly heterogeneous in the future.

The need for Flexibility

A power system is said to be flexible if it can, within economic boundaries, respond rapidly to large fluctuations in demand and supply, both scheduled and unforeseen events, ramping down production when demand decreases, and ramping up when it rises [START_REF]Empowering variable renewables: Options for Flexible Electricity Systems[END_REF]. In terms of variable renewables, a flexible system is the one capable of both absorbing large quantities of VRES and disposing the surplus in a cost-effective way.

Power system flexibility can be obtained from a number of factors. On the supply side, the resources include rapidly dispatchable power plants, interconnections, and energy storage systems.

In addition, a significant flexibility resource is also accessible on the demand side: demand response to deal with the power fluctuations. This is still somewhat under-exploited. Flexibility is an intrinsic feature of interconnected networks. Electricity grids have an inherent tolerance as actual operating conditions may depart from the assumptions made by planning engineers. Flexibility assessment is not yet a common practice. Some TSO and DSO are pushing the growth of VRES with a learning-as-we-go approach. A very simplified approach is suggested in [START_REF]Empowering variable renewables: Options for Flexible Electricity Systems[END_REF] to provide a broad picture of the factors. The first step is to identify the flexibility resource. The scale of the existing, available resource of a power system depends on how it has evolved over time. Several main sources of flexibility are as follows:

 The quantity of fast response capacity in the generation portfolio  Storage availability: capacity and duration  Demand side management (DSM) response: the potential of consumers to alter their electricity use in response to supply abundance/shortage.

Experience in Denmark shows that at times of high wind energy production, the electricity price falls significantly. If low price periods can be capitalized by consumers, for example by shifting their demand to such periods, the need for peaking plants can be reduced, and when it is high, the need for storage systems or power export can be minimized. The second step is to take into account the existing requirements for flexibility, such as existing balancing needs, errors in demand forecast, and contingencies. The last step is to pay attention to the net flexible resource. If the targeted amount of VRE generation exceeds what is possibly accommodated by the net flexibility resource, additional measures must be taken to avoid power system stability problems.

In many markets, incentives designed to encourage renewable energy production tacitly assume that conventional generation continues to supply needed grid support services such as frequency control, contingency reserves, voltage control, and balancing services. As systems rely more heavily on variable renewable resources, those grid services will increasingly need to come from the renewable resources themselves.

Today, energy storage is inevitably a corner stone of massive VRES penetration levels. Today's balancing supply and demand is accomplished largely at the primary energy input level, by adjusting the supply of power from dispatchable generators to match the power demand. As VRES become dominant in the power generation mix, the role of conventional power plants on balancing declines and alternative solutions are indispensable. Such longer term energy storage is termed bulk energy storage to distinguish it from energy storage providing shorter-term system flexibility needs. One important challenge of massive penetration levels is finding bulk energy storage options that are not prohibitively expensive. Such a process may seem not economic today, but could be economically sound in the future.

Inertia Problem

An analysis performed by Ecofys and Digsilent [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF] concludes that the maximum allowable share of non-synchronous instantaneous generation inertia lies in the range of 60-80%. In order to reach higher shares of variable renewables, actions should be taken to ensure that there is sufficient inertia in the system. One key strategy for tackling this challenge is to enable power electronic interfaced power sources (PEIPS) to provide inertia, or to keep synchronous machines such as synchronous condensers online for provision of system services.

Synchronous condensers' spinning rotor's inertia, which makes the machines more tolerant of grid disturbances, is exactly their key advantage over power electronic devices such as static VAR compensators. New synchronous condensers remain 10-20% more costly per VAR of reactive power capacity than an SVC [START_REF]Empowering variable renewables: Options for Flexible Electricity Systems[END_REF]. But repurposing old power-plant generators upon decommissioning and transforming those to synchronous condensers can be a quick and cheap solution. For example, gas fired-power plants can now be equipped with clutches that decouple the turbines and generators, allowing the machines to work as condensers. Another wild card is to absorb some power from the wind turbines' rotating mass. This is a strategy that could be used in the future to tackle the inertia challenge. A number of more intelligent elements are being integrated into power systems. They include smart or communicating meters, actuators, fast switching devices, powerful sensors, and advanced functions of network supervision and control, and batteries.

ICTs for power grids exist as embedded software, whether at the level of components or control centers, and means of physical communications [START_REF] Hadjsaid | Smart Grids: Motivation, Stakes, and Perspectives[END_REF]. A particular interest is associated with the

Load

A wide variety of loads are supplied by a power system, such as electrical motors (pumps, compressors), heating, lighting, and electronics, which may be controllable or not. They must be appropriately modeled in power system studies. Improper load modeling may lead to an erroneous conclusion of a study, as discussed in [START_REF] Arguence | Modélisation des ilots non-intentionnels et caractérisation des méthodes passives de détection d'ilotage[END_REF], [START_REF] Miller | Western Wind and Solar Integration Study Phase 3A: Low Levels of Synchronous Generation[END_REF]. Some load models are compiled in Table 2.9 from the literature review. Special care also should be taken to parameter choice. Incorrect parameters may also lead to incorrect results.

It should be noted that there is an important difference between static loads and dynamic loads.

Static loads are more suitable for static studies such as load flow analysis. The model is suitable for steady state, where the dynamics following frequency and voltage changes are not the main focus.

On the other hand, dynamic load models can capture the behavior of a load following frequency and voltage changes, including the phenomena of load rebounding and delays.

P = f°(V) Q = f°(V) P = f°(f) Q = f°(f)

Model Simplicity Knowledge of the parameters

Static Load ZIP ✓ ✓ ✗ ✗ ✓ 4 par. ✓ Exponential ✓ ✓ ✓ ✓ ✓ 4 par. ✓ RLC ✓ ✓ ✗ ✓ ✓ 1 par. ~+ RLC + RC ✓ ✓ ✓ ✓ ✓ 3 par. ~- Dynamic Load Models (black box) Modified Exponential ✓ ✓ ✓ ✓ ~ 7-8 par. ✓ Mod. Exponential + Cap (CRIEPI) ✓ ✓ ✓ ✓ ~ 8-9 par. ✓ General Load Model (Power Factory) ✓ ✓ ✓ ✓ ✓ 4-17 par.

✓

It is noteworthy that the number of parameters relate to the number of parameters of the load model (excluding P0 and Q0). Here, the general load model is discussed more thoroughly. This model is often used throughout the thesis because of its flexibility, simplicity, suitability for static and dynamic analyses, knowledge of parameters, and the availability in the chosen software program. The discussion on other load models and their comparison can be found in [START_REF] Arguence | Modélisation des ilots non-intentionnels et caractérisation des méthodes passives de détection d'ilotage[END_REF]. [START_REF]Digsilent PowerFactory 2018 Technical Reference Documentation General Load[END_REF] Where: The sum of p1, p2, and p3 must be equal to 1. The same applies for the sum of q1, q2, and q3.

Δf K pf + s•t pf 1 + s•t 1 K qf + s•t qf 1 + s•t 1 1 1 Δu 1 + s• 1 + s•t 1 1 + s•t 1 1 1 + + + + + + + + x x p 1 •V kpu0 + p 2 •V kpu1 + p 3 •V kpu q 1 •V kqu0 + q 2 •V kqu1 + q 3 •V kqu P Q P 0 Q 0 t pu /k put 1 + s•t qu /k qut Figure 2.

-Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads

P, Q = Active
ZIP model has a long history of being employed in power system studies. The classical equations are shown as follows [START_REF] Kundur | Power System Stability And Control[END_REF].

𝑃 = 𝑃 0 [𝑝 1 + 𝑝 2 𝑉 + 𝑝 3 𝑉 2 ](1 + 𝐾 𝑝𝑓 ∆𝑓) Eq. 2.4 𝑄 = 𝑄 0 [𝑞 1 + 𝑞 2 𝑉 + 𝑞 3 𝑉 2 ](1 + 𝐾 𝑞𝑓 ∆𝑓) Eq. 2.5
This particular model has an important drawback. Frequency dependency is not represented.

This may be acceptable for load flow studies or for dynamic studies on stiff grids since the deviation of frequency is very minor. Considering that the grid inertia is decreasing and more frequent load imbalance might occur due to intermittent sources, frequency becomes an important factor to take into account in load modeling. Here, the modified ZIP model seems convenient and promising. The model takes frequency dependence and load dynamics into consideration. It is worth mentioning that this model is also a particular case of power factory's general load model. [START_REF] Banjar-Nahor | Study on Renewable Penetration Limits in a Typical Indonesian Islanded Microgrid considering the Impact of Variable Renewables Integration and the Empowering Flexibility on Grid Stability[END_REF] The variables p1, p2, p3 as well as q1, q2, and q3 may be either positive or negative. This is useful in defining the models which may have zero active or reactive power at nominal operating conditions but may absorb power under frequency or voltage excursion.

Δf K pf 1 + s t 1 K qf 1 + s t 1 1 1 Δu 1 1 + s t 1 1 1 + s t 1 1 1 + + + + + + + + x x p 1 + p 2 V + p 3 V 2 q 1 + q 2 V + q 3 V 2 P Q P 0 Q 0 Figure 2.

-Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads

Power electronic converters

The integration of more variable renewable energies will stimulate the evolution of generation interface technology. Power generation was initially developed around synchronous machine technology. However, inverters as an interface between the energy source and the network are becoming more and more common.

Depending on their operation in an AC microgrid, power converters can be classified into gridfeeding, grid supporting, and grid-forming power converters [START_REF] Rocabert | Control of Power Converters in AC Microgrids[END_REF]- [START_REF] Brabandere | A Voltage and Frequency Droop Control Method for Parallel Inverters[END_REF]. Grid forming converters can be represented as an ideal ac voltage sources with a low output impedance, setting the voltage amplitude E* and frequency ω* of the local grid by using a proper control loop. A standby UPS is an example of this type of power inverter. Power sharing among grid forming converters is a function of the value of their output impedances. In a microgrid, the ac voltage generated by the grid-forming power converter will be used as a reference for the rest of grid-feeding power converters connected to it. In industrial applications, these power converters are fed by stable dc voltage sources driven by batteries, fuel cells, or other stable primary sources.

On the other hand, the grid feeding power converters are mainly designed to deliver power to an energized grid. They can be represented as an ideal current source connected to the grid in parallel with high impedance or its dual circuit. It is important to outline that the current source should be perfectly synchronized with the AC voltage at the connection point, in order to regulate accurately the active and reactive power exchanged with the grid.

Grid feeding power converters are controlled current sources, presenting high parallel output impedance. These converters are suitable to operate in parallel with other grid feeding power converters in grid connected mode. Currently, most of the power converters belonging to DG systems operate in grid-feeding mode, like PV and wind systems. However, they can participate in the control of the microgrid ac voltage amplitude and frequency by adjusting the references of active and reactive powers to be delivered.

Finally, the grid supporting converters can be represented either as an ideal ac-controlled current source in parallel with a shunt impedance, or as an ideal ac voltage sources in series with a link impedance. These converters regulate their output current/voltage to keep the value of the grid frequency and voltage amplitude close to their rated values.

The main objective of grid supporting power converter is to deliver proper values of active and reactive power to contribute to the regulation of the grid frequency and the voltage. A grid supporting power converter is controlled as a voltage source with a link-impedance, or alternatively, as a current source with a parallel impedance. In any case, its main objective is to participate in the regulation of the ac grid voltage amplitude E* and frequency ω* by controlling the active and reactive power delivered to the grid. An example of this type of power inverter is line-interactive UPS systems.

Regulation and Standards

Regulation

The frequency regulations are typically classified as follows [START_REF] Kundur | Power System Stability And Control[END_REF], [START_REF]ENTSO-E's supporting document to the submitted Network Code on Load-Frequency Control and Reserves[END_REF], [START_REF] Mongkoltanatas | Energy Storage for stability of microgrids[END_REF], [START_REF] Kirby | Frequency Regulation Basics and Trends[END_REF].

primary regulation (0 -10s)

Sometimes it is referred to as the frequency containment process. The objective is to stabilize the frequency after a disturbance at a steady state value within the permissible maximum steady state frequency deviation by a joint action of frequency containment resources within the system.

The frequency responsive spinning reserve is responsible for this function. It is comprised of online synchronous machines controlled by speed droops. According to a study on change proposals to the grid codes in England & Wales and in Scotland [START_REF]New Generation Technologies and GB Grid Codes[END_REF], the characteristic reduction in the network demand due to frequency fall of typically 2% per Hz may be taken into account as a part of operating reserves in primary regulation.

During the first 10 seconds, it is possible that the frequency drops below the permissible value, and this consequently can trigger the automatic load shedding scheme.

secondary regulation (~10s -10 minutes)

It is also referred to as the frequency restoration process. It controls the frequency towards its nominal value by the activation of frequency restoration reserve and replaces the activated frequency containment reserve. This process can be performed either automatically or manually.

All spinning reserve capable of changing the power output immediately, as well as offline generators capable of being synchronized within 10 minutes is responsible for this function.

Sometimes it requires manipulation of the speed/load reference.

Tertiary regulation (>10 min)

It is sometimes referred to as the reserve replacement process. It replaces the activated frequency restoration reserve (FRR) and/or supports FRR activation by activation of the reserve replacement. Reserve replacement is comprised of all generators having the response speed on the time scale of more than 10 minutes. Tertiary regulation is sometimes not necessary, depending on the severity of the fault.

According to Indonesian Grid Codes [100]-[103], some supplementary actions other than the three frequency regulation strategies may be taken when necessary. They are as follows:

1. Manual dispatching command to power plants 2. Voltage set point reduction (also known as brown-out) to reduce active power demand 3. Manual load shedding 4. Automatic load shedding (with underfrequency relays)

Generator tripping by overfrequency relays

Similar to frequency regulations, there exist also some regulation strategies concerning the voltage stability, as presented below [START_REF] Mousavi | Literature Survey on Fundamental Issues of Voltage and Reactive Power Control[END_REF]:

1. Primary voltage regulation (0 -10s)

The primary voltage regulation (PVR) is performed by automatic and rapid voltage regulators which control reactive power output so that the output voltage magnitudes are kept at specified values. PVR has only local scope targeting the control in the particular bus assigned to the controllable device. Generally, the primary voltage control is performed by the generator's automatic voltage regulator (AVR). The AVR regulates the voltage by controlling the excitation system. The other controllable devices such as synchronous condenser, SVC, and STATCOM can also be used for PVR.

Secondary voltage regulation (~10s -10 minutes)

The coordination and the supervision of the PVR set point values within a given geographical zone are the tasks of the secondary voltage regulation (SVR). The main idea behind SVR is to coordinate the various regional reactive power resources in such a manner that they control the voltage at given pilot nodes. Pilot nodes are selected such that the voltage magnitude at the pilot node represents the voltage profile over the associated zone. Another method for pilot node selection is based on electrical distance concept between nodes.

Tertiary voltage regulation (>10 mins)

The basic idea behind the tertiary voltage regulation (TVR) is to increase the operating security and efficiency of the system through a centralized coordination of the zonal SVR structure. The TVR considers counteract coupling between controls at the SVR levels. In fact, TVR defines the optimal voltage points for the SVR pilot nodes.

Regulation in Microgrids

The frequency and voltage regulations in microgrids marked by high level of power electronics are classified as follows [START_REF] Rocabert | Control of Power Converters in AC Microgrids[END_REF]. This regulation is also applicable to microgrids, where different DG technologies form various primary resources (oil, gas, wind, sun, tide, water, etc.) and with a broad variety of roles (grid-feeding, grid-supporting, and grid-forming) may be interconnected.

The primary control level

Also known as local control, it allows multiple actors to work together with the aim of maintaining local variables such as voltage, frequency, or current injection within the accepted range. A vital feature of the primary control is to distribute the power injected into the microgrid to each DG unit. The local controllers may include droop strategy and virtual impedance control techniques available on each DG unit.

The secondary control level

It acts as a centralized automatic generation controller and compensates quasi-steady-state errors. Under any voltage or frequency deviation, a secondary control action is applied to multiple DG units in the microgrid to restore their nominal values, for example by adjusting the droop characteristic coefficients or by changing the active power and reactive power references.

Compared with conventional generators, this secondary control has faster response, but limited by some factors such as the battery ratings or the primary resource availability. This control uses communications and wide-area monitoring systems to harmonize the actions of all generation units within the power grid. The time response is in the range of minutes, which is slower compared to primary control.

The tertiary control level

It is in charge of the optimization of microgrid operation, normally based on economic criteria, taking into consideration the generation cost, the demand and supply balance and its short term forecast. It acts over the secondary control level with the objective to restore the secondary control reserve, as well as to set the microgrid voltage and frequency to their nominal values in case the secondary reserve is not effective enough.

Codes and Standards

Due to future challenges introduced by high penetration of power electronic interfaced sources, normally employed for intermittent source interconnection, in 2017 ENTSO-E published a guidance document for national implementation for network codes on grid connection [START_REF]High Penetration of Power Electronic Interfaced Power Sources (HPoPEIPS)[END_REF]. This guidance focuses on RES power sources interfaced via power electronics. Important aspects such as capabilities to manage low total system inertia (TSI), low synchronizing torque, low short-circuit power, and low dynamic voltage support are some problems that the guidance deals with. The guidance also identifies stability challenges and potential remedial actions, including their side effects. The possible remedial actions include costly conventional approaches (synchronous generators, synchronous compensators), and the holistic approach in which the power electronic interfaced sources contribute to system strength. Control strategies can be implemented into power electronics. Strategies such as swing equation based inertial response and grid-forming control strategies. However, care should be taken to ensure that delays in measurement and controls are carefully taken into account to avoid adverse impact on system stability.

The same challenges also affected North American standards. As discussed in [START_REF]IEEE 1547 -New Interconnection Requirements for Distributed Energy Resources Fact Sheet[END_REF], [106]- [START_REF] Nagarajan | Greening the Grid -Best Practicse for Grid Codes for Renewable Energy Generators[END_REF],

IEEE 1547 standard which deals with DER of 10 MVA or less, and is technology neutral, has undergone several important updates, as shown in Table 2.10. A comparison of applicable grid standards in North America from a technical point of view is presented as follows [START_REF]IEEE 1547 -New Interconnection Requirements for Distributed Energy Resources Fact Sheet[END_REF].

    Fixed reactive power    Volt-Var     Volt-Watt    Watt-Var

 

Legend:  Prohibited,  Allowed by mutual agreement,  capability required 2.5. Microgrids

Introduction

Small isolated grids have existed for years in remote communities. However, the microgrid concept was formally introduced in 2001 by Bob Lasseter as a concept to deal with distributed renewable energy [START_REF] Lasseter | Microgrids [distributed power generation[END_REF]. In general, microgrid is defined as an integrated energy system within clearly defined electrical boundaries consisting of distributed energy resources and multiple electrical loads operating as single, autonomous grid either in parallel to or islanded from the existing utility power grid. However, The exact definition of microgrids varies in terms of size, capacity, components, and behaviors [118]- [START_REF] Jayawarna | Stability of a MicroGrid[END_REF].

Microgrid is often regarded as an important part of smart grid, since it offers enhancements to power systems, notably in reliability, sustainability, and economic aspects. However, there are several regional/national focuses regarding microgrid concept, as discussed in [START_REF] Tao | From laboratory Microgrid to real markets -Challenges and opportunities[END_REF]. The US views microgrid as a handy alternative of waiting for reinforcement of their ageing transmission, so as to postpone or even to avoid further investment, especially in transmission network. As reported in [START_REF] Bollman | An experimental study of frequency droop control in a low-inertia microgrid[END_REF], the US also values the importance of reliability and robustness of electrical network of important infrastructure, particularly in relation with national security issues such as military installation. In Europe, the utilities are putting hopes in microgrid as to absorb more renewable energies in the distribution grid without threatening supply quality and security. In Japan and other countries with high dependency in fossil fuel, microgrid is an inspiration of energy self-independence for policy makers. In emerging countries, microgrids are regarded as a viable option for remote areas, as the case for Thailand [START_REF] Mongkoltanatas | Energy Storage for stability of microgrids[END_REF], Cambodia [START_REF] Vai | Planification du réseau de distribution basse tension avec intégration de sources photovoltaïques et stockage : cas du réseau du Cambodge[END_REF], and Indonesia [START_REF] Römer | Pioneering smart grids for Indonesia -the case of a smart grid roadmap development[END_REF]. A comparison about smart grid technologies in US and Europe is discussed in [START_REF] Simoes | A Comparison of Smart Grid Technologies and Progresses in Europe and the U.S[END_REF]. There exist two forms of microgrids, grid connected and isolated. In both operating modes, a microgrid should be capable of maintaining balance between power generation and consumption [START_REF]Microgrid Stability Definitions, Analysis, and Modeling[END_REF].

Government agencies, utilities, military bases, universities, and research centers have been deploying microgrids, and the positive trend is expected to continue in the next decade [START_REF]Global Microgrid Market 2016-2020[END_REF], driven by environmental issues, the need for electricity in remote communities, and the prospect of increased resiliency and reliability [START_REF] Ton | A More Resilient Grid: The U.S. Department of Energy Joins with Stakeholders in an R amp;amp;D Plan[END_REF]- [START_REF] Hirsch | Microgrids: A review of technologies, key drivers, and outstanding issues[END_REF].

Several well-known microgrids are in service and can be found in detail in [136]. Some examples are Sendai Microgrid in Japan, which gained popularity due to its reliability and effectiveness during 2011 earthquake and tsunami, Santa Rita Jail, and Illinois Institute of Technology.

Microgrids, especially those with massive penetration of renewables, still pose several technical challenges that need to be tackled in order to function properly. As presented in [START_REF] Roche | Energy Management at the Grid Edge[END_REF], challenges of microgrids can be classified into cost and behavioral challenges, technical challenges, and management challenges. Behavioral challenges include user acceptance, such as cost and comfort issues, as well as the willingness of main stakeholders to collaborate. From a managerial point of view, this new concept needs the evolvement of business models, governance, and regulation. While in technical point of view, microgrids raise questions about the sizing of the equipment (DER, storage, etc), system modeling, stability and control, and interdependencies, notably with communication systems. It should be noted that in some cases, customers in microgrids may enjoy different quality of energy delivery and may not have the same degree of freedom compared to those of interconnected grids.

In this thesis, we focus on standalone AC microgrids, with a peak load ranging from 1 MW to 100 MW. Such characteristics are displayed by either newly-constructed power grids in rural areas and on small islands or microgrids serving as the last resort following major disruptive events which strike an interconnected grid. Only the technical challenges are addressed in the discussions in the second part of this thesis.

Indonesia's point of view

Romer et. Al. discussed the road map of smart grid development in Indonesia in [START_REF] Römer | Pioneering smart grids for Indonesia -the case of a smart grid roadmap development[END_REF]. One of the most important challenges to tackle in the archipelago is how to supply more than 250 million people with access to electricity. Other than the population growth which is expected to reach 300 million people in 15 years, the outlook of economic growth will lead to a heavy increase of electricity demand. An additional challenge is how to bring energy access to all of Indonesian population, considering the country's geographic situation, where the inhabitants are spreading over 5000 islands.

Smart grid approaches are also necessary in order to efficiently achieve energy access for all, which will push welfare creation. The optimal approach is a mixture between on-grid and off-grid solutions depending on local characteristics. The grid should be made fit for renewable energies, which are variable in most cases. The variability can be handled through approaches such as integrated storage systems or demand side management mechanisms.

Stability Behavior

The definition of stability in microgrids and in conventional interconnected power systems is principally based on the same principle. As stated in [START_REF]Microgrid Stability Definitions, Analysis, and Modeling[END_REF], a microgrid is considered stable if, after being subjected to a perturbation, all state variables recover to (possibly new) steady state values which satisfy operational constraints. And a microgrid should be considered stable if it fulfils its main objective. For example, when a microgrid is constructed for supplying power to important loads and it fails to do so, the microgrid is said to be unstable.

The nature of stability problem and dynamic power performance of a microgrid are different from those of a conventional power system discussed previously in Section 2.2. The most important distinguishing factors are identified in [START_REF] Shuai | Microgrid stability: Classification and a review[END_REF], [START_REF]Microgrid Stability Definitions, Analysis, and Modeling[END_REF], as follows:

1. Smaller system size 2. Higher penetration of (V)RES 3. Higher uncertainty in the system 4. Lower system inertia 5. Higher R/X ratio of the feeders, especially in low voltage 6. Low short circuit capacities 7. Relatively unbalanced three-phase loadings, especially for small community grids

The evolution of power system classification over time in the literature is illustrated in Figure 2.16.

IEEE/CIGRE classification

As discussed in Section 2.2, in order to facilitate power system stability analysis, IEEE/CIGRE Joint Task Force [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF] in 2004 classifies power system stability into three main categories: rotor angle stability, frequency stability, and voltage stability. This classification is based on the structure of conventional power systems, supplied mostly by dispatchable synchronous machines. Nevertheless, it is mentioned in the document that in isolated island systems, frequency stability could be of concern due to frequent imbalance between power generation and demand [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF], [138].

Majumder's classification

In 2013, Majumder pubished a journal article [START_REF] Majumder | Some Aspects of Stability in Microgrids[END_REF] which classifies microgrid stability into three stability. This is due to the fact that the inrush current during a fault may be dangerous to inverters and it happens in the time span of milliseconds. Furthermore, angle stability is not acknowledged as a category.

IEEE Classification

Recently, IEEE Task force issued a technical report draft in which they define a new classification of microgrid stability [START_REF]Microgrid Stability Definitions, Analysis, and Modeling[END_REF]. This report has also been published as a journal article [START_REF] Farrokhabadi | Microgrid Stability Definitions, Analysis, and Examples[END_REF].

A number of differences in terms of stability issues in microgrids and in conventional interconnected grids are identified. In isolated microgrids, maintaining frequency stability proves to be challenging because of the low system inertia and high levels of VRES, contrary to the case of conventional interconnected systems where angle and voltage stability problems occur more often. Problems such as inter-area oscillations and voltage collapse have not been detected in isolated microgrids.

The new classification is based on partial stability concept, in which stability problems can be classified according to the physical cause of instability, the relative size of the perturbation, the physical components involed, the time-span during which the instability manifests itself, and the methodology to analyze the instability. It firstly divides microgrid stability into two main categories:

power supply and balance stability and control system stability.

Power supply and balance deals with the ability of the system to maintain the power balance and effective active and reactive power sharing among DGs. This category is furthermore subcategorized into frequency and voltage stability. The task force also noticed that due to the higher R/X ratio in microgrids, the decoupling of active power flow and voltage magnitude is not valid anymore.

Therefore, voltage-frequency stability coupling should be considered for stability analysis. With respect to voltage stability, the task force observes with the current trend, the sensitivity of load power consumption to voltage and DG current limits may be influential factors in microgrids. This may result in unacceptable low steady-state and dynamic voltages. Besides system voltage stability, this classification introduces DC-link voltage stability. Voltage ripples of the capacitor depend on the instantaneous power of the inverter. When the power injection of the inverter is close to its limit, undamped DC voltage ripples may occur, which will result in large fluctuations in the active and reactive power output of DERs.

Control system stability issues may occur because of inadequate control schemes and/or poor tuning of one or more controllers. This category is further split into electric machine and converter stability. With respect to conventional interconnected systems, the issues of out of synchronism of synchronous machines have not been observed in this classification. Electric machine stability in microgrids is dominantly associated with poor tuning of the exciter and governor, which could result in undamped oscillation and continuous increase/decrease of voltage and frequency. Converter stability issues are caused by poor controller tuning and the impact of the usage of phase-locked loop (PLL). Synchronization stability problems linked with PLL performance are more pronounced in weak grids, as discussed in [START_REF] Taul | An Overview of Assessment Methods for Synchronization Stability of Grid-Connected Converters under Severe Symmetrical Grid Faults[END_REF]. PLL introduces negative parallel admittance to the input admittance which may provoke instabilities. The choice of PLL bandwidth must be carefully taken. Higher bandwidth introduces negative admittance, and low bandwidth may cause the PLL to fail to properly detect zero crossings which deteriorates the synchronization process. Both variables are coupled due to and the higher R/X ratio, the behavior of grid forming elements (i.e. frequency affects armature voltage for synchronous machines), and the behavior of loads (i.e.

active and reactive power demands are dependent on voltage and frequency). Power balance instability may arise even when the power system has enough reserve to respond to power demand, for example due to poor power sharing among sources or loadability limit. Control stability is concerned with machine physical behavior, control strategies, their interaction, and their tuning. It is divided into small signal stability and large perturbation stability. Instability often manifests itself as undamped oscillations or uncontrolled hysteresis.

Contrary to Reference [START_REF]Microgrid Stability Definitions, Analysis, and Modeling[END_REF] which reported that loss of synchronism and voltage collapse have not been observed in microgrids, this research found out that out-of-synchronism and voltage collapse may still exist in microgrids as reported in [START_REF] Banjar-Nahor | Study on Renewable Penetration Limits in a Typical Indonesian Islanded Microgrid considering the Impact of Variable Renewables Integration and the Empowering Flexibility on Grid Stability[END_REF], [START_REF] Banjar-Nahor | Study on Renewable Penetration Limits in a Typical Indonesian Islanded Microgrid Considering the Impact of Variable Renewables Integration and the Empowering Flexibility on Grid Stability[END_REF]. This conclusion is based on our study on a typical isolated microgrid in Indonesia which is characterized by long distribution lines and distributed synchronous machines, in contrast to microgrids reported in [START_REF]Microgrid Stability Definitions, Analysis, and Modeling[END_REF] which assume short feeders.

Single point small signal stability might not be very useful as microgrid's point of operation changes constantly. However, it is important to verify small signal stability to guarantee power system stability. Therefore, in this research, small signal analysis is conducted at the same time as transient stability analysis. Time domain simulation is utilized to study both transient and small signal stability.

Stable non-oscillatory variables are ensured at the initialization and the post-perturbation state in order to verify small signal stability.

PLL plays a very important role in the performance of a grid connected power converters. A precise synchronization algorithm is needed to estimate the grid voltage parameters (voltage amplitude, frequency, and phase angle) accurately. These values are crucial in controlling active and reactive power exchange between the IBG and the grid and in the performance of the protection schemes. However, PLL algorithms are making promising progress [START_REF] Taul | An Overview of Assessment Methods for Synchronization Stability of Grid-Connected Converters under Severe Symmetrical Grid Faults[END_REF] as numerous grid codes start to require generators to remain connected for voltage step changes, phase-angle jumps, and negative sequence loadings, such as the case of the Irish, Danish, and British power systems [START_REF] Etxegarai | Review of grid connection requirements for generation assets in weak power grids[END_REF].

The classification that we use and the associated issues that we treat in this thesis are illustrated in Figure 2.17.

Lessons from non-land-based Microgrids

With regard to the implementation of microgrids, there are three major areas: airplanes, ships, and land-based islands. A general comparison among these microgrids is presented as follows. Traditionally, the propulsion system and the power consumption are separated. However, with movements towards more electric architectures for aircrafts and ships, there is a trend towards integrated electric propulsion where a single set of generators provides electric power for both propulsion and other loads aboard the ship. This transformation is driven by efficiency, survivability, and the anticipated development of high powered sensors and weapons. This can furthermore result in new frequency and voltage choices.

From such a comparison, several interesting points containing possible cross-fertilization, especially between island microgrids and ship microgrids of comparable size, are summarized as follows [START_REF] Hebner | Technical cross-fertilization between terrestrial microgrids and ship power systems[END_REF].

Design and operation

In electrical systems, load and generation must be balanced at all times. In microgrids, the available generation is typically sized to provide continuous supply to critical loads. Therefore, non-critical loads occasionally must be shed either manually or automatically, depending on their system design and protection, in order to maintain the power balance. Demand response plays a vital role in this matter.

In terrestrial microgrids, load shedding is typically triggered by under-frequency relays, whereas load shedding in vessel power systems is based on power sensors which monitor generator power output. When the demand exceeds a certain percentage of the generator rating within a defined time delay, a predetermined load shedding scheme is triggered. An important difference is that in land-based microgrids, the power provider and the customers are different entities, hence negotiation with regard to load shedding is necessary. It is normally conducted in advance, or else a complete shutdown may be inevitable. On ships, the entire system, including the loads, belongs to the same entity, hence less negotiation for load shedding.

Generation

The generation system of both types of microgrids is sized to supply loads. In land-based microgrids, the electricity may be generated by conventional generators or non-synchronous generators (inverters, induction generator), either with renewable energy or fossil fuel as the primary energy. Although there are many forms of generation for vessel systems, the most common way to generate electric power is through gas turbines or diesel generators, working collectively to supply both critical and non-critical loads.

Load Types

The characteristics of loads in land-based microgrids are similar to those of the larger grids.

The difference manifests itself in the scale and numbers. In general, the following features can be identified for loads in both types of microgrids: They tend to be conventional and have comparable electrical characteristics; they tend to be continuous, typically varying on time scales of minutes to hours, however some loads in future warships may have intermittent nature, such as electric guns and weaponry; no single load is dominant, except propulsion loads for ships (those may comprise 90% of the installed power capacity. However, propulsion can be controlled accordingly so as not to severely impact the system's stability); individual loads are typically switched on and off in discrete increments, but their accumulation remains smooth and can be modeled as a mildly varying function of time; total system load tends to be predictable based on historical data.

Dynamic Balancing

Dynamic balancing is accomplished by adjusting generation set points and controlling noncritical loads. However, non-critical load management on vessel systems may have an extra complexity, because most of the loads are supplied through two redundant feeders.

Stability

Compared to terrestrial microgrids, ships may have a higher proportion of constant power loads, which have destabilizing effects. Consequently, the design of practical stabilizing strategies for ships becomes more demanding.

Boundary controllers can be applied in both types of microgrids. Boundary controllers designed for electric ships provide faster dynamic responses than classical PID controllers. This is also a desirable characteristic for land-based microgrids due to its capability to obtain fast compensation following generation or load impacts.

It should be noted that the generation-side on ships is more controllable than that of landbased microgrids. Therefore, both generation and load management can be exploited to deal with frequency and voltage stability for ships. In land-based microgrids, both generation and load management can also be utilized to maintain system stability. However, the options are rather limited based on the agreement between multiple entities in the grid (i.e. DSO, customers, generation) and the type of land-based microgrid (e.g. campus microgrid, islanded microgrids, military base).

Autonomous operation and communication infrastructure

Locally available droop based schemes are commonly employed for power management purposes within terrestrial microgrids. In contrast, a ship power system is conventionally designed in a centralized manner in order to obtain a high level of security and dependability. In this application, the communication system is vital. Over the last decade, there has been a move toward the widespread installation of smart meters in land-based grids. The goal is to achieve a truly dynamic contractual relationship between energy providers and users. This is an area where terrestrial microgirds may be leading the way compared to the vessel counterpart.

In microgrids equipped with communication systems, the data collected from local measurements are communicated to the central supervision infrastructure and processed in real time. Action signal commands may be sent out to maintain system stability, to conserve equilibrium between generation and load, or to perform any other energy management functions, as ordered by the operator or automatically by the system. In ship microgrids, the full control over the loads enables more flexibility during shedding operations.

