Nicolas Manduley

Contribution to Insulation Coordination Studies for VSC-HVDC Systems Declaration

HVDC power transmission systems are developing and expanding rapidly all over the world. Some of the main reasons behind this growth are the restrictions and limitations regarding the use of the Right-of-Way (ROW) and the increasing commissioning of offshore wind parks. Both cases converge into solutions involving the installation of long underground or submarine cables, for which AC technologies are not suitable over long distances. Moreover, HVDC transmission offer a series of advantages over HVAC in terms of power transmission capacity and reduction of losses, which may lead to an increase in the commissioning of HVDC lines and the conversion of existing AC overhead lines into DC.

It is within this context that this thesis is presented as a contribution to the development of high-scale HVDC systems, particularly regarding insulation coordination for Voltage Source Converter (VSC) based technologies. In particular, the Modular Multilevel Converter (MMC) represents one of the most promising VSC implementations in HVDC transmission.

Insulation coordination consists of the selection of the required dielectric strength of the insulating materials in a utility. It ensures the safe operation of the system in both steady state and transient conditions such as faults, lightning strikes and other phenomena generating overvoltages. Therefore, insulation coordination is a crucial stage of any engineering project in order to guarantee not only the integrity of the components, but also the safety of the staff at the installations.

Existing standards provide procedures and guidelines on how to conduct insulation coordination studies for HVAC and LCC systems. As of today, no existing standard covers VSC insulation coordination. This thesis aims to constitute a contribution towards the development of detailed insulation coordination procedures for VSCs, and particularly for the MMC, taking into account the specific characteristics and transient behaviour of VSCs, and their differences with AC and LCC systems.

In line with such purposes, an exhaustive study of the literature is performed in order to identify the fundamental aspects that need to be considered to adapt the insulation coordination principles to VSC-HVDC systems. Studies are conducted using electromagnetic transient modelling in EMTP to study in detail the behaviour of VSC-HVDC systems under transient events leading to the highest overvoltage levels which, in combination with the installation of surge arresters, will determine the insulation requirements of the system.

A procedure is proposed to conduct insulation coordination studies on MMC-HVDC systems. The proposed procedure takes into account all the factors determined to have an influence on the way in which the insulation coordination principles should be applied to MMC-HVDC systems.

Résumé

Les systèmes de transport d'énergie en courant continu (HVDC) se développent très rapidement dans le monde entier. Certaines des principales raisons de cette croissance sont les restrictions et les limites concernant l'utilisation des droits de passage et la mise en service des parcs éoliens offshore. Les deux cas décrits ci-dessus convergent vers des solutions impliquant l'installation de longs câbles souterrains ou sous-marins, pour lesquels les technologies AC ne conviennent pas sur de longues distances. De plus, le transport d'énergie en HVDC offre une série d'avantages par rapport au HVAC en termes de capacité de transmission de puissance et de réduction des pertes.

C'est dans ce contexte que cette thèse est présentée comme une contribution au développement des systèmes HVDC à grande échelle, en particulier en ce qui concerne la coordination d'isolement pour les technologies fondées sur les convertisseurs de source de tension (VSC). En particulier, le convertisseur modulaire multiniveaux (MMC) représente l'une des implémentations VSC les plus prometteuses dans le domaine du HVDC.

La coordination d'isolement est la procédure de sélection de la tenue diélectrique du matériel isolant des équipements d'un système électrique. Il garantit sécurité opérationnelle du système en régime permanent, ainsi qu'en régime transitoire en cas de défauts, chocs de foudre et autres phénomènes générant des surtensions importantes. Par conséquent, la coordination d'isolement est une étape cruciale de tout projet d'ingénierie pour garantir non seulement l'intégrité des composants qui y sont connectés, mais également la sécurité du personnel dans les installations.

Les normes existantes proportionnent des procédures et recommandations pour la réalisation des études de coordination d'isolement pour les systèmes AC et LCC. À ce jour, aucune norme existante n'adresse la coordination d'isolement pour des systèmes VSC. Cette thèse a pour objectif de contribuer au développement de procédures détaillées de coordination d'isolement pour les systèmes VSC, et en particulier pour le MMC, prenant compte de ses caractéristiques et comportement en régime transitoire, ainsi que ses différences avec les systèmes AC et LCC.

Dans cette optique, nous avons réalisé une étude exhaustive de la littérature afin d'identifier les aspects fondamentaux à prendre en compte pour adapter les principes de coordination d'isolement aux systèmes VSC. Ces études ont été menées en utilisant des simulations de transitoires électromagnétiques dans EMTP pour étudier en détail le comportement des systèmes VSC sous des événements transitoires conduisant aux niveaux de surtension les plus élevés qui, en combinaison avec les équipements de limitation de surtension, détermineront les exigences de tenue diélectrique du système.

Bertrand, you accepted me as a student and agreed to supervise my thesis without knowing me. I understand what a leap of faith that is, and it has motivated me to do my best since day one. And from that day on, I have always valued and admired your dedication, your patience and your pedagogy to transmit your ideas. Thank you for being my supervisor, for your trust, your engagement, your wisdom and your always-present sense of humour.

Alain, thank you for sharing your expertise and introducing me to the complex domain of insulation coordination. It was a difficult subject to grab at first, but you contributed greatly for me to constantly gain a better understanding of it, not only at the beginning, but also throughout the whole development of the thesis. Every meeting and every discussion with you I would learn something new or gain a deeper understanding of the domain. But even more importantly, I always felt that I could count on you whenever I had doubts, questions or just felt stuck. I never underestimated the time and the efforts that you have invested to make this work possible, and I could not thank you enough for that. Sellé, it is very difficult to put into words how much I have learned and grown, personally and professionally, working by your side during all of these years. Your kindness, your honesty and your unconditional support during both the good and the bad times are only a few of the many virtues I admire in you and that I will always remember. More than once you gave me the push and the motivation I needed to go on, especially during this last year. You were there when I needed it the most, as a mentor, as a colleague, as a friend. And for that, I am eternally grateful.

Professor Pack, it has been a real pleasure and honour to work with you during the last years. Not only did I have the opportunity to discover a whole field that was a complete mystery to me, but also to grow a lot as a researcher through your supervision. Your advice was always good advice, and contributed significantly to improve my critical and scientific thinking. Thank you for teaching me so much and for making my stays in Graz a complete and unforgettable experience through your guidance, support and your daily dose of sense of humour.

To all of you: thank you. I could not even imagine a better team of supervisors, as each one of you has greatly contributed to this work, not only individually, but also as a group. It is rare to find a group with such a good synergy, where every single meeting and discussion was always a step forward. You can be sure that it was a true honour working with you, and that I consider myself immensely lucky for having you as my supervisors.

I wish to thank as well all my colleagues at the SuperGrid Institute. It was a true pleasure to spend the last four years among such kind, friendly and brilliant people who made the work environment a nice and enjoyable place to be. Thank you for all the laughs, the discussions beside the coffee machine, and in short, for all the good times spent together.

On a final and more personal note, I want to thank my family and friends who supported me, no matter the distance or the circumstances. You were always there for me and motivated me to keep moving forward. I could not have done this without all the love and support you showed me during these years. The horizontal axis features the current amplitudes for the first stroke, while the vertical axis provides the probability for the lightning current amplitude to be equal or lower than the considered value. ... List of Tables Table 1. There are several reasons for this phenomenon, which include both technical and economic constraints that may lead to prefer HVDC transmission over HVAC for several applications.

List of Figures

On one hand, the difficulty associated to the construction of new overhead lines because of restrictions on the use of the Right-of-Way (ROW) makes that solutions involving the use of underground cables become more and more common. On the other hand, the increasing development of offshore wind parks several kilometres away from the coast also requires the use of submarine cables. In both cases above, AC transmission is limited by the capacitive currents generated by the cable insulation and geometry, and after a certain distance, it becomes impossible to transmit any active power through an AC cable without including shunt compensation equipment. In such cases, the use of DC transmission is a technical and economic decision since DC cables allow transmitting large amounts of power efficiently along great distances without the need of shunt compensation.

Besides the technical reasons regarding the use of cables, HVDC transmission has a number of general advantages over HVAC. For instance, the absence of skin effect under normal operating conditions allows a better utilisation of the cable section, and thus higher power transmission without increasing the temperature and losses due to the heating of the conductor. This reduction in the losses along the line could compensate the higher costs of the substations (due to the high cost of the converters and associated equipment) and make it an economically better option than AC, especially over long distances (see CIGRE TB 186).

Furthermore, since there are no varying electromagnetic fields along the line in normal operation, the regular transposition of the conductors is not required in DC to avoid introducing unbalances in the line. In addition, a DC link only requires two cables to operate, while AC lines require a minimum of three (in both cases, not considering the shield wires or metallic returns).

Moreover, it has been shown that by converting existing AC overhead lines to DC, it is possible to significantly increase the transmitted power with minor modifications to the line itself. This allows optimizing the use of the existing corridors, especially when restrictions regarding the use of the Right-of-Way make it impossible to build a new corridor.

It is clear that there is great interest in continuing to develop HVDC technologies, especially for the transmission or large amounts of power over very long distances. Besides providing an efficient link between the greatest generation and consumption nodes of the grid, it would Introduction Nicolas Manduley 2020 Page 2 allow the massive integration of renewable energies in an efficient and reliable way. Projects such as the European supergrid would increase the scale of the integration of renewable energies in the region, as well as increasing the reliability and stability of the European grid, through the HVDC interconnection of all the regional transmission system operators.

It is within this context that this thesis is presented as a contribution to the development of high-scale HVDC systems, particularly regarding insulation coordination.

Insulation coordination is the procedure for the selection of the required dielectric strength of the insulating materials in a utility. It ensures that not only the equipment connected to the system will be able to operate safely in steady state, but also that it will withstand long and short duration overvoltage levels due to faults, switching operations, lightning strikes on the overhead lines and other sources of transients.

Therefore, insulation coordination is a crucial stage of any engineering project, and should absolutely be covered in order to guarantee the safe operation of the system, the integrity of the components connected to it and the safety of the staff around it. Furthermore, even if the manufacturer is in charge of specifying the insulation coordination-which is also often specified by the system operators-the utility should be also able to evaluate the appropriateness of the choices made by the manufacturer and verify that the final design meets the requirements and ensures a safe operation.

Current standards provide procedures and guidelines on how to conduct insulation coordination studies for HVAC systems (IEC 60071 Part 1 and Part 2) and for Line Commutated Converters (LCC-HVDC) systems (IEC 60071 Part 5). Such standards are the result of physical analyses combined with several decades of experience in such kind of systems, which have allowed to improve the methods throughout the years. However, the application of Voltage Source Converters (VSC) to high voltage direct current (HVDC) transmission systems is relatively recent, especially regarding the Modular Multi-level Converter (MMC). The first commercial application was completed in 2010 (Trans Bay Cable, San Francisco, USA). Therefore, there is still little experience regarding the achievement of such type of projects and how they should be designed in terms of insulation and overvoltage protection. As of today, no existing standard covers for VSC-HVDC or MMC-HVDC insulation coordination.

In addition, although there is significant experience in HVDC systems using LCC technologies, there are no universally recognized procedures for insulation coordination in HVDC. This includes the absence of standard rated withstand voltages for the equipment, which is one of the fundamental aspects allowing to provide detailed procedures in the insulation coordination standards for HVAC (IEC 60071-1 and 2) based on the highest voltage of the equipment. This is due to the fact that a simple transposition of the AC insulation coordination rules to DC is not possible due to the fundamental differences in the architecture, behaviour Introduction under transient conditions and other reasons that will be discussed later. For instance, surge arresters in DC might be used to limit temporary overvoltages, in spite of the arrester energy duty concerns, which is never the case in HVAC.

Similarly, it is expectable that the fundamental differences between LCC and VSC exclude the possibility of performing a direct transposition of the LCC-HVDC standard to VSC-HVDC systems.

The presence of power electronic components (e.g. thyristors or IGBTs) also makes it difficult to define a clear frontier between the role of the utility and the role of the manufacturer regarding the withstand voltage of the equipment. In AC systems, this is clearly defined in the standards as there are preferential associations between the standard withstand levels and the highest voltages for equipment. As explained above, there are no equivalent associations for HVDC.

Even more, since insulation coordination is a subject that concerns mainly the industrial actors of an engineering project, there is very scarce scientific literature available because each utility may prefer to keep confidential the procedures and the methodology leading to the final design.

Summarizing, the main challenges towards the development of insulation coordination procedures for VSC-HVDC systems can be listed as follows:

 Limited experience in HVDC utilities, despite of decades of existence of LCC-HVDC systems.

 Absence of recognized procedures for HVDC insulation coordination studies.

 Limited standardization, especially regarding the rated withstand voltages for DC applications and their respective associations with the highest voltage of the equipment, as there is for HVAC systems.

 Impossibility of performing a direct transposition of the AC principles to DC, as well as from LCC to VSC.

 Unclear frontier between the role of the utility and the role of the manufacturer regarding insulation coordination.

 Scarce scientific literature on the subject.

The main goal of this thesis is to contribute to remedy these major deficiencies in the context of HVDC insulation coordination, and specifically for VSC-MMC systems.

In the particular case of DC overhead lines, an additional aspect besides DC insulation coordination is assessed, and concerns the continuity of service. Lightning is generally the main source of faults in overhead lines, and consequently, it is of particular interest to Introduction Nicolas Manduley 2020 Page 4

investigate how the lightning performance of a DC overhead line should be evaluated, as well as the measures to be taken in order to get an acceptable number of faults from an industrial point of view. It is a timely subject considering the benefits of HVDC transmission discussed above, as well as the restrictions that may lead to the conversion of AC overhead lines to DC.

Thesis Objectives

In order to contribute to overcome the above challenges and deficiencies regarding insulation coordination, this dissertation is split into two main axes: insulation coordination of VSC-HVDC systems, and the evaluation and improvement of the lightning performance of HVDC overhead lines. It is important to note that, although both subjects will be addressed and developed separately, they are not independent from each other, from both a scientific and an industrial point of view. From the scientific point of view, in both cases the electromagnetic behaviour of the system is considered. From an industrial point of view, the lightning overvoltages produced along the line are related to the withstand voltage of the insulator strings, which at the same time are related to the general specifications of the system.

Regarding the insulation coordination of HVDC systems, the main objectives are:

 To provide a base on which the insulation coordination of MMC-HVDC stations can be performed, inspired on the approach of AC and DC insulation coordination standards and how it should be adapted to VSC-MMC systems taking into account their respective features and characteristics.

 To propose a methodology to perform transient studies in order to estimate the required withstand voltages of the different apparatuses of MMC-HVDC stations.

 To provide guidelines and recommendations on how the overvoltage protection strategy should be designed, particularly regarding the characteristics of the arresters and their energy duty.

Concerning the lightning performance of HVDC overhead lines, the main objectives are:

 To adapt an existing procedure for the evaluation of the lightning performance of overhead lines to HVDC transmission allowing to consider asymmetrical configurations of the towers or overhead lines, non-linear devices and double flashovers.

 Propose and assess solutions for the improvement of the lightning performance of HVDC overhead lines considering both single and multiple insulator flashovers due to lightning strikes.

 Provide a better understanding of how HVDC systems behave in case of lightning strikes (applicable to both VSC-HVDC and LCC-HVDC). Introduction

Thesis Outline

This thesis is structured in four chapters, each developing one of the fundamental aspects towards the achievements of the objectives above listed.

Chapter 1 constitutes an overview of the state of the art and literature review concerning insulation coordination of HVDC systems. It presents the general philosophy of insulation coordination, the procedures for HVAC systems and the specificities of HVDC that need to be taken into consideration to adapt the fundamental insulation coordination principles given in the standards to DC, and in particular for VSC-HVDC. Moreover, a general overview on lightning is provided from the electrisation of the clouds to the statistical distribution of lightning strike parameters and the methods to determine their impact points. Over this base, the stakes of the estimation of the overhead line lightning performance are introduced.

Chapter 2 presents all the aspects relative to electromagnetic modelling of the different components considered throughout the achievement of this research. It covers from numerical considerations and individual component modelling (e.g. overhead lines, transmission towers, insulators, surge arresters, faults and lightning strikes) to the modelling of systems including several components (such as MMC stations and the general model used for lightning studies).

In Chapter 3, studies are conducted aiming to analyse the overvoltage profiles and overvoltage protection strategies of MMC-HVDC systems considering different architectures and topologies of the MMC, as well as the influence of the surge arrester characteristics and arrangement on the overvoltage profiles. A procedure is proposed to perform insulation coordination studies on MMC-HVDC stations, particularly considering slow-front overvoltages (SFO) due to faults, which typically lead to the highest overvoltage levels in transmission systems (excluding external source faults as lightning). Guidelines are provided regarding the design of the different surge arresters that may be present in the station for the overvoltage protection strategy.

Chapter 4 deals with the evaluation and improvement of the lightning performance in HVDC overhead lines. It introduces the hypotheses considered for the adaptation of the procedures described in Chapter 1 to be able to consider asymmetric configurations-regarding the transmission tower or the overhead lines-, surge arresters and double flashovers. Then, a study is presented aiming to determine the influence of the position of the DC poles of each polarity within a double-circuit HVDC overhead line, followed by the research on the proposed techniques for the improvement of the lightning performance of HVDC lines.

Recommendations for the specification of the line surge arrester characteristics are provided.

Thesis Contributions

The main goal of this thesis is to contribute to the development of insulation coordination procedures for VSC-HVDC systems, particularly regarding the MMC which is the main type of VSC used for high voltage applications. In order to take into account the behaviour of the system under transient conditions, as well as the effect of surge arresters, breakdown of insulators and other complex phenomena that influence the transient behaviour, the studies presented in this work are mostly based on electromagnetic transient simulations. In the interest of scientific rigor, qualitative and quantitative interpretations of the obtained results are given as much as possible so that the proposed methods, procedures and recommendations remain within the scientific domain and can be used for technical and engineering applications.

In this context, the main contributions of this thesis are:

 Through a comprehensive study of the existing literature and standards, the challenges and main influencing factors in the development of a procedure for insulation coordination of VSC-HVDC systems have been identified.

 Fundamental schemes for MMC-HVDC systems have been proposed in which insulation coordination can be based on, inspired on the approach adopted in IEC 60071-5 for LCC-HVDC systems. Such schemes are designed to be as detailed as possible, while also being able to represent each possible topology (monopolar, bipolar with or without metallic return and their respective operating modes in steady state), configuration (point-to-point or MTDC), link technology (underground or submarine cables, overhead lines, hybrid lines) and architecture (e.g. arm reactors on the AC or the DC line).

 Protection rules and guidelines for the overvoltage protection of MMC-HVDC systems have been proposed based on qualitative and quantitative analysis for monopolar and bipolar configurations. This includes design rules based on the maximum overvoltage levels at each point of the system, design and location of surge arresters.

 The effect of the surge arrester configuration within a station, their interactions and consequences on the system and overall design have been studied under fault conditions. Recommendations for the arrangement and design of the surge arresters are provided based on the results.

 The upgrade of an existing procedure for the estimation of the lightning performance is provided so that it is able to consider asymmetric configurations regarding the transmission towers or overhead lines, line surge arresters and double-pole flashovers while also keeping and up-to-date modelling of the lightning strokes. Introduction Nicolas Manduley 2020 Page 7

 The lightning back-flashover performance of different pole arrangements has been studied and explained for HVDC double-circuit configurations, which are likely to become more popular in the future due to the restrictions concerning the Right-of-Way.

 The use of unbalanced insulation have been studied to improve the lightning backflashover and double back-flashover performance of HVDC double-circuit configurations with the same DC polarity on each cross arm. It has been shown that similar or even better performances can be obtained using this solution compared to the most commonly studied configuration with mixed polarities on each cross arm.

 The use of line surge arresters have been also studied to improve the overall lightning performance of HVDC overhead lines. Recommendations are provided regarding the number and location of surge arresters per tower, as well as on how the surge arresters should be designed and specified.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 1: State of the Art and Literature Review

Chapter 1 State of the Art and Literature Review

Introduction

The main goals of this chapter are to provide a general overview of the state of the art regarding insulation coordination through the available literature, and to present the scientific and technical foundations of the topics presented in this dissertation. This will allow to introduce the current challenges concerning the insulation coordination of HVDC systems, and in particular for the high voltage applications of Voltage Source Converters (VSC-HVDC).

Firstly, the generalities of insulation coordination are presented to set the bases and provide some context for the different aspects discussed in this chapter. Then, the specificities of HVAC insulation coordination are explained based on the definitions and procedures given in the IEC insulation coordination standards for HVAC. Next, the specificities of HVDC are discussed by identifying the fundamental differences between AC and DC, and how these differences have been taken into account to adapt the AC insulation coordination to DC in the case of Line Commutated Converters (LCC). Similarly, the fundamental characteristics of VSC, as well as their differences with LCC, are assessed to identify the specific challenges about how the insulation coordination should be performed for such systems in a future standard.

Afterwards, a general overview on lightning is included so that the physical principles, as well as the adequate vocabulary, are provided to support the discussions regarding lightning studies in further chapters. Finally, after all of the above described aspects, the particular contributions of this thesis are presented so that they can be easily put within the context of insulation coordination, especially regarding VSC-HVDC systems.

Generalities Regarding Insulation Coordination

When designing an electrical network, it is essential that the insulation strength of all equipment connected to it is designed to be higher than the maximum stresses expected to appear in the network. This includes not only the nominal stresses, but also stresses due to faults, malfunctioning, switching operations, or any kind of action that could introduce a disturbance to the system. These disturbances may compromise the integrity of the equipment as well as the safety of the operators.

From the previous paragraph it is possible to extract the fundamental mechanism behind insulation coordination: the relations and interactions between stresses and insulation strengths, and the need for the latter to be higher than the former. In order to achieve this objective, there are two possibilities: either increase the strength, or reduce the stress through voltage limitation devices, such as surge arresters or spark gaps.

According to IEC 60071 standards, insulation coordination is defined as: Insulation coordination can be thus described as a relative process consisting of the harmonization between the insulation strengths of the equipment connected to the network and the stresses that may appear during a wide spectrum of possible events. The final choice is usually made on the basis of technical and economic considerations, by finding a balance between the tolerated risk of failure and the total overall costs of the project.

The main difficulties associated to insulation coordination can be grouped in three categories: a) the statistical nature of the procedure, b) the compatibility of stress and strength, and c) the standardization requirements (Hutzler, 1994).

The fact that the physical phenomena behind the possible failure modes of the equipment are of statistical nature represents one of the fundamental complexities of insulation coordination. For each overvoltage value U, there is a probability f(U) for such overvoltage to appear in the system, and a probability P(U) for the insulation to break down under the stress of U. The risk of failure R is thus expressed as the convolution of f(U) and P(U) as shown in equation (1-1) and illustrated in Figure 1.1.

𝑅 = ∫ 𝑓(𝑈) × 𝑃(𝑈) 𝑑𝑈

𝑈 𝑡 𝑈 50 -4𝑍

(1-1)

where, as defined in IEC 60071-2 standard:

f(U)
is the probability density of overvoltage occurrence described by a truncated Gaussian or a Weibull function; P(U)

is the discharge probability of insulation described by a modified Weibull function; U t is the truncation value of the overvoltage probability distribution; U 50 -4Z

is the truncation value of the discharge probability distribution However, in some cases the insulation strength is specified as a single value for each class of overvoltage (which are discussed in §3). In such cases, no statistical distribution of the strength is available and the use of deterministic methods is required.

The issue of compatibility between stress and strength also adds some complexity to the approach, because the stress refers to the voltages and overvoltages in service conditions, while the strength refers to the results obtained from tests under laboratory conditions. More precisely, the stress consists in voltages and overvoltages which may have various shapes and durations, while the strength results from laboratory tests performed under standard voltage shapes (Hutzler, 1994). To adequately harmonize both parameters, they must be expressed as a function of compatible parameters. As it will be discussed later in this chapter, this leads to the definition of:

 Representative voltages and overvoltages (U rp ): the voltage which, if applied to the insulation through a standard shape under laboratory conditions, would produce the same stress as the actual voltage in service.

 Coordination withstand voltages (U cw ): the required strength of the equipment if the conditions were those prevailing on site rather than those of the laboratory.

Finally, the role of standardization is to limit the choice of the strength for each class of voltages and overvoltages to a restricted number of levels, so that it is possible to effectively test the strength of a given equipment using the standard shapes.

The following sections will address in more depth the principles of insulation coordination for HVAC systems based on the relevant standards (IEC 60071-1, 2011;IEC 60071-2, 2018), as well

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 1: State of the Art and Literature Review as how these principles are currently applied for LCC-HVDC transmission according to its respective standard (IEC 60071-5, 2014). Next, the overall principles of VSC-HVDC transmission, and particularly regarding the Modular Multi-level Converter (MMC) will be discussed. This will allow to point out the principles and challenges regarding overvoltage protection of these kinds of systems which will need to be addressed in a future VSC-HVDC insulation coordination standard.

Specificities of HVAC Regarding Insulation Coordination

The basis of insulation coordination for three-phase AC systems above 1 kV are described in the standard IEC 60071 Part 1: Definitions, principles and rules, followed by an application guide in IEC 60071 Part 2. They specify the procedure for the selection of the withstand voltages of the insulation and protection schemes (e.g. with surge arresters).

The following sections present an overview on the different types of insulation, overvoltage classes and protection schemes, which will allow presenting the overall insulation coordination approach described in the standards.

Insulation Configurations and Types

The three insulation configurations considered in the IEC 60071 standards are illustrated in Figure 1.2 and are classified as phase-to-earth, phase-to-phase and longitudinal insulation.

Longitudinal insulation corresponds to the insulation between the terminals of the same phase of an open device, such as a circuit breaker. Important overvoltages may appear in such sections, for instance, when a reclosing operation is performed while there exists trapped charge, or when the two sections correspond to the same phase of two non-synchronous networks. Insulation types can be classified into two categories: self-restoring and non-self-restoring insulation. Self-restoring insulation recovers its insulating properties after a disruptive discharge (after up to a few minutes). This concerns mainly insulation in air (air clearances), but can also include internal gaseous insulation (e.g. SF6), vacuum or some liquids. Non-selfrestoring insulation loses its insulating properties or does not recover them completely after a disruptive discharge (e.g. solid insulation) (Sabot & Xémard (EDF R&D), 2016).

Voltage and Overvoltage Classes

Continuous Voltages

Correspond to the voltage levels under normal operating conditions for each component. Two values are of particular interest, which are the highest voltage of the system (U s ) and the highest voltage for equipment (U m ).

The highest voltage of a system (U s ) is the highest value of the phase-to-phase operating voltage (RMS) which occurs under normal operating conditions at any time and at any point in the system. The highest voltage for equipment (U m ) corresponds to the highest value of phase-to-phase voltage (RMS) for which the equipment is designed in respect of its insulation.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 1: State of the Art and Literature Review Nicolas Manduley 2020 Page 14

As it will be seen, the highest voltage for equipment U m will be chosen to be at least as high as U s , and for which the required standard withstand voltages are defined.

Temporary Overvoltages (TOV)

Temporary overvoltages in AC are defined as power frequency overvoltages of relatively long duration (from one cycle up to several minutes). They can originate from faults, load shedding, resonance, ferroresonance or combinations of the above. Compared to other overvoltage classes, the amplitudes of TOVs are generally low, but they also present the longest durations of all overvoltage classes. For this reason, TOVs are often associated to high energy levels.

Slow-Front Overvoltages (SFO)

Similarly as for TOVs, slow-front overvoltages can originate from faults and switching operations, and in some cases as a result of distant direct lightning strokes to the conductors of overhead lines. They are also referred to as switching overvoltages.

SFOs are characterized by front times in the order of 20 -5000 µs and a total duration of one cycle or less. The typically used standard shape for testing is represented by a double exponential function with a front time of 250 µs and a tail of 2500 µs (see Figure 1.3).

Often, faults and switching operations generate both SFOs and TOVs.

Fast-Front Overvoltages (FFO)

Fast-front overvoltages are mainly generated by lightning strokes, but may also originate from some switching operations or faults. They are also referred to as lightning overvoltages.

FFOs are characterized by front times in the order of 0.1 -20 µs and a total duration of 300 µs or less. The typically used standard shape for testing is represented by a double exponential function with a front time of 1.2 µs and a tail of 50 µs (see Figure 1.3).

Very Fast-Front Overvoltages (VFFO)

Very Fast-Front Overvoltages can originate from faults or switching operations in gasinsulated stations (GIS). They are very high frequency transients which can go up to 100 MHz. No standard wave shape is available for this class, so the respective testing shall be determined by the relevant apparatus committee.

Characteristics of Overvoltage Protection Devices

As discussed at the beginning of this chapter, insulation coordination consists of the harmonization between the insulation strength (i.e. voltage withstand) and the stresses (i.e. overvoltages) in service. Once the stresses have been determined and classified according to Figure 1.3 for each part of the system, there are two main options: either design the insulation levels to be higher than the observed overvoltages, or limit the amplitude of these voltages so that a lower standard withstand voltage can be selected.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 1: State of the Art and Literature Review Metal-oxide surge arresters (MOSA) without gaps are the most widely used arresters to directly protect the equipment and lines from overvoltages. The fundamental characteristics and selection rules of metal-oxide arresters without gaps for AC systems are covered in their respective standards (IEC 60099-4, 2014;IEC 60099-5, 2000).

Surge arresters consist of a non-linear resistance which presents a very high impedance under normal operating conditions which is dramatically reduced when high overvoltages appear across its terminals. This property is represented by their respective voltage-current (V-I) characteristic, such as the one shown in Figure 1.4, which illustrates their performance under normal and transient conditions. In particular, some of the most relevant concepts concerning surge arresters are defined below:

 U c (continuous operating voltage): maximum voltage that can be continuously applied to a surge arrester without any type of restriction.

 U r (rated voltage): typically defined as the voltage that can be applied to the arrester during 10 seconds; it characterizes the capability of the arrester to deal with temporary overvoltages (TOV) in AC.

 SIPL (Switching Impulse Protective Level): residual voltage that appears across the arrester when a switching impulse current flows through it (typically with the 30/60 µs impulse shape (IEC 60099-4, 2014) at 1 kA or 2 kA nominal discharge current).

 LIPL (Lightning Impulse Protective Level): residual voltage that appears across the arrester when a lightning impulse current flows through it (typically with the 8/20 µs impulse shape (IEC 60099-4, 2014) at 10 kA or 20 kA nominal discharge current). The general procedure for the selection of surge arresters is recommended in IEC 60099-5, and consists of the specification of each of the above parameters (i.e. U c , U r , SIPL and LIPL) by taking into account the energy absorption level of the surge arresters, in order to avoid thermal failure.

These surge arrester parameters are specified by the constructor by applying standard current waveshape and measuring the voltage that appears across the surge arrester (which is referred to as the residual voltage of the arrester). For instance, the LIPL is measured as the residual voltage that appears when a 20 kA, 8/20 µs current waveshape is applied to the arrester. The constructor may specify the residual voltages for several peak currents with the 8/20 µs curve (e.g. 10, 20, 40 kA) which provides more points to model the V-I characteristic more precisely. Therefore, the reference value of the LIPL is obtained by choosing one of these points on the V-I characteristic. For high voltage applications, typically the 20 kA value is used as reference. A similar reasoning can be applied to the determination of the SIPL.

Since the TOVs are generally the most critical overvoltages for the surge arresters in terms of energy absorption (due to their long duration), AC arresters are often designed so that the rated voltage of the arrester (U r ) matches the maximum TOV of the system. Since the rated voltage U r can be described as the voltage level that the arrester can withstand during 10 s, this approach generally ensures that the arrester will not absorb great amounts of energy, and will only conduct significant currents during switching or lightning overvoltages. Then, it must be verified that the continuous operating voltage (U c ) of the arrester is higher than the maximum voltage under normal operating conditions, and finally, the values of SIPL and LIPL are determined.

As it will be seen in the next section, this is an iterative procedure. For a given initial design, several iterations may be required until an optimal design is obtained which fits the performance criterion and does not result in thermal overload of the surge arresters.

Insulation Coordination Procedure for AC Systems

The general procedure for insulation coordination can be now described as the selection of the highest voltage of the equipment together with a corresponding set of standard rated withstand voltages which characterize the insulation of the equipment needed for the application (IEC 60071-1, 2011). This procedure is illustrated in Figure 1.5 and can be explained through the calculation of four parameters: the representative voltages (U rp ), the coordination withstand voltages (U cw ), the required withstand voltage (U rw ) and the standard insulation level (U w ).

Representative Overvoltages, U rp

The first step is to perform a system analysis to assess the overvoltage classes and levels that could appear in the system due to the different overvoltage sources (see 3.2). This shall take into account the insulation characteristics and the protective levels of overvoltage limiting devices such as surge arresters.

This process leads to the estimation of the representative overvoltages of the system, U rp , for each voltage class. Representative overvoltages are defined as the overvoltages that, when applied to the insulation using the corresponding standard voltage shape (see Figure 1.3), are assumed to have the same effect as the actual overvoltage appearing in service conditions.

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Chapter 1: State of the Art and Literature Review Nicolas Manduley 2020 Page 18

Coordination Withstand Overvoltages, U cw

Coordination withstand voltages have the same shape as representative voltages (i.e. the standard voltage shapes shown in Figure 1.3). While representative overvoltages are the values producing the same stress on the insulation, the coordination withstand voltages refer to the minimum strength of the insulation which would satisfy the performance criterion (i.e. the risk of failure defined as tolerable) under in-site conditions. Hence, the coordination withstand U cw can be calculated by multiplying the representative overvoltage U rp by a coordination factor, which will depend on how the representative voltages were obtained.

Alternatively, by performing simulations of overvoltage events with the simultaneous evaluation of the risk of failure permits the direct determination of the U cw without calculating the U rp .

Required Withstand Voltage, U rw

When the minimum strength of the insulation satisfying the performance criterion is determined (represented by the coordination withstand U cw ), the next step is to adjust this strength to appropriate standard test conditions considering the actual in-service conditions. This is done by multiplying the U cw by a factor accounting for possible variabilities associated to the atmospheric conditions, the dispersion in the product quality, the installation, the ageing of the insulation and other factors that may be considered appropriate.

Rated Insulation Level, U w

Finally, after the minimum required insulation strength is calculated, the last step is to specify the standard withstand strength by selecting among the available existing values listed in the IEC 60071 standards for each voltage level. To do so, the chosen rated voltage shall be higher or at least equal to the required withstand voltage U rw calculated in the previous step for each voltage class.

All of the above process described in the previous paragraphs may lead to different insulation requirements depending on the initial conditions (e.g. surge arrester locations and specifications, insulation characteristics…) or the initial requirements (e.g. performance criterion) provided in the initial step. Throughout the process, one or more of these aspects may be modified to adjust the final design and find an optimal solution from a technical and economical point of view. Therefore, it can be concluded that insulation coordination is in itself a process of iterative nature, and several iterations may be required before reaching the final design.

Specificities of HVDC

Currently, the only available insulation coordination standard for HVDC applications concerns LCC-HVDC converters (IEC 60071-5, 2014). In this section, the fundamental differences between AC and DC regarding insulation coordination will be analysed, as well as how the insulation coordination philosophy has been adapted from the AC standards to DC in IEC 60071-5 taking into account the specificities of DC insulation coordination. Then, the particular differences between VSC-HVDC and LCC-HVDC transmission will be discussed, in order to explain how the general insulation coordination philosophy should be adapted for VSC-HVDC applications.

Main Differences with AC

According to the bibliographical study performed in this work, the fundamental differences between AC and DC regarding insulation coordination can be grouped into three main categories: pollution, voltage levels and pre-stresses and environmental factors. In this section, the most important aspects of each one are discussed, and an overall comparison is presented in Table 1.1 for AC and DC.

The knowledge of these differences will be of great use to understand how the insulation coordination principles from the AC standards should be transposed to DC. This will help to understand how these fundamental principles were transposed to LCC-HVDC, as well as to provide some hints on how they should be applied to VSC-HVDC systems in a future standard.

Some relevant references consulted to make this classification: (CENELEC 50341, 2012;CIGRE TB 158, 2000;CIGRE TB 518, 2012;CIGRE TB 72, 1992;Cortina et al., 1984;IEC 60052, 2002;[START_REF] Udo | Dc high-voltage sparkover characteristics of gaps and insulator strings[END_REF][START_REF] Watanabe | Influence of preexisting DC voltage on switching surge flashover characteristics[END_REF].

Pollution

One of the most influencing factors that differentiate AC from DC insulation coordination is the effect of pollution in the design of the overhead line insulators. Figure 1.6 illustrates the strong impact that pollution has on the calculation of the minimum insulation distances in HVDC whenever line insulator strings are present, while in HVAC switching overvoltages are typically the determining parameter. The contaminating process is determined by the force that brings the contaminant particles towards the insulator surface (CIGRE TB 158, 2000). This force is the result of the combined effect of the wind, gravity and electric field, as shown in equation (1-2):

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

𝐹 𝑝 ⃗⃗⃗ = 𝐹 𝑤 ⃗⃗⃗⃗ + 𝐹 𝑔 ⃗⃗⃗ + 𝐹 𝑒 ⃗⃗⃗ (1-2)
where F p is the resulting force F w is the force due to wind F g is the force due to gravity F e is the force due to the electric field. For electrically charged particles, it is the electrostatic force. If the particle is not electrically charged, it represents the dielectrophoretic force 1 For AC voltages, wind is the dominating factor for wind speeds between 2 and 3 m/s and above. For lower wind speeds, gravity is the dominating factor. Electrophoretic force is weaker than the former two. For DC voltages, however, the electrostatic force is the dominating factor in the pollution accumulation (CIGRE TB 518, 2012;[START_REF] Watanabe | Influence of preexisting DC voltage on switching surge flashover characteristics[END_REF]. In this case, high wind speeds could even moderate the rate of accumulation of the contaminants as it moves them away from the electric field produces by the DC energization. Compared to AC, the rate of 1 Force that is exerted on a dielectric particle when subjected to a non-uniform electric field pollution deposit in DC can be up to 10 times higher (CIGRE TB 518, 2012) and generally represents a more serious situation for DC systems than for AC (X. Li, Zhou, He, & Wang, 2017).

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

In addition to the higher rates of accumulation of pollution, the fact that the insulator strings are subjected to a constant DC voltage also affects the flashover mechanism of the insulator.

Experimental studies have shown that under DC voltage the arc propagation across the surface of the insulator differs from that under AC energisation (CIGRE TB 518, 2012). In general, the arc tends to propagate along the surface of the insulator, and after the first ignition is produced, the arc may "jump" between the sheds across the air. This is less likely to happen in AC because the arc needs to reignite after each zero-crossing of the voltage, and thus there is less time for these jumps to occur. Conversely, since in DC there is no zerocrossing of the voltage, arcs are more likely to propagate through the air jumping across the sheds, as shown in Figure 1.7 (left). This effect is magnified when combined with the formation of dry bands due to the nonuniform accumulation of pollution and/or wetting of the surface of the insulator. The lower conductivity of such dry bands may produce small jumps along some sections of the surface of the insulation, thus reducing the effective creepage distance before the first ignition. The flashover process due to pollution including the presence of dry bands is illustrated in Figure 1.7 (right).

As a result of the increased attraction to contaminants, the variation in the flashover mechanism, and the formation of dry bands along the surface of the insulator, the overall design of DC insulators differs significantly from that of AC insulators. Some of the most remarkable differences are:

 Considerably longer strings are required to compensate the reduction of the effective creepage distance;  Different shed profiles (as well as the spacings between the sheds) may be used to minimize the accumulation of pollution on the surface of the insulator, optimize the pollution flashover performance (by reducing the probability of "jumps" to occur between the sheds due to the difference in the flashover mechanism seen in Figure 1.7) and minimize risks of ageing of the insulator;

 The use of different surfaces and materials such as polymeric housings for ceramic insulators, composite insulators, hydrophobicity transfer materials (HTM), application of grease or coatings, etc. to improve the flashover performance under wet and polluted conditions;

 Larger shed diameters are usually required.

Consequently, the design of HVDC insulators is mainly based on the pollution performance, as illustrated in Figure 1.6 above. In this respect, several factors must be taken into account for the specific project, such as the type(s) of pollution present in the region, the climate (tropical, dry, desert, etc.), the mechanisms of accumulation of the contamination (e.g. wind, rain, electrostatic forces…), wetting mechanisms (e.g. condensation, precipitation, hygroscopic behaviour of the contaminants…) to determine the shapes, materials and lengths of the insulator strings.

Voltage Levels and Pre-Stresses

The effects of the continuous application of an AC or DC voltage on the dielectric strength have been tested and reported for different gap distances, geometries and voltage levels in (CENELEC 50341, 2012;CIGRE TB 72, 1992;Cortina et al., 1984). It has been found that there are significant differences in the dielectric strength depending on the shape and polarity of the voltage. The influence of AC or DC pre-stresses on the dielectric strength of air gaps and insulators have also been assessed and are discussed briefly below.

For plain air gaps under AC, the breakdown voltage presents a logarithmic behaviour as the length of the gap increases (see Figure 1.8). For a rod-plane configuration, the gradient varies approximately from about 500 kV peak /m for a 1 meter gap, to about 325 kV peak /m for a 5 meter gap (CIGRE TB 72, 1992). Under DC stresses, however, the behaviour appears to be consistently linear with the distance, with a minimum gradient slightly lower than 500 kV/m for a rod-plane configuration with positive polarity and wet environmental conditions (see Figure 1.9). A design value of about 400 kV/m is thus considered as conservative for the design of air clearances in DC. When insulators are considered, a strong reduction in the strength is observed for both AC and DC energised insulators under rain, while under dry conditions, only a slight variation is produced on DC insulators compared to the strength of an air gap.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

In case of voltage impulses (i.e. switching and lightning surges) applied with pre-existing stresses, little to no variation of the strength seems to exist for AC pre-stresses in general (except for insulators under polluted conditions). Moreover, the effect of pre-existing DC stresses only seem to be significant for wet insulators (clean or polluted) under switching and lighting impulses (see Table 1.1).

However, it is very common to install arcing horns in parallel with the insulators (e.g. for line insulators) to protect them from discharges along the surface or through the interior of the insulating material. In such cases, insulators may be considered to behave as the corresponding air gap represented by the arcing horns, where no significant variations are observed. For more details, consult Table 1.1 below.

Environmental Factors

Finally, some environmental factors may also have slightly different effects in DC compared to AC. For instance, the deposit of snow in the surface of the insulator may result in withstand voltages much lower than under dry and clean conditions, and seems to be especially constraining in DC [START_REF] Udo | Dc high-voltage sparkover characteristics of gaps and insulator strings[END_REF]. The wind, as explained in §4.1.1, is the main mechanism behind the accumulation of pollution in AC insulators. In the case of DC insulators, it might attenuate the accumulation of pollution by countering the effect of the electrostatic field.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Additionally, some particular considerations are made regarding the temperature, air density and humidity correction for AC (CENELEC 50341, 2012;IEC 60052, 2002) and DC [START_REF] Watanabe | Influence of preexisting DC voltage on switching surge flashover characteristics[END_REF]. However, it is not clear whether these approaches would produce a significantly different effect in DC compared to AC. Page 26

DC Insulation Coordination (IEC 60071-5)

The principles of insulation coordination for transmission based on Line Commutated Converters (LCC-HVDC) are explained in the IEC 60071 standard, part 5, and currently it is the only existing standard addressing insulation coordination in DC. The proposal of this dissertation is to apply the same philosophy to MMC-HVDC systems. Therefore, this section presents the fundamental principles and procedures for insulation coordination of LCC-HVDC which will be of use in the next section-and in more details in Chapter 3-to identify the factors that need to be taken into account to adapt the philosophy to MMC-HVDC systems.

Fundamental Principles

The overall philosophy presented in the AC standards remains essentially unchanged, and is based on the estimation of the representative voltages U rp , coordination withstand voltages U cw , required withstand voltage U rw and the standard required withstand voltage U w . The general objectives of insulation coordination, as well as the definitions of the different voltage and overvoltage classes (and standard shapes) remain the same as for AC systems (see §3).

The main differences compared to AC insulation coordination concern the following aspects:

 The installation of surge arresters across longitudinal sections due to the presence of series-connected valve groups (while in AC systems, surge arresters are installed almost exclusively between the phase and the ground).

 Design of the surge arresters in terms of energy handling capability (arresters are used to limit temporary overvoltages (TOV), which is very uncommon in AC).

 The specific topology of the converter circuits, as well as their respective operating modes (see Figure 1.10).

 The presence of reactive power sources and/or filters on both the AC and DC sides.

 Applications involving long overhead transmission lines and/or cables without intermediate switching stations.

 The presence of converter transformers with the converter side not directly connected to the ground, and a DC offset in some cases (e.g. bipolar configurations).

 The presence of composite voltages (e.g. power frequency voltage with a DC offset) within the converter due to the operation of the thyristor valves.

 Control malfunction of the thyristors.

 Voltage polarity of DC stress (i.e. effects of pollution, voltage levels and environmental factors, see previous section)

 Interactions between the AC and DC systems.

 The fact that no standard insulation levels exist for DC systems.

 The definition of a new overvoltage shape is defined as a kind of fast-front overvoltage caused by earth faults in the HVDC converter station with a front time between 3 ns and 1.2 µs.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 1: State of the Art and Literature Review

As for AC, insulation coordination for LCC-HVDC systems is an iterative process by nature. The procedure can be explained through the fundamental scheme shown in Figure 1.11. In this scheme, all the components of an LCC-HVDC station are represented including the AC side, DC side, converter station and all the locations where surge arresters may be installed according to the particular configuration and design. The different switches allow representing the possible operating modes of the station such as bipolar with or without metallic return. To select the surge arrester arrangement, three fundamental principles are to be considered:

 Overvoltages generated on the AC side should be limited by arresters on the AC side.

 Similarly, overvoltages generated on the DC side or earth electrode should be limited by arresters on the DC side (DC bus/line/cables, converter arresters, neutral arresters).

 Critical components should be directly protected by arresters connected close to the components.

By considering these principles (after establishing the system topology, configuration, operating mode, etc.), a surge arrester arrangement can be proposed and the insulation coordination procedure can be initiated.

Procedure

After considering all of the above described particularities and principles of LCC-HVDC insulation coordination, the actual procedure remains very similar to that of AC (refer to §3.4).

Representative voltages U rp are defined identically as for AC (see §3.4), but a particular application of this concept to DC is to consider them as equal to the protection levels of the surge arresters for directly protected equipment. If such voltages are the highest value for reasonable contingencies, the coordination withstand voltage U cw may be taken as equal to U rp . This can be achieved through electromagnetic transient (EMT) simulation software by considering all the relevant overvoltage conditions that may occur in the system.

Similarly as for AC, the required withstand voltages U rw are determined by multiplying the corresponding coordination withstand voltages (U cw ) by a factor including altitude correction (K a ) and a safety factor (K s ). Minimum reference values K s are given in IEC 60071-5-for altitudes below and up to 1000 m-as the minimum ratio between U rw and the protective levels of the arresters for switching, lightning and steep-fronts (SIPL, LIPL and STIPL, respectively) for each type of equipment present in the station. If the minimum values are used, it is assumed that surge arresters are placed directly between the terminals of the protected equipment.

The procedure is repeated in a similar way as illustrated by the flowchart in Figure 1.5 until an optimal solution is found, including the parameters of the surge arresters and their energy duties.

VSC-HVDC: Modular Multi-level Converter (MMC)

Even though both Voltage Source Converters (VSC) and Line Commutated Converters (LCC) are HVDC technologies and several of the insulation coordination principles from IEC 60071-5 can be directly applied to VSC-HVDC systems, there are some fundamental differences between both kinds of converters that should be taken into account. In this section, the differences between LCC-HVDC and VSC-HVDC transmission will be discussed. Then, a basic description of the Modular Multi-level Converter (MMC) is provided, which is the type of converter that concerns most of the HVDC applications of VSC. The main differences derived from the commutation principle are:

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

 VSC does not require a voltage source in the AC system, while LCC depends on the AC grid for the commutation process.

 VSC can be controlled to generate or absorb reactive power as required and independently from the active power control, while LCC always consume reactive power for the commutation process.

 VSC does not have major requirements on the ratio between the short circuit power at the connection point and the DC power of the transmission (i.e. short circuit ratio, SCR), while LCC may incur in voltage stability below a certain value.

 LCC generates harmonics of the order of 6n ± 1, where n is the number of 6-pulse bridges in the configuration (for example, Figure 1.11 features a 12-pulse bridge), and thus harmonic filters are required. VSC can operate at frequencies in the order of kHz, which allows the harmonic generation to be compensated. Hence, VSC may not present significant (if any) filtering requirements.

 During an AC system fault, VSC can continue to transfer active power, depending on the severity of the fault, while LCC might suffer a commutation failure and interrupt the power transmission.

Regarding the source type, the following differences are derived:

 Power flow reversal in LCC is only possible by reversing the voltage polarity of the system (because the current direction cannot be changed). Therefore:

o Low cost extruded polymeric cables cannot be used in LCC (because polarity reversal is not allowed in such cables).

o In a multi-terminal DC (MTDC) configuration, a polarity change of the DC voltage would mean a power flow reversal of the whole grid; hence, multiterminal HVDC configurations become complex with LCC technologies. Conversely, the power flow reversal in VSC technologies is achieved by reversing the current and maintaining the voltage constant, which makes this technology more suitable to build MTDC grids.

 In case of DC system faults, LCC can easily limit the fault current, and effectively disconnect the converter by blocking the thyristors. In VSC, this is only possible if full-

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 1: State of the Art and Literature Review bridge submodules are used. VSC with half-bridge submodules-which is the most common configuration-will allow the DC current to flow to the fault through the free-wheeling diodes even if the IGBTs are blocked.

Therefore, the main differences between AC and DC regarding insulation coordination-in the context of VSC-HVDC converters-remain the same as those listed in §4.1, except for: filtering requirements (little to none), control malfunction of the thyristors (redundant IGBT modules and higher frequency operation allow to limit overshoots and possible distortions due to errors in the commutation) and interactions between AC and DC systems (as VSC transmission is less dependent on the AC side of the system).

Basic Description of the Modular Multi-level Converter (MMC)

The MMC is a type of VSC that has been gaining increasing attention since its development (Marquardt, 2001), especially for HVDC applications. It consists of a series of cascaded submodules, each containing a power cell with a capacitor and a switch arrangement (see Figure 1.12). The switch arrangement consists-in the case of a half-bridge scheme, as shown in the figure-of two IGBTs with an anti-parallel diode controlled with complementary signals, whose state determines if the capacitor is connected or bypassed with respect to the total array of capacitors of the converter arm 2 (Kouro et al., 2010). In case of failure, the converter is blocked by turning off both IGBTs on all the modules, which allows the current to circulate freely through the diodes 3 . 2 Arm: converter section consisting of the cascaded power cells (or submodules) and reactors between the DC pole and the AC side of the converter. Two arms constitute one leg. Conventionally, there is one leg (two arms) for each AC phase. 3 In reality, when the converter is blocked, the diodes are bypassed by thyristors for current withstand.

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Under normal conditions, the capacitors can be considered as ideal voltage sources, and the MMC control determines how many capacitors are connected in series for each arm. Therefore, the total DC side voltage is the sum of all the capacitor voltages in one leg.

Since the output voltage waveform can be produced with a very large number of individual capacitors (up to a few hundreds), it is possible to operate the submodules with a very low switching frequency and with a minimal harmonic distortion due to the small variation rate of the voltage at each step and low ripple (Du, Dekka, Wu, & Zargari, 2017). This not only makes the MMC suitable for a very wide range of voltage levels, but also reduces drastically the need for harmonic filtering, which is an important drawback of LCC-HVDC systems.

Principles and Challenges of Overvoltage Protection

Even though the MMC overcomes many of the drawbacks of LCC-HVDC systems (i.e. harmonic generation and filter requirements, reactive power control, dependence on the AC system and flexibility of power flow reversal in MTDC schemes), there are several aspects that need to be assessed in terms of insulation coordination that are bound to differ significantly from the LCC approach from IEC 60071-5. Based on the different issues addressed in this section, some of the main differences between LCC and VSC regarding insulation coordination are listed below:

 Architecture of the converter (and associated equipment)

 Location and design of the surge arresters

 Internal converter faults  Overvoltage levels
In addition, to this date LCC-HVDC systems concern almost exclusively bipolar configurations (or asymmetric monopolar with a future extension to bipolar planned). For VSC-HVDC systems, the use of symmetric monopoles is becoming more common, and in some cases, two parallel symmetric monopoles might be preferred over a single bipolar configuration (see Figure 1.10).

These aspects, along with the overall differences between AC and LCC listed in §4.2 (except for those previously discussed that do not concern VSC) are thus expected to constitute the main challenges of overvoltage protection of VSC-HVDC systems.

Lightning Overview

Generalities

Lightning consists of a high-current electric discharge in air which can be produced inside a cloud, between clouds or between a cloud and the ground or other objects in the atmosphere (CIGRE TB 549, 2013). They are the result of the accumulation of charge in the clouds when the electric field between the two (or more) regions involved reaches a critical value in which the air becomes ionized and a lightning channel is formed. As a result, electric charges flow from one region to another, and the charge distribution is rebalanced. Because of the potentially high effects that such events can have in the electric grid, it is of particular interest to accurately describe the nature of lightning so that it can be adequately represented for the purposes of lightning studies. Since this mainly concerns discharges to the ground, the following sections will focus on this kind of lightning discharge.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

As defined in CIGRE TB 549, the term "lightning strike" refers to lightning discharges involving an object on ground or in the atmosphere, while "stroke" refers uniquely to components of cloud-to-ground discharges. This section discusses the essential mechanisms behind the formation of lightning strokes and their classification which will be of use in further sections and chapters.

Electrisation of the Clouds and Lightning Classification

Stormy clouds are characterized by the presence of huge water masses (in the form of steam, droplets, ice crystals, hail, etc.) along with strong warm and cold air currents producing winds which can reach velocities of more than 100 km/h. The intense activity in the cloud produces, through complex meteorological processes not yet fully understood (Cooray, 2014), the separation of electric charges in such a way that water droplets get negatively charged and ice crystals (or flakes) get positively charged. Because of the difference in density of liquid and solid water, the water droplets with the negative charge tend to accumulate in the lower part of the cloud due to the action of gravity, while the positive charges tend to accumulate in the upper part of the cloud.

As a result, most (about 90% as per CIGRE TB 549) of the discharges between the clouds and the ground consist of negative charges flowing from the cloud to the ground (also referred to as a negative strokes). However, lightning strokes between the ground and the positive region of a cloud are also possible (i.e. positive strokes), as well as for lightning channels to form from the cloud to the ground and vice versa (i.e. downward and upward strokes, respectively). This classification is illustrated in Figure 1.13.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Characterization of the Lightning Currents

The charge transfer between the cloud and the ground can occur in three main modes: dart leader/return stroke sequences, continuing currents and M-components (CIGRE TB 549, 2013).

After the lightning channel is produced, a first stroke occurs. In the case of a negative downward lightning stroke, this means that negative charges are transferred from the cloud to the ground. The return stroke follows the same path, but transfers positive charge from the ground to the cloud, thus neutralizing the charge of the leader (CIGRE TB 549, 2013).

If additional charges are still present at the upper part of the channel, a continuous additional arc-a dart leader-can propagate, thus forming a subsequent stroke [START_REF] Xémard | Modélisation électromagnétique des effets de la foudre sur les réseaux d'énergie électrique[END_REF].

Negative strokes are typically composed of 3 to 5 strokes, though the largest recorded number of subsequent stokes is 26 as per (CIGRE TB 549, 2013).

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Nicolas Manduley 2020 Page 37

The continuing currents are a quasi-stationary arc of tens to hundreds of amperes between the cloud and the ground, and can last up to some hundreds of milliseconds. Finally, Mcomponents are perturbations in the continuing currents which produce variations in the luminosity of the channel.

Characterization of Regional Lightning Activity

The lightning activity of a region is typically characterized by the average number of flashes per unit of surface per year (e.g. flashes/km²/year), N g . For the purposes of lightning studies on the electric systems, only ground flashes are considered, and the parameter N g is referred to as ground flash density.

The value of N g can significantly vary from one year to another, which is why this value is characterized by an average of the measurements and estimations of the different systems.

An example of this is illustrated in Figure 1.15 for the region of North America (Orville, Huffines, Burrows, & Cummins, 2011), where significant variances are observed between the yearly mean values of N g for the period between 2001 and 2004. Furthermore, there are different methods to estimate the value N g , including lightning flash counters (LFC), lightning locating systems (LLS), and satellite-based optical or radio-frequency detectors (CIGRE TB 549, 2013). Each method introduces different levels of uncertainty, which may come from the sensitivity of the sensors, non-detection of a lightning event, confusion between first and subsequent strokes or the non-ability to distinguish between inter or intra cloud flashes and ground flashes [START_REF] Xémard | Modélisation électromagnétique des effets de la foudre sur les réseaux d'énergie électrique[END_REF].

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Based on the value of N g , it is possible to estimate the lightning incidence N L for a transmission line as shown in equation (1-3) below (as indicated in CIGRE TB 63)

𝑁 𝐿 = 𝑁 𝑔 ( 28 𝐻 𝑇 0.6 + 𝑏 10 ) (1-3)
where:

Lightning Waveshapes of Negative Downward Strokes

To perform lightning studies, it is of interest to study the waveshape and relevant parameters to adequately model lightning strokes. This has been done by gathering and analysing data from several measurements, and current models rely on this data for the modelling and representation of lightning strokes. Since most of the gathered data comes from recordings of downward negative strokes (see §5.2), the representation presented in this section concerns only this type of strokes (which is also the most common type).

It has been found that a downward negative lightning stroke can be characterized by four main parameters: the peak current, the front time (t f ), the maximum steepness (S m ) and the tail or time to half value (t h ). These parameters are illustrated in Figure 1.16 and discussed in the following sections. Lightning data obtained through different measurements have been already analysed and comprehensibly summarised [START_REF] Anderson | Lightning parameters for engineering application[END_REF][START_REF] Berger | Parameters of lightning flashes[END_REF]CIGRE TB 63, 1991). This allows to make statistical estimations of each of the parameters displayed in Figure 1.16 for an approximate representation of a lightning stroke. Even though more recent measurements are available, it is still recommended in CIGRE TB 549 to use the data presented in CIGRE TB 63 which is based on 408 measurements of lightning currents from heights inferior to 60 m. The following sections aim to describe the distributions of each of these parameters based on the gathered data, as well as the correlations between them. As it will be seen, these correlations provide a way to estimate, from a given peak current I F , the rest of the parameters required to model the lightning stroke using the CIGRE concave shape model (Figure 1.16), which is convenient when performing lightning studies where several peak currents have to be applied to the system.

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Chapter 1: State of the Art and Literature Review Nicolas Manduley 2020 Page 40

Peak Current (I F )

As a result from the above mentioned measurements, it has been found that the distribution of lightning peak currents may be represented by a log-normal approximation as defined below:

𝑓(𝑥) = 1 √2𝑛 β x 𝑒 -𝑧 2 2
(1-4)

and

𝑧 = ln 𝑥 𝑀 𝛽 (1-5)
where M is the median parameter value; β is the logarithmic standard deviation;

x is the parameter to be represented by this distribution (CIGRE TB 63, 1991). For negative downward first strokes, which represent the majority of the cloud-to-ground discharges (about 90% as per CIGRE TB 549), the distribution of the peak currents is characterized by the parameters M = 31.1 kA and β = 0.484 for the distribution shown in equations (1-4) and (1-5). For convenience, this distribution is often split in two ranges: the shielding failure domain (below or equal to 20 kA) and the back-flash domain (above 20 kA). The parameters corresponding to each of these domains are summarized in For subsequent strokes, there seems to be no correlation with the first stroke, but they tend to be lower regarding the peak amplitudes (about 40% on average), though for lower peak amplitudes in the shielding failure domain, sometimes the amplitude of the subsequent stroke can be higher than that of the first stroke (CIGRE TB 63, 1991). The resulting distribution is characterized by M = 12.3 kA and β = 0.53.

In the case of positive strokes, there is a very limited number of recordings, which makes it difficult to make a recommendation regarding their peak current distribution and associated parameters. However, since the frequency of this type of discharge is relatively low (roughly 10% of the total number of discharges to the ground, as per CIGRE TB 549), it is recommended in (CIGRE TB 63, 1991) to disregard these events in normal lightning performance studies. The

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Chapter 1: State of the Art and Literature Review Nicolas Manduley 2020 Page 41 impact of positive strokes may be greater when dealing with very tall structures (about 200 m) or regions with frequent winter thunderstorms, where the incidence of positive strokes may be higher.

The distribution of the peak currents based on the gathered data for CIGRE and IEEE approaches is illustrated in Figure 1.17 below. A simple alternative method has been provided by Anderson, which is shown in equation (1-6) below. This equation provides very similar values to those obtained by integrating the expression from equation (1-4) for the current peak amplitude.

𝑃(𝐼 ≥ 𝐼

𝑓 ) = 1 1 + ( 𝐼 31 ) 2.6
(1-6)

Front Time (t f )

First stroke currents typically start with a concave front followed by an abrupt rise around the half peak, after which the maximum steepness (S m ) is reached, followed by the peak current value. Different definitions of the front time are found in (CIGRE TB 63, 1991), but the one that is recommended for lightning studies is given by the time interval between the instant of the

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Chapter 1: State of the Art and Literature Review Nicolas Manduley 2020 Page 42 maximum peak and the intersection with the horizontal axis of the line crossing the 30% and 90% of the peak current (blue line in Figure 1.16), which is noted as t f .

The front time is also approximated by a log-normal distribution with the parameters indicated in Table 1.3. As it can be observed, the same parameters are recommended for all cases including both current ranges of first strokes, as well as subsequent strokes.

Log

Maximum Steepness (S m )

After the initial concave front and the abrupt rise above mentioned, a point of maximum steepness (i.e. maximum rate of rise of the current) is reached and is specified in kA/µs. It is graphically represented in Figure 1.16 (red line) and its log-normal representation is given by the parameters shown in Table 1.4 for first and subsequent strokes.

Log-normal parameters of t

Time to Half Value (t h )

After the peak current value is reached, the lightning current starts to decrease slowly. This decrease is parametrized by the time to half value t h , or tail time, which specifies the total duration of the stroke until it falls down to 50% of the peak current. For about 90% of the strokes, the tail time can range between 30-200 µs for first strokes and between 6.5-140 µs for subsequent strokes (according to the 408 measurements from CIGRE TB 63).

However, it has been stated that the exact value of the tail time does not have a significant impact on the lightning performance, and the use of the median values is recommended. The median values of the tail time for first and subsequent strokes are 77.5 µs and 30.2 µs, respectively.

Correlations and Derived Statistics

The correlations between the parameters discussed above and the peak currents have been also studied. Through these correlations it has been possible to derive expressions to estimate the values of t f and S m using the value of the peak current I F (CIGRE TB 63, 1991), which is

Foundations of the Determination of the Impact Point

In addition to the modelling of the currents, it is also important to estimate the impact point of the lightning stroke, as it will have a direct effect on the lightning performance whether it hits a tower (or a shield wire) or a power conductor, as it will be discussed later in §6.1.

There are several methods to determine the impact point of a lightning stroke, and they are based on the concept of lightning attachment. The most relevant methods can be grouped into four main classes: electrogeometric models (EGM), leader progression models (LPM), statistical models and fractal models. These methods are presented and explained in CIGRE TB 704 (CIGRE TB 704, 2017), and they differ mainly on their respective representation of the lightning attachment process.

Electrogeometric models (EGM) provide a very simple approach to the estimation of the impact point, and are based on the principle of striking distance. However, these methods, along with statistical models, tend to fail to adequately represent the lightning attachment process for extra and ultra-high voltage levels (EHV and UHV, respectively) (CIGRE TB 704, 2017). For these voltage levels, leader progression models (LPM) and fractal models yield better approximations. Fractal models constitute a very complex approach which requires a huge amount of computational resources, while the uncertainties originated by the measurement or estimation of the ground flash density (which may be very significant, see §5.4) remain present in the modelling. Therefore, it is questionable whether these methods are viable for practical studies. While the rigorous application of LPM would also require significant computational resources (as it will be seen in the following sections), the application of regressions to the results obtained through the complete implementation of the LPMs over a range of values allows to obtain equivalent expressions (CIGRE TB 704, 2017;Cooray, 2014), similar to those obtained through EGMs and improved EGMs.

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For the reasons listed above, in this work only EGM and the simplified equivalent LPM models are addressed, so that an adequate representation of the lightning attachment process can be done while also keeping the approach as simple as possible. The following sections describe the fundamentals of lightning attachment, followed by the basic principles of EGM and LPM methods that will be of use later in this work to estimate the lightning performance of a system.

Lightning Attachment Principle

The following explanation has been partially extracted from (Cooray, 2014), where more details can be found regarding lightning attachment.

Consider a downward stroke. As the descending leader approaches the structure, the electric field at the grounded structure increases steadily. When this value reaches a critical value of about 3000 kV/m (i.e. the corona inception value), electron avalanches start being generated from the tip of the grounded structure. The electric field continues to increase, until a critical value of about 10 8 -10 9 V/m and the local electron avalanches are transformed into a streamer discharge (i.e. avalanche to streamer transition). When the charge at the streamer burst is high enough, the streamer to leader transition occurs, leading to the inception of the connecting leader. The connecting leader then starts growing towards the descending leader, and when the potential gradient between the tips of both leaders reaches a critical value of about 500 kV/m, the final jump occurs and both leaders connect, leading to the rapid neutralization of the stepped leader charge (i.e. a return stroke, see §5.3).

In the case of upward strokes, the process is very similar to the above described, except that they tend to occur when tall grounded structures are involved. In addition, typically several subsequent strokes take place when the leader initiated from the tall structure reaches the charge centre of the cloud.

It is clear from the above paragraphs that a correct representation of the lightning attachment involves the study and modelling of very complex processes and the computational cost can increase rapidly. The upcoming sections discuss the fundamental aspects of EGM and LPM which, as previously mentioned, provide a simple approach to represent the lightning attachment.

Electrogeometric Models (EGM)

Electrogeometric models are based on the concept of striking distance to represent, in a simplified way, the lightning attachment. The basic principles and assumptions of the electrogeometric models are:

 When a downward leader reaches a certain critical distance to the conductor, the inception of the upward leader occurs. It is assumed that the final jump between the tip of the descending leader and the grounded structure is produced when this distance is reached. This critical distance is defined as striking distance.

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 Only vertically descending leaders are considered.

The basic principle of the electrogeometric model is illustrated in Figure 1.18. The striking distance is represented as a radius around the conductors and noted r c , while the striking distance for the ground is represented as a vertical distance r g . As indicated in the figure, the relation between these parameters is given by equation (1-7):

𝑟 𝑐 = 𝐴 𝐼 𝐵 = 𝛾 𝑟 𝑔 (1-7)
Where A, B and γ are constants whose values are adjusted according to each implementation of the EGM, and I is the amplitude of the lightning current.

Then, the total exposure width D c of a conductor is defined as the horizontal distance between the limit of the protective radius (i.e. the striking distance) of the shield wire and the intersection between the striking distances of the conductor and the ground (see Figure 1.18). A leader descending vertically within this interval is assumed to strike the conductor. Similarly, leaders descending outside this interval, are assumed to strike either the shield wire or the ground, depending on which striking distance they intersect.

As it is represented in equation (1-7) above, the striking distances are proportional to the amplitude of the lightning current. As the amplitude increases, so do the striking distances, and the exposure width decreases until reaching a critical current amplitude value for which D c is equal to zero (Figure 1.19). This critical value is called maximum shielding failure current, and is noted as I msf . For current amplitudes equal or higher than I msf , it is considered that all strokes will terminate on the shield wires.

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𝐷 𝑐 (𝐼) = { 𝐴 𝐼 𝐵 [cos 𝜃 -cos(𝛼 + 𝛽)] 𝑓𝑜𝑟 𝐼 > ( 𝛾ℎ 𝑐 𝐴 ) 1 𝐵 ⁄ 𝐴 𝐼 𝐵 [1 -𝑐𝑜𝑠(𝛼 + 𝛽)] 𝑓𝑜𝑟 𝐼 ≤ ( 𝛾ℎ 𝑐 𝐴 ) 1 𝐵 ⁄ (1-8)
And

𝐼 𝑚𝑠𝑓 = [ 𝛾(ℎ 𝑠 + ℎ 𝑐 ) 2 𝐴(1 -𝛾 sin 𝛼) ] 1 𝐵 (1-9)
where α is the shielding angle; β is the angle of the perpendicular bisector of the isosceles triangle formed by the shield wire, the conductor and the intersection point of their respective striking distances (see Figure 1.20); h s , h c are respectively the heights of the shield wire and the power conductor To summarize, the application of the electrogeometric model consists on the determination of the striking distance, which is the distance at which it is assumed that the attachment of the descending leader and the grounding structure is produced. This is done through equation (1-7), where the parameters A, B and γ depend on the specific assumptions of each implementation of the electrogeometric model. A set of parameters from different authors of typically used models are given in Table 1.7. Finally, these values are used to estimate the total exposure width (D c ) and maximum shielding failure current (I msf ) as shown in equations (1-8) and (1-9), which will be required for the calculation of the SFFOR, as it will be explained in §6.4.2.

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A B γ

Armstrong & Whitehead 6.7 0.8 1.11 As a result of the comparison of models from different authors with recorded data, it has been found that the Armstrong & Whitehead (Armstrong & Whitehead, 1968a) relation fits well the recorded points (Cooray, 2014). E.R. Love's relation (Love, 1973) has also been proposed by IEEE WG as a model providing adequate mean values of the striking distance [START_REF] Report | Estimating lightning performance of transmission lines. II. Updates to analytical models[END_REF]. Throughout this research, whenever the EGM is used to model the lightning attachment process, these two implementations will be considered.

E.

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Leader Progression Models (LPM)

As discussed in the previous section, the electrogeometric model assumes that the lightning attachment is produced whenever a certain critical distance between the tip of the descending leader and the grounded structure is reached. This representation neglects many of the physics associated to the lightning attachment process, such as the formation of streamers from the grounded structure, their streamer to leader transition, and the upward leader propagation towards the descending leader until the final jump is produced and the channel is formed (CIGRE TB 704, 2017).

Leader progression models (LPM) make a more detailed representation which takes into account not only the upwards leader inception, but also its subsequent propagation and final connection to the downward stepped leader. In (CIGRE TB 704, 2017), five leader progression models considering the aspects above mentioned are described: Eriksson, Dellera & Garbagnati, Rizk, Becerra & Cooray and Vargas & Torres. They differ in their respective assumptions regarding the path of the downward stepped leader, the charge distribution along the leader, the criteria for the inception of the upward leader (and its influence on the downward stepped leader), the speed propagation and the final attachment criteria.

A complete implementation of LPMs shall consider three-dimensional models of the line and surroundings, in which the electric field is evaluated for each structure (i.e. the tower, the ground and different points along the span length of the conductors) for several random leaders forming from a certain height above the line. It is clear that such approach, considering all of the factors described above for each simulation step, would require a very significant amount of computational resources.

However, it is possible to simplify the approach by applying regressions over a range of values to obtain similar equations as those used for the EGM. In such expressions, not only the influence of the current amplitude on the equivalent radius, but also the height of the structure, as shown in equation (1-10).

𝑅 = 𝜉ℎ 𝐸 𝐼 𝐹 + 𝜁ℎ 𝐺 (1-10)
where R is referred to as the attractive radius or attractive distance (instead of striking distance for EGM), h is the height of the conductor and I is the current amplitude. The parameters ξ, ζ, E, F and G are the constants which are characteristic to each regression of the LPM model implementation.

From the LPM approaches mentioned above, such regressions have been performed by Rizk over current values between 5 -31 kA and conductor heights between 10 -50 m (F. [START_REF] Rizk | Modeling of transmission line exposure to direct lightning strokes[END_REF]. The associated parameters are shown in Table 1.8, along with the parameters resulting from similar regressions from other authors. In this research, the Rizk model will be used as the reference implementation of the LPM as it has been further tested and validated in more recent studies (F. A. [START_REF] Rizk | Modeling of UHV and double-circuit EHV transmission-line exposure to direct lightning strikes[END_REF][START_REF] Rizk | A simplified approach for assessment of exposure of EHV and UHV lines to direct lightning strikes[END_REF][START_REF] Rizk | Modeling of transmission line exposure to direct lightning strokes[END_REF].

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ξ E F ζ G Rizk 1.57 0.45 0.69 0 0 Borghetti 0.028 1 1 3 0.6
Cooray & Becerra 2.17 0.5 0.57 0 0 Similarly as for EGMs, the total exposure width (D c ) and the maximum shielding failure current (I msf ) are estimated by the following expressions:

𝐷 𝑐 (𝐼) = 𝜉(ℎ 𝑐 𝐸 -ℎ 𝑠 𝐸 ) + 𝜁(ℎ 𝑐 𝐺 -ℎ 𝑠 𝐺 ) + (ℎ 𝑠 -ℎ 𝑐 ) tan 𝛼 (1-11)
And

𝐼 𝑚𝑠𝑓 = [ (ℎ 𝑠 -ℎ 𝑐 ) tan 𝛼 -𝜁(ℎ 𝑠 𝐺 -ℎ 𝑐 𝐺 ) 𝜉(ℎ 𝑠 𝐸 -ℎ 𝑐 𝐸 ) ] 1 𝐹 (1-12)
where α is the shielding angle (as depicted in Figure 1.20); h s , h c are respectively the heights of the shield wire and the power conductor.

Stakes of the Estimation of the Overhead Line Lightning Performance

Origin of Flashovers due to Lightning Strokes

There are three main flashover mechanisms due to the impact of a lightning stroke on an overhead line: back-flashovers, shielding failure flashovers and mid-span flashovers (Westinghouse Electrical Transmission and Distribution Reference Book, 1964). However, the mid-span flashovers are insignificant compared to flashovers in the tower and may be neglected for most situations (CIGRE TB 63, 1991). In this work, only back-flashovers and shielding failure flashovers are addressed.

Back-flashovers occur due to the voltage increase of the grounded structure (i.e. the tower) until the voltage difference across the insulators reaches a critical value in which a flashover is produced. In the case of shielding failure flashovers, lightning strokes terminate directly on the power conductor, thus increasing its potential with respect to the tower which can eventually lead to a flashover.

In other words, the fundamental difference between back-flashovers and shielding failure flashovers relies on the striking point of the lightning stroke: on the tower (or shield wire(s), if present) for back-flashovers, and on the power conductors for shielding failure flashovers. The striking point depends on a number of factors, such as, for instance, the height of the conductors, the current intensity of the lightning stroke and the direction from which the lightning stroke approaches the line. The influence of each of these and other factors can be assessed through the representation of the lightning attachment process, which describes the different phases of the interactions between the downward or upward lightning flash and the grounded structure.

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The following sections discuss the general principle of lightning attachment, as well as more in-depth description of the mechanisms leading to each type of flashover mentioned above.

Back-Flashovers

When lightning strikes the tower structure or the shield wires, a portion of the current flows to the ground through the tower structure, while the rest is split in both directions of the shield wires, as illustrated by the green arrows in Figure 1.21. How much current is diverted in each direction depends mainly on the value of the footing resistance of the tower, which also has a major effect in the total voltage rise of the tower structure as the lightning current flows through it. The voltage rise of the head of the tower V(t) can be approximated in the form illustrated in equation (1-13) [START_REF] Xémard | Modélisation électromagnétique des effets de la foudre sur les réseaux d'énergie électrique[END_REF]:

𝑉(𝑡) = 𝐿 𝑑 𝑖(𝑡) 𝑑𝑡 + 𝑅 𝑔𝑛𝑑 𝑖(𝑡) (1-13)
where is the amplitude of the lightning current R gnd is the footing resistance of the tower Since the voltage across the insulator is the difference between the power conductor and the cross arm of the tower structure (as also illustrated in Figure 1.21), as the voltage of the tower rises, so does the insulator voltage. If the peak amplitude of the stroke is higher than some critical value, a back-flashover occurs.

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The value of the footing resistance depends mostly on the resistivity of the soil and the shape and geometry of the electrodes (Grcev, 2009). It determines the magnitude of the voltage rise of the tower due to the lightning current flowing to the ground. The higher the footing resistance, the higher the increase in potential of the structure, and therefore also across the insulators.

There are other factors that also influence the probability of a back-flashover to occur. For instance, the coupling between the conductors and the shield wires [START_REF] Sargent | Lightning performance of double-circuit transmission lines[END_REF], the length of the insulator strings (CIGRE TB 72, 1992;Cortina et al., 1984), the polarity of the impulse [START_REF] Strelec | Disparity in the lightning performance between the poles of the Cahora-Bassa HVDC lines[END_REF] and the voltage drops along the different sections of the tower structure [START_REF] Sargent | Lightning performance of double-circuit transmission lines[END_REF] may also play a role in determining the back-flashover risk.

As a result of the coupling between the conductors and the shield wires, the portion of the lightning current which is diverted in both directions of the shield wires induces a voltage in the neighbouring conductors. Because the induced voltage is proportional to the derivative of the current, it reaches its peak value at the instant of maximum steepness of the lightning stroke (see example of Figure 1.22 for a double-circuit HVDC system). The shorter the distance between the shield wire and the conductor, the greater will be the amplitude of the induced voltage. As it is observed in Figure 1.22, the induced voltage rises in the same direction as the tower structure, thus countering the voltage rise across the insulators. As a result, the conductors closer to the shield wires are less likely to flashover, since they are better protected by the coupling effect. For this reason, it is usually the lower poles which flashover first in case of direct strikes to the tower, similarly as for AC systems [START_REF] Sargent | Lightning performance of double-circuit transmission lines[END_REF].

Because the flashover occurs approximately when the breakdown voltage across the string is reached, the insulator string length also has a strong influence. Generally, line insulators are equipped with arcing horns so that whenever a flashover occurs, it does not occur over the surface or through the insulator itself, but through the air gap of the arcing horns. As a result, the breakdown voltage of the line insulator is "tuned" by the arcing horns. This is particularly relevant for HVDC systems where the insulator strings are generally longer than for HVAC systems (CIGRE TB 158, 2000;CIGRE TB 518, 2012), and thus the breakdown voltages tend to be higher. In the case of HVDC overhead lines, polarity of the impulse is of particular importance. In HVAC systems, at any given instant, a phase conductor could be at a positive or negative voltage value. This would ultimately determine the voltage difference across every insulator on the system, and they would change continuously according to the power frequency of the system. In HVDC systems, however, there are only constant positive and negative DC poles. Therefore, each DC insulator is more susceptible to flashover under a specific stroke polarity. Since about 90% of the strokes are negative (CIGRE TB 549, 2013;CIGRE TB 63, 1991), in most cases the voltage rise of the tower will be negative and thus, positive poles are generally more likely to flashover in HVDC systems. Additionally, the breakdown voltage of an air gap is lower under positive impulses than for negative impulses (CIGRE TB 72, 1992;Cortina et al., 1984), which would also influence the flashover risk to a certain extent.

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Finally, the voltage drops across the tower may also play a role in the lightning performance, especially for multi-circuit configurations such as the one depicted in the example of Figure 1.22 (right). In such configurations, the voltage drop between the upper and lower cross arm produces a difference between the voltages of the tower structure seen by each one, being slightly higher for the upper cross arm. However, as it is observed in Figure 1.22, this effect tends to be smaller than the difference produced by the coupling effect for most cases.

Shielding Failures

The purpose of the shield wires is to provide a protection to the phase conductors against lightning strokes. By placing them over the conductors, it constitutes a structure which is more

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Chapter 1: State of the Art and Literature Review likely to be struck by lightning (as per the lightning attachment principles described before) if leaders are developing close to the transmission line.

However, the protection provided by the shield wires is not perfect, and it is still possible for a power conductor to be struck by lightning. This phenomenon is referred to as shielding failure, as the lightning stroke bypasses the protection area of the shield wires and finds its way to the power conductor.

When a conductor is struck by lightning, a voltage wave starts to propagate from the impact point in both directions of the conductor, as illustrated in Figure 1.23. The amplitude V(t) of this wave is given by the following expression [START_REF] Xémard | Modélisation électromagnétique des effets de la foudre sur les réseaux d'énergie électrique[END_REF]:

𝑉(𝑡) = 1 2 𝑖(𝑡)𝑍 𝑐 (1-14)
where i(t) is the amplitude of the lightning current; Z c is the characteristic impedance of the conductor When this wave reaches the transmission tower, a flashover is produced if the amplitude is higher than the withstand voltage of the insulator between the tower and the struck conductor. This is thus referred to as a shielding failure flashover. When the flashover occurs, a significant portion of the current enters the tower, part of which flows to the ground and produces a voltage rise of the tower structure which depends strongly on the footing resistance. This, as well as other mechanisms associated to the shielding failure, will be addressed in more details in Chapter 4.

Significance of Lightning as a Source of Faults

Lightning is one of the most common causes of outages in transmission systems (CIGRE TB 704). Between 2002 and 2013, they represented from 36% to over 50% of the total transmission line outages in Malaysia [START_REF] Rawi | A case study and observation on cause of transmission line outages in Malaysia[END_REF], and between 53% and up to 83% of the outages in Japan between 1997 and 2012 [START_REF] Shindo | Lightning occurrence data observed with lightning location systems of electric power companies in Japan: 2009-2013[END_REF].

Moreover, there is generally a significant correlation between outages of short duration (between 1 second and 3 minutes) and the total incidence of lightning in a region. For instance, a summary of the average ground flash density (N g ) and short outages frequency of France is presented in Figure 1.24 for the period between 2010 and 2019. The data has been obtained from RTE's Electrical Report for 2019 (RTE, Bilan Electrique, 2019). As it can be observed, there is a non-negligible correlation between the lightning activity and the outage frequency, especially between the years 2010 and 2014 (Pearson correlation factor of about 0.85). Even though the correlation is less evident for the period between 2014 and 2019, this could be at least partially explained through the high variability of N g (as discussed in §5.4) and by the fact that the lightning density illustrated includes all ground flashes, which do not necessarily occur on or near a transmission line. Improvements on the lightning performance of the transmission line implemented through the years may also play a role.

Nevertheless, it is clear that moderate to high correlations can be found between the lightning activity and the total number of short outages of a region. This is also shown in Figure 1.25, which illustrates the average ground flash density and the average short outages per region in France for the year 2019 (also extracted from RTE, Bilan Electrique, 2019). It is observed that the short outage rates tend to be directly proportional to the lightning activity of each particular region.

Consequences of Lightning Flashovers on the Transmission System Performance

A flashover due to lightning can introduce disturbances at the delivery points of the transmission grid (i.e. distribution grid or industrial clients). These disturbances can be classified into three categories (RTE, Bilan Electrique, 2019; Xémard, 2008):

 Short outages, of which the duration of the voltage interruption is between one second and three minutes.

 Very short outages, of which the duration of the voltage interruption is inferior to one second.

 Voltage dips, which are short (usually less than one second) and temporary drops of the system voltage, which may cause malfunctions on some equipment connected to the grid, depending on their amplitude and duration.

Long outages (of a duration of more than three minutes) are never produced by faults originated by lightning. However, if the flashover occurs on an important or strategic line of the system, it could in some rare cases compromise the stability of the system [START_REF] Xémard | Modélisation électromagnétique des effets de la foudre sur les réseaux d'énergie électrique[END_REF].

Estimation of the Overhead Line Lightning Performance

The lightning performance is expressed as the average number of flashovers due to lightning expected to occur for a 100 km line segment over a year (flashovers/100 km/year). As discussed in §6.1, there are two types of flashovers that can arise due to lightning: backflashovers and shielding failure flashovers. The overall lightning performance of a system is given as the sum of both the back-flashover rates (BFOR) and shielding failure flashover rates (SFFOR). The following sections present the methods for the estimation of each of these flashover rates.

Back-Flashover Rate (BFOR)

The procedure for the calculation of the back-flashover rate (BFOR) is presented in (CIGRE TB 63, 1991) and has been developed for AC lines and negative downward strokes. The procedure is discussed below.

The first step consists of the estimation of the critical current amplitude I f . The current I f is defined as the minimum current amplitude for which a flashover occurs. It is thus assumed that strokes with equal or higher current intensities will produce a back-flashover across at least one of the insulators of the tower.

The next step is to estimate the probability of having a current amplitude equal or higher than the critical current I f , or P(I ≥ I f ). This is done by integrating the probability density function of the current amplitudes [obtained from equations (1-4) and (1-5)] between the considered value and infinite, which yields a distribution as the one shown in Figure 1.17 and equation (1-6).

It is also important to include the probability for a lightning stroke to impact the tower or the shield wire along the span (for lines equipped with shield wires). Since for an impact along the span the current is split in two, less current reaches the tower and thus back-flashovers are less likely to occur. A study presented in (CIGRE TB 63, 1991) shows that the effect of impacts along the span can be taken into account by multiplying the BFOR obtained as if all the strokes were produced on the tower, by a factor of 0.6. With this factor, the estimation remains conservative.

The BFOR is therefore calculated as shown in equation (1-15):

𝐵𝐹𝑂𝑅 = 0.6 𝑁 𝐿 𝑃(𝐼 ≥ 𝐼 𝑓 ) (1-15)
where N L is the lightning incidence for a transmission line; see equation (1-3);

P(I ≥ I f )
is the probability for a given current amplitude I to be equal or higher than the critical peak current I f ; see equation (1-6). It is worth mentioning that the 0.6 factor above mentioned seems to work properly for span lengths up to 300 m. For spans of 400-600 m, where the sag may be greater, factors in the order of 0.8 or more may be more appropriate [START_REF] Silveira | The Impact of the Distribution of Lightning Strikes along the Span on Backflashover Rate of Transmission Lines[END_REF]. Consequently, the use of the 0.6 factor on span lengths longer than 300 m might result in an underestimation of the back-flashover performance of the line.

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Chapter 1: State of the Art and Literature Review Nicolas Manduley 2020 Page 57

Shielding Failure Flashover Rate (SFFOR)

As discussed in previous sections, the protection of the shield wires is not perfect. There exists a probability that a downward leader bypasses the protection zone of the shield wires and strikes directly the conductors. Therefore, this probability is strongly influenced by the way in which the lightning attachment process is represented.

As discussed in §5.6, EGMs tend to fail to adequately represent the lightning attachment process when the system voltage reaches the domain of extra or ultra-high voltage (EHV and UHV, respectively). For this reason, for voltage ranges in the order of 345 kV and above, the simplified LPM approach will be preferred for the estimation of D c and I msf , which will be required for the estimation of the lightning performance under shielding failure.

Within this context, there are two relevant factors to be considered: the annual number of strokes to power conductors (i.e. shielding failures), and the number for such strokes to produce a flashover across the insulators of the conductors. These factors are given by the Shielding Failure Rate (SFR) and Shielding Failure Flashover Rate (SFFOR), respectively.

The SFR considers all the possible values for the current amplitude between zero and the maximum shielding failure current (I msf ). This accounts for all the strokes terminating on a power conductor over a year, whether they produce a flashover or not. The SFR is given in flashes/km²/year, and is calculated by the following expression, as indicated in (CIGRE TB 704, 2017):

𝑆𝐹𝑅 = 0.2 𝑁 𝑔 ∫ 𝐷 𝑐 (𝐼) 𝑓(𝐼) 𝑑𝐼 𝐼 𝑚𝑠𝑓 0 (1-16)
where N g is the regional ground flash density [flashes/km²/year];

I msf is the maximum current level that can produce a shielding failure; D c (I) is the total exposure width of the conductor as a function of the current amplitude;

f(I) is the probability density function of the current amplitude, as given by equation (1-4). A factor of 0.1 accounts for the conversion of D c from meters to kilometres, multiplied by one hundred (so that the output is given per 100 km of overhead line). By assuming that the exact same conductor configuration is found on the other side of the tower (i.e. the tower geometry is symmetric), the total SFR considering both sides is twice the SFR for one side, thus obtaining the factor 0.2 from equation (1-16).