Real Operational Microgrids

A number of current real-world microgrids are assembled from the literature [3], [4], [START_REF] Mongkoltanatas | Energy Storage for stability of microgrids[END_REF], [START_REF] Vai | Planification du réseau de distribution basse tension avec intégration de sources photovoltaïques et stockage : cas du réseau du Cambodge[END_REF], [START_REF] Hossain | Microgrid testbeds around the world: State of art[END_REF], [START_REF] Martin-Martínez | A literature review of Microgrids: A functional layer based classification[END_REF]- [START_REF] Kroposki | Making microgrids work[END_REF]. A number of projects from all over the world are listed as follows. A number of real-world microgrid projects have been constructed to evaluate and study the performance of microgrids with respect to the concept's promised key benefits, such as renewable energy integration, higher energy efficiency (through CHP plants), and resilience. Some projects have successfully demonstrated the performance of the concept when dealing with natural disasters, as

shown by Sendai microgrid in Japan and Princeton university microgrid in the US. Some other projects have contributed to the development and testing of the technical blocks within the concept.

Extensive R&D efforts are still in progress.

Challenges in Power System Stability in Microgrids (Weak Grid)

In small isolated grids, there might be problems related to the power quality of the grid, which impact the operation of distributed generations. Frequency and voltage may vary outside the nominal range of operation prescribed by the grid codes or standards [START_REF] Lorenzen | Control of a grid connected converter during weak grid conditions[END_REF]. Such characteristics are displayed by what we call a "weak grid". An AC grid can be considered weak from two aspects: system impedance reflected by the short circuit ratio (SCR) and system mechanical inertia.

SCR is an index borrowed from the screening of grid strength near HVDC converters, and is also applied to DER plants [START_REF]Short-Circuit Modeling and System Strength[END_REF]. It is defined as the ratio of the short circuit power capability (Scc) at the point of common coupling (PCC) and the rated power of the installed generator (SN).

𝑆𝐶𝑅 = 𝑆 𝑐𝑐 𝑆 𝑁

A grid is said to be weak when the SCR is lower than 6-10, and strong when the SCR is above 20-25 [START_REF] Etxegarai | Review of grid connection requirements for generation assets in weak power grids[END_REF]. When the weak impedance is the concern, the system is considered far electrically from the bulk system.

Concerning DER interconnection, voltage regulation becomes complicated as significant fluctuations in bus voltages may occur due to small active or reactive power injection at the point of interconnection. This might also provoke small signal and control instability among system elements on the bulk power system (BPS). However, such issues are strongly associated with voltage stability problems due to power transfer in an interconnected network and can be eased by applying control strategies which are capable of regulating local voltages. For example, voltage source converter solutions or synchronous condensers can be used [START_REF]Integrating Inverter-Based Resources into Weak Power Systems -Reliability Guideline[END_REF], [START_REF] Lorenzen | Control of a grid connected converter during weak grid conditions[END_REF].

Dynamic weakness of a power system can be characterized by the overall inertia constant and the frequency response characteristics β, also known as stiffness [START_REF] Kundur | Power System Stability And Control[END_REF], [START_REF] Etxegarai | Review of grid connection requirements for generation assets in weak power grids[END_REF]. Isolated grids typically have a low inertia and limited regulation capability. Consequently, ROCOF and steady-state frequency deviation following an active power mismatch may reach high values [START_REF] Etxegarai | Review of grid connection requirements for generation assets in weak power grids[END_REF]. The situation is aggravated by the intermittent and inertialess nature of renewable energy sources which are increasingly interconnected into microgrids. For comparison, if an isolated microgrid is operating at 80% renewable energy from PV, cloud cover on solar panels could drop that capability by as much as half in under 60 seconds. For a utility grid, such an event is catastrophic, the equivalent of several nuclear plants tripping simultaneously [START_REF]Integrating High Levels of Renewables into Microgrids[END_REF]. Events equivalent to this magnitude are a routine occurrence in microgrids.

With more and more electronically coupled renewables installed, inverters will eventually replace synchronous generators and they have to be able to provide the services that synchronous machines were previously responsible for. Several obstacles such as limited overcurrent of inverters, less inertia, and less stored energy in the power conversion process still leave the stability problem of microgrids challenging. In many aspects, it has been demonstrated in this PhD research that the use of today's indispatchable IBGs as replacements for dispatchable synchronous generators provoke instability. The microgrid is becoming more prone to blackouts and to large excursions of key state variables, as reported in [START_REF] Banjar-Nahor | Study on Renewable Penetration Limits in a Typical Indonesian Islanded Microgrid considering the Impact of Variable Renewables Integration and the Empowering Flexibility on Grid Stability[END_REF], [START_REF] Banjar-Nahor | Critical clearing time transformation upon renewables integration through static converters, a case in microgrids[END_REF].

Conclusion

In this chapter, the discussions on the development and the evolution of power system stability, especially towards microgrids with more renewable energy sources, are addressed. A short historical review regarding the topic and how power system stability is traditionally classified are presented in the first part. Here, power system stability problems are strongly associated with the behavior of synchronous machines and are divided into three categories: angle stability, frequency stability, and voltage stability.

Next, the simulation tools for stability assessment are reviewed with regard to their method of calculation and their functionalities. Several power system simulation programs have become standard tools and are endorsed by the grid codes. Digsilent Power Factory was chosen as the dedicated simulation software in this PhD research. Then, the evolution of power system towards smarter and greener vision is presented from various points of view. The discussion also includes load modeling and IBG modeling which are necessary for the analysis of the future power grid.

Finally, the microgrid concept, as an essential building block of the grid of the future, is discussed. The concept brings along new hopes of increasing the reliability at higher level of renewable energy penetrations. As discussed, the exact definition of microgrids varies in terms of size, capacity, components, and behaviors. The discussion includes power system stability behavior in microgrids, its classification, and an overview of the associated challenges that need to be tackled in order to make the concept work.

Critical Clearing Time

Critical clearing time (CCT) is a useful index for the assessment of power system stability, notably the transient stability. IEEE/CIGRE joint task force defined CCT as the maximum permissible duration of the fault for which the subsequent system response remains stable [START_REF] Kundur | Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[END_REF]. The index is typically calculated through time-domain simulations. A more stringent definition of CCT was proposed in [START_REF] Alaboudy | Critical clearing time for isolating microgrids with inverter and synchronous based Distributed Generation[END_REF], in which CCT is defined as the maximum fault duration during which the system is still able to restore its pre-fault conditions.

A number of articles focused on finding methods to avoid lengthy time-domain analyses in CCT calculation, as proposed in [START_REF] Vu | Toward Simulation-Free Estimation of Critical Clearing Time[END_REF], [START_REF] Folly | Critical clearing time prediction using recurrent neural networks[END_REF]. Several articles have recognized the introduction of IBG in the power system [START_REF] Alaboudy | Critical clearing time for isolating microgrids with inverter and synchronous based Distributed Generation[END_REF], [START_REF] Folly | Critical clearing time prediction using recurrent neural networks[END_REF], but failed to take their behavior into consideration in CCT calculation.

Decreasing transient stability of a power system is indicated by the decrease of CCTs for a specific fault and a higher number of faults with low CCTs [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF].

CCT is traditionally calculated based on the swing equation and the out-of-synchronism criterion, both of which are only valid for synchronous machines. A progress was made in [START_REF] Goulielmakis | Hybrid industrial power systems mixing photovoltaic & diesel power generation[END_REF],

where power quality criteria, such as frequency and voltage limits, are introduced into CCT calculation. However, it does not consider the behavior of synchronous machines operating in the system. A CCT calculation which takes into account the behavior of all generator technologies which could be present in the grid was not found in the literature.

Traditional Critical Clearing Time

Since the conventional power system is mostly fed by synchronous machines, CCT is traditionally associated only with the transient behavior of synchronous machines, i.e. the swing equation, in particular with the critical clearing angle [START_REF] Kundur | Power System Stability And Control[END_REF], [START_REF] Morison | Transient Stability[END_REF]. A synchronous machine cannot return to stability if the critical clearing angle is exceeded during a fault. This event is called out-ofstep, and the power system is considered unstable if this happens. The CCT is defined as the duration to reach the critical clearing angle. With the same logic, the power system is considered unstable when CCT is exceeded.

Proposed Critical Clearing Time

With more and more VRES being integrated via power electronic converters, the traditional CCT assessment is no longer adequate. More explanation! Explain that the classical chritera is sufficient for classical grids without intermittents. But now it's not the case. Inverter-based generation (IBG) is not physically regulated by the swing equation and has the capability of delivering very fast response compared to the synchronous machine counterparts. This fact thus leads to our proposal to update the calculation of CCT, which has been discussed more thoroughly in [START_REF] Banjar-Nahor | Critical clearing time transformation upon renewables integration through static converters, a case in microgrids[END_REF].

The CCT here is still associated with the maximum permissible duration of a fault. However, a more demanding post-fault state is adopted. If a fault is cleared faster than CCT, the system has to be able to restore its pre-fault operating point. Consequently, when IBGs such as wind farms, PV and batteries are present in the system, they must not trip during the perturbation, or else the system will lose some reactive power support during the disturbance state and both active and reactive power supply in the post-disturbance state.

The topic of fault ride through of IBG is discussed in Subsection 4.3.2. Physical and control limitations restrict the ride through capability of IBG. For instance, in wind power generation (WPG) systems with a full-scale converter interface, the power is limited by the current rating. Two consequences may occur when system voltage drops and the current limit is attained. The blade speed may increase or the DC-link voltage may rise [START_REF] Bak | Low-Voltage Ride-Through Control Strategy for a Grid-Connected Energy Storage System[END_REF]. Both may be fatal to the WPG system. For solar power generation (SPG) systems, system voltage drop may also provoke the DC link voltage rise, which is potentially dangerous to the inverter. The more demanding the ride-through requirements, the more costly the design is [START_REF] Enayati | Revised IEEE 1547 Standard for Interconnecting Distributed Energy Resources with Electric POwer Systems-National Grid Solar Program[END_REF].

Current grid codes and standards discussed in [START_REF]IEEE Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces[END_REF], [START_REF] Etxegarai | Review of grid connection requirements for generation assets in weak power grids[END_REF], [START_REF] Rodrigues | Grid code reinforcements for deeper renewable generation in insular energy systems[END_REF] utilize ride through capability requirements for bridging the trade-off between of power system support and the design limitations of static converters. Taking into account both the behavior of synchronous machines and the required ride through capability of power electronic devices, new criteria of CCT calculation are proposed.

The outline is given in Table 3.1. It should be noted that in the proposed novel CCT, oscillation-free steady state is formally required. This is important since the system inertia is considerably lower, leading to a less stable system. Low system inertia combined with fast response and poor tuning may provoke oscillatory steady states [START_REF]Microgrid Stability Definitions, Analysis, and Modeling[END_REF], [START_REF] Goulielmakis | Hybrid industrial power systems mixing photovoltaic & diesel power generation[END_REF]. This index was used for transient stability assessment in [START_REF] Banjar-Nahor | Study on Renewable Penetration Limits in a Typical Indonesian Islanded Microgrid considering the Impact of Variable Renewables Integration and the Empowering Flexibility on Grid Stability[END_REF] The algorithm of the proposed CCT calculation is depicted in the following flowchart.

Renewable Penetration

The topic of high levels of renewable penetration appears frequently in discussions on electricity.

Occasionally, it is only a jargon with no technical interpretation. However, most of the time, it represents clear technical significance. In the literature, there exist four definitions of renewable penetration level, depending on the nature of the study, as discussed in [START_REF] Banjar-Nahor | Indices Relating to Variable Renewable Penetration Level For Preliminary Microgrid Stability Assessment[END_REF].

Percentage of Annual Energy Generated

Also known as percentage of net electricity generation, this definition is generally utilized in long term and techno-economic studies, such as in [START_REF] Denny | The impact of increased interconnection on electricity systems with large penetrations of wind generation: A case study of Ireland and Great Britain[END_REF]- [START_REF] Reilly | High Penetration of Renewable Energy: Possible Scenarios, Implications, and Best Practices from International Experience[END_REF]. It is also widely used by the policy makers, such as the case in EU's Renewable Energy Directive [170] and Indonesian renewable energy ratio target [171]. The definition is given by the following equation.

𝑃𝑒𝑛 𝑉𝑅𝐸𝑆,1 = 𝐴𝑛𝑛𝑢𝑎𝑙 𝑉𝑅𝐸𝑆 𝐸𝑛𝑒𝑟𝑔𝑦 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑇𝑜𝑡𝑎𝑙 𝐴𝑛𝑛𝑢𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 Eq. 3.1
The energy is typically expressed in MWh or kWh.

Attaining high VRE penetration based on this definition is very challenging, since energy is the integral of active power over time. With regard to power system stability, the definition does not take into account flexibility options such as storage and demand-side management. Additionally, it does not provide information on operational condition of the system, making it impossible to derive the power system stability status.

Percentage of Total System Installed Capacity

Otherwise known as percentage of power mix, this definition is also typically used in technoeconomic studies, such as in [START_REF] Zappa | Is a 100% renewable European power system feasible by 2050?[END_REF]. It is useful when more emphasis is put on the technical side, especially concerning the intermittency and power system flexibility needs. The following equation presents the definition.

𝑃𝑒𝑛 𝑉𝑅𝐸𝑆,2 = 𝑇𝑜𝑡𝑎𝑙 𝑉𝑅𝐸𝑆 𝐼𝑛𝑠𝑡𝑎𝑙𝑙𝑒𝑑 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑇𝑜𝑡𝑎𝑙 𝑆𝑦𝑠𝑡𝑒𝑚 𝐼𝑛𝑠𝑡𝑎𝑙𝑙𝑒𝑑 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦

Eq. 3.2
The installed capacity is typically expressed in kW or MW. Some studies have been conducted to explore the impact of this type of renewable penetration level on power system operations. Electricity utility companies often adopt this definition for the planning of their power systems because it provides a general overview of the problems that need to be addressed in order to satisfy operational constraints. For instance, the worst generation variation which is directly linked to the maximum frequency deviation can be derived from this definition.

The French utility company, EDF, imposes limitations on the penetration level of VRES based on this definition [START_REF] Selosse | The renewable energy revolution of reunion island[END_REF], [173]. From the discussions in the literature, it is inferred that the infamous 30% limit was put in place to guarantee the operational constraints of today's power systems without significant changes in the business-as-usual operation and infrastructure. Nevertheless, Reference

[173] also reveals that this value is a generalization, meaning that the actual limit may vary for different power systems. As reported in [3], [START_REF] Kroposki | Integrating high levels of variable renewable energy into electric power systems[END_REF], power system operation at 65% renewable penetration or even 100% is technically possible when special measures are taken, such as the installation of batteries and flywheels. This shows that this definition does not provide comprehensive information on the flexibility options which play a very important role in power system stability.

Percentage of Peak Load Demand

This definition is often used for steady state assessment purposes, such as in [START_REF] Hoke | Steady-State Analysis of Maximum Photovoltaic Penetration Levels on Typical Distribution Feeders[END_REF], which studies various levels of PV penetration in distribution systems. The equation is as follows.

𝑃𝑒𝑛 𝑉𝑅𝐸𝑆,3 = 𝑃𝑒𝑎𝑘 𝑉𝑅𝐸𝑆 𝑃𝑜𝑤𝑒𝑟 𝑃𝑒𝑎𝑘 𝐿𝑜𝑎𝑑 𝑃𝑜𝑤𝑒𝑟

Eq. 3.3
Both active and apparent power may be employed in the equation, hence MW or MVA. It is reported in [START_REF] Hoke | Steady-State Analysis of Maximum Photovoltaic Penetration Levels on Typical Distribution Feeders[END_REF] that the maximum PV penetration in distribution systems is found to be a bit over 30% before causing steady state voltage or current overloading problems.

Similar to the previous definitions, this definition also does not provide any information on the flexibility options which are important to power system stability.

Percentage of Instantaneous System Load

This definition is often used for operational studies, such as static analysis or dynamic stability.

This definition was used to study the limits of renewable energy penetration in a typical islanded microgrid in Indonesia [START_REF] Banjar-Nahor | Study on Renewable Penetration Limits in a Typical Indonesian Islanded Microgrid considering the Impact of Variable Renewables Integration and the Empowering Flexibility on Grid Stability[END_REF] and in the European interconnected system [START_REF] Wang | Impact of high penetration of variable renewable generation on frequency dynamics in the continental Europe interconnected system[END_REF]. Reference [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF] Both VRES Power and Load Demand are expressed in kW or MW. Contrary to the preceding definitions, the value of this penetration level varies at any point of time.

When power export and import through HVDC are taken into account, the equation is modified as follows.

𝑃𝑒𝑛 𝑉𝑅𝐸𝑆,5 = 𝐼𝑛𝑠𝑡 𝑉𝑅𝐸𝑆 𝑃𝑜𝑤𝑒𝑟 + 𝐻𝑉𝐷𝐶 𝐼𝑚𝑝𝑜𝑟𝑡 𝐼𝑛𝑠𝑡 𝑑𝑒𝑚𝑎𝑛𝑑 + 𝐻𝑉𝐷𝐶 𝐸𝑥𝑝𝑜𝑟𝑡 Eq. 3.5

The above definition is also known as system non-synchronous penetration. This definition may be used to review the operational strategy upon more VRES penetration [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF], [START_REF] Mc Garrigle | How much wind energy will be curtailed on the 2020 Irish power system?[END_REF]. In the articles, the maximum instantaneous penetration is found to be around 60-80%. The values are calculated based on certain requirements, e.g. ROCOF and frequency nadir, and some important simplifications, which are only valid for the system under study.

As discussed in [START_REF] Banjar-Nahor | Study on Renewable Penetration Limits in a Typical Indonesian Islanded Microgrid considering the Impact of Variable Renewables Integration and the Empowering Flexibility on Grid Stability[END_REF], [START_REF] Taneja | A comparative study of high renewables penetration electricity grids[END_REF], the value of this index provides some insights, yet not comprehensive information on power system stability status, as the limits may vary on a case-per-case basis.

Although this definition is useful in obtaining real-time condition of the system operation, it still does not provide information on flexibility options which are vital in power system stability.

Frequency Excursion

Frequency is an important variable in power system stability and operations. Traditionally, the balance of power production and consumption can be known by monitoring the frequency. If the load consumption is more than the production, the frequency decreases, vice versa. Primary frequency regulation was constructed with this behavior in mind.

Traditionally, synchronous machines dominate the generation side of power systems. This is why the frequency behavior of power systems follows the swing equation described previously in Eq.

2.2. The equivalent inertia of a power system is calculated with the following equation [START_REF] Kundur | Power System Stability And Control[END_REF], [START_REF] Zhang | Online Identification of Power System Equivalent Inertia Constant[END_REF].

𝐻 𝑇𝑜𝑡𝑎𝑙 • 𝑆 𝑇𝑜𝑡𝑎𝑙 = ∑ 𝐻 𝑖 • 𝑆 𝑖 𝑁 𝑖=1
Eq. 3.6

Where:

Htotal = Equivalent system inertia constant Stotal = System Capacity Hi = Inertia constant of ith generator Si = capacity of ith generator
However, as more and more inertialess VRES are integrated, the system equivalent inertia has been decreasing. This causes the power systems to become weaker and weaker dynamically, as discussed in Subsection 2.5.5. With regard to this issue, two indices are widely used in power systems, discussed as follows. They are mainly calculated through time domain simulations.

Frequency Nadir

Frequency nadir is the lowest frequency recorded during a transient event, such as load impact or loss of generator. The index is influenced by the magnitude of the transient event, the system inertia, and the response of primary regulation. It is important as in many grid codes and norms, the frequency limits are stated and grid operators have to satisfy the requirements. In addition, certain protection schemes and load shedding actions are based on the frequency measurement.

Frequency nadir should not be confused with quasi steady state frequency. The latter relates to the frequency after the response of primary regulation and before the activation of secondary regulation, as illustrated in Figure 3.2.

Frequency nadir

Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance

Frequency nadir is imposed in several grid codes and norms, through the operational frequency limits, as shown in Table 2.7 and in [START_REF] Etxegarai | Review of grid connection requirements for generation assets in weak power grids[END_REF]. Studies of maximum VRES level often use this index as one of the limiting factors, such as the study of Irish power system [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF] and Sulawesi power system [START_REF]Tolo and Takalar Generating Systems Connection Study and Renewable Penetration Report[END_REF].

ROCOF

ROCOF is the time derivative of voltage frequency. In more detail, it corresponds to the frequency gradient following an imbalance of active power generation and demand. It is defined analytically as follows.

𝑅𝑂𝐶𝑂𝐹(𝑡) = 𝑑𝑓(𝑡) 𝑑𝑡

Eq. 3.7

With more and more renewables being integrated, the ROCOF is becoming higher. Two main things are causing this: the lower system inertia and the higher and more frequent occurrence of power imbalance due to the intermittency. Stable frequency is therefore more difficult to achieve.

In reality, it can be measured by numerical approach, by measuring frequency at two points separated by a defined time delay, also known as the measurement window. This is formulated by the following equation.

𝑅𝑂𝐶𝑂𝐹(𝑡) = 𝑓(𝑡) -𝑓(𝑡 -𝑇) 𝑇

Eq. 3.8

Calculation methods and the choice of measurement window T are essential in the calculation, as discussed in [START_REF] Arguence | Modélisation des ilots non-intentionnels et caractérisation des méthodes passives de détection d'ilotage[END_REF], [182]. Important dynamics may be missed when a large measurement window is used, while the ripple and power quality problems may interfere with a small window [START_REF]High Penetration of Power Electronic Interfaced Power Sources (HPoPEIPS)[END_REF]. IEEE 1547 requires that the ROCOF is calculated over an averaging window of at least 0.1 s [START_REF]IEEE Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces[END_REF]. Other grid codes require 0.5s and 1s time windows, causing the measurement to be observable with time delay [START_REF]High Penetration of Power Electronic Interfaced Power Sources (HPoPEIPS)[END_REF].

In recent norms and grid codes, the ROCOF requirements for different generator technologies started to appear. For instance, IEEE 1547 require DER to be able to ride through frequency excursions having ROCOF up to 3 Hz/s [START_REF]IEEE Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces[END_REF], while some grid codes, such as Australian grid codes, require wind farm to ride through for ROCOF as high as 4 Hz/s [START_REF] Etxegarai | Review of grid connection requirements for generation assets in weak power grids[END_REF], [182].

Apart from the protection systems, ROCOF measurement is also be used in the regulation of power electronics, such as in synthetic inertia response. ROCOF is also important in phase tracking of power electronic apparatus. This will be discussed further in Subsection 4.3.

Indices based on PV and QV Curves

PV and QV curves are useful for voltage stability analysis. They visualize how close a certain operating point to voltage instability. Distance to instability can be expressed through physical quantities, such as load level or active/reactive power flow. A simple mathematical formulation can be derived for a simple system consisting of a voltage source, transmission lines modeled as impedance, and a load modeled as an impedance [START_REF] Kundur | Power System Stability And Control[END_REF], which results in a typical curve illustrated in Figure 3.3 (a). However, for a complex power system, the curve is constructed based on the load flow analysis, such as used in [START_REF] Kundur | Power System Stability And Control[END_REF], [START_REF] Banjar-Nahor | Study on Renewable Penetration Limits in a Typical Indonesian Islanded Microgrid considering the Impact of Variable Renewables Integration and the Empowering Flexibility on Grid Stability[END_REF]. Consequently, only stable operating points up to its nose point can be found, as power flow tends not to converge beyond this limit. This is illustrated in The active or reactive power shown in PV or QV curves may correspond to the power at a certain bus or feeder. In the former, the Vr is taken at the associated bus while the latter, at the feeder end.

Since the analysis is based on load flow analysis, sensitivity analysis to active and reactive power can be carried out. Voltage instability, occurring at the nose point, is closer when dV/dP or dV/dQ increases, and occurs when dV/dP or dV/dQ is very high [START_REF] Kundur | Power System Stability And Control[END_REF]. PV and QV curve-based analyses are also applicable for microgrids in the presence of significant IBG [START_REF] Majumder | Some Aspects of Stability in Microgrids[END_REF].

Various voltage stability indices are reviewed in [START_REF] Prasad | Assessment on various node voltage stability indices -A review[END_REF], most of which serve as a proximity indicator to voltage instability and are derived from PV or QV curves. The values of the indices typically range from 0 to 1. Voltage instability occurs at either one of two extremities. Another useful index relating to loadability can be obtained by calculating the ratio of the critical loading, which causes voltage instability, to the current loading. The loadability index indicates how far the bus under consideration can be loaded with respect to the current loading.

Several voltage stability indices are listed in Table 3.2.

Proposed New Indices

When dealing with power system stability, the balance of power production and consumption must be maintained. However, doing it at all times upon every possible scenario is impractical and uneconomical. The best practice is only to anticipate credible scenarios. In order to do this, a list of credible scenarios must be firstly defined.

Traditionally, power systems are designed to comply with N-1 criterion. This means that a power system is planned such that, with all facilities are in service, it is operating in a secure state, and with one credible contingency event, the system moves to a satisfactory state. ENTSO-E requires that the frequency containment reserves, defined as the operational reserves activated to contain system frequency after the occurrence of an imbalance, is sized to the reference incident that may cause the biggest active power imbalance with an N-1 failure [START_REF]ENTSO-E's supporting document to the submitted Network Code on Load-Frequency Control and Reserves[END_REF]. The same is also widely practiced in the industry. However, due to the intermittent nature of variable renewables in power systems, it becomes more complicated to define and satisfy the N-1 criterion. The novel indices still stick with the necessary condition of maintaining power equilibrium upon credible scenarios since failure to do so may result in undesired blackouts. This approach is therefore deterministic. However, the way that the scenarios are considered evolves as both generation and demand may be either variable or controllable. The factors to take into account may vary based on the type of the microgrid and the flexibility available for use.

The factors that must be taken into consideration in power system stability are shown in Table 3.3. Here, we are trying to be as general as possible in terms of microgrids considered. In the above table, VRES curtailment is a condition where the production from VRES is intentionally curtailed from its maximum potential. The objective may be twofold: to avoid overproduction of active power and to help maintain grid stability. For the latter, it serves similarly to primary reserve. Demand side management consists of two methods: communication-based and non-communication based. In the former, a central supervision system sends out orders to non-critical loads to respond to system conditions. In the latter, decentralized controls which respond to frequency and voltage excursions may be used. In this regard, it is similar to load shedding. Additionally, some grid codes authorize brownouts, an action in which the grid voltage is intentionally decreased to reduce the power demand [START_REF] Banjar-Nahor | Study on Renewable Penetration Limits in a Typical Indonesian Islanded Microgrid considering the Impact of Variable Renewables Integration and the Empowering Flexibility on Grid Stability[END_REF], [103], [START_REF] Delille | Taking advantage of load voltage sensitivity to stabilize power system frequency[END_REF].

Dynamic balancing problem is illustrated in Figure 3.4. In this analogy, the deviation of the scale from the horizontal axis is analogous to the frequency deviation from the nominal value. The shaded boxes are subject to variability. In physics, the response speed of the scale due to weight imbalance depends on the gravitational acceleration. In this illustration, the gravitational acceleration is inversely proportional to the system inertia, meaning that the frequency deviates more when the inertia is low. The flexibility options are chosen based on the priority set by the system operator. The controls and activation strategy of the flexibility can be local or centralized. In the literature, the maximum penetration level is often seen from grid code's point of view. If a loss of the largest power plant results in a frequency violation, the maximum VRES penetration has been exceeded [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF], [START_REF] Wang | Impact of high penetration of variable renewable generation on frequency dynamics in the continental Europe interconnected system[END_REF], [START_REF] Tambunan | Maximum Allowable Intermittent Renewable Energy Source Penetration in Java-Bali Power System[END_REF]. One major problem that arises from this approach relates to the simplifying assumptions. For example, the event is the largest generation loss, which might not the worst case scenario. The coincident production drop of VRES can be of higher magnitude. For comparison, if an isolated microgrid is operating at 80% VRES from PV, cloud cover on solar panels could drop that capability by as much as half in under 60 seconds [START_REF]Integrating High Levels of Renewables into Microgrids[END_REF]. Furthermore, sometimes it is assumed that sufficient primary reserve can always be dispatched [START_REF] Wang | Impact of high penetration of variable renewable generation on frequency dynamics in the continental Europe interconnected system[END_REF], which is not true. On top of that, one should ask a question concerning the relation between frequency violation based on grid codes and power system stability. A power system can return to a stable frequency upon an important perturbation even though the frequency limit is violated temporarily in the process.

Interconnection

Storage

There is not a single critical instantaneous penetration rate since the system dynamics depend on several factors that change from one period to the other [START_REF] Banjar-Nahor | Study on Renewable Penetration Limits in a Typical Indonesian Islanded Microgrid considering the Impact of Variable Renewables Integration and the Empowering Flexibility on Grid Stability[END_REF], [START_REF] Wang | Impact of high penetration of variable renewable generation on frequency dynamics in the continental Europe interconnected system[END_REF].

The indices associated to VRES penetration that we propose are presented as follows. Where 𝑃 ̂𝑉𝑅𝐸𝑆 is the anticipated maximum VRES production, 𝑃 𝑑𝑖𝑠𝑝𝑎𝑡𝑐ℎ𝑎𝑏𝑙𝑒 is the capacity of dispatchable generation, 𝑃 𝑠𝑡𝑜𝑟𝑎𝑔𝑒 is the capacity of storage elements, 𝑃 𝑚𝑎𝑥 𝑢𝑛𝑖𝑡 is the highest unit capacity of dispatchable and storage elements, 𝑃 ̂𝑑𝑒𝑚𝑎𝑛𝑑 is the anticipated peak demand comprising of both critical and non-critical loads, 𝑃 ̂𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 is the anticipated peak demand of critical loads, 𝑃 𝑎𝑐𝑡𝑙 𝑔𝑒𝑛 is the actual generated active power, 𝑃 𝑖𝑚𝑝𝑜𝑟𝑡 is the actual power import at interconnection points, P Prim is the total available primary reserve, 𝑃 𝑁-1 is the power loss due to the worst contingency event, and 𝑃 𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 is the total actual demand of critical loads.

Design indices do not vary over time whereas the monitoring index does. Consequently, the monitoring index needs to be constantly monitored. It should be noted that non-critical demand is deemed to be available to participate in demand response but considered separately from the primary reserve (𝑃 𝑃𝑟𝑖𝑚 ) in the Table above. Only dispatchable generation and storage systems account for P Prim . Regarding the total available primary reserve (𝑃 𝑁-1 ), the capacity is taken into account for dispatchable units and the total of actual generation plus curtailed power for VRES. Furthermore, the interconnection is not taken into account in the design indices, reflecting the worst case off-grid mode of operation. Here, the philosophy is to supply critical loads at any given time, while non-critical loads are only supplied when the generation is available. For dynamic stability index, the contingency under consideration may either be interconnection loss, VRES production drop, or largest generator loss. It depends on the operation mode and the point of operation of the microgrid.

The VRES mix index differs from renewable penetration level PenVRES,2 in a way that instead of the total capacity, it uses the total expected peak power production of installed VRES in the calculation. This is due to the fact that some VRES generate electricity only during certain period of the day. PVs only generate electricity during the daytime whereas in some regions, wind farm produces more electricity in the nighttime. Consequently, the peak VRES production may not be identical to the total installed VRES capacity. With regard to supply and balance stability, the worst case scenario relates to the sudden drop of VRES production at peak production. Therefore, taking into account the peak VRES production is more representative stability-wise.

An illustration of the variables of design indices is introduced in Figure 3.5. The indices can be thought of as a filter for microgrid practitioners. However, supplementary power system stability studies may still be necessary to ensure the dynamic stability in different configurations of microgrids. The assessment is typically performed through time domain simulations, taking credible scenarios into consideration. It should be noted that a more thorough analysis should also be conducted for off-peak periods because fewer synchronous generations are online, resulting in lower system inertia.

The summary of indices useful for microgrid planning and operations in terms of stability issues is as follows. These indices reflect minimum necessary requirements, which signify that it is impossible to guarantee power system stability without satisfying the indices. It should be noted that inertia problems are not taken into account in the preliminary analysis.

The usability and the practicality of the indices have been tested against time-domain-simulation data with satisfactory results, as reported in [START_REF] Banjar-Nahor | Indices Relating to Variable Renewable Penetration Level For Preliminary Microgrid Stability Assessment[END_REF].

Conclusion

A number of indices around power system stability in the presence of VRES have been discussed in this chapter. Due to the advent of more inverter-based generators and the VRES, some indices need to be rethought. For example, ride through capability should be added to critical clearing time calculations. Some classical indices such as frequency excursions and voltage stability indices are still useful in the IBG era, as most of the current inverter technologies are of grid feeding or grid supporting types, which means they still rely on a grid former, such as synchronous generators, to provide them with the voltage and frequency reference.

The definitions of the VRES penetration level are also reviewed to obtain better understanding of their significance. Some indices provide technical meaning, while the others serve different purposes, such as economic and political ones. From here, we conclude that the maximum VRES penetration level varies on a case-by-case basis. We then propose a set of indices based on the power equilibrium criteria, which are useful as a time-efficient filter to assess microgrid stability.

PART II

Efforts to preserve power system dynamic stability in microgrids characterized by massive levels of renewables Chapter 4 Efforts to Accommodate Massive Shares of VRES in Future Power Grids

In this chapter, the main challenges with regard to the power system stability due to more VRES interconnection and the current efforts are reviewed, which have shown that the current solutions focus on maintaining the philosophy of a classical power grid. With the advent of more and more VRES, the current efforts have proven to be costly. Thus, a new perspective is proposed. Here, the generating elements and the customers are exposed with higher deviations in main variables such as the voltage and the frequency, which are necessary to maintain the power equilibrium and the stability of the microgrid.

Introduction

Power systems are traditionally designed to comply with N-k (typically N-1) criterion in the normal state [START_REF] Machado | Grid Codes Comparison[END_REF]. This means that a power system is planned such that, with all facilities are in service, it is operating in a secure state, and with one credible contingency event, the system moves to a satisfactory state.

Following a contingency, the power system may enter alert state, where all the constraints are satisfied but N-1 criterion is not assured anymore for certain contingency events. If the situation aggravates, the system may move to emergency states, where some constraints are not satisfied anymore. However, corrective actions such as generation tripping or load curtailment may still be carried out and widespread blackout does not take place. If the perturbation is severe and the corrective actions are not sufficient, the system may enter in extremis state. It is the condition where cascaded blackouts occur, resulting in a shut-down of a major portion of the power system. Following this, restorative actions where all the facilities, including generation, transmission, and loads, are reconnected are carried out to restore the functionality of the power system. These states are illustrated in Figure 4.1. With more and more shares of variable renewables in power systems, it becomes more complicated to satisfy the N-1 criterion at all times, notably concerning the problem of maintaining the power balance between production and consumption. Classically, generators are operated such that upon any trip of a single unit of generator, the system moves to a new satisfactory state without any load shedding. Thus, it is necessary to have total grid spinning reserve of at least the active power rating of the largest unit of generator in service. In the worst case scenario and with insufficient spinning reserve, an event (e.g. largest generator loss) may cause continuingly decreasing frequency and eventually may result in a blackout.

Not satisfying N-k (typically N-1) criterion creates higher risk of blackouts, as pointed out in [START_REF] Velay | An analysis of large-scale transmission power blackouts from 2005 to 2016[END_REF]. The Initiating events vary from case to case, ranging from protection failures or malfunctioning, overloading, faults, natural disasters, to terrorist attacks [START_REF] Velay | An analysis of large-scale transmission power blackouts from 2005 to 2016[END_REF]- [START_REF] Rahman | Largest blackouts around the world: Trends and data analyses[END_REF]. The initiating event may then be followed by cascading events leading to widespread loss of elements, known as blackouts. Major blackouts typically occur as a result of the inability of the power system to support the demand for generation power delivery [START_REF] Evans | Influence of power system protection on system blackouts[END_REF].