Hence, solving the integral shown in equation (1-16) allows to estimate the probability for a flashover to occur considering all current levels between zero and the maximum level that could strike the conductor, I msf . For the estimation of the Shielding Failure Flashover Rate (SFFOR), however, an additional parameter has to be considered: the minimum shielding failure flashover current, which is the minimum current that, in case of striking the conductor, could produce a flashover across the insulator. This current is noted I c and it can be approximated by the following expression (CIGRE TB 63, 1991;CIGRE TB 704, 2017):

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

𝐼 𝑐 = 2𝑈 50 𝑍 𝑠 (1-17)
where U 50 is the critical flashover voltage (i.e. the voltage with 50% probability of producing a flashover across the insulator) Z s is the surge impedance of the conductor under corona The detailed procedure for the estimation of Z s , as well as a sensitivity analysis are presented in Appendix A. Some issues concerning its applicability on AC and DC systems are discussed in Appendix B.

Since it is considered that for any value below I c no flashovers occur on the struck conductor, the Shielding Failure Flashover Rate (SFFOR) is thus calculated similarly as for the SFR, but with the limits of the integral going from I c to I msf :

𝑆𝐹𝐹𝑂𝑅 = 0.2𝑁 𝑔 ∫ 𝐷 𝑐 (𝐼)𝑓(𝐼)𝑑𝐼 𝐼𝑚𝑠𝑓 𝐼 𝑐 (1-18)
where N g is the regional ground flash density; I c is the minimum flashover current; I msf is the maximum current level that can produce a shielding failure; D c (I) is the total exposure width; f(I) is the probability density function of the current amplitude. Therefore, the SFFOR is calculated in the same way as the SFR, but without considering the range of current amplitudes for which no flashovers can be produced across the insulators.

From the above definitions and from equations (1-16) and (1-18), it is clear that the SFR should always have a higher value than SFFOR. At this point, there are two approaches described in (CIGRE TB 704, 2017;IEEE Std. 1243, 1997) to specify the lightning performance:

a)
Using the SFR According to equation (1-17), a flashover does not occur if the lightning stroke current is less than the minimum shielding failure current, I c . However, this expression concerns only first strokes. As discussed previously in this chapter, first strokes are often followed by one or more subsequent strokes, and it has been observed that for low current amplitudes of the first stroke (approx. below 20 kA), the peak amplitude of subsequent strokes may be higher than that of the first stroke. Therefore, since for most overhead lines shielding failures are associated to relatively low first stroke current amplitudes, there could be subsequent strokes of higher amplitude that may be responsible for the flashover.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

By assuming that, even if the first return stroke is lower than I c , one or more subsequent strokes will exceed the value of I c , then the SFFOR is equated to SFR.

b)

Using the SFFOR Alternatively, the SFFOR expression given in equation (1-18) can be used to specify the lightning performance of the line regarding the first stroke, and the total SFFOR is obtained by adding an additional term SFFOR s to it, representing the rate of flashover due to subsequent strokes, which is expressed as:

𝑆𝐹𝐹𝑂𝑅 𝑠 = 0.2 𝑁 𝑔 𝑃 𝑠 ∫ 𝐷 𝑐 (𝐼)𝑓(𝐼)𝑑𝐼 𝐼 𝑐 0 (1-19)
where P s is the probability of flashover on any subsequent stroke given that no flashover has occurred with previous strokes. P s is estimated by assuming no correlation between first and subsequent return-stroke currents as (CIGRE TB 704, 2017;IEEE Std. 1243, 1997):

𝑃 𝑠 = ∑ 𝑃 𝑛 (1 -[1 -𝑃(𝐼 > 𝐼 𝑐 )] 𝑛-1 ) ∞ 𝑛=2 (1-20)
where P n is the probability that there are n strokes/flash from data in [START_REF] Anderson | Lightning parameters for engineering application[END_REF], and P(I > I c ) is the probability for a given current stroke amplitude to exceed I c .

On average, downward negative strokes are constituted by about 3.1 discharges, and only about 5% are constituted by ten or more discharges [START_REF] Anderson | Lightning parameters for engineering application[END_REF]. For a conservative approach, a maximum value of n = 10 is used in this work for the evaluation of P s in equation (1-20). P(I > I c ) is calculated by integrating the probability density function of subsequent strokes as given in equation (1-4), with the median amplitude M = 12.3 kA and logarithmic standard deviation β = 0.53 (see Table 1.2). Alternatively, an expression for P(I > I c ) similar to that provided for P(I ≥ I f ) in equation (1-6), is provided in (IEEE Std. 1243, 1997) as follows:

𝑃(𝐼 > 𝐼 𝑐 ) = 1 1 + ( 𝐼 12 ) 2.7
(1-21)

It has been found in this work that this latter approach (i.e. calculating the SFFOR for firststrokes and subsequent strokes separately and adding them together) may result, in some cases, in higher values of the total SFFOR than the SFR obtained through equation (1-16). Therefore, for more conservative results, this will be the preferred approach throughout this work. However, since the SFFOR cannot be greater than the SFR, in such cases the SFFOR will be considered as equal to the SFR.

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Chapter 1: State of the Art and Literature Review Nicolas Manduley 2020 Page 60

Limitations of the Presented Approach

Even though the approach above presented constitute a simple method to estimate the lightning performance of transmission line, and that it generally yields results which are coherent with the available experience (CIGRE TB 63, 1991;CIGRE TB 704, 2017), these results are often difficult to interpret [START_REF] Xémard | Modélisation électromagnétique des effets de la foudre sur les réseaux d'énergie électrique[END_REF]. The presented approach considers homogeneous lines, plain terrains or downward leaders descending vertically (thus in theory a negative shielding angle α would provide perfect protection to the conductor, which is not true in practice due to stepped leaders approaching horizontally or in an angle). Some approaches are proposed to modify these methods to take into account the inclination of the terrain (e.g. for mountainous areas) or for stepped leaders approaching in an angle, it is not yet clear whether a thorough application of electrogeometric models can actually yield accurate and realistic results. In addition, this approach is not suitable on its own for studies considering asymmetric configurations, non-linear devices (such as surge arresters) and multicircuit lines.

Even more, the lightning activity may vary according to the region, season and even from one year to another (represented by the value of the ground flash density, N g ), which is difficult to take into account properly. An additional uncertainty is also introduced by the fact that the parameters used to model the lightning currents are obtained using the median values of the data presented in CIGRE TB 63, gathered from different regions of the world. Therefore, a relatively high dispersion around the median value of each of these parameters may be expected in real strokes.

Despite these limitations, it is also important to highlight the key strengths of the presented approach, for it allows to compare quantitatively different solutions aiming to reduce the flashover rates of a given configuration by taking into account the current scientific knowledge on the nature of lightning. Moreover, some of the limitations evoked above-such as the line homogeneity, the presence of non-linear devices, asymmetric configurations and multi-circuit lines-can be compensated by combining it with electromagnetic transient (EMT) simulations, as it will be discussed in Chapter 2.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 2: Tools and Electromagnetic Modelling

Chapter 2 Tools and Electromagnetic Modelling

Introduction

As discussed in the previous chapter, one of the fundamental steps in the insulation coordination is the estimation of the overvoltage levels that can appear in the system due to faults, switching operations, lightning strokes, resonance, etc.

Electricity utilities make use of simulation programs which take into account the electromagnetic behaviour of the components and their interactions. The accuracy of the results depends directly on the accuracy of the models. In this research, EMTP has been used.

EMTP is a software program for the calculation of electromagnetic transients occurring in an electrical system, and is a broadly used tool for electrical system simulations. It includes a graphical user interface with a component library, based on which the user builds the system, and a calculation engine for computing load-flow, steady state and time-domain solutions (Mahseredjian, Dennetière, Dubé, Khodabakhchian, & Gérin-Lajoie, 2007).

EMTP allows solving both voltage and current distributions from the steady state to the high frequency transients region considering not only the main equipment, but also the control functions and non-linear effects and devices (e.g. surge arresters, transformer saturation).

Clearly, an appropriate modelling of the components, as well as a correct choice of their respective parameters, is required to obtain accurate results. This chapter addresses the modelling aspects regarding the system and components used in this work. The main goal is to provide a clear and comprehensive description of the choices that have been made to model each component of the system where EMT simulations have been performed to support the studies. This has been done after a detailed analysis of the literature, and the guidelines used here may be used as a guide for further similar studies.

Numerical Considerations

This section discusses the numerical considerations to be taken into account in order to obtain an accurate representation of the overvoltages present in the system using electromagnetic transient simulations. This includes issues related to the initialization of the system, time step choice, duration of the simulation, oscillations (of physical or numerical nature) and non-linear elements. These issues are explained in IEC 60071-4 and are briefly summarized below.

The solution of a transient phenomenon is dependent on the initial conditions with which the transient is started (IEC 60071-4, 2004). Therefore, it is important to ensure that the correct conditions are met when the transient event is simulated for analysis. The simplest approach to initialize the system in EMT-like simulations is to start the calculation and let the transients settle down to steady-state conditions. For cases where this approach may result in very long

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 2: Tools and Electromagnetic Modelling convergence times, a steady-state solution with non-linear branches disconnected (or linearized) can be performed beforehand. In EMTP there is a specific initialization procedure which is based on the performance of a multi-phase load-flow.

The selection of the time step relies on the consideration of two aspects: the frequency of the transient event to be studied, and the propagation elements present in the system. For a correct representation of the transients, a time step of one tenth of the period of the highest frequency transient is advised in IEC 60071-4. Regarding the propagation elements, the time step should be at least half of the total traveling time across the shortest element present in the system.

The duration of the simulation should be at least long enough for the maximum overvoltages to be recorded (as well as the specific transient phenomena under study, if other than just the overvoltages).

Oscillations may occur during the simulation, and they may be due to physical or numerical nature. In case of numerical oscillations, EMTP can switch from the trapezoidal integration method to the backward Euler rule for a few steps to eliminate the oscillations (Lin & Marti, 1990). In some specific cases, it is also possible to add damping resistances in parallel or in series with inductive and capacitive elements, respectively, causing the oscillations.

Non-linear elements must be represented by a large enough number of elements to produce credible results and avoid inaccuracies. As an example, Figure 2.1 illustrates a typical nonlinear V-I characteristic represented by three, four and six linear segments. It is observed that the greater the number of segments used to represent the characteristic, the smaller the error with respect to the true characteristic. Nevertheless, the points where the characteristic is not differentiable can still be a source of inaccuracies. This is due to the fact that when the transient forces the model to switch the specific segment, non-physical oscillations or numerical errors which are difficult to treat may appear.

Modelling Aspects

This section discusses the modelling aspects for each of the components considered in this research to guarantee that the conditions presented in this section are met for each case study.

Overhead Lines and Cables

Several models based on the line-theory exist for the representation of overhead lines and cables for transient simulations. Among them, the traveling-wave types can be considered the most important models implemented in EMTP, which allow representing the propagation of the waves produced by transient events such as faults, lightning strokes, switching operations, etc. Considering their respective characteristics and limitations (IEC 60071-4, 2004;[START_REF] Ramos | Wideband Line/Cable Models for Real-Time and Off-Line Simulations of Electromagnetic Transients[END_REF] which are explained below, the following line models are considered in this research: constant parameters (CP), frequency dependent (FD) and wideband (WB) models. Their main characteristics are explained below, and summarized in Table 2.1 along with their respective applications.

The CP model is obtained by assuming the transmission line model parameters R, L, G and C as constant (i.e. independent from the frequency). With this simplification, the time domain representation of the line model does not contain convolutions. As a result, the model is computationally efficient, but loses accuracy and tends to exaggerate transient phenomena [START_REF] Ramos | Wideband Line/Cable Models for Real-Time and Off-Line Simulations of Electromagnetic Transients[END_REF]. For multi-phase lines, the system is solved in the modal domain through a transformation matrix which is assumed to be real and constant. As it will be discussed in the following subsection, this model is well suited to represent the tower structure because it can be represented as a single line.

The FD model takes into account the frequency dependency of the line parameters, which results in a model that contains convolutions, and the transformation matrix is also assumed to be real and constant within the frequency range of study [START_REF] Ramos | Wideband Line/Cable Models for Real-Time and Off-Line Simulations of Electromagnetic Transients[END_REF]. As a result, this model provides a more accurate representation of transient events for many multiphase lines, such as typical overhead lines, but is not well suited for cases with frequency dependence of the transformation matrix (e.g. underground/submarine cables).

The WB model solves the issues of configurations with strong frequency dependence of their parameters, such as underground or submarine cables, by formulating the line directly in the phase domain. The modes are calculated in order to accurately establish the parameters of

Transmission Towers

For slow-front overvoltages (and lower frequency studies), the equivalent capacitance of towers is negligible compared to the capacitance of the lines. Only high frequency studies require a more detailed representation of the tower (i.e. lightning studies, fast-front overvoltages). For such cases, transmission towers are constituted by two main parts: the grounding and the tower structure.

Tower Grounding

The grounding of the tower concerns the representation of the electrodes that connect the tower structure to the ground. Different tower grounding schemes for lightning currents are available which include: RLC model, transmission line approach and electromagnetic approach (Grcev, 2009).

In the RLC approach, passive elements are included to account for the capacitive and inductive behaviours of the ground during fast transients. Formulas are given in (Grcev, 2009) for the

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 2: Tools and Electromagnetic Modelling Nicolas Manduley 2020 Page 65 calculation of the equivalent footing impedance of the tower. On the other hand, the implementation of the transmission line and electromagnetic approaches is complex, and may present some limitations when non-linear phenomena are present (Grcev, 2009;IEC 60071-4, 2004). Therefore, the RLC model is the recommended approach for lightning studies. In most cases, a single resistance is sufficient to represent the grounding impedance (IEC 60071-4, 2004).

Besides the representation of the electrodes, there are two effects that may be taken into account: the non-linear effect of the ionization of the soil, and the frequency dependence of the parameters of the soil. The ionization of the soil is a very local phenomenon which is typically not relevant for long electrodes buried in soils with moderate to high resistivity [START_REF] Visacro | Lightning performance of transmission lines: requirements of tower-footing electrodes consisting of long counterpoise wires[END_REF] and usually requires very large current amplitudes to occur. It may become relevant for small electrodes in high resistivity soils and high currents. The frequency dependence of the parameters of the soil is independent from the current amplitude and may affect the values of the elements of the RLC model (CIGRE TB 781).

However, for both effects above described, the overall effect is to reduce the value of the footing impedance, which represents a favourable effect in terms of lightning performance of the tower. Therefore, and in order to obtain more conservative results, they will be not considered in this research and the grounding of the tower will be represented by a single resistance.

Tower Structure

The tower structure can be subdivided into the sections corresponding to the tower body, cross arms and support for the shield wires. The tower body can be modelled as an equivalent inductance, as a lossless propagation line with constant parameters (with or without a damping inductance) or as a radiating structure (IEC 60071-4, 2004).

In order to consider the wave reflections and their respective traveling time between the conductors and the ground, the body of the tower in our research has been modelled as a propagation line with constant parameters (CP model). However, using this model for the cross arms and shield wire support structures would have required, because of their short lengths, very small simulation time steps. This would have significantly increased the computational requirements, without a major gain in accuracy of the results. For these sections, a simple inductance is used with a value of 1 µH/m, as advised in IEC 60071-4.

Air Gaps, Line Insulators

In this research, the modelling of insulators and/or their respective air gaps concerns only the analysis of fast-front overvoltages (FFO, see Chapter 1, §3.2.4). For such cases, it is recommended in IEC 60071-4 to model both the flashover trigger and the flashover process.

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Chapter 2: Tools and Electromagnetic Modelling Nicolas Manduley 2020 Page 66

For the flashover trigger, three approaches are recommended in IEC 60071-4 standard to determine the instant of the flashover: the use of a volt-time (V-t) characteristic, an air gap model using the area criterion and an air gap model based on the leader propagation representation (CIGRE TB 63 and 72). The V-t characteristic is constructed based on standard impulses in the laboratory, and hence it may not be accurate for non-standard impulses. The air gap model using the area criterion can be adjusted for different polarities and gap configurations. Based on comparisons with experimental data, this model is only recommended for small air gaps (lower than 1.2 m). For longer air gaps, a leader propagation representation is recommended (CIGRE TB 63, 1991;IEC 60071-4, 2004).

The leader propagation representation considers the three phases of a breakdown: corona inception, streamer propagation and leader propagation (though the corona inception phase can be often neglected for practical purposes, as stated in CIGRE TB 63). A model of this type has been proposed by [START_REF] Shindo | A new calculation method of breakdown voltage-time characteristics of long air gaps[END_REF], and has been validated through experimental tests for rod-rod and rod-plane configurations with different polarity configurations for gap lengths up to 7 m.

The model proposed by Shindo & Suzuki is available in the EMTP library. For the gap lengths considered in this research (about 2.75 m -5.2 m), it has been observed that using the EMTP default values, significant pre-discharge currents flow through the gap before the actual flashover occurs. As a result, the knee of the voltage curve corresponding to the flashover instant is rounded, and the flashover time becomes significantly larger than what it is observed in real flashover tests (e.g. Hagenguth, Rohlfs, & Degnan, 1952). In this research, EMTP tests have been performed in order to configure the parameters of the model and adjust the predischarge currents to a more realistic level. It has been found that, for the insulator string lengths considered in this work, changing the default value of the capacitance between the leader and the ground of the Shindo & Suzuki model from 500 pF/m (default) to 50 pF/m, the pre-discharge current levels (and thus the breakdown curves) correspond to what it is observed in the laboratory for similar gap lengths.

Surge Arresters

Whenever surge arresters are considered, the model used is determined by the frequency of the studied transients. For slow-front overvoltages (SFO) and lower frequency studies, the native EMTP surge arrester model (type 92 device) is used, which corresponds to a non-linear resistance with a V-I characteristic represented by several exponential segments.

For fast-front overvoltages (e.g. lightning), however, surge arresters present an inductive behaviour. As a result, the maximum current peak instant does not correspond with the maximum voltage peak instant across the surge arrester. For such cases, a high frequency surge arrester model must be used. There are different high frequency models proposed in -Velasco, 2010-Velasco, , 2015)).

The IEEE model (Figure 2.2a) has shown to be accurate for crest times between 0.5 µs and 45 µs (Pinceti & Giannettoni, 1999). It is the most complete model to date as it takes into account physical and electrical data for its implementation. However, it usually requires several iterations to achieve a satisfactory set of values [START_REF] Bayadi | Parameter identification of ZnO surge arrester models based on genetic algorithms[END_REF]Pinceti & Giannettoni, 1999), and it is particularly difficult to implement when no physical data is available. The Pinceti model is a variation of the IEEE model and it is depicted in (Figure 2.2b). It has proved to be accurate within a wide range of crest times (from 1 µs to 30 µs) with a maximum error of about 4.5% (Pinceti & Giannettoni, 1999). The main advantages of this model are that it only requires electrical data to determine its parameters, and that it does not require additional iterations to achieve the level of accuracy mentioned above.

For the above reasons, the Pinceti model will be the preferred surge arrester model for high frequency studies in this research. For the EMTP model and the control functions, the model 3 has been used, which corresponds to an average model of the MMC arm with an equivalent capacitor, assuming that the capacitor voltages of each arm are balanced (Hani Saad et al., 2014), i.e. that the MMC is able to control the charge-discharge cycles of the capacitors in such a way that they can be considered to be constant. The equivalent capacitor is then calculated based on an equivalent switching arm function depending on the number n of identical capacitors connected in series at a given instant. When the IGBTs of the submodule are in the blocked state, the submodule is represented by a half-bridge diode connected to the equivalent capacitor.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems Chapter 2: Tools and Electromagnetic Modelling

This model allows to perform slow-front overvoltage studies with a relatively low requirement of computational resources without affecting significantly the accuracy on the dynamic response of the system (Peralta, Saad, Dennetière, Mahseredjian, & Nguefeu, 2012;[START_REF] Saad | Dynamic averaged and simplified models for MMC-based HVDC transmission systems[END_REF].

Faults

Phase-to-ground and phase-to-phase faults are considered in this research.

For ground faults, a fault resistance is placed between the faulted conductor and the ground.

In the particular case of faults on underground cables, the sheath of the cable must be included in the fault model. In such case, the fault is represented as a short circuit between the core of the cable and the sheath, and the fault resistance is placed between the sheath and the ground.

In case of faults between phases, no fault resistance is considered, and only a small resistance (0.1 mΩ) is placed to avoid potential numeric errors due to branches with impedance equal to zero.

A value of 15 Ω is used as the fault resistance, as it is within the range of values that may be expected for power systems with short-circuit currents above 1 kA (De Andrade & Sorrentino, 2010). In addition, it is a high enough value to be considered as conservative in terms of maximum overvoltage levels generated.

On a side note, in case of faults on overhead lines, it is also necessary to consider that the fault current will flow also through the shield wires and through the neighbouring grounding electrodes. As a result, in such case the value of the fault resistance as defined above will only be valid during the first instants after the fault, and as the current loops through the other towers, the equivalent resistance will decrease.

Lightning Strokes

Lightning strokes are modelled as a current source in parallel with an impedance, representing the impedance of the channel, as illustrated in Figure 2.4. The implementation of this model is discussed in the following paragraphs.

Number of Strokes

Only first strokes are considered in EMTP simulations. This is justified by the following reasons:

 In back-flashover studies, typically high current amplitudes are involved. For such current levels, subsequent strokes tend to have a lower amplitude compared to the first stroke, and thus may not contribute significantly to the flashover risk (CIGRE TB 63).

 In the shielding failure domain (I ≤ 20 kA), sometimes the amplitude of a subsequent stroke might be greater than that of the first stroke (CIGRE TB 63). The influence of subsequent strokes in the flashover risk due to shielding failure is taken into account in the analytical estimation of the SFFOR (see Chapter 1, §6.4.2 or CIGRE TB 704), where no EMTP simulations are involved. EMTP simulations are reserved to the study of the behaviour of the system when a shielding failure occurs, in which the influence of subsequent strikes is neglected for simplicity.

 In terms of energy absorption of the surge arresters, subsequent strokes are not expected to contribute significantly, except maybe for shielding failures. However, as it will be seen in Chapter 4, the energy absorption levels associated to shielding failures are significantly lower than for the back-flashovers, in which case the current amplitude of subsequent strokes tend to be much lower than for first strokes.

Lightning Waveshape and Parameters

Negative strokes are modelled using the CIGRE concave shape (Figure 1.16) with the parameters obtained from the statistical analysis of the data gathered for negative strokes, as discussed in Chapter 1. Concretely, the median values (M) of the maximum steepness (S m ) and front time (t f ) are used, and are calculated as a function of the peak current (I F ) using the derived statistics from Table 1.5.

In absence of comparable data for positive strokes, whenever positive lightning is considered, it is assumed to have the same waveshape parameters from the data corresponding to negative strokes. Although there are some known differences between positive and negative strokes, this assumption allows to-qualitatively and quantitatively-investigate the effect of the polarity of the lightning strike on the system and its lightning performance.

Characterization of the Lightning Channel Impedance

When the lightning channel is formed, a conductive path is formed between the cloud and the ground. This means that an equivalent impedance is introduced to the system. Different estimations and measurements (e.g. [START_REF] Wagner | Surge impedance and its application to the lightning stroke[END_REF]Gorin & Shkilev, 1984; Rakov,

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 2: Tools and Electromagnetic Modelling 1998) have finally determined that the average resistance of the channel can range from several hundred to a few kilo ohms5 , as stated in CIGRE TB 549.

When the impedance of the structure on which lightning strikes is much smaller than the resistance of the channel, the current source can be modelled as an ideal source (i.e. with an infinite impedance) without introducing any significant error to the results. However, this is not usually the case with overhead lines and towers, where the typical surge impedance values vary from some to several hundred ohms, in which case the resistance of the channel must be taken into account.

Simulation studies suggest that below 1 kΩ, both the BFOR and the SFFOR of overhead transmission lines vary significantly with the value of the lightning channel impedance, while for values above 1 kΩ both remain relatively constant (Datsios, Mikropoulos, & Tsovilis, 2019;Grebovic & Oprasic, 2018). Since the main consequence of reducing the lightning channel impedance is to reduce the equivalent current that is injected to the transmission line, this reduction would result in less conservative results. Therefore, a value of 1 kΩ has been chosen to conduct the studies in this research.

General Representation of Overhead Lines for Fast-Front Overvoltage Studies

The following considerations must be taken into account when performing fast-front overvoltage studies in overhead lines.

For the region close to the stroke inception point, a line section of about 2000 m must be accurately modelled (IEC 60071-4, 2004), including a detailed model of the towers, the spans and equipment considered in the studies (e.g. insulators, air gaps, surge arresters…). This means that if the impact point is considered to be in the middle of the line, a 4000 m line section must be modelled. Far from the stroke inception point, the line can be terminated in its equivalent surge impedance to avoid undesired reflections (see Figure 2.5).

To avoid such reflections, the line section under study is isolated from the termination points by adding a long line section at each extremity (e.g. 50 km) with the same characteristics as the spans between the towers. To initialize the system to the normal operating conditions before the transient event, ideal voltage and current sources are installed at each extremity after the long line section.

Conclusion

EMTP is a simulation software specifically designed for the study of transient phenomena. An accurate representation of such phenomena is crucial for a correct evaluation of the overvoltage levels that can occur in a system, which is one of the fundamental pillars of insulation coordination. As for any other software, it is of great importance to specify the modelling procedures and hypotheses required to obtain accurate results.

This chapter presents all the modelling aspects regarding the overvoltage studies conducted in this research, including individual equipment specifications as well as more complex arrangements of components such as an MMC station and an overhead line section for lightning studies. The case studies considered throughout this work are built based on the justifications presented in this chapter to guarantee that the results obtained are representative of the phenomena under study.

Chapter 3 Protection of the MMC against Slow-Front and Temporary Overvoltages

Introduction

As discussed in previous chapters, there are some inherent differences between HVDC technologies based on line commutated converters (LCC) and voltage source converters (VSC). These differences concern mainly the commutation principle and the source type (see Chapter 1, §4.3.1), from which it is reasonable to expect that, even though the fundamental principles of insulation coordination are the same, some of them may need to be adapted to VSC technologies, especially regarding modular multilevel converters (MMC).

The main difficulties associated to the insulation coordination of MMC-HVDC stations is that no current standard defines the procedures for insulation coordination of VSC-HVDC systems and the scientific literature on the subject is very scarce-even at the CIGRE and IEEE. A thorough study of the insulation coordination standards for AC and LCC-HVDC has been necessary in order to determine how the fundamental principles should be adapted to VSC-HVDC systems.

The main goals of this chapter are:

 To provide a base on which the insulation coordination of MMC-HVDC stations can be performed, inspired on the approach of AC and DC insulation coordination standards and taking into account the differences and features of MMC converters.

 To propose a methodology to perform temporary and slow-front overvoltage studies in order to estimate the required withstand voltage of the different apparatuses.

 To determine the location and the characteristics of the arresters, especially regarding the energy duty.

As discussed in Chapter 1, some of the main aspects that differentiate VSC systems from LCC regarding insulation coordination include: the architecture of the converter, the use of a wider variety of station configurations (e.g. symmetric monopolar or bipolar configuration), the location and design of the surge arresters, the transient behaviour and the overvoltage levels.

In this chapter, all of the aspects above mentioned are addressed in order to propose an insulation coordination procedure adapted to the features and characteristics of MMC-HVDC stations.

Such procedure is fundamentally based on performing EMT simulations for determining the maximum overvoltage levels and analysing the behaviour of the system. The feasibility, limitations and practical advantages and disadvantages of a qualitative approach independent from the numerical analysis have been also considered and analysed, and are presented in detail in Appendix D. As a result of such analysis, it was determined that there are major fundamental limitations on such kind of approach which make it difficult to perform the insulation coordination without performing numerical simulations. This provides solid justification to the fact that the insulation coordination procedures proposed in this chapter are based on the assumption that electromagnetic transient simulations are performed.

As a result of the research presented on this chapter, and inspired on the approach of LCC-HVDC insulation coordination standard (IEC 60071-5), two fundamental schemes are proposed in order to be able to take into account any possible architecture, station configuration and surge arrester locations. Hence, such schemes constitute the base for the case studies presented in this chapter, as well as for the proposed procedures for the insulation coordination of MMC-HVDC systems.

This chapter is structured as follows. First, the fundamental schemes proposed are presented and explained. Next, the voltage shapes and sources of MMC-HVDC systems under normal and transient conditions are discussed. Then, the overvoltage analysis of MMC-HVDC stations performed in EMTP is presented for different configurations and architectures. The influence of the surge arrester arrangement-as well as their respective interactions-on the behaviour and overvoltage profile of the system under transient conditions is also investigated. After presenting and discussing the results of the studies, recommendations are provided with respect to the particular procedures that shall be followed for the insulation coordination of MMC-HVDC systems, as well as for the characteristics of the different arresters that may be considered for the overvoltage protection strategy of any such system.

Fundamental Schemes

As already mentioned in Chapter 1, MMC-HVDC stations can have two main architectures based on the location of the arm reactor. For a clearer definition of the principles developed in this chapter, and inspired on the approach of the IEC 60071-5 standard, a fundamental scheme has been proposed for each architecture. Such architectures correspond to a configuration with the arm reactor on the AC or DC side of the converter, and are illustrated in Figure 3.1 and Figure 3.2, respectively.

Each figure features the different equipment present in the station: the converter transformer, the arm reactors (BR), the MMC submodules (SM), the transmission line (cable, overhead line or hybrid), possible grounding schemes (star-point reactor on the AC side of the converter or through an impedance on the DC side) and the different surge arresters that may be present at each location. The meaning, as well as the design recommendations for each of such arresters, will be discussed in detail in §5.2. Each fundamental scheme is conceived so that the general procedures of insulation coordination can be described based on them and be applicable to any possible topology derived from such schemes. For instance, the switchgear displayed in the figures allow the configuration of the station as a symmetrical monopole by connecting the lower bus of the station to the DC pole and a star-point reactor on the secondary side of the AC transformer, or as an asymmetrical monopole by connecting the lower bus to a grounding scheme with or without metallic return. A bipolar configuration is achieved by joining two asymmetrical monopoles together for the positive and negative poles. In addition, the diagrams feature all possible locations for surge arresters within the station-as well as in a possible junction between overhead lines and underground/submarine cables-in which the overvoltage protection strategy may be based. Note that some of them may be removed depending on the design of the overvoltage protection strategy.

Therefore, the procedures and case studies presented in this chapter concerning overvoltage protection of MMC-HVDC stations against temporary and slow-front overvoltages (TOV and SFO, respectively) will be based on the fundamental blocks from Figure 3.1 and Figure 3.2. The next sections will cover the voltages in service (i.e. under normal operating conditions) and the possible sources of TOV and SFO which need to be considered for overvoltage protection of the station.

Voltages and Overvoltages in MMC-HVDC Stations

Voltages in Service

In AC systems, components are usually installed phase-to-ground, and thus their respective voltages in service are easily determined. On the contrary, in HVDC systems, some components are installed in series, and others may present a DC offset over a sinusoidal shape. Consequently, it is more difficult to determine rapidly the voltage in service between their terminals.

The shape of the voltage in service is a fundamental element for the specification of the components, as well as for their respective surge arresters. Therefore, the goal of this section is to provide information on the shapes and amplitudes of the voltages at the different locations under normal operating conditions. .2, and concern the phaseto-ground voltages of the primary and secondary side of the converter transformer (V 1 and V 2 , respectively), the intermediate point between the arm reactor and the MMC submodules (V 3 ), the DC pole voltages (V 4 ) and the voltages across the bridge arm reactors (V BR ) and the MMC submodules (V SM ).

It is observed that the major differences between the figures correspond to the voltages V3.

In addition, DC offsets are observed in the MMC submodules and in some other locations in Voltage V 1 is a regular sinusoid given by the nominal voltage of the primary side of the converter transformer.

V 2 is the phase-to-ground voltage of the secondary of the converter transformer. This voltage may have a DC offset depending on the grounding scheme of the configuration, which is characterized below. For easier future reference, a voltage V* will be defined as a typical sinusoidal voltage at the power frequency:

𝑉 * = √2 √3 𝑈 𝑠𝑒𝑐 sin(𝜔𝑡 + 𝜑) (3-1)
Where U sec is the phase-to-phase RMS nominal voltage at the secondary of the converter transformer.

The voltage across the bridge arm reactors (V BR ) is a function of the inductance and the derivative of the current circulating through it. If no circulating currents are assumed to exist between the converter arms, the current through the arm reactor is given by one third of the Circulating currents may introduce some distortion to this expression and increase the ripple of the submodule voltages [START_REF] Saad | Dynamic averaged and simplified models for MMC-based HVDC transmission systems[END_REF]. However, these currents can be eliminated by using active or passive filtering over the voltage reference (Peralta et al., 2012;[START_REF] Tu | Reduced switching-frequency modulation and circulating current suppression for modular multilevel converters[END_REF], which is implemented in the MMC control strategies. Therefore, the hypothesis that circulating currents can be neglected remain valid for most cases, and hence the voltage across the arm reactor is given by:

𝑉 𝐵𝑅 (𝑢𝑝,𝑙𝑜𝑤) = ±𝐿 𝑑 𝑑𝑡 ( 𝑖 𝐴𝐶 2 ) (3-3)
For the rest of the equipment and locations, great insight can be obtained by writing and analysing the Kirchhoff's voltage loop equations, as well as the fundamental differences between the different station configurations. The equations for both architectures with the arm reactor on the AC and the DC side are illustrated in Table 3.1 and Table 3.2, respectively. The bars above the expressions indicates a complex form.

As it can be noted, the main differences between both architectures lie in the equation loops 1, 2, 5 and 6, where the terms associated to the voltage of the submodules (V SM ) and the arm reactors (V BR ) are exchanged.

By considering equal DC output voltages and power for the monopolar and bipolar configurations, as well as their respective grounding schemes, it is possible to deduce analytical expressions for the voltage shapes in service conditions for the rest of the equipment and locations of interest within the converter station based on the fundamental schemes of Figure 3.1 and Figure 3.2 and the Kirchhoff's voltage loop equations for each architecture (see Table 3.1 and Table 3.2). This exercise has been performed for a monopolar and bipolar configuration with the arm reactors on the AC and the DC side, and is summarized in Table 3.3.

The voltage V 4up corresponds to the positive DC pole voltage, assuming that for the bipolar configuration, the schemes from Figure 3.1 and Figure 3.2 represent the positive half of the substation. Under such hypothesis, the voltage V 4low would represent the negative DC voltage for the monopolar configuration, and the ground voltage for the bipolar configuration.

Because of the zero voltage reference being placed in V 4low in the bipolar configurations, an offset is introduced to V 2 which is equal to half of the nominal DC voltage. To achieve equal power and voltage outputs, the nominal voltage of each converter transformer of the bipolar configuration is half of that of the monopolar configuration. Therefore, the voltage V 2 in the Voltages V 3 differ significantly depending on the position of the arm reactor and the configuration of the station. When the arm reactor is on the AC side, V 3 has the same shape as V 2 with only a small variation introduced by the voltage of the corresponding arm reactor (loop equations 1 and 2 in Table 3.1). When the arm reactor is on the DC side, V 3 resembles V 4 , which is a DC voltage, with a superposed AC wave equal to the voltage of the corresponding arm reactor (loop equations 5 and 6 in Table 3.2). Furthermore, in the bipolar configuration, V 3low presents a particularly low voltage level because the voltage V 4low corresponds to the zero voltage reference. All the above conclusions are also illustrated in Figure 3.3 and Figure 3.4. Finally, the MMC submodule voltages (V SM ) consist of an AC voltage with a DC offset and no zero-crossing. They are characterized by the expressions given in Table 3.3, obtained from the loops 3 and 4 from Table 3.1 and Table 3.2. Since in bipolar configurations there are more total submodules between the DC poles, the total voltage across the submodules is about half as those of the monopolar configuration, which is also observed in Figure 3.3 and Figure 3.4. This is proven analytically by substituting the corresponding values of V 4 and V 2 in the expressions given in Table 3.3.

Sources of Temporary Overvoltages (TOV)

Temporary overvoltages are an oscillatory overvoltage of relatively long duration which is undamped or only weakly damped (IEC 60071-5). As for LCC-HVDC systems, temporary overvoltages are mainly produced by switching operations and faults on either the AC or the DC side of the converter, as well as resonance and ferroresonance.

In the case of VSC-MMC systems, faults occurring in symmetric monopolar configurations may result in the permanent charge or discharge of one of the DC poles. In the former case, this would represent a permanent DC overvoltage (not oscillatory, as defined in the standards). Such overvoltages will be also considered temporary overvoltages (see §4).

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 3: Slow-Front Overvoltages and Fault Analysis Because of their long duration6 , temporary overvoltages may be decisive in setting the rated voltage of surge arresters installed for the overvoltage protection strategy, especially in the case of permanent DC overvoltages.

On the AC side

Usually switching operations or faults are at the origin of the highest TOVs on the AC side.

Some faults on the DC side may introduce an offset on the AC side of the converter, thus producing oscillations at-or close to-the power frequency of the system that can last until the blocking of the MMC or the opening of the AC or DC breakers.

Asymmetric faults on the AC side (e.g. single phase-to-ground fault) may also result in significant TOV levels on the AC side of the converter.

As in LCC-HVDC systems, the presence of filters may also contribute to the appearance of long duration oscillations. However, as explained in Chapter 1, the harmonic distortion of MMC converters is negligible, for which it is less common to install harmonic filters in MMC-HVDC stations.

On the DC side

Ground faults on the DC side may cause an excessive charge of the healthy pole, particularly in systems with underground or submarine cables due to the fault current being able to loop through the sheaths of the cables, to the ground and to the opposite pole (when a highimpedance grounding scheme is used at the station, as in symmetric monopolar configurations).

Asymmetric faults on the AC side, as well as internal converter faults to the ground, may also result in long duration overvoltages on the DC side or inside the converter station. This is mainly due to the fault current flowing to the ground and reaching one of the DC poles through its respective sheath, as in the case described above.

As a consequence of the blocking of the MMC submodules, the converter station behaves as an uncontrolled diode rectifier. In such case, a power-frequency oscillation may be applied inside the converter and transmitted to the DC poles, lasting until the opening of the AC breaker.

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Chapter 3: Slow-Front Overvoltages and Fault Analysis Nicolas Manduley 2020 Page 83

Sources of Slow-Front Overvoltages (SFO)

Slow-front overvoltages are voltage impulses with a time to front in the order of 20 -5000 µs (IEC 60071). These overvoltages typically represent the highest overvoltage levels obtained in a system due to switching operations and the initiation or clearing of faults.

On the AC side

Asymmetric faults on the AC network may produce SFOs and TOVs on the healthy phases of the AC side.

Due to the architecture of MMC stations, internal converter faults or DC faults may also transmit significant voltage impulses to the AC side (in addition to the TOVs discussed in §3.2.1).

Both symmetric and asymmetric faults could result in transformer saturation, which may have an influence on the overvoltage levels depending on the fault instant and clearance.

On the DC side

Most slow-front overvoltages on the DC side are produced by faults on the DC side or inside the converter station (CIGRE TB 388, 2009;Neumann et al., 2016). However, significant SFOs can also appear due to asymmetric faults on the AC side of the converter station.

Overvoltage Limitation with Arresters

The overvoltage protection strategy consists of an arrangement of surge arresters placed at different locations to ensure that the maximum overvoltage levels are below the insulation withstand voltage of the equipment, as illustrated in Figure 3.1 and Figure 3.2.

The arresters featured in Figure 3.1 and Figure 3.2 represent all the locations and equipment that may require to be directly protected by a surge arrester. They have been placed such that it is always possible to design a surge arrester arrangement that respect the three fundamental principles for the overvoltage protection of HVDC systems (see Chapter 1, §4.2.1):

 Overvoltages generated on the AC side should be limited by arresters on the AC side.

 Overvoltages generated on the DC side or earth electrode should be limited by arresters on the DC side.

 Critical equipment should be directly protected by arresters connected close to the components.

The effect of the particular arrangement of surge arresters-as well as their interactions during a transient event-on the overvoltage profile of a system is analysed in detail in §4.4, and guidelines for the design of each of the arresters in Figure 3.1 and Figure 3.2 are given in §5.2.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 3: Slow-Front Overvoltages and Fault Analysis

Overvoltage Analysis of MMC-HVDC Stations

In this section, different architectures of MMC-HVDC stations are studied through EMTP to investigate the maximum overvoltage levels on which the insulation coordination will be based. A symmetrical monopole and a bipole without metallic return are considered for an MMC architecture with the arm reactor on the DC side. Afterwards, a symmetrical monopole with the arm reactor on the AC side is also assessed with different arrangements of surge arresters to study the effect of the surge arrester configurations on the overvoltage protection strategy, as well as their interactions and consequences on the system. In all cases, 100% underground cable links are considered.

Modelling Aspects

As discussed in Chapter 2, MMC submodules are represented as an equivalent switching arm function that determines the equivalent capacitance of each arm at a given instant (model 3 in EMTP).

For the symmetrical monopole, the base parameters of the station are those illustrated in Table 2.2, which are based on the France-Spain (INELFE) link (Dennetière, Nguefeu, [START_REF] Saad | Dynamic averaged and simplified models for MMC-based HVDC transmission systems[END_REF]. The grounding scheme consists of a star-point reactor acting as a high impedance at the secondary side of the converter transformer.

In the bipolar configuration, the same parameters have been used for each MMC, except for the AC voltage at the secondary of the transformer and rated power, which have been halved so that the operating conditions are the same as in the monopolar configuration (i.e. same rated DC current and total voltage difference between the positive and negative pole). A solid grounding scheme is placed between the two MMCs (point 4 low for the positive half represented in the figures above).

In all case studies, XLPE cables are used for the power transmission between the two stations. The total length of the cable is 100 km, and it has been modelled through the wideband (WB) model, as discussed in Chapter 2. The geometry and parameters for the core, sheath and insulation considered for the EMTP model are illustrated in Figure 3.7 and are based on the parameters from the INELFE link (Dennetière et al., 2013). As represented in the figures above, the sheath is solidly grounded at each station.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

MMC-HVDC Station with the Arm Reactor on the DC Side

As discussed in §3.2 and §3.3, there are different sources of temporary and slow-front overvoltages, such as system faults, switching operations, resonance phenomena, among others. However, the highest overvoltage levels in DC are usually obtained through system faults (CIGRE TB 388, 2009). Line energization and reclosing need not to be considered because the DC energisation from zero voltage is smooth and controlled, and the deenergisation of the line before the reclosing eliminates the trapped charge (Neumann et al., 2016), which is an important source of overvoltages in AC systems. Therefore, only system faults are considered in this section.

The fault scenarios considered in this section are illustrated and described in Figure 3.8 and Table 3.4, respectively. Note that no surge arresters are considered in this part. Fault N Bus-to-bus fault between the positive and negative DC poles Fault N2 Pole-to-pole fault between the positive and negative DC poles at the middle of the cable length (50 km from the station) Table 3.4 Description of the faults considered in the overvoltage studies for an MMC-HVDC station with the arm reactor on the DC side Faults to the ground have been modelled as an ideal switch with a resistance of 15 Ω in series, which is a high enough value to be considered as conservative for the studied system (De Andrade & Sorrentino, 2010) and which may lead to the highest overvoltage levels. For the short circuit of the submodule only a small resistance (0.1 mΩ) has been placed to avoid numerical issues due to zero impedance branches.

Under normal operating conditions, the absolute value of the peak voltage levels at the different locations are summarized in Table 3.5 for both the symmetrical monopole and bipole configuration without metallic return. The values are expressed in p.u. by considering the nominal DC voltage (i.e. 320 kV) equal to 1 p.u. The values obtained through simulation are in agreement with the values calculated through the analytical expressions from Table 3.3. The values presented in Table 3.5 constitute the main reference to determine whether a transient voltage for each location or equipment constitutes an overvoltage or not. Such overvoltages will be also classified as temporary overvoltage (TOV) or slow-front overvoltage (SFO) according to the conventional classification from IEC 60071 standards (see Figure 1.3).

V 2 V 3up V 3low V 4up V 4low V SM V BR Monopole 0.
After analysing the simulation results for all the fault cases, the maximum SFO and TOV levels for each location are summarized in Table 3.6 for the monopolar and bipolar configuration with no arresters, as well as which fault produced it. It should be mentioned that the particular case of the short-circuit of the MMC submodules (fault I) constitutes a very particular condition, and it is illustrated in Figure 3.9. At the instant of the fault, all inserted capacitors (i.e. the capacitors in the submodules with the IGBTs in the on-state) discharge through a low-resistive path, potentially producing a very high current up to more than 190 kA for the studied case which loops inside the submodule. Even though capacitors are normally designed to withstand such current levels (CIGRE TB 447, 2011), neither the IGBTs nor the anti-parallel diodes can, resulting in their immediate destruction and, consequently, the complete loss of the entire faulted submodule. For the reasons explained above, this fault should not be considered for insulation coordination, and it has been excluded from the overvoltage analysis summarized in Table 3.6. Suitable measures shall be taken to completely avoid the risk of occurrence of this fault within the station, as it represents a catastrophic condition for the converter (Manduley, Touré, Xémard, Raison, & Poullain, 2019).

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 3: Slow-Front Overvoltages and Fault Analysis Nicolas Manduley 2020 Page 89

From the results displayed in Table 3.6, it is important to note the following aspects (Manduley, 2018):

 V 2 is heavily demanded in the symmetric monopolar configuration in terms of temporary overvoltages, while in bipolar configuration is not demanded at all (i.e. the amplitude and duration of the generated transients were smaller than the operating voltage shown in Table 3.5). Hence, in the bipolar configuration this point could be dimensioned considering only fast-front overvoltages (FFO).

 V 3 is heavily demanded in symmetric monopolar configurations, reaching not only high slow-front overvoltages (SFO) but also high temporary overvoltages (TOV), which are long duration overvoltages associated with high energy absorption rated for the arresters. In bipolar configurations, the overvoltage levels are significantly lower due to the solid grounding and, because the grounding is located on the DC side, the locations 3 up and 3 low are not equivalent-as it is the case of the monopolar configuration. This implies that voltages, and therefore overvoltages, may not be symmetric at such locations for the bipolar configuration. Hence:

o Different protective levels may be used for the arresters to protect the points V 3up and V 3low in the bipolar configuration.

o In the bipolar configuration, there could be less requirements for the arresters in terms of protective levels (because of the lower SFOs) and energy absorption (because of the lower TOV), compared to those for the monopolar configuration.

 V 4 is exposed to very high long duration overvoltages in monopolar configuration, but it is not the case for the bipolar configuration. This is due to the fact that such high voltages are reached when the healthy pole is progressively charged as a consequence of a fault. In the case of a bipolar configuration, the positive pole is decoupled from the negative pole as a result of having a solid grounding to the earth at the mid-point between them. Therefore, in bipolar configuration the healthy pole will not be charged due to a fault on the other pole.

 Some overvoltages are observed between the terminals of the MMC submodules (V SM ), especially during a single phase-to-ground fault on the AC side (fault G). However, it can be noted that they do not represent a very significant overvoltage when compared to the voltage levels under normal operating conditions (Table 3.5).

 Arm reactors are similarly demanded for both configurations in terms of energy (i.e. TOV levels), while in terms of slow-front overvoltages (SFO), the reactors of the monopolar configuration are approximately 38% more demanded than those of the bipolar configuration.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 3: Slow-Front Overvoltages and Fault Analysis Nicolas Manduley 2020 Page 90

 Overall, the most critical faults are fault L (DC pole-to-pole), K (DC bus-to-bus), J (ground fault of location 3), which is in agreement with similar studies in the literature (Y. L. Gu et al., 2013;[START_REF] Saad | Study on transient overvoltages in converter station of MMC-HVDC links[END_REF].

Based on the obtained results, some general guidelines can be provided to take into account for the overvoltage protection criteria for each location. It seems clear that for the monopolar configuration, dedicated arresters are required to protect locations 2, 3 and 4 against slowfront and temporary voltages (SFO and TOV, respectively). In the bipolar configuration, overvoltages produced at such locations are significantly lower; for such locations, surge arresters are not likely to be subjected to great energy absorption levels due to SFO and TOV. However, they may still be required for lightning protection (fast-front overvoltages, FFO). This shall be determined through fast-front overvoltage analysis on the station considering the adequate high-frequency modelling of the components and special protection equipment (CIGRE TB 447, 2011;IEEE Std. 998, 2012).

In all cases, no significant overvoltage levels appear across the MMC submodules. Compared to the normal operating voltage, the highest overvoltage levels observed are about 14% and 21% higher for the monopolar and bipolar configurations, respectively. With an adequate design of the valve (see CIGRE TB 447), no arresters may be needed to protect it directly against SFOs and TOVs. Since the station is generally well protected against lightning and inductive elements are located between the valve and the line, generally overvoltages due to lightning are not of concern for the MMC valve, as stated in CIGRE TB 447.

As shown in the fundamental schemes from Figure 3.1 and Figure 3.2, it would be also possible to consider installing a surge arrester in parallel with the arm reactors. However, it is important to remember that such inductances, as well as the smoothing reactor, also play a crucial role in limiting the rise of the fault current during transients. If a surge arrester is placed in parallel with a reactor, it would mean that after reaching a certain overvoltage level the reactor will be by-passed by the surge arrester and thus stop limiting the rise of the fault current. Therefore, this arrester shall be carefully designed, and preferably avoided unless the integrity of the reactor may be compromised during a transient.

The above and other considerations are summarized in Table 3.7 for the cases studied in this section. • If required, arresters shall be designed for SFO/TOV withstand • Special care shall be taken to not compromise the role of the reactor in limiting the rise of the fault current Table 3.7 Conclusions and particular recommendations to take into account for the overvoltage protection strategy for monopolar and bipolar MMC-HVDC configurations with the arm reactor on the DC side.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

MMC-HVDC Station with the Arm Reactor on the AC Side

The same analysis presented in the above section ( §4.2) is now performed for a topology with the arm reactor on the AC side. The analysis shown in this and the next subsection was partially published in the International Conference on Power System Transients -IPST 2019 (Manduley, Touré, et al., 2019). In this case, only the symmetric monopolar configuration is considered because, as seen in the previous subsection, it is the configuration that presents the highest overvoltage levels. Also, only DC and internal converter faults are considered (except for the short-circuit of the MMC submodule-fault I-for the same reasons as for the previous case), which are illustrated in Figure 3.10.

Note that in this study, a single operating point has been considered. For a complete overvoltage profile, parametric studies over several operating points and fault instants are necessary. As for the previous case, the voltages under normal operating conditions for each location are determined by simulation and are shown in Table 3.8. The differences observed with respect to the configuration with the arm reactor on the DC side are in agreement with the analytical equations presented in Table 3.3, and concern especially the amplitude of the voltage at location 3 (i.e. V 3up and V 3low ), for which the equations are different.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Location V 2 V 3up V 3low V 4up V 4low V SM V BR
Voltage (p.u.) 0.88 0.90 0.90 1.01 1.01 1.90 0.08 Table 3.8 Absolute value (in p.u.) of the peak voltage levels under normal operating conditions at the different locations of the MMC-HVDC station obtained through simulation for the symmetric monopolar configuration with the arm reactor on the AC side. The value in p.u. is calculated by considering 1 p.u. = 320 kV (the nominal DC voltage).

Since faults J, K, and L considered for this study are located on the positive side (upper arm) of the station, they may generate different overvoltage levels and shapes on the upper and lower arms (for instance, for locations V 3up and V 3low or V 4up and V 4low ). However, due to the symmetry of the configuration, if such faults were located on the negative side (lower arm) of the station, the same results would be obtained, but reversed in comparison to the studied cases. Therefore, for simplicity, only the highest maximum SFO and TOV values for each pair are displayed in Table 3.9 as V 3 and V 4 instead of their corresponding up/low arm subindices. A complete table with all the maximum overvoltage levels for each location and each fault is provided in Appendix C. It is observed that the location of the arm reactor influences the overvoltage profile of the MMC station. For instance, the maximum overvoltage levels at locations 2, 3 and 4 are significantly higher than for the configuration with the arm reactor on the DC side (see Table 3.6), as well as slightly higher for the MMC valve (V SM ) and lower across the arm reactor (V BR ). This is one of the reasons why two separate fundamental schemes are considered for the architecture and insulation coordination of the MMC station. As it will be seen later in the next subsection, this essential difference also influences the interactions between the surge arresters and thus their respective modelling.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

An important aspect to consider is that no smoothing reactor is present in this configuration. As a result, some low inductance paths may appear, for instance, during the DC bus-to-ground or pole-to-ground faults along which the fault current will not be sufficiently limited by inductive elements, and therefore may allow some transient spikes to appear on the DC bus. This explains the 2.25 p.u. SFO at location 4 (DC bus) which did not occur in the configuration with the arm reactor on the DC side. For this reason, typically a smoothing reactor is required in MMC configurations with the arm reactor on the AC side, to limit the short-circuit current and attenuate the slow-front spikes that may be generated by DC faults.

In the case of the submodule and arm reactor voltages, the overvoltage levels do not change significantly compared to those obtained for the configuration with the arm reactor on the DC side. Therefore, the guidelines and recommendations for the overvoltage protection strategy are the same as those given in Table 3.7. Table 3.10 summarizes the general observations and recommendations to consider when designing the overvoltage protection strategy for the critical locations of an MMC station with the arm reactor on the DC side in a monopolar configuration, based on the obtained results and the above discussion.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 3: Slow-Front Overvoltages and Fault Analysis Nicolas Manduley 2020 Page 94

Observations and Recommendations

V 2

• Heavily demanded in terms of both SFO and TOV (especially TOV)

• Arresters shall be designed for SFO/TOV withstand V 3

• Heavily demanded in terms of SFO, with significant TOV levels • Arresters shall be designed for SFO/TOV withstand V 4

• Highly demanded, mostly due to the charge of the healthy pole during a pole-to-ground fault (fault L or K) • A smoothing reactor is required to limit the short-circuit current and slow-front transients • Arresters shall be designed for TOV withstand V SM

• Overvoltages around 15-16% higher than the regular voltage • May not require a dedicated arrester • If required, arresters shall be designed for SFO/TOV withstand V BR

• If required, arresters shall be designed for SFO/TOV withstand • Special care shall be taken to not compromise the role of the reactor in limiting the rise of the fault current

Table 3.10 Conclusions and particular recommendations to take into account for the overvoltage protection strategy of the symmetric monopolar MMC-HVDC configuration with the arm reactor on the AC side

The following subsection will continue to use the present configuration to study the effect of the surge arrester arrangement on the overvoltage profile of the configuration, as well as their interactions and influence on the behaviour of the system.

Surge Arrester Interactions

The same base configuration depicted in the previous section (see Figure 3.10) is considered in this subsection for the studies with different surge arrester arrangements. The main goal is to study the impact of the surge arrester arrangement on the overvoltage profile of the configuration.

Setup

The detailed model with the considered arresters and faults is illustrated in Figure 3.11.

As discussed in Chapter 1, one of the fundamental principles of insulation coordination in DC is that overvoltages generated on the AC side shall be limited by arresters on the AC side, and idem for overvoltages generated on the DC side. Following this principle, arresters A1 and A2 are designed to play a more active role during AC faults on the primary and secondary side of the converter transformer, respectively. Similarly, arresters A3 and C are expected to play a major role in the overvoltage protection and energy dissipation in case of DC and converter faults, which are the faults considered in this research.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Surge Arrester Design and Parameters

The initial parameters of the surge arresters have been determined differently for AC and DC side arresters, and are presented in Table 3.11 for both the maximum continuous operating voltage (U c ) and rated voltage (U r ) of the arresters in their equivalent RMS value. The V-I matrix used is shown in Figure 1.4 (obtained from Hinrichsen 2012), and has been scaled to match the required rated voltage of the arresters.

Since the surge arrester specification is a fundamental part of insulation coordination, which is a naturally iterative process, it is clear that a precise specification of the surge arrester parameters is also an iterative process. Because the goal of this section is to study the interactions of the surge arresters and the effects of having different arrester arrangements within the configuration, the procedures described below aim to obtain a reasonable and realistic value that may be found in real applications. The hypotheses considered to reach this goal are also described in the upcoming paragraphs.

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Arresters A1 and A2 have been specified by using typical values of arresters used for such nominal AC voltage levels (i.e. 400 kV and 320 kV, respectively). Since the nominal voltages refer to phase-to-phase voltages, the respective phase-to-ground voltages in RMS are 231 kV and 185 kV. As explained in Chapter 1, AC arresters are typically designed based on the rated voltage of the arrester (U r ) and TOV withstand. The maximum TOV values depend on the earth fault factor, which can range from 1.25 to 1.73. Considering earth faults and load shedding, a value around 1.5 may be considered conservative as values around 1.3 and 1.4 are expected for such events (IEC 60071-2). Therefore, by considering the earth fault factor and the corresponding nominal voltage levels, the U r values for A1 and A2 are given as follows:

U r_A1 = 231 𝑘𝑉 𝑅𝑀𝑆 (1.5) = 347 𝑘𝑉 𝑅𝑀𝑆 (3-4) 𝑈 𝑟_𝐴2 = 185 𝑘𝑉 𝑅𝑀𝑆 (1.5) = 278 𝑘𝑉 𝑅𝑀𝑆 (3-5)
Which, adjusting for the next higher standard arrester rated voltage for AC, yields the values shown in Table 3.11.

As the relationship between U r and U c of surge arresters in general is constant (Hinrichsen, 2012), the specification of arresters A1 and A2 can be also expressed as a function of U c and a coefficient, such that:

𝑐𝑜𝑒𝑓𝑓 𝐴1 = 𝑈 𝑐_𝐴1 𝑉 1 = 288 𝑘𝑉 𝑅𝑀𝑆 400 𝑘𝑉 𝑅𝑀𝑆 √3 ⁄ = 1.247 (3-6)
and

𝑐𝑜𝑒𝑓𝑓 𝐴2 = 𝑈 𝑐_𝐴2 𝑉 2 = 231 𝑘𝑉 𝑅𝑀𝑆 320 𝑘𝑉 𝑅𝑀𝑆 √3 ⁄ = 1.250 (3-7)
For converter and DC arresters (i.e. A3 and C), the design is done by considering the maximum continuous voltage (U c ) and the nominal voltage under normal operating conditions. In order to maintain a certain uniformity in the overall design of the arresters, a similar coefficient is applied to the peak voltage of the location under normal operating conditions where the surge arrester is located. However, since AC arresters are typically designed to not conduct significant currents during SFO events, a slightly lower coefficient is used for arresters A3 and C to ensure that the protective level will be lower so that the arresters will conduct during fault events and their interactions can be studied. For the purposes of this study, a coefficient of 1.20 is used for such arresters as a hypothesis to establish a reasonable initial specification of the arresters.

Arrester A3 is placed in location 3 (see Figure 3.10), which presents a regular sinusoidal waveshape with no offset (see Figure 3.3) with a peak amplitude of 0.9 p.u. or 288 kV peak . To lookup the corresponding value in a surge arrester catalog, it is convenient to convert this value in an equivalent RMS value, as it is usually specified in the datasheets. Therefore: By applying the coefficient of 1.20 to V 3 :

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

U c_A3 = 204 𝑘𝑉 𝑅𝑀𝑆 (1.2) = 245 𝑘𝑉 𝑅𝑀𝑆 (3-9)
Similarly, arrester C is placed at the DC bus where the rated voltage has a DC shape and a rated value of 320 kV. Since it is a DC amplitude, this value can be considered a peak value when designing the arrester.

By applying the 1.20 coefficient:

𝑈 𝑐_𝐶 = 320 𝑘𝑉 (1.2) = 384 𝑘𝑉 𝑝𝑒𝑎𝑘 (3-10)
Surge arrester catalogs typically provide the RMS values of U c and U r for AC applications. Since the arrester technologies are the same for DC-and only the selection procedures differ-, the U c values obtained for DC arresters can be expressed in their equivalent RMS value:

𝑈 𝑐_𝐶 = 384 𝑘𝑉 𝑝𝑒𝑎𝑘 √2 = 272 𝑘𝑉 𝑅𝑀𝑆 (3-11)
All the values calculated above are summarized in Table 3

Results

The comparison of the maximum overvoltage levels obtained at each location is illustrated in Figure 3.13 and Figure 3.14 for slow-front and temporary overvoltages, respectively.

It is observed that the SFO levels on the primary side of the transformer (voltage V 1 ) are close to its normal operating voltage (i.e. around 1.04 p.u. or 327 kV peak p-g ), which means that the AC side is not significantly affected by the faults on the DC and converter side, as expected according to the insulation coordination principles previously mentioned (see §4.2.1 in Chapter 1). Also, no TOVs are transferred to the primary side of the converter transformer (Figure 3.14).

It can be also seen that configurations A1-A2 and A1-A2-C are almost equivalent in terms of overvoltage limitation for both SFOs and TOVs, except at location 4 where the arrester C effectively limits the overvoltage levels on the DC pole. The same is observed for configurations A1-A2-A3 and A1-A2-A3-C, except that in this case the effect of arrester C is less important than in configuration A1-A2-C. This suggests that arrester A3 is more active in

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the overvoltage limitation, and/or that the protective level of arrester C is too high and could be lowered, if the minimum withstand voltage of the protected equipment allows it. The energy absorption levels will determine the feasibility of this possibility, along with the withstand levels of the DC cable.

Furthermore, it is observed that the SFO levels are higher for all points and equipment in the configuration without surge arresters (NS configuration), except for the arm reactors (V BR in Figure 3.13). In this case, the SFO levels are higher in all surge arrester configurations than in the base case without surge arresters. This is explained through the fact that when a surge arrester starts conducting, a new current path is created within the system. Consequently, the voltage and current distribution changes within the converter, as well as the voltage levels attained which could be different at each point compared to the case without surge arresters. This concerns particularly the arm inductances, since they are the only components that are able to react instantaneously to the rapid voltage variation during the first instants after the fault.

Special care shall be then taken to the possible loops created by the conduction of the surge arresters, as it could even create paths without limiting inductors, potentially resulting in very high currents through the MMC submodules and other equipment. This is because when an overvoltage is applied to a point directly protected by an arrester, current will start flowing through it according to the V-I characteristic of the arrester, and a new current path is created.

One of the most critical scenarios found is depicted in Figure 3.15 and corresponds to the current path created during fault L through arrester A3. When the propagating wave reaches the station, current starts flowing through the arrester according to its V-I characteristic due to the overvoltage that appears between its terminals. Since no inductance is present in the loop created (red path in Figure 3.15), this current will continue to increase for at least 40 µs (Figure 3.16 left, green curve) and most of it will flow directly into the valve (see Figure 3.16 left, blue curve). Longer MMC blocking delays imply even higher current levels. This represents a potentially dangerous condition for the IGBTs inside the submodules. This supports the fact that the installation of a smoothing reactor in installations with the arm reactor on the AC side is considered mandatory. This way, no loops without inductive elements can be created through the MMC submodules.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 3: Slow-Front Overvoltages and Fault Analysis Nicolas Manduley 2020 Page 99 The energy absorption levels of the surge arresters for each configuration is shown in Figure 3.17. Energy absorption levels for arrester A1 were negligible in all cases, hence it is not represented in the graphs.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems Chapter 3: Slow-Front Overvoltages and Fault Analysis

It can be observed that arrester C absorbs the most energy when A3 is not present (Figure 3.17b). When arrester A3 is present, the incorporation of arrester C does not produce major variations on the energy absorption levels (Figure 3.17c and Figure 3.17d).

Arrester energy absorption capability is frequently specified in kJ/kV of their rated voltage (U r ) (IEC 60099-4, 2014) and it typically ranges between 4 and 16 kJ/kV of U r (SIEMENS, 2014), depending on the energy class. For the arrester ratings used in this work (see Table 3.11), this represents a minimum between 1.15 -1.44 MJ, up to a maximum between 4.61 -5.76 MJ of total energy handling capability. It is thus concluded that for the specific scheme studied in this work, and for any configuration considered, a single-column arrester is likely to be enough to guarantee the safe operation of the surge arresters in the studied configurations, resulting in the overvoltage profiles presented in Figure 3.

Discussion

A summary of the maximum overvoltages at the different locations and the faults originating them is presented in Table 3.12. The complete detailed results for all faults, locations and configurations are provided in Appendix C.

When compared to the case without any surge arresters (Table 3.9), it is clear that the fault scenarios leading to the highest overvoltage levels do not change, except for the voltage

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across the arm reactor, in which case the most critical fault becomes the DC pole-to-pole fault at the middle of the cable length (fault N2) instead of the DC pole-to-ground fault at the middle of the cable length (fault L). This is explained by the fact that fault N2 provides a direct and low resistive path from one DC pole to the opposite pole, and thus most of the fault current loops between the two poles and through the converter stations. As a result, the arm rectors are highly demanded in terms of current limitation, which produces the highest voltage variations across them.

However, it is also observed that there is a significant reduction in the overvoltage levels at most locations (as also seen in Figure 3.13 and Figure 3.14).

Overvoltages 3.12 Maximum SFO and TOV levels in configuration A1-A2-A3-C

SFO max Fault TOV max Fault V1 1.14 J 0 - V2 1.73 L 1.61 J V3 2.02 L 1.59 J V4 1.92 K 1.80 K V SM 2.10 J 2.18 J V BR 1.21 N2 0.25 J Table
In general terms, the absolute energy levels absorbed by the arresters in this study were relatively low. Considering that the surge arresters can effectively withstand much higher energy levels than those obtained in this work, it would be possible to lower the protective levels of the arresters for even better overvoltage protection. In case of critical energy absorption levels, it is possible to include multiple columns of arresters in parallel for better energy dissipation (IEC 60071-5, 2014;IEC 60099-9, 2014).

Based on these results, it can be concluded that surge arresters for this study were chosen based on very conservative criteria regarding energy absorption levels. Protective levels may be lowered, considering that:  Arrester current under normal operating conditions shall not result in overheating of the arrester in steady-state.

 Energy absorbed shall remain within the energy handling capability of the arrester.

 Current paths created by the sudden conduction of the arresters do not result in an undesired overcurrent for critical or sensitive equipment

Conclusions on the Effect of the Surge Arrester Configuration

The effect of the surge arresters on the electromagnetic transients occurring in case of fault on a DC system depends on the surge arrester scheme considered. This implies that the

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Chapter 3: Slow-Front Overvoltages and Fault Analysis Nicolas Manduley 2020 Page 103 selection of the surge arrester configuration and their individual parameters does not only depend on the overvoltage levels of the component to be protected, but also on the other arresters and their effect on the system dynamics.

The operating principle of the surge arresters involves the formation of temporary current paths during the transient state. Whenever a new surge arrester configuration is studied, special care shall be taken to the possible loops created by the action of the surge arresters in case of overvoltage.

For MMC-HVDC systems presenting the arm reactor on the AC side, the smoothing reactor will also play a role in limiting the fault current through the MMC valve when the arm-toground arrester starts conducting by avoiding the creation of a low-inductance path. Its installation is thus considered mandatory on MMC-HVDC systems with the arm reactor on the AC side. In configurations with the surge arrester on the DC side, such paths would not be created, and thus the installation of a dedicated smoothing reactor on the DC bus would not be necessary for such purpose.

The installation of surge arresters could effectively increase the longitudinal withstand voltage requirements of the inductances present in the system, as seen in the case of the arm reactors. This effect, though relatively small, shall be taken into account for the design of the clearances and insulation of the reactors, and can be considered as a key factor to decide whether the inductances will require a dedicated overvoltage protection (i.e. a surge arrester in parallel).

The most critical faults found in terms of both overvoltages and energy dissipation levels associated are the pole-to-ground, bus-to-ground and arm-to-ground fault (faults L, K and J, respectively), which is consistent with what has been found in the existing literature (Y. L. Gu et al., 2013;[START_REF] Saad | Study on transient overvoltages in converter station of MMC-HVDC links[END_REF].

Proposed Procedures for the Insulation Coordination of MMC-HVDC Systems Regarding Temporary and Slow-Front Overvoltages

As for LCC-HVDC systems, the fundamental principle of insulation coordination of MMC-HVDC systems-regarding slow-front and temporary overvoltages-involves the determination of the representative, coordination and required voltages and overvoltages (U rp , U cw and U rw , respectively). The essential differences with LCC-HVDC insulation coordination concern mainly, as hypothesized in Chapter 1, §4. These are basic blocks from which any setup can be obtained taking into account the configuration (e.g. symmetrical or asymmetrical monopole, bipole with or without metallic return), the topology (point-to-point or MTDC), the architecture (arm reactor on the AC or DC side-and its implications), type of link (underground/submarine cable, overhead line or hybrid) and possible locations of the arresters. The insulation coordination procedure can be thus adapted to MMC-HVDC by applying the essential insulation coordination philosophy from IEC standards to the fundamental schemes proposed in this chapter.

The last two points are given by the detailed electromagnetic transient simulations, through which the behavioural differences between configurations and overvoltage levels during transients have been identified, as well as the differences with LCC-HVDC systems.

Therefore, the proposed procedure for insulation coordination for MMC-HVDC systems is based directly on the fundamental schemes from Figure 3.1 and Figure 3.2 and is described in §5.1 below. Next, recommendations for the overvoltage protection, and in particular for the specification of the arresters shown in the proposed fundamental schemes, are given in §5.2 based on the results obtained through this research.

Procedure

Because of the critical need to consider the effect of non-linear devices as the surge arresters in the insulation coordination, this procedure assumes that detailed studies are performed through electromagnetic transient simulations.

Four main stages can be identified in the insulation coordination of MMC-HVDC systems, and are illustrated in Figure 3.18.

In the first stage, a system analysis is performed taking into consideration the configuration and architecture of the system, which can be done by adjusting the fundamental schemes from Figure 3.1 and Figure 3.2 to the particular case (as it was done in §4.2 and §4.3, see Figure 3.8 and Figure 3.10). The insulation configuration and types, as well as a surge arrester arrangement, must be also established in this section to determine the desired final outputs of the design. Then, the voltages in service can be estimated analytically for each location (for instance, using the equations from Table 3.3), which provides a first estimation of the representative voltages U rp (and/or the coordination withstand voltages, depending on the coordination factor considered) under normal operating conditions for the different locations.

An initial value of the parameters of the surge arresters can be calculated based on U rp or U cw .

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Next, the system is modelled in the electromagnetic transient (EMT) tool used to conduct the studies, and the transient events are defined (faults, disconnections, resonance, ferroresonance, etc.). Multiple iterations may be required in order to optimize the surge arrester parameters while meeting the performance criterion and respecting the surge arrester energy absorption capability. The maximum slow-front and temporary overvoltages resulting from all the considered events constitute the minimum coordination withstand voltage (U cw ), as suggested in IEC 60071-5, for each location under transient conditions.

After obtaining all the values for U cw , the required withstand voltage U rw for each location is obtained by taking into account a safety factor and an altitude correction factor, as defined in IEC 60071-5 for LCC-HVDC systems. The same reference factors indicated in IEC 60071-5 may be used for MMC-HVDC since they are given according to the general station location (AC or DC switchyard, valve hall equipment, transformers, etc.). These required withstand voltage values will constitute one of the main input parameters for the calculation of the required air clearances (following the procedures from IEC 60071-2 or CENELEC 50341) and general insulation design (as specified, for instance, in IEC 60815 standards for AC and DC insulators).

Finally, the design is completed by specifying the dielectric strength for every equipment of the system along with the location and parameters of the surge arresters used for the overvoltage protection strategy. In the case of AC systems, a standard dielectric strength may be selected. In absence of standard values for DC, the final specification consists of the minimum required withstand calculated in the previous step. Alternatively, the standard values for AC may be used. The preferred procedure should be specified by the technical committee.

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Chapter 3: Slow-Front Overvoltages and Fault Analysis Nicolas Manduley 2020 Page 106 The final design may include considerations regarding technical feasibility (e.g. available space for equipment, size of the station, maximum number of arrester columns, etc.) and economical aspects. To allow the possibility of investigating several designs, the flowchart shown in Figure 3.18 allows to go back to the first or second step so that the configuration, insulation types, architectures, fault scenarios and/or other parameters can be modified to perform the procedure again with the same methodology.

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Overvoltage Protection

This section provides a series of indications and recommendations for the design of the different surge arresters illustrated in Figure 3.1 and Figure 3.2, and are given based on the results obtained in this research and explained in previous sections of this chapter.

Arrester A1 (Primary Side of the Converter Transformer)

Arrester A1 is installed to protect the windings of the primary side of the converter transformer. Since no significant overvoltages are transmitted to the primary side due to AC, DC or converter faults, no significant energy is absorbed by this arrester during slow-front and temporary overvoltages coming from the secondary side. Therefore, and considering that generally the station is well designed to avoid such events to originate within the station, arrester A1 shall be dimensioned for fast-front overvoltage (FFO) withstand in case of lightning strokes hitting the station.

The conventional method used for the design of AC arresters based on the estimation of the maximum TOV (see IEC 60071-1 and 2) shall be enough to guarantee an adequate overvoltage limitation on the windings of the transformer in case of FFO, as well as the safe operation of the arrester in terms of energy absorption and service conditions.

Arrester A2 (Secondary Side of the Converter Transformer)

As for arrester A1, with three main differences:

 Significant overvoltages may appear at location 2 due to faults coming from the converter or the DC line.

 In case of a bipolar configuration, the phase-to-ground voltage of location 2 is not a regular sinusoidal, but a sinusoidal with a DC offset (see Figure 3.3 and Figure 3.4).

 The overvoltage levels are significantly lower for bipolar configurations than for monopolar configurations.

Therefore, even though the conventional method for the design of AC arresters from IEC 60071 standards may yield an adequate design, simulation studies shall determine if the overvoltage levels in case of events generating slow-front and temporary overvoltages do not represent a dangerous scenario in terms of energy absorption of the arrester, especially for monopolar configurations.

Arrester A3 (Intermediate Point between the MMC Submodules and the Arm Reactor)

Arrester A3 is subjected to different overvoltage conditions depending on the location of the arm reactor (AC or DC side) and, in case of a bipolar configuration, its location within the converter leg (upper or lower arm).

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The most critical overvoltage levels are reached by the symmetric monopolar configuration with the arm reactor on the AC side, where location 3 can reach overvoltage values up to approximately 2.65 p.u. for a DC pole-to-ground fault at the middle of the cable section (fault L, see §4.3). Slightly lower overvoltages are reached for a configuration with the arm reactor on the DC side, in the order of 2.33 p.u. Therefore, for all symmetric monopolar configurations, special attention shall be paid to the energy absorption level of arrester A3 and its energy handling capability to ensure a safe operation. Multiple parallel columns may be used if needed with this respect.

In bipolar configurations, overvoltage levels are generally not very significant due to the low grounding resistance of the system, which naturally reduces the overvoltage levels during faults. However, in certain cases, some discontinuities may be found on the soil resistivity, which would affect the maximum overvoltage levels during transients. In such cases, the grounding scheme should adequately represent this case.

For configurations with the arm reactor on the AC side, arrester A 3low can be considered equivalent to arrester V (in case of solid grounding of the neutral point). In such case, arrester A 3low may be omitted. If another grounding scheme is used for the neutral point, the U c of arrester A 3low shall be at least as high as the operating voltage of the MMC valve, and the overvoltage levels to which it would be subjected would depend on the grounding scheme, being directly proportional to the impedance of the grounding scheme used. Simulation studies shall then determine the utility of this arrester.

Similarly, for bipolar configurations with the arm reactor on the DC side, arrester A 3low can be considered equivalent to arrester BR (in case of solid grounding of the neutral point), and thus be omitted. In case of a different grounding scheme for the neutral point, it might still conduct significant currents that would not be limited by the arm reactor, which represents a potential danger to the system. In such case, which have not been considered in this research, simulation studies shall determine the need for this arrester. If needed, there is interest on keeping the protective levels as high as possible to prevent the fault currents from bypassing the arm reactor.

Arrester BR (Bridge Arm Reactor)

The arm reactor plays a significant role in limiting the rise of the fault current that enters the converter station and flows through the MMC valves. The conduction of arrester BR would bypass the arm reactor and thus prevent it from limiting the di/dt of the fault current, which represents a potentially dangerous condition for the MMC valve.

Therefore, arrester BR should only be installed if the overvoltage levels that may appear across the arm reactor may reach or surpass the withstand voltage of the reactor. In such case, there

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is special interest in keeping the protective level of arrester BR as high as possible to not sacrifice the ability of the arm reactor to limit the rise of the currents entering the station.

Arresters C/D (DC Bus) and DL/DC (Line/Cable Departure)

These arresters are installed to protect the DC switchyard equipment connected to the DC pole and may be subjected to different kinds of stresses depending on the configuration. In a bipolar configuration, such arresters are mainly subjected to lightning stresses, while in symmetric monopolar configurations they can be also subjected to slow-front and temporary overvoltages, as seen in the studies presented in this chapter.

Within the context of lightning protection, due to the high rise rate of lightning currents, several arresters may be required at various locations to provide protection to different areas of the station. For instance, arresters C and D provide direct protection to the DC bus, and some indirect protection to the smoothing reactor (for configurations where a smoothing reactor is present). Arresters DL and DC provide protection to the departure of the line or cable, respectively.

For a symmetric monopolar configuration, DC bus/cable/line arresters may be heavily demanded, mainly due to the charge of the healthy pole in case of a ground fault on the DC bus or cable/line. In such cases, special care shall be taken when specifying such arresters to guarantee the safe operation of the arresters, particularly in terms of energy absorption capability.

For all arresters above, the minimum continuous operating voltage U c is the maximum nominal DC voltage at which the system is designed to operate.

For a 100% cable link where no significant SFOs or TOVs occur, arrester DC may be omitted since the cable may not be exposed to lightning overvoltages (IEC 60071-5).

Arrester E, EL and EM (Neutral Bus)

Since arresters E, EL and EM only concern bipolar configurations (and their respective operating modes), the specification of such arresters follows the same methodology described in IEC 60071-5 for LCC-HVDC systems.

Briefly, during balanced bipolar operation, the neutral point is subjected to very low voltages under normal operating conditions (in case of a solid grounding scheme). However, during asymmetric monopolar or unbalanced bipolar operation, usually a metallic return is present, and more significant voltage levels may appear in normal operating conditions due to the voltage drop produced by the return current across the metallic return. Arresters shall be capable of operating at such levels, if the station is designed to operate in such modes in normal operating conditions.

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In addition, neutral bus arresters shall be capable of discharging large amounts of energy. This may become difficult, as the energy handling capability is proportional to the rated voltage of the arrester. Since the voltage drop in the metallic return is small (compared, for instance, to the nominal DC voltage), it is likely that the energy handling capability of the neutral arresters is not high enough to guarantee the safe functioning of the arrester during such discharge of energy. When this is the case, several arrester columns may be installed in parallel for higher energy absorption capability. In case of excessive energy ratings, a sacrificial arrester may be installed.

Arresters J and JM (Junction between Cables and Overhead Lines)

Whenever a hybrid line is present, a surge arrester may be placed in the cable -overhead line junction to prevent excessive overvoltages on the cable (IEC 60071-5). The procedures and considerations for the specifications of the parameters of arresters J and JM are the same as for arresters of the DC bus or line (arresters C, D, DL/DC in §5.2.5) and for the neutral bus (arrester EM in §5.2.6).

Arrester SPR (Star-Point Reactor Resistance)

The star-point reactor represents a high-impedance grounding scheme for the secondary side of the converter transformer. The goal of the resistance is to limit as much as possible the current flowing through the ground and avoid the saturation of the reactors connected to the phases of the secondary side of the transformer. This way, the star-point reactor can effectively provide a zero-voltage reference to the system.

Therefore, arrester SPR should only be installed if the overvoltage levels that may appear across the resistance of the star-point reactor may reach or surpass the withstand voltage of the resistance. If needed, there is particular interest in keeping the protective levels of the arrester as high as possible to avoid the saturation of the inductances of the star-point reactor.

Arrester SR (Smoothing Reactor)

Similarly as for arrester BR, the smoothing reactor plays a significant role in limiting the fault currents entering the station, and particularly in case of fast-front overvoltages due to lightning strikes coming from the line.

Therefore, arrester SR should only be installed if the overvoltage levels that may appear across the smoothing reactor may reach or surpass the withstand voltage of the reactor. In such case, there is special interest in keeping the protective level of arrester SR as high as possible to not sacrifice the ability of the smoothing reactor to limit the rise of the currents entering the station.

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Chapter 3: Slow-Front Overvoltages and Fault Analysis

Arrester V (MMC Valve)

The minimum operating voltage U c of the arrester shall be at least as high as the normal operating voltage of the MMC submodule (V SM ). However, as seen in previous sections, overvoltage levels across the MMC submodule are barely above the voltage under normal operating conditions (about 10 -20% higher). As a result, no significant currents would flow through arrester V during SFOs and TOVs, and therefore it may be omitted for most applications.

Furthermore, the design rules of semiconductor components typically result in relatively high overvoltage withstand. For instance, an IGBT may be designed for 3 kV and selected to operate at 1.5 kV. In such a case, a dedicated overvoltage protection through surge arresters would not be justified since the maximum overvoltage is significantly inferior to the maximum withstand voltage of the component.

Algorithm for the Specification of the Surge Arresters

An algorithm is proposed for the specification of the parameters of the surge arresters taking into consideration the main conclusions from this research. It consists of an iterative process involving electromagnetic transient simulations of faults, switching operations and other phenomena leading to slow-front and temporary overvoltages. Throughout the process, the specifications of the surge arresters are adjusted after each iteration by considering the energy absorption levels of each arrester, as well as the maximum overvoltage levels for each location.

However, this algorithm has not yet been tested, for which is it presented and explained in Appendix E. Further studies shall investigate the performance of this algorithm and its capacity to obtain an optimal specification of the surge arresters for the overvoltage protection strategy of the MMC-HVDC station, based on the fundamental principles described in this chapter.

Conclusion

Insulation coordination consists of the selection of the dielectric strength of the insulating materials taking into account the action of overvoltage limitation devices, such as surge arresters. To complete this task, it is fundamental to understand the behaviour of the system under both normal and transient conditions to be able to design an adequate overvoltage protection strategy leading to an optimal design of the insulation of the system.

One of the current challenges regarding VSC-HVDC systems, and particularly the MMC, is that there are currently no standards providing the guidelines on how the insulation coordination should be performed for such systems.

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Chapter 3: Slow-Front Overvoltages and Fault Analysis Nicolas Manduley 2020 Page 112

In this chapter, the fundamental principles of insulation coordination, extracted from the HVAC and LCC-HVDC standards, have been adapted to MMC-HVDC configurations within the context of slow-front and temporary overvoltages. The procedures have been adapted by considering the essential differences between AC and DC, and also the specific differences between LCC-HVDC and VSC-HVDC systems. The latter includes mainly: the architecture of the converter, the use of a wider variety of station configurations (e.g. symmetric monopolar or bipolar configuration), the location and design of the surge arresters, the transient behaviour and the overvoltage levels.

Inspired on the approach of IEC 60071-5 for LCC-HVDC systems, two fundamental schemes are proposed in this work to constitute the base for the insulation coordination studies for MMC-HVDC stations. Such fundamental schemes allow extending the insulation coordination principles to any architecture (with the arm reactor on the AC or DC side), configuration (monopolar, bipolar, MTDC) and possible locations for the surge arresters for the overvoltage protection strategy. They also include the possibility to have different link technologies (cable, overhead lines or hybrid links) and analyse different operating modes with or without metallic returns.

A voltage and overvoltage analyses have been performed using both analytical expressions and simulation studies to characterise the types of overvoltages that may occur at the critical locations and components, as well as their causes. The results have been analysed in order to provide general insights on the potential stresses that may appear for each location and the aspects to be considered for the design of their respective surge arresters. In addition, the influence of the surge arrester arrangement within the station have been investigated by analysing various surge arrester configurations, all designed with the same criteria for each case, under the most critical fault scenarios as defined by the studies presented in this chapter as well as studies available in the literature. It has been concluded that the particular arrangement of surge arresters chosen for the overvoltage protection strategy has a very significant impact on the role that each arrester plays during transients, as well as on the selection of their individual parameters.

Based on the analysis of the results and individual conclusions for each section, a general insulation coordination procedure for MMC-HVDC systems has been proposed. The proposed approach addresses all the aspects discussed in Chapter 1 and at the beginning of this chapter that have been determined to be essential in adapting the fundamental principles of insulation coordination to such systems. It also provides specific guidelines for the design of each of the surge arresters that may be considered in the overvoltage protection strategy. On the same line, an algorithm for the specification of the surge arresters has been proposed, which is presented in Appendix E. The proposed algorithm allows selecting the protective levels of the

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Chapter 3: Slow-Front Overvoltages and Fault Analysis Nicolas Manduley 2020 Page 113

surge arresters and number of parallel columns based on the energy absorption levels obtained through the electromagnetic transient simulations.

It is worth mentioning that a fully qualitative method for the study and analysis of the transient behaviour of a system has been proposed, which is presented in Appendix D. The method proves to be useful for obtaining valuable information about potentially critical events leading to overvoltages, as well as the most vulnerable points and the most critical instants for each fault type to occur, without the need for performing electromagnetic transient simulations.

However, there are often several phenomena that may have a significant influence on the overvoltage levels that cannot be considered through the simplified approach. The method is therefore considered a useful additional tool in addition to the EMT simulations, which can help achieve a better understanding of the fundamental behaviour of the system, but cannot constitute an accurate analysis method on its own.

The conclusions obtained in this last part justify the choice of laying the foundations of the insulation coordination approach proposed in this chapter on simulation studies.

In the next chapter, the specificities of HVDC are analysed in the context of overvoltage protection of HVDC lines against fast-front overvoltages due to lightning strokes on the lines, as well as other aspects regarding lightning protection that concerns MMC-HVDC systems with overhead lines. Chapter 4 Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Introduction

Lightning strokes are the most common source of fast-front overvoltages in overhead lines. The impacts can be produced at either the tower and/or shield wires (back-flashover) or directly to the power conductors (shielding failure). The estimation of lightning performance consists of the calculation of the flashover risk in both above mentioned cases, namely the back-flashover rate (BFOR) and shielding failure flashover rate (SFFOR).

The main goal of this chapter is to provide information on how to perform lightning studies for HVDC systems according to the existing standards and guidelines (CIGRE TB 549, 2013;CIGRE TB 63, 1991;CIGRE TB 704, 2017;IEC 60071-1, 2011;IEC 60071-2, 2018;IEC 60071-5, 2014;IEEE Std. 1243, 1997), and use this knowledge to achieve a better understanding of how HVDC (and specially VSC-HVDC) systems behave and to propose solutions for the improvement of the lightning performance in such systems. The calculation methods and procedures followed for the estimation of both the BFOR and SFFOR are explained in detail in Chapter 1, §6.4.

To do so, the specific particularities of HVDC systems are addressed. Special emphasis will be placed on the case of double-circuit HVDC configurations since they present the potentially most critical conditions in terms of lightning performance and loss of transmitted power, while also including all the issues associated to single circuit lines.

Next, case studies will be presented to analyse the impact of the configuration of the DC poles on the lightning performance of double circuit configurations. Factors such as the footing resistance of the tower, the coupling of the conductors, the polarity of the stroke and the voltage drops across the tower are considered to perform the analysis.