Main Challenges

The grid of the future is discussed previously in Subsection 2.4.2. Renewable energy is one of the key axes of the grid of the future. More and more intermittent renewables are interconnected to power systems nowadays through inverter interface. This initially created only few problems when the proportion was still low. However, as more and more VRES are integrated into power systems through inverters, some issues started to arise, notably lack of inertia and energy intermittency. These two factors have a great impact on power system stability, especially on frequency stability.

The topic of achieving 100% renewable grid is discussed in [START_REF] Kroposki | Achieving a 100% Renewable Grid: Operating Electric Power Systems with Extremely High Levels of Variable Renewable Energy[END_REF]. Several countries have successfully operated their grids with high levels of renewables based on hydropower and geothermal, such as Norway, Iceland, and Costa Rica (above 90% based on annual energy generated). However, systems like these are limited by geographic topology and natural resources. Around the world, other areas have the possibility to achieve 100% renewable grids by exploiting variable renewable energy options, such as wind and PV systems. With the reduction in costs during the last decade, large-scale deployments are a taking place around the globe.

Variability and Predictability

VRES are different from thermal generators because of the variability and uncertainty of the outputs. Grid-wise, the challenges of grid operations become more apparent as the imbalance between power production and consumption occurs more frequently in higher magnitudes. VRES are not dispatchable and thus require greater grid flexibility in grid operations, as discussed in Subsection 2.4.3. In terms of imbalance phenomena in power systems, ENTSO-E classifies them into four types, as depicted in Figure 4.2. Traditionally, type 1 is the worst case. However, with more and more intermittent sources, type 3 can be problematic for the grid operator. In PV installations, the irradiance may drop 75% in less than 40 seconds, such as the case in Indonesia [START_REF] Tambunan | Maximum Allowable Intermittent Renewable Energy Source Penetration in Java-Bali Power System[END_REF], which increases the complication of operating a microgrid at high levels of VRES.

Reserve margin is a function of the load factor, the load factor, the magnitude of the load, the load shape, reliability requirements, and the availability of the DER [START_REF]IEEE Guide for Design, Operation, and Integration of Distributed Resource Island Systems with Electric Power Systems[END_REF]. In island mode, there is a need to provide dynamic response from the DER. For example, following a motor starting, the DER should be able to maintain voltage and frequency stability. Transient stability following perturbations such as load steps, DER unit outage, and faults, should be maintained. There should be enough monitoring to operate and understand the status of the island. If multiple DER units exist in the island, their operation should be managed and coordinated to meet the needs of the island.

In rural areas, the lack of skills of locals in grid management makes it even more difficult to forecast the stochastic behavior of loads and VRES. Consequently, blackouts occur frequently with today's grid regulation and management.

Low inertia

The other major phenomenon is the lack of inertia. With the present strategy of grid regulation, this issue contributes to more frequent and significant frequency deviation. Traditionally, the grids are dominated by conventional synchronous generators. As opposed to inverters, they have stationary part (stator) and rotating part (rotor) which produce a rotating magnetic field, which induces a voltage within the stator windings. This process creates AC electricity at a specified voltage and frequency levels. These machines have important characteristics which have dictated how power systems have been planned and operated since its first conception. This includes the swing equation, as well as voltage and frequency regulations.

From a physics point of view, the turbine system and rotating components of synchronous machines exhibit mechanical inertia, which stores kinetic energy in the rotating mass. That energy can be extracted from or absorbed into these rotating masses in case of system perturbations, so that the power systems can withstand temporary fluctuations in net load and generation. In contrast, VRE technologies employ different technologies for energy conversion and interfacing to the grid. Aside from concentrating solar power, VRES are typically integrated to the AC grid through inverters. The associated controllers are executed on digital controllers where real-time measurements are processed and processed. User defined controls are programmed and executed continuously. It is noteworthy that the chosen control strategy, instead of inverter's physical properties, dictates the electrical dynamics of the inverters during disturbances and how they interact with the grid [START_REF] Kroposki | Achieving a 100% Renewable Grid: Operating Electric Power Systems with Extremely High Levels of Variable Renewable Energy[END_REF]. This poses both challenge and opportunity to control engineers. Since no physical inertial response is available on inverter's power converting process, they are often said to have zero inertia. However, if appropriate controls are applied, they can help improve the grid stability.

A literature study on the low inertia power systems are reported in [START_REF] Milano | Foundations and Challenges of Low-Inertia Systems[END_REF]. In a hypothetical system where there are no synchronous machines at all, the frequency is fully decoupled from the power balance of the system, except if supplementary controls are in force. In this case, no element of the grid responds naturally to power imbalance and a control system must be in place to preserve the power balance at every instant. Here, the electrical frequency may still be a global variable, but is not anymore a physical variable associated to the rotating magnetic field of synchronous machines.

Instead, it is a controlled variable.

Since IBGs do not naturally respond to power variations, specifically designed controls are necessary. The inertial response can be implemented as a control loop, and is thus subject to delays, malfunctioning, saturation, and other unexpected dynamics that may lead to instabilities. In addition, some strategies are dependent on communication systems and are, in general, neither fully reliable nor easy to implement.

In future very low inertia power systems, the roles of synchronous machines have to be replaced by other grid formers, which will be discussed in Subsection 4.3.4. The current strategy of IBGs as grid followers will no longer work because the reference of voltage and frequency is required.

Principally, the stability problems do not change much: voltage collapse, transient stability, and frequency stability. Transient stability may not be as important as before as inverters are not inherently regulated by the swing equation. Although the swing equation can be embedded into inverter regulation strategy, the out of synchronism phenomenon can be avoided with supplementary algorithms. However, problems caused by the grid configuration and transfer impedance such as voltage collapse stay the same.

Additional Challenges for Microgrids

Currently, most islanded microgrids rely on fossil-based synchronous generators to provide voltage and frequency reference [START_REF]Integrating High Levels of Renewables into Microgrids[END_REF]. In developing countries around the world, the main objectives of small island systems and isolated networks are to provide universal energy access and to move away from the dependency on fossil fuel transport [START_REF] Römer | Pioneering smart grids for Indonesia -the case of a smart grid roadmap development[END_REF]. Such areas typically lack skilled human forces. Thus, simple operation and reliable devices are necessary so that minimum operation and maintenance efforts are required. In addition, industrial activities which demand high quality electricity are minimal in such areas, and residential loads dominate. Consequently, affordable electricity is of high importance and high power quality is not top priority, as the point here is to improve the living quality and the human development index.

Microgrids are different from large interconnected grids in many aspects. Microgrids do not have to be compatible with the legacy-system [START_REF] Milano | Foundations and Challenges of Low-Inertia Systems[END_REF]. As pointed out in [START_REF] Hossain | Microgrid testbeds around the world: State of art[END_REF], remote microgrids are normally isolated and the power quality requirement is relaxed. Maximum power use may be limited for the customers. It is difficult to maintain the standard level of voltage, frequency, and power quality while preserving the balance between intermittent supply and fluctuating demand.

Current Efforts

Efforts are needed to tackle the challenges of the grid of the future. Researchers and engineers propose numerous strategies and approaches to deal with the challenges of high levels of VRES. The efforts to deal with variable renewables in the form of flexibility are reviewed previously in Subsection 2.4.3. Here, the other aspects are discussed.

Efforts to improve predictability

Predictability is the key to better grid operation. Meteorological forecasting, while steadily improving, is still subject to uncertainty. In this sense, the challenge with VRES is not so much its variability, but rather its predictability. If output could be forecast with 100% certainty, the only challenge would be to meet the ramp rates. Forecasting technologies are particularly important for wave, wind, and solar technologies, the output of which varies irregularly. The tidal resource also varies, but is well predictable. Flexibility in grids also fluctuates. It varies over time, and with the extent of demand. VRES can be predicted with greater accuracy as the time ahead of delivery reduces, reducing the need for the fast-response, high-premium variety.

Demand for electricity, being based on regularly repeating patterns of social behavior, may be relatively easy to predict. However, unexpected peaks can still occur: as temperatures rise or fall unexpectedly, or system wide consumer behavior coincides for other reasons. Experience has shown that sometimes the forecast fits the reality, sometimes it does not. For example, generation of PV plants in cloudy days is not very predictable [START_REF] Reilly | High Penetration of Renewable Energy: Possible Scenarios, Implications, and Best Practices from International Experience[END_REF]. Improving the predictability by refining the forecasting method is the most straightforward way. Furthermore, there exist three important efforts to improve the predictability of VRES: choosing anti-coincident siteslarger area interconnection, balancing anti-coincident renewables, such as wind and solar, and employing dispatchable renewables, such as hydro and geothermal [START_REF] Reilly | High Penetration of Renewable Energy: Possible Scenarios, Implications, and Best Practices from International Experience[END_REF].

Regulatory Efforts

The recent energy transition towards large-scale integration of renewables into power systems is leading grid operators and standards bodies to specify more stringent operation and flexibility requirements for generating equipment in order to assure the power system operation and stability.

For all technologies of DER, both classical synchronous machines or VRES connected through inverters, new capabilities with regard to fault ride through, frequency range and control, ramp rates requirement, reactive range and voltage control start to be required [START_REF]New Generation Technologies and GB Grid Codes[END_REF].

Fault Ride Through

Recent standards and grid codes mandate voltage and frequency ride through capabilities state for all technologies of generating units in order to support the grid stability [START_REF]Integrating Inverter-Based Resources into Weak Power Systems -Reliability Guideline[END_REF], [START_REF]IEEE Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces[END_REF], [START_REF] Etxegarai | Review of grid connection requirements for generation assets in weak power grids[END_REF], [START_REF] Rodrigues | Grid code reinforcements for deeper renewable generation in insular energy systems[END_REF].

IEEE 1547 defines ride through capability is defined as the ability to withstand voltage or frequency disturbances inside defined limits and continue operating [START_REF]IEEE Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces[END_REF], while the EU Network code defines it as the capability of a generator to be able to remain connected to the network and operate though periods of low voltage at the connected point caused by secured faults [182], [START_REF][END_REF]. Some ride through requirements imposed by a number of grid codes are illustrated in Figure 4.3 and Table 4.1. The generator may disconnect outside the defined ride through requirements [START_REF]IEEE Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces[END_REF], [START_REF] Enayati | Revised IEEE 1547 Standard for Interconnecting Distributed Energy Resources with Electric POwer Systems-National Grid Solar Program[END_REF].

Wider range of operation

Operators have started to require DER to be capable of functioning in wider range of frequency and voltage. In European grid, the protection settings for automatic disconnection of DER from the grid are formerly not in line with those of the transmission system. The settings for distributed generation are in the range of 50.2 -50.5 Hz for over frequency and around 49.8-49.5 Hz for under frequency whereas the ranges to mandatory remain connected within the European transmission system is 47.5 -51.5 Hz [START_REF]Dispersed Generation Impact on CE Region Security[END_REF]. This results in some countries with a significant capacity of installed non-compliant generation units with respect to interconnected system stability. Italy and Germany have launched programs to retrofit older generators to make them comply with the latest connection requirements of DER, to ensure all generating modules are capable of remaining connected in the range of 47.5 -51.5 Hz.

IEEE C.50. 13 [197] and IEC 60034-3 mandate that synchronous generators shall be thermally capable of continuous and limited operation within the prescribed range of voltage and frequency Numerous grid codes require the capability of generators to provide maximum active power output during under frequency conditions. The main objective is to limit the potential reduction of active power generation after a disturbance, thus avoiding more severe disturbances. It is mandated in the European grid code [START_REF][END_REF] that all power generating modules shall be capable of maintaining constant power output at its target active power value regardless of changes in frequency. The relevant TSO may specify admissible active power reduction from maximum output at severe under frequency conditions, as to accommodate the technologies such as gas-turbine plants which are not able to provide full active power during under frequency. This is illustrated in Figure 4.5. In addition, some grid codes require generators to remain connected for voltage step changes, phase-angle jumps, and negative sequence loadings, such as the case of the Irish, Danish, and British power systems [START_REF] Etxegarai | Review of grid connection requirements for generation assets in weak power grids[END_REF]. 2.10. These requirements include voltage control, frequency control, blackstart, in addition to voltage and frequency ride through [START_REF] Zhao | Power system support functions provided by smart inverters-A review[END_REF]. These capabilities are vital, considering that the penetration of VRES continues to increase [START_REF] Von Appen | Time in the Sun: The Challenge of High PV Penetration in the German Electric Grid[END_REF].

Boundary mandated by The European Grid Code

The inverters capable of providing ancillary services to the grid, such as frequency and voltage support, are known as grid supporting inverters. The classification is discussed previously in Subsection 2.4.4.3. The new IEEE 1547-2018 requires that DER are capable of responding to voltage variations within the normal operating range through voltage-reactive power control and voltageactive power control [START_REF]IEEE Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces[END_REF]. The required voltage and reactive power control functions include constant power factor mode, voltage-reactive power mode, active-reactive power mode, and constant reactive power mode, whereas the voltage and active power control function includes voltage-active power (volt-watt) mode. However, the usage of such functions remains in the hands of the power system operator.

One of the ways to help stabilizing the grid frequency is through synthetic inertia (SI), which has been the subject of many research efforts, e.g. [START_REF] Rahman | Optimization of virtual inertia considering system frequency protection scheme[END_REF], [START_REF] Kerdphol | Virtual Inertia Control-Based Model Predictive Control for Microgrid Frequency Stabilization Considering High Renewable Energy Integration[END_REF]. On short time scales, synchronous machines maintain the power balance through instantaneously available physical storage in the form of inertia, and later through their primary control which takes effect more slowly. In contrast, IBG works differently: the analogy of synchronous machine's inertia is the energy stored in the DC-side capacitor, which is typically much smaller compared to the synchronous machine's inertia of the same power capacity. On the other hand, power electronic sources can be actuated on much faster time scales and thus contribute to power balancing, provided that the DC-side energy supply is capable of supporting this. Consequently, the lack of physical inertia can potentially be compensated through fast DC-side energy storage equipped with appropriate control strategies.

In contrast to synchronous machines, frequency changes have to be detected first by the control systems. Applied filtering might lead to time delays and thus reduce the performance of emulated inertial response [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF]. If the delays are too long, then the synthetic inertia (SI) will provide no mitigation of the initial ROCOF during an event. If the delay happens to lead to a phase lag that is 180 degrees different to the equivalent true inertial response, then the output power modulation provided by the SI can operate in complete anti-phase to the rotor swings of a real synchronous machine, encouraging classical rotor oscillations, and thereby degrading network stability [START_REF]High Penetration of Power Electronic Interfaced Power Sources (HPoPEIPS)[END_REF].

Operational Efforts

With regard to intermittent renewables, John Reilly from NREL proposes the following actions to deal with the VRES and to assure power supply [START_REF] Reilly | High Penetration of Renewable Energy: Possible Scenarios, Implications, and Best Practices from International Experience[END_REF]: balancing with storage, such as pumped hydro or battery, and balancing with dispatchable generation plants, such as natural gas turbine or combined cycle plants.

In very high level of VRES scenarios (60-100% energy-based), batteries and demand response are deemed important in order to maintain the balance of active power production and consumption, as reported in [START_REF]Integrating High Levels of Renewables into Microgrids[END_REF], [202]. Primary reserve with droop-like response may also be carried out by VRES via active power curtailment [START_REF] Bullich-Massagué | Power plant control in large-scale photovoltaic plants: design, implementation and validation in a 9.4 MW photovoltaic plant[END_REF]. However, this strategy results in curtailed energy, as the harvested energy is curtailed form the maximum potential, which is normally not desired. This technology has long been identified as a solution for power infeed through line-commutated HVDC to a weak system, or even to a system without any generation, due to its capability to maintain frequency and voltage at an acceptable levels during system perturbations and its inherent inertia [START_REF]IEEE Guide for Planning DC Links Terminating at AC Locations Having Low Short-Circuit Capacities[END_REF]. However, until recently, there was not much interest into this technology because power systems were supplied mostly by dispatchable synchronous machines, hence enough inertia.

However, as the penetration of VRES keeps increasing, several engineering companies and TSOs started to show interest in this relatively mature technology, such as ABB [START_REF]Rise of renewables leads to synchronous condenser revival -Synchronous condensers | ABB[END_REF] and Siemens [START_REF]A stable grid in the era of renewables[END_REF].

Siemens even states that the synchronous condensers are a proven solution to stabilize the grid.

Projects of conversion of old synchronous generators to synchronous condensers have marked the revival of synchronous condensers, such as the conversion of Biblis nuclear power plant in Germany in 2012 and Ensted coal-fired power plant in Denmark in 2013 [START_REF] Deecke | Usage of existing power plants as synchronous condenser[END_REF].

AC Grid

Voltage regulator

Excitation voltage

Grid voltage

Synchronous condenser As the majority of IBG are of grid following and grid supporting type, synchronous condenser technology could be a straightforward solution to the grid stability problem, where the VRES connected via IBG are responsible for power generation and the synchronous machine for grid stability and the reference of voltage and frequency. This concept and the construction of the machine are well understood by researchers and engineers, as the technology is already mature. The classical inherent behavior of synchronous machines and power systems based on the swing equation is still applicable here, hence familiarity with the classical power system engineering practice. An important downside of active power losses has to be taken into account in the operation.

In this PhD thesis, we propose new power system regulation strategy suitable with this technology, which will be thoroughly discussed in Chapter 5.

Grid forming inverters

A grid forming inverter is an inverter which has the capability to form a grid, i.e. to provide voltage and frequency reference to the grid. This approach typically requires controllable and fast response energy storage on the DC side. A grid forming inverter can be modeled as a voltage source parallel with low impedance, as discussed in Subsection 2.4.4.3. It should be capable of providing a reference and support for frequency and voltage, robust synchronization mechanism, and performing black-start, all of which are traditionally offered primarily by synchronous machines [START_REF] Milano | Foundations and Challenges of Low-Inertia Systems[END_REF].

Inverters have no natural interactions with the AC grid. The interactions between the IBG, the other resources, and the grid are therefore determined by the chosen control approach. An important limitation of inverters that has to be taken into consideration is the narrow limits of current overshoots, as opposed to high overloading and overcurrent capability of synchronous machines.

Virtual synchronous machine (VSM) is one of the control strategies of grid forming inverters.

The concept was introduced in 2008 by Driesen and Visscher [START_REF] Driesen | Virtual synchronous generators[END_REF]. The idea is to help stabilize the grid by controlling an inverter (or a group of inverters) to emulate the characteristics of a synchronous machine, including the inertia, damping properties, and primary regulations (i.e. frequency and voltage droop). Existing VSG topologies and applications are reviewed in [START_REF] Bevrani | Virtual synchronous generators: A survey and new perspectives[END_REF]- [START_REF] Zhong | Virtual Synchronous Machines: A unified interface for grid integration[END_REF] while a review of detailed control strategies of VSM is presented in [START_REF] Hua | A control strategy for inverter: Virtual synchronous generator[END_REF]. Contrary to synchronous machines which have inherent synchronization mechanism, the VSM need a synchronization unit. Currently, some strategies use a PLL to provide the phase and frequency of the grid voltage as to attain smooth synchronization. However, PLLs may cause many problems leading to reduced performance, increased complexity, or even instability [START_REF] Zhong | Virtual Synchronous Machines: A unified interface for grid integration[END_REF]. Recent advances have shown that a VSM can synchronize itself with the grid an embedded synchronization mechanism and therefore the PLL can be removed. This concept is called self-synchronized synchronverter [START_REF] Zhong | Self-Synchronized Synchronverters: Inverters Without a Dedicated Synchronization Unit[END_REF]. Aside from higher frequency noise due to static switching, there is no difference between the electrical appearance of an electromechanical synchronous generator and a completely electrical virtual synchronous generator within the unsaturated operating region from the grid point of view. As the inverters behave similarly to synchronous machines, legacy practices in power systems are not much altered.

Some researchers commented that controlling a converter to behave like a synchronous machine is wasteful as the key resources and strengths of the converter are not fully exploited, such as in [START_REF] Milano | Foundations and Challenges of Low-Inertia Systems[END_REF].

However, as the power system world is accustomed to the notion introduced by synchronous machines and its effectivity has been well proven, one can benefit from the understanding of how power systems work with synchronous machine-like behavior and from the capability of virtual synchronous machine to have dynamic parameters based on what is best for the power system.

New Perspective on Quality of Supply

The needs that a power system must serve will evolve over time, as discussed recently in early 2019 in IEEE power & energy magazine [START_REF] Kristov | The Bottom-Up (R)Evolution of the Electric Power System: The Pathway to the Integrated-Decentralized System[END_REF]. For most of the 20 th century, the society needs industrial growth, universal access to electricity, growth of cities and suburban areas, and expansion of the customer economy. The 20 th century power systems were constructed to serve a reliability philosophy, where customers' appliances must always come on when they switch them on. This drove infrastructure investment to satisfy peak load conditions which occur only during short period. Now in the 21 st century, the societal needs of power systems have changed: reduction of greenhouses gases, greater resilience to disruptive events, elimination of the bad health impacts due to fossil plants, fostering a diverse and competitive arena of new energy technologies, and more options and control of their energy sources and uses.

Driving force of Renewables

The main driving force behind renewable energy development is different in different places across the globe. In Europe, it is to fight against green-house effects caused by fossil fuels. Due to slow growth in electricity demand, old fossil-based generation plants have been envisaged to be replaced by renewables. Whereas in developing countries where the electricity growth is tremendous and some people still live without electricity, the motivation is to provide affordable universal electricity and to respond to demand growth, meaning that the renewable plants are constructed with the hope of increasing the system capacity.

Microgrids are important for economic development, as argued by the CEO of Homer [START_REF] Homer Energy | Exploring Use Cases for Wind + Solar Hybrid Microgrids with[END_REF].

However, all over the world, islanded microgrids often utilize diesel generators, which are noisy, not eco-friendly, and expensive. As the price of renewable technologies such as PV and battery is decreasing, the outlook seems to be in favor of VRES. This is a different segment of market with separate value prepositions. In both grid connected and off-grid operating modes, a microgrid should be capable of maintaining balance between power generation and consumption [START_REF]Microgrid Stability Definitions, Analysis, and Modeling[END_REF]. Government agencies, utilities, military bases, universities, and research centers have been deploying microgrids, and the positive trend is expected to continue in the next decade [START_REF]Global Microgrid Market 2016-2020[END_REF], driven by environmental issues, the need for electricity in remote communities, and the prospect of increased resilience and reliability. However, the focus objective may vary for different microgrids, as discussed in 2.5.1.

Reference [START_REF] Kroposki | Integrating high levels of variable renewable energy into electric power systems[END_REF] revealed that high penetration level of variable renewables often takes place in small power systems (i.e. smaller than 100 MW), which fall into isolated microgrid category.

Views on Electric Power Quality and Grid Operation

In power grid operation, power quality nowadays is expected to be within certain strict boundaries even at high levels of renewable penetration. Consequently, high investment and operation costs are inevitable. The generation side is currently evolving with the integration of more variable renewables. However, system regulation strategy does not change too much. Thus, power systems are more prone to blackout due to the failure in maintaining the power balance. In many grid operation schemes, load shedding serves as the last resort in order to avoid the in extremis state as shown in Figure 4.1. It is triggered only when the imbalance is severe and it is typically predetermined. Furthermore, the shed load might be more than necessary, which results in overfrequency [START_REF] Potel | A Real-Time Adjustment Method of Conventional Under-Frequency Load Shedding Thresholds[END_REF]. Reestablishing the frequency back to nominal values is normally carried out later, which takes time. Only then will the shed load be brought back into service.

In order to reach 100% VRES, the grid may need to rely on the IBG for stability and grid regulation, and thus standalone rules that are system dependent may be necessary [START_REF] Driesen | Virtual synchronous generators[END_REF]. In China, as discussed in [3], there exists an operational microgrid composed by 7 MW of PV Units, 1 MW of energy storage (2h of full discharge). When PV output decreases significantly, the security and stability control will shed non-critical loads. The energy storage will be in discharging mode to maintain the supply to critical loads. Then, other diesel generators will then be started and the shed loads will be brought back into service. Obviously, this microgrid operation is different from how a grid operation and regulation are normally managed.

Over the last decade, demand response has attracted much research attention. It is one of the flexibility options in a power system. Its main idea is to shift the demand in order to suit the availability of the supply. However, this strategy is typically realized with the support of (fast) communication systems to send the price signals or dispatch instructions [START_REF] Li | Optimal demand response based on utility maximization in power networks[END_REF]- [START_REF] Yu | From passive demand response to proactive demand participation[END_REF] or local measurements which also require local computing resources (e.g. smart meters) [START_REF] Nandkeolyar | Management of time-flexible demand to provide power system frequency response[END_REF]- [START_REF] Samarakoon | Demand side primary frequency response support through smart meter control[END_REF].

The operational constraints in terms of voltage characteristics of electricity supplied by public distribution systems required by EN 50160 [START_REF]Voltage Characteristics of Electricity Supplied by Public Distribution Systems[END_REF] As presented in Figure 4.8, even for momentary variations, the permissible limits are small compared to the total area possibly covered, i.e. all areas where the frequency is lower than 84% are not permitted, neither 0-50% of voltage. The strict operational ranges are imposed to guarantee the power quality of electric supply in order to obtain satisfactory performance of electrical and electronic appliances. Here, the focus is on the load side, to make sure that the loads are functioning properly according to what is expected by the customers.

In terms of real units (in Volts and Hertz), the operational ranges for several appliances, notably devices working with power supply, are wider even in steady state, as illustrated in Figure 4.9. The values are based on a number of power supply design guides [START_REF]Power Supply Design Guideline for 2008 Dual-Socket Servers and Workstations[END_REF]- [START_REF]ATX12V Power Supply Design Guide[END_REF]. This indicates that certain appliances in power systems are designed to function in wider range of voltage and frequency. As discussed previously in Subsection 4.4.1, the objective of the use of renewable energy and the construction of microgrids varies across the globe. Consequently, the operation ranges should adapt to the main objectives, especially in microgrids functioning with massive levels of renewables.

Chapter 4 Efforts to Accommodate Massive Shares of VRES in

As suggested in [START_REF] Driesen | Virtual synchronous generators[END_REF], the operation and management of power systems with high penetration of variable renewables may be different from the conventional ones. Several adjustments are necessary.

The grid codes may be unique only for a handful of cases. In this regard, if the main motive of a microgrid development is for universal electricity access to low human development index (HDI) regions, then the grid codes, as well as the management and operation, should be designed and adjusted accordingly.

A key question arising here is why not utilize the degraded ranges (i.e. wider voltage and frequency ranges) only momentarily for maintaining the power balance in the system and for reducing the investment and operation costs. The approach indeed needs to take into account the impact on the devices in the grid and the public acceptance.

Views on Energy Security, Reliability and Operating States

The topic of energy security is discussed in [START_REF]Keeping Some of the Lights On: Redefining Energy Security[END_REF]. Although various definitions of energy security exist in the literature, they all share a common idea that the energy supply should meet the demand. In other words, abundant availability of energy sources is the key [232]. However, with the integration of high levels of VRES, we encounter fundamental challenges to the current understanding of energy security, notably due to their inherent intermittent behavior.

The US Department of Energy defines reliability as the ability of the system or its components to withstand instability, uncontrolled events, cascading failures, or unanticipated loss of system components. In the context of system planning, reliability-driven investment decisions are based on N-k (typically N-1) reliability criterion [START_REF]The Definition and Quantification of Resilience[END_REF].

IEEE PES Industry Technical Support Task Force defines resilience as the ability to withstand and reduce the magnitude and/or duration of disruptive events, which includes the capability to anticipate, absorb, adapt to, and/or rapidly recover from such an event [START_REF]The Definition and Quantification of Resilience[END_REF]. The concept of resilience covers all events, including high impact but unlikely events which are normally excluded from reliability analysis. Both reliability, which is generally expressed by the number and duration of power outages, and resilience, especially due to natural disasters, can be improved with microgrid concept [START_REF]Energy Reliability with Microgrids | Storm & Disaster Recovery -NEMA[END_REF], as proven by the cases in Japan and the US.

Resilience-driven designs may not be aligned with reliability-driven ones. A study suggests that for distribution systems, it is more resilience-effective to design a smarter and responsive network than opting for more redundancy [START_REF] Panteli | Power System Resilience to Extreme Weather: Fragility Modeling, Probabilistic Impact Assessment, and Adaptation Measures[END_REF]. A widely used resilience diagram is shown as follows, which goes along with the proposed operation states in microgrids marked with massive VRES in Figure 4.11. As far as islanded microgrids are concerned, maintaining high electrical energy security in the presence of high levels of VRES is possible with the help of technologies such as storage systems, but it is proven to be costly. A compromise between reliability, economic cost, and sustainability is therefore necessary, with the focus on meeting the main objective of the grid. For example, if the priority is to achieve optimum sustainable energy use at affordable cost, compromises in reliability which requires customer behavior adjustment in electricity use are vital.

Resilience

Here, we propose a new perspective which aligns with the demand response (DR) philosophy, in regard to the view on maintaining the power balance in a power system using the demand side.

Instead of only ensuring that the generation side is capable of meeting the load demand; the loads must follow the available power generation. In addition, the implementation should not depend on predetermined load shedding, local measurements, or fast communication systems, which marks a distinguishing point from a typical DR implementation. Consequently, this strategy is relatively affordable and cost-effective. These features are highly desired in post-disaster recovery and low HDI community cases. However, a tradeoff in power quality is inevitable. The technical implementation of this proposal will be discussed in detail in Chapter 5.

With regard to energy security, the overall analysis should be comprehensive and consider other types of energy besides electricity. The energy is principally needed for the daily activities, which have certain flexibility in time. When measures such as variable frequency and voltage are taken, the main question is whether or not that will still respond to the needs of the customers. In communities previously living without electricity, the dependency and attachment to electricity are not yet developed. Therefore, the introduction of electricity itself will increase the local energy security.

In the era where VRES dominate the generation side, the operation states as illustrated in Figure 4.1 becomes obsolete. The current definition of normal state and the requirement of N-1 criterion in the generation side are not suitable anymore with massive VRES development, as the grid is rarely is the "normal" operating state considering the worst expected contingency event (i.e. high variability of VRES). The grid should now be considered secure in a sense that blackouts are evitable and the system can reestablish normal operating conditions according to the (voluntary) actions of customers and grid operator within the defined time following the perturbation. In addition, DR is not considered the last resort anymore. It is one of the main flexibility to achieve power balance and power system stability. However, load shedding of critical loads may be necessary when the degraded mode is still ineffective. The proposed operation states in microgrids marked by massive penetration of VRES are illustrated in Figure 4.11.

The illustrations of the grid operation and its proposed changes are shown in Figure 4.12 and

Conclusion

This chapter has reviewed the main challenges of massive VRES, and discussed the current efforts to accommodate massive shares of VRES. The two main challenges are the variability and the low inertia. The efforts come from different actors, starting from the regulator, the operator, and the power system and equipment designer. However, those efforts are still focused on minimizing the impact introduced by VRES and IBG in order to continue enjoying the electricity like the way we used to be when we mostly depended on dispatchable fossil fuel. This causes the efforts to be costly and inefficient. In the last part of the chapter, we offer a new perspective on quality of supply, in which we accept the variability brought by VRES and its consequences. It will cause higher deviations in the main variables in electricity, such as the voltage magnitude and the frequency. For several applications, such as for universal electricity and for post-disaster situations, accepting higher deviations can be acceptable and will allow more VRES and IBG to be integrated into power systems.

Chapter 5 Voltage to frequency ratio regulation and its features

In this chapter, the new perspective on quality of supply is developed into a novel regulation strategy in which the system frequency and voltage are maintained in such a way to keep their ratio essentially constant. The implementation of the proposed strategy on two main grid forming elements:

synchronous machine and grid forming inverter are addressed. The benefits and the consequences of employing this strategy are also discussed.

Background

In islanded microgrids, external interconnections are not available; thus the grid has to be selfsufficient. Most of the present solutions to prevent blackouts utilize power system flexibility. The options include (1) the use of batteries [START_REF] Delille | Dynamic frequency control support: A virtual inertia provided by distributed energy storage to isolated power systems[END_REF], [START_REF] Miranda | Impact of energy storage on island grid dynamics: A case study of Bonaire[END_REF], (2) virtual synchronous machines (consisting of renewables, battery, and sophisticated controls to mimic a synchronous machine) [START_REF] Rahmani | Virtual synchronous generators for microgrid stabilization : Modeling, implementation and experimental validation on a microgrid laboratory[END_REF], (3) traditional primary reserve, e.g. dispatchable generators [START_REF] Banjar-Nahor | Study on Renewable Penetration Limits in a Typical Indonesian Islanded Microgrid considering the Impact of Variable Renewables Integration and the Empowering Flexibility on Grid Stability[END_REF], and (4) demand response (communication channels are generally necessary) . They are managed such that at any given moment they are able to maintain the power equilibrium in the power system. However, such actions need high investments and are not very efficient because new devices need to be installed and dispatchable generations are often operated at low loading which decreases the generation efficiency. With the current power system regulation strategy, the power system becomes prone to blackouts.

Compared to interconnected grids, maintaining the equilibrium between power generation and consumption is more complicated especially in isolated microgrids operating with massive renewables. It should be noted that renewables are often the technology of choice for rural off-grid applications [238]. However, as the power system is smaller, it is generally more vulnerable to outages. Consequently, blackstart as an initiating event in the restorative mode is a necessity.

Blackstart in microgrids is discussed in [START_REF] Lopes | Evaluation of the Emergency Strategies during Islanding and Black Start[END_REF], which does not differ much from the blackstart of interconnected grids. The procedure starts with complete disconnection of loads, and then the building of smaller networks. In this second stage, the storage devices and controllable microsources are responsible for the energization. This will then be followed by synchronization of those small networks into a large one and the connection of the controllable loads to the network. Subsequently, non-controllable generators and loads are connected. Finally, set-point and control mode changes can be carried out.

It is well understood that the most important issue in frequency stability is the active power equilibrium. The act of maintaining the balance between power production and consumption is often called dynamic balancing. The classical approaches generally control the production side to match the power consumption, under the assumption that enough spinning reserves are available. The spinning reserve problem is relatively simple to deal with when all generators are dispatchable or fully predictable. However, with variable, somewhat unpredictable, and undispatchable nature induced by VRES, power production may decrease at the same time due to sudden weather change.

This complicates the calculation of the necessary spinning reserve. More and more new approaches may comprise the emulation of the classical strategy behavior and employ demand response strategies enabled by the communication technology. Indeed, as the spinning reserve problem is problematic especially in systems incorporating high shares of variable renewables, dynamic balancing by controlling both production and consumption sides makes more sense.