Finally, and over the base constructed in the above mentioned sections, two solutions aiming to improve the lightning performance are investigated, namely the installation of line surge arresters and the use of unbalanced insulation for double-circuit HVDC lines.

Specificities of HVDC Overhead Lines Regarding Lightning Performance

This section addresses different aspects regarding the lightning performance of HVDC systems. Generally speaking, the fundamental factors playing a role in the lightning performance of HVDC lines are the same as those for HVAC lines (see Chapter 1). The main differences are associated to the insulator string lengths, which are typically longer for HVDC insulators, and the power frequency voltages of the phases.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance Nicolas Manduley 2020 Page 116

As in HVAC lines the voltage across the insulators is constantly changing, the flashover risk of each phase will depend on the instantaneous voltage when the stroke is produced. Because each phase goes through positive and negative semi-cycles, the overall risk associated to the polarity of the conductors is averaged over the whole cycles of each phase. Conversely, in HVDC systems the voltages are constant, and the flashover risk of each DC conductor is different depending on their respective polarity and does not depend on the instant when lightning strikes.

This fact introduces a particular problem when double (or multi) circuit HVDC configurations are considered. Since the polarities and amplitudes of the conductors are constant, the geometric configuration of the DC poles within the tower may have a significant effect on the overall lightning performance against strikes of either polarity. Additionally, when the operating voltages of two separate circuits are the same, it means that there are always two conductors guaranteed to have the same voltage level at the moment of the strike. In other words, two conductors from different circuits may be equally or similarly likely to flashover, which could lead to the simultaneous loss of two circuits due to the same stroke.

In this section, the consequences of faults due to lightning strokes on a DC system are discussed, as well as the mechanisms involved in the lightning performance of HVDC systems, and in particular for double-circuit HVDC configurations.

Consequences of Faults due to Lightning Strokes on a DC System

Whenever a flashover due to lightning occurs, a temporary pole-to-ground fault appears. Depending on the protection strategy of the DC system, an AC or DC circuit breaker may be required to open to interrupt the fault current (CIGRE TB 269, 2005). Except in the cases where the extinction of the arc is produced before the protection reacts [START_REF] Woodford | Symmetrical monopole VSC transmission[END_REF], this may result in a significant temporary loss of transmitted power. As discussed in Chapter 1, this may result in disturbances which may last less than a second to up to one minute, and in some cases, it could compromise the stability of the system.

In the case of double circuit DC transmission towers, and particularly for direct strikes to the tower or shield wires, this risk may be especially high since two DC poles of the same polarity could back-flashover at the same time due to the same stroke, potentially resulting in an even higher loss of transmitted power. In single circuit configurations, this risk is significantly lower because the only two poles present are of opposite polarities, and therefore the voltage variation across their respective insulators due to the voltage rise of the tower will tend to add to the previous voltage level of one, and subtract from the other.

For instance, consider the insulator of a positive DC pole. In the event of a negative stroke, the voltage of the tower increases negatively, and thus the total difference between the positive

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance pole and the tower becomes greater. Conversely, for a positive stroke, the voltage across the insulator will decrease, and a zero-crossing will be produced before the voltage rises again. In other words, positive DC poles are more likely to flashover due to a negative stroke. The same analysis can be performed for negative DC poles.

Therefore, it is of special interest of this section to focus on the particularities of double circuit HVDC overhead lines, and the specific risks that may appear in such kind of systems.

Particularities of Double Circuit HVDC Overhead Lines

The particularities of multi-circuit configurations for HVAC systems have been addressed in the past (Kawai & Azuma, 1965;Z. Li, Yu, Wang, & He, 2012;[START_REF] Sargent | Lightning performance of double-circuit transmission lines[END_REF][START_REF] Wei-Gang | Lightning performance of 500-kV double-circuit line schemes for the three-gorge project[END_REF] and are well known nowadays in terms of configurations and solutions that ensure a better lightning performance of the system. However, there is little knowledge about the case of double circuit configurations in HVDC.

One of the main differences, as mentioned before, is associated to the fact that in HVDC systems the voltages at the conductors are constant. As a result, the repartition of the electric fields along and around the tower is different from that of AC systems (Liu, Zou, Tian, & Yuan, 2009; [START_REF] Yang | A calculation method for the electric field under double-circuit HVDC transmission lines[END_REF][START_REF] Yong | Study on simulating test of total electric field of double-circuit DC transmission line[END_REF] and the flashover risk of each DC conductor is relatively constant and depends on its polarity.

For instance, consider a double-circuit HVDC configuration with two cross arms, as depicted in There are four ways in which the different polarities can be placed within the tower, and they are labelled relative to the position of the positive poles as Top (positives on top), Bot (positives at the bottom), Side (positives on one side of the tower) and Xed (positives crossed).

Because the polarities are always constant, it is possible to study and predict the overall behaviour of each one in the event of a stroke, as well as to determine the overall lightning performance and the poles that are most likely to flashover.

The next section assesses the effect of the pole configuration on the lightning performance of double-circuit HVDC lines to achieve a better overall understanding of the behaviour of the system and to determine the relevance of the position of the DC poles before continuing with the techniques for the improvement of the lightning performance.

Hypotheses and Procedures

Some of the procedures presented in the literature review (0) are not well suited to consider double-pole flashovers, non-linearities (i.e. surge arresters) or asymmetric configurations of the tower or conductors, all of which are of great interest for the purposes of this chapter. In order to adequately study the system under such conditions, some new features are added to the procedures presented in Chapter 1. In this respect, the following hypotheses and procedures are adopted:

 Positive and negative strokes are considered according to the hypotheses discussed in Chapter 2.

 For the estimation of the back-flashover rate (BFOR), the critical flashover current I f is determined by dichotomy through EMTP simulations. Successive values of current amplitudes within a defined range are evaluated through EMTP. The evaluation range is progressively reduced depending on whether the evaluated value resulted in a backflashover or not until the convergence criterion is met (see Figure 4.2).  After the value of I f is estimated, the back-flashover rate (BFOR) is calculated according to the procedures explained in Chapter 1, §6.4.1.

 The total BFOR is the sum of the rates corresponding to positive and negative strokes.

A factor of 0.1 and 0.9, respectively, is applied to each one to consider an incidence of positive strokes of 10%, and 90% for negative strokes.

 Whenever EMTP is used to simulate lightning strokes, only first strokes are modelled (subsequent strokes are not considered in simulation studies).

 The shielding failure flashover rate (SFFOR) is calculated following the procedures presented in Chapter 1, §6.4.2. In all cases, the effect of subsequent strokes are considered in the calculations. No EMTP simulations are involved in this procedure.

 The studied overhead line is considered homogeneous, including the line models, transmission towers, line insulators and grounding resistances.

 Only a few points of impact are considered: either at the tower or at one third of the span length of the shield wire or the power conductor.

These hypotheses allow to combine the standard procedures and electromagnetic transient simulations to obtain detailed and accurate results in double circuit configurations including surge arresters and/or asymmetries, which constitute some of the main objectives of this chapter. In addition, they allow to make use of an up-to-date modelling of all the different components considered in the system.

Effect of the Configuration of the DC Poles

The different pole configurations considered for this study are depicted in Figure 4.1 and, in a more compact way for quick reference, in Table 4.1 below. As the methods for the estimation of the shielding failure flashover rate (SFFOR) used in this work does not consider the specific polarity of each conductor (EGM and simplified LPM, see Chapter 1), only the effect on the back-flashover rate (BFOR) will be assessed and discussed in this section. However, as it will be seen later in this chapter, shielding failure flashovers typically concern exclusively the struck conductor, and multiple conductor flashovers are very unlikely, if even possible. It will thus be assumed for this section that the effect of the configuration of the DC poles within the tower will mainly concern the back-flashover performance.

Top

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Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance Nicolas Manduley 2020 Page 120

Therefore, the effect of the pole configuration on the overall and double back-flashover lightning performance is investigated for two voltage levels (320 kV and 500 kV)-in line with the current tendencies for the construction of HVDC lines in Europe-and different values of the tower resistance ranging from 10 to 100 Ω. The contents and the results presented in this section have been submitted by the author to EPSR journal in October 2020.

Case Study Setup

The studies have been carried out using EMTP, and each component has been modelled following the guidelines and methods discussed in Chapter 2.

The general simulation setup used in this work for lightning studies, based on the guidelines presented in Chapter 2, is illustrated in Figure 4.3 and Figure 4.4. A section of eleven towers has been modelled to take into consideration the effect of successive reflections on neighbouring towers. Line sections of 300 m are used to represent the spans between the towers. A long line section (50 km) is placed at both ends to avoid reflections with the stations. The initial conditions are set with ideal voltage and current sources at the ends of the line section (see Figure 4.3a and Figure 4.3b). This EMTP model allows to apply strokes on either the shield wires or the power conductors, either at the tower level or along the span (see Figure 4.3b).

Overhead lines, including the spans and the 50 km sections, are represented by a frequency dependent (FD) model. Two and three-bundle conductors configurations are used for the 320 kV and 500 kV systems, respectively, as it is typical for such voltage levels (CIGRE TB 388, 2009). To consider the skin effect, each individual conductor is modelled as a solid conductor in EMTP.

Insulator strings are represented through their arcing horns using the leader model proposed by Shindo (with the adaptations specified in Chapter 2), which is recommended for long gaps and considers the streamer and leader formation phases of a flashover [START_REF] Shindo | A new calculation method of breakdown voltage-time characteristics of long air gaps[END_REF], as well as the polarity of the impulse. The base string length of the insulators were chosen as typical approximate values presented in (CIGRE TB 388, 2009) for HVDC links for both voltage levels, and are 3.42 m and 5.2 m for the 320 kV and 500 kV systems, respectively. Their respective air distances between the arcing horns are 2.74 m and 4.16 m, which are the values used to model the air gap between the arcing horns.

Lightning strokes are applied at the middle of the considered line section (i.e. tower 6).

Lightning currents up to 350 kA were considered. If no flashovers were produced at 350 kA, the corresponding value of back-flashover rate (BFOR) is considered to be zero. This is justified by the extremely low probability for a stroke of such intensity to occur, for which it can be neglected in the calculations. It is worth mentioning that the overall BFOR includes all kinds of lightning back-flashovers. Thus, when speaking about double back-flashover rates, it refers to the portion of the overall BFOR which is constituted by two or more flashovers.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Results

The overall and double back-flashover rates (BFOR) for the 320 kV and 500 kV systems are shown in Figure 4.5 and Figure 4.6, respectively, for all pole configurations.

In all cases, the results are greatly influenced by the footing resistance of the towers, which is in agreement with what was found in the literature (see Chapter 1). . This means that in those two configurations, the critical current I f required to produce a first flashover will most likely produce a double flashover in the system.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

In the case of the Side and Xed configurations (yellow and purple bars), the overall BFOR tends to be slightly higher than in the above-mentioned configurations, but the proportion of double flashovers is greatly reduced. As it will be discussed later, this is due to the coupling of the conductors, because for any given stroke and polarity, the two poles which are more susceptible to flashover are in different cross arms. Therefore, the upper pole is closer to the shield wires, and thus better protected by the coupling effect. The results illustrated in Figure 4.5 and Figure 4.6 can be explained by considering three main factors: the conductor coupling, the polarity of the impulse and the voltage drops along the tower (see Chapter 1). Additionally, the EMTP model used in this work is perfectly symmetrical (i.e. the left side of the tower is mathematically identical to the right side). In real applications, small asymmetries inherent to the construction of the line and/or the dielectric properties of individual insulators may make the results obtained through the simulations to differ-to a certain extent-from what is observed in practice (e.g. slightly different breakdown voltages of nominally identical insulators). However, it will be assumed that the influence of this factor is small and that the obtained results are representative of the behaviour of real applications.

As already mentioned in Chapter 1, the coupling of the conductors causes an additional voltage to arise in the DC pole due to the induced voltage from the current flowing through the shield wires [START_REF] Sargent | Lightning performance of double-circuit transmission lines[END_REF]. Since this voltage rise goes in the same direction as that of the tower, the induced voltage provides some protection to the pole by reducing the total voltage across the insulators. This is illustrated in Figure 4.7, which features a positive stroke of 120 kA on a Xed configuration. This figure has been already presented in Chapter 1 (Figure 1.20) but has been included also here for easier reference.

Additionally, because the pole voltages are constant and the dielectric strength of an air gap is different for positive and negative impulses (CIGRE TB 72, 1992;Cortina et al., 1984), the polarity of the stroke also determines which insulator strings are more susceptible to flashovers. For instance, in case of a negative stroke (which represents about 90% of the lightning discharges to the ground (CIGRE TB 549, 2013;CIGRE TB 63, 1991)), the positive poles are more likely to flashover first.

Finally, the voltage drop across the different sections of the tower may also play a role in the performance. As it can be observed in Figure 4.8, the voltage drop across the upper section (V t_up ) concerns only the poles in the upper cross arm. As a result, the upper cross arm sees a slightly higher voltage drop of the tower than the lower cross arm. This is also illustrated in Figure 4.7 (red and green curves). As it can be noticed, this effect counters the protective effect of the line coupling. However, this effect tends to be significantly smaller than the coupling effect for most cases. Very low values of footing resistance and unusually high current intensities are required for this effect to become more significant than the coupling effect. Therefore, this effect may be often disregarded, but could still explain the behaviour of the system under very specific conditions. Following the notation presented in Figure 4.8 and the aspects previously discussed, and neglecting the induced voltages due to the coupling between the different parts of the tower, the voltages of the upper and lower insulators are expressed as follows:

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

𝑉 𝑖𝑛𝑠_𝑢𝑝 = 𝑉 𝑔𝑛𝑑 + 𝑉 𝑡_𝑏𝑜𝑑𝑦 + 𝑉 𝑡_𝑢𝑝 -𝑉 𝑥𝑎𝑟𝑚_𝑢𝑝 -𝑉 𝐷𝐶_𝑢𝑝 (4-1) 𝑉 𝑖𝑛𝑠_𝑙𝑜𝑤 = 𝑉 𝑔𝑛𝑑 + 𝑉 𝑡_𝑏𝑜𝑑𝑦 -𝑉 𝑥𝑎𝑟𝑚_𝑙𝑜𝑤 -𝑉 𝐷𝐶_𝑙𝑜𝑤 (4-2)
If the induced voltages due to the coupling between the conductors only8 are taken into account, the above equations are rewritten as:

𝑉 𝑖𝑛𝑠_𝑢𝑝 = 𝑉 𝑔𝑛𝑑 + 𝑉 𝑡_𝑏𝑜𝑑𝑦 + 𝑉 𝑡_𝑢𝑝 -𝑉 𝑥𝑎𝑟𝑚_𝑢𝑝 -(𝑉 𝐷𝐶_𝑢𝑝 + 𝑉 𝑖𝑛𝑑_𝑢𝑝 ) (4-3) 𝑉 𝑖𝑛𝑠_𝑙𝑜𝑤 = 𝑉 𝑔𝑛𝑑 + 𝑉 𝑡_𝑏𝑜𝑑𝑦 -𝑉 𝑥𝑎𝑟𝑚_𝑙𝑜𝑤 -(𝑉 𝐷𝐶_𝑙𝑜𝑤 + 𝑉 𝑖𝑛𝑑_𝑙𝑜𝑤 ) (4-4)
Therefore, the difference in voltage between an upper and a lower insulator is given by equation (4-6):

𝛥𝑉 𝑖𝑛𝑠 = 𝑉 𝑖𝑛𝑠_𝑢𝑝 -𝑉 𝑖𝑛𝑠_𝑙𝑜𝑤 (4-5) 𝛥𝑉 𝑖𝑛𝑠 = 𝑉 𝑡_𝑢𝑝 + (𝑉 𝑥𝑎𝑟𝑚_𝑙𝑜𝑤 -𝑉 𝑥𝑎𝑟𝑚_𝑢𝑝 ) + (𝑉 𝐷𝐶_𝑙𝑜𝑤 -𝑉 𝐷𝐶_𝑢𝑝 ) + (𝑉 𝑖𝑛𝑑_𝑙𝑜𝑤 -𝑉 𝑖𝑛𝑑_𝑢𝑝 ) (4-6)
Since before the first flashover occurs, little to no current flows through the cross arms. In those cases, it is possible to disregard the terms V xarm_low and V xarm_up . The simplified expression is shown in equation (4-7) below:

𝛥𝑉 𝑖𝑛𝑠 = 𝑉 𝑡_𝑢𝑝 + (𝑉 𝐷𝐶_𝑙𝑜𝑤 -𝑉 𝐷𝐶_𝑢𝑝 ) + (𝑉 𝑖𝑛𝑑_𝑙𝑜𝑤 -𝑉 𝑖𝑛𝑑_𝑢𝑝 ) (4-7)
where V t_up represents the voltage drop at the tower section between both cross arms (difference between the red and green curves in Figure 4.7), V DC_up and V DC_low represent the nominal DC voltages of the lines and V ind_up and V ind_low represent the induced voltages as a result of the coupling between the conductors.

For instance, consider a positive lightning stroke on a crossed (Xed) configuration (see Table 4.1), where the negative poles (which present the highest flashover risk in case of positive strikes) are located at different cross arms. Since the nominal voltages are the same, the V DC_low and V DC_up terms cancel out, and the total difference between the upper and lower insulators depends only on the voltage drop of the tower section between the cross arms (V t_up ) and the difference between the induced voltages, as expressed below:

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance Nicolas Manduley 2020 Page 126

𝛥𝑉 𝑖𝑛𝑠 = 𝑉 𝑡_𝑢𝑝 + (𝑉 𝑖𝑛𝑑_𝑙𝑜𝑤 -𝑉 𝑖𝑛𝑑_𝑢𝑝 ) (4-8)
Because the conductors at the upper cross arm present a higher coupling factor with the shield wires, the term V ind_up will be larger than V ind_low , resulting in an overall negative induced voltage difference between the upper and lower insulators. On the other hand, the voltage drop at the tower section V t_up has the same polarity as the lightning stroke. Therefore, both effects (i.e. the voltage drop and the coupling effect) counter each other.

However, as stated before in this chapter, the voltage drop at such a short section of the tower is typically small, and the coupling effect tends to prevail in magnitude (as it can be also observed in Figure 4.7). Hence, the total difference ΔV ins between the upper and lower insulators is, in most cases, a negative value in case of a positive lightning stroke, and a positive value in case of a negative lightning stroke. In the above example with a positive lightning stroke, this means that the voltage across the lower insulator is higher than for the upper insulator, and thus, the lower pole is more likely to flashover due to the action of the coupling effect.

The studies presented in this chapter are based on line and circuit theory. However, there are some more complex electromagnetic interactions that are not considered with this approach (e.g. electromagnetic fields around the tower, conductors or lightning strikes and their respective interactions). A more detailed analysis would require the use of a field calculation program. For instance, the finite-difference time-domain (FDTD) method allows making precise predictions of the electromagnetic fields around a transmission line (Paladian, Bonnet, Lallechere, Xemard, & Miry, 2014; Tatematsu, 2019).

The next section discusses the obtained results considering the influencing factors described in this section.

Discussion

Considering all of the above, it is possible to explain the differences between the four pole configurations studied.

First of all, it is observed that the overall results are identical for both voltage levels investigated (i.e. 320 kV and 500 kV), except for the magnitude of the flashover rates. In spite of the height of the tower (which increases the lightning incidence), the flashover rates are lower for the 500 kV system than for the 320 kV system. This is explained by the fact that the insulator strings are naturally longer for the 500 kV system, and thus, a higher critical current is required for a flashover to occur than for the 320 kV system.

The fact that both the Top and Bot configurations (see used and the coupling of the conductors. Both poles on any given cross arm will see the same voltage rise of the tower and, regardless of the polarity of the stroke, the protective effect of the coupling will be almost identical on both sides (because the currents flowing on both shield wires are roughly the same).

However, to explain why the Top configuration presents a better overall performance than the Bot configuration, it is required to consider the fact that most strokes are negative. In case of direct negative strokes, the positive poles are more likely to flashover, and in the Top configuration both positive poles are located closer to the shield wires, and thus are better protected by the coupling effect than in the Bot configuration. For this same reason, the Bot configuration presents a slightly better performance than the Top configuration under positive strikes, but since this only represents about 10% of the cases, the overall performance of the Top configuration remains superior.

Similarly, the fact that both the Side and Xed configurations present the same overall BFOR, but different distributions of double flashovers, is also explained through the coupling effect. Both configurations have a positive and a negative pole in the lower cross arm. Hence, regardless of the polarity of the stroke, one of the lower poles will flashover first (as the upper poles are better protected by coupling effect). These effects are almost identical for both configurations during the first flashover.

However, as the first insulator flashes, a significant current is injected into the DC pole. This has two main consequences: firstly, the current flowing through the tower to the ground will decrease, and thus, the voltage of the tower structure will also drop (remind 0, Figure 1.21), making it more difficult for a second flashover to occur. Secondly, the variation of the current being injected to the DC pole will also induce a voltage on neighbouring conductors with the same polarity as the one originated by the shield wires, hence also contributing to the protection of the other insulators and associated poles.

In the Side configuration, the second insulator that could flashover is right above the faulted pole, and thus closer than in the Xed configuration and better protected by the induction from the faulted DC pole. Consequently, for a second flashover to occur, a higher critical current I f is required in the Side configuration than in the Xed configuration, thus producing the difference on double BFOR observed in Figure 4.5 and Figure 4.6.

Nevertheless, the Side configuration may present a series of practical drawbacks. In particular, the unbalanced distribution of the electric field which could result in a wider corridor (Liu et al., 2009;[START_REF] Yang | A calculation method for the electric field under double-circuit HVDC transmission lines[END_REF], and the maintenance of a single circuit may be complicated because both poles would necessarily be on opposite sides of the tower. These potential drawbacks are naturally avoided with the Xed configuration.

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Conclusions and Final Considerations

All the differences in performance between the different configurations can be analysed in terms of coupling effect, distribution of the polarity of the strokes and voltage drops across the tower. Nevertheless, in all cases, the dominant factor regarding lightning performance is the footing resistance of the towers, which is in agreement with the literature. The procedure described in this chapter allows conducting qualitative analyses on the lightning performance of an overhead line combining lightning statistics, the application of the electrogeometric model and EMTP transient calculations.

In addition, the overall behaviour and conclusions extracted from these studies are the same regardless of the system voltage level considered (i.e. 320 kV and 500 kV).

The Top configuration presents the best overall back-flashover performance (i.e. lower overall BFOR value in Figure 4.5a and Figure 4.6a), mainly due to the conductor coupling effect. However, when the critical current I f is reached, it is most likely that both poles will flashover at the same time. This constitutes a major drawback since in case of flashover, 100% of the transmitted power is lost.

The Side and Xed configurations present a slightly higher BFOR than the Top and Bot configurations, but a significantly lower incidence of double flashovers.

Techniques for the Improvement of the Lightning Performance of HVDC Overhead Lines

Taking into account the previously discussed factors playing a role in the lightning performance of an HVDC overhead line, it is possible to list a series of possible techniques to improve the lightning performance.

Since the shielding failure flashover rates (SFFOR) depend mostly on the tower geometry, the most common solution involves the installation of additional shield wires to provide better protection to the conductors and reduce their probability of being struck by lightning. Therefore, the solutions for the improvement of the lightning performance addressed in this section concern mainly the improvement of the back-flashover rates (BFOR).

One of the most obvious and well-known solutions is the improvement of the tower grounding. This can be done by directly modifying the shape, depth or materials of the grounding grid or electrodes [START_REF] Zhenghua | Research on reducing grounding resistance of transmission line tower grounding grid[END_REF], depending on the specific case. Other solutions involve the installation of underbuilt wires [START_REF] Visacro | The use of underbuilt wires to improve the lightning performance of transmission lines[END_REF], which physically connect several towers in series so that the equivalent grounding resistance in case of a stroke is reduced. These solutions are well known and in many cases can effectively help improve the back-flashover performance for areas with high soil resistivity.

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However, this is not always an easy task, especially for regions with really poor soil resistivity. The impedance of the grounding electrode depends strongly on the soil resistivity, and along with the propagation in the ground, it may become impossible to improve the grounding sufficiently to reach an acceptable value of the grounding resistance. In those cases, other solutions are required to improve the lightning performance.

In this section, two solutions are investigated for the improvement of the lightning performance of HVDC overhead lines: one involving the installation of line surge arresters (LSA) on specific towers along the line (see CIGRE TB 440), and another concerning the use of different air distances between the arcing horns of the insulators of each circuit. The latter can be achieved by either using different insulator string lengths, or using the same insulator strings and designing different distances between the arcing horns of each circuit. This solution is referred to as unbalanced insulation of the DC circuits (Kawai & Azuma, 1965;Lundquist & Lilliecrona, 2012;Manduley, Pack, et al., 2019).

Since in the previous section the overall results and behaviour of the system were found to be identical for both system voltage levels, both solutions were studied considering only a 500 kV system. Considering the advantages and drawbacks of each configuration discussed in the previous section, the Xed configuration has been selected to study the line surge arresters solution, and the Top configuration for the unbalanced insulation solution.

Installation of Line Surge Arresters (LSA)

The installation of LSA aims to improve the overall lightning performance, and it is well documented in the literature (S. Gu, Wang, Wan, Cao, & He, 2018;IEC 60099-9, 2014;IEEE Std. 1243, 1997;[START_REF] Visacro | Concerns on surge-arrester application for improving the backflashover rate of transmission lines[END_REF]. Even though it is a very effective solution to improve the lightning performance, it is often considered not economically viable to install LSA all along a transmission line. Therefore, this solution is implemented on specific critical points where the lightning performance is abnormally low (due to high altitude zones, mountainous regions, high soil resistivity areas, high lightning activity, etc.).

In this section, different configurations of LSA are investigated for the improvement of the lightning performance of a double-circuit HVDC line. The simulation setup is the same as in the previous section, but installing the different combinations of LSA (see Figure 4.9) in the tower which is struck by lightning (tower 6, at the middle of the eleven towers considered).

The surge arrester configurations considered in this section were chosen as follows. Since most strokes are negative and thus it is the lower positive pole which is most likely to flashover (as discussed in previous sections), the base configuration consists of a single line arrester protecting the lower positive DC pole (LP configuration in Figure 4.9). Therefore, all Though installing three or even four surge arresters would clearly result in a lower BFOR, these solution might not be economically viable in real applications. Furthermore, as it will be seen in the upcoming sections, a great improvement can be achieved with a single surge arrester, and in some cases the addition of a second arrester does not improve the performance very significantly. Therefore, combinations of more than two line arresters are not considered in this study.

The surge arrester parameters were chosen as follows. Firstly, the continuous operating voltage U c was obtained by multiplying the nominal voltage by a factor of 1.05 (which is a typical margin used in practice (Hinrichsen, 2012)). The base V-I characteristic used for the implementation is illustrated in Figure 4.10 (Hinrichsen, 2012) for a surge arrester of rated voltage U r equal to 336 kV (rms). This characteristic was fitted through EMTP to match the required parameters. Since the study is in the high frequency domain, the Pinceti model (Pinceti & Giannettoni, 1999) was used to represent the surge arrester in the EMT simulations. After the fitting, the corresponding lightning impulse protective (LIPL) obtained was 1123 kV (for a 10 kA impulse current) and 1229 kV (for a 20 kA impulse current). These parameters are summarized in Table 4. The results and comparisons of the obtained overall and double back-flashover rates (BFOR) are presented in Figure 4.11 and Figure 4.12, respectively. Both figures plot the corresponding BFOR vs the footing resistance of the towers.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

The following sections will discuss in detail the results presented in Figure 4.11 and Figure 4.12 for each configuration illustrated in Figure 4.9 separately. Next, the case in which the impact is produced on a neighbouring tower is analysed. Then, the effect of a surge arrester solution regarding the shielding failure flashover rate is assessed. Finally, some additional considerations and conclusions are provided concerning the installation of line surge arresters as a method for the improvement of the lightning performance. As already stated before, due to the fact that 90% of the strikes are negative, back-flashovers are more likely to be produced in the positive poles. In the LP configuration, because the upper positive pole is closer to the shield wires (and thus better protected by the coupling effect), the lower positive pole is the most likely to flashover. As it can be observed in Figure 4.11 and Figure 4.12, by directly protecting only the lower positive pole (LP configuration, see Figure 4.9), a great improvement of both the overall and double back-flashover rates can be achieved.

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Though double flashovers are still possible under positive strikes (because both negative poles remain unprotected) and very intense negative strikes (enough to make the lower negative pole flashover after the upper positive pole), the sum of the double BFOR due to these two scenarios is still significantly lower than in the base case (red bars in Figure 4.12).

LPLN Configuration

The poles in the lower cross arm are the ones with the highest probability to flashover because the protective coupling effect from the shield wires is weaker than for the poles in the upper arm. If both positive and negative lower poles are protected, as it can be observed in Figure 4.11, there is a significant improvement of the overall performance (especially at higher values of the footing resistance).

Even more interesting is the fact that, with this configuration, the probability of double flashovers is almost zero for the studied system and the footing resistances considered (see Figure 4.12). Since the lower positive and negative poles are directly protected by the surge arresters, regardless of the polarity of the strike, it is in the upper pole where the first flashover must be produced. Therefore, for a double flashover to occur, the current peak value must be sufficiently high to produce the second flashover in the pole with the opposite polarity, while also countering the coupling effect from the shield wires.

LPUP Configuration

If the second arrester is placed on the upper positive pole, the tower is almost perfectly protected against any negative strike (except for strikes sufficiently intense to produce a backflashover in the negative poles). The overall back-flashover rate (BFOR) is significantly lower than in the LP configuration (>50% lower) and it is the lowest among all the studied configurations (Figure 4.11). The portion of the overall BFOR constituted by double flashovers is also among the lowers obtained, right after the LPLN configuration (Figure 4.12).

LPUN Configuration

Generally, the upper negative pole is not very likely to flashover except in the case of very intense positive strikes producing double flashovers (since under normal conditions, the lower pole will flashover first). Therefore, as it is shown in Figure 4.11 and Figure 4.12, the LPUN configuration does limit the occurrence of double flashovers, but the overall improvement compared to the LP configuration is not very significant.

Effect on Neighbouring Towers

In this section, the objective is to determine if the surge arresters installed in a neighbouring tower can provide some protection to the tower struck by lightning. The base case (Xed configuration) has been compared to the case where the neighbouring tower is protected by a single surge arrester in the lower positive pole (LP configuration) or by an arrester in all four The results are presented in Figure 4.13 for overall and double BFOR performances.

It is observed that if lightning strikes a tower which is adjacent to a protected tower, the overall back-flashover performance is significantly improved. In addition, there is no significant difference if one or all DC poles of the neighbouring tower are protected by surge arresters. However, even though the overall performance is improved, the incidence of double flashovers seems to be slightly higher in the case where the neighbouring tower is protected by only one arrester. This is explained by the fact that whenever the considered tower is struck by lightning, part of the current flows through the shield wires to the adjacent towers (as discussed in previous sections), thus provoking a voltage increase of the adjacent tower as well. As the tower voltage increases, some current starts flowing through the surge arresters and injected to the DC pole (see Figure 4.14). As a result, the current flowing through the shield wires also increases, thus improving the protective action of the coupling effect. However, a part of this current returns to the struck tower with the opposite direction as the current flowing through the shield wires, thus partially countering the coupling effect that normally protects the poles from flashovers. In the case when the adjacent tower is protected by a single arrester in the lower positive pole, when negative lightning strikes the tower, some current will flow through the adjacent tower's surge arrester and will come back to the struck tower. When a first flashover is produced in the lower positive pole of the struck tower, the coupling effect that normally provides some protection to the upper pole is countered by the current flowing through the lower DC pole because of the action of the surge arresters, thus increasing the risk of a double flashover. If the neighbouring tower is protected by surge arresters on all the DC poles, when negative lightning strikes the tower, two things occur in comparison to the previous case: firstly, more current is drawn by the surge arresters (since both positive poles of the neighbouring tower are protected), thus increasing the protective action of the coupling effect. Secondly, the total current that returns to the struck tower due to the action of the neighbouring surge arresters is distributed in both positive DC poles. Therefore, the countering of the coupling effect with the shield wires is reduced by the action of the surge arresters, thus further reducing the double back-flashover rates.

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Considerations Regarding the Effect on the SFFOR

The evaluation of the shielding failure flashover rate (SFFOR) using the simplified LPM approach (see Chapter 1) yields a value of 0 flashovers/100 km/year (using Rizk's implementation, see Table 1.8) for the base model illustrated in Figure 4.4. This suggests that for the 500 kV HVDC system considered in this section, the overall lightning performance would be dominated by the back-flashover rate (BFOR), and that the effect of the SFFOR would be negligible.

As discussed in Chapter 1, the EGM tends to overestimate the value of the SFFOR for extrahigh voltage (EHV) levels and above. Therefore, the application of the EGM to the studied system is expected to result in a very conservative estimation of the SFFOR. Under this hypothesis, and using the Armstrong & Whitehead model (see Table 1.7), a value of 0.08622 flashovers/100 km/year is obtained for the base case without arresters, which is more comparable to (or even higher than) the BFOR for low footing resistances (see Figure 4.11).

By considering a second hypothesis that protecting a DC pole directly with a line surge arrester no flashovers can occur on that pole, it is possible to see that each surge arrester configuration depicted in Figure 4.9 results in a different value of SFFOR. As it is observed in Figure 4.15, the It is important to keep in mind that the above results are likely to represent an overestimation of the SFFOR because of the use of the electrogeometric model, which is known to tend to exaggerate the value of the flashover rate for EHV and UHV systems (ref. 0). With the simplified approach considered in this work, the leader progression model (LPM) predicts zero failures. Nevertheless, given the limitations of this implementation of the LPM (discussed in Chapter 1), it is considered that the performance of real applications might differ from this result. In such case, with a non-zero SFFOR, the results illustrated in Figure 4.15 show that the line arrester configuration may also help to significantly reduce the SFFOR of the system. For a correct assessment of this effect, further detailed studies shall be conducted.

Additional Considerations and Partial Conclusions

In most cases, a single arrester in the pole with the highest probability of flashover may be enough to significantly improve the lightning performance of a given tower.

In case a single line arrester installed in the tower is not enough to reach the desired lightning performance (e.g. because of very high soil resistivity), the LPLN configurations seems to be the best option as it significantly reduces the BFOR, and the probability of having double flashovers practically drops to zero.

In case lightning strikes a tower adjacent to a protected tower, the action of the surge arresters can help reduce the overall back-flashover rates of the struck tower. depending on the configuration, the incidence of double flashovers might be slightly increased. This may also depend on the configuration of the poles within the tower, the length of the span and the point of impact (for instance, if the stroke terminates along the span between a protected and an unprotected tower). Further studies are required for a better understanding of this effect, as well as to consider more possible scenarios and influencing factors (e.g. different grounding conditions between the towers).

Use of Unbalanced Insulation

The unbalanced insulation solution consists in using different air gap lengths (i.e. distances in air between the arcing horns of the insulators) in one or more of the DC circuits. This way, it is possible to determine in advance which circuit will flashover first in case of lightning stroke, and thus prevent the incidence of flashovers on the other circuit.

This technique has been studied in the past for AC systems also aiming to reduce multi-circuit flashovers (Kawai & Azuma, 1965;Z. Li et al., 2012), but their efficiency is quite limited due to the fact that in AC the phase voltages change constantly. Because in DC systems all voltages are constant, double circuit DC applications might take greater benefit from this technique.

For DC, this technique has only been addressed for the SouthWest Link project, which features a horizontal disposition of the poles (Lundquist &Lilliecrona, 2012), andin (Manduley, Pack, et al., 2019) for a generic two cross arm configuration. This section aims to dig deeper further into the applicability of the unbalanced insulation of DC systems.

As a reminder from previous sections, the base distance between the arcing horns used is 4.16 m, and the unbalance has been introduced by reducing the length on one of the sides by 10, 30 and/or 50 cm. The case studies considered are illustrated in Figure 4.16. As stated at the beginning of this section, the Top configuration has been chosen to perform these studies, based on the conclusions from §3. It is observed in Figure 4.17 that reducing the air gap on one side increases the overall backflashover rate, as expected. The increase is significant for a difference of 50 cm, small for 30 cm and not very significant for 10 cm. However, for all cases, a significant reduction of the occurrence of double flashovers is obtained, which is the main benefit of this solution.

It is also noticed that when increasing the difference from 30 to 50 cm, the increase in the overall back-flashover rate (BFOR) begins to be more significant than the reduction of the double BFOR. From 10 to 30 cm, both the increase of the overall BFOR and the reduction of the double BFOR are smaller, but significant.

Based on these results and considerations, it is concluded that an optimal value may range between 30 and 50 cm.

In addition, it was concluded in (Manduley, Pack, et al., 2019) that huge differences between the air gap lengths of both DC circuits (above 80 cm) may not necessarily contribute significantly to the improvement of the lightning performance, and that an optimal value may be close to 40 cm. In (Lundquist & Lilliecrona, 2012), a difference of 50 cm was found to be optimal for the design used in SouthWest Link. Therefore, it can be concluded that the results obtained in this work are in agreement with the existing studies available in the literature, and provides further evidence supporting that the optimal value for an unbalanced insulation solution should range between 30 cm and 50 cm.

Unbalanced Insulation: Reduction of the Length of a Single Insulator

As an alternative solution, this section aims to study the effect of the reduction of the length of a single insulator. Similarly as in the single surge arrester case previously discussed, the unbalance is introduced in one of the upper positive pole (see Figure 4.16) because their higher likelihood to flashover due to a negative stroke. For this case, a single unbalance of 50 cm has been introduced, since it is the highest unbalance considered to be reasonable for the limitation of double flashovers (Lundquist & Lilliecrona, 2012;Manduley, Pack, et al., 2019).

The results are compared with the case where the same unbalance is used for the full single circuit (see previous section) and the base case, and are presented in Figure 4.19.

It can be observed that when the unbalanced insulation is applied to a single positive DC pole, the overall BFOR with respect to the base case is slightly lower than when the solution is applied on both poles of the circuit. However, the double BFOR is slightly higher.

These results are explained by the fact that by reducing only the length of the gap of the positive pole, the system is protected identically against negative strikes, which represent the majority of the cases. However, against positive strikes, the system behaves as the base case with identical air gap lengths on all of the DC poles. With the base length in the negative poles, there are less total flashovers in case of positive strikes, but roughly all of them produce double flashovers (as discussed in the previous sections). To conclude, these results suggest that this solution might be of interest when the unbalance is associated to different physical string lengths (not only the arcing horns). In other words, a smaller number of insulator units are used for each string. In such case, it would be absolutely necessary to evaluate the impact of this reduction on the incidence of faults due to pollution. If, however, the insulator strings are identical and the unbalance is introduced only through the design of the arcing horns, it may be preferable to introduce the unbalance on both poles of one circuit, such that the incidence of double flashovers are reduced to a minimum value.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Overall Comparison

Taking into account the results and conclusions from this section, a general comparison between both solutions and their respective base cases is shown in Figure 4.20. It features the solutions considered as the best alternatives for each case: the LP and LPLN configurations for the surge arrester solution, and differences of 30-50 cm in the air gap length for the unbalanced insulation solution. As expected, the surge arrester solution is much more effective in improving the lightning performance. However, this solution is only economically viable to improve the performance of some critical towers along the line. The unbalanced solution, on the other hand, can be implemented and studied along the whole line from the initial design, and due to the short distances involved in the unbalance, mechanical constraints are not likely to represent a serious problem.

From the results presented in Figure 4.20, it is noticed that a pole configuration with both positive poles on the upper arm (Top), combined with the unbalanced insulation solution, can present a slightly better overall lightning performance for length unbalances between 30 and 50 cm. The resulting incidence of double flashovers reaches similar values as in the crossed (Xed) configuration, where the unbalance is naturally introduced by placing both poles of the same polarity at different heights.

It should be also noted that the increase in the BFOR observed in the unbalanced insulation solution is due to the fact that the air gap length is reduced (with respect to the base value) on one side. If the solution is considered from the conception of the line (as it is intended to be), the alternative of increasing the air gap length on one side should be prioritized whenever possible. In that case, the overall BFOR would remain at least the same as in the base case (because it is dictated by the circuit with the shortest air gap lengths), as also seen in (Manduley, Pack, et al., 2019), and even better performances can be achieved. In the worst case scenario, only slight modifications to the design of the tower shall be made to guarantee that all the minimum clearances are respected. However, the applicability of this alternative is likely to be limited if it is to be applied to an existing double circuit overhead line where the transmission towers are already built and no much room may be available to increase the length of the insulator strings.

With a proper design of the insulation, the Top configuration may present better lightning performances than the most typically used crossed (Xed) configuration, as found for example in (Dong et al., 2013;Hu, Xie, & Tai, 2017;J. Li et al., 2018;Ma, Li, Wang, & Wu, 2018). In any case, the technical study must be amended by an economic study.

Surge Arrester Specifications

As seen in previous sections, the installation of line surge arresters is an effective way to limit lightning overvoltages and avoid the occurrence of flashovers (and double flashovers) across the tower insulators. To effectively reach this goal, it is essential to adequately specify the protective level of the arrester as well as its energy handling capability, such that it provides a maximum protection while keeping a low risk of failure.

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Surge Arrester Energy Handling Capability

To this date, the current surge arrester standards address the issue of the energy handling capability in terms of thermal stability tests (such as the switching surge operating duty test) to verify that, under certain conditions, the surge arrester will not absorb more energy than it can dissipate until reaching a critical point where failure occurs due to thermal runaway (IEC 60099-4, 2014). Other tests performed by the manufacturers may provide some direct or indirect information about the energy stresses that a surge arrester can handle. However, with the current state of the art of metal-oxide arresters, new applications have become possible (including HVDC and line arresters) (Hinrichsen, Reinhard, & Richter, 2007) and the procedures featured in the standards in terms of the specification of the line discharge class normally apply to classical arrester applications. There is still no clear definition of the energy handling capability which is valid or directly applicable to all cases (Hinrichsen et al., 2007).

Hence, manufacturers typically specify the line discharge class in terms of the specific energy withstand as a result of the standard tests and as a function of the rated voltage U r (in RMS) or continuous operating voltage U c (or MCOV in American standards), and is given in kJ/kV. While more adequate definitions of energy handling capability and specific procedures are developed, the measurement of the total energy absorbed by the surge arrester seems to be the method which is closest to be in agreement with the current developments and recommendations from the standards.

In order to provide some insights on how to specify the surge arresters for an HVDC overhead line applications, this section will analyse the behaviour and energy absorption levels of the surge arrester under different scenarios. Concretely, direct strikes to the tower or shield wires (potentially leading to back-flashovers) and shielding failures are considered. The main goal of this study is to assess the behaviour of the surge arrester and compare the different energy absorption levels, and thus provide recommendations on how should the arrester characteristics be specified for HVDC overhead line applications.

A double-circuit HVDC 500 kV base system model has been used to conduct the studies with the same tower and insulation parameters as in the previous section. In this case, only a single surge arrester has been placed in the lower positive pole (configuration LP, Figure 4.9) and different lightning current peak amplitudes have been tested to study the behaviour and energy absorption of the arresters under different conditions.

Direct Strikes to the Tower

Different lightning peak current amplitudes were applied between 50 kA and 250 kA in steps of 50 kA. Ten values for the tower grounding resistance were considered between 10 Ω and 100 Ω (as in the previous sections). Firstly, it is observed that the energy absorption levels are significantly higher for negative strikes than for positive strikes. This is because, as discussed in the previous sections, in case of direct strokes to the tower or the shield wire, the voltage of the tower rises with the same polarity as the stroke, and thus it is in the insulators of opposite polarity where the highest voltage difference will be observed. Since the arrester is placed in the lower positive pole (which is the most likely to flashover in such configuration), it is expected that negative strokes would produce the highest voltage difference at that point and thus, that the highest energy absorption levels were obtained.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Secondly, as the grounding resistance increases, an increase is also observed in the energy absorption levels of the arrester. This is because the higher the grounding resistance, the higher will be also the total voltage difference seen by the insulators (and hence the surge arrester). In some points, however, a negative variation in the slope of the curves in Figure 4.21 is observed. This indicates that a flashover has occurred between the two resistances. Or in other words, that for some value of the grounding resistance between the two where the slope variation is observed, the applied current amplitude corresponds to the critical flashover current I f . When it is the case, a portion of the current is drawn by the fault and thus the total voltage rise of the tower drops. As a result, the stress across the arrester is reduced as well and the increase in the total energy absorbed may be inferior compared to the previous tendency.