Reference [START_REF] Short | Stabilization of Grid Frequency Through Dynamic Demand Control[END_REF] investigates the possibility of improving the frequency stability by applying dynamic demand control into certain customer appliances. However, a communication channel is necessary, yet it is not very favorable due to the high investment and the absence of plug-and-play feature, both of which are important in islanded grids. Furthermore, it is widely known that loads are dependent on frequency and voltage, as discussed in [START_REF] Bokhari | Experimental Determination of the ZIP Coefficients for Modern Residential, Commercial, and Industrial Loads[END_REF], [START_REF] Concordia | Load Representation in Power System Stability Studies[END_REF], [START_REF] Delille | Taking advantage of load voltage sensitivity to stabilize power system frequency[END_REF], [START_REF] Cui | Excitation Voltage Control for Emergency Frequency Regulation of Island Power Systems With Voltage-Dependent Loads[END_REF]. Frequency-responsive loads can be used to maintain grid stability, which acts as demand response, and is investigated in [START_REF] Short | Stabilization of Grid Frequency Through Dynamic Demand Control[END_REF]. In [START_REF] Cui | Excitation Voltage Control for Emergency Frequency Regulation of Island Power Systems With Voltage-Dependent Loads[END_REF], a generator excitation voltage control strategy in island grids for maintaining frequency stability is proposed thanks to the contribution of voltage dependent loads. It has been demonstrated that the system becomes capable of regulating the load voltage and power consumption even when there are no power reserves. Reference [START_REF] Delille | Taking advantage of load voltage sensitivity to stabilize power system frequency[END_REF] proposes a demand response strategy without communication by reducing the operating voltage temporarily. Although the strategy of reducing the operating voltage might be an old-school strategy also known as brownout, this might potentially be an affordable and effective solution for islanded grids. In order to access more demand response, frequency-sensitive loads are also exploited in the proposed regulation.

It is known that system operation requirements are and should be more flexible in islanded microgrids, as discussed in Subsection 4.4. Higher momentary frequency and voltage deviations are allowed. Generators are designed considering ride through capability and wider range of operation.

Consequently, these facts may support the grid in terms of stability performance. This empowers the usage of frequency and voltage variation for dynamic balancing purposes. The proposed strategy in this PhD research capitalizes this concept. Here, we propose a strategy to ensure power system stability with minimum communication systems, modular design, and minimum surveillance in operation. The goal is to transfer power when it is available and ensure that the grid continues to function following variation in generation or demand. This concept fits with resilience concept, as following a natural disaster, can we deploy VRES-based microgrids without a lot of preplanning, which reduces the dependency on fuel logistics (e.g. oil).

This chapter of PhD research presents a new proposal of grid regulation strategy which deals with mid-size microgrids, with the capacity range of 1 MW to 100 MW. This means that it covers medium voltage distribution systems. Dynamic balancing (instead of frequency issues) is the main issue that the proposed strategy deals with. Less dependency on communication systems means that this strategy is easy to implement, more reliable, and affordable. In synchronous machine-based power systems, failure to manage the dynamic balancing leads to frequency drop and ultimately will result in blackout. We propose a method to guarantee stability at all times, even when spinning reserve is insufficient. In addition, from the electromechanical point of view, this invention features protection against lifetime degradation for electrical machinery, e.g. induction machines, synchronous machines, transformers, which are important building bricks of a power system.

Concept and Implementation

Concept

In classical power systems, dispatchable synchronous machines play a central role: voltage and frequency reference, energy producer (coming from mechanical power), and short-term storage through rotating inertia. However, with more VRES, the elements which assume these roles have to be rethought, as one role can be assigned to different elements in the power system. Our proposal and the comparison to today's situation are presented in Table 5.1. An illustration in a simple microgrids fully supplied by IBG is depicted in Figure 5.1. In this Figure, the text in sea green illustrates the ideal behavior of the elements. The roles of elements in current microgrids are identified from microgrid projects across the globe as listed in Table 2.13.

Grid formers are elements which serve as the reference of voltage and frequency to the rest of the elements in the grid, notably grid following inverters and loads. They do not necessarily produce energy. The energy is produced mainly by inverter-based generation which harvests VRES. There are two major methods of controlling inverters: Grid following and grid forming. Grid-following controllers represent the most common type of control strategy for grid-connected PV and wind inverters [START_REF] Kroposki | Achieving a 100% Renewable Grid: Operating Electric Power Systems with Extremely High Levels of Variable Renewable Energy[END_REF]. A grid following controller uses a PLL to estimate the angle of the sinusoidal voltage at the inverter terminal at any moment, so that it can inject a controlled current into the grid. This means that a major share of IBG nowadays needs a voltage reference to function. All inverters in the The loads, which typically vary depending on applied voltage and frequency, serve as the power balancing components, meaning that the variation of load demand due to voltage and frequency variations will maintain the active power equilibrium in the system. In the ideal scenario, the power generation is independent of voltage and frequency, meaning that only the loads will decrease their active power consumption when the active power production drops due to the intermittency.

SC

The proposed regulation method guarantees the stability for microgrids operating with massive levels of variable renewable based sources. The key points are:

 Controlling the source voltage (V) and the frequency (f) in such a way as to keep the ratio V/f essentially constant. This is performed by the grid formers  Granting the power equilibrium based on the self-adjusting characteristics of loads, thanks to their dependence on the applied voltage and frequency.

 Suitability with massive levels of DER (up to 100%), with today grid-tied inverter technology without the need of storage systems This strategy is therefore capable of providing smooth transition from classical grids to future grids, considering the elements in the existing grids dominated by electrical machinery (transformers, motors, generators, etc.) and the power-electronics dominated future grids (batteries, VRE, static machines). Here, it is imagined that the priority is to go green and to acquire affordable microgrid, both in its construction and operation phases. If better power quality is deemed to be necessary in the future, upgrades can be made accordingly. The concept is introduced in Subsection 4.4.3.

The impact of voltage and frequency variations on active power consumption in a typical residential microgrid in Indonesia is illustrated in Figure 5.2. The load model is depicted in Figure 2.12, the load proportions are taken from [START_REF] Palaloi | Analisis Penggunaan Energi Listrik pada Pelanggan Rumah Tangga Kapasitas Kontrak 450 VA[END_REF], while the ZIP and frequency-dependency coefficients from [START_REF] Bokhari | Experimental Determination of the ZIP Coefficients for Modern Residential, Commercial, and Industrial Loads[END_REF], [START_REF] Concordia | Load Representation in Power System Stability Studies[END_REF]. They are considered adequate for the purpose of our research. Newer research on ZIP coefficient exists, such as in [START_REF] Bichik | Impact of Voltage Variation on Domestic and Commercial Loads[END_REF], where the load consumption is still typically found to decrease as the voltage drops. The same behavior is also detected with frequency drop [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF], [START_REF] Wang | Impact of high penetration of variable renewable generation on frequency dynamics in the continental Europe interconnected system[END_REF] typically at 1-2.5% per hertz. As shown in Figure 5.2, optimum reduction of power consumption occurs when both frequency and voltage are decreased. This action also exhibits supplementary benefits, as the ratio of voltage and frequency is maintained at around unity, which satisfies the overfluxing limitations of the electrical machinery devices. It should be noted that voltage reduction without frequency reduction (also known as brownout) is authorized by some grid codes and is effective to shave the load in low active power reserves [START_REF] Cui | Excitation Voltage Control for Emergency Frequency Regulation of Island Power Systems With Voltage-Dependent Loads[END_REF]. However, it may be associated with stalling problems on induction motors. On the other hand, frequency reduction without voltage reduction increases the V/f ratio which may harm electrical machinery devices at excessive values. A number of grid codes and standards require that the V/f ratio shall be maintained less than 1.1 in per unit [START_REF]IEEE Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces[END_REF], [182]. Other consequences associated with the V/f strategy are discussed in more detail in Subsection 5.3.

It should also be clear that this strategy works if the load demand is dependent on voltage and frequency variations. Consequently, constant power loads (already known to be demanding in classical grids [START_REF] Bravo | Dynamic performance of residential motor loads[END_REF]) are onerous and huge proportion of this type of load in the microgrid may cause this strategy to fail. V and f variation

V variation f variation

The main benefits of this strategy are twofold. Firstly, the use of storage elements for stability purposes can be minimized. A local use of storage only for very important loads is of course possible.

Secondly, fast communication systems are not necessary, as the frequency, a global system variable, is used. When the microgrid is small, the voltage drop is small hence the voltage is ultimately uniform.

However, if the microgrid comprises long lines such that the voltage drop may be significant, several grid formers (note that they do not have to produce energy) may be installed at several points in the grid.

The new concept is proposed based on the fact that power consumption in a grid is dependent and sensitive to voltage and frequency variations. Varying the voltage can be performed in short time even in classical grids based on synchronous machine technology because this action typically does not involve slow mechanical process. The voltage is reduced accordingly so as to maintain the power equilibrium and the voltage to frequency ratio. The loads react in a solidary manner to reduce their active power consumption upon frequency and voltage variations.

This strategy provides additional time for the grid operator and costumers to react to power equilibrium occurring within the microgrid, as illustrated in Figure 5.3. Corrective actions such as manual load disconnection or the activation of non-spinning reserves can be done if deemed necessary. It should be noted that the system operates in mode "Potentially stable, demand response necessary" based on the new proposed indices of stability in Table 3.5. Demand response is then applied through V/f regulation to the loads, assuming that the loads are all solidary. This patent-pending concept [START_REF] Banjar-Nahor | Regulation method of an electrical distribution network[END_REF] aims to preserve power system stability upon sudden decrease due to the intermittency of VRES. The strategy has never been used for this specific purpose of maintaining production and consumption equilibrium in any other study prior to this research. With regard to Figure 2.9, this concept is positioned within the evolution framework, where the changes are transformative and incremental. We should keep in mind that the goal here is to transfer the available power and to maintain the power balance at any instant.

Implementation on Synchronous Condenser

The proposed V/f strategy can be implemented on the grid forming elements, such as on synchronous machines (including synchronous condensers) and grid forming inverters. It should be noted that the reactive power injection strategy on grid supporting inverters may also need adjustments due to the implementation of the strategy, as lower terminal voltage does not necessarily mean reactive power insufficiency anymore, as discussed in Subchapter 5.4.

Key points of the implementation of the proposed regulation strategy are as follows.

 Provided that the power variation is within the limit of power reserve, the system follows the classical regulation (droop). A number of grid-supporting inverters function with droop regulation.

 If the power variation is larger than the power reserve, the V/f regulation varies the If a variable V/f value is desired, a further modification is necessary, as depicted in Figure 5.5.

A new input of the voltage-to-frequency ratio VF_setpoint is added. Here, the target voltage is maintained to be equal to the multiplication of the frequency and the V/f ratio setpoint. This strategy is self-regulating, as the controls will adjust the terminal voltage until the frequency is stable, meaning the power equilibrium is achieved. It should be noted that the exciter's apparent power rating is typically less than 0.5% of the rating of the synchronous condenser. The voltage to frequency ratio is maintained around 1, however the exact value may vary depending on several considerations, such as reactive power sharing among grid formers, voltage setpoint at nominal operating condition, and load behavior. In practice, the frequency can be acquired based on the measurement of the rotor speeds.

According to current design rules, generators may go as low as 0.9 pu in voltage while maintaining the nominal frequency. With the V/f strategy, the voltage should be allowed to drop even lower, but the voltage to frequency ratio shall be maintained so as to avoid overheating and damage to electrical machinery. Special signals with slow communication systems may be employed for setpoint setting purposes, for example for setting the voltage setpoint or to send out certain signals to customers or directly to the devices.

Analyses such as time domain simulations may be necessary to confirm the microgrid stability with this strategy. In this research, the reference test cases common in the industry are utilized to test the proposed strategy. From the simulations with typical microgrids, it is found that the synchronous condensers should be rated around 15-25% of the peak load in order to maintain a stable frequency.

Implementation on Grid Forming Inverter

The V/f concept can also be implemented on grid forming inverters, such as on virtual synchronous machine (VSM)-like elements. Here, the element is said to be VSM-like (and not VSM) due to several differences in terms of functions, i.e. in steady state, the grid forming inverter is not strictly required to be capable of producing energy and is only needed to provide frequency and voltage references to grid-tied elements, as opposed to a normal concept of VSM where the element functions as energy producer or as energy storage. However, if desired, the grid forming elements may also produce energy or even function similarly to normal VSM, but the active power droop must be deactivated in order to take advantage of the V/f regulation.

The signal connections between the inverter and the control elements are depicted in Figure 5.7.

Here, the frequency and voltage generated by the grid forming inverters will vary, at the V/f setpoint, in order to reach power balance in the microgrid. A swing-equation-like function defined by Eq. 5.1 can be embedded into the frequency control.

𝐼 𝑑𝑓 𝑑𝑡 = 𝑃 𝑠𝑒𝑡 -𝑃 𝑜𝑢𝑡 Eq. 5.1

Where I is inertia constant, f frequency, Pset active power setpoint, and Pout output active power.

Pset is the target active power production, which is achieved in steady state and in quasi-steady state.

During the transient process, the grid forming inverters may need to deviated from the active power setpoint Pset.

It is noteworthy that inverters have strict overcurrent limitations. This is the reason why the terminal voltage is controlled indirectly through current injection iset. To avoid overcurrent, saturation strategy is put in place and will result in voltage output drop. The voltage control, including the current limitation, is shown in Figure 5.8. This topic will be discussed in more detail in Subchapter 6.2. As mentioned previously, the V/f ratio is maintained essentially around unity, however the value may be optimized based on certain objectives, such as to maximize the reduction of power consumption at minimal voltage and frequency deviations.

In the illustration presented in Table 5.2 and Figure 5.2, the load proportions and parameters are taken from the typical values. An illustration of the impact of the V/f ratio on load consumption is shown in Figure 5.9. As the load demand for a typical residential customer is more sensitive to voltage than to frequency, employing a lower V/f ratio will reduce the load demand more effectively.

However, it should be noted that these parameters may vary for different loads, therefore the optimal V/f ratio may also vary for different microgrids. strategy. This eases the power balance monitoring within the microgrid. We may imagine using simple bulbs or fans as indicators of power balance which are directly accessible to customers, as the brightness (for bulbs) and speed (for fan) will decrease when the active power production is lower than the demand. The customers therefore can react based on this information to adjust their electricity usage accordingly. For example, when the bulbs shine less brightly, this is an alarm that the system is experiencing underproduction, and the customers can manually turn off their devices. This process is not time sensitive, as long as the voltage and frequency deviations are acceptable to everybody in the microgrid. In this regard, the customers are not only consumers anymore as they are becoming actors who actively help manage the microgrid. Therefore the costumers can be said to become consumactors. This concept has been successfully tested with real time hardware-in-the-loop (HIL) experiments as discussed in Chapter 7. The underproduction can be quantified by the microgrid operator from the measurement of frequency and voltage with the knowledge of load behavior, for example the one presented in Figure 5.2 for a typical residential microgrid. From such information, the microgrid operator can obtain the approximate active power required to bring the microgrid back to the normal operations, with respect to the actual active power production. Then, the operator can react accordingly, for example by starting a diesel generator set. Again, this process is not time-sensitive as long as the frequency and voltage deviations are accepted.

Multiple grid formers

Although microgrids typically have short power lines [START_REF]Microgrid Stability Definitions, Analysis, and Modeling[END_REF], certain types of microgrids may cover wider area and hence longer power lines, such as the case in developing countries [START_REF] Banjar-Nahor | Study on Renewable Penetration Limits in a Typical Indonesian Islanded Microgrid considering the Impact of Variable Renewables Integration and the Empowering Flexibility on Grid Stability[END_REF]. This condition means that the voltage-to-frequency ratio may differ at different locations within the microgrid due to the voltage drop. Furthermore, single non-redundant grid forming element is rather risky to the grid operation, as its failure will cause a grid-wide blackout. In this proposed V/f strategy, multiple grid forming elements can be installed at different points within the microgrid. They are responsible for maintaining local voltage-to-frequency ratio. Here, the term "local" applies to the area electrically close to the grid former such that the voltage drop is negligible.

System mitosis

Here, mitosis is defined as a process in which a microgrid is further split into a number of smaller grids. Each smaller grid is independent of one another and has to possess energy producing elements, loads, and at least one grid forming element. The mitosis typically results in several grids operating at different frequency and voltage in post-disturbance quasi steady state. A typical mitosis is illustrated in Subchapter 6.1.4.

However, anti-mitosis strategies are yet to be explored as the exact reverse of mitosis without proper coordination may lead to very high transient current that will harm the transition.

Consequences of the larger voltage and frequency deviations in V/f strategy

The implementation of the V/f strategy brings along a number of consequences for microgrid operation and for the components in the microgrid, as higher deviations of frequency and voltage in the grid are intentionally authorized. They impact a number of grid operations, as follows.

Load shedding schemes

The current load shedding schemes are set based on frequency deviation criteria (either with or without time delays) according to the operator experience. This will have to change when the V/f strategy is implemented, as the frequency is expected to deviate more often and more freely from the nominal value.

Protection coordination

The current power system protection strategy is often based on current, voltage and frequency measurements to detect main events such as active or reactive power imbalance or faults. However, due to the higher authorized deviations in voltage and frequency in the V/f strategy, some legacy protection strategies may need to be rethought.

More specific issues are discussed in the following main points.

Consequences of voltage excursion

Voltage deviations from the rated value may have the following consequences for electrical equipment besides the desired power consumption reduction [START_REF] Markiewicz | Standard EN 50160 Voltage Characteristics in Public Distribution Systems[END_REF]

This includes reduced heat for radiators, which is harmless, reduced luminosity for certain types of bulbs, and reduced torque for fans and motors. It should be noted that typically terminal voltages higher than 85% and 70% are considered satisfactory for heavy load motors and light load motors, respectively. Electronic devices working with power supply have wider operational ranges and tolerant to voltage variations, as discussed in Subchapter 4.3.3. With regard to V/f strategy implementation, the performance of a number of typical residential loads is visually monitored, as reported in Chapter 7.

Consequences of frequency excursion

When the frequency deviates from the nominal value, it may have the following consequences for elements in a microgrid.

Inductive reactance and capacitive susceptance

As discussed in [START_REF] Kersting | Distribution System Modeling and Analysis[END_REF], the line inductance is independent of the system frequency. When the frequency decreases, the inductive reactance and capacitive susceptance decrease linearly and their variations may need to be taken into account in the calculations if deemed necessary.

Generators

Frequency drop may be problematic to generators. Cooling systems are running below normal speed. If the AVR is controlled to maintain the terminal voltage, there is a risk of overfluxing. The thermal power plant output decreases because the blast of the cooling fans decreases, causing a reduced output.

Turbines

Steam turbine technology is used to convert steam to electric power. The blades of a steam turbine have several natural frequencies associated with higher mechanical stresses. High deviation of frequency thus causes the turbine to work closer to these hazardous regions of operation. The damage is rather cumulative. Underfrequency events are generally more stressful. Typically the concern is when the frequency deviates more than about 5% [START_REF] Kirby | Frequency Control Concerns in the North American Electric Power System[END_REF].

On the other hand, frequency deviation shows no meaningful impacts on hydraulic turbines [START_REF]Deterministic frequency deviationsroot causes and proposals for potential solutions[END_REF].

Generator protection

Relays based on ROCOF are often installed on distributed generations to keep them from running in an unintended island. High levels of ROCOF in combinations with improper settings can thus cause disconnections of DGs which will worsen the situation in underfrequency situations.

Auxiliary systems

Auxiliary systems providing services such as cooling, feeding, and fans are normally coupled with induction machines. Their performance, especially speed, will decrease as the frequency drops.

Flux Density of electrical machinery components

Most components of a power system are electrical machinery, functioning based on magnetic material. They are sensitive to the flux density passing through them, which is directly proportional to voltage and inversely proportional to frequency [START_REF] Kirby | Frequency Control Concerns in the North American Electric Power System[END_REF], [START_REF] Chapman | Electric Machinery Fundamentals[END_REF]. Violation of the flux density limit may cause heat losses and saturation of magnetic core.

Industrial loads

Poor power system frequency controls may degrade the power quality [START_REF] Kirby | Frequency Control Concerns in the North American Electric Power System[END_REF]. However, the power quality impacts of frequency variations are somewhat unclear. Most industrial processes which are sensitive to frequency variations have variable frequency drives which are normally insensitive to frequency disturbances.

Clocks

Clocks that depend on the supply frequency will be affected [START_REF] Nömm | An Analysis of Frequency Variations and its Implications on Connected Equipment for a Nanogrid during Islanded Operation[END_REF]. For example, the clocks would be off by about two minutes every hour for a deviation of 2 Hz from the nominal value.

5.3.3.

Further Discussion on the Consequences of the V/f strategy In discussions about frequency and voltage variations and their effects on equipment, the V/f ratio is always brought up as a potential risk that requires attention. When the V/f ratio is kept constant, electrical machinery such as induction motors can operate successfully [252]. For frequency variation up to 50% of the nominal value, the starting torque capability does not change much and the motors are still able to provide the full rated load torque, as shown in Figure 5.10. However, prolonged voltage and frequency variations on induction motors may still result in winding temperature increase, even at constant flux density [START_REF] Bonnett | Effect of Power Deviations on Squirrel-Cage Induction Motors: Addressing the Impact of Voltage and Frequency Variations[END_REF]. This happens due to several reasons, such as reduced fan speed influencing the cooling systems.

Starting torque

Pullout torque

Full-load torque With respect to the voltage nose point often discussed in voltage stability, voltage reductions may bring the nose point closer, meaning that the voltage collapse occurs at a lower loading level. On the other hand, frequency reductions will decrease the reactance, which will result in the nose point shifting to the right, yielding more voltage stability. The phenomena are illustrated in Figure 5.12.

The simulation is performed on a simplified system depicted in Figure 5.11 for a constant load power factor of 0.9 lagging. In order to obtain realistic conditions in distribution systems, the R/X ratio of the system impedance is assumed to be relatively high, at 0.66.

Z T Ðq T Z L Ðq L V s V r P + jQ

Figure 5.12 -PV Curves illustrating voltage stability changes either due to voltage or frequency variation

In Figure 5.12, Vr is the receiving voltage, while Pmax is the maximum active power transfer at nominal voltage and frequency.

When frequency and voltage variations are intentionally done simultaneously, the resulting P-V curve is shown in Figure 5.13 (a). It is noticeable that the nose-point of the P-V curve when both the voltage and frequency are reduced is located in the right side of that when only the voltage is decreased.

Let us study the impact of load increase when there are no available primary reserves. This is illustrated in Figure 5.13 (b). P1(V,f) and P2(V,f) are active power consumption characteristics of the loads, which are functions of the terminal voltage and the system frequency. The operating point is initially at t0. A load impact then occurs, normally shifting the operating point to t1. However, as no primary reserves are available, the V/f strategy reacts by decreasing the voltage and the frequency simultaneously, bringing the operating point to t3, where the final active power demand is the same as the initial one. In this case, the final operating point is at Vs = 0.9 p.u. and f = 0.9 p.u. The resulting loadability indices (defined by Eq. 3.10) of point t1 and t2 are comparable.

Vr

Vs = 1 p.u., f = 1 p.u. Vs = 0.9 p.u., f = 0.9 p.u. The final analysis on whether or not the microgrid becomes better in terms of voltage stability with respect to the V/f strategy depends on several factors, such as the system impedance and the load behavior. As discussed previously, voltage reductions will shift the nose point to the left while frequency reductions will shift the nose point to the right due to the reactance drop.

P 1 (V,f) P 2 (V,f) t 0 t 1 t 2 (b)
As for the load behavior, the more the load is solidary to voltage and frequency deviations; the better it is in terms of voltage stability. This is illustrated in Figure 5.14. Let us say that the initial operating point at nominal voltage and frequency is at t0, very close to the nose point but is still in the voltage-stable region. Upon a perturbation of total production drop from G0 to G1, the operating point will move to a new stable operating point t1 if the load behavior follows the function P1(V,f). However, if the load behavior follows the function P2(V,f), it does not cross the stable region regardless of the V/f regulation strategy, therefore a new voltage-stable operating point cannot be achieved, and the blackout is inevitable.

Vr

Vs = 1 p.u., f = 1 p.u. Vs = 0.9 p.u., f = 0.9 p.u.

P 1 (V,f) t 0 P 2 (V,f) t 1 t' 1 G 0 G 1

Impact of V/f regulation on grid supporting elements

Grid supporting elements function in such a way that they help maintain voltage and frequency around the nominal values. They may produce or absorb reactive power, as reflected in (newer) grid codes [START_REF]IEEE Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces[END_REF]. However, as the V/f strategy intentionally varies the voltage and frequency in order to acquire power equilibrium, the traditional operation mode of grid supporting elements may need to change.

Grid supporting elements are capable of providing dynamic voltage support because they can modify the behavior during voltage excursions in order to provide reactive power exchanges [START_REF]IEEE Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces[END_REF], [START_REF]Voltage and Frequency Dependency, System Operability Framework[END_REF]. However, according to IEEE 1547, the capability of the DER (not necessarily reactive current injection) may be utilized during mandatory or permissive operations under an agreement with the distribution grid operator. This opens up the possibility of utilizing not only reactive power exchange capability, but also active power exchanges when necessary and available.

Let us consider a simple network shown in Figure 5.15. Let's study a case where a short circuit occurs at the receiving side (bus 2), and a grid supporting element is injecting current into the sending side (bus 1) as a response to short circuit, with the objective of maintaining the voltage level. To simplify the analysis, the R/X ratio of 0.66 is considered in order to represent a distribution network. The relations between the sending voltage vs, current injection into the sending bus is, and the network impedance Zt is as follows.

𝑣 𝑠 = 𝑣 𝑟 + 𝑖 𝑠 * 𝑍 𝑡 Eq. 5.2

Let us define

𝑣 𝑠 = |𝐸 1 |∠𝛿 𝑣 𝑣 𝑟 = |𝐸 2 |∠0 𝑖 𝑠 = |𝐼 1 |∠𝛿 𝑖 𝑍 𝑡 = |𝑍|∠𝜃 𝑧 Therefore |𝐸 1 |∠𝛿 𝑣 = |𝐸 2 |∠0 + |𝐼 1 | * |𝑍|∠(𝛿 𝑖 + 𝜃 𝑧 ) Eq. 5.3
Here, the impact of active power on the voltage is not negligible anymore due to the higher line resistance. In order to visualize the impact of current injection on dynamic voltage support, the short circuit is assumed to drop the voltage at the receiving bus to 0. The power injection into the sending bus is the multiplication of the sending voltage and the conjugate of the current injection. Consequently, the type of injected power can be known by inspecting the angle difference between the sending voltage δv and current injection δi. In Figure 5.16 (a), the network is inductive, 𝜃 𝑧 = 90°, and maximum sending voltage |E1| is achieved when the angle difference sending voltage and injected current (δv -δi) is 90°, meaning the injected current is completely reactive. Likewise, when the network's R/X is 0.578 (𝜃 𝑧 = 60°) and R/X is 1 (𝜃 𝑧 = 45°), the maximum sending voltage |E1| is achieved when the angle difference sending voltage and injected current (δv -δi) is 60° and 45°, respectively, meaning that the injected current contains both active and reactive parts. It is therefore found that the optimum dynamic voltage support is achieved when the injected current's angle with respect to the voltage angle at the PCC matches the angle of the network impedance. This conclusion has been compared to other dynamic voltage support strategies with simulations using real data in [START_REF] Lammert | Impact of fault ride-through and dynamic reactive power support of photovoltaic systems on short-term voltage stability[END_REF]. Nonetheless, the reported study only focuses on the voltage aspect, neglecting the impact on frequency.

When dealing with distribution networks and the V/f strategy, one has to consider the impact of short-circuits on the frequency as well. As the grid former is not necessarily an energy producer and the network is characterized by higher R/X values, the impact of the dynamic voltage support on the power equilibrium during short-circuit, should be taken into consideration. This will also influence the critical clearing time.

The network described in Figure 5.17 illustrates the issue. The V/f regulations are implemented on all the grid formers, namely GF and the reference machine. The load's active power demand and the network losses are supplied solely by the energy producer in steady state. The reference machine is assumed to have higher inertia constant compared to grid former GF. If a three-phase short circuit with small fault impedance occurs at bus 2, the impacts of different dynamic voltage support strategies are presented in Figure 5.18. In Figure 5.18, the dynamic voltage support strategies are implemented when short circuit occurs, which is detected when the PCC voltage drops to below 0.7 p.u. The reactive current priority is when the PV inverter only injects reactive current during a fault, the adaptive angle is when the PV inverter injects current whose angle (with respect to the PCC voltage angle) matches the angle of the network impedance, and the available active power priority is when the PV inverter prioritizes the active current with the objective of maintaining the available active power (2 MW in this case), as long as the current limit of the inverter is not exceeded. In the latter, when the current limit is attained, the injected active power decreases linearly to the voltage drop. In all cases, the current injection during the short-circuit is at full rating of the PV inverter, at 1 p.u.

Energy Producer

We can see that there exists a tradeoff between voltage support and frequency deviations. When the reactive current is prioritized during a fault, the active power flow from bus 1 due to the rotor angle dynamics (as illustrated later in Figure 6.2 (b)) is supplied by the grid former GF, consequently the frequency (as well as the rotor angle) decreases during the first swing. When the adaptive angle strategy is implemented, a slightly better voltage support is obtained. Furthermore, the PV inverter helps compensate the active power transfer during short circuit, causing slower dynamics of GF rotor angle and frequency. This indeed increases the critical clearing time of the grid former if the synchronous condenser technology is chosen. When the available active power priority strategy is employed, the voltage support is not as good, and the active power transfer during short circuit may be overcompensated, resulting in rotor acceleration. In this simple case, the adaptive angle strategy comes out as the best option, as it supports both the voltage during a short-circuit, and slows down the rotor deceleration, which improves the critical clearing time of the grid forming element GF.

Nevertheless, this topic can be further developed, as the network R/X may vary for different fault locations, and the power-angle curves during short circuits are a function of the remaining short circuit voltage, the fault location, and the fault impedance. An optimization problem on the dynamic voltage support strategy, taking into account the impact on both voltage and frequency, can be constructed, which is an interesting future research topic to look into.

Possible Application in Microgrids

Besides in low-HDI areas previously living without electricity and in post-disaster relief situations, the V/f regulation is suitable to be implemented for a number of other reasons in microgrids, depending on the operational objectives. Several opportunities that we identified are as follows.

1. Improving the efficiency and reducing the operation cost.

Even when diesel generators are available, the microgrid operators can opt not to operate them just for dealing with the contingency events. This is a major improvement, especially when the operator intends to operate at 100% of renewables most of the time, as the operation of diesel generators at minimal loading is not efficient at all. In this regard, diesel generators are only when needed when it is deemed so according to the situation (e.g. restoration of the frequency and voltage to the nominal values, bad weather reasons). By employing the V/f strategy, the operator acquires a new dimension of flexibility, i.e. time, without having to go through the blackout state upon sudden reduction of renewable production.

Limitation of charge-discharge cycles of batteries

Batteries are limited in the number of charge-discharge cycles. This means that their implementation in enhancing power system stability can be costly, as it requires frequent operations. The V/f strategy can help reduce the number of battery operations, hence optimizing the lifetime of the batteries and focusing the usage for energy balancing purposes.

Operation with limited storage systems (sizing benefits)

As the V/f strategy (through the grid formers) can maintain the power equilibrium during transient states, the power sizing of storage elements can be reduced, if desired.

Enhancing the last defense strategy

Working side-by-side with load shedding procedure, this strategy can be employed to avoid frequent blackouts in microgrids, especially the ones operating in remote areas. As the proposed strategy is compatible with the widely-used active power droop regulation, the microgrid operation does not change much when the primary reserves are sufficient, which will mean that the nominal frequency can be maintained in steady state. However, when an unexpected event occurs, which will create high power imbalance, the V/f strategy will react to maintain the power equilibrium within the microgrid and avoid the occurrence of blackout. In this regard, the microgrid becomes more resilient, especially when the system is dependent on batteries, which could be out of stored energy.

Furthermore, if power quality problems are considered important and the loads require power conditioning, on-line UPS or solid state transformers can be utilized for a handful of loads, as a high proportion of this type of load will cancel out the benefits of employing the V/f strategy. This has been demonstrated in Sendai microgrid in Japan [START_REF]Microgrid Projects[END_REF], [START_REF] Hirose | The Sendai Microgrid Operational Experience in the Aftermath of the Tohoku Earthquake: A Case Study[END_REF], in which the loads are served at different power quality through the use of an integrated power supply (see Figure 5.19). In this regard, the loads connected through power conditioning elements will be seen as constant-power loads by the microgrid.

Conclusion

This chapter has provided clear explanation on the concept of voltage-to-frequency regulation that we propose. In this concept, the elements in a microgrid can be categorized into three categories: grid forming element, energy producing element, and power balancer. The grid forming elements function at zero active power in steady state. They maintain the stability of a microgrid so as to avoid blackouts, making the microgrid more resilient. It should be noted that they still can work along with continuous and discrete load shedding and local controls if desired.

As the current power systems mostly use electrical machinery, such as electric motors and transformers, the overfluxing problem needs to be taken into account. This strategy ensures that the voltage to frequency ratio is maintained around 1, ensuring that it does not harm the electrical machinery. Furthermore, this strategy ensures the plug-and-play feature for newly connected energy producing elements, loads, and grid forming elements. It is compatible with current grid-tied inverter technologies and does not require fast communication systems. Still, possible future communication upgrades can always be accommodated without problems. Finally, this proposed strategy is easy to implement and does not require revolution in terms of power system equipment and control. Today's elements, such as electrical machinery and grid-tied inverters, are compatible with this approach. The main drawback is that we have to accept higher deviations in voltage and frequency. In return, we can accommodate massive level of VRES even at very low primary reserves, without communication system, and we are given time flexibility to deal with power inequilibrium.

Chapter 6 Performance of the voltage to frequency regulation in Time-Domain

Simulations

This chapter addresses the performance of the proposed voltage-to-frequency regulation implemented on synchronous condensers and grid-forming inverters through RMS time-domain simulations with Power Factory. The angle stability behavior of synchronous condensers operating in distribution systems is also discussed. Several scenarios are taken into account to understand the behavior of the system following typical perturbations that may occur in microgrid operations.

V/f regulation applied on Synchronous Condensers

One of the most discussed problems of the synchronous machine stability is concerning the out of synchronism. Upon exceeding the critical clearing angle, a synchronous machine cannot reestablish synchronous operation with the grid and then it loses its stability. An elementary view of this phenomenon is normally explained with the equal area criterion considering a short circuit as a perturbation [START_REF] Morison | Transient Stability[END_REF], [START_REF] Kundur | Power System Stability And Control[END_REF]. This approach is a graphical method using the classical representation of synchronous machines, which studies the stability of a one-machine system connected to an infinite bus and uses the concept of energy. In this manner, it is not necessary to plot the swing curve to determine the stability based on the angle trajectory [START_REF] Pavella | Transient Stability of Power Systems: A Unified Approach to Assessment and Control[END_REF].

However, due to the higher R/X ratio, the classical power-angle curve constructed with an assumption of lossless network (shown in Eq. 2.3) is not valid anymore. Its usage may lead to misguided conclusions, as synchronous condensers seem to be always stable if the network is assumed to be lossless. This is illustrated in Figure 6.2 (a).

Let us derive the full equations based on a two-bus system in Figure 6.1. Where vs is the sending voltage, Zt the transfer impedance, and vr the receiving voltage.

The admittance matrix for the network is As stated in [START_REF] Grainger | Power system analysis[END_REF], the power injection at bus 1 is given by the following equations. If we assume that the R/X ratio is 0.66 to simulate an actual distribution network, the resulting power-angle curves based on Eq. 6.7 are presented in Figure 6.2 (b). If the network is assumed to be lossless, the power-angle curve follows the blue line in Figure 6.2 (a) in normal condition. The initial angle difference between the sending bus and the receiving bus is zero, as the synchronous condenser does not inject active power to the network in steady state.