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Shielding Failure Case

In case of shielding failure, two main scenarios have been considered. One, where the impact is produced directly in the conductor protected by the surge arrester, and another where the impact is produced on the conductor on the opposite side of the same cross arm (lower cross arm). These two scenarios are illustrated in Figure 4.22. Positive and negative strokes were considered for both scenarios to assess each one in the cases where the polarities of the conductor and the lightning stroke are equal or opposite. The case where the stroke is produced at the conductor protected by the surge arrester will be analysed first. Next, the case with the stroke on the opposite conductor will be analysed and compared to the first case. Both stroke polarities are considered in all cases.

Stroke on the Protected Conductor

Since the stroke is produced directly on the conductor, it is expected that the worst case scenario is associated to the lightning stroke with the same polarity as the struck conductor. This is illustrated in Figure 4.23, where it is observed that for a positive stroke (Figure 4.23a), the voltage across the insulator increases in the same direction as the already existing voltage, while for a negative stroke (Figure 4.23b) the insulator voltage crosses zero before that it starts increasing in the positive direction. As a result, when there is no surge arrester, a higher maximum overvoltage is reached when the polarity of the stroke matches the polarity of the struck conductor and hence, the flashover is produced at a lower current amplitude (in the case presented in Figure 4.23, for I peak = +20 kA a flashover is produced in the struck pole, while for I peak = -20 kA no flashover is produced). It is also observed that when the surge arrester is present (blue curves) the maximum overvoltages across the insulator are very similar to each other regardless of the lightning polarity. This is because in both cases the overvoltage levels were much higher than the LIPL of the arrester (i.e. 1229 kV, see Table 4.2), and thus the surge arrester is able to maintain the voltage across the insulator in a value close to its LIPL due to its non-linearity. In fact, this holds true even for higher peak currents up to 50 kA, as it can be seen in Figure 4.24 where the maximum overvoltage levels are in the order of 1500 kV.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

As a side note, it is important to remember that this particular analysis focuses only on the behaviour of the arrester if a lightning stroke of the specified amplitude strikes the conductor.

It does not take into account the actual maximum shielding failure current (I msf ) that could land on the conductor, which can be estimated through the application of electrogeometric or leader progression models, as explained previously in this chapter.

It is observed in Figure 4.24 that when lightning strikes the protected conductor no flashovers are produced regardless of the lightning intensity, as expected assuming a correct behaviour of the arrester. Additionally, the grounding resistance seems to have little influence on the overvoltage levels, the latter being slightly higher for lower grounding resistances. This is explained by the fact that the lower the grounding resistance, the more current will be drawn to the ground and less will be split in both directions of the struck conductor (Figure 4.25). Hence, even though the grounding resistance normally does not have a significant impact on the flashover mechanism due to a shielding failure when surge arresters are not present, it is to be expected that it will have a significant impact on the total energy absorbed by the surge arrester. This is illustrated in Figure 4.26. It is observed that for both positive and negative strokes, the total energy absorbed increases as the grounding resistance gets higher. Additionally, the total energy absorption levels reach the maximum values when a lightning of positive polarity strikes the conductor. This is due to the fact that for a positive conductor, a positive lightning stroke would produce a higher voltage difference across the insulator, so that when a surge arrester is installed to protect the insulator, the stress will be higher compared to the case of a negative stroke.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Stroke on the Unprotected Conductor

A similar analysis is performed in the case where the stroke is produced on the opposite conductor of the lower cross arm (Figure 4.22b). The goal of this part is to determine whether the surge arrester installed on the opposite pole can provide some protection to the struck pole. As the stroke is produced in the lower negative pole, it is expected that a negative stroke will produce the highest voltage different across the insulator of the struck conductor. This is illustrated in Figure 4.27, where it can be observed that when no surge arresters are present, the maximum overvoltage levels are quite similar as in Figure 4.23, but with the polarities reversed. In this case, it is the negative stroke which produces the highest overvoltage level on the struck conductor.

However, there is not a very significant difference when a surge arrester is present or not in the opposite conductor. This is because in this case, virtually no current enters the tower before the flashover is produced and thus all the current is split in both directions of the struck conductor (as shown in Figure 4.28). After the flashover, most of the lightning current flows across the insulator arcing horns and significantly less current is diverted in both directions of the shield wires (Figure 4.28). The current entering the tower is then split again between the grounding resistance, the surge arrester and the top of the tower towards the shield wires.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance

The current flowing to the ground is determined the grounding resistance, being significantly lower for higher values (Figure 4.33). However, for high grounding resistances, even though the current is lower, the total voltage drop is higher, which is reflected on the voltage drop of the insulators. Because of this fact, the voltage stress for the surge arrester is more significant for higher grounding resistances and thus more current flows through the surge arrester, according to its respective V-I characteristic (Figure 4.30 and Figure 4.31). The rest of the current is diverted to the shield wires (Figure 4.32 for one of the directions of one of the shield wires).

It is thus seen that the arrester has little to no effect regarding the flashover probability of the unprotected pole, but after the flashover occurs, significant currents can still flow through it due to the flashover current flowing to the ground and increasing the voltage of the tower structure.

Finally, the absolute energy absorbed by the surge arresters is presented in Figure 4.34. Firstly, it is observed that, as expected, the overall energy absorption levels are significantly lower than when the stroke is produced on the protected conductor (about 5% of the total energy absorbed in such case). This is because when lightning strikes the protected conductor, the propagating voltage wave reaches the surge arrester directly, while when the unprotected pole is struck, this voltage wave practically only affects the insulators of that conductor, where no surge arrester is present and no current flows until a flashover is produced. The energy absorption levels in this case are thus associated to the flashover current entering the tower and flowing to the ground, and to some extent to the induced voltages on the shield wires, which also produce a small voltage drop of the tower due to the current that flows through the ground.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line

Secondly, it can be seen in Figure 4.34 that the energy absorption levels are significantly higher for negative strokes, and almost negligible for positive strokes. For negative strokes, it can be seen in Figure 4.31b that the surge arrester only starts conducting current after the flashover has been produced. In this case, the voltage induced to the shield wires produces a current flowing towards the ground and the voltage of the tower structure becomes "more positive", which initially reduces the resulting voltage across the surge arrester placed on the positive DC pole. For this reason, the effect of the induced voltages on the energy absorbed before the flashover is negligible. However, when the stroke is of positive polarity, the induced voltage generates a current flowing from the ground and away from the tower through the shield wires. In other words, the tower becomes "more negative", thus increasing right away the voltage across the surge arrester on the positive DC pole and producing the currents observed in Figure 4.31a. In this case, when the flashover is produced, the voltage drop increases in the opposite direction, which reduces the voltage across the surge arrester.

To summarize, for a positive stroke, the dominant mechanism influencing the energy absorption of the surge arrester is the coupling of the conductors, while for a negative stroke it is the flashover current. Nevertheless, for the former, the absolute maximum values are almost negligible (in the order of about 1 kJ), and even for the latter, the maximum values obtained represent only about 5% of the energy absorption levels compared to the case where the stroke terminates on the protected conductor. Therefore, it can be concluded that the surge arrester provides little to no protection to conductors other than the one directly protected by it.

Discussion

Based on the results obtained in this section, it has been seen that, even though the footing resistance influences the energy absorbed by the surge arresters in both the back-flashover and shielding failure cases, higher energy absorption levels are likely to appear when high amplitude negative strokes terminate on the tower or the shield wires, combined with high footing resistances. However, as shown in Chapter 1, both the CIGRE and IEEE approaches point out that about 95% of negative downward strokes have amplitudes of less than 100 kA (see Figure 1.17). According to Figure 4.21, this would mean that for about 95% of the strokes the energy absorption levels of the surge arresters would be in the order of 250 kJ. As discussed in §6.1, the specific energy withstand of the surge arrester is given by dividing the total energy absorbed by the rated voltage of the arrester (U r ). In this case, 250 kJ divided by 464 kV RMS yields 0.54 kJ/kV. Line discharge class 1 arresters typically have an energy absorption capability of about 1-2.5 kJ/kV [START_REF] Abb | Simplified Selection Procedure (Buyer's Guide)[END_REF][START_REF] Abb | High Voltage Surge Arresters[END_REF][START_REF] Siemens | High-voltage surge arresters (product guide)[END_REF], which would be largely enough to withstand the energy absorption levels associated to this case. Even if the most extreme case illustrated in Figure 4.21 (i.e. 250 kA, 100 Ω) is considered, the total energy absorbed by the arrester is in the order of 2100 kJ, which would correspond to a specific [START_REF] Abb | Simplified Selection Procedure (Buyer's Guide)[END_REF], 2016;[START_REF] Siemens | High-voltage surge arresters (product guide)[END_REF], which would be capable of withstanding such elevated energy absorption levels. If the same exercise is performed for a 200 kA stroke (which is the typically used maximum value for negative lightning strokes (CIGRE TB 704, 2017)), the energy absorption levels would be in the order of 1000 kJ, or 2.14 kJ/kV for the current application. In this case, it is clear that a line discharge class 2 arrester would be largely enough for such applications.

In the case of shielding failure, significantly lower energy absorption levels were obtained even for the most extreme cases, going up to about 850 kJ for 50 kA strokes with a footing resistance of 100 Ω. However, the value of 50 kA was chosen to be the absolute maximum value used for the studies, but it is actually very unlikely for a lightning current of such amplitude to strike the power conductor. By applying the electrogeometric model analysis on the considered case study, the maximum shielding failure current (I msf ) is estimated to be between 17-20 kA using the models of Armstrong & Whitehead (1968b) and Love (1973) (see Chapter 1). From Figure 4.26, it is observed that for currents of such orders of magnitude, the maximum energy absorbed by the surge arresters may be in the range of about 90-250 kJ, which is similar but lower than the values expected when strokes terminate on the shield wires or the tower. Moreover, as discussed in Chapter 1, EGM tends to overestimate the SFFOR for EHV and UHV systems (CIGRE TB 704, 2017). By applying the simplified LPM approach of [START_REF] Rizk | Modeling of transmission line exposure to direct lightning strokes[END_REF], the I msf obtained is in the range of 2-3 kA for the considered system, for which the energy absorption levels of the arrester would be virtually negligible as per Figure 4.26.

It is worth mentioning the fact that there is a family of lightning strokes that are not considered. In the presented studies, positive strokes are modelled using the statistics gathered for downward negative strokes. Although positive strokes represent roughly 10% of all strikes to the ground (CIGRE TB 549), the available data indicates that such strokes are significantly more likely to feature long duration continuing currents in the order of milliseconds which would be much more stressing for the arresters.

One direct and potentially serious consequence of the facts mentioned in the previous paragraph is that after failure, arresters behave like short-circuits, thus introducing a permanent fault to the overhead line. For such scenario, a possibility may be to use arresters with air gaps which are able to withstand the permanent voltage and the switching overvoltages that may appear (excluding those due to faults along the same pole). This solution is discussed in CIGRE TB 440 and IEC 60099-8 for AC systems. However, it remains a very complex issue to coordinate the gap of the arrester with the gap of the insulator string of the tower, which requires empiric approaches. Moreover, the application of surge arresters in HVDC systems is only covered by IEC 60099-9 standard, which concerns gapless arresters only. Although this standard concerns the HVDC converter stations, it may be used as a reference for HVDC overhead lines in absence of a dedicated standard for such case.

Another important aspect concerns the energy withstand capability of surge arresters. In IEC 60099-9 standard, the notion of charge transfer rating is used to specify the energy withstand of an arrester instead of the concept of line discharge class. Such approach involve a classification in thermal energy ratings based on the capacity of the arrester to withstand successive impulse currents with a duration going up to 200 µs for lightning impulses. Such approach may be more appropriate for specifying the energy withstand of HVDC arresters.

Although the notion of line discharge classes used in this dissertation is not standardized anymore in IEC standards, it is still in favour in the industry. Furthermore, a comparison between both approaches is presented in annex L of IEC 60099-4. In all cases, it is clear that the choice of the energy duty of arresters remain a very complex subject, and special care must be taken when dealing with this issue, especially regarding HVDC arresters.

Summary and Conclusions

To recapitulate: in this section, the energy absorption levels of the line surge arresters-and the mechanisms associated to them-were investigated for both the back-flashover and shielding failure cases. The main motivation behind this study was to determine the aspects that must be taken into account to design and specify the line surge arresters for a given application.

It has been seen that strokes terminating on the tower or the shield wires are likely to lead to the highest energy absorption levels of the surge arrester. For many cases (about 95%), a line discharge class 1 arrester may be capable of withstanding the associated energy absorption levels, while a class 2 is very likely to be largely enough for current amplitudes up to 200 kA, which is the typical maximum value considered for lightning studies.

In both the cases of direct strike on the tower or shield wires and shielding failure, the footing resistance proved to be an influencing factor in the overall energy absorbed by the surge arrester. This is due to the fact that whenever a surge arrester is present, currents can flow between the conductors and the tower structure which only depend on the V-I characteristic of the arrester. If no surge arresters are present, a flashover is required to occur so that a current can flow between the tower and the conductors.

Furthermore, it was confirmed that the protective effect of the surge arrester concerns only the insulator directly protected by it. For strokes produced on other conductors not protected by surge arresters, little to no protective action is performed by the surge arrester.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance

It has been also discussed that the aspects regarding the energy withstand capability of the surge arresters still constitute a very complex subject that shall be treated with care. Besides the issue of the specification of the arrester in terms of energy handling capability, it also makes difficult to estimate the risk of failure of a surge arrester and the solutions that may be used, especially regarding HVDC applications, for which no standard covers the application of gapped surge arresters.

Conclusion

The estimation of the lightning performance of an overhead line consists of the analysis of two main scenarios that may occur: direct strikes to the tower or shield wires (leading to a backflashover) and strikes to the power conductors (due to a shielding failure). The back-flashover rate (BFOR) depends strongly on the grounding resistance of the considered tower, and also on the coupling between the conductors, the polarity of the stroke and considered conductors, and the different voltage drops across the tower structure. The shielding failure flashover rate (SFFOR) depends mainly on the tower and conductor geometry, insulator characteristics and regional lightning data. The sum of both the BFOR and SFFOR constitutes the overall lightning performance of a given system.

Even though there are certain similarities in the behaviour of HVAC and HVDC lines regarding lightning strokes, the characteristics of HVDC systems make the lightning performance analysis of HVDC overhead lines differ from the HVAC case. In particular, the fact that the voltage levels are constant at all times in HVDC systems removes the dependency of the lightning performance on the instant when lightning strikes the system.

In double circuit HVDC configurations, the position of the DC poles plays a major role in the overall and double back-flashover rates because of the high effect of the conductor coupling and the polarity of the lightning stroke. In this work, the effect of the configuration of the DC poles has been analysed in details to provide a better understanding on its impact on the lightning performance of double-circuit HVDC overhead lines.

Additionally, two solutions for the improvement of the lightning performance have been studied to contribute to the insulation coordination of HVDC overhead lines: the installation of line surge arresters and the use of unbalanced insulation in double-circuit HVDC overhead lines.

It has been found that the installation of line surge arresters can significantly improve the performance of a given tower. A very significant improvement may still be achieved with one surge arrester on a single positive pole (in the case of double-circuit configurations, in the lower positive pole which has the highest flashover risk). For practical and economic reasons, this solution is to be used only on specific towers presenting high flashover rates, most commonly due to poor grounding conditions.

In addition, the results suggest that surge arrester may also help to significantly reduce the shielding failure rate, and that the degree of improvement depends greatly on the surge arrester configuration considered. Further studies are required to correctly assess the relevance of this effect.

In terms of line surge arrester specifications, one of the most important parameters to consider is the energy absorption level of the arresters, to avoid potential failures due to excess of energy absorbed due to a lightning stroke. The striking point proved to be of importance, as strokes terminating on the tower or shield wires may lead to higher energy absorption levels than the case of shielding failure. In both cases, however, a line discharge class 1 or 2 arrester is likely to be enough to withstand the absolute energy absorption levels associated to lightning strokes on the transmission line.

The unbalanced insulation solution consists of the use of different insulator (or arcing horns) lengths for each circuit in a double circuit configuration. It represents a solution that can be implemented along the whole line from its very conception phase and that can significantly improve the lightning performance of double-circuit HVDC lines, especially regarding the risk of double flashovers. Concretely, it has been found that the use of an unbalanced insulation can effectively improve the double back-flashover performance of a system in which both poles of the same polarity are placed at the same height (Top configuration, Figure 4.1). With a proper design, such configuration, combined with an unbalanced insulation solution, can achieve similar or even better lightning performances than the most commonly used configuration with the polarities crossed (Xed configuration).

For the effects of the application of the unbalanced insulation solution, an unbalance of about

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Conclusion

HVDC power transmission technologies are in constant development and growth worldwide.

As it has been discussed, HVDC offers a series of advantages over HVAC in terms of power transmission capacity and reduction of losses over long distances. HVDC technologies based on Voltage Source Converters (VSC) have proven to be very promising regarding the massive integration of renewable energies to the grid, as well as in providing a feasible way to interconnect several transmission systems through HVDC, thus increasing the reliability and stability of the grid. Advances in such developments are likely to translate into several actions, such as the increase of the commissioning of VSC-HVDC projects-especially regarding Modular Multilevel Converters (MMC)-the construction of new HVDC links, or the conversion of existing AC overhead lines into DC.

For any engineering project of the kind, insulation coordination is a crucial stage in the design phase of the project as it deals with the insulation requirements and overvoltage protection strategy of the system and the equipment connected to it. However, there are no universally recognized procedures for insulation coordination in HVDC. Current insulation coordination standards for high voltage engineering only cover HVAC, and HVDC technologies based on Line Commutated Converters (LCC) only. Even in the case of LCC-HVDC, there is an absence of standard rated withstand voltages for DC equipment in general, which also represents a significant obstacle to the development of detailed insulation coordination procedures. Moreover, a direct transposition of the AC or LCC principles to VSC is not possible, as already discussed in this dissertation, and the scientific literature on the subject is scarce. All of the above makes it difficult to develop adequate insulation coordination guidelines for HVDC systems, including VSC.

This thesis is intended to contribute to remedy such major deficiencies surrounding the development of insulation coordination procedures for HVDC systems, particularly regarding VSC-MMC architectures.

To do so, a thorough state of the art and literature review was presented regarding insulation coordination in Chapter 1. The current methods and procedures described in the standards, as well as in technical brochures, scientific papers, PhD dissertations and books, were discussed in order to establish the current state of development on the different subjects addressed in this dissertation. This literature review has allowed to identify the fundamental aspects that differentiates VSC technologies from AC and LCC within the context of insulation coordination, and that need to be taken into account for the development of detailed insulation coordination procedures for such systems.

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Then, the methodology used to conduct the studies performed in this research was described in Chapter 2. It includes all the details regarding the electromagnetic transient modelling of individual components, as well as the guidelines to build the case studies presented in this dissertation.

Over the above foundations, the different objectives of the thesis have been addressed. As discussed in the introduction, they concern two main axes: insulation coordination of VSC-HVDC systems, and the evaluation and improvement of the lightning performance of HVDC overhead lines. The main conclusions of both are described below.

Regarding the first axis, three main objectives were established. The first, to provide a base on how the insulation coordination procedures should be adapted to VSC-HVDC systems. The second, the proposal of a methodology to perform insulation coordination studies for such systems. The third, to provide guidelines and recommendations on how the overvoltage protection strategy should be designed.

The fundamental principles of insulation coordination have been adapted to VSC-MMC technologies taking into account the essential differences between AC and DC, as well as between LCC and VSC technologies identified previously. Inspired on the approach from LCC-HVDC insulation coordination standard, two fundamental schemes of MMC stations are proposed which allow to generalize the insulation coordination principles based on such schemes, and remain valid for any possible architecture, topology, operating mode of the station or surge arrester arrangement for the overvoltage protection strategy. This establishes a solid base over which the insulation coordination principles can be adapted to VSC-MMC technologies, which covers the first objective.

The overvoltage profiles have been characterised for different architectures and topologies with and without surge arresters, in order to study the behaviour of MMC stations and provide general guidelines for the design of the overvoltage protection strategy. It has been found that all the above factors influence the transient behaviour and the overvoltage profiles of the system significantly. Moreover, it has been shown that the particular arrangement of surge arresters has a very significant influence on the response of the system under transient stresses due to the complex interactions between the different surge arresters and the system. Consequently, individual arresters should be characterised by taking into account not only the voltage and overvoltage levels of the system, but also the particular arrangement or combination of arresters chosen for the overvoltage protection strategy.

Based on the conclusions of the above studies, a general insulation coordination procedure for MMC-HVDC systems has been proposed, which covers all the aspects identified to be essential on adapting the fundamental principles of insulation coordination to such systems and the results obtained from the studies described above. The procedure consists of different

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design phases-as well as the inputs and outputs of each one-and recommendations on the possible location, as well as guidelines for the characterisation, of each one of the surge arresters that may be considered for the overvoltage protection strategy of the system. Following such procedure allows to effectively perform insulation coordination studies on VSC-MMC based systems. In combination with the previous paragraph, this covers for the second and third objectives regarding the insulation coordination of HVDC systems.

Furthermore, the feasibility of developing a fully qualitative approach to estimate the maximum overvoltage levels of a system without performing numerical simulations has been studied and discussed. It has been proven that such an approach may be considered to constitute a useful tool in addition to the numerical analysis, but that is not able to accurately predict the behaviour of the system on its own. This provides an important justification regarding the choice of basing the general insulation coordination procedures on EMT simulations.

Regarding the second axis, three main objectives were established. The first consists of the adaptation the existing procedures for the evaluation of the lightning performance of overhead lines to VSC-HVDC applications, including the possibility to analyse asymmetric configurations, non-linear devices and double flashovers. The second objective involves the proposal and study of solutions for the improvement of the lightning performance considering both single and multiple insulator flashovers. The third concerns an overall improvement in the understanding of the behaviour of HVDC overhead lines in case of lightning strikes.

The procedure used to estimate the lightning performance with the specified requirements consists of a combination of the existing methods documented in the literature and numerical simulations using electromagnetic transient modelling of the system and components. This allows a precise estimation of the critical flashover currents for each system taking into consideration an adequate modelling of the overhead lines, surge arresters, asymmetric configurations (such as the unbalanced insulation solution), grounding conditions and other parameters. Then, the calculation of the flashover rate is performed using the traditional methods recommended in the literature. This covers the first objective listed above.

Through the application of the method described above, it has been found that there are significant differences between the behaviours of AC and DC overhead lines in case of lightning strikes. For instance, the fact that the voltage levels are constant in DC removes the dependency on the instant during which lightning strikes the line, while in AC it can play a major role in determining which phase is more likely to flashover. Moreover, it has been found that the position of the DC poles within the transmission tower is a very significant influencing factor on the lightning performance of double-circuit HVDC overhead lines, mainly due to the coupling between the conductors. Also, the fact that in such configurations two conductors

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Nicolas Manduley 2020 Page 162 may be permanently subjected to the same voltage level increases the probability of double flashovers to occur.

Based on the obtained results and analysis, two solutions for the improvement of the lightning performance of double-circuit HVDC overhead lines have been studied, which covers for the second objective: the installation of line surge arresters and the use of unbalanced insulation. Different scenarios using one or two arresters have been investigated, as well as their respective advantages and disadvantages. It has been found in this work that very significant improvements in the lightning performance can be achieved by installing even a single surge arrester on the lower positive pole. Recommendations for the specification of line arresters are also provided, particularly in terms of the energy absorption levels of the surge arresters in case of direct strikes and shielding failures. In the case of the unbalanced insulation solution, it has been shown in this research that this solution can effectively improve the double backflashover performance of a system, and that similar or better lightning performances can be obtained by combining this solution with DC pole configurations not typically used in practice.

It has been also determined that for an unbalance beyond 50 cm the improvement on the lightning performance increases very slowly. An unbalance of 30 to 50 cm seems to be optimal for practical applications.

The results and the analysis of all the above studies constitute altogether a contribution to the better overall understanding of the behaviour of HVDC overhead lines under lightning strikes, which accounts for the third objective of this axis.

In summary, this thesis presents a series of developments aiming to contribute to compensate the scarcity of scientific knowledge on insulation coordination for VSC-HVDC, and particularly for the MMC. Concretely, contributions in the areas related to the development of detailed insulation coordination procedures for such systems are presented, as well as in the areas of lightning performance of HVDC overhead lines. Particular effort has been put into the transposition of the insulation coordination principles for HVAC and LCC-HVDC by taking into consideration all the influencing factors and essential differences between each kind of system.

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Perspectives and Future Research

Insulation coordination involves an extremely wide range of subjects, and each one of them is important to ensure a correct design of the insulation and the overvoltage protection strategy of a system. As such, there are still several aspects that need to be studied thoroughly before being able to standardize the insulation coordination procedures for VSC-HVDC systems that were not included in this research.

Among the natural next steps of this research, the following subjects have been identified:

 Application of the developed procedure on other case studies and thus provide further validation of the obtained conclusions.

 Perform the overvoltage analysis on MMC-HVDC systems involving both cable and overhead lines. This and the task above may be performed jointly by considering a hybrid line case, such as the SouthWest Link, for both tasks.

 Validation and further development of an algorithm allowing to conduct the iterative design of the surge arresters for the overvoltage protection of the system.

 Development of a tool allowing to automate the procedures, from the modelling of the system to the specification of the required air clearances, dielectric strengths insulating materials and overvoltage protection strategies.

Among the subjects considered for future research, the following areas might be of interest:

 Lightning protection of the MMC-HVDC station. Such studies require a detailed highfrequency modelling of the components as well as of the grounding grid of the station. Moreover, different applications of the electrogeometric or leader progression models (EGM and LPM, respectively) are found in the station, such as the case of tall lightning rods placed in different locations of the installations, which constitutes a more complex scenario regarding lightning protection that may require particular and dedicated studies.

 Analysis of case studies featuring multi-terminal topologies (MTDC). One of the longterm goals of VSC-HVDC transmission is the interconnection of large transmission systems and the formation of true HVDC grids where each node may be connected to several other nodes. Therefore, it is of great interest to conduct studies considering multi-terminal topologies and the potential impact of such schemes on insulation coordination.

 Transient analysis of other phenomena potentially leading to overvoltages, such as resonance, ferroresonance, load shedding or unexpected opening of AC or DC breakers. Although such phenomena may not lead to the maximum overvoltage levels, they are required to constitute a detailed overvoltage profile of the system and to

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Perspectives and Future Research Nicolas Manduley 2020 Page 164 ensure that they do not represent a danger for the operation of the surge arrestersand therefore to the system as well.

A.2.1 Applied Voltage on the Conductor (V)

The voltage (V) in equation [A-2] is equal to the voltage applied to the conductor. For a direct stroke to a phase conductor (i.e. shielding failure) this value shall be equal to the flashover voltage of the insulator at about 6 µs (EPRI Transmission Line Reference Book, 345 kV and Above, 1982). It is also observed in CIGRE TB 72 (CIGRE TB 72, 1992) that in a typical V-t characteristic of an air gap or insulator, after 6 µs the flashover voltage is slightly higher than the critical flashover voltage U 50 (see Fig. A-1). Hence, if no detailed data from the manufacturer is available, a reasonable approximation of V may be obtained by introducing a multiplying factor of 1.0 -1.1 to the value of U 50 .

A.2.2 Limiting Corona Gradient (E 0 )

For AC systems, a value of E 0 = 1500 kV/m is recommended for the estimation of R c , as stated in (EPRI Transmission Line Reference Book, 345 kV and Above, 1982). No particular recommendation has been found for DC systems. Some studies have been conducted in this work aiming to estimate the adequate value of E 0 for DC systems, and are explained in detail in Appendix B. In general terms, it has been concluded that for most applications, the value of 1500 kV/m is applicable for DC systems, except for cases of extreme pollution levels, where this value might be too high. For the purposes of this work, a value of 1500 kV/m has been used for the calculations.

A.3 Sensitivity Analysis

To determine the impact of the height of the conductor (h p ) and the applied voltage (V) on the value of R c and on the value of Z s , equation [A-2] has been solved for R c using the Newton-Raphson algorithm for different values of h (with h avg calculated for plain areas when needed (China Electric Power Research Institute, 2017)) and V.

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Typical values for HVDC tower configurations are given in (CIGRE TB 388, 2009) for different voltage levels. Tbl. A-1 presents the base values used for the calculations, as well as the ranges applied for the values of h p and V. For h p , it has been observed that for 300 kV and 500 kV HVDC systems, typical conductor heights range between 40 and 60 m. Therefore, a range from 35 to 100 m has been investigated to cover all this range and also possible higher tower configurations.

For the applied voltage on the conductor, a range from 1000 kV to 4000 kV has been investigated. As indicated in (EPRI Transmission Line Reference Book, 345 kV and Above, 1982) (and also discussed in §A.1 above), the value of V can be estimated as the breakdown voltage of the insulator at 6 µs. If no detailed data from the manufacturer is available, a rough approximation can be done by observing that for a typical V-t characteristic (see Fig. A-1), the breakdown voltage approaches the value of U 50 as the time increases. At the point of t = 6 µs, the breakdown voltage can be approximated as 1.0 -1.1 times the value of U 50 . Assuming that the influence of DC pre-stresses is negligible for lightning impulses across the arcing horns (as found in (Cortina et al., 1984)), the U 50 can be estimated through equation and with the above adjustment, the corresponding value of V can be approximated.

As obtained from (CIGRE TB 388, 2009), typical insulator lengths for 300 kV and 500 kV HVDC systems range are 3.2 m and 5.2 m, respectively. Through the above explained approximations, this corresponds to values of V of about 2000-2200 kV and 3300-3600 kV for 300 kV and 500 kV, respectively. Hence, the range of 1000-4000 kV has been considered to adequately cover for the voltage levels investigated in this work.

The results of the performed analysis are displayed in

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In Fig. A-2 it can be seen that the corona radius R c varies significantly with the applied voltage V, while the variation with the height h p seem to be relatively small. It is not the case with surge impedance under corona, as seen in Fig.

A-3, where Z s varies in similar proportions with the height h p and the applied voltage V.

However, even though both h p and V have similar effects on the value of Z s , this value remains in the range of 360-440 Ω for the investigated ranges of height (i.e. around 40-60 m) and applied voltage (i.e. around 2000-3500 kV). This is also the case when smaller conductor radius are considered, where just slightly higher values are obtained.

Taking these results into account, it can be concluded that the surge impedance under corona does not vary significantly along the cases considered in this study. Therefore, it may not have a critical impact on the evaluation of the SFR and SFFOR values even if a constant value (within the specified range) is used for all cases.

Appendix B. Limiting Corona Gradient and Surface Conductor Gradient in DC B.1 Problem

As the voltage on a conductor increases, so does the electric field on its surface. The capacitive coupling with other neighbouring conductors may also contribute to the increase of the electric field on the surface of the considered conductor. When this electric field reaches a critical value, corona discharges start to appear in the vicinities of the conductor. This critical value is known as corona onset gradient E c .

The limiting corona gradient E 0 is thus defined as the maximum electrical field that manufacturers will allow to appear in the surface of the conductor under normal operating conditions to avoid the formation of corona discharges. As a general rule, it is recommended that the maximum surface gradient of the conductor does not exceed 95% of the onset gradient (CIGRE TB 388, 2009).

For AC systems, a value of E 0 = 1500 kV/m is recommended for the estimation of R c , as stated in (EPRI Transmission Line Reference Book, 345 kV and Above, 1982). However, no particular recommendation has been found for DC systems. Therefore, the goal of this section is to study the correct way to determine the limiting corona gradient applied to DC systems.

B.2 Estimation of E 0 and E c

As previously mentioned, the limiting corona gradient (E 0 ) is the maximum value of the electric field allowed to appear on the surface of the conductor to avoid reaching the corona onset gradient (E c ), which is the value at which visible corona appears on the conductor (CIGRE TB 583, 2014). The general recommendation is that E 0 does not exceed 95% of E c (CIGRE TB 388, 2009).

In the 1920's, Peek (Peek, 1920(Peek, , 1929) ) derived an empirical formula for the calculation of the corona onset gradient, E c , which is shown in equation [B-1] below:

𝐸 𝑐 = 𝐾 1 𝛿 𝑚 (1 + 𝐾 2 √𝛿 𝑟 ) [B-1]
Where δ is the relative air density, m is the irregularity factor, r is the radius of the conductor and K 1 and K 2 are fixed constants. These constants have been found to be different for AC, positive DC and negative DC polarities, and their respective values are given in CIGRE TB 583 (CIGRE TB 583, 2014).

However, one of the most determining factors seems to be the irregularity factor m, which is influenced by the geometry of the conductor and the accumulation of pollution on its surface.

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Some aspects related to the irregularity factor m (for AC and DC cables) are discussed in (CIGRE TB 388, 2009;CIGRE TB 583, 2014;Peek, 1920Peek, , 1929) ) and are summarized below:

For AC systems:

 m = 0.93-0.98 for roughened/weathered cables  m = 0.83-0.87 for some seven-strand cables  m = 0.70 is likely to be the lowest limit for AC cables [24] For DC systems, the higher attraction of pollution contributes to the formation of more irregularities on the surface of the cable, especially for positive polarities (CIGRE TB 583, 2014).

The irregularity factors are thus generally lower than for DC.

 For reasonably clean stranded conductors, values of m can be in the range of 0.75 to 0.85 (CIGRE TB 388, 2009).

 Surface irregularities may reduce m to values in the range of 0.6 to 0.8, while conductor surface deposits and precipitation may further reduce it to 0.3 to 0.6 (CIGRE TB 388, 2009).

 Practical values for DC are in the range of about 0.4 to 0.8, where lower values occur particularly when the conductor is positive, because of the higher attraction of pollutants (CIGRE TB 583, 2014).

By taking into account all of the previous considerations, studies have been conducted to estimate the adequate value of E 0 for DC systems. For all cases, a conductor radius of 3.82 cm was used under standard environmental conditions 9 . The values for K 1 and K 2 are as given in (CIGRE TB 583, 2014), and are shown in Tbl. B-1. 1.14 0.00 1.07 0.00 1.10 0.00 0.00 0.00 0.00 0.00 V 2 0.00 1.61 1.71 1.41 1.73 1.41 0.00 0.00 0.00 0.00 V 3

AC

1.92 1.60 1.95 1.41 2.03 1.41 1.72 0.00 1.91 0.00 V 4

1.94 1.63 1.83 1.81 1.82 1.81 0.00 0.00 0.00 0.00

V BR

0.43 0.27 0.76 0.00 0.98 0.24 0.97 0.24 1.21 0.18

V SM

2.10 2.18 1.99 1.81 2.08 1.80 0.00 0.00 0.00 0.00 Tbl. C-4 For the configuration with arresters A1, A2 and A3: slow-front and temporary overvoltage levels (SFO and TOV, respectively) for each location during the different fault scenarios considered. The values are given in p.u. (with 1 p.u. = 320 kV). A value of zero indicates that no disturbances were measured to be above the normal operating voltage level.

Fault J

Fault K Fault L Fault N Fault N2 1.15 0.00 1.12 0.00 1.09 0.00 0.00 0.00 0.00 0.00 V 2 0.00 1.70 1.86 1.41 1.87 1.41 0.00 0.00 0.00 0.00 V 3

I [A] E [kJ] I [A] E [kJ] I [A] E [kJ] I [A] E [kJ] I [

1.93 1.68 2.00 1.41 2.65 1.41 1.81 0.00 1.96 0.00 V 4

1.93 1.66 2.00 1.80 1.99 1.80 0.00 0.00 0.00 0.00 1.14 0.00 1.07 0.00 1.10 0.00 0.00 0.00 0.00 0.00 V 2 0.00 1.61 1.71 1.41 1.73 1.41 0.00 0.00 0.00 0.00 V 3

V
1.92 1.59 1.95 1.41 2.02 1.41 1.72 0.00 1.91 0.00 V 4

1.92 1.63 1.82 1.80 1.81 1.79 0.00 0.00 0.00 0.00

V BR

0.47 0.25 0.76 0.00 0.98 0.00 0.97 0.24 1.21 0.18

V SM

2.10 2.18 1.99 1.81 2.08 1.79 0.00 0.00 0.00 0.00 Tbl. C-8 For the configuration with arresters A1, A2, A3 and C: slow-front and temporary overvoltage levels (SFO and TOV, respectively) for each location during the different fault scenarios considered. The values are given in p.u. (with 1 p.u. = 320 kV). A value of zero indicates that no disturbances were measured to be above the normal operating voltage level.

Fault J

Fault K Fault L Fault N Fault N2 With such approach, transient events such as system faults can be represented as known values of the voltage variations of one or more of the variables from Tbl. D-1.

I [A] E [kJ] I [A] E [kJ] I [A] E [kJ] I [A] E [kJ] I [

In general, faults associated to MMC-HVDC stations can be divided in four main phases (Manduley, 2018):

 Phase 1: fault inception. The fault occurs and travelling waves propagate within the system, thus causing a sudden variation of the voltage levels across inductive elements. During a short period after the fault, voltages across capacitive elements and currents flowing through inductive elements can be considered constant, which will determine the initial repartition of the voltages resulting from the occurrence of the fault.

 Phase 2: before MMC blocking. After the first instants, capacitive elements (such as the DC poles or the MMC submodules) can get charged or discharged slowly, while current across inductive elements (such as arm reactors or smoothing reactors) increase or decrease slowly.

 Phase 3: MMC blocking. Similarly as in phase 1, the blocking of the MMC constitutes a sudden voltage variation across the MMC submodules, thus generating new travelling waves and transients. Therefore, during a short period after the blocking of the MMC, voltages across capacitive elements and currents flowing through inductive elements can be considered constant.

 Phase 4: after MMC blocking. As in phase 2, currents and voltages at the different locations evolve according to the nature of their respective passive elements towards an equilibrium state.

Since the method described in this section concerns only the first instants after a fault, it is only applicable to phases 1 and 3. For phases 2 and 4, more elaborate methods are required to estimate the behaviour of the system. However, for phases 1 and 3 it is possible to obtain an accurate distribution of the voltages right after the fault-given that the initial conditions are known-allowing to identify critical conditions and particular vulnerabilities of the system during a given event.

D.3 Case Study: Positive DC Bus-to-Ground Fault (Fault K)

Consider a positive DC bus-to-ground fault (fault K) on a symmetric monopolar configuration with the arm reactor on the DC side. In this case, the fault implies that the voltage of the positive DC pole goes from V 4up = 1 p.u. to V 4up = 0, and thus ΔV 4up = -1 p.u.

In addition, since the voltage across the MMC submodules (V SM ) and the healthy pole (V 4low ) are considered to remain constant during the first instants, the voltage variations at such locations (ΔV SM and ΔV 4low respectively) are considered equal to zero.

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By doing the corresponding substitutions, the equations from Tbl. D-1 remain as follows: From loop 7 in Tbl. D-2, it is clear that the only elements in the circuit that are able to balance the voltage variation on the faulted pole are the arm reactors V BR . Hence, each arm reactor will experience a positive voltage increase of which the sum is equal to 1 p.u. (i.e. the amplitude of ΔV 4up ). Since both reactors are identical, each sees an increase of approximately 0.5 p.u. Therefore:

Loop

𝛥𝑉 𝐵𝑅 𝑢𝑝 = 𝛥𝑉 𝐵𝑅 𝑙𝑜𝑤 ≈ 0.5 𝑝. 𝑢.

[D-5]

From loops 5 and 6, it is obtained that:

𝛥𝑉 3 𝑢𝑝 = 𝛥𝑉 𝐵𝑅 𝑢𝑝 -1 ≈ -0.5 𝑝. 𝑢.

[D-6]

𝛥𝑉 3 𝑙𝑜𝑤 = -𝛥𝑉 𝐵𝑅 𝑙𝑜𝑤 ≈ -0.5 𝑝. 𝑢

[D-7]

Furthermore, from loops 1 and 2 it can be seen that any variation occurring on V 3 is also imposed in V 2 :

𝛥𝑉 2 = 𝛥𝑉 3 𝑢𝑝 = 𝛥𝑉 3 𝑙𝑜𝑤

[D-8]

Therefore, it is evident that the occurrence of fault K on the positive DC pole would produce a negative displacement of the voltage in locations 2, 3 up and 3 low . This allows identifying the most critical condition for such locations during fault K, which consists of the instant in which any of the three phases are at its most negative value. Considering the maximum peak amplitudes of such locations (calculated through the expressions given in Table 3.3), if the fault occurs during the negative semi-cycle, the voltages observed at locations 2 and 3 right after fault K occurs are:

𝑉 2 𝑚𝑎𝑥 = 𝑉 2 + 𝛥𝑉 2 = -0.82 𝑝. 𝑢. -0.5 𝑝. 𝑢. = -1.32 𝑝. 𝑢.

[D-9]

𝑉 3 𝑚𝑎𝑥 = 𝑉 3 + 𝛥𝑉 3 = -1.00 𝑝. 𝑢. -0.5 𝑝. 𝑢. = -1.50 𝑝. 𝑢. During phase 2, the voltage variations on V 2 and V 3 depend mainly on the discharge of the arm reactors, the discharge of the MMC submodules and the charge of the healthy (negative) pole through the cable sheaths and the ground (see loops 3-6 in Figure 3.13). However, an accurate estimation of the evolution of the voltages during this phase would require, as discussed previously, other methods involving detailed modelling and numerical analysis.

Nevertheless, if a longer time span is observed for the different phases of the fault, it is observed the maximum overvoltage levels are reached during phase 2. This is attributable to the charge of the healthy DC pole, as it has an influence on V 3 as shown in Table 3.3, and variations in V 3 (i.e. ΔV 3 ) may carry a variation in V 2 (i.e. ΔV 2 ), as shown in After the blocking of the MMC (phase 4), more complex interactions play a significant role on the overvoltage levels, such as the successive reflections of travelling waves-generated by the fault and the blocking of the MMC-and the charge of the healthy pole through the cable sheaths. However, this concerns mainly TOVs, while maximum SFOs are typically reached right after the occurrence of the fault or in some particular cases, right after the blocking of the MMC-i.e. during phases 1 and 3 (Manduley, 2018).

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Nicolas Manduley 2020 Page 196 However, in the particular example considered in this section, if a wider time window is observed, it can be seen that the overvoltage levels measured during phase 4 can reach higher values than those previously estimated (see Fig. D-3). Such values are the result of the combination of several phenomena, including the charge of the healthy DC pole, resonance of the passive elements within the station and the effect of successive reflections. These phenomena cannot be adequately considered with the above approach. This constitutes a major limitation of the presented approach in many cases.

D.4 Discussion and Conclusion

A simplified approach such as the one presented in this appendix allows providing an initial understanding of the overall behaviour of the system and a fairly accurate approximation of the expected overvoltage levels at the different locations during the first instants after a fault. In addition, it makes possible to identify the potentially dangerous conditions leading to the

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Nicolas Manduley 2020 Page 197 maximum overvoltage levels (e.g. the most critical fault instant or phase or location more vulnerable during a specific type of fault) without the need of performing simulations.

However, these estimations are only pertinent if the maximum overvoltage effectively occurs right after the fault or the blocking of the MMC and the initial conditions are known. As it has been shown, there are other phenomena that may lead to higher overvoltages during phase 4 (after the blocking of the MMC), including the charge of the healthy DC pole, resonance of the passive elements within the station and the effect of successive reflections between the station and the fault location and/or the other station.

The study of such phenomena would require more appropriate and detailed models. On the other hand, increasing the complexity of the model increases the difficulty to maintain a fully qualitative approach, for the reasons explained in Chapter 3. Although there may be ways of implementing a simplified method that would not require the use of numerical methods for its resolution, it would only be valid if no surge arresters are present, because of their nonlinearity.

Therefore, it seems difficult to make conclusions based only on a simplified approach such as the one presented in this appendix. There are interactions between non-linear elements which cannot be taken into account by such kind of methods, as well as other complex phenomena which play an important role in the transient behaviour of the system and that has a direct impact on the overvoltage levels.

Nevertheless, this approach makes possible to identify the most critical events leading to a sequence of slow-front and/or temporary overvoltages (SFO and TOV, respectively), as well as the most vulnerable points and the most critical instants for each fault type to occur. This allows having a rough approximation of the overvoltage profile of the system before performing detailed EMT simulations, the critical scenarios and an initial point for the overvoltage protection strategy. In addition, it can help achieve a better understanding of the fundamental behaviour of the system.

The qualitative approach can therefore constitute a useful additional tool during the system analysis phase of insulation coordination for any system (see Figure 3.18). In all cases, detailed EMT simulation studies are necessary to make accurate estimations of the overvoltage profile of the system, a correct design of the overvoltage protection strategy and general insulation coordination of MMC-HVDC systems.

By default, the initial number of columns for each arrester is one regardless of the maximum allowed by the user.

The factor k represents the ratio between the withstand voltage of the equipment (SIWV) and the protective level of the arrester (SIPL). By knowing the absolute maximum overvoltage levels without arresters (U 2% ), a maximum value of SIWV may be established by considering that the maximum withstand voltage of the equipment corresponds to the dielectric strength which is equal or higher to the maximum overvoltage. One way of doing this is by making SIWV equal (or proportional by a given factor) to U 2% , as typically done in IEC 60071 standards for switching overvoltages. Then, the maximum SIPL can be specified as follows:

𝑆𝐼𝑃𝐿 𝑚𝑎𝑥 = 𝑈 2% 𝑘 [E-4]
As discussed in §4.2 in Chapter 1, the minimum values for this factor are given in IEC 60071-5 standard. This value is used to provide a stopping criterion in case one or more arresters reach the maximum overvoltage protection level, in which case the initial conditions provided do not converge into an optimal solution.

E.4 EMT Simulations

After the initial values are set, they are transferred to a data structure from which they can be read by the function in charge of modifying the netlist of the base EMTP case to set the simulation case. The base EMTP case used should include all the arresters that may be present in the configuration. The surge arresters which are not present in the current configuration may be set to a sufficiently high protective level so that it is guaranteed that they will always behave as an infinite resistance. This method allows to easily modify the surge arrester arrangement using the same EMTP base case.

Once the netlist of the EMTP base case has been modified to include all the considered arresters, the simulations are launched. They may include different scenarios producing transients such as faults, switching operations, disconnections, resonance and other sources of slow-front and temporary overvoltage (see §3.2 and §3.3 in Chapter 3).

E.5 Modification of the Surge Arrester Specifications

The results of the EMTP simulations are extracted and treated to constitute the maximum overvoltage profile of the system, as well as the maximum total energy absorbed by the arresters. For each arrester:

 If the total energy absorbed is lower E max , no modifications are required for such arrester.

 If the total energy absorbed is higher than E max and the current number of columns is lower than the maximum admitted (N col_max ), a column is added.

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 If the total energy absorbed is higher than E max and the current number of columns is the maximum admitted, the protective level of the surge arrester (SIPL) is increased by a defined step. In such case, the number of columns is reset to one for the next iteration.

If with the maximum number of columns the SIPL reaches the maximum value (SIPL max , see equation [E-4]), a warning shall be prompted indicating that the design is not possible using the specified number of parallel columns of arresters for the concerned location. In such case, either a higher number of columns shall be specified, or an alternative solution may be considered (e.g. different arrester arrangement, the removal of such arrester, or the use of sacrificial arresters).

E.6 Stopping Criteria

The algorithm stops when the considered design does not result in an excess of energy absorbed by any of the arresters present in the configuration. Also, if one or more arresters reach their maximum SIPL level, no further modifications will be performed on such arresters, and a warning shall be prompted indicating that the design is not possible with the provided specifications

E.7 Discussion

Since the installation of multiple columns of arresters may carry some problems regarding the distribution of the currents between the different columns (IEC 60099-9), solutions with a single column will typically be preferred unless absolutely necessary. In this respect, an initial approach could be to set the maximum number or parallel columns to one to all arresters. If the final design features unacceptably high energy absorption levels for one or more arresters, the procedure may be repeated by modifying the maximum number of columns for the concerned arresters until a satisfactory design is obtain.

The same principle applies if the energy absorption levels are acceptable but not the final maximum overvoltage levels at one or more specific locations.

Furthermore, in this proposal, a progressive increase of the SIPL is performed whenever the energy absorption levels are too high. Whenever the SIPL has to be increased, it is done in defined small steps in order to progressively reduce the energy absorption levels of the considered arrester. Therefore, no reductions of the SIPL are considered at any point of the algorithm to avoid initiating infinite loops in which several arresters are modified in each step and no optimal solution is reached. However, other approaches to adjust the SIPL may be considered after further studies. It might be possible to determine the final value of SIPL by dichotomy considering one or more arresters at a time, or even the number of columns

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present at each location in the current/previous iteration. This shall be addressed in future studies.

Therefore, this algorithm shall be tested in future studies to determine the best methods for obtaining an optimal specification of the surge arresters of a given configuration considering:

 The procedures for the modification of the SIPL on each iteration  How to deal with the addition or removal of parallel columns  The resulting overvoltage profile and insulation design

Figure 1 . 1

 11 Figure 1.1 Graphical representation of the evaluation of the risk of failure as a function of the probability density of the overvoltage f(U) and the discharge probability of the insulation P(U). Extracted from IEC 60071-2. ............................................................................................................................................. Figure 1.2 Insulation configurations considered in the IEC insulation coordination standards ....................... Figure 1.3 Classes and shapes of overvoltages, standard voltage shapes and standard withstand voltage tests. Extracted from IEC 60071-1. ................................................................................................................ Figure 1.4 V-I characteristic for a SIEMENS surge arrester rated Ur = 336 kV (rms), typically used for an AC system rated U s = 420 kV; extracted from Hinrichsen (2012). ............................................................... Figure 1.5 Flow chart for the determination of the rated or standard insulation levels; extracted from IEC 60071-1. ............................................................................................................................................. Figure 1.6 AC vs DC comparison of the indicative insulation distance requirements for switching (blue), lightning (red) and pollution (green). Extracted from CIGRE TB 518 ..................................................... Figure 1.7 Left: AC versus DC arcing differences across the insulator (extracted from CIGRE TB 518). Right: Flashover process in polluted insulators in presence of dry bands along the surface (from CIGRE TB 158). ................................................................................................................................................... Figure 1.8 AC breakdown voltage (in RMS) for different gap configurations. Extracted from CIGRE TB 72. .... Figure 1.9 DC breakdown voltage as a function of the gap clearance for a rod-plane configuration. Extracted from CIGRE TB 72................................................................................................................................ Figure 1.10 Examples of the main converter topologies in HVDC systems ..................................................... Figure 1.11 Fundamental scheme of a base 12-pulse LCC-HVDC station including the AC side, DC side, converter station and components, switches and possible surge arresters which could be decided to install for a given configuration. Extracted from IEC 60071-5. .............................................................. Figure 1.12 Modular Multi-level Converter basic scheme. Extracted from Kouro et al., 2010. ....................... Figure 1.13 Classification of lightning strokes according to their polarity (positive or negative) and the direction of the propagation of the initial leader (upward or downward) indicated by the arrow. Figures extracted from CIGRE TB 549. ............................................................................................................. Figure 1.14 Illustration of the first and subsequent strokes that can occur during a cloud-to-ground flash. ... Figure 1.15 Mean annual ground flash density maps for North America in the 2001 -2004 period. Extracted from Orville et al. 2011. ...................................................................................................................... Figure 1.16 Shape and front parameters of the CIGRE concave shape used to represent lightning strokes, where I is the peak amplitude, S m the maximum steepness (or rate of rise) and t f the equivalent front duration. ............................................................................................................................................ Figure 1.17 Reference distributions for negative lightning current amplitudes (extracted from CIGRE TB 063). The horizontal axis features the current amplitudes for the first stroke, while the vertical axis provides the probability for the lightning current amplitude to be equal or lower than the considered value. ... Figure 1.18 Illustration of the fundamental principles of the electrogeometric model (EGM) based on the striking distance to each conductor (r c ) and to the ground (r g ) to determine the impact point of the lightning stroke. ................................................................................................................................. Figure 1.19 Evolution of the striking distances as the lightning amplitude increases until reaching a critical value where the total exposure D c = 0, for which the corresponding current is I msf . Since the total exposure is zero, it is considered that no shielding failures can occur for current amplitudes higher to I msf . .....................................................................................................................................................

Figure

  Figure 1.1 Graphical representation of the evaluation of the risk of failure as a function of the probability density of the overvoltage f(U) and the discharge probability of the insulation P(U). Extracted from IEC 60071-2. ............................................................................................................................................. Figure 1.2 Insulation configurations considered in the IEC insulation coordination standards ....................... Figure 1.3 Classes and shapes of overvoltages, standard voltage shapes and standard withstand voltage tests. Extracted from IEC 60071-1. ................................................................................................................ Figure 1.4 V-I characteristic for a SIEMENS surge arrester rated Ur = 336 kV (rms), typically used for an AC system rated U s = 420 kV; extracted from Hinrichsen (2012). ............................................................... Figure 1.5 Flow chart for the determination of the rated or standard insulation levels; extracted from IEC 60071-1. ............................................................................................................................................. Figure 1.6 AC vs DC comparison of the indicative insulation distance requirements for switching (blue), lightning (red) and pollution (green). Extracted from CIGRE TB 518 ..................................................... Figure 1.7 Left: AC versus DC arcing differences across the insulator (extracted from CIGRE TB 518). Right: Flashover process in polluted insulators in presence of dry bands along the surface (from CIGRE TB 158). ................................................................................................................................................... Figure 1.8 AC breakdown voltage (in RMS) for different gap configurations. Extracted from CIGRE TB 72. .... Figure 1.9 DC breakdown voltage as a function of the gap clearance for a rod-plane configuration. Extracted from CIGRE TB 72................................................................................................................................ Figure 1.10 Examples of the main converter topologies in HVDC systems ..................................................... Figure 1.11 Fundamental scheme of a base 12-pulse LCC-HVDC station including the AC side, DC side, converter station and components, switches and possible surge arresters which could be decided to install for a given configuration. Extracted from IEC 60071-5. .............................................................. Figure 1.12 Modular Multi-level Converter basic scheme. Extracted from Kouro et al., 2010. ....................... Figure 1.13 Classification of lightning strokes according to their polarity (positive or negative) and the direction of the propagation of the initial leader (upward or downward) indicated by the arrow. Figures extracted from CIGRE TB 549. ............................................................................................................. Figure 1.14 Illustration of the first and subsequent strokes that can occur during a cloud-to-ground flash. ... Figure 1.15 Mean annual ground flash density maps for North America in the 2001 -2004 period. Extracted from Orville et al. 2011. ...................................................................................................................... Figure 1.16 Shape and front parameters of the CIGRE concave shape used to represent lightning strokes, where I is the peak amplitude, S m the maximum steepness (or rate of rise) and t f the equivalent front duration. ............................................................................................................................................ Figure 1.17 Reference distributions for negative lightning current amplitudes (extracted from CIGRE TB 063). The horizontal axis features the current amplitudes for the first stroke, while the vertical axis provides the probability for the lightning current amplitude to be equal or lower than the considered value. ... Figure 1.18 Illustration of the fundamental principles of the electrogeometric model (EGM) based on the striking distance to each conductor (r c ) and to the ground (r g ) to determine the impact point of the lightning stroke. ................................................................................................................................. Figure 1.19 Evolution of the striking distances as the lightning amplitude increases until reaching a critical value where the total exposure D c = 0, for which the corresponding current is I msf . Since the total exposure is zero, it is considered that no shielding failures can occur for current amplitudes higher to I msf . .....................................................................................................................................................

Figure 1 .

 1 Figure 1.20 Illustration of the different angles and parameters required for the calculation of the total exposure width (D c ) and maximum shielding failure current (I msf ) required for the estimation of the shielding failure flashover rate (SFFOR) using the electrogeometric model (EGM) ............................... Figure 1.21 Scheme illustrating the repartition of the current for a direct strike on the tower and the main back-flashover mechanism. For simplicity and for easier visualization, the curves in the figure correspond to a positive lightning stroke, and according to the voltage convention, the voltage V ins corresponds to the insulator of a positive DC conductor. ..................................................................... Figure 1.22 a) Upper section: CIGRE concave shape model for a lightning stroke of +120 kA. Lower section: potential rise of the tower at the upper and lower cross arms (red and green curves) and effect of the inductive coupling between the lines (blue and pink curves); b) Voltage measurements and tower geometry used for this example. ......................................................................................................... Figure 1.23 Scheme illustrating the repartition of the current for a shielding failure. For simplicity and for easier visualization, the curves in the figure correspond to a positive lightning stroke, and according to the voltage convention, the voltage V ins corresponds to the insulator of a positive DC conductor. ....... Figure 1.24 Average lightning flash density [flashes/km²/year] and frequency of short outages [tripouts/site] in France over the period between 2010 -2019. ................................................................................. Figure 1.25 Comparison of the average ground flash density and short outages per region in France for 2019, extracted from RTE, Bilan Electrique, 2019. Short outage rates tend to be directly proportional to the lightning activity of each particular region. ......................................................................................... Figure 2.1 Example of a typical non-linear V-I characteristic represented by three, four and six linear segments ............................................................................................................................................ Figure 2.2 a) IEEE model and b) Pinceti model of the surge arrester for high frequency studies ..................... Figure 2.3 MMC architectures with the arm reactor a) on the AC side, and b) on the DC side (for a symmetrical monopole) ...................................................................................................................... Figure 2.4 Modelling of the lightning stroke for EMTP simulations ............................................................... Figure 2.5 Schematic representation of the overhead line section to be modelled for fast-front overvoltage (FFO) studies. ..................................................................................................................................... Figure 3.1 Fundamental scheme of an MMC-HVDC station including all the basic components and possible locations for the surge arresters for a station architecture with the arm reactor on the AC side. The green arrows indicate the voltage convention of the longitudinal elements. ....................................... Figure 3.2 Fundamental scheme of an MMC-HVDC station including all the basic components and possible locations for the surge arresters for a station architecture with the arm reactor on the DC side. The green arrows indicate the voltage convention of the longitudinal elements. ....................................... Figure 3.3 Voltages in service of the main components and locations of an MMC-HVDC architecture with the arm reactor on the AC side. ................................................................................................................ Figure 3.4 Voltages in service of the main components and locations of an MMC-HVDC architecture with the arm reactor on the DC side ................................................................................................................. Figure 3.5 Reduced fundamental scheme for an MMC-HVDC substation with the arm rector on the AC side. The surge arresters, as well as the sections corresponding to the metallic return and overhead lines have been removed. The smoothing reactor has been also omitted. ................................................... Figure 3.6 Reduced fundamental scheme for an MMC-HVDC substation with the arm rector on the DC side. The surge arresters, as well as the sections corresponding to the metallic return and overhead lines have been removed. ........................................................................................................................... Figure 3.7 Cable geometry and parameters used to build the EMTP model for the overvoltage studies ........ Figure 3.8 Fault scenarios considered for the temporary and slow-front overvoltage studies for an MMC-HVDC station with the arm reactor on the DC side ..............................................................................

Figure 4 .

 4 Figure 4.12 Double back-flashover rates for the cases with line surge arresters as a function of the footing resistance ......................................................................................................................................... 132 Figure 4.13 Overall (left) and double (right) back-flashover performances for the strikes on adjacent towers ........................................................................................................................................................ 134 Figure 4.14 Illustration of the path of the current when lightning strikes a tower adjacent to another which is protected by line surge arresters. ..................................................................................................... 135 Figure 4.15 Shielding failure flashover rates (SFFOR) for each surge arrester configuration considered for the double circuit 500 kV HVDC system studied using the electrogeometric model (EGM). ...................... 136 Figure 4.16 Case study for the unbalanced insulation solution including a reduced air gap on a complete circuit. All cases are performed on a configuration with both positive poles in the upper cross arm .. 137 Figure 4.17 Overall back-flashover rate comparison using various values for the difference in distance between the arcing horns of the insulators of both circuits ............................................................... 138 Figure 4.18 Double back-flashover rate comparison using various values for the difference in distance between the arcing horns of the insulators of both circuits ............................................................... 138 Figure 4.19 Overall (left) and double (right) back-flashover rate (BFOR) for an unbalanced insulation solution on a single positive pole insulator and on both insulators on one side ............................................... 140 Figure 4.20 Comparison of the overall (left) and double (right) back-flashover rates of the surge arrester and unbalanced insulation solutions ....................................................................................................... 140 Figure 4.21 Total energy absorbed by the surge arrester for a) direct positive and b) direct negative strokes to the top of the tower ......................................................................................................................... 143 Figure 4.22 a) Direct stroke to the conductor protected by the surge arrester, and b) direct stroke to the conductor in the opposite side of the cross arm (not protected by a surge arrester) .......................... 144 Figure 4.23 Insulator longitudinal voltages with and without surge arrester (blue and red curves, respectively) for a) positive stroke and b) negative stroke (parameters used: I peak = ±20 kA and R gnd = 10 Ω) ..................................................................................................................................................... 145 Figure 4.24 Insulator longitudinal voltages when a surge arrester is present for I peak of ±10 and ±50 kA and grounding resistances of 10 Ω and 100 Ω for a) positive strokes and b) negative strokes ................... 146 Figure 4.25 Comparison of the current distribution for a positive 50 kA lightning stroke on the conductor directly protected by the surge arrester (i.e. lower positive DC pole) for grounding resistances of 10 Ω and 100 Ω (left and right, respectively). ............................................................................................ 146 Figure 4.26 Surge arrester total energy absorption levels for different peak current intensities (10-50 kA) and grounding resistances (10-100 Ω) for a) positive strokes and b) negative strokes on the protected DC pole .................................................................................................................................................. 147 Figure 4.27 Insulator longitudinal voltages of the struck pole with and without surge arrester (blue and red curves, respectively) for a) positive stroke and b) negative stroke on the unprotected pole (parameters used: I peak = ±20 kA and R gnd = 10 Ω) .................................................................................................. 148 Figure 4.28 Comparison of the current distribution for a positive 50 kA lightning stroke on the unprotected conductor (i.e. lower negative DC pole) for grounding resistances of 10 Ω and 100 Ω (left and right, respectively) ..................................................................................................................................... 148 Figure 4.29 Insulator longitudinal voltages on the unprotected pole (i.e. lower negative DC pole) when a surge arrester is installed on the opposite pole of the cross arm (i.e. lower positive DC pole) for I peak of ±20 and ±50 kA and grounding resistances of 10 Ω and 100 Ω for a) a positive stroke and b) a negative stroke. Note: in this figure, 20 kA was chosen as the minimum value because for 10 kA no flashovers are produced for either polarity. ....................................................................................................... 149 Figure 4.30 Insulator longitudinal voltages on the pole protected by a surge arrester (i.e. lower positive DC pole) when lightning strikes the unprotected pole (i.e. the lower negative DC pole) for I peak of ±10 and

  logarithmic standard deviation (β) for the overall distribution of the peak current of downward negative strokes, the shielding failure domain (below or equal to 20 kA), the back-flash domain (above 20 kA) and for subsequent strokes. ............................................................................. Table 1.3 Median (M) and logarithmic standard deviation (β) for the log-normal representation of the front time t f of downward negative strokes. The same parameters are recommended for both ranges of first strokes (i.e. shielding failure and back-flash domains) and subsequent strokes. .................................. Table 1.4 Median (M) and logarithmic standard deviation (β) for the log-normal representation of the maximum steepness S m of downward negative strokes. ......................................................................Table 1.5 Derived statistics for the estimation of the maximum steepness S m and the front time t f as a function of the peak current I F (first strokes) ....................................................................................... Table 1.6 Derived statistics for the estimation of the maximum steepness S m and the front time t f as a function of the peak current I F (subsequent strokes) ........................................................................... Table 1.7 Parameters for the electrogeometric model implementation from different authors .................... Table 1.8 Parameters for the simplified leader progression model implementation resulting from applying regressions over a certain range of values of current and conductor height from different authors. .... Table 2.1 Summary of the different transmission line models, their main characteristics and respective applications considered in this research. ............................................................................................. Table 2.2 MMC model setup and parameters for EMTP simulations ............................................................. Table 3.1 Kirchhoff's voltage equations from the fundamental MMC-HVDC scheme with the arm reactor on the expressions of the service voltages of the different components of the MMC-HVDC station in monopolar and bipolar configurations, and with the arm reactor on the AC and DC sides of the converter. The comparison assumes identical DC outputs. ............................................................ Table 3.4 Description of the faults considered in the overvoltage studies for an MMC-HVDC station with the arm reactor on the DC side ................................................................................................................. Table 3.5 Absolute value (in p.u.) of the peak voltage levels at the different locations of the MMC-HVDC station obtained through simulation for the monopolar and bipolar configurations with the arm reactor on the DC side. The value in p.u. is calculated by considering 1 p.u. = 320 kV (the nominal DC voltage)slow-front overvoltage (SFO) and temporary overvoltage (TOV) levels at each location of the monopolar and bipolar MMC-HVDC stations with the arm reactor on the DC side. The values are expressed in p.u. with 1 p.u. equal to 320 kV (i.e. the nominal DC voltage).......................................... Table 3.7 Conclusions and particular recommendations to take into account for the overvoltage protection strategy for monopolar and bipolar MMC-HVDC configurations with the arm reactor on the DC side. . Table 3.8 Absolute value (in p.u.) of the peak voltage levels under normal operating conditions at the different locations of the MMC-HVDC station obtained through simulation for the symmetric monopolar configuration with the arm reactor on the AC side. The value in p.u. is calculated by considering 1 p.u. = 320 kV (the nominal DC voltage). ......................................................................... slow-front overvoltage (SFO) and temporary overvoltage (TOV) levels at each location of the symmetric monopolar MMC-HVDC station with the arm reactor on the AC side. The values are expressed in p.u. with 1 p.u. equal to 320 kV (i.e. the nominal DC voltage).......................................... 93 Table 3.10 Conclusions and particular recommendations to take into account for the overvoltage protection strategy of the symmetric monopolar MMC-HVDC configuration with the arm reactor on the AC side . 94 Table 3.11 Ratings of the surge arresters used in the study .......................................................................... 97 Table 3.12 Maximum SFO and TOV levels in configuration A1-A2-A3-C ....................................................... 102 Table 4.1 Different pole configurations labelled with respect to the position of the positive poles in the arrangement as: Top (positives on top), Bot (positives at the bottom), Side (positives on one sideof the surge arrester parameters used in this chapter .................................................. 131 Tbl. A-1 Base inputs for the parametric study conducted ........................................................................... 179 Tbl. B-1 Summary of the values of K 1 and K 2 for AC, positive DC and negative DC polarities for the estimation of the onset corona gradient E c ......................................................................................................... 184 Tbl. C-1 For the configuration without surge arresters: slow-front and temporary overvoltage levels (SFO and TOV, respectively) for each location during the different fault scenarios considered. The values are given in p.u. (with 1 p.u. = 320 kV). A value of zero indicates that no disturbances were measured to be above the normal operating voltage. ................................................................................................ 187 Tbl. C-2 For the configuration with arresters A1 and A2: slow-front and temporary overvoltage levels (SFO and TOV, respectively) for each location during the different fault scenarios considered. The values are given in p.u. (with 1 p.u. = 320 kV). A value of zero indicates that no disturbances were measured to be above the normal operating voltage. ................................................................................................ 187 Tbl. C-3 Maximum current and energy absorption levels for each fault and for each arrester in the configuration. Current values under 1 mA are considered zero. ......................................................... 187 Tbl. C-4 For the configuration with arresters A1, A2 and A3: slow-front and temporary overvoltage levels (SFO and TOV, respectively) for each location during the different fault scenarios considered. The values are given in p.u. (with 1 p.u. = 320 kV). A value of zero indicates that no disturbances were measured to be above the normal operating voltage level. ............................................................... 188 Tbl. C-5 Maximum current and energy absorption levels for each fault and for each arrester in the configuration. Current values under 1 mA are considered zero. ......................................................... 188 Tbl. C-6 For the configuration with arresters A1, A2 and C: slow-front and temporary overvoltage levels (SFO and TOV, respectively) for each location during the different fault scenarios considered. The values are given in p.u. (with 1 p.u. = 320 kV). A value of zero indicates that no disturbances were measured to be above the normal operating voltage level. .current and energy absorption levels for each fault and for each arrester in the configuration. Current values under 1 mA are considered zero. ......................................................... 190 Tbl. D-1 General variation equations for configurations based on the fundamental scheme of MMC-HVDC stations with the arm reactor on the DC side .................................................................................... 192

Figure 1 . 1

 11 Figure 1.1 Graphical representation of the evaluation of the risk of failure as a function of the probability density of the overvoltage f(U) and the discharge probability of the insulation P(U). Extracted from IEC 60071-2.

Figure 1 . 2

 12 Figure 1.2 Insulation configurations considered in the IEC insulation coordination standards

  IEC 60071 standards define five different classes of voltages and overvoltages: continuous (or power frequency) voltage, temporary overvoltages (TOV), slow-front overvoltages (SFO), fastfront overvoltages (FFO) and very fast-front overvoltages (VFFO). These overvoltage types and their respective definitions and standard shapes are illustrated in Figure1.3.

Figure 1 . 3

 13 Figure 1.3 Classes and shapes of overvoltages, standard voltage shapes and standard withstand voltage tests. Extracted from IEC 60071-1.

Figure

  Figure 1.4 V-I characteristic for a SIEMENS surge arrester rated Ur = 336 kV (rms), typically used for an AC system rated U s = 420 kV; extracted from Hinrichsen (2012).

Figure 1 . 5

 15 Figure 1.5 Flow chart for the determination of the rated or standard insulation levels; extracted from IEC 60071-1.

Figure 1

 1 Figure 1.6 AC vs DC comparison of the indicative insulation distance requirements for switching (blue), lightning (red) and pollution (green). Extracted from CIGRE TB 518

Figure 1 . 7

 17 Figure 1.7 Left: AC versus DC arcing differences across the insulator (extracted from CIGRE TB 518). Right: Flashover process in polluted insulators in presence of dry bands along the surface (from CIGRE TB 158).

  Figure 1.8 AC breakdown voltage (in RMS) for different gap configurations. Extracted from CIGRE TB 72.

  Figure 1.9 DC breakdown voltage as a function of the gap clearance for a rod-plane configuration. Extracted from CIGRE TB 72.

  Figure 1.11 Fundamental scheme of a base 12-pulse LCC-HVDC station including the AC side, DC side, converter station and components, switches and possible surge arresters which could be decided to install for a given configuration. Extracted from IEC 60071-5.

Figure 1 .

 1 Figure 1.12 Modular Multi-level Converter basic scheme. Extracted from Kouro et al., 2010.

  Figure 1.13 Classification of lightning strokes according to their polarity (positive or negative) and the direction of the propagation of the initial leader (upward or downward) indicated by the arrow. Figures extracted from CIGRE TB 549.

Figure 1 .

 1 Figure 1.14 Illustration of the first and subsequent strokes that can occur during a cloudto-ground flash.

Figure 1 .

 1 Figure 1.15 Mean annual ground flash density maps for North America in the 2001 -2004 period. Extracted from Orville et al. 2011.

Figure 1 .

 1 Figure 1.16 Shape and front parameters of the CIGRE concave shape used to represent lightning strokes, where I is the peak amplitude, S m the maximum steepness (or rate of rise) and t f the equivalent front duration.

Figure 1 .

 1 Figure1.17 Reference distributions for negative lightning current amplitudes (extracted from CIGRE TB 063). The horizontal axis features the current amplitudes for the first stroke, while the vertical axis provides the probability for the lightning current amplitude to be equal or lower than the considered value.

Figure 1 .

 1 Figure 1.18 Illustration of the fundamental principles of the electrogeometric model (EGM) based on the striking distance to each conductor (r c ) and to the ground (r g ) to determine the impact point of the lightning stroke.

Figure 1 .

 1 Figure 1.19 Evolution of the striking distances as the lightning amplitude increases until reaching a critical value where the total exposure D c = 0, for which the corresponding current is I msf . Since the total exposure is zero, it is considered that no shielding failures can occur for current amplitudes higher to I msf . Both the exposure width D c (I) and the maximum shielding failure current I msf are required for the estimation of the SFFOR, and are given-for electrogeometric models-by the following expressions (CIGRE TB 704, 2017) (following the notation of Figure 1.20):

Figure 1 .

 1 Figure 1.20 Illustration of the different angles and parameters required for the calculation of the total exposure width (D c ) and maximum shielding failure current (I msf ) required for the estimation of the shielding failure flashover rate (SFFOR) using the electrogeometric model (EGM)

Figure 1 .

 1 Figure 1.21 Scheme illustrating the repartition of the current for a direct strike on the tower and the main back-flashover mechanism. For simplicity and for easier visualization, the curves in the figure correspond to a positive lightning stroke, and according to the voltage convention, the voltage V ins corresponds to the insulator of a positive DC conductor.

  Figure 1.22 a) Upper section: CIGRE concave shape model for a lightning stroke of +120 kA. Lower section: potential rise of the tower at the upper and lower cross arms (red and green curves) and effect of the inductive coupling between the lines (blue and pink curves); b) Voltage measurements and tower geometry used for this example.

Figure 1 .

 1 Figure 1.23 Scheme illustrating the repartition of the current for a shielding failure. For simplicity and for easier visualization, the curves in the figure correspond to a positive lightning stroke, and according to the voltage convention, the voltage V ins corresponds to the insulator of a positive DC conductor.

Figure 1 .

 1 Figure 1.24 Average lightning flash density [flashes/km²/year] and frequency of short outages [tripouts/site] in France over the period between 2010 -2019.

  Contribution to Insulation Coordination Studies for VSC-HVDC SystemsChapter 1: State of the Art and Literature Review Nicolas Manduley 2020 Page 55

Figure 1 .

 1 Figure 1.25 Comparison of the average ground flash density and short outages per region in France for 2019, extracted from RTE, Bilan Electrique, 2019. Short outage rates tend to be directly proportional to the lightning activity of each particular region.

  Chapter 1: State of the Art and Literature Review Nicolas Manduley 2020 Page 58

  Chapter 1: State of the Art and Literature Review Nicolas Manduley 2020 Page 59

Figure 2 . 1

 21 Figure 2.1 Example of a typical non-linear V-I characteristic represented by three, four and six linear segments

  Figure 2.2 a) IEEE model and b) Pinceti model of the surge arrester for high frequency studies3.5 Modular Multi-level Converter (MMC)Two architectures of the MMC are considered depending on the position of the arm reactor 4 , which can be on the AC or the DC side. This is illustrated in Figure2.3 for a symmetrical monopole, including the star-point reactor which is the typical grounding scheme for this architecture. In the case of a bipolar configuration, the star point reactor is removed and one of the DC sides represented in the figure is solidly grounded, thus representing one half of the bipole.

Figure 2 . 4

 24 Figure 2.4 Modelling of the lightning stroke for EMTP simulations

Figure 2 . 5

 25 Figure 2.5 Schematic representation of the overhead line section to be modelled for fastfront overvoltage (FFO) studies.

Figure 3 . 1

 31 Figure 3.1 Fundamental scheme of an MMC-HVDC station including all the basic components and possible locations for the surge arresters for a station architecture with the arm reactor on the AC side. The green arrows indicate the voltage convention of the longitudinal elements.

Figure 3 . 2

 32 Figure 3.2 Fundamental scheme of an MMC-HVDC station including all the basic components and possible locations for the surge arresters for a station architecture with the arm reactor on the DC side. The green arrows indicate the voltage convention of the longitudinal elements.

Figure 3 .

 3 Figure 3.3 and Figure 3.4 show typical waveforms of the voltages in service at various locations of an MMC-HVDC architecture with the arm reactor on the AC and the DC side. The locations chosen use the nomenclature indicated in Figure 3.1 and Figure3.2, and concern the phaseto-ground voltages of the primary and secondary side of the converter transformer (V 1 and V 2 , respectively), the intermediate point between the arm reactor and the MMC submodules (V 3 ), the DC pole voltages (V 4 ) and the voltages across the bridge arm reactors (V BR ) and the MMC submodules (V SM ).

  configuration. These differences are discussed and characterised in detail below for each location.

Figure 3 . 3

 33 Figure 3.3 Voltages in service of the main components and locations of an MMC-HVDC architecture with the arm reactor on the AC side.

Figure 3 . 4

 34 Figure 3.4 Voltages in service of the main components and locations of an MMC-HVDC architecture with the arm reactor on the DC side

  expressed as half of the sum of the DC voltage (V 4up ) and the regular sinusoid used for the monopolar configuration (V*), as also illustrated in Figure3.3 and Figure3.4.

Figure 3 .

 3 Figure 3.5 and Figure 3.6 illustrate a reduced fundamental scheme for MMC stations with the arm reactor on the AC and DC side of the converter, respectively, based on the fundamental schemes from Figure 3.1 and Figure 3.2. They feature the different grounding schemes considered: a star-point reactor for the symmetrical monopole and a solid grounding for the bipole at the mid-point between the positive and negative half of the station 7 .

Figure 3 . 5 Figure 3 . 6

 3536 Figure 3.5 Reduced fundamental scheme for an MMC-HVDC substation with the arm rector on the AC side. The surge arresters, as well as the sections corresponding to the metallic return and overhead lines have been removed. The smoothing reactor has been also omitted.

Figure 3 . 8

 38 Figure 3.8 Fault scenarios considered for the temporary and slow-front overvoltage studies for an MMC-HVDC station with the arm reactor on the DC side

  u.) of the peak voltage levels at the different locations of the MMC-HVDC station obtained through simulation for the monopolar and bipolar configurations with the arm reactor on the DC side. The value in p.u. is calculated by considering 1 p.u. = 320 kV (the nominal DC voltage).

Figure 3 . 9

 39 Figure 3.9 Magnitude and path of the fault current through the MMC submodule during a short-circuit of the MMC submodule (fault I)

Figure 3 .

 3 Figure 3.10 Fault scenarios considered for the temporary and slow-front overvoltage studies for an MMC-HVDC station with the arm reactor on the AC side

Figure 3 .

 3 Figure 3.11 Symmetric monopolar configuration scheme including the faults and surge arresters considered in the study Therefore, the surge arrester configurations considered are thus combinations of arresters A3 and C while arresters A1-A2 will be present in all configurations, as shown in Figure 3.12 Name Description NS No surge arresters A1-A2 Transformer arresters A1-A2-A3 Transformer and arm-to-ground arresters A1-A2-C Transformer and DC pole arresters A1-A2-A3-C All arresters considered Figure 3.12 Surge arrester configurations considered All scenarios have been simulated in EMTP for each surge arrester configuration, giving a total of 30 study cases.

Figure 3 .

 3 Figure 3.13 Maximum slow-front overvoltages (SFO) obtained for each considered component and for each considered arrangement of arresters. The maximum value is indicated above the corresponding configuration.

FigureFigure 3 .

 3 Figure 3.14 Maximum temporary overvoltages (TOV) obtained for each considered component and for each considered arrangement of arresters. The maximum value is indicated above the corresponding configuration.

Figure 3 .

 3 Figure 3.16 Comparison between the case without surge arresters (NS, red) and the A1-A2-A3 configuration (blue) for DC pole to ground fault. On the left, the currents flowing through the MMC submodules (phase B), including the current of the corresponding upper surge arrester A3 (green). On the right, the voltage levels at the point protected by arrester A3 (upper valve). It is seen how the overvoltage levels are effectively limited by the surge arrester.

  Figure 3.17 Energy absorption levels of each surge arrester in every configuration



  Architecture of the converter (and associated equipment)  Configuration of the station (such as symmetrical monopole or bipole with/without metallic return)  Location and specification of the surge arresters  Internal converter faults and general fault behaviour Contribution to Insulation Coordination Studies for VSC-HVDC Systems Chapter 3: Slow-Front Overvoltages and Fault points are covered by the fundamental schemes from Figure 3.1 and Figure 3.2.

Figure 3 .

 3 Figure 3.18 Flowchart illustrating the different steps of the procedure for insulation coordination of MMC-HVDC systems using electromagnetic transient simulations.

Figure

  Figure 4.1 Four possible pole configurations in a two-cross arm double-circuit HVDC configuration: a) both positives on top (Top), b) both positives at the bottom (Bot), c) both positives on one side (Side) and d) crossed polarities (Xed) Contribution to Insulation Coordination Studies for VSC-HVDC Systems Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance Nicolas Manduley 2020 Page 118

Figure 4 . 2

 42 Figure 4.2 Illustration of the dichotomy method used to determine the critical flashover current I f through successive EMTP simulations

  pole configurations labelled with respect to the position of the positive poles in the arrangement as: Top (positives on top), Bot (positives at the bottom), Side (positives on one side) and Xed (positives crossed)

Figure 4 . 4

 44 Figure 4.3 Detailed view of the a) voltage source, b) central and c) current source side of the EMTP model for the double monopolar configuration

  Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance As shown in Figure 4.5a and Figure 4.6a, the Top and Bot configurations (blue and red bars) present the lowest overall back-flashover rates. However, these flashover rates are almost entirely constituted by double flashovers (i.e. they are the same height in Figure 4.5b and Figure 4.6b)

  Figure 4.5 a) Overall and b) double back-flashover rates for all configurations in the 320 kV system

  Figure 4.7 a) Upper section: CIGRE concave shape model for a lightning stroke of +120 kA. Lower section: potential rise of the tower at the upper and lower cross arms (red and green curves) and effect of the inductive coupling between the lines (blue and pink curves); b) Voltage measurements in the crossed (Xed) configuration used for this example.

Figure 4 . 8

 48 Figure 4.8 Scheme of the tower model including the grounding, tower structure, cross arms, air gaps of the insulators and DC poles of one side of the tower

  Contribution to Insulation Coordination Studies for VSC-HVDC SystemsChapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance Nicolas Manduley 2020 Page 130 configurations with two surge arresters considered in this section are obtained by placing an additional arrester to the LP configuration on each of the other three poles of the tower.

Figure 4 . 9

 49 Figure 4.9 The different surge arrester arrangements considered for a Xed configuration. Each configuration is named based on its respective cross arm (upper or lower) and the polarity of the pole (positive or negative).

  Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance Nicolas Manduley 2020 Page 131

Figure 4 .

 4 Figure 4.10 Base V-I characteristic used corresponding to a surge arrester with a rated voltage of 336 kV (rms). Extracted from Hinrichsen (2012).

  Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance Nicolas Manduley 2020 Page 132

Figure 4 .

 4 Figure 4.11 Overall back-flashover rates for the cases with line surge arresters as a function of the footing resistance

Figure 4 .

 4 Figure 4.13 Overall (left) and double (right) back-flashover performances for the strikes on adjacent towers

  Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance Nicolas Manduley 2020 Page 135

Figure 4 .

 4 Figure 4.14 Illustration of the path of the current when lightning strikes a tower adjacent to another which is protected by line surge arresters.

Figure 4 .

 4 Figure 4.15 Shielding failure flashover rates (SFFOR) for each surge arrester configuration considered for the double circuit 500 kV HVDC system studied using the electrogeometric model (EGM).

Figure 4 .

 4 Figure 4.16 Case study for the unbalanced insulation solution including a reduced air gap on a complete circuit. All cases are performed on a configuration with both positive poles in the upper cross arm

Figure 4 .

 4 Figure 4.17 Overall back-flashover rate comparison using various values for the difference in distance between the arcing horns of the insulators of both circuits

  Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance Nicolas Manduley 2020 Page 140

Figure 4 .

 4 Figure 4.19 Overall (left) and double (right) back-flashover rate (BFOR) for an unbalanced insulation solution on a single positive pole insulator and on both insulators on one side

Figure 4 .

 4 Figure 4.20 Comparison of the overall (left) and double (right) back-flashover rates of the surge arrester and unbalanced insulation solutions

  Figure 4.21 Total energy absorbed by the surge arrester for a) direct positive and b) direct negative strokes to the top of the tower

  Figure 4.22 a) Direct stroke to the conductor protected by the surge arrester, and b) direct stroke to the conductor in the opposite side of the cross arm (not protected by a surge arrester)

  Figure 4.23 Insulator longitudinal voltages with and without surge arrester (blue and red curves, respectively) for a) positive stroke and b) negative stroke (parameters used: I peak = ±20 kA and R gnd = 10 Ω)

  Figure 4.24 Insulator longitudinal voltages when a surge arrester is present for I peak of ±10 and ±50 kA and grounding resistances of 10 Ω and 100 Ω for a) positive strokes and b) negative strokes

  Figure 4.26 Surge arrester total energy absorption levels for different peak current intensities (10-50 kA) and grounding resistances (10-100 Ω) for a) positive strokes and b) negative strokes on the protected DC pole

  Figure 4.27 Insulator longitudinal voltages of the struck pole with and without surge arrester (blue and red curves, respectively) for a) positive stroke and b) negative stroke on the unprotected pole (parameters used: I peak = ±20 kA and R gnd = 10 Ω)

Figure 4 .

 4 Figure 4.34 Surge arrester total energy absorption levels for different peak current intensities (10-50 kA) and grounding resistances (10-100 Ω) for a) positive strokes and b) negative strokes on the unprotected conductor.

Fig. A- 1

 1 Fig. A-1 Typical V-t characteristic of a rod-rod gap (left) and a string insulator (right). The vertical axis represents the ratio between the breakdown voltage (U B ) and the critical flashover voltage (U 50 ), while the horizontal axis features the total time to breakdown in µs. Extracted from CIGRE TB 72.

  [A-3] used to estimate the value of U 50 for AC systems under lightning impulses(CENELEC 50341, 2012

Fig

Fig. A- 2

 2 Fig. A-2 Impact of the conductor height (h p ) and applied voltage (V) on the corona radius (R c ). The blue lines represent the h p vs. R c curves for different fixed values of V, while the red lines represent the V vs. R c curves for different fixed values of h p .

  of the values of K 1 and K 2 for AC, positive DC and negative DC polarities for the estimation of the onset corona gradient E c The results of such studies are summarized and commented below.  For the same irregularity factors m, the corona onset voltage gradient E c is lower than for AC.  When typical irregularity factors are used for AC and DC, the corona onset voltage gradient E c are similar for AC and DC. Particularly, if values of 0.87-0.93 are used for AC Fault Maximum current and energy absorption levels for each fault and for each arrester in the configuration. Current values under 1 mA are considered zero.

  current and energy absorption levels for each fault and for each arrester in the configuration. Current values under 1 mA are considered zero.

  the configuration with arresters A1, A2 and C: slow-front and temporary overvoltage levels (SFO and TOV, respectively) for each location during the different fault scenarios considered. The values are given in p.u. (with 1 p.u. = 320 kV). A value of zero indicates that no disturbances were measured to be above the normal operating voltage level. current and energy absorption levels for each fault and for each arrester in the configuration. Current values under 1 mA are considered zero.

  current and energy absorption levels for each fault and for each arrester in the configuration. Current values under 1 mA are considered zero.

  equations for the first instants after a positive DC bus-to-ground fault (fault K) on a symmetric monopolar configuration with the arm reactor on the DC side

[D- 10 ]

 10 These estimations are validated by EMTP and illustrated in Fig.D-1, where a voltage drop of 161 kV (0.5 p.u.) is measured right after the instant of the fault for both V 2 and V 3 . It is Contribution to Insulation Coordination Studies for VSCabsolute maximum values for V 2 and V 3 are in agreement with the estimations from equations [D-9] and [D-10] with a very low margin of error (less than 3%).