𝑃
If a symmetrical short circuit occurs at bus 2, the power-angle follows the orange line. From the curve, the synchronous condenser does not inject or absorb any active power to/from the grid, hence no acceleration or deceleration. Therefore, the synchronous condenser appears to be always stable regardless of the fault duration.

The assumption of lossless network could be misleading for the application on medium voltage network. As depicted in Figure 6.2 (b), the power-angle curve follows the blue line in normal condition. Initially, the angle difference is also zero as the synchronous condenser does not inject active power. However, when a symmetrical short circuit at bus 2 is taking place, the power-angle curve follows the orange line. In this state, the synchronous condenser injects active power to the faulty grid, causing rotor deceleration. After the clearance of the fault, the power-angle curve returns to the blue line, which shows that the synchronous condenser is now absorbing power from the grid.

If the energy released during the short circuit (depicted by the shaded light blue area) is equal to the absorbed energy during the post-short circuit state (depicted by the shaded green area), the synchronous condenser can reestablish synchronism with the grid. However, if the shaded light blue area is smaller than the shaded green one, the synchronous condenser will continue to suffer from deceleration and end up losing the synchronism.

This clearly illustrates that a stability limit of synchronous condensers still exists. In a sense, equal-area criterion is still useful to describe the phenomenon. However, the issue here is rotor deceleration, as opposed to the rotor acceleration often occurring in the first swing of synchronous generators. It should be noted that the power-angle characteristic during short circuit (the orange line) is affected by several factors, such as fault impedance and location.

These findings have been verified with time domain simulations with Digsilent Power Factory, as shown in Figure 6.3. When the network is not considered lossless, out-of-synchronism can be detected and if this happens, the synchronous condenser continues to decelerate even after short circuit clearance. A simple microgrid is used to illustrate the implementation of V/f regulation on synchronous generators. The studied microgrid and the initial conditions are depicted in Figure 6.5. The loads are modeled based on the modified ZIP model in Figure 2.12 with parameters as displayed in Table 5.2.

The equivalent ZIP load model of the typical Indonesian microgrid is given in Table 6.1. More detailed data of the elements in the microgrid are presented in Table 6.2. The V/f regulation shown in Figure 5.5 is implemented on the grid formers. As shown above, in the initial condition, the grid formers absorb a small amount of active power from the grid to compensate the losses.

All cases are simulated with Power Factory version 2018, a simulation program widely requested and trusted by industrial customers. The studied disturbances consist of scenarios widely used in industrial applications, such as load impacts, generation impacts (including generation variation and loss), and network faults [START_REF] Poller | All Island TSO Facilitation of Renewables Studies[END_REF], [START_REF]Tolo and Takalar Generating Systems Connection Study and Renewable Penetration Report[END_REF], [START_REF]System Impact Study of the Eastern Grid of Sumba Island, Indonesia[END_REF], [START_REF]System Impact Studies of Wind Turbine connection in Sumba Island, Indonesia[END_REF]. An additional scenario of islanding is also considered to show the additional benefit of employing the proposed strategy. This is done to ensure that the industrial customers can accept the validation of the proposed implementation, as they are typically familiar with the scenarios.

Load impact

This subsection is dedicated to the simulations of possible load impacts occurring in a real microgrid operation. The simulated perturbations comprise 4 load events, as listed in Table 6.3. The total simulation duration is 30s.

The amplitude is set with respect to the demand in the initial condition. In the end, the final loading is at 123% with respect to the system initial loading. It should be noted that the irradiation of the PVs is considered constant throughout the simulation period. The results are shown in Figure 6.6.

As shown in Figure 6.6 (a), the grid frequency and voltage at both grid former terminals are maintained at a prescribed ratio, the ratio is 1 in this case. When the microgrid suffers from underproduction, the frequency naturally drops due to the swing equation, and the V/f regulation implemented on the voltage regulator will maintain the voltage to frequency ratio. This results in a decrease in power demand due to the solidary behavior of loads, and the microgrid ends up in a new stable operating point.

When the system loses a portion of load (for example due to manual action of microgrid operator or due to voluntary actions of the consumactors), the frequency increases. The system will eventually find a new stable operation point where the power equilibrium is reached.

In all the cases, the PV is able to maintain its active power production throughout the simulation. This is in line with the overview of the V/f strategy described in Figure 5.1 where energy producers possess constant power behavior with respect to voltage and frequency variations. Understandably, the current has to increase when the voltage drops in order to maintain the same power output. In this case, the current limit (typically around 1.1 p.u.) is not attained. Otherwise, the active power production may have to be reduced to satisfy the current limit. However, this is not likely to happen as the capacity of VRES is still typically designed well above the peak load demand of a system due to their low capacity factor [START_REF] Kroposki | Integrating high levels of variable renewable energy into electric power systems[END_REF].

Generation Impact

This subsection is dedicated to the simulations of possible generation drops occurring in a real microgrid operation due to the intermittency of the VRES such as clouds. The simulated perturbations comprise of 4 events as listed in Table 6.4. The total simulation time is 30 s. The amplitude shown above is set with respect to the PV active power generation in the initial condition. In the process, the generation drops to 70% and finally moves to 85% with respect to the initial generation. The results are shown as follows. Again, the grid frequency and voltage at grid former terminals are maintained at a prescribed ratio, the ratio is 1 in this case. When the microgrid suffers from underproduction, the frequency will naturally drop, and the V/f regulation implemented on the voltage regulator will maintain the voltage to frequency ratio. The system will eventually find a new stable operating point where the power balance is preserved.

Here, the behavior of the elements is all in line with the expectation in the V/f strategy described in Figure 5.1, where energy producers possess constant power behavior with respect to voltage and frequency variations and the loads are solidary.

Short Circuit

This subsection is dedicated to studying the impact of short circuit. The simulated perturbation is a 100-ms short circuit occurring at t=1. At t = 1.1s, the fault suddenly disappears without any switching involved. The fault occurs at the line, at 30% of the length from Terminal Left. The total simulation time is 10s. The grid frequency and voltage at grid former terminals are maintained at the prescribed ratio, which is 1 in this case. The frequency of the grid formers firstly drops during the first swing, due to the decrease in PV active power caused by voltage drop and the additional losses caused by the high short circuit current supplied by the grid former at higher R/X during the fault. This phenomenon is illustrated in Figure 6.8 (b). Once the short circuit is cleared, the system eventually reaches a new stable operating point where the power balance is preserved.

It should be noted that during the process at t around 2s, there is a tiny drop in PV active power production. This is triggered by the high frequency during the swing, causing the active power droop of PV to operate.

Islanding

This subsection is dedicated to studying the impact of system separation, otherwise known as islanding. Islanding may happen due to several reasons, such as protection system operation or fault isolation in radial networks. Here, as what will be demonstrated in the simulations, the V/f regulation implemented on the grid formers is capable of guaranteeing stable islands, irrespective of the power balance in the prospective islands prior to the system separation. We name this feature "system mitosis".

The simulated perturbation is a disconnection of the line at t = 1s through a switching event, creating two islands where overproduction occurs in one prospective island and underproduction in the other. Prior to the system splitting, the active power flow is from the system on the right to the system on the left, as shown in Figure 6.9. Consequently, overproduction is happening in the right subsystem and underproduction in the left subsystem. After the system is separated into two islands, both islands can eventually reach a new stable operating point. The system on the right is able to maintain the operation at nominal operating conditions, where the voltage and frequency are maintained close to 1 per unit. The overproduction naturally increases the frequency of the grid former, which in turn triggers the active power droop of the PV, causing the active power production to be curtailed. This is why the final frequency is slightly over 1 per unit.

On the other hand, the system on the left, characterized by underproduction prior to the separation, experiences higher deviations in voltage and frequency at the new stable operating point, where the power equilibrium is preserved. Here, the PV is again capable of maintaining the constant power producing behavior and the loads are solidary to the voltage and frequency variations.

V/f regulation applied on Grid Forming Inverters

In the following discussions, the V/f strategy is implemented on grid forming converters, which serve as the grid forming elements. The technical background of the implementation is discussed in Contrary to synchronous condensers, important parameters of grid forming inverters, such as inertia constant, can be changed at any moment as they are not physical quantities anymore. There is no physical relation between the amount of power absorbed/released and the rate of change of frequency. Although the swing equation is implemented in the control systems of the grid forming converters, the out-of-step phenomenon can always be avoided, as sudden frequency change and phase jumps are possible when the appropriate control strategies are in place.

In the simulations, two sets of load coefficients are investigated. They are shown as follows. The first load represents a typical residential-commercial load (provided by Schneider Electric), while the other one represents a standard impedance load. It should be noted that the residential-commercial load has a considerable level of constant power.

Load impact

This subsection is dedicated to the simulations of possible load impacts occurring in a real microgrid operation. The simulated perturbations comprise 4 load events, as listed in Table 6.7. The total simulation duration is 30s. The amplitude is set with respect to the demand in the initial condition. In the end, the final loading is at 123% with respect to the system initial loading. It should be noted that the irradiation of the PVs is considered constant throughout the simulation period. The results for the impedance load are shown in Figure 6.11 while those for the residential-commercial loads in Figure 6.12. When the loads are of impedance-type, the grid forming converters are capable of varying the frequency and voltage in such a way in transient state, that the V/f ratio is maintained and the microgrid reaches a new state where the power equilibrium is preserved, thanks to the solidary loads.

However, this is not always the case. As shown in the following curves, when the residentialcommercial load type is considered in the simulation, the load contains high constant-power share which will cause the transient state to become more demanding. The current may soar when the voltage drops. As the grid forming inverters are characterized by strict current limits, this may cause the microgrid to fail to survive the transient period due to the inability to recover the voltage. As shown in Figure 6.12 for scenarios where residential-commercial-type loads are studied, the grid frequency and voltage at grid former terminals are maintained at a prescribed ratio for all ramp load impacts. However, for the last step load impact at t = 10s, the transient period is very demanding, as the load demands high current during this period. As the grid forming elements have attained the current limits, as shown in Figure 6.12 (a), the terminal voltage drops and the voltage recovery cannot be accomplished, leaving the system to go into a blackout.

Generation Impact

This part is dedicated to the simulations of possible generation drops occurring in a real microgrid operation due to the intermittency of the VRES. The simulated perturbations comprise of 4 events as listed in Table 6.8. The total simulation time is 30 s. The amplitude shown above is set with respect to the PV active power generation in the initial condition. In the process, the total system generation, comprising of generation from grid forming inverters and the PVs, drops to 82% and finally settles down at 91% with respect to the total initial generation. The results for the impedance load are shown in Figure 6.13 while those for the residential-commercial loads in Figure 6.14. Again, when the loads are of impedance-type, the grid forming converters are capable of varying the frequency and voltage in such a way in transient state the grid frequency and voltage at grid former terminals are maintained at the prescribed ratio. When the microgrid suffers from underproduction, the frequency will drop due to the swing equation which is integrated in the control strategy, and the V/f regulation will maintain the voltage to frequency ratio. The system will eventually find a new stable operating point where the power balance is preserved. The problems with regard to current limits of converters are not found.

When the residential-commercial load type is considered in the simulation, the transient state due to the simulated perturbations becomes more demanding. The current soars when the voltage drops. As shown in Figure 6.14 (a), the grid forming inverters are strictly limited in current (as opposed to synchronous machine technology), which causes the microgrid to fail to survive the voltage recovery period.

Short Circuit

This subsection is dedicated to studying the impact of short circuit. The simulated perturbation is a 100-ms low impedance short circuit occurring at t=1. At t = 1.1s, the fault suddenly disappears without any switching involved. The fault occurs at the line, 30% the length from bus Term_Left. During the fault, slight deviations in frequency occur. The grid formers try to maintain the voltage-to-frequency ratio at the terminal by injecting more current. In the process, the grid forming converters eventually reach the current saturation limit (at 1.1 per unit), causing the voltage terminal voltage to drop. After the fault disappears, the power system survives the transition to regain a stable steady state at the prescribed voltage to frequency ratio. It should be noted that impedance-type loads are considered in the results shown in Figure 6.15.

In Figure 6.16, an identical short circuit event is simulated, but with residential-commercial-type loads under consideration. During the short-circuit, the frequency deviates according to the swing equation implemented in the controls. As what happens in the previous case with the impedance-type loads, the V/f regulation tries to maintain the voltage to frequency ratio by injecting more current.

Eventually, the grid forming converters reach the saturation limit in current at 1.1 per unit. However, in this case the system fails to regain the stability after the short circuit is removed. This is due to the inability of the grid formers to recover the voltage. During the transient state after the fault is removed, the current demanded by the loads is high. This is because the proportion of constant-power element is more significant, causing the current to be more inversely proportional to applied voltage.

Consequently, high current is necessary in the voltage recovery stage.

Islanding

This subsection is dedicated to studying the impact of the system separation, otherwise known as islanding. Typically, the V/f strategy is capable of guaranteeing stable islands, irrespective of the power balance in the prospective islands prior to the system separation. As a reminder, this feature is what we call "system mitosis".

The simulated perturbation is a disconnection of the line at t = 1s through a switching event, creating two islands where overproduction occurs in one prospective island and underproduction in the other. The total simulation time is 30s. The simulations results considering the impedance-type loads are shown in Figure 6.17 while the residential-commercial-type loads in Figure 6.18. Prior to the system splitting, the active power flow is from the system on the right to the system on the left, as shown in Figure 6.10. Consequently, the overproduction is happening in the right subsystem and the underproduction in the left subsystem.

Once the system is separated into two islands, both islands can eventually reach a new stable operating point for the cases considering the impedance-type loads. The system on the right is able to maintain the operation at nominal operating conditions, where the voltage and frequency are maintained close to 1 per unit. The overproduction increases the frequency of the grid former due to the implemented swing equation in the controls, which activates the active power droop of the PV, causing the active power production to be curtailed. This is why the final frequency is slightly over 1 per unit. On the other hand, the underproducing system on the left experiences higher deviations in voltage and frequency at the new stable operating point, where the power equilibrium is preserved thanks to the solidary characteristics of the loads. Here, the PV is again capable of maintaining the constant power behavior.

However, when the residential-commercial type loads are studied, different results are obtained.

The proportion of constant-power element in the load model is higher which causes difficulties in the transitory phase following the system splitting. As the grid forming converters are strictly limited in current, both new microgrids are not able to survive the transition and end up in the blackout.

Comment on the voltage recovery problem

When the microgrid contains a considerable portion of constant power loads, voltage recovery period is very demanding for grid forming converters. This particular type of load is very onerous during voltage excursions as the demanded current is inversely proportional to the applied voltage.

As shown in the Figures in Subchapter Figure 6.2, the grid forming converters deliver the expected performance when the loads are not demanding, i.e. the impedance-type loads. However, when the loads comprise of high proportions of constant power element, the grid forming inverters may struggle during the transitory period, as they are limited by a strict current limit which may cause a failure at recovering the voltage. It should be noted that this particular problem is not observed for the implementation on synchronous condensers. Consequently, the type of load need to be taken into account when selecting the grid former technology, or supplementary strategies may need to be developed if an inverter, which is strictly limited in current by design, is chosen as the grid forming element. Otherwise, oversizing may be a potential solution, but it may outweigh the benefits of employing static converters in the first place.

Comparison with the Present Grid Forming Solutions

This subchapter is dedicated to the comparison of several grid forming solutions, namely the V/f-implemented grid formers, the VSG, and the UPS. The main distinguishing point is that the grid formers in the V/f strategy are not required to produce energy in the steady state, contrary to the other grid forming solutions.

A comparison on the control strategy, the sizing, and the system design is summarized in the following table. It should also be noted that only diesel generators produce the electrical energy on their own, while UPS and VSG are basically a storage element. Currently, the operation of multiple UPS without a centralized controller is not yet mature. In its implementation, the UPS is also typically oversized compared to the loads it supplies. When V/f-implemented grid formers are in place, only small energy storage is necessary to support the grid during the transient state. On the other hand, VSG and UPS require larger energy storage to function. The effectivity of the UPS and VSG is entirely dependent on the stored energy in the storage element. Once the stored energy runs out, the impact to the grid is equivalent to that of generator loss.

153

The discussions in this subchapter only consider one grid forming element for a microgrid. This is to get a straightforward comparison of the basic cases.

The simulated system for the comparison is shown as follows. It should be noted that the case of employing the UPS is not simulated as it will always result in the operation at the nominal values, as long as the load demand does not exceed the UPS's power limit where the UPS will fail. The simulated loads consist of 20% of induction motor (the dynamic model is used), 40% of impedance, and 40% of constant power loads. The same load models are used in all of the test cases. The tested scenario is a load impact on the impedance load. Figure 6.20 presents the system steady state frequency upon a load increase event. As expected, the performance of V/f strategy is worse than that of the other grid forming solutions when the stored energy is available. However, once they run out of stored energy, the system will experience power imbalance which will lead to a blackout. As illustrated in the Figure, at no primary reserves, the performance of the V/f-implemented grid former is better than that of the classical grid former. It should be noted here that the classical grid former is typically equipped with an AVR which will try to maintain the terminal voltage, which would maintain the load demand and worsen the frequency drop. This is not the case with the V/f regulation, because the voltage is intentionally reduced depending on the frequency, which will balance the power demand and the power generation within the microgrid. deviation compared to that with the VSG or diesel generator set. However, the microgrid with a V/fimplemented grid former is more resilient to cases where the grid former is running out of stored energy.

AM

Source

Loads

Grid

When the V/f strategy is implemented on grid forming inverters, the inertia constant, which is not anymore a physical parameter, can be changed and modified accordingly. This accommodates the desired time response upon an event. This means the time to reach a new steady state can be selected by setting the inertia constant. This feature can be invaluable for grid operators as the transition to the "degraded state" can be more subtle, thus providing more time flexibility while maintaining reasonable deviations from the nominal operating conditions. For this, the remaining stored energy within the small battery on the DC-side of the inverter needs to be taken into account, as a grid forming inverter with a higher inertia constant will require more energy to reach a new steady state. The principles behind VSG are mostly the same as synchronous generators, which include regulations such as automatic voltage regulator (AVR), governor, etc. However, the parameters often do not represent physical quantities anymore, therefore theoretically parameters, such as inertia constant (H) and modeled impedance, can be changed accordingly if desired. The main difference is that a strict current limitation is exercised in VSG. This creates complication when dealing with postcontingency events, where overloading is more likely to occur [START_REF] Milano | Foundations and Challenges of Low-Inertia Systems[END_REF]. Theoretically, the V/f regulation is possible to be implemented on VSG.

In the isosynchronous regulation normally used for UPS application, the active power sharing is not well controlled and it brings important drawbacks. The loading is different on each generator. The closest generator with respect to the load center handles more active power and is potentially overloaded. This may trigger the overload protection and the rest of the system may cascade out. Due to the absence of the physical inertia, the implementation of isosynchonrous regulation on multiple UPS systems without a centralized control become even more complicated, as all the UPS systems need to be perfectly synchronized in frequency.

Conclusion

In this chapter, the simulation results and the comparison of the present grid forming solutions are presented. When implemented on synchronous condensers, the necessary modifications are minimal. The main modification is only on the excitation system of every grid forming element in the microgrid, which has to function based on the V/f regulation. As the synchronous machines have inherent inertia and overcurrent capability, they are better suited to deal with typical dynamic events, which often include power inequilibrium problems and voltage recovery problems. In contrast, the inverter-based grid formers have difficulty in dealing with voltage recovery or step transition, because they are limited by current saturation. However, such problems arise from the design approach of inverters, and not from the V/f strategy. The nominal characteristics of P+, the amplifier representing the power system, is as follows As shown in Figure 7.2, several physical elements are used to create dynamic events such as short circuit and load variations. The real loads are also used for visual monitoring purposes. For creating a fault, a remotely-controlled switch and a variable resistor are used. They are also used to simulate a load increase, depending on the resistance value. Other real loads which are tested include LED bulbs, a compact-fluorescent bulb, a filament bulb, a fan, a radiator, and a laptop (with the battery being taken off). All those domestic loads use single phase connections. As the nominal voltage of the AC amplifier is lower than that of the normal power grid, a step up transformer is used to convert the voltage to 230 V. The domestic loads are then connected to this normal voltage level.

Validation Plan

Blackstart

This section is dedicated to the simulation of a blackstart. The proposed ideal blackstart procedure when a synchronous condenser is employed as a grid former is shown as follows.

1) Manual DC excitation feeding the rotor of the synchronous machine is activated 2) A group of batteries acts as a stiff grid former in voltage mode. The frequency and the voltage are increased accordingly to start the synchronous condenser.

3) Loads and IBG are connected accordingly.

4) Batteries are switched to grid-supporting mode, or can be disconnected.

5) The excitation system mode is switched to the V/f regulation.

Synchronous machine is intended to rotate at the synchronous speed, therefore applying a direct on-line procedure to start the machine is not possible, as the rotor cannot instantaneously reach the nominal speed. Applying the direct-on-line method will only create vibrations. This is why the variable frequency-variable voltage strategy is used for starting the synchronous condenser, which will serve as a grid forming element. With this method, the frequency is ramped up slowly, which will give enough time to the rotor to catch up with the electrical frequency.

However, as in the simulation platform only one AC amplifier is available, the blackstart process has to be modified. It is performed in the real-time HIL simulation as follows.

1) Manual DC excitation feeding the rotor of the synchronous machine is activated

2) The AC amplifier is controlled to function as the grid former, functioning in current mode. The frequency and the current are increased accordingly to start the synchronous condenser.

3) In the real time simulator RT-Lab, the setpoints of the loads and the PV are set accordingly, the generation and consumption in the microgrid should be equal. In this step, the output signals of the microgrid simulated in the real time simulator have not been sent to the AC amplifier 4) The operation mode of the AC amplifier is switched to microgrid simulation.

5) The excitation system mode is switched to the V/f regulation.

Please note that the AC amplifier is controlled in the current mode during the blackstart process due to the difficulty to switch from the voltage mode to the current mode during an ongoing real time simulation. To protect the synchronous machine, a resistor bank is installed in parallel, which serves as a circuit where the excess current flows. Ideally, in real implementations, a variable voltage source is typically used to start a synchronous machine.

When the system is already functional, it can be considered the initial condition prior to the tested dynamic events. The measured terminal voltage of the synchronous condenser during the blackstart process is shown in Figure 7.8 and Figure 7.9. The proposed procedure is capable of blackstarting the microgrid.

The AC amplifier firstly serves as a grid former to start the synchronous condenser, and then its mode of operation is switched to simulate a microgrid, in which the power balance is reached. It should be noticeable in Figure 7.9 that the voltage deviates a bit following the mode switching. This is partly due to the switching delay, which causes the condenser to slow down, as no element is producing power to compensate the condenser's friction losses. However, when the switching is done, the frequency ramps up and is back to the initial value, and a minor voltage decrease is observed. This is normal considering that the synchronous condenser is still fed by constant DC current during the mode switching, meaning that a constant internal voltage, instead of a constant terminal voltage, is maintained. Consequently, the terminal voltage may vary according to the power flow.

Shortly after the mode switching, the V/f regulation implemented on the excitation system is activated. This serves as the initial conditions for all the dynamic scenarios in the experiment. The initial conditions for all the dynamic scenarios are as follows. 7.10. The V/f ratios in the initial state, the quasi-steady-state, and the final state are 1, meaning that the regulation is capable of maintaining the V/f ratio while balancing the power demand against the production in all the states. We would like to remind that the system is working without any primary reserves.

The load step is 56% of the initial power generation, representing a very significant load impact.

As the load impact is conducted on a resistance, which is quadratically proportional to the applied voltage, the voltage reduction is very effective in reducing the load demand. As shown in the voltage record, the frequency decreases following the load increase. This is because the machine will maintain the power equilibrium within the microgrid by injecting active power, which causes the frequency to drop according to the swing equation. As the V/f regulation is put in place, the excitation system maintains the voltage to frequency ratio at the setpoint, and the terminal voltage is intentionally decreased to maintain the V/f ratio, which causes the demand reduction within the microgrid. The microgrid finally reaches a stable operating point in the "degraded mode", where the frequency and the voltage deviate relatively far from the nominal values.

After the 930 W resistors are finally shed, the microgrid is now experiencing overproduction.

The synchronous machine is responsible for maintaining the power balance by absorbing the excess power, causing the frequency to rise according to the swing equation. Again, due to the implemented V/f regulation, the voltage is also ramping up, causing the demand increase within the microgrid. The system finally reaches a new stable operating point, which is identical to the initial one. This is expected, as the power production is kept constant during the whole simulation period. The second load increase is a 900 W ZIP ramp, simulated by modifying the load demand setpoint in RT-Lab. The load increase is equivalent to 54% of the initial microgrid generation. What is happening during the simulation can be explained in an identical way as the previous case with a 900-W load step. In this scenario, the microgrid also successfully reaches a new stable operating state without any available primary reserves. The V/f ratios in the initial and final states are maintained at 1 pu/pu.

Visual and Acoustic Observation

During the experiment, we also conducted visual and acoustic observations to the physical loads upon load variations. Among the domestic loads in the set-up, there are a 60-W laptop (with a detached battery), a 2000-W radiator, a number of LED, CFL, and filament bulbs, each consumes less than 60 W, and a 75-W fan. The domestic loads use single phase connections, which mean they create phase imbalance when connected.

As we use a step up transformer to supply the domestic loads, the initial voltage and frequency are 230 V and 50 Hz, respectively. When the highest load (the 2000-W radiator) is turned on, the microgrid does not experience blackout, it rather moves to a new stable degraded state at 118 V, 30

Hz. Here, if we consider that the nominal voltage is 230 V and the nominal frequency is 50 Hz, the V/f ratio of the phase where the single phase loads are connected is at 0.86. As this particular phase supplies more power compared to the other phases, a higher voltage drop naturally occurs, this is why the V/f ratio is less than 1. It is noteworthy that in the V/f strategy, the voltage used in the calculation is the average line to neutral voltage.

We conducted a number of random load variations to see the impact of the degraded state to the performance of the loads, to understand what it feels like to be a customer of this microgrid, and to imagine better what it feels like to be a consumactor. The impact of the degraded state on the domestic loads varies based on the load, as presented in Table 7.3. The performance is not impacted, even at the worst degraded state at 118 V and 30 Hz

Fan

The speed and the noise are reduced in the degraded state

Radiator (Fan-Radiator)

The fan speed and the produced heat decrease, the indicator lamp's brightness decreases in the degraded state

LED bulb

Upon a certain voltage level (less than around 140 V), the LED is completely off, however it turns back on when the voltage returns to normal. Up until the point where it turns off, the brightness does not seem to be affected by the voltage and frequency levels

CFL bulb

The brightness decreases in the degraded state

Filament bulb

The brightness decreases in the degraded state

The impact due to the frequency and voltage variations is visually and acoustically noticeable directly on most of the devices. However, devices functioning with rectifiers may not be very much impacted by the variations because they are designed to operate in a wide range of voltage and frequency, as discussed previously in subsection 4.4.2. Of course, a dedicated indicator can be made based on the voltage and frequency signals available locally. However, even the change in the load performance can be used as an instant indicator for the customers. They can notice the productionconsumption status of the microgrid and can react based on that information. For example, when we turn on the fan, the CFL bulb, the laptop, and the filament bulb consecutively, we directly notice that the fan speed decreases and the brightness of the lamps is also reduced. We then turn off the lamps, causing the fan speed to increase. The same thing can possibly happen in real scenarios. When the customers notice that the lamps are shining less brightly, and the fan speed decreases, they know that the microgrid is experiencing underproduction. They can then react by turning off the not critical loads, voluntarily. This is also a proof of the time flexibility provided by the strategy, as the grid does not fall to a blackout even at no primary reserves. The time is also very valuable to the micrgrid operator, as they can have more time to react, for example by starting a diesel generator.

Typical AVR

In the experiment, we also conducted a simple test to see how the system would react if a typical AVR is implemented on the grid former. The AVR model ESAC8B with typical parameters is implemented, and an overfluxing protection set at 1.2 is put in place. Not surprisingly, the frequency is continuously decreasing even upon a relatively small power imbalance, which triggers the overfluxing protection which will then cause a blackout. This phenomenon has also been observed in the simulations. As the AVR is maintaining the terminal voltage at the nominal value, the frequency will keep decreasing until the load demand equals the production. However, as loads are typically more sensitive to voltage, this results in high frequency deviation, which will trigger the overfluxing protection.

Scenario 2: Generation Variation

This section covers a generation variation event, for example to simulate a generation variation of VRES, for instance due to the weather in real microgrid operations. A 8-s 900 W ramp production loss is simulated in RT-Lab, the measured terminal voltage is shown in Figure 7.12. Here, the system is losing 54% of its initial generation, which is more than half of its initial generation.

Because the load demand drops as the voltage and frequency drop according to their dependency on the voltage and the frequency, the power equilibrium is finally reestablished. As we can see on the signal record, a new stable state, where the frequency and the voltage are stable, is eventually achieved. The frequency and voltage severely drop 35%, and the V/f ratio is maintained at 1 pu/pu.

More importantly, the microgrid does not fall into a blackout. Here, the PV is working in constant power factor mode, meaning that it still produces active power even when the voltage drops severely. As the fault impedance is resistive, the event is similar to a very significant load step. It is equivalent to a 1850-W load step occurring on a resistance load.

Naturally, the grid former converts the kinetic energy into the electric energy to balance the power within the microgrid, which causes the frequency to drop. The V/f regulation then intentionally makes the voltage to also drop, maintaining the voltage-to-frequency ratio. Finally, the microgrid reaches a new stable operating point where the power equilibrium is achieved. However, due to the high active power step, the degraded mode occurs very far from the nominal values. When the fault is removed, it is equivalent to shedding the excess load. The microgrid will then move according to the swing equation and the control imposed by the V/f regulation, to a new state, where the power balance is achieved and the operating variables such as voltage and frequency are very close to the nominal values. This final state is in fact identical to the initial one.

Conclusion

This chapter presents the experimentation on the real-time hardware-in-the-loop platform in RTlab in order to test out the effectivity of the proposed strategy in real life applications. We have shown that the experiment results are in accordance with the simulations. The system can satisfactorily deal with dynamic events such as load impacts, generation variability, and faults, even when there are no primary reserves available.

The performance of several domestic loads is also reviewed with visual and acoustic monitoring.

The impact is noticeable to bulbs, motors, and radiators, but not at all significant to electronics whose input voltage is conditioned by rectifiers. A description on the benefits of time flexibility offered by this approach, as well as the new type of actor: consumactor is provided, which can be very valuable in the era of massive renewable penetration levels.

Chapter 8 General Conclusions and Future Work

General Conclusions

This thesis is dedicated to the stability assessment in microgrids in the presence of high levels of variable renewable energy penetration. This PhD is carried out under the collaboration between G2elab, Schneider Electric, and Institut Teknologi Bandung.

Firstly, the discussions on the development and the evolution of power system stability, especially towards microgrids with more renewable energy sources, are addressed. A short historical review regarding the topic and how power system stability is traditionally classified are presented.

Power system stability problems are strongly linked with the behavior of synchronous machines and are divided into three categories: angle stability, frequency stability, and voltage stability.

The microgrid concept has been reviewed, as an essential building block of the grid of the future.

The concept brings along new hopes of increasing the reliability at higher level of renewable energy penetrations. The discussion includes power system stability behavior in microgrids, its classification, and an overview of the associated challenges that need to be tackled in order to make the concept work.

A number of indices around power system stability in the presence of VRES have been discussed and proposed. Due to the advent of more inverter-based generators and the VRES, some indices need to be rethought. Some classical indices such as frequency excursions and voltage stability indices are still useful in the IBG era, as most of the current inverter technologies are of grid feeding or grid supporting types. The definitions of the VRES penetration level are also reviewed to obtain better understanding. Some indices provide technical meaning, while the others serve different purposes, such as economic and political ones. From here, we conclude that the maximum VRES penetration level varies on a case-by-case basis. We then propose a set of indices based on the power equilibrium criteria, which are useful for microgrid practitioners as a time-efficient filter to assess microgrid stability.

The main challenges of massive VRES and the current efforts to accommodate massive shares of VRES are reviewed. The two main challenges are the variability and the low inertia. The efforts come from different actors, starting from the regulator, the operator, and the power system and equipment designer. However, those efforts are still focused on minimizing the impact introduced by VRES and IBG in order to continue enjoying the electricity like the way we used to be when we mostly depended on dispatchable fossil fuel. This causes the efforts to be costly and inefficient. In the last part of the chapter, we offer a new perspective on quality of supply, in which we accept the variability brought by VRES and its consequences. It will cause higher deviations in the main variables in electricity, such as the voltage magnitude and the frequency. For several applications, such as for universal electricity and for post-disaster situations, accepting higher deviations can be acceptable and will allow more VRES and IBG to be integrated into power systems.

This thesis has provided clear explanation on the concept of voltage-to-frequency regulation that we propose. In this concept, the elements in a microgrid can be categorized into three categories: grid forming element, energy producing element, and power balancer. The grid forming elements function at zero active power in steady state. They maintain the stability of a microgrid so as to avoid blackouts, making the microgrid more resilient. As the current power systems mostly use electrical machinery, such as electric motors and transformers, the overfluxing problem needs to be considered. This strategy ensures that the voltage to frequency ratio is maintained around 1, ensuring that it does not harm the electrical machinery. Furthermore, this strategy ensures the plug-and-play feature for newly connected energy producing elements, loads, and grid forming elements. It is compatible with current grid-tied inverter technologies and does not require fast communication systems. This proposed strategy is easy to implement and does not require revolution in terms of power system equipment and control. Today's elements, such as electrical machinery and grid-tied inverters, are compatible with this approach. The main drawback is that we have to accept higher deviations in voltage and frequency. In return, the microgrid can accommodate high levels of VRES even at very low primary reserves, without communication system, and the operator is given more time flexibility to deal with power inequilibrium.

The effectivity and usability of the proposed V/f regulation have been validated with the simulations and experiments in the real time hardware in the loop platform. The comparison of the present grid forming solutions is presented. When implemented on synchronous condensers, the necessary modifications are minimal. The main modification is only on the excitation system of every grid forming element in the microgrid, which has to function based on the V/f regulation. As the synchronous machines have inherent inertia and overcurrent capability, they are better suited to deal with typical dynamic events, which often include power inequilibrium problems and voltage recovery problems. In contrast, the inverter-based grid formers have difficulty in dealing with voltage recovery or step transition, because they are limited by current saturation. However, such problems arise from the design approach of inverters, and not from the V/f strategy.

This thesis presents the experimentation on the real-time hardware-in-the-loop platform in RTlab in order to test out the effectivity of the proposed strategy in real life applications. The system can satisfactorily deal with dynamic events such as load impacts, generation variability, and faults, even when there are no primary reserves available.

The performance of several domestic loads is also reviewed with visual and acoustic monitoring.

The impact is noticeable to bulbs, motors, and radiators, but not at all significant to electronics whose input voltage is conditioned by rectifiers. A description on the benefits of time flexibility offered by this approach, as well as the new type of actor: consumactor is provided, which can be very valuable in the era of massive renewable penetration levels.

Future Work

The future work includes a pilot project involving real microgrid actors, which will become a monumental step in order to better understand both the technical aspects, such as the performance and lifetime of the devices and the overall grid stability, and the non-technical aspects, such as the acceptance of the customers, the and the behavioral changes of the microgrid actors. This will take place in Riau Islands, Indonesia. An agreement with a local state university, local government, and local utility company is in progress to realize the pilot project.

Furthermore, the aspects that have not been taken into consideration in detail in this PhD research should also be addressed. They include the unbalanced operation on the effectivity of the proposed strategy and the impact of the proposed strategy on microgrid protection systems.

un pays émergent peuplée de villageois pourrait être considérée comme un exemple. Cela signifie que ces micro-réseaux ne bénéficient probablement pas de beaucoup de flexibilité, de puissance de calcul et d'intelligence. Cependant, l'électricité reste cruciale dans ces régions pour stimuler la croissance économique locale [START_REF] Fittrin | Optimal configuration of PV-Wind turbine-grid-battery in low potency energy resources[END_REF] - [START_REF] Lorde | The importance of electrical energy for economic growth in Barbados[END_REF]. La même situation peut être présumée en ce qui concerne le rôle des micro-réseaux dans la reprise après une catastrophe, comme indiqué dans [START_REF] Kinn | To what Extent is Electricity Central to Resilience and Disaster Management of the Built Environment?[END_REF].

Problematique

Contributions principales

Les contributions de cette thèse concernent un certain nombre de problèmes clés dans les microréseaux autonomes avec une puissance de calcul et des communications limitées en présence d'une pénétration massive d'énergies renouvelables variables. Ils sont présentés ci-dessous.

Stabilité du réseau électrique et sa classification

Les contributions comprennent: La troisième partie comprend le chapitre 8, une liste de références, une liste de publications et un bref résumé en français. La conclusion et la perspective sont présentées au chapitre 8.

Bref Résumé

Cette thèse traite des problèmes de stabilité introduits par l'interconnexion d'énergies renouvelables massives dans un micro-réseau isolé. Cette recherche vise à identifier les problèmes liés au sujet, les indices permettant de mieux comprendre ces problèmes, ainsi que la stratégie visant à améliorer la stabilité des microréseaux du point de vue du réseau électrique.

Dans la première partie, un état de l'art sur l'évolution de la stabilité du réseau electrique est abordé.

Un bref historique de la stabilité du système électrique depuis sa première identification et son Mots-clés: stabilité, micro-réseaux, énergies renouvelables, onduleur, grid forming

  Abstract .......................................................................................................................................................... i vii List of Tables

1 -

 1 List of Well-Known Simulation Tools ..................................................................................... Table 2.2 -Comparison of Basic Capabilities of several simulation tools ................................................ Table 2.3 -Further Comparison Concerning some Potentially Required Features .................................... Table 2.4 -Key Points of System Modeling in Several Simulation Tools ................................................ Table

  ......................................................... Table 2.6 -Classifications of DGs [70] ...................................................................................................... Table

  .............................................................. Table

  ............................................................................ Table 2.10 -History of IEEE 1547 ............................................................................................................. Table 2.11 -Comparison of North American Standards ............................................................................ Table

  -Selected Operational Islanded Microgrids ............................................................................. Table 3.1 -Critical Clearing Time Transformation .................................................................................... Table 3.2 -Some Voltage Stability Indices ................................................................................................ Table 3.3 -Factors Influencing Power System Stability ............................................................................ Table 3.4 -Proposed Indices of VRES Penetration for Microgrid Stability Assessment ........................... Table 3.5 -Indices and their Criteria .......................................................................................................... Table 4.1 -Comparison of Several Frequency Ride Trough Requirements [142] ..................................... Table 5.1 -Separation of Roles among Power System Elements in Normal Operation ........................... Table 5.2 -Load proportion and coefficients in a typical residential microgrid in Indonesia .................. Table 6.1 -Load proportion and coefficients for the simulations ............................................................. Table 6.2 -Data and Parameters for the simulations with synchronous condensers ................................ Table 6.3 -Simulated Load Impacts ......................................................................................................... Table 6.4 -Simulated Generation Impacts ............................................................................................... Table 6.5 -Data and Parameters the simulations with grid forming inverters ......................................... Table 6.6 -Load proportion and coefficients for the simulations ............................................................ Table 6.7 -Simulated Load Impacts ......................................................................................................... Table 6.8 -Simulated Generation Impacts ............................................................................................... Table 6.9 -Comparison of the current grid forming solutions ................................................................. Table 7.1 -List of input and output signals processed by RT-Lab ........................................................... Table 7.2 -Initial conditions for the dynamic scenarios ........................................................................... Table 7.3 -Impact of the degraded state to domestic loads ...................................................................... viii List of Figures

Figure 2 .

 2 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

1 -

 1 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 2 . 2 -

 22 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 2 . 3 -

 23 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 2 . 4 -

 24 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 2 . 5 -

 25 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 2 . 7 -

 27 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 2 . 8 -

 28 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 2 . 9 -

 29 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 2 . 10 -

 210 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 2 . 11 -

 211 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 2 . 16 -

 216 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 2 . 17 -

 217 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 2 . 18 -

 218 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 4 . 1 -

 41 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 4 . 2 -

 42 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 4 . 3 -

 43 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 4 . 4 -

 44 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 4 . 5 -

 45 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 4 . 6 -

 46 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 4 . 7 -

 47 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 4 . 8 -

 48 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 4 .

 4 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 4 .Figure 4 . 12 -

 4412 Figure 2.1 -Planned Construction of VRES plants in Indonesia .................................................................Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26] .Figure 2.3 -Simple Model of Generator connected to an infinity bus [38] ................................................Figure 2.4 -Frequency Trajectory, Conventional Power Systems .............................................................Figure 2.5 -Dynamic Hierarchy of Load-Frequency Control Processes [40] ............................................ Figure 2.7 -Comparison of RMS and EMT Simulation Results [53] ....................................................... Figure 2.8 -Shares of Simulation Tools Usage for Power System Stability Analysis ............................... Figure 2.9 -Impact of PV penetration on island networks in case of loss of generation [58] .................... Figure 2.10 -Scenarios for Emerging Power Systems [85] ........................................................................ Figure 2.11 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87] ........................................................................................................................ Figure 2.12 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [92] ................................................................................................................................................ Figure 2.13 -Power Factory's General Load Model to approximate the behavior of non-linear dynamic loads [94] ................................................................................................................................................Figure 2.14 -Simplified representation of grid-connected power converters. (a) grid forming, (b) gridfeeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95] ................................................................................................................................................................ Figure 2.15 -Microgrids and their Value Propositions [130] .....................................................................Figure 2.16 -Classification of Microgrid Applications [131] ....................................................................Figure 2.17 -Stability Classifications in Microgrids in Literature .............................................................Figure 2.18 -Microgrid Stability Classification and the Associated Issues Treated in This Research ....... Figure 3.1 -Flowchart of the algorithm of CCT Calculation ..................................................................... Figure 3.2 -Illustration of Frequency Response Following a generation-demand imbalance ................... Figure 3.3 -Typical PV Curves at constant Power Factor ......................................................................... Figure 3.4 -Illustration of Flexibility in Dynamic Balancing ................................................................... Figure 3.5 -Illustration of Variables Used in Design Indices ...................................................................Figure 4.1 -Power System Operating States according to Kundur [29] ....................................................Figure 4.2types of power active power imbalance according to ENTSO-E [40] ....................................Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements [142] ........................................Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182] .....................Figure 4.5 -Power Capability Requirement during Under Frequency [182] .............................................Figure 4.6 -Synchronous condenser structure ............................................................................................Figure 4.7 -General structure of virtual synchronous machine ..................................................................Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160 ...................................................................................................................................................... Figure 4.9 -Ranges of operation of universal power supply [230] ............................................................Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233] ............................................Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES ............................................

Figure 4 .

 4 Figure 4.12 -Classical Operation with N-1 criterion, normal operating state based on classical philosophy (a) Battery-VRES (e.g. PV) (b) Diesel-VRES-Curtailment ................................................................... Figure 4.13 -Operation with the new philosophy, Emphasizing on Demand Response and Depending on the Operational Objective (a) 1 MVA-Battery-VRES-DR (b) Battery only in charging mode-VRES-DR (c) Dump Load-Curtailment-DR ............................................................................................................ Figure 4.14 -Step-by-step Electricity Development enabling Adaptive Investment, VRES development as one of the main objectives ...................................................................................................................... Figure 5.1 -Roles in Microgrids with massive VRES and the Desired Behavior ....................................Figure 5.2 -Impact of terminal voltage and/or frequency on a typical residential microgrid .................. Figure 5.3 -Comparison of traditional regulation vs V/f regulation when N-1 criterion in power generation is not satisfied ..................................................................................................................... Figure 5.4 -Modification on AVR of synchronous machines (ESAC8B Model), V/f ratio = 1 .............. Figure 5.5 -Implementation of V/f strategy on synchronous machine's AVR (ESAC8B Model), changeable V/f ratio ............................................................................................................................. Figure 5.6 -Implementation of V/f strategy on Synchronous Condenser as a grid former (a) classical AVR (b) V/f regulation .................................................................................................................................. Figure 5.7 -Implementation of V/f strategy on Grid Forming Inverters .................................................. Figure 5.8 -Indirect Voltage Control of Grid Forming Inverters for V/f implementation .......................Figure 5.9 -Impact of V/f ratio on active power demand in a typical residential microgrid ................... Figure 5.10 -Torque-speed characteristic curves for speeds below base speed (nominal speed at 1800 rpm), line voltage is derated linearly with frequency [250] ................................................................. Figure 5.11 -Simplified system for P-V curve construction .................................................................... Figure 5.12 -PV Curves illustrating voltage stability changes either due to voltage or frequency variation .............................................................................................................................................................. Figure 5.13 -Voltage stability changes due to the V/f strategy (a) Typical V(P) curves (b) operating point progress upon load increase ................................................................................................................. Figure 5.14 -Voltage stability due to V/f strategy: Importance of P(V,f) ................................................ Figure 5.15 -Schematic diagram of a simple two-bus network ............................................................... Figure 5.16 -Impact of current injection of grid supporting elements on PCC Voltage during short Circuit (a) system R/X =0 (b) system R/X = 0.578 (c) system R/X = 1 .......................................................... Figure 5.17 -Simple network for dynamic voltage support study with the V/f strategy .......................... Figure 5.18 -Time domain simulations of different grid supporting element's dynamic voltage support strategies during short circuit and voltage recovery period (a) Trajectory of PCC Voltage (b) Trajectory of Grid Former Frequency (c) Trajectory of Relative rotor angle with respect to the reference machine .............................................................................................................................................................. Figure 5.19 -Single Line Diagram showing different classes of loads in Sendai Microgrid [258] .........Figure 6.1 -Schematic diagram of a simple two-bus network .................................................................Figure 6.2 -Rotor Response superimposed on Power Angle Curve (a) lossless network (b) distribution network ................................................................................................................................................. Figure 6.3 -Time domain Rotor Response with respect to reference angle following a 500ms short circuit at t=1s (a) Rotor Angle (b) Rotor Speed .............................................................................................. Figure 6.4 -Power Capability Curve of PV and battery Inverters as a function of terminal voltage [260], [261] .....................................................................................................................................................

Figure 5 . 2 -

 52 Figure 4.12 -Classical Operation with N-1 criterion, normal operating state based on classical philosophy (a) Battery-VRES (e.g. PV) (b) Diesel-VRES-Curtailment ................................................................... Figure 4.13 -Operation with the new philosophy, Emphasizing on Demand Response and Depending on the Operational Objective (a) 1 MVA-Battery-VRES-DR (b) Battery only in charging mode-VRES-DR (c) Dump Load-Curtailment-DR ............................................................................................................ Figure 4.14 -Step-by-step Electricity Development enabling Adaptive Investment, VRES development as one of the main objectives ...................................................................................................................... Figure 5.1 -Roles in Microgrids with massive VRES and the Desired Behavior ....................................Figure 5.2 -Impact of terminal voltage and/or frequency on a typical residential microgrid .................. Figure 5.3 -Comparison of traditional regulation vs V/f regulation when N-1 criterion in power generation is not satisfied ..................................................................................................................... Figure 5.4 -Modification on AVR of synchronous machines (ESAC8B Model), V/f ratio = 1 .............. Figure 5.5 -Implementation of V/f strategy on synchronous machine's AVR (ESAC8B Model), changeable V/f ratio ............................................................................................................................. Figure 5.6 -Implementation of V/f strategy on Synchronous Condenser as a grid former (a) classical AVR (b) V/f regulation .................................................................................................................................. Figure 5.7 -Implementation of V/f strategy on Grid Forming Inverters .................................................. Figure 5.8 -Indirect Voltage Control of Grid Forming Inverters for V/f implementation .......................Figure 5.9 -Impact of V/f ratio on active power demand in a typical residential microgrid ................... Figure 5.10 -Torque-speed characteristic curves for speeds below base speed (nominal speed at 1800 rpm), line voltage is derated linearly with frequency [250] ................................................................. Figure 5.11 -Simplified system for P-V curve construction .................................................................... Figure 5.12 -PV Curves illustrating voltage stability changes either due to voltage or frequency variation .............................................................................................................................................................. Figure 5.13 -Voltage stability changes due to the V/f strategy (a) Typical V(P) curves (b) operating point progress upon load increase ................................................................................................................. Figure 5.14 -Voltage stability due to V/f strategy: Importance of P(V,f) ................................................ Figure 5.15 -Schematic diagram of a simple two-bus network ............................................................... Figure 5.16 -Impact of current injection of grid supporting elements on PCC Voltage during short Circuit (a) system R/X =0 (b) system R/X = 0.578 (c) system R/X = 1 .......................................................... Figure 5.17 -Simple network for dynamic voltage support study with the V/f strategy .......................... Figure 5.18 -Time domain simulations of different grid supporting element's dynamic voltage support strategies during short circuit and voltage recovery period (a) Trajectory of PCC Voltage (b) Trajectory of Grid Former Frequency (c) Trajectory of Relative rotor angle with respect to the reference machine .............................................................................................................................................................. Figure 5.19 -Single Line Diagram showing different classes of loads in Sendai Microgrid [258] .........Figure 6.1 -Schematic diagram of a simple two-bus network .................................................................Figure 6.2 -Rotor Response superimposed on Power Angle Curve (a) lossless network (b) distribution network ................................................................................................................................................. Figure 6.3 -Time domain Rotor Response with respect to reference angle following a 500ms short circuit at t=1s (a) Rotor Angle (b) Rotor Speed .............................................................................................. Figure 6.4 -Power Capability Curve of PV and battery Inverters as a function of terminal voltage [260], [261] .....................................................................................................................................................

Figure 6 . 1 -

 61 Figure 4.12 -Classical Operation with N-1 criterion, normal operating state based on classical philosophy (a) Battery-VRES (e.g. PV) (b) Diesel-VRES-Curtailment ................................................................... Figure 4.13 -Operation with the new philosophy, Emphasizing on Demand Response and Depending on the Operational Objective (a) 1 MVA-Battery-VRES-DR (b) Battery only in charging mode-VRES-DR (c) Dump Load-Curtailment-DR ............................................................................................................ Figure 4.14 -Step-by-step Electricity Development enabling Adaptive Investment, VRES development as one of the main objectives ...................................................................................................................... Figure 5.1 -Roles in Microgrids with massive VRES and the Desired Behavior ....................................Figure 5.2 -Impact of terminal voltage and/or frequency on a typical residential microgrid .................. Figure 5.3 -Comparison of traditional regulation vs V/f regulation when N-1 criterion in power generation is not satisfied ..................................................................................................................... Figure 5.4 -Modification on AVR of synchronous machines (ESAC8B Model), V/f ratio = 1 .............. Figure 5.5 -Implementation of V/f strategy on synchronous machine's AVR (ESAC8B Model), changeable V/f ratio ............................................................................................................................. Figure 5.6 -Implementation of V/f strategy on Synchronous Condenser as a grid former (a) classical AVR (b) V/f regulation .................................................................................................................................. Figure 5.7 -Implementation of V/f strategy on Grid Forming Inverters .................................................. Figure 5.8 -Indirect Voltage Control of Grid Forming Inverters for V/f implementation .......................Figure 5.9 -Impact of V/f ratio on active power demand in a typical residential microgrid ................... Figure 5.10 -Torque-speed characteristic curves for speeds below base speed (nominal speed at 1800 rpm), line voltage is derated linearly with frequency [250] ................................................................. Figure 5.11 -Simplified system for P-V curve construction .................................................................... Figure 5.12 -PV Curves illustrating voltage stability changes either due to voltage or frequency variation .............................................................................................................................................................. Figure 5.13 -Voltage stability changes due to the V/f strategy (a) Typical V(P) curves (b) operating point progress upon load increase ................................................................................................................. Figure 5.14 -Voltage stability due to V/f strategy: Importance of P(V,f) ................................................ Figure 5.15 -Schematic diagram of a simple two-bus network ............................................................... Figure 5.16 -Impact of current injection of grid supporting elements on PCC Voltage during short Circuit (a) system R/X =0 (b) system R/X = 0.578 (c) system R/X = 1 .......................................................... Figure 5.17 -Simple network for dynamic voltage support study with the V/f strategy .......................... Figure 5.18 -Time domain simulations of different grid supporting element's dynamic voltage support strategies during short circuit and voltage recovery period (a) Trajectory of PCC Voltage (b) Trajectory of Grid Former Frequency (c) Trajectory of Relative rotor angle with respect to the reference machine .............................................................................................................................................................. Figure 5.19 -Single Line Diagram showing different classes of loads in Sendai Microgrid [258] .........Figure 6.1 -Schematic diagram of a simple two-bus network .................................................................Figure 6.2 -Rotor Response superimposed on Power Angle Curve (a) lossless network (b) distribution network ................................................................................................................................................. Figure 6.3 -Time domain Rotor Response with respect to reference angle following a 500ms short circuit at t=1s (a) Rotor Angle (b) Rotor Speed .............................................................................................. Figure 6.4 -Power Capability Curve of PV and battery Inverters as a function of terminal voltage [260], [261] .....................................................................................................................................................

Figure 6 . 2 -Figure 6 . 5 -

 6265 Figure 4.12 -Classical Operation with N-1 criterion, normal operating state based on classical philosophy (a) Battery-VRES (e.g. PV) (b) Diesel-VRES-Curtailment ................................................................... Figure 4.13 -Operation with the new philosophy, Emphasizing on Demand Response and Depending on the Operational Objective (a) 1 MVA-Battery-VRES-DR (b) Battery only in charging mode-VRES-DR (c) Dump Load-Curtailment-DR ............................................................................................................ Figure 4.14 -Step-by-step Electricity Development enabling Adaptive Investment, VRES development as one of the main objectives ...................................................................................................................... Figure 5.1 -Roles in Microgrids with massive VRES and the Desired Behavior ....................................Figure 5.2 -Impact of terminal voltage and/or frequency on a typical residential microgrid .................. Figure 5.3 -Comparison of traditional regulation vs V/f regulation when N-1 criterion in power generation is not satisfied ..................................................................................................................... Figure 5.4 -Modification on AVR of synchronous machines (ESAC8B Model), V/f ratio = 1 .............. Figure 5.5 -Implementation of V/f strategy on synchronous machine's AVR (ESAC8B Model), changeable V/f ratio ............................................................................................................................. Figure 5.6 -Implementation of V/f strategy on Synchronous Condenser as a grid former (a) classical AVR (b) V/f regulation .................................................................................................................................. Figure 5.7 -Implementation of V/f strategy on Grid Forming Inverters .................................................. Figure 5.8 -Indirect Voltage Control of Grid Forming Inverters for V/f implementation .......................Figure 5.9 -Impact of V/f ratio on active power demand in a typical residential microgrid ................... Figure 5.10 -Torque-speed characteristic curves for speeds below base speed (nominal speed at 1800 rpm), line voltage is derated linearly with frequency [250] ................................................................. Figure 5.11 -Simplified system for P-V curve construction .................................................................... Figure 5.12 -PV Curves illustrating voltage stability changes either due to voltage or frequency variation .............................................................................................................................................................. Figure 5.13 -Voltage stability changes due to the V/f strategy (a) Typical V(P) curves (b) operating point progress upon load increase ................................................................................................................. Figure 5.14 -Voltage stability due to V/f strategy: Importance of P(V,f) ................................................ Figure 5.15 -Schematic diagram of a simple two-bus network ............................................................... Figure 5.16 -Impact of current injection of grid supporting elements on PCC Voltage during short Circuit (a) system R/X =0 (b) system R/X = 0.578 (c) system R/X = 1 .......................................................... Figure 5.17 -Simple network for dynamic voltage support study with the V/f strategy .......................... Figure 5.18 -Time domain simulations of different grid supporting element's dynamic voltage support strategies during short circuit and voltage recovery period (a) Trajectory of PCC Voltage (b) Trajectory of Grid Former Frequency (c) Trajectory of Relative rotor angle with respect to the reference machine .............................................................................................................................................................. Figure 5.19 -Single Line Diagram showing different classes of loads in Sendai Microgrid [258] .........Figure 6.1 -Schematic diagram of a simple two-bus network .................................................................Figure 6.2 -Rotor Response superimposed on Power Angle Curve (a) lossless network (b) distribution network ................................................................................................................................................. Figure 6.3 -Time domain Rotor Response with respect to reference angle following a 500ms short circuit at t=1s (a) Rotor Angle (b) Rotor Speed .............................................................................................. Figure 6.4 -Power Capability Curve of PV and battery Inverters as a function of terminal voltage [260], [261] .....................................................................................................................................................

Figure

  Figure 6.5 -Simple Microgrid Under Consideration for V/F Implementation on Synchronous Condensers .............................................................................................................................................................. Figure 6.6 -V/f strategy performance following load impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................................... Figure 6.7 -V/f strategy performance following generation impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.8 -V/f strategy performance following a short circuit, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.9 -V/f strategy performance following system mitosis, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.10 -Simple Microgrid under Consideration for V/F Implementation on Grid Forming Converters .............................................................................................................................................................. Figure 6.11 -V/f strategy performance following load impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.19 -Single Line Diagram of the test system .............................................................................. Figure 6.20 -Comparison of different grid forming solutions, primary reserves are available for all solutions except for V/f-implemented grid formers ............................................................................. Figure 6.21 -Time-domain response of different grid forming solutions upon a load impact event .......Figure 7.1 -Set-up of the experiment in the Hardware-in-the-loop platform...........................................Figure 7.2 -Real time HIL test bench in G2Elab .....................................................................................Figure 7.3 -RT-lab model created in Simulink ........................................................................................Figure 7.4 -Overview of the PV model in RT-Lab ..................................................................................Figure 7.5 -Overview of the ZIP load model in RT-Lab .........................................................................Figure 7.6 -Single line diagram of the microgrid in the real time HIL experiment .................................Figure 7.7 -Overview of the Excitation system based on the V/f regulation modeled in RT-Lab ..........Figure 7.8 -Voltage measurement during the synchronous condenser starting -Blackstart phase 1 ......Figure 7.9 -Voltage measurement following the AC amplifier operation mode switching -Blackstart phase 2 .................................................................................................................................................. Figure 7.10 -Measured terminal voltage upon a physical load impact, 900 W step increase followed by 900 W shedding ....................................................................................................................................

  Figure 6.5 -Simple Microgrid Under Consideration for V/F Implementation on Synchronous Condensers .............................................................................................................................................................. Figure 6.6 -V/f strategy performance following load impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................................... Figure 6.7 -V/f strategy performance following generation impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.8 -V/f strategy performance following a short circuit, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.9 -V/f strategy performance following system mitosis, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.10 -Simple Microgrid under Consideration for V/F Implementation on Grid Forming Converters .............................................................................................................................................................. Figure 6.11 -V/f strategy performance following load impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.19 -Single Line Diagram of the test system .............................................................................. Figure 6.20 -Comparison of different grid forming solutions, primary reserves are available for all solutions except for V/f-implemented grid formers ............................................................................. Figure 6.21 -Time-domain response of different grid forming solutions upon a load impact event .......Figure 7.1 -Set-up of the experiment in the Hardware-in-the-loop platform...........................................Figure 7.2 -Real time HIL test bench in G2Elab .....................................................................................Figure 7.3 -RT-lab model created in Simulink ........................................................................................Figure 7.4 -Overview of the PV model in RT-Lab ..................................................................................Figure 7.5 -Overview of the ZIP load model in RT-Lab .........................................................................Figure 7.6 -Single line diagram of the microgrid in the real time HIL experiment .................................Figure 7.7 -Overview of the Excitation system based on the V/f regulation modeled in RT-Lab ..........Figure 7.8 -Voltage measurement during the synchronous condenser starting -Blackstart phase 1 ......Figure 7.9 -Voltage measurement following the AC amplifier operation mode switching -Blackstart phase 2 .................................................................................................................................................. Figure 7.10 -Measured terminal voltage upon a physical load impact, 900 W step increase followed by 900 W shedding ....................................................................................................................................

Figure 7 . 1 -

 71 Figure 6.5 -Simple Microgrid Under Consideration for V/F Implementation on Synchronous Condensers .............................................................................................................................................................. Figure 6.6 -V/f strategy performance following load impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................................... Figure 6.7 -V/f strategy performance following generation impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.8 -V/f strategy performance following a short circuit, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.9 -V/f strategy performance following system mitosis, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.10 -Simple Microgrid under Consideration for V/F Implementation on Grid Forming Converters .............................................................................................................................................................. Figure 6.11 -V/f strategy performance following load impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.19 -Single Line Diagram of the test system .............................................................................. Figure 6.20 -Comparison of different grid forming solutions, primary reserves are available for all solutions except for V/f-implemented grid formers ............................................................................. Figure 6.21 -Time-domain response of different grid forming solutions upon a load impact event .......Figure 7.1 -Set-up of the experiment in the Hardware-in-the-loop platform...........................................Figure 7.2 -Real time HIL test bench in G2Elab .....................................................................................Figure 7.3 -RT-lab model created in Simulink ........................................................................................Figure 7.4 -Overview of the PV model in RT-Lab ..................................................................................Figure 7.5 -Overview of the ZIP load model in RT-Lab .........................................................................Figure 7.6 -Single line diagram of the microgrid in the real time HIL experiment .................................Figure 7.7 -Overview of the Excitation system based on the V/f regulation modeled in RT-Lab ..........Figure 7.8 -Voltage measurement during the synchronous condenser starting -Blackstart phase 1 ......Figure 7.9 -Voltage measurement following the AC amplifier operation mode switching -Blackstart phase 2 .................................................................................................................................................. Figure 7.10 -Measured terminal voltage upon a physical load impact, 900 W step increase followed by 900 W shedding ....................................................................................................................................

Figure 7 . 2 -

 72 Figure 6.5 -Simple Microgrid Under Consideration for V/F Implementation on Synchronous Condensers .............................................................................................................................................................. Figure 6.6 -V/f strategy performance following load impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................................... Figure 6.7 -V/f strategy performance following generation impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.8 -V/f strategy performance following a short circuit, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.9 -V/f strategy performance following system mitosis, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.10 -Simple Microgrid under Consideration for V/F Implementation on Grid Forming Converters .............................................................................................................................................................. Figure 6.11 -V/f strategy performance following load impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.19 -Single Line Diagram of the test system .............................................................................. Figure 6.20 -Comparison of different grid forming solutions, primary reserves are available for all solutions except for V/f-implemented grid formers ............................................................................. Figure 6.21 -Time-domain response of different grid forming solutions upon a load impact event .......Figure 7.1 -Set-up of the experiment in the Hardware-in-the-loop platform...........................................Figure 7.2 -Real time HIL test bench in G2Elab .....................................................................................Figure 7.3 -RT-lab model created in Simulink ........................................................................................Figure 7.4 -Overview of the PV model in RT-Lab ..................................................................................Figure 7.5 -Overview of the ZIP load model in RT-Lab .........................................................................Figure 7.6 -Single line diagram of the microgrid in the real time HIL experiment .................................Figure 7.7 -Overview of the Excitation system based on the V/f regulation modeled in RT-Lab ..........Figure 7.8 -Voltage measurement during the synchronous condenser starting -Blackstart phase 1 ......Figure 7.9 -Voltage measurement following the AC amplifier operation mode switching -Blackstart phase 2 .................................................................................................................................................. Figure 7.10 -Measured terminal voltage upon a physical load impact, 900 W step increase followed by 900 W shedding ....................................................................................................................................

Figure 7 . 3 -

 73 Figure 6.5 -Simple Microgrid Under Consideration for V/F Implementation on Synchronous Condensers .............................................................................................................................................................. Figure 6.6 -V/f strategy performance following load impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................................... Figure 6.7 -V/f strategy performance following generation impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.8 -V/f strategy performance following a short circuit, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.9 -V/f strategy performance following system mitosis, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.10 -Simple Microgrid under Consideration for V/F Implementation on Grid Forming Converters .............................................................................................................................................................. Figure 6.11 -V/f strategy performance following load impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.19 -Single Line Diagram of the test system .............................................................................. Figure 6.20 -Comparison of different grid forming solutions, primary reserves are available for all solutions except for V/f-implemented grid formers ............................................................................. Figure 6.21 -Time-domain response of different grid forming solutions upon a load impact event .......Figure 7.1 -Set-up of the experiment in the Hardware-in-the-loop platform...........................................Figure 7.2 -Real time HIL test bench in G2Elab .....................................................................................Figure 7.3 -RT-lab model created in Simulink ........................................................................................Figure 7.4 -Overview of the PV model in RT-Lab ..................................................................................Figure 7.5 -Overview of the ZIP load model in RT-Lab .........................................................................Figure 7.6 -Single line diagram of the microgrid in the real time HIL experiment .................................Figure 7.7 -Overview of the Excitation system based on the V/f regulation modeled in RT-Lab ..........Figure 7.8 -Voltage measurement during the synchronous condenser starting -Blackstart phase 1 ......Figure 7.9 -Voltage measurement following the AC amplifier operation mode switching -Blackstart phase 2 .................................................................................................................................................. Figure 7.10 -Measured terminal voltage upon a physical load impact, 900 W step increase followed by 900 W shedding ....................................................................................................................................

Figure 7 . 4 -

 74 Figure 6.5 -Simple Microgrid Under Consideration for V/F Implementation on Synchronous Condensers .............................................................................................................................................................. Figure 6.6 -V/f strategy performance following load impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................................... Figure 6.7 -V/f strategy performance following generation impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.8 -V/f strategy performance following a short circuit, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.9 -V/f strategy performance following system mitosis, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.10 -Simple Microgrid under Consideration for V/F Implementation on Grid Forming Converters .............................................................................................................................................................. Figure 6.11 -V/f strategy performance following load impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.19 -Single Line Diagram of the test system .............................................................................. Figure 6.20 -Comparison of different grid forming solutions, primary reserves are available for all solutions except for V/f-implemented grid formers ............................................................................. Figure 6.21 -Time-domain response of different grid forming solutions upon a load impact event .......Figure 7.1 -Set-up of the experiment in the Hardware-in-the-loop platform...........................................Figure 7.2 -Real time HIL test bench in G2Elab .....................................................................................Figure 7.3 -RT-lab model created in Simulink ........................................................................................Figure 7.4 -Overview of the PV model in RT-Lab ..................................................................................Figure 7.5 -Overview of the ZIP load model in RT-Lab .........................................................................Figure 7.6 -Single line diagram of the microgrid in the real time HIL experiment .................................Figure 7.7 -Overview of the Excitation system based on the V/f regulation modeled in RT-Lab ..........Figure 7.8 -Voltage measurement during the synchronous condenser starting -Blackstart phase 1 ......Figure 7.9 -Voltage measurement following the AC amplifier operation mode switching -Blackstart phase 2 .................................................................................................................................................. Figure 7.10 -Measured terminal voltage upon a physical load impact, 900 W step increase followed by 900 W shedding ....................................................................................................................................

Figure 7 . 5 -

 75 Figure 6.5 -Simple Microgrid Under Consideration for V/F Implementation on Synchronous Condensers .............................................................................................................................................................. Figure 6.6 -V/f strategy performance following load impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................................... Figure 6.7 -V/f strategy performance following generation impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.8 -V/f strategy performance following a short circuit, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.9 -V/f strategy performance following system mitosis, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.10 -Simple Microgrid under Consideration for V/F Implementation on Grid Forming Converters .............................................................................................................................................................. Figure 6.11 -V/f strategy performance following load impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.19 -Single Line Diagram of the test system .............................................................................. Figure 6.20 -Comparison of different grid forming solutions, primary reserves are available for all solutions except for V/f-implemented grid formers ............................................................................. Figure 6.21 -Time-domain response of different grid forming solutions upon a load impact event .......Figure 7.1 -Set-up of the experiment in the Hardware-in-the-loop platform...........................................Figure 7.2 -Real time HIL test bench in G2Elab .....................................................................................Figure 7.3 -RT-lab model created in Simulink ........................................................................................Figure 7.4 -Overview of the PV model in RT-Lab ..................................................................................Figure 7.5 -Overview of the ZIP load model in RT-Lab .........................................................................Figure 7.6 -Single line diagram of the microgrid in the real time HIL experiment .................................Figure 7.7 -Overview of the Excitation system based on the V/f regulation modeled in RT-Lab ..........Figure 7.8 -Voltage measurement during the synchronous condenser starting -Blackstart phase 1 ......Figure 7.9 -Voltage measurement following the AC amplifier operation mode switching -Blackstart phase 2 .................................................................................................................................................. Figure 7.10 -Measured terminal voltage upon a physical load impact, 900 W step increase followed by 900 W shedding ....................................................................................................................................

Figure 7 . 6 -

 76 Figure 6.5 -Simple Microgrid Under Consideration for V/F Implementation on Synchronous Condensers .............................................................................................................................................................. Figure 6.6 -V/f strategy performance following load impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................................... Figure 6.7 -V/f strategy performance following generation impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.8 -V/f strategy performance following a short circuit, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.9 -V/f strategy performance following system mitosis, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.10 -Simple Microgrid under Consideration for V/F Implementation on Grid Forming Converters .............................................................................................................................................................. Figure 6.11 -V/f strategy performance following load impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.19 -Single Line Diagram of the test system .............................................................................. Figure 6.20 -Comparison of different grid forming solutions, primary reserves are available for all solutions except for V/f-implemented grid formers ............................................................................. Figure 6.21 -Time-domain response of different grid forming solutions upon a load impact event .......Figure 7.1 -Set-up of the experiment in the Hardware-in-the-loop platform...........................................Figure 7.2 -Real time HIL test bench in G2Elab .....................................................................................Figure 7.3 -RT-lab model created in Simulink ........................................................................................Figure 7.4 -Overview of the PV model in RT-Lab ..................................................................................Figure 7.5 -Overview of the ZIP load model in RT-Lab .........................................................................Figure 7.6 -Single line diagram of the microgrid in the real time HIL experiment .................................Figure 7.7 -Overview of the Excitation system based on the V/f regulation modeled in RT-Lab ..........Figure 7.8 -Voltage measurement during the synchronous condenser starting -Blackstart phase 1 ......Figure 7.9 -Voltage measurement following the AC amplifier operation mode switching -Blackstart phase 2 .................................................................................................................................................. Figure 7.10 -Measured terminal voltage upon a physical load impact, 900 W step increase followed by 900 W shedding ....................................................................................................................................

Figure 7 . 7 -

 77 Figure 6.5 -Simple Microgrid Under Consideration for V/F Implementation on Synchronous Condensers .............................................................................................................................................................. Figure 6.6 -V/f strategy performance following load impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................................... Figure 6.7 -V/f strategy performance following generation impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.8 -V/f strategy performance following a short circuit, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.9 -V/f strategy performance following system mitosis, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.10 -Simple Microgrid under Consideration for V/F Implementation on Grid Forming Converters .............................................................................................................................................................. Figure 6.11 -V/f strategy performance following load impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.19 -Single Line Diagram of the test system .............................................................................. Figure 6.20 -Comparison of different grid forming solutions, primary reserves are available for all solutions except for V/f-implemented grid formers ............................................................................. Figure 6.21 -Time-domain response of different grid forming solutions upon a load impact event .......Figure 7.1 -Set-up of the experiment in the Hardware-in-the-loop platform...........................................Figure 7.2 -Real time HIL test bench in G2Elab .....................................................................................Figure 7.3 -RT-lab model created in Simulink ........................................................................................Figure 7.4 -Overview of the PV model in RT-Lab ..................................................................................Figure 7.5 -Overview of the ZIP load model in RT-Lab .........................................................................Figure 7.6 -Single line diagram of the microgrid in the real time HIL experiment .................................Figure 7.7 -Overview of the Excitation system based on the V/f regulation modeled in RT-Lab ..........Figure 7.8 -Voltage measurement during the synchronous condenser starting -Blackstart phase 1 ......Figure 7.9 -Voltage measurement following the AC amplifier operation mode switching -Blackstart phase 2 .................................................................................................................................................. Figure 7.10 -Measured terminal voltage upon a physical load impact, 900 W step increase followed by 900 W shedding ....................................................................................................................................

Figure 7 . 8 -

 78 Figure 6.5 -Simple Microgrid Under Consideration for V/F Implementation on Synchronous Condensers .............................................................................................................................................................. Figure 6.6 -V/f strategy performance following load impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................................... Figure 6.7 -V/f strategy performance following generation impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.8 -V/f strategy performance following a short circuit, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.9 -V/f strategy performance following system mitosis, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.10 -Simple Microgrid under Consideration for V/F Implementation on Grid Forming Converters .............................................................................................................................................................. Figure 6.11 -V/f strategy performance following load impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.19 -Single Line Diagram of the test system .............................................................................. Figure 6.20 -Comparison of different grid forming solutions, primary reserves are available for all solutions except for V/f-implemented grid formers ............................................................................. Figure 6.21 -Time-domain response of different grid forming solutions upon a load impact event .......Figure 7.1 -Set-up of the experiment in the Hardware-in-the-loop platform...........................................Figure 7.2 -Real time HIL test bench in G2Elab .....................................................................................Figure 7.3 -RT-lab model created in Simulink ........................................................................................Figure 7.4 -Overview of the PV model in RT-Lab ..................................................................................Figure 7.5 -Overview of the ZIP load model in RT-Lab .........................................................................Figure 7.6 -Single line diagram of the microgrid in the real time HIL experiment .................................Figure 7.7 -Overview of the Excitation system based on the V/f regulation modeled in RT-Lab ..........Figure 7.8 -Voltage measurement during the synchronous condenser starting -Blackstart phase 1 ......Figure 7.9 -Voltage measurement following the AC amplifier operation mode switching -Blackstart phase 2 .................................................................................................................................................. Figure 7.10 -Measured terminal voltage upon a physical load impact, 900 W step increase followed by 900 W shedding ....................................................................................................................................

Figure 7 . 9 -Figure 7 . 11 -

 79711 Figure 6.5 -Simple Microgrid Under Consideration for V/F Implementation on Synchronous Condensers .............................................................................................................................................................. Figure 6.6 -V/f strategy performance following load impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................................... Figure 6.7 -V/f strategy performance following generation impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.8 -V/f strategy performance following a short circuit, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.9 -V/f strategy performance following system mitosis, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads ............................................. Figure 6.10 -Simple Microgrid under Consideration for V/F Implementation on Grid Forming Converters .............................................................................................................................................................. Figure 6.11 -V/f strategy performance following load impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads ................... Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads Figure 6.19 -Single Line Diagram of the test system .............................................................................. Figure 6.20 -Comparison of different grid forming solutions, primary reserves are available for all solutions except for V/f-implemented grid formers ............................................................................. Figure 6.21 -Time-domain response of different grid forming solutions upon a load impact event .......Figure 7.1 -Set-up of the experiment in the Hardware-in-the-loop platform...........................................Figure 7.2 -Real time HIL test bench in G2Elab .....................................................................................Figure 7.3 -RT-lab model created in Simulink ........................................................................................Figure 7.4 -Overview of the PV model in RT-Lab ..................................................................................Figure 7.5 -Overview of the ZIP load model in RT-Lab .........................................................................Figure 7.6 -Single line diagram of the microgrid in the real time HIL experiment .................................Figure 7.7 -Overview of the Excitation system based on the V/f regulation modeled in RT-Lab ..........Figure 7.8 -Voltage measurement during the synchronous condenser starting -Blackstart phase 1 ......Figure 7.9 -Voltage measurement following the AC amplifier operation mode switching -Blackstart phase 2 .................................................................................................................................................. Figure 7.10 -Measured terminal voltage upon a physical load impact, 900 W step increase followed by 900 W shedding ....................................................................................................................................

1 . 4 .

 14 century, several changes have occurred in the society of the 21 st century. The views on the issue are discussed and novel views to help accommodate massive VRES in power systems, notable microgrids, are proposed. C.7. Analysis of better current injection strategies under a fault taking into account the typical X/R ratio in microgrids Due to the domination of medium voltage distribution network in microgrids, characterized by a value of X/R close to unity, a compromise between active and reactive current injections is necessary in order to maintain both frequency and voltage stability. This current injection strategy performs satisfactorily with the V/f regulation proposed in this thesis. C.8. Development of V/F strategy to preserve the dynamic stability of microgrids Power quality requirements in microgrids are less stringent. Furthermore, the operation in degraded mode can be carried out when necessary. This opens up the possibility of exploiting the system flexibility through voltage and frequency variation. The developed strategy is capable of reducing the operational cost of primary reserve and the dependency on communication and computation infrastructure while assuring power system stability. Furthermore, this strategy appears to be promising and may open new possibilities in power system operation strategy. C.9. Validation of V/f strategy in real-time hardware-in-the-loop platform The strategy proposed in C.8 is validated on simple power systems through computer simulations and real-time hardware in the loop experiments in the laboratory. Promising results were achieved. Organization of the Thesis This thesis is organized in three parts, composed of eight chapters. The first chapter, chapter 1, introduces the context, problem statement, and main contributions of the work. Part I, consisting of chapters 2 and 3, deals with the topic of power system stability in microgrids. Chapter 2 presents the classical perspective on power system stability and how it is expected to change in the future due to the shift in power grids towards more renewable production and microgrid vision. Chapter 3 addresses the methods and indices useful for dynamic stability assessment and how they could be adjusted to accommodate the fundamental changes in the future grids.In Part II, the efforts to preserve power system dynamic stability in microgrids characterized by massive level of renewables are addressed. This part comprises Chapter 4, Chapter 5, Chapter 6 and Chapter 7. Chapter 4 discusses the efforts to smooth the transition to future power systems. This chapter summarizes the state of the art of the topic and presents the main ideas inspiring the V/f strategy which will be discussed more thoroughly in the chapters that follow. The principles of V/f strategy, the control schemes, and associated consequences are presented in Chapter 5. In Chapter 6, the simulation scenarios and results are discussed. A comparison among the grid forming solutions to deal with inverter based generation (IBG) is also reviewed. Chapter 7 presents the experimentation setup in the real-time hardware-in-the-loop platform, the scenarios, and the results that serve as a means to verify the effectiveness of the proposed control strategy.Part III is composed of Chapter 8, a list of references, a list of publications, and a brief summary in French. The conclusion and the perspective of the work are delivered in Chapter 8.

Figure 2 . 1 -

 21 Figure 2.1 -Planned Construction of VRES plants in Indonesia

Figure 2 . 2 -

 22 Figure 2.2 -Classification of Power System Stability according to IEEE/CIGRE Joint Task Force [26]

  moment of inertia of the rotor masses, in kg-m 2 δm = angular displacement of the rotor, in mechanical radians t = time, in seconds Tm = mechanical torque, in N-m Te = electromagnetic torque, in N-m Another form of the swing equation is obtained by multiplying both sides of the equation by the angular velocity ωm in addition to moving to a per unit system. If the angular velocity is assumed to be around the synchronous speed, the equation becomes: energy in MJ at synchronous speed divided by machine rating in MVA δ = angular displacement of the rotor, in mechanical/electrical radians ωs = synchronous speed, in mechanical/electrical radians per second Pm = mechanical power, in per unit (same base as H) Pe = electromechanical power, in per unit (same base as H)

Figure 2 . 4 -Figure 2 . 5 -

 2425 Figure 2.4 -Frequency Trajectory, Conventional Power Systems

Figure 2 . 6 -

 26 Figure 2.6 -Comparison of RMS and EMT Simulation Results [53]

•

  The loads and their characteristics • The parameters of the synchronous machines • The excitation systems of the synchronous machines • The mechanical turbine and speed governor • Other important components of the power plant that influence the mechanical torque • Other supplementary controls, such as tie-line controls, deemed necessary in the mathematical description of the system

Figure 2 . 7 -

 27 Figure 2.7 -Shares of Simulation Tools Usage for Power System Stability Analysis

Figure 2 . 8 -

 28 Figure 2.8 -Impact of PV penetration on island networks in case of loss of generation [58]

Figure 2 . 9 -

 29 Figure 2.9 -Scenarios for Emerging Power Systems[START_REF] Zinaman | Power Systems of the Future: A 21st Century Power Partnership Thought Leadership Report[END_REF]

Figure 2 . 10 -

 210 Figure 2.10 -The key elements for the transition to power systems relying almost entirely on variable renewable resources [87]



  The smart meter with its different variants: broadband bidirectional communication, possibility of load control tools and energy service  Advanced devices for energy management, either linked to smart meters or extension of ADSL potentials The intelligence associated with various domestic, tertiary, or industrial consumption components. The typical example is decentralized and intelligent load-shedding based on the grid frequency or voltage  Observability and supervisory control and network management linked with electricity production and consumption  The intelligence carried by devices in the electrical network characterizing the following process: measure, analyze, decide, act, and communicate. It is the main concern of the whole distribution automation.

  Power factory's general load model is a highly flexible model. The classical ZIP model, the exponential model, and the modified exponential model are all specific cases of the general load model. The model is depicted in the Figure and Equations below.

  power, reactive power P0, Q0 = Active power, reactive power at nominal voltage V = Voltage in per unit p1, p2, p3 = coefficients of voltage dependency for active power kpu0, kpu1, kpu = exponential coefficients of voltage dependency for active power q1, q2, q3 = coefficients of voltage dependency for reactive power kqu0, kqu1, kqu = exponential coefficients of voltage dependency for reactive power Kpf, Kqf = coefficient of frequency dependency for active power and reactive power Δu = voltage deviation in per unit Δf = frequency deviation in per unit

Figure 2 . 13 -

 213 Figure 2.13 -Simplified representation of grid-connected power converters. (a) grid forming, (b) grid-feeding, (c) current sources based grid supporting, and (d) voltage sources based grid supporting [95]

Figure 2 .

 2 14 and Figure 2.15 illustrate the main value propositions of the microgrid concept and where real-world microgrids are positioned.Microgrid operators typically focus only on certain value proposition(s). Under certain criteria, functional objectives of microgrids overlap and it is an opportunity for microgrid operators to consider multiple objectives simultaneously[START_REF]Integrating High Levels of Renewables into Microgrids[END_REF].

Figure 2 . 14 -Figure 2 . 15 -

 214215 Figure 2.14 -Microgrids and their Value Propositions [130]

  main categories: small signal stability, transient stability, and voltage stability. The classification does not formally include frequency and angle stability although they are implicitly defined under small signal and transient stability, as identified from the state variables.Here, a microgrid is composed of synchronous generators, inverter-based DG, lines, electrical machinery loads, and impedance loads. It may work in grid-connected or islanded modes. Small signal stability is analyzed with linearized model. It is strongly associated with feedback controllers.All state variables are used to derive state space models. Then, Eigen value analysis complimented by time domain simulation can be used for the analysis. Transient stability is concerned with large perturbations. It is analyzed with nonlinear model through the construction of the Lyapunov function or time-domain simulation. It deals mostly with the protection strategy and the balance between power generation and consumption. Voltage stability focuses more on load-side rather. It can be demonstrated with the P-V and Q-V curves. It is strongly associated with current limiters, tapchangers, and load regulations. The author identified that due to the much faster time response of VSC with respect to synchronous machines, oscillation may exist if the control strategies are not carefully chosen.Shuai's ClassificationShuai et. Al published a journal article devoted to microgrid stability classification[START_REF] Shuai | Microgrid stability: Classification and a review[END_REF] in 2016.The authors considers that IBGs are the main power supply in a microgrid. Consequently, the dynamic process is more complicated. They firstly classifies microgrid stability into two cases: grid connected microgrid and islanded microgrid. Only the further classification under islanded microgrid category is of interest in this discussion. Here, islanded microgrid stability is classified into frequency stability and voltage stability. Both are further classified into small disturbance stability and transient stability. With respect to the classical classifications proposed by IEEE/CIGRE Joint Task Force in 2004, Shuai et. Al introduce ultra-short term stability under transient stability cases for both voltage stability and frequency

Chapter 3 -

 3 Methods and Indices for Microgrid Stability AssessmentTo start our work in stability of microgrid, it is very important to select criteria and to useful indices in the technical aspects. Power system stability is often assessed with the help of several indicators. Those indicators are calculated with different methods, often to represent the performance in a specific classification of power system stability. This chapter is devoted to this topic. A number of widely used indices are compiled and presented in this chapter. This chapter discusses our contribution of creating new indices which may provide us with quick stability assessment of the microgrid stability-wise. Some modifications of the indices and a number of new microgrid stability indices are also proposed.

Figure 3 . 1 -

 31 Figure 3.1 -Flowchart of the algorithm of CCT Calculation

Figure 3 Figure 3 . 3 -

 333 Figure 3.3 -Typical PV Curves at constant Power Factor

Figure 3 . 4 -

 34 Figure 3.4 -Illustration of Flexibility in Dynamic Balancing

Figure 3 . 5 -

 35 Figure 3.5 -Illustration of Variables Used in Design Indices

Figure 4 . 1 -

 41 Figure 4.1 -Power System Operating States according to Kundur [29]

Figure 4 . 2 -

 42 Figure 4.2 -types of power active power imbalance according to ENTSO-E [40]

Figure 4 . 3 -

 43 Figure 4.3 -Comparison of Several Voltage Ride Trough Requirements[START_REF] Etxegarai | Review of grid connection requirements for generation assets in weak power grids[END_REF]

[

  182]. Furthermore, the requirements of the majority of grid codes are more demanding, such as the case of Nordic grid code as illustrated in Figure4.4.

Figure 4 . 4 -

 44 Figure 4.4 -Comparison of the requirements of IEC/IEEE vs. the Nordic Grid Code [182]

Figure 4 . 5 -

 45 Figure 4.5 -Power Capability Requirement during Under Frequency [182] 4.3.2.3. Other required ancillary services The required capability of inverter-based generators is evolving. Now, most standards require DER to be capable of providing ancillary services, such as prescribed by IEEE 1547-2008 presented in Table 2.10. These requirements include voltage control, frequency control, blackstart, in addition

Figure 4 . 6 -

 46 Figure 4.6 -Synchronous condenser structure

Figure 4 . 7 -

 47 Figure 4.7 -General structure of virtual synchronous machineOther control strategies of grid forming inverters include stiff grid forming inverters widely utilized in uninterruptible power supply (UPS). Stiff grid forming strategy behaves similarly to perfect voltage source, which ensures that the terminal voltage and frequency are maintained at nominal values at any moment. Consequently, load sharing and synchronization could be among major problems when multiple grid formers function in the grid, particularly with the absence of a global controller and fast communication systems.

Figure 4 . 8 -

 48 Figure 4.8 -Voltage characteristics of electricity supplied by public distribution systems required by EN 50160

Figure 4 . 9 -

 49 Figure 4.9 -Ranges of operation of universal power supply [230]

Figure 4 . 10 -

 410 Figure 4.10 -Resilience Trapezoid associated with a disruptive event [233]

Figure 4 . 13 .

 413 Figure 4.13. They depict the management of power equilibrium within the classical framework (where generation should always meet the demand) and the new framework with massive VRES characterized by DR.

Figure 4 . 11 -Figure 4 . 12 -Figure 4 . 13 -

 411412413 Figure 4.11 -Operation States in Microgrids with Massive Levels of VRES

Figure 4 .

 4 Figure 4.14 -Step-by-step Electricity Development enabling Adaptive Investment, VRES development as one of the main objectives

Figure 5 . 1 -

 51 Figure 5.1 -Roles in Microgrids with massive VRES and the Desired Behavior

Figure above are of

  Figure above are of grid-tied type, as commonly utilized in today's implementation. Fast communication systems are not necessary as the strategy works with voltage and frequency information available inherently at every busbar in the microgrid.

Figure 5 . 3 -

 53 Figure 5.3 -Comparison of traditional regulation vs V/f regulation when N-1 criterion in power generation is not satisfied

  voltage to achieve a new stable operating point A modification on the input of the classical AVR is necessary in the implementation of the V/f strategy on synchronous machines, such as depicted in Figure 5.4. The main variables include the measured voltage u, the measured frequency frequency, and the excitation voltage uerrs. The voltage setpoint input in the classical AVR, named u_setpoint in the diagram, is replaced with the measured frequency, named frequency in the diagram. The objective here is to maintain the value of the terminal voltage identical to the frequency.

Figure 5 . 4 -

 54 Figure 5.4 -Modification on AVR of synchronous machines (ESAC8B Model), V/f ratio = 1

Figure 5 . 5 -

 55 Figure 5.5 -Implementation of V/f strategy on synchronous machine's AVR (ESAC8B Model), changeable V/f ratio The implementation of the V/f regulation on synchronous condensers impacts the voltage regulation. The simplified signal connection between the synchronous condenser and the voltage controls is depicted in Figure 5.6. It is noteworthy to recall that the governor is non-existent in this technology. As explained in Subchapter 5.2.1, in the V/f strategy, grid formers are not required to produce energy. They serve as the voltage and frequency references and are temporarily responsible for power balancing during transient period. This task is possible with synchronous condensers thanks to their mechanical inertia.

Figure 5 . 6 -

 56 Figure 5.6 -Implementation of V/f strategy on Synchronous Condenser as a grid former (a) classical AVR (b) V/f regulation

Figure 5 . 7 -Figure 5 . 8 -

 5758 Figure 5.7 -Implementation of V/f strategy on Grid Forming Inverters

Figure 5 . 9 -

 59 Figure 5.9 -Impact of V/f ratio on active power demand in a typical residential microgrid 5.2.4.2. Indicator of underproduction Instead of using fast and costly communication systems to send out command signals in typical microgrid regulation strategy, slower to no-communication systems can be employed in the V/f

Figure 5 . 10 -

 510 Figure 5.10 -Torque-speed characteristic curves for speeds below base speed (nominal speed at 1800 rpm), line voltage is derated linearly with frequency [250]

Figure 5 . 11 -

 511 Figure 5.11 -Simplified system for P-V curve construction In Figure 5.11 above, Vs is the source voltage, ZT the transmission impedance, Vr the voltage at load terminal, P the load active power, Q the load reactive power, and ZL the load impedance.

  p.u., f = 1 p.u. Vs = 0.9 p.u., f = 0.9 p.u.

Figure 5 . 13 -

 513 Figure 5.13 -Voltage stability changes due to the V/f strategy (a) Typical V(P) curves (b) operating point progress upon load increase

Figure 5 . 14 -

 514 Figure 5.14 -Voltage stability due to V/f strategy: Importance of P(V,f)

Figure 5 . 15 -

 515 Figure 5.15 -Schematic diagram of a simple two-bus network

  3 per unit. Let us use the following per unit values, derived while taking typical distribution network and inverter-based generation into account: The impact of the angle of the current injection δi on the sending voltage at three different R/X values is presented in Figure 5.16.

Figure 5 . 16 -

 516 Figure 5.16 -Impact of current injection of grid supporting elements on PCC Voltage during short Circuit (a) system R/X =0 (b) system R/X = 0.578 (c) system R/X = 1

Figure 5 . 17 -

 517 Figure 5.17 -Simple network for dynamic voltage support study with the V/f strategy

Figure 5 . 18 -

 518 Figure 5.18 -Time domain simulations of different grid supporting element's dynamic voltage support strategies during short circuit and voltage recovery period (a) Trajectory of PCC Voltage (b) Trajectory of Grid Former Frequency (c) Trajectory of Relative rotor angle with respect to the reference machine

Figure 5 . 19 -

 519 Figure 5.19 -Single Line Diagram showing different classes of loads in Sendai Microgrid [258]

Figure 6 . 1 -

 61 Figure 6.1 -Schematic diagram of a simple two-bus network

Chapter 6 Figure 6 . 2 -

 662 Figure 6.2 -Rotor Response superimposed on Power Angle Curve (a) lossless network (b) distribution network

Figure 6 . 3 -

 63 Figure 6.3 -Time domain Rotor Response with respect to reference angle following a 500ms short circuit at t=1s (a) Rotor Angle (b) Rotor Speed It is therefore found that the out of synchronism phenomenon still exists for synchronous condensers in distribution networks. In the first swing, they suffer from rotor deceleration for the application in distribution grids. Consequently, indices such as critical clearing angle and critical clearing time are still useful.In the following discussions, the V/f strategy is implemented on synchronous condensers, which serve as the grid forming elements. The grid-tied inverters, which include grid-supporting battery and PV systems, are modeled based on Schneider Electric's Conext Series [260],[START_REF]ConextTM Core XC ESS and XC-NA ESS Series Grid-Tie Photovoltaic Inverter Grid Support Guide[END_REF] and considered adequate for the purpose of this study. The battery inverters are capable of providing dynamic voltage support and frequency support based on droop strategy, while the PV inverters possess similar capabilities, however the active power droop only applies for overfrequency (active power curtailment), as the PVs do not have primary reserves by default. The inverters possess circular capability curves, as illustrated in Figure5.13.

Figure 6 . 4 -

 64 Figure 6.4 -Power Capability Curve of PV and battery Inverters as a function of terminal voltage [260], [261]

Figure 6 . 6 -

 66 Figure 6.6 -V/f strategy performance following load impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads

Figure 6 . 7 -

 67 Figure 6.7 -V/f strategy performance following generation impacts, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads

Figure 6 . 8 -

 68 Figure 6.8 -V/f strategy performance following a short circuit, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads

Figure 6 . 9 -

 69 Figure 6.9 -V/f strategy performance following system mitosis, implementation on synchronous condensers (a) measurement at grid formers (b) PV Inverters (c) Loads

Subchapter 5 . 2 . 3 .

 523 The same models of PV inverters and loads as those in Subchapter 6.1 are employed. A simple microgrid is used to illustrate the performance of the implementation. The single line diagram and the initial conditions are shown in Figure6.10. The following data, unless otherwise stated, are used in the model:

Figure 6 . 10 -

 610 Figure 6.10 -Simple Microgrid under Consideration for V/F Implementation on Grid Forming Converters Again, all cases are simulated with Power Factory version 2018, a simulation program widely trusted by industrial customers. The studied disturbances consist of scenarios widely used in industrial applications.

Figure 6 .

 6 Figure 6.11 -V/f strategy performance following load impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads

Figure 6 .

 6 Figure 6.12 -V/f strategy performance following load impacts, implementation on grid forming converters, residential-commercial loads (a) measurement at grid formers (b) PV Inverters (c) Load

Figure 6 .

 6 Figure 6.13 -V/f strategy performance following generation impacts, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads

Figure 6 .

 6 Figure 6.14 -V/f strategy performance following generation impacts, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads

Figure 6 .

 6 Figure 6.15 -V/f strategy performance following a short circuit, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads

Figure 6 .

 6 Figure 6.16 -V/f strategy performance following a short circuit, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads

Figure 6 .

 6 Figure 6.17 -V/f strategy performance following system mitosis, implementation on grid forming converters, impedance load (a) measurement at grid formers (b) PV Inverters (c) Loads

Figure 6 .

 6 Figure 6.18 -V/f strategy performance following system mitosis, implementation on grid forming converters, residential-commercial load (a) measurement at grid formers (b) PV Inverters (c) Loads 6.2.5. Comment on the voltage recovery problem

Figure 6 . 19 -

 619 Figure 6.19 -Single Line Diagram of the test system

Figure 6 . 20 -Figure 6 .

 6206 Figure 6.20 -Comparison of different grid forming solutions, primary reserves are available for all solutions except for V/f-implemented grid formers Figure 6.21 illustrates the typical time-domain response of the different solutions upon a 6% increase of load demand at t = 0. H is the inertia constant. An event of a full discharge of the battery is simulated at t = 40s. It is equivalent to a diesel generator running out of fuel. As shown in the Figure, the microgrid with a V/f-implemented grid former has a higher steady state frequency

Figure 6 . 21 -

 621 Figure 6.21 -Time-domain response of different grid forming solutions upon a load impact event

7. 2 . 1 .Figure 7 . 1 -Figure 7 . 2 -

 217172 Figure 7.1 -Set-up of the experiment in the Hardware-in-the-loop platform

[ 265 ]Figure 7 . 4 -Figure 7 . 5 -Figure 7 . 6 -

 265747576 Figure 7.4 -Overview of the PV model in RT-Lab

Figure 7 . 7 -

 77 Figure 7.7 -Overview of the Excitation system based on the V/f regulation modeled in RT-Lab

7. 2 . 3 . 1 ) 1 )

 2311 Scenario 1: Load Variation with the V/f regulation This section is dedicated to the simulation of load impacts. The proposed procedure is shown as follows. Verification of the initial condition 2) Load variation events (ramp or step) either by modifying the load setpoints in RT-Lab or by switching on/off the physical loads 7.2.4. Scenario 2: Generation variation with the V/f regulation This section is dedicated to the simulation of generation variations. The proposed procedure is shown as follows. Verification of the initial condition 2) Generation variation events (ramp or step) by modifying the generation setpoints in RT-Lab 7.2.5. Scenario 3: Short Circuit with the V/f regulation This section is dedicated to the simulation of a short circuit. The proposed procedure is shown as follows. 1) Verification of the initial condition 2) Adjustment of the current limiting impedance 3) Short circuit simulation by connecting the "fault" breaker 4) Short circuit clearance by disconnecting the "fault" breaker 7.3. Results and Validation 7.3.1. Blackstart

Figure 7 . 8 - 1 Figure 7 . 9 -

 78179 Figure 7.8 -Voltage measurement during the synchronous condenser starting -Blackstart phase 1

Figure 7 . 10 -

 710 Figure 7.10 -Measured terminal voltage upon a physical load impact, 900 W step increase followed by 900 W shedding

Figure 7 . 11 -

 711 Figure 7.11 -Measured terminal voltage upon a simulated load impact, 1-minute 900 W ramp increase

Figure 7 . 12 -

 712 Figure 7.12 -Measured terminal voltage upon a simulated generation variation, 8-s 900 W ramp decrease 7.3.4. Scenario 3: Short Circuit This section covers a fault event. However, due to the limitations of the switch used to create the short circuit and to avoid the disconnection of the AC amplifier during simulations, a limiting resistor of 16.5 Ω is installed. A physical three phase fault is triggered through a remotely-controlled switch. The measured terminal voltage is shown in Figure 7.13.

Figure 7 . 13 -

 713 Figure 7.13 -Measured terminal voltage upon a simulated short circuit with high fault impedance

  La transition vers l'utilisation de plus d'énergies renouvelables affecte les systèmes d'alimentation électrique à bien des égards. Traditionnellement, le côté génération est dominé par les générateurs dispatchable, ce qui signifie que la puissance active produite peut être facilement contrôlée. Cependant, la situation est en train de changer car de plus en plus de sources d'énergies renouvelables variables (VRES) sont intégrées aux réseaux électriques. En conséquence, la production et la consommation fluctuent constamment, ce qui pourrait aggraver la stabilité du réseau électrique. Le réseau devient plus sujet aux perturbations et peut subir davantage de pannes.Les stratégies de fonctionnement et de contrôle du système électrique ont été développées sur la base de l'hypothèse classique selon laquelle le côté de la production est dispatchable et peut être contrôlé pour satisfaire la demande à tout moment. Les contrôles de fréquence (c'est-à-dire les contrôles primaire, secondaire et tertiaire) ont évolué en fonction de cette hypothèse. Avec la transition du côté de la génération, qui devient moins contrôlable, cette hypothèse pourrait ne plus être vraie. Les opérateurs de système ont pris un certain nombre de mesures pour s'assurer que l'hypothèse est toujours acceptable, de sorte que les contrôles et protections classiques restent applicables. Ces actions incluent l'utilisation de la flexibilité disponible, y compris des générateurs à réponse rapide en attente, une capacité de stockage, une capacité d'interconnexion avec des réseaux adjacents et une réponse à la demande, en plus du niveau de pénétration limité de VRES. Les micro-réseaux sous forme de petit réseau électrique indépendant constituent souvent le début d'un réseau électrique. Il pourrait devenir un réseau plus grand et éventuellement devenir un macroréseau. Cependant, pour assurer la fiabilité et la résilience du réseau, ingénieurs et chercheurs envisagent maintenant de diviser un micro-réseau en plusieurs micro-réseaux. Chaque micro-réseau doit pouvoir fonctionner lorsque le macro-réseau principal tombe en raison d'événements perturbateurs. Certains défis cruciaux découlent de cette vision. Lors d'événements perturbateurs, nous pensons qu'un micro-réseau doit survivre avec un minimum de puissance de calcul et de communication. Il doit en outre être en mesure de faire face à la pénétration massive d'énergies renouvelables variables avec une flexibilité limitée, donc un minimum de sources dispatchable. À cet égard, nous voudrions également contester la stratégie de limitation des énergies renouvelables, par exemple la limite VRES de 30% en France, qui est également en vigueur dans plusieurs départements et régions d'outre-mer français. Afin de relever ces défis, nous avons mené cette thèse de doctorat portant sur les micro-réseaux autonomes en courant alternatif, avec une charge maximale variant de 1 à 100 MW. Ces caractéristiques se manifestent soit dans les réseaux électriques nouvellement construits dans les zones rurales et sur les petites îles, soit dans les microgrids utilisés en dernier recours après des événements perturbateurs qui ont touché un macro-réseau. Par conséquent, ces micro-réseaux peuvent être constitués d'éléments normalement disponibles dans les réseaux alternatifs actuels, tels que des générateurs, des transformateurs, des batteries, des PV et d'autres sources non dispatchable, des lignes de distribution à moyenne tension et des charges. La principale question que nous abordons dans cette thèse est de savoir comment le réseau évoluera avec les nouvelles exigences, notamment la pénétration massive d'énergies renouvelables variables allant jusqu'à 100%. Les problèmes importants sont identifiés, puis les stratégies visant à préserver la stabilité dynamique du système électrique sont repensées. Considérant que l'évolution est normalement mieux acceptée que la révolution, les stratégies de contrôle visant à préserver la stabilité du réseau électrique sont développées autour des stratégies de contrôle de système classiques. Ceci est fait pour s'assurer que les solutions seront facilement comprises par les ingénieurs et les chercheurs habitués à la notion classique de stabilité du réseau électrique.

C1.

  Etat de l'art de l'évolution de la stabilité du réseau électrique et de sa classification Les connaissances sur la stabilité du réseau électrique sont basées sur le comportement de la machine synchrone. Avec l'interconnexion de plus en plus de générations basées sur des onduleurs dans les réseaux électriques, la stabilité du réseau électrique doit moins dépendre des machines synchrones, voire même être indépendante de celles-ci. Les sujets examinés incluent les problèmes généraux de stabilité et de classification des systèmes d'alimentation, les outils de simulation, les changements de stratégie de régulation et les normes de réseau.203C2. Identification des défis rencontrés dans les micro-réseaux fonctionnant avec des sources d'énergie renouvelables variables (VRES) massives connectées via des onduleurs et efforts déployés pour résoudre ces problèmes Les microgrids ont un comportement différent des grands réseaux interconnectés, ce qui pose de nouveaux défis. Ces défis doivent être résolus pour que le microréseau fonctionne de manière fiable, comme prévu. Les principaux défis à relever et les efforts déployés pour prendre en charge une VRES massive dans des microréseaux sont discutés.Indices de stabilité des micro-réseauxEn ce qui concerne le développement des indices traitant de la stabilité des micro-réseaux, les contributions de cette recherche sont les suivantes: C3. Etat de l'art des indices utilisés dans l'évaluation de la stabilité des systèmes électriques La définition, l'approche et la signification des indices tels que le temps critique, le niveau de pénétration de l'énergie renouvelable, l'excursion de fréquence et les indices dérivés de l'analyse des valeurs propres et des courbes PV / QV sont également examinés.C4. Définition mise à jour du temps de compensation critiqueLe calcul classique du temps de compensation critique est basé sur le comportement des machines synchrones. Cette définition doit être mise à jour avec l'apparition de plus de générateurs à onduleur dans le réseau.C5. Nouveaux indices pour l'évaluation préliminaire de la stabilité des micro-réseaux Étant donné que la limite de pénétration des énergies renouvelables variables varie au cas par cas, de nouveaux indices sont nécessaires pour guider la conception et le fonctionnement des micro-réseaux. Les nouveaux indices sont introduits en fonction des exigences pratiques du maintien de l'alimentation et de la stabilité de la balance. Ils sont utiles et pratiques pour la planification et l'exploitation de micro-réseaux.Stratégie visant à préserver la stabilité des micro-réseaux fonctionnant avec une VRES massiveLes contributions aux stratégies visant à préserver la stabilité des micro-réseaux sont énumérées ci-dessous.C6. Nouveaux points de vue sur la qualité d'alimentation des réseaux fonctionnant avec des VRES massifsLes besoins de la société auxquels répondent les moyens de l'énergie électrique évoluent avec le temps. Comme les systèmes d'alimentation électrique ont été principalement développés au 20ème siècle, plusieurs changements se sont produits dans pour l'évaluation de la stabilité dynamique et de la manière dont ils pourraient être ajustés pour tenir compte des changements fondamentaux dans les futurs réseaux.Dans la partie II, les efforts visant à préserver la stabilité dynamique des micro-réseaux caractérisés par un niveau massif d'énergies renouvelables sont abordés. Cette partie comprend le chapitre 4, le chapitre 5, le chapitre 6 et le chapitre 7. Le chapitre 4 traite des efforts déployés pour faciliter la transition vers les futurs systèmes électriques. Ce chapitre résume l'état de l'art sur le sujet et présente les idées principales qui ont inspiré la stratégie V / f, qui seront examinées plus en détail dans les chapitres suivants. Les principes de la stratégie V / f, les schémas de commande et les conséquences associées sont présentés au chapitre 5. Le chapitre 6 décrit les scénarios de simulation et les résultats. Une comparaison entre les solutions de grid forming pour traiter la génération basée sur onduleur (IBG) est également examinée. Le chapitre 7 présente la configuration des expérimentations sur une plateforme hardware-in-the-loop en temps réel, les scénarios et les résultats qui permettent de vérifier l'efficacité de la stratégie de contrôle proposée.

  évolution a été présenté. Une revue des indices pratiques d'évaluation de la stabilité du réseau est également présentée, y compris ceux que nous proposons. Cette partie est également utile pour analyser le positionnement de cette thèse La deuxième partie de la thèse présente les efforts pour améliorer la stabilité dynamique des microréseaux caractérisés par une pénétration massive des énergies renouvelables. Les principaux défis et les efforts en cours sont passés en revue, qui ont montré que les solutions actuelles se concentrent sur le maintien de la philosophie d'un réseau électrique classique. Avec l'avènement des énergies plus intermittentes, les efforts actuels se sont révélés coûteux. Par conséquent, une nouvelle perspective est proposée. Ici, les générateurs et les clients sont exposés à des écarts de tension et de fréquence plus élevés, qui sont nécessaires pour maintenir l'équilibre de puissance et la stabilité du microréseau. Cette perspective convient avec le concept de micro-réseau pour réaliser le rêve de l'électricité universelle. Le concept est ensuite développé en une nouvelle stratégie de régulation dans laquelle le rapport de la fréquence et la tension du système sont maintenues essentiellement constant autour de 1 (en per unit). Cette stratégie peut potentiellement être mise en oeuvre sur toutes les technologies de grid forming. Les avantages de cette stratégie sont l'assurance que les machines électriques ne sont pas endommagées, la fonctionnalité plug-and-play, la compatibilité avec les technologies actuelles d'onduleurs et l'absence de systèmes de communication rapides. Enfin, la stratégie proposée est facile à mettre en oeuvre et ne nécessite pas de révolution en termes d'équipement et de contrôle du réseau électrique. Cette mise en oeuvre de ce concept offre un élément de flexibilité très précieux: le temps, qui améliore la résilience et la stabilité d'un microréseau. Cependant, des écarts de fréquence et de tension plus importants se produisent et doivent être acceptés par tous les acteurs du microréseau. Une validation par des simulations numériques en Power Factory et des expérimentations dans une plateforme hardware-in-the-loop en temps réel ont été réalisées avec des résultats satisfaisants.

Table 2 .2 -Comparison of Basic Capabilities of several simulation tools Simulation Program

 2

	1. Modeling assumptions and mathematical formulation
	2. Selection of appropriate stability definition
	3. Analysis and/or simulation to determine stability, typically using a scenario of events
	4. Review of the results, comparison with the engineering experience, and repetition if
	necessary

Table 2

 2 .3 and Table 2.4.

Table 2 .3 -Further Comparison Concerning some Potentially Required Features Simulation Program Inter- simulator Interface Scripting Language Custom Designed Controller Well Provided Library

 2

	Digsilent Power Factory	✓	✓	✓	✓
	Eurostag	✓	✓	✓	✓
	Matlab/Simulink	✓	✓	✓	✓
	Open DSS	✓	✓	✓	✓
	PSCAD/EMTDC	✓	✓	✓	✓
	PSD-BPA	✓	?	?	?
	Siemens PSS/E	✓	✓	✓	✓
	ETAP	✓	X	✓	✓

Table 2 .4 -Key Points of System Modeling in Several Simulation Tools Simulation Program Scripting Language How to make a custom controller? GUI provided?

 2

	Digsilent Power Factory	DPL	Script, Block Diagrams (DSL)	✓
		Matlab, phyton, C++, all
	Eurostag	languages able to interact with C	Block Diagrams	✓
		language
	Matlab/Simulink	Matlab language	Script, Block Diagrams	✓
	Open DSS	DSS command language syntax	Script	X
	PSCAD/EMTDC	Fortran	Script	✓
	PSD-BPA	Insufficient Information	Insufficient Information	✓
	Siemens PSS/E	Phyton, Fortran	Script	✓
	ETAP	-	Block Diagram	✓

Table 2 .5 -Comparison of Today's Grid and Smart Grid [65], [66] Preferred Characteristics Today's Grid Smart Grid Active consumer participation

 2

	Consumers are uninformed and	Consumers are informed,
	do not participate	participate in demand response
		and DER

Preferred Characteristics Today's Grid Smart Grid Accommodation of all generation and storage options

		Dominated by central generation	Many DER with plug-and-play
		-many obstacles for DER	convenience focus on
		interconnection	renewables
	New products, sevices, and	Limited, poorly integrated	Mature, well-integrated
	markets	wholesale markets, limited	wholesale markets, growth of
		opportunities for consumers	new electricity markets for
			consumers
	Provision

of power quality for the digital economy

		Focus on outages -slow	Power quality a priority with a
		response to power quality issues	variety of quality/price options -
			rapid resolution of issues
	Optimization of assets and	Little integration of operational	Expanded data acquisition of grid
	operates efficiently	data with asset management	parameters; focus on prevention
	Anticipating responses to	Responds to prevent further	Automatically detects and
	system disturbances (self-	damage, focus on protecting	responds to problems, focus on
	healing)	assets upon a fault	prevention and minimizing
			impact to consumers

Resiliency against cyber-attack and natural disasters

	Vulnerable to malicious acts of	Resilient to cyber-attack and
	terror and natural disasters, slow	natural disasters, quick
	response	restoration capability

Table 2 .6 -Classifications of DGs [70]

 2

	DG Technology	Controllable Non-Controllable
	Conventional Fossil-Based Generation	✓
	Microturbines	✓
	Combined Heat and Power (CHP Plants)	✓
	Small Hydro Power Plants	✓
	Wind Turbines	✓
	Photovoltaics	✓
	Fuel Cells	✓
	Geothermal Power Plants	✓
	Biomass Power Plants	✓
	Tidal Power Plants	✓
	Wave Power Plants	✓

Table 2 .7 -Comparison of supply voltage requirements of microgrids according to some standards [78] Parameter 60092-101 [79] STANAG 1008 [80] EN 50160 [81] EN 61000-2-4 [82] ships Land Steady-state voltage deviations

 2

		+6%, -10%	±5% (±6%)	±10%	±10%
	Phase-to-phase voltage unbalance (cont)	3%	2%	2%	2%
	Voltage momentary deviation	±20%	±16% (±20%)	±40%	±90%
	Voltage transients recovery time	1.5 s	2 s	1 s	3 s
	Steady-state frequency deviations	±5%	±3%	±2%	±4%
	Frequency momentary deviations	±10%	±4% (±5.5%)	±15%	to be agreed
	Frequency transients recovery time	5 s	2 s	Not specified	2 s

Table 2 .8 -Characteristics of Energy Storage Systems [71], [84] Type Energy Efficiency (%) Energy Density (Wh/kg) Power Density (W/kg) Cycle Life (cycles) Self- Discharge Pumped hydro (PHES)

 2

		65-80	0.3	-	>20 years	Negligible
	Compressed Air	40-50	10-30	-	>20 years	-
	Energy Storage (CAES)
	Flywheel (steel)	95	5-30	1000	> 20000	Very high
	Flywheel (composite)	95	>50	5000	> 20000	Very high
	Pb-acid	70-80	20-35	25	200-2000	Low
	Ni-Cd	60-90	40-60	140-180	500-2000	Low
	Ni-MH	50-80	60-80	220	<3000	High
	Li-ion	70-85	100-200	360	500-2000	Med
	Li-polymer	70	200	250-1000	>1200	Med
	NaS	70	120	120	2000	-
	VRB	80	25	80-150	>16000	Negligible
	EDLC	95	<50	4000	>50000	Very High

Table 2 .9 -Summary of load modelling [88], [90]-[93]

 2

	Voltage Dependency	Frequency Dependency	General Characteris tics

Table 2 .10 -History of IEEE 1547 Year Event 2003

 2

	Year

IEEE 1547-2003

[START_REF]IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems[END_REF]

(Standard for Interconnecting Distributed Resources with Electrical Power Systems) was published as a voluntary industry standard. It was originally developed with an assumption of a low penetration of DER. It provides requirements regarding the performance, operation, testing, safety, and maintenance of the interconnection, including general requirements, responses to abnormal conditions, power quality, islanding, and test requirements.

2005

Energy Policy Act cites IEEE 1547 Standard as the best practice for interconnection and it is adopted by all states.

requirements, tips, techniques, and rules of thumb was approved.

2011

IEEE Standard 1547.4

[START_REF]IEEE Guide for Design, Operation, and Integration of Distributed Resource Island Systems with Electric Power Systems[END_REF]

providing approaches and good practice for the design, operation, and integration of microgrids was approved and published.

IEEE Standard 1547.6

[START_REF]IEEE Recommended Practice for Interconnecting Distributed Resources with Electric Power Systems Distribution Secondary Networks[END_REF]

for recommended practices that address spot and grid distribution networks was published. It also provides solutions for the interconnection of DER on distribution systems.

2013

Amendment 1 (IEEE 1547a

[START_REF]IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems -Amendment 1[END_REF]

) was passed to voltage and frequency regulation in December 2013 -the process to completely revise IEEE Standard 1547 began. IEEE Standard 1547.7 [115] addressing criteria, scope, and extent for grid impact studies due to DER. 2014 Amandment 1 (IEEE Standard 1547a-2014) was adopted in May 2014. It removed restrictions against DER from actively participating in grid voltage regulation. 2017 IEEE 1547 full revision was balloted and approved 2018 IEEE Standard 1547-2018 [116] (revision of IEEE Standard 1547-2003) was approved and published. Here, requirements and specifications of DER for reactive power capability, voltage and frequency support, and ride through capability, and performance when connected to an intentional island are provided.

Table 2 .11 -Comparison of North American Standards

 2

	Function	Advanced Functions	IEEE 1547-	IEEE 1547a-	IEEE 1547-	CA Rule 21-
	Set		2003	2014	2018	2015
	Static	Adjustable Trip Settings			
	Controlling	Power Curtailment			
		Ramp Rate Control				
	Frequency	L/H Frequency Ride Through				
	Support	ROCOF Ride-Through			
		Frequency-Watt			
	Voltage	L/G Voltage Ride Through (VRT)				
	Support	Dynamic Voltage Support during VRT			
		Voltage Phase Angle Jump Ride-Through			
		Fixed power factor

16 -Stability Classifications in Microgrids in Literature Comments on Microgrid Stability Classification In

  general, the stability classification proposed in 2018 IEEE classification accommodates the results of this PhD research. It lays important emphasis on differentiating the stability issues due to power balance and control problems. However, it is necessary to complement the explanations based on the findings in this PhD research. In line with 2018 IEEE Classification, this research discovered that in microgrids, stability problems are classified into power balance stability and control stability. Power balance stability deals with the law of energy conservation and covers frequency and voltage stability. It is concerned with the capability of the ensemble of the network (including elements such as sources, transformers and feeders) to deliver load demand. High excursions of frequency and voltage are common in microgrids.

			Power System
				Stability
			Power Supply and Balance Stability					Control System Stability
	Rotor Angle Stability	Small Signal Stability	Frequency Stability	Transient Stability	Voltage Stability	Electric Machine Stability	Converter Stability
							System Voltage		DC-Link Voltage
			Small		Large	Stability		stability
	Small-Disturbance Angle Stability	Transient Stability	Disturbance	Disturbance			Small Disturbance	Large Disturbance
	Short Term	Short Term	Long Term	Ultra short term	Small-Disturbance Voltage Stability	Large-Disturbance Voltage Stability	Short Term	Long Term
	Legend:	IEEE/CIGRE Task Force, 2004 Majumder, 2013				Short Term Long Term	Ultra short term
		Shuai, 2015
		IEEE Task Force, 2018
			Figure 2.

17 -Microgrid Stability Classification and the Associated Issues Treated in This Research

			Microgrid Stability
	Power Balance		Control System
	Stability			Stability
	Frequency	Voltage		Electric Machine	Converter
	Stability	Stability		Stability	stability
			Fault
	Small Disturbance	Large Disturbance	Islanding Loss of Generation	Large Disturbance	Small Disturbance	Small perturbation System damping
						Voltage sensitivity
			Load Impact
	Loadability	Power Sharing		Out-of-synchronism
		Power Limit		AVR/GOV tuning
		Current Limit		Controller tuning
	Figure 2.

Table 2 .12 -General Comparison Among Three Types of Microgrids [143]-[146]

 2

		Island	Ship	Airplane
	Power Plant Capacity	<200 MW	<200 MW	<80 MW
	Consumption without propulsion	<200 MW	A few MW	<1 MW
	AC/DC	AC	AC	AC and DC
	Frequency	50/60 Hz	Mostly 60 Hz	400 Hz, Variable, DC
	Common Voltage Level	Distribution voltages (20 kV, 11 kV, 6.6 kV, 400 V)	Low voltage (400-450 V) distribution systems	200 V AC, 28 V DC
	Generation	Synchronous machines, induction machines, static converters	Synchronous Machines	Synchronous machines

Table 2 .13 -Selected Operational Islanded Microgrids

 2 It should be noted that there are three categories of control strategy which may be employed in a microgrid, as discussed in[START_REF] Barnes | Real-World MicroGrids-An Overview[END_REF]. These control strategies relate to how the microgrid handles transient stability. A microgrid can either use centralized control, decentralized control, or central unit control. In centralized control scheme, a control scheme samples state variables and dispatches signals to all micro sources, hence fast telecommunications are necessary. In decentralized control scheme, each unit responds locally to variation in local state variables. A slow communication channel may be employed to send out steady-state set-points and update controller parameters.Finally, a microgrid is said to operate in central unit control scheme when a large plant (either generating plant or energy storage) is responsible for handling transient stability and for providing voltage and frequency reference of the microgrid.

	MG project	Site	Thermal	Energy or Power Mix Wind Solar	Others	Energy Storage	Loads	Backbone feeder	Control, Communication	Mode of Operation
	Hybrid PV Energy Storage	Yanglong Town, China			3087 kWp		5.2 MWh (battery)	Residential, mining industrial	10 kV	no info	Isolated, operational
	Yuanxian Island	Yuanxian Island, China	2 MW (Diesel)		500 kWp		1 MWh (battery)	Island	10 kV	no info	Isolated, operational
	Sumba Microgrid	Sumba, Indonesia	220 kW (Diesel)		500 kWp		480 kWh (battery)	Residential	20 kV	Distributed, SCADA	Two modes, Pilot Project
	Sendai Microgrid	Sendai, Japan	700 kW (CHP)		50 kWp		200 kW (fuel cell)	Residential, Hospital, Commercial	6.6 kV	centralized	Two modes, demonstration project
	Princeton University	New Jersey, USA	15000 kW (CHP)		4500 kWp		-	campus, laboratory, servers, hospital	26.4 kV	central unit	Two modes, operational
	DeMoTec	Kassel, Germany	26 kW (diesel)	15 kW	3 kWp		20 kW (battery)	simulated loads, residential, small business	10 kV	centralized and decentralized	Experimental and Demonstrator
	CERTS	Walnut, OH, USA	180 kW (CHP)				unknown capacity (battery)	Variable Z banks (285 kW), 20 hp motor	480 V	Distributed, SCADA	Two modes, experimental
	Mad River	Vermont, USA	480 kW (diesel)		unknown capacity			office, business, mixed load set	7.2 kV	Centralized	Two modes, operational
	BC Hydro Boston Bar	British Columbia, Canada	50 kW (diesel)			8.6 MVA (hydro)		mixed load (distribution feeder)	69 kV	central unit	Two modes, experimental, research

Table 3 .1 -Critical Clearing Time Transformation

 3

	No	Conventional CCT	Proposed Novel CCT
	1	Associated with critical	Considers ride through capability
		clearing angle and out of	(represented by power quality criteria) of
		synchronism criterion	inverters in addition to critical clearing
			angle and out of synchronism (OoS) of
			synchronous machines
	2	Assesses the stability of	Assesses the stability of synchronous
		synchronous machines	machines and the limitation of IBG
	3	Based on swing equation and	Based on swing equation, power angle
		power angle equation	equation, and inverter ride through
			capability
	4	-	Requires oscillation-free steady state

Table 3 .2 -Some Voltage Stability Indices

 3

	Index		Equation		Note
	Voltage Stability Index (VSI) [184]	𝑉𝑆𝐼 𝑖 = 1 + ( 𝑉 𝑖 𝐼 𝑖	) ( ∆𝑉 𝑖 ∆𝐼 𝑖	)	Eq. 3.9	Instability at VSI = 0 ∆ = incremental change I = load current
	Loadability index	𝐿 𝑖 =	𝑃 𝑖,𝑐𝑟𝑖𝑡 𝑃 𝑖,𝑜𝑝		Eq. 3.10	Should be accompanied by power factor op = operating point, crit = critical

Table 3 .3 -Factors Influencing Power System Stability

 3

	No	Factor	Explanation
	1	Credible Disturbance	Loss of largest plant (N-1 criterion), Predictability of Loads and VRES
	2	Nature of Credible Disturbance	Step or ramp, time response
			Fast response generators, governor tuning, storage,
	3	Flexibility Options	VRES curtailment, demand side management (communication and non-
			communication based), interconnection

Table 3 .4 -Proposed Indices of VRES Penetration for Microgrid Stability Assessment Index Equation

 3

			VRES Mix Index			𝐼 𝐷1 =	𝑃 ̂𝑉𝑅𝐸𝑆 ∑ 𝑃 𝑑𝑖𝑠𝑝𝑎𝑡𝑐ℎ𝑎𝑏𝑙𝑒 + 𝑃 ̂𝑉𝑅𝐸𝑆	Eq. 3.11
	Design Indices	Generation-side readiness index	𝐼 𝐷2 =	∑ 𝑃 𝑑𝑖𝑠𝑝𝑎𝑡𝑐ℎ𝑎𝑏𝑙𝑒 + ∑ 𝑃 𝑠𝑡𝑜𝑟𝑎𝑔𝑒 -𝑃 𝑚𝑎𝑥 𝑢𝑛𝑖𝑡 𝑃 ̂𝑑𝑒𝑚𝑎𝑛𝑑	Eq. 3.12
			Critical-load supply index			𝐼 𝐷3 =	𝑃 ̂𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 𝑃 ̂𝑑𝑒𝑚𝑎𝑛𝑑	Eq. 3.13
	Monitoring	index	Dynamic Stability Index	𝐼 𝑀1 =	𝑃 𝑎𝑐𝑡𝑙 𝑔𝑒𝑛 + 𝑃 𝑖𝑚𝑝𝑜𝑟𝑡 + 𝑃 𝑃𝑟𝑖𝑚 -𝑃 𝑁-1 𝑃 𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑	Eq. 3.14

Table 3 .5 -Indices and their Criteria

 3

	No	Conditions	Requirement(s)
	1	Potentially stable, demand response	ID2≥1
		not necessary
	2	Potentially stable, demand response	ID2<1,ID2/ID3 ≥1
		necessary
	3	Potentially stable operation	IM1 ≥1
	4	High VRES penetration	ID1≥predefined percentange

Table 4 .1 -Comparison of Several Frequency Ride Trough Requirements [142]

 4

	Frequency (Hz)	Denmark	French SEI	Great Britain	Ireland	Spain SEIE
	52-54		5 s
	51.5-52			15 mn		1 h
	51-51.5	15 mn		90 mn	60 mn
	50.5-51
	49.5-50.5	Cont.	Cont.	Cont.	Cont.	Cont.
	49.49.5	5 h
	48-49	30 mn		90 mn	60 mn
	47.5-48	3 mn				1 h
	47-47.5	20 s	3 mn	20 s	20 s	3 s
	46-47
	44-46		30 s

  technologies, e.g. virtual synchronous machine[203], both of which are able to fill in the role of (dispatchable) synchronous generators, notably with regard to the capability to provide voltage and frequency reference and to stabilize the grid upon perturbations.

	4.3.4.1. Synchronous condensers
	Synchronous condensers are synchronous machines which are not connected to any mechanical
	loads or turbines, hence not dispatchable. They were formerly used mostly only for reactive power
	source. However, as the penetration of IBG increases, other key features of synchronous condensers
	which may help stabilize the grid are sought after, such as high short circuit current and voltage
	recovery capability, inertial response, and the capability to provide the reference of voltage and
	frequency.
	Demand response can be accomplished with the support of communication or local
	measurements. ICT, previously discussed in Subsection 2.4.4.1, plays an important role in this
	function. Load shedding is still considered important as the last resort to maintaining frequency
	stability. The details of operational efforts are also reviewed in Section 3.5, and the significance of
	the efforts can be assessed through the proposed indices [165].
	4.3.4.	Technical Efforts

With regard to technical issues introduced by the variability and low inertia, the French transmission system operator, RTE, identified 2 possible solutions: synchronous condensers and grid forming inverter

  are illustrated in Figure4.8. For various reasons, the range is very strict for interconnected systems in steady state, while it is a bit less strict for islanded grids. Momentary voltage and frequency deviations are allowed in wider ranges. As the inertia is

	Chapter 4 Efforts to Accommodate Massive Shares of VRES in Future Power Grids
		110
		100	steady state, interconnected steady state, islanded
		90
		80	Momentary, interconnected
	Voltage [%]	40 50 60 70	Momentary, islanded
		30
		20
		10
		0	10 20 30 40 50 60 70 80 90 100 110
			Frequency [%]
	typically much lower in islanded grids, the permissible frequency deviations are relatively wider in
	islanded systems.
	92

Table 5 .1 -Separation of Roles among Power System Elements in Normal Operation

 5

		Grid Former	Energy Production	Power Balancing Transient State Steady State
	Classical Power	Synchronous	Synchronous	Synchronous	Synchronous
	System	Generators	Generators	Generators	Generators
	Current Microgrids with high levels of VRES	Synchronous Generators	Synchronous Generators, IBG	Battery, Synchronous Generator	Battery, Synchronous Generator
	Proposed strategy	Synchronous		Synchronous
	in Microgrids with	Condensers, Grid	IBG	Condensers, Grid	Loads, Battery
	massive VRES	forming inverters		Forming Inverters

Table 5 .2 -Load proportion and coefficients in a typical residential microgrid in Indonesia

 5

	Load	Pro-portion	p1	p2	p3	q1	q2	q3	Kpf
	CFL Bulb	15%	-0.03	1.66	-0.63	-0.06	1.4	-0.34	1
	Incandescent Light	5%	-0.04	0.5	0.54	0.03	0.51	0.46	0
	Sodium Lamp	5%	-0.04	1.2	-0.16	1.85	-4.11	3.26	0
	Fan	15%	-0.16	0.9	0.26	-0.12	0.62	0.5	1
	LCD TV	14%	1.24	-0.57	0.33	15.22	-33.22	19	0
	Refrigerator	29%	4.45	-8.48	5.03	12.18	-28.62	17.44	0.5
	Rice Cooker	12%	-0.02	0.1	0.92	-0.01	0.86	0.15	0
	Washing Machine	5%	1.07	-0.84	0.77	6.56	-13.65	8.09	0.1

Impact of terminal voltage and/or frequency on a typical residential microgrid

  1 + 𝑗𝑄 1 = 𝑣 𝑠 (𝑌 11 𝑣 𝑠 ) * + 𝑣 𝑠 (𝑌 12 𝑣 𝑟 ) * 𝑄 1 = -|𝐸 1 | 2 𝐵 11 + |𝐸 1 ||𝐸 2 ||𝑌 12 | cos(𝛿 -𝛾)

			Eq. 6.4
	Let us define
	𝑣 𝑠 = |𝐸 1 |∠𝛿
	𝑣 𝑟 = |𝐸 2 |∠0
	𝑌 11 = 𝐺 11 + 𝑗𝐵 11
	𝑌 12 = |𝑌 12 |∠𝜃
	Using the definitions above into Eq. 6.4 yields
	𝑃 1 = |𝐸 1 | 2 𝐺 11 + |𝐸 1 ||𝐸 2 ||𝑌 12 | cos(𝛿 -𝜃)	Eq. 6.5
	𝑄 1 = -|𝐸 1 | 2 𝐵 11 + |𝐸 1 ||𝐸 2 ||𝑌 12 | sin(𝛿 -𝜃)	Eq. 6.6
	The angle 𝜃 is between 𝜋/2 and 𝜋. If we define
	𝛾 = 𝜃 -	𝜋 2
	Then we can derive that
	𝑃 1 = |𝐸 1 | 2 𝐺 11 + |𝐸 1 ||𝐸 2 ||𝑌 12 | sin(𝛿 -𝛾)	Eq. 6.7
			Eq. 6.8

Table 6 .1 -Load proportion and coefficients for the simulations

 6

	Load	p1	p2	p3	q1	q2	q3	Kpf
	Microgrid Equivalent Load	1.48	-2.10	1.62	6.06	-13.41	8.35	0.45

Table 6 .2 -Data and Parameters for the simulations with synchronous condensers Element Data/Parameter Value Unit Grid Formers (GF-Left, GF-Right)

 6

		MVA rating	0.5	MVA
		Nominal Voltage	1	kV
		Inertia Constant H	1	s
		V/f constant	1	pu/pu
	PV Inverter (PV_Left, PV_Right)	MVA Rating MWp Rating Nominal Voltage	2.4 2 0.575	MVA MWp kV
		MVA Rating	2.4	MVA
	Transformer	Primary Voltage	0.575	kV
		Secondary Voltage	1	kV
		Length	1	km
	Line	Resistance per km	0.08	Ω
		Reactance per km	0.08	Ω

Simple Microgrid Under Consideration for V/F Implementation on Synchronous Condensers

Table 6 .3 -Simulated Load Impacts

 6

			Time	Target		Impact	Amplitude Ramp/	Duration
										Step
			t = 1s	Load Left		P and Q		+10%	Step	-
			t = 2s	Load Left		P and Q		-10%	Ramp	2s
			t = 5s	Load Left		P and Q		+25%	Ramp	2s
			t = 8s	Load Right		P and Q		+20%	Ramp	2s
	1.03							1.03
	[p.u.]						[p.u.]
	0.99							0.99
	0.95							0.95
											27.842 s 0.851 p.u.
	0.91			27.702 s 0.851 p.u.				0.91
	0.87							0.87
	-1.0000 0.83	5.2000	11.400	17.600	23.800	[s]	30.000	-1.0000 0.83	5.2000	11.400	17.600	23.800	[s]	30.000
		GF-Left: Speed							GF-Left: Terminal Voltage
		GF-Right: Speed							GF-Right: Terminal Voltage
							(a)

Table 6 .4 -Simulated Generation Impacts

 6

	Time	Target	Impact	Amplitude Ramp/	Duration
					Step
	t = 1s	PV_Left	P	-30%	Ramp	2s
	t = 2s	PV_Right	P	-30%	Ramp	2s
	t = 5s	PV_Left	P	+15%	Ramp	5s
	t = 6s	PV_Right	P	+15%	Ramp	5s

  The total simulation time is 10s.

	1.20													1.30
	[p.u.]												[p.u.]
	1.10													1.20
										9.538 s 1.003 p.u.				1.003 p.u. 9.438 s
	1.00													1.10
	0.90													1.00
	0.80													0.90
										9.838 s 0.878 p.u.					9.648 s 0.877 p.u.
	-1.0000 0.70	1.2000				3.4000	5.6000	7.8000	[s]	10.000	-1.0000 0.80	1.2000	3.4000	5.6000	7.8000	[s]	10.000
		GF-Left: Speed										GF-Left: Terminal Voltage
		GF-Right: Speed									GF-Right: Terminal Voltage
													(a)
	1.525													0.80
	[MW]												[p.u.]
	1.400													0.70
	1.275													0.60
	1.150													0.50
	1.025													0.40
	0.900													0.30
	-1.0000	1.2000				3.4000	5.6000	7.8000	[s]	10.000	-1.0000	1.2000	3.4000	5.6000	7.8000	[s]	10.000
		PV_Left: Active Power								PV_Left: Positive-Sequence Current, Magnitude
		PV_Right: Active Power							PV_Right: Positive-Sequence Current, Magnitude
													(b)
	1.80												0.925
	[MW]												[Mvar]
	1.60												0.800
	1.40												0.675
	1.20												0.550
	1.00												0.425
	0.80												0.300
	-1.0000	1.2000				3.4000	5.6000	7.8000	[s]	10.000	-1.0000	1.2000	3.4000	5.6000	7.8000	[s]	10.000
		Load	Left:	Total	Active	Power						Load	Left:	Total	Reactive	Power
		Load	Right:	Total	Active	Power						Load	Right:	Total	Reactive	Power
	138

Table 6 .5 -Data and Parameters the simulations with grid forming inverters Element Data/Parameter Value Unit Grid Formers (GF-Left, GF-Right)

 6

		MVA rating	1	MVA
		Nominal Voltage	1	kV
		Inertia Constant I	5	s
		V/f constant	1	pu/pu
	PV Inverter (PV_Left, PV_Right)	MVA Rating MWp Rating Nominal Voltage	2.4 2 0.575	MVA MWp kV
		MVA Rating	2.4	MVA
	Transformer	Primary Voltage	0.575	kV
		Secondary Voltage	1	kV
		Length	1	km
	Line	Resistance per km	0.08	Ω
		Reactance per km	0.08	Ω

Table 6 .6 -Load proportion and coefficients for the simulations

 6

				Load	p1	p2	p3	q1	q2	q3	Kpf
		Residential-commercial Load	0.76	-0.52	0.76	5.83	-11.75	6.92	0.5
		Impedance Load	0	0	1	0	0	1	0
				Load Left					Load Right
						Line_1
						21.5
				1.500 MW	-0.248 MW			0.253 ..	1.000 MW
				0.726 Mvar	0.253 Mvar			-0.248 M..	0.484 M..
				0.962 kA	0.204 kA			0.205 kA	0.641 kA
				0.900	-0.701			0.714	0.900
	Term_Left	1.000 kV					1.000 kV		Term_Right
		1.000 p.u. -1.399 d..	-0.752 MW -0.491 Mvar 0.519 kA -0.837	0.699 0.403 kA 0.512 Mvar 0.500 MW		1.000 p.u. -0.251 d..	0.883 0.323 kA 0.266 Mvar 0.500 MW	-0.753 MW 0.014 Mvar 0.435 kA -1.000
		Tr..							Tr..
		2-Winding	38.2		Grid Former Left			Grid Former Right	2-Winding	31.4
				0.828 0.920 kA 0.512 Mvar 0.755 MW					1.000 0.756 kA -0.000 Mvar 0.755 MW
	Term_PV_Left						Term_PV_Left..
		0.572 kV 0.995 p.u. 29.594 deg					0.576 kV 1.002 p.u. 30.817 deg
				0.755 MW					0.755 MW
				0.512 Mvar					-0.000 Mvar
				0.920 kA					0.756 kA
				0.828					1.000
				PV_Left 38.0					PV_Left(1) 31.5

Table 6 .7 -Simulated Load Impacts

 6

	Time	Target	Impact	Amplitude Ramp/	Duration
					Step
	t = 1s	Load Left	P and Q	+25%	Ramp	2s
	t = 4s	Load Left	P and Q	-25%	Ramp	2s
	t = 7s	Load Left	P and Q	+25%	Ramp	2s
	t = 10s	Load Right	P and Q	20%	Step	-

Table 6 .8 -Simulated Generation Impacts

 6

	Time	Target	Impact	Amplitude Ramp/	Duration
					Step
	t = 1s	PV_Left	P	-30%	Ramp	2s
	t = 2s	PV_Right	P	-30%	Ramp	2s
	t = 5s	PV_Left	P	+15%	Ramp	5s
	t = 6s	PV_Right	P	+15%	Ramp	5s

Table 6 .9 -Comparison of the current grid forming solutions

 6

	Solution	System regulation	MVA Sizing	Multi grid formers
				currently possible?
	Diesel Genset	Classical regulations (droop, AVR)	Peak load	Yes
	UPS	Isosynchronous, AVR	3 times the excepted peak load	No
	VSG	classical regulations (droop, AVR)	1.1-1.2 times the peak load	Yes
	V/f-implemented grid formers	V/f strategy	Around 25% of system peak load	Yes

Table 7 .2 -Initial conditions for the dynamic scenarios

 7 Scenario 1: Load Variation with the V/f regulation This section covers several load impact events. The first one is a 930 W load step, followed by a 930 W load shedding, simulated by switching the physical resistance bank. The measured terminal voltage is depicted in Figure

	Variable	Value	Unit	Note
	Excitation current	15.9	A

Table 7 .3 -Impact of the degraded state to domestic loads Domestic Load Visual/Acoustic Impact Laptop (detached battery)

 7

Acknowledgements Acknowledgements ....................................................................................................................................... ii Table of Contents ......................................................................................................................................... iii

Chapter 7 Validation of the voltage to frequency regulation through Real-time HIL Simulations

This chapter addresses the performance of the proposed voltage-to-frequency regulation implemented on a synchronous condenser through the experimentation in real-time hardware-in-theloop platform based on RT-Lab. A simple test system comprised of a number of simulated and physical elements has been constructed for this purpose. Several scenarios are taken into account to understand the behavior of the system following typical perturbations that may occur in microgrid operations.

Introduction to Hardware in-the-loop Real-Time Simulation

Digital real-time simulation (DRTS) of an electric power system provides an accurate reproduction of the output waveforms (voltage and current), useful for representing the real power system being modeled [START_REF] Faruque | Real-Time Simulation Technologies for Power Systems Design, Testing, and Analysis[END_REF]. It solves the model equations within the same time in real-world clock, although the output is in discrete time intervals due to the use of time-step.

Hardware in the loop (HIL) is one of two categories of DRTS, the other one being fully digital real-time simulation. It refers to the condition where certain parts of the digital simulation include real physical components. The physical components are connected via input-output interfaces, such as digital-to-analog or analog-to-digital converters and filters. HIL is used for prototyping. For powerhardware-in-the-loop (PHIL) applications, amplifiers are necessary for reproducing the actual signals (e.g. current, voltage) and supplying the power exchange to the physical elements. A real-time simulator's time step is typically around 50 μs or smaller, which is considered suitable for a dynamic study in 50/60 Hz power systems.

OPAL RT

RT LAB is a brand of digital real-time simulator capable of performing HIL simulations developed and marketed by OPAL RT Technology, a Canada-based company. Modeling can be carried out in Matlab's Simulink and this product is compatible with Simulink solvers. Real time HIL simulations with OPAL RT are suitable for studies on power electronics, power systems, and control systems.

The DC amplifier, Cinergia, is employed to represent the excitation system feeding the rotor of the V/f-implemented grid former. The maximum current output of this amplifier is 25 A.

The RT-Lab real time simulator is used, where the time step is 50 μs. This is considered adequate for reproducing the dynamic phenomena that we are interested in. The input and output signals of the real time simulator are listed in Table 7.1. It is noticeable that the experiment does not require complicated sets of measurement, as one of the main benefits of the V/f strategy is its simplicity. The model created in RT-Lab consists of 3 subsystems: setpoint and monitoring subsystem, power system subsystem, and excitation subsystem, as shown in Figure 7.3. Each subsystem is connected to each other through the input/output signals.

Setpoint and Monitoring

Power System (AC Amplifier)

Excitation System (DC Amplifier)

Figure 7.3 -RT-lab model created in Simulink

The setpoint and monitoring subsystem is the only subsystem accessible during the real time simulation. Here, we can monitor and visualized certain pre-defined signals and modify the setpoints.

In the power system subsystem, power system elements are modeled. The ZIP model with typical residential microgrid parameters presented in

Organisation de la thèse

Cette thèse est organisée en trois parties, composées de huit chapitres. Le premier chapitre, le chapitre 1, présente le contexte, la problématique, et les principales contributions des travaux. La première partie, composée des chapitres 2 et 3, traite de la stabilité des micro-réseaux. Le chapitre 2 présente la perspective classique de la stabilité des systèmes électriques et de la manière dont elle devrait changer à l'avenir en raison de l'évolution des réseaux électriques vers une production plus renouvelable et une vision des micro-réseaux. Le chapitre 3 traite des méthodes et des indices utiles