Fig. D- 1

 1 Fig. D-1 Voltages V 2 and V 3low after the occurrence of fault K (before the blocking of the MMC)

  Fig. D-2. However, such overvoltage levels are only slightly higher than the estimations from equations [D-9] and [D-10] at the end of phase 2. The maximum slow-front overvoltage levels for V 2 and V 3low during fault K are about 1.38 p.u. and 1.67 p.u. respectively, and are reached just before the blocking of the MMC (phase 3), as shown in Fig. D-2. The time window observed in Fig. D-1 and Fig. D-2 is in the order of 1 millisecond.

Fig. D- 2

 2 Fig. D-2 Voltages V 2 and V 3low after the occurrence of fault K before and after the blocking of the converter (from phase 1 to the beginning of phase 4)

Fig. D- 3

 3 Fig. D-3 Voltages V 3 and V 4 (positive and negative DC poles) after the occurrence of fault K before and after the blocking of the converter (phases 1 through 4)

to Insulation Coordination Studies for VSC-HVDC Systems Glossary

	Glossary SFR Shielding Failure Rate [flashes/100 km/year] Introduction
	SIPL	Switching Impulse Protective Level
	BFOR Back-Flashover Rate SIWV Switching Impulse Withstand Voltage 1. Motivation
	CFO S m	Critical Flashover Voltage (also U 50 ) Maximum front steepness (CIGRE concave shape)
	CP STIPL Steep Impulse Protective Level Constant Parameters line model
	CSC STIWV Steep Impulse Withstand Voltage Current Source Converter
	D c t b	Total exposure width for which a conductor is exposed to shielding failures Time to breakdown across an air gap or insulator under a transient stress
	DMR E 0 t d30 E c t f EGM t h EHV TOV EMT FD U 50	producing a flashover Dedicated Metallic Return (also MR) Equivalent front duration of an impulse (also t f ) Limiting corona gradient Equivalent front duration of an impulse (also t d30 ) Corona onset gradient Time to half value of an impulse shape Electrogeometric Model Temporary Overvoltages. Long duration transients caused by system faults, load Extra-High Voltage shedding, disconnections, resonance, etc. Electromagnetic Transient Frequency Dependent line model Overvoltage with 50% probability of producing a disruptive discharge in an air gap
	FFO U 50RP	Fast-Front Overvoltage Overvoltage with 50% probability of producing a disruptive discharge in a rod-
	H T	Height of the tower plane gap
	U b U U cw I IGBT UHV	Breakdown voltage Coordination withstand voltage Insulated Gate Bipolar Transistor Ultra-High Voltage
	I msf U m	Maximum shielding failure current that can bypass the protection of the shield Highest voltage for equipment
	U n	wires Nominal system voltage
	LCC U r	Line Commutated Converter Rated voltage of the surge arrester
	LIPL U rp	Lightning Impulse Protective Level Representative voltage or overvoltage
	LIWV Lightning Impulse Withstand Voltage U rw Required withstand voltage
	LPM U s	Leader Progression Model Highest system voltage (in AC, the maximum RMS phase to phase voltage under
	MMC Modular Multi-level Converter normal conditions; in DC, the maximum DC voltage under normal conditions)
	MR	Metallic Return (also DMR)
	N g	Ground flash density [flashes/km²/year]
	N L	Lightning incidence [flashes/100 km/year]
	OHL	Overhead Lines
	R c	Corona radius
	r c	Striking distance to the conductors in electrogeometric models
	r Nicolas Manduley	2020	Page xxviii

c Minimum lightning current amplitude producing a flashover across an insulator in case of shielding failure I f Minimum lightning current amplitude producing a back-flashover across an insulator in case of direct strike to the tower or shield wires g Striking distance to the ground in electrogeometric models SFFOR Shielding Failure Flashover Rate [flashes/100 km/year] SFO Slow-Front Overvoltage Contribution c Maximum continuous voltage that can be applied across a surge arrester. in IEEE standards, it is named Maximum Continuous Operating Voltage (MCOV). HVDC power transmission technologies are in constant growth and development worldwide.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

  Selection of dielectric strength of equipment in relation to the operating voltages and overvoltages which can appear on the system for which the equipment is intended and taking into account the service environment and the characteristics of the available preventing and protective devices"

	Chapter 1: State of the Art and Literature Review
	"
	Nicolas Manduley	2020	Page 10

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

	Chapter 1: State of the Art and Literature Review
	Nicolas Manduley	2020	Page 16

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

	Chapter 1: State of the Art and Literature Review
	Nicolas Manduley	2020	Page 19

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

	Chapter 1: State of the Art and Literature Review
	Nicolas Manduley	2020	Page 22

Table 1 .1 Comparative matrix on the fundamental differences between AC and DC regarding insulation coordination Page 28 Table 1.1 (continuation) Comparative matrix on the fundamental differences between AC and DC regarding insulation coordination Contribution to Insulation Coordination Studies for VSC-HVDC Systems

 1

	Chapter 1: State of the Art and Literature Review

.1. Main Differences between VSC-HVDC and LCC-HVDC

	Chapter 1: State of the Art and Literature Review
	4.3The fundamental differences between VSC and LCC transmission in HVDC result from two
	main factors: the commutation principle and the source type (CIGRE TB 269, 2005). On the
	commutation principle, LCC technologies use thyristors, which are closed by a gate signal, but
	require a zero-crossing to open. VSC technologies use transistors (typically IGBTs), which are
	switches with a controlled turn-on and turn-off capability that enables self-commutation. On
	the source type, LCC are a specific type of Current Source Converters (CSC) which stores the
	DC side energy in inductors, while Voltage Source Converters store the energy in capacitors.
	Nicolas Manduley	2020	Page 32

Table 1 .2. Log-normal parameters of I F Overall Distribution Shielding Failure Domain (I ≤ 20 kA) Back-flash Domain (I > 20 kA)

 1

	Subsequent
	Strokes

Table 1 .2 Median (M) and logarithmic standard deviation (β) for the overall distribution of the peak current of downward negative strokes, the shielding failure domain (below or equal to 20 kA), the back-flash domain (above 20 kA) and for subsequent strokes.

 1

-normal parameters of t f

		Shielding Failure Domain	Back-flash Domain	Subsequent
		(I F ≤ 20 kA)	(I F > 20 kA)	Strokes
	M	3.83 µs	3.83 µs	3.83 µs
	β	0.553	0.553	0.553

Table 1 .3 Median (M) and logarithmic standard deviation (β) for the log-normal representation of the front time t f of downward negative strokes. The same parameters are recommended for both ranges of first strokes (i.e. shielding failure and back-flash domains) and subsequent strokes.

 1

Table 1 .4 Median (M) and logarithmic standard deviation (β) for the log-normal representation of the maximum steepness S m of downward negative strokes.

 1

		Shielding Failure Domain	Back-flash Domain	Subsequent
		(I F ≤ 20 kA)	(I F > 20 kA)	Strokes
	M	24.3 kA/µs	24.3 kA/µs	39.9 kA/µs
	β	0.599	0.599	0.852

f

Contribution to Insulation Coordination Studies for VSC-HVDC Systems Chapter

  The derived relationships for the front time t f and maximum steepness S m are presented for first and subsequent strokes in Table1.5 and Table1.6, respectively.

	Parameter	S m |I F (I F ≤ 20 kA))	t f |I F ((I F ≤ 20 kA))	S m |I F (I F > 20 kA)	t f |I F (I F > 20 kA)
	M	12 I F 0.171	1.77 I F 0.188	6.5 I F 0.376	0.906 I F 0.411
	β	0.554	0.494	0.554	0.494

1: State of the Art and Literature Review Nicolas Manduley 2020 Page 43

convenient for lightning studies where different values of the peak current may be applied successively.

Table 1 .5 Derived statistics for the estimation of the maximum steepness S m and the front time t f as a function of the peak current I F (first strokes)

 1

	Parameter	S m |I F (subsequent strokes)	t f |I F (subsequent strokes)
	M	4.17 I F 0.9	0.24 I F 0.998
	β	0.706	0.706

Table 1 .6 Derived statistics for the estimation of the maximum steepness S m and the front time t f as a function of the peak current I F (subsequent strokes)

 1

Table 1 .7 Parameters for the electrogeometric model implementation from different authors

 1

	R. Love	10	0.65	1
	E.R. Whitehead	9.4	0.67	1
	Wagner et al.	14.2 0.42	1
	Suzuki et al.	3.3	0.78	1

Table 1 .8 Parameters for the simplified leader progression model implementation resulting from applying regressions over a certain range of values of current and conductor height from different authors.

 1

  Chapter 1: State of the Art and Literature Review

	L	is the equivalent inductance of the tower
	i(t)
	Nicolas Manduley	2020	Page 51

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

	Chapter 1: State of the Art and Literature Review
	Nicolas Manduley	2020	Page 56

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

  especially the modal delays), but when the model operates, it does completely in the phase domain instead of the modal domain (as the previous models). As a result, a much more accurate representation of transients is obtained for such configurations, in exchange of a significantly lower computational efficiency. This model will be thus reserved for cases where underground/submarine cables are considered.

	Chapter 2: Tools and Electromagnetic Modelling
	the model (Model	Characteristics	Applications
		 Parameters are calculated at a single
	Constant Parameters (CP)	frequency  Constant transformation matrix  Computationally efficient	Transmission tower sections
		 Tends to exaggerate transient phenomena
		 Parameters are calculated for a wide range of
	Frequency Dependent (FD)	frequencies  Constant transformation matrix  Less computationally efficient than CP, but	Overhead lines (single and multiple circuits)
		significantly more accurate
		 Directly formulated in the time domain
	Wideband (WB)	 Transformation matrix is frequency dependent  Less computationally efficient than FD, but avoids errors related to applications strongly	Underground or submarine cables
		frequency dependent
	Nicolas Manduley	2020	Page 64

Table 2 .1 Summary of the different transmission line models, their main characteristics and respective applications considered in this research.

 2

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

	Chapter 2: Tools and Electromagnetic Modelling
	the literature, like the IEEE model (IEEE Working Group 3.4.11, 1992), Pinceti model (Pinceti
	& Giannettoni, 1999), Fernandez model (Fernandez & Diaz, 2001), CIGRE model, among others
	(Martinez
	Nicolas Manduley	2020	Page 67

Table 2 .2 MMC model setup and parameters for EMTP simulations

 2

	Parameter	Value
	Rated power	1000 MVA
	Primary AC voltage	400 kV (p-p rms)
	Secondary AC voltage	320 kV (p-p rms)
	DC pole to pole voltage	640 kV
	Transformer reactance	0.18 p.u.
	Arm reactor	0.15 p.u.
	Capacitor energy	40 kJ/MVA (per submodule)
	# of submodules per arm	400
	Cable length	100 km (WB model)
	Overcurrent protection	2 p.u.
	MMC blocking delay	40 µs (EMTP native value)
	AC breaker opening time	40 ms

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

	Chapter 3: Slow-Front Overvoltages and Fault Analysis
	Nicolas Manduley	2020	Page 76

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

  DC current plus/minus (for the upper and lower arm reactor, respectively) one half of the AC current coming from the converter transformer:

	Chapter 3: Slow-Front Overvoltages and Fault Analysis
	𝑖 𝐵𝑅 (𝑢𝑝,𝑙𝑜𝑤) =	𝑖 𝐷𝐶 3	±	2 𝑖 𝐴𝐶	(3-2)
	Nicolas Manduley	2020		Page 79

Table 3 .1 Kirchhoff's voltage equations from the fundamental MMC-HVDC scheme with the arm reactor on the AC side

 3 𝑢𝑝 -𝑉 4 𝑙𝑜𝑤 + 𝑉 𝐵𝑅 𝑢𝑝 + 𝑉 𝐵𝑅 𝑙𝑜𝑤 -𝑉 𝑆𝑀 𝑢𝑝 -𝑉 𝑆𝑀 𝑙𝑜𝑤 = 0 𝑢𝑝 -𝑉 4 𝑙𝑜𝑤 + 𝑉 𝐵𝑅 𝑢𝑝 + 𝑉 𝐵𝑅 𝑙𝑜𝑤 -𝑉 𝑆𝑀 𝑢𝑝 -𝑉 𝑆𝑀 𝑙𝑜𝑤 = 0

	Loop		Equation
	1		𝑉 2 -𝑉 𝐵𝑅 𝑢𝑝 -𝑉 3 𝑢𝑝 = 0
	2		𝑉 2 + 𝑉 𝐵𝑅 𝑙𝑜𝑤 -𝑉 3 𝑙𝑜𝑤 = 0
	3		𝑉 2 + 𝑉 𝑆𝑀 𝑢𝑝 -𝑉 𝐵𝑅 𝑢𝑝 -𝑉 4 𝑢𝑝 = 0
	4		𝑉 2 -𝑉 𝑆𝑀 𝑙𝑜𝑤 + 𝑉 𝐵𝑅 𝑙𝑜𝑤 -𝑉 4 𝑙𝑜𝑤 = 0
	5		𝑉 3 𝑢𝑝 + 𝑉 𝑆𝑀 𝑢𝑝 -𝑉 4 𝑢𝑝 = 0
	6		𝑉 3 𝑙𝑜𝑤 -𝑉 𝑆𝑀 𝑙𝑜𝑤 -𝑉 4 𝑙𝑜𝑤 = 0
	7 𝑉 4 Loop	Equation
	1		𝑉 2 + 𝑉 𝑆𝑀 𝑢𝑝 -𝑉 3 𝑢𝑝 = 0
	2		𝑉 2 -𝑉 𝑆𝑀 𝑙𝑜𝑤 -𝑉 3 𝑙𝑜𝑤 = 0
	3		𝑉 2 + 𝑉 𝑆𝑀 𝑢𝑝 -𝑉 𝐵𝑅 𝑢𝑝 -𝑉 4 𝑢𝑝 = 0
	4		𝑉 2 -𝑉 𝑆𝑀 𝑙𝑜𝑤 + 𝑉 𝐵𝑅 𝑙𝑜𝑤 -𝑉 4 𝑙𝑜𝑤 = 0
	5		𝑉 3 𝑢𝑝 -𝑉 𝐵𝑅 𝑢𝑝 -𝑉 4 𝑢𝑝 = 0
	6		𝑉 3 𝑙𝑜𝑤 + 𝑉 𝐵𝑅 𝑙𝑜𝑤 -𝑉 4 𝑙𝑜𝑤 = 0
	7	𝑉 4

Table 3 .2 Kirchhoff's voltage equations from the fundamental MMC-HVDC scheme with the arm reactor on the DC side Contribution to Insulation Coordination Studies for VSC-HVDC Systems

 3 Differences between the configurations are given by their respective location of the zero voltage reference.iiConsidering that the ground voltage is zero, the voltage V3low is equal to the voltage across the arm reactor.

	Chapter 3: Slow-Front Overvoltages and Fault Analysis

Table 3 .3 Analytical expressions of the service voltages of the different components of the MMC-HVDC station in monopolar and bipolar configurations, and with the arm reactor on the AC and DC sides of the converter. The comparison assumes identical DC outputs.

 3

7 Cable geometry and parameters used to build the EMTP model for the overvoltage studies

		Cable Parameters
	D cable [mm]	139.2	D core [mm]	64
	ρ core [Ω⋅m]	1.84e-8 ρ sheath [Ω⋅m] 2.8e-8
	ε r1	2.3	ε r2	2.3
	tan ϕ 1	0.0004	tan ϕ 1	0.001
	r in [mm]	52	r out [mm]	55.1
	Figure 3.

Chapter 3: Slow-Front Overvoltages and Fault Analysis Nicolas Manduley 2020 Page 86

Table 3 .5 Absolute value (in p.

 3

		82	1.08	1.08	1.00	1.00	1.88	0.07
	Bipole	0.91	1.08	0.07	1.00	0	0.96	0.07

.u.) Fault TOV (p.u.) Fault SFO (p.u.) Fault TOV (p.u.) Fault

	Chapter 3: Slow-Front Overvoltages and Fault Analysis
			Monopole			Bipole
	SFO (pV 2 1.49	L	1.59	J	-	-	-	-
	V 3up	1.49	L	1.57	G	1.66	G	1.10	G
	V 3low	2.33	J	2.02	J	1.00	J	0.21	G
	V 4up	-	-	-	-	-	-	-	-
	V 4low	-	-	1.96	K	-	-	1.10	G
	V SM	2.15	G	2.13	G	1.11	G	1.08	G
	V BR	1.38	K	0.38	J	1.00	J	0.36	J
	Nicolas Manduley			2020				Page 88

Table 3 .6 Maximum slow-front overvoltage (SFO) and temporary overvoltage (TOV) levels at each location of the monopolar and bipolar MMC-HVDC stations with the arm reactor on the DC side. The values are expressed in p.u. with 1 p.u. equal to 320 kV (i.e. the nominal DC voltage).

 3

Table 3 .9 Maximum slow-front overvoltage (SFO) and temporary overvoltage (TOV) levels at each location of the symmetric monopolar MMC-HVDC station with the arm reactor on the AC side. The values are expressed in p.u. with 1 p.u. equal to 320 kV (i.e. the nominal DC voltage).

 3

	Chapter 3: Slow-Front Overvoltages and Fault Analysis

Table 3 .11 Ratings of the surge arresters used in the study

 3 .11 including their respective equivalent RMS value of U c and U r .

	Arrester	A1	A2	A3	C
	U c (RMS)	288 kV	231 kV	245 kV	272 kV
	U r (RMS)	360 kV	288 kV	306 kV	340 kV

  Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance

	Contribution to Insulation Coordination Studies for VSC-HVDC Systems
	Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning
	Performance
	Nicolas Manduley	2020	Page 115

  Table 4.1) are almost entirely constituted by double flashovers is explained through the intrinsic symmetry of the model

	Contribution to Insulation Coordination Studies for VSC-HVDC Systems
	Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning
	Performance
	Nicolas Manduley	2020	Page 127

Table 4 .2 Summary of the surge arrester parameters used in this chapter

 4

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

  By this way, it is possible to study the best and worst case scenarios of strikes on towers adjacent to a protected tower.

	Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning
	Performance
	DC poles.
	Nicolas Manduley	2020	Page 134

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

	Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning
	Performance
	base SFFOR can be reduced by 30 to 60% depending on the surge arrester configuration
	considered.
	Nicolas Manduley	2020	Page 136

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

	Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning
	Performance
	Nicolas Manduley	2020	Page 139

Contribution to Insulation Coordination Studies for VSC-HVDC Systems Chapter

  4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning Performance

	Nicolas Manduley	2020	Page 147

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

	Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning
	Performance
	energy withstand of about 4.48 kJ/kV. Line discharge class 2 arresters typically have an energy
	absorption capability of roughly 5 kJ/kV (ABB
	Nicolas Manduley	2020	Page 154

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

	Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning
	Performance
	Nicolas Manduley	2020	Page 155

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

	Chapter 4: Fast-Front Overvoltage Analysis and Improvement of the Overhead Line Lightning
	Performance
	Nicolas Manduley	2020	Page 157

Nicolas Manduley 2020

Table 1.1 (continuation) Comparative matrix on the fundamental differences between AC and DC regarding insulation coordination

Also called bridge arm reactor, from which the notation V BR was chosen

In fact, the resistance of the channel is a function of the current flowing through the channel. However, for most practical applications it is possible to represent it as a constant resistance, as explained and recommended in CIGRE Technical Brochure 549.

Typically longer than one power frequency period, and up to one hour (3600 s)

In case of a bipolar configuration, only the positive half is represented in the scheme, with the grounding located at point 4 low .

Coupling between other parts of the tower structure and the conductors may exist. However, such phenomena require other kind of studies involving a detailed electromagnetic modelling of which EMTP is not capable. Those effects are thus not considered in the present research.

For the purposes of this analysis, the voltage drop across the diodes and thyristors of the MMC in blocked state is neglected.

Acknowledgements Nicolas Manduley 2020 Acknowledgements Nicolas Manduley 2020 Page xi Acknowledgements Acknowledgements Nicolas Manduley 2020 Appendices Nicolas Manduley 2020

, kindness and invaluable advice. To my SuperGrid Institute supervisor, Sellé Touré, for his expertise and his daily encouragement since my first day at the institute. Finally yet importantly, a very special mention to Stephan Pack, for his precious guidance and support through the collaboration between the SuperGrid Institute and the TU Graz.

China Electric Power Research Institute. (2017). UHV Transmission Technology. China EPRI. CIGRE TB 158, W. G. 33. 04. 0. (2000). CIGRE Technical Brochure 158: Polluted Insulators: A Review of Current Knowledge. CIGRE. CIGRE TB 186, W. G. 14. 2. (2001). CIGRE Technical Brochure 186: Economic assessmment of HVDC links. CIGRE. CIGRE TB 269, W. G. B. 3. (2005). CIGRE Technical Brochure 269: VSC Transmission. CIGRE. CIGRE TB 388, J. W. G. B. 1. (2009). CIGRE Technical Brochure 388: Impacts of HVDC lines on the economics of HVDC projects. CIGRE.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

References Nicolas Manduley 2020 Page 166 CIGRE TB 440, W. G. C. 30. (2010). CIGRE Technical Brochure 440: Use of Surge Arresters for Lightning Protection of Transmission Lines. CIGRE. CIGRE TB 447, W. G. B. 4. (2011). CIGRE Technical Brochure 447: Component Testing of VSC System for HVDC Applications. CIGRE. CIGRE TB 518, W. G. C. 30. (2012). CIGRE Technical Brochure 518: Outdoor Insulation in Polluted Conditions: Guidelines for Selection and Dimensioning -Part 2: The DC Case. CIGRE. CIGRE TB 549, W. G. C. 40. (2013). CIGRE Technical Brochure 549: Lightning Parameters for Engineering Applications. CIGRE. CIGRE TB 583, W. G. B. 4. (2014). CIGRE Technical Brochure 583: Guide to the Conversion of Existing AC Lines to DC Operation. CIGRE. CIGRE TB 63, W. G. 33. 0. (1991). CIGRE Technical Brochure 063: Guide to Procedures for Estimating the Lightning Performance of Transmission Lines. CIGRE. CIGRE TB 704, W. G. C. 2. (2017). CIGRE Technical Brochure 704: Evaluation of Lightning Shielding Analysis Methods for EHV and UHV DC and AC Transmission Lines. CIGRE. CIGRE TB 72, W. G. 33. 0. (1992). CIGRE Technical Brochure 072: Guidelines for the Evaluation of the Dielectric Strength of External Insulation. CIGRE. CIGRE TB 781, W. G. C. 3. (2019). CIGRE Technical Brochure 781: Impact of soil-parameter frequency dependence on the response of grounding electrodes and on the lightning performance of electrical systems. CIGRE. Cooray, G. V. (2014). The lightning flash. Iet. Contribution to Insulation Coordination Studies for VSC-HVDC Systems References Nicolas Manduley 2020 Page 167 Cortina, R., Marrone, G., Pigini, A., Thione, L., Petrusch, W., & Verma, M. P. (1984). Study of the Dielectric Strength of External Insulation of HVDC Systems and Application to Design and Testing. International Conference on Large High Voltage Electric Systems. Datsios, Z. G., Mikropoulos, P. N., & Tsovilis, T. E. (2019). Effects of Lightning Channel Equivalent Impedance on Lightning Performance of Overhead Transmission Lines. IEEE Transactions on Electromagnetic Compatibility, 61(3), 623-630. De Andrade, V., & Sorrentino, E. (2010). Typical expected values of the fault resistance in power systems. 2010 IEEE/PES Transmission and Distribution Conference and Exposition: Latin America (T&D-LA) (pp. 602-609). IEEE. Dennetière, S., Nguefeu, S., Saad, H., & Mahseredjian, J. (2013). Modeling of modular multilevel converters for the France-Spain link. Star, 2(3), 4. Dong, M., Yuan, Z., Li, T., Zhao, X., Zhang, J., & He, J. (2013). Protection of±500 kV HVDC Double-circuit Converter Station from Lightning Induced Overvoltage. 高电压技术, 39(8). Du, S., Dekka, A., Wu, B., & Zargari, N. (2017). Modular multilevel converters: analysis, control, and applications. John Wiley & Sons. EPRI Transmission Line Reference Book, 345 kV and Above. (1982). (2nd ed.). EPRI. Fernandez, F., & Diaz, R. (2001). Metal oxide surge arrester model for fast transient simulations. The Int. Conf. on Power System Transients IPAT (Vol. 1). Citeseer. Grcev, L. (2009). Modeling of grounding electrodes under lightning currents. IEEE Transactions on Electromagnetic Compatibility, 51(3), 559-571. Contribution to Insulation Coordination Studies for VSC-HVDC Systems References Nicolas Manduley 2020 Page 168 Grebovic, S., & Oprasic, N. (2018). Influence of Lightning Channel Impedance and Nonuniform Tower Footing Resistance Distribution on Line Surge Arrester Energy Duty. 2018 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe) (pp. 1-5). Gu, S., Wang, J., Wan, S., Cao, W., & He, J. (2018). Comparison and Analysis on Key Performance of EHV/UHV DC Transmission Line Surge Arresters. 2018 34th International Conference on Lightning Protection (ICLP) (pp. 1-6). IEEE. Gu, Y. L., Huang, X. M., Qiu, P., Hua, W., Zhang, Z. R., & Xu, Z. (2013). Study of Overvoltage Protection and Insulation Coordination for MMC based HVDC. Applied Mechanics and Materials (Vol. 347, pp. 1812-1817). Trans Tech Publ. Hagenguth, J., Rohlfs, A., & Degnan, W. (1952). Sixty-Cycle and Impulse Sparkover of Large Gap Spacings [includes discussion]. Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems, 71(1), 455-460. Hinrichsen, V. (2012). Metal-Oxide Surge Arresters in High-Voltage Power Systems Fundamentals (3rd ed.). SIEMENS. Hinrichsen, V., Reinhard, M., & Richter, B. (2007). Energy handling capability of high-voltage metal-oxide surge arresters part 1: a critical review of the standards. Cigré International Colloquium-September 12th and 13th. Hu, B., Xie, K., & Tai, H.-M. (2017). Reliability Evaluation and Weak Component Identification of±500kV HVDC Transmission Systems with Double-Circuit Lines on the Same Tower. IEEE Transactions on Power Delivery. Hutzler, B. (1994). Evolution of Insulation Coordination Standards. Conference presented at the homage to Gianguido Carrara at the Centro Elettrotecnico Sperimentale Italiano (CESI). Contribution to Insulation Coordination Studies for VSC-HVDC Systems References Nicolas Manduley 2020 Page 169 IEC 60052 Voltage measurement by means of standard air gaps (2002). International Electrotechnical Commission (IEC). IEC 60071-1 Insulation Coordination Part 1: Definitions, principles and rules (2011). International Electrotechnical Commission (IEC). IEC 60071-2 Insulation Coordination Part 2: Application Guide (2018). International Electrotechnical Commission (IEC). IEC 60071-4 Insulation Coordination Part 4: Computational guide to insulation co-ordination and modelling of electrical network (2004). International Electrotechnical Commission (IEC). IEC 60071-5 Insulation Coordination Part 5: Procedures for HVDC converter stations (2014). International Electrotechnical Commission (IEC). IEC 60099-4 Surge arresters -Part 4: Metal-oxide surge arresters without gaps for a.c. systems (2014). International Electrotechnical Commission (IEC). IEC 60099-5 Surge arresters -Part 5: Selection and application recommendations (2000). International Electrotechnical Commission (IEC). IEC 60099-8 Surge arresters -Part 8: Metal-oxide surge arresters with external series gap (EGLA) for overhead transmission and distribution lines of a.c. systems above 1 kV (2017). International Electrotechnical Commission (IEC). IEC 60099-9 Surge arresters -Part 9: Metal-oxide surge arresters without gaps for HVDC converter stations (2014). International Electrotechnical Commission (IEC). IEEE Std. 1243 Guide for improving the lightning performance of transmission lines (1997). New York: IEEE Press. Contribution to Insulation Coordination Studies for VSC-HVDC Systems References Nicolas Manduley 2020 Page 170 IEEE Std. 998 Guide for Direct Lightning Stroke Shielding of Substations (2012). New York: IEEE Press. IEEE Working Group 3.4.11. (1992). Modeling of metal oxide surge arresters. IEEE Transactions on Power Delivery, 7(1), 302-309. Kawai, M., & Azuma, H. (1965). Design and performance of unbalanced insulation in doublecircuit transmission lines. IEEE Transactions on Power Apparatus and Systems, 84(9), 839-846. Kouro, S., Malinowski, M., Gopakumar, K., Pou, J., Franquelo, L. G., Wu, B., Rodriguez, J., et al. (2010). Recent advances and industrial applications of multilevel converters. IEEE Transactions on industrial electronics, 57(8), 2553-2580. Li, J., Ren, H., Xu, L., Long, C., Yang, Q., & Xiang, Y. (2018). Research on Lightning Performance of Back-flashover of UHV Direct Current Double-circuit Mixed-voltage Transmission Lines on the Same Tower. 2018 10th International Conference on Communications, Circuits and Systems (ICCCAS) (pp. 50-54). IEEE. Li, X., Zhou, P., He, H., & Wang, L. (2017). Study of overvoltage and insulation coordination of UHV DC transmission line. Electrical Materials and Power Equipment (ICEMPE), 2017 1st International Conference on (pp. 354-358). IEEE. doi:10.1109/icempe.2017.7982102 Li, Z., Yu, Z., Wang, X., & He, J. (2012). A design of unbalanced insulation to improve the lightning performance of multi-circuit transmission lines. 2012 International Conference on Lightning Protection (ICLP) (pp. 1-4). IEEE. Lin, J., & Marti, J. R. (1990). Implementation of the CDA procedure in the EMTP. IEEE Transactions on Power Systems, 5(2), 394-402. Contribution to Insulation Coordination Studies for VSC-HVDC Systems References Nicolas Manduley 2020 Page 171 Liu, J., Zou, J., Tian, J., & Yuan, J. (2009). Analysis of electric field, ion flow density, and corona loss of same-tower double-circuit HVDC lines using improved FEM. IEEE Transactions on Power Delivery, 24(1), 482-483. Love, E. R. (1973). Improvements in lightning stroke modeling and applications to design of EHV and UHV transmission lines. University of Colorado. Lundquist, J., & Lilliecrona, J. (2012). Novel design for parallel VSC HVDC links on common overhead line towers. CIGRE Colloquium, San Francisco, USA. Ma, Y., Li, H., Wang, G., & Wu, J. (2018). Fault Analysis and Traveling-Wave-Based Protection Scheme for Double-Circuit LCC-HVDC Transmission Lines With Shared Towers. IEEE Transactions on Power Delivery, 33(3), 1479-1488. Mahseredjian, J., Dennetière, S., Dubé, L., Khodabakhchian, B., & Gérin-Lajoie, L. (2007). On a new approach for the simulation of transients in power systems. Electric power systems research, 77(11), 1514-1520. Manduley, N. (2018). Monopole vs Bipole without Metallic Return Comparison for Insulation Coordination Studies (SGI Internal Technical Report). SuperGrid Institute. Manduley, N., Pack, S., Touré, S., Xémard, A., Raison, B., & Poullain, S. (2019). Use of Unbalanced Insulation for the Limitation of Double-Pole Lightning Flashovers in Double Circuit HVDC Overhead Lines. International Colloquium on Lightning and Power Systems (ICLPS 2019). Manduley, N., Touré, S., Xémard, A., Raison, B., & Poullain, S. (2019). Effect of the Surge Arrester Configuration in MMC-HVDC Systems under DC and Converter Fault Conditions. International Conference on Power System Transients (IPST 2019). Contribution to Insulation Coordination Studies for VSC-HVDC Systems References Nicolas Manduley 2020 Page 172 Marquardt, R. (2001). Stromrichterschaltungen mit verteilten energiespeichern. German Patent DE10103031A1, 24. Martinez-Velasco, J. A. (2010). Power system transients: parameter determination. CRC press. Martinez-Velasco, J. A. (2015). Transient analysis of power systems: solution techniques, tools and applications. John Wiley & Sons. Neumann, C., Wasserrab, A., Balzer, G., Rusek, B., Steevens, S., & Kleinekorte, K. (2016). Aspects of insulation coordination for DC links using hybrid lines. CIGRE-IEC Colloquium. Orville, R. E., Huffines, G. R., Burrows, W. R., & Cummins, K. L. (2011). The North American lightning detection network (NALDN)-Analysis of flash data: 2001-09. Monthly Weather Review, 139(5), 1305-1322. Paladian, F., Bonnet, P., Lallechere, S., Xemard, A., & Miry, C. (2014). On the numerical analysis of lightning effect on power installations. International Colloquium on Lightning and Power Systems, Lyon, France. Peek, F. W. (1920). Dielectric phenomena in high voltage engineering (First.). McGraw-Hill Book Company, Incorporated. Peek, F. W. (1929). Dielectric phenomena in high voltage engineering (Third.). McGraw-Hill Book Company, Incorporated. Peralta, J., Saad, H., Dennetière, S., Mahseredjian, J., & Nguefeu, S. (2012). Detailed and averaged models for a 401-level MMC-HVDC system. IEEE Transactions on Power Delivery, 27(3), 1501. Pinceti, P., & Giannettoni, M. (1999). A simplified model for zinc oxide surge arresters. IEEE transactions on power delivery, 14(2), 393-398.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

Contribution to Insulation Coordination Studies for VSC-HVDC Systems Appendices

Appendix A. Estimation of the Surge Impedance under Corona

A.1 Surge Impedance under Corona

When a high voltage impulse is applied on a conductor, electron avalanches can form in the vicinities of the conductor which may result in corona. As a result, the equivalent radius of the conductor may be increased, therefore modifying the equivalent impedance of the conductor (EPRI Transmission Line Reference Book, 345 kV and Above, 1982).

The surge impedance under corona Z s is thus given by:

Where h p is the height of the conductor, r cond is the radius of the conductor and R c is the corona radius.

The corona radius can be neglected when bundled conductors are used, because the increase in the equivalent radius due to corona may be insignificant compared to the bundle equivalent radius (EPRI Transmission Line Reference Book, 345 kV and Above, 1982). If no bundled conductors are used, or if the effects of corona are to be taken into account, the estimation of the corona radius R c is discussed in the next section.

A.2 Corona Radius

The expression for the corona radius can be derived from Gauss' Law for a coaxial cable (EPRI Transmission Line Reference Book, 345 kV and Above, 1982), and is given by the following expression:

Where h avg is the average height of the conductor, V the applied voltage on the conductor and E 0 the limiting corona gradient.

However, it can be noted that the expression shown in equation [A-2] has no straightforward analytical solution for R c . A sensitivity analysis has been conducted to determine the impact of the height of the conductor (h) and the applied voltage (V) on the value of R c and on the value of Z s . For these purposes, equation [A-2] has been solved for R c using the Newton-Raphson algorithm for different values of h (with h avg calculated for plain areas when needed (China Electric Power Research Institute, 2017)) and V.

Before presenting the results of this study, the parameters V and E 0 will be discussed in the following sections.

Contribution to Insulation Coordination Studies for VSC-HVDC Systems Appendices

Nicolas Manduley 2020 Page 185 and 0.6 for DC, the values of E c range between 2100-2300 kV/m for all AC, positive DC and negative DC polarities.

 For values of m under 0.45, the value of 1500 kV/m starts being higher than the recommended 0.95 E c . This is more likely to happen for the positive pole under certain pollution conditions. For these cases, it may be necessary to consider a lower value of E 0 .

 For all cases, the obtained values for E c are strongly influenced by the relative air density (δ) and the irregularity factor (m).

Consequently, it is concluded that the value E 0 = 1500 kV/m is adequate for DC applications with irregularity factors (m) as low as 0.5-0.6, as long as standard environmental conditions (25 °C and 760 mmHg) are assumed. These values correspond to DC conductors in a region with moderate to severe pollution conditions. For high temperatures and/or high altitudes, lower values might be necessary.

Therefore, for the purposes of this work, the value E 0 = 1500 kV/m is considered as a good approximation for the studies regarding the calculation of the corona radius and surge impedance under corona, assuming normal environmental conditions and moderate pollution conditions.

Appendix C. Effect of the Surge Arrester Configuration on the Overvoltage Analysis: Full Results

This appendix presents the complete overvoltages for each location and each fault considered in the studies presented in §4.3 and §4.4 of Chapter 3. In addition, the maximum current and energy levels of the arresters are presented.

C.1

No Arresters (Configuration NS)

1.15 0.00 1.10 0.00 1.13 0.00 0.00 0.00 0.00 0.00

0.00 1.74 1.98 1.58 2.16 1.56 0.00 0.00 0.00 0.00

1.97 1.68 2.23 1.58 2.65 1.56 1.81 0.00 1.96 0.00

1.96 1.68 2.25 2.16 2.21 2.16 0.00 0.00 0.00 0.00

V BR

0.43 0.27 0.80 0.00 1.02 0.00 0.98 0.20 1.10 0.18

V SM

2.21 2.17 0.00 2.14 2.19 2.14 0.00 0.00 0.00 0.00 Tbl. C-1 For the configuration without surge arresters: slow-front and temporary overvoltage levels (SFO and TOV, respectively) for each location during the different fault scenarios considered. The values are given in p.u. (with 1 p.u. = 320 kV). A value of zero indicates that no disturbances were measured to be above the normal operating voltage.

C.2

Configuration with Arresters A1-A2

1.15 0.00 1.11 0.00 1.13 0.00 0.00 0.00 0.00 0.00 V 2 0.00 1.72 1.87 1.52 1.88 1.48 0.00 0.00 0.00 0.00

1.94 1.68 2.17 1.50 2.65 1.48 1.81 0.00 1.96 0.00 V 4

1.95 1.67 2.18 2.09 2.13 2.08 0.00 0.00 0.00 0.00

V BR

0.43 0.27 1.00 0.00 1.19 0.00 0.98 0.20 1.10 0.18

V SM

2.21 2.17 0.00 2.09 2.19 2.11 0.00 0.00 0.00 0.00 Tbl. C-2 For the configuration with arresters A1 and A2: slow-front and temporary overvoltage levels (SFO and TOV, respectively) for each location during the different fault scenarios considered. The values are given in p.u. (with 1 p.u. = 320 kV). A value of zero indicates that no disturbances were measured to be above the normal operating voltage.

Appendix D. Overvoltage Analysis: Qualitative Approach

The studies presented in chapter Chapter 3 address an approach to insulation coordination of MMC-HVDC stations based mainly on quantitative analysis through simulations. It would be of great interest to have also a qualitative approach that allows extracting essential information of the system without the need of performing several detailed simulations.

It is important to note that any analysis involving the solution of a system of differential equations of five or more unknowns is most likely to involve numerical methods for its solution rather than a fully analytical solution. This is due to the Abel-Ruffini theorem, which states that there is no solution in radicals to general polynomials of order five or higher [START_REF] Rosen | Niels Hendrik Abel and equations of the fifth degree[END_REF]. Since many methods for the solution of high-order differential equations involve their conversion to algebraic polynomials through the Laplace transform, the Abel-Ruffini theorem represents an important limitation regarding the possibility of obtaining general analytical solutions of a system with five or more unknowns.

In this context, a simplified qualitative approach has been investigated to explore the depth of the knowledge that is possible to obtain from a given architecture about its behaviour, and is explained below.

D.1 Hypotheses and Assumptions

The presented analysis involves the use of Kirchhoff's loop equations (see Table 3.1 and Table 3.2) and a series of hypotheses and simplifications allowing to make a rough estimation of the behaviour of a system during the first instants of transient events.

The main hypotheses considered for this analysis are listed below:

 MMC submodules can be approximated as a capacitor (see Chapter 2, §3.3). Therefore, since its voltage cannot change instantly, it can be considered constant during the first instants after a fault or another event.

 In case of underground or submarine cables, due to their high stray capacitance, it is also assumed that the voltage does not vary instantly, and can be considered constant after a fault (except at the location of the fault, if it occurs directly on the cable).

 Current variations are limited by the inductances present in the considered loop.

 When the MMC is blocked (i.e. the series capacitors are simultaneously disconnected from the circuit), its voltage drops to zero instantly 10 .

 When a specific point is connected to the ground, its voltage drops to zero instantly.

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Nicolas Manduley 2020 Page 192

 All components present in the system are assumed to have a linear behaviour.

These hypotheses allow making a simplified formulation of the behaviour of the system during the first instants of transient phenomena, as it is described in the next section.

D.2 Method Description

Assuming linear behaviour, the value of a state variable x shortly after a fault is given by its initial state x 0 plus its variation Δx during the first instants:

If, as stated previously, all the components present in the system are assumed to have a linear behaviour, the same substitution can be done for all the variables. For instance, consider an equation in the form of:

Shortly after a fault, equation [D-2] can be written as:

But since the sum of the x 0 , y 0 and z 0 elements yields exactly equation [D-2] under the initial conditions, and therefore their sum is zero. The resulting equation, from now on called variation equation, is then written as:

The system can be thus analysed through the variation equations during the first instants after a transient by establishing which parameters can change instantly (i.e. for which Δx ≠ 0) and which cannot (i.e. for which Δx = 0). This is done through the hypotheses stated in the previous section, by establishing which components present an inductive or capacitive behaviour.

Consider the general equations for a generic MMC-HVDC station with the arm reactor on the DC side as given in Table 3.2 (see also Figure 3.2 for the fundamental scheme). By performing the procedure described above on such equations, the respective variation equations can be obtained for the considered configuration. The resulting equations are shown in Tbl. D-1.

Loop Variation Equations

Tbl. D-1 General variation equations for configurations based on the fundamental scheme of MMC-HVDC stations with the arm reactor on the DC side

Contribution to Insulation Coordination Studies for VSC-HVDC Systems Appendices

Contribution to Insulation Coordination Studies for VSC-HVDC Systems Appendices

Nicolas Manduley 2020 Page 199

Appendix E. Algorithm for the Iterative Specification of Surge Arresters

As discussed in previous chapters, insulation coordination is an iterative process. The parameters of the surge arresters depend not only on the specific voltages and overvoltages of the location or component protected directly by the arrester, but also on the specifications of other arresters present, the complex interactions between them and with the system (Manduley, Touré, et al., 2019), as also discussed in Chapter 3 of this dissertation.

In this appendix, an algorithm is proposed for the specification of the parameters of the surge arresters. It consists of an iterative process involving electromagnetic transient simulations of faults, switching operations and other phenomena leading to slow-front and temporary overvoltages. Throughout the process, the specifications of the surge arresters are adjusted after each iteration by considering:

 The energy absorption level of each arrester  The maximum overvoltage levels for each location Depending on the results and the requirements established for the design, the surge arrester specifications are adapted in terms of their protective level and the number of parallel columns until the stopping criteria are met.

E.1 Fundamental Description

The flowchart of the proposed algorithm is illustrated in Fig. E-1.

First, the input values are entered by the user, which include the maximum voltage and overvoltage levels at each location without surge arresters, the arrangement of surge arresters desired (based on the fundamental schemes from Figure 3.1 and Figure 3.2) and the energy absorption capability and maximum number of parallel columns allowed for each one. The user may also provide a particular V-I characteristic to be used for each location. For detailed information about the inputs, consult Tbl. E-1.

Next, the provided information is used to configure the base case that will be used for the EMT simulations. Then, successive iterations are conducted and evaluated in terms of the energy absorbed by the surge arresters and the overvoltage levels obtained with each configuration. The arrester specifications are modified according to the obtained results and the next iteration is prepared.

Finally, the process is repeated until the stopping criteria are met.

The details of the processes that take place at each step of the algorithm are discussed in the following sections. U max a) Specified by user b) Calculated analytically from the nominal values (see Table 3.3) Tbl. E-1 Input required for the initialisation of the iterative procedure through the proposed algorithm

Contribution to Insulation Coordination Studies for VSC-HVDC Systems

E.3 Initial Design and Parameters

The initial specifications of the surge arresters are defined according to the minimum protective levels possible. This is done by setting the continuous operating voltage of the arrester (U c ) slightly above the maximum voltage level under normal conditions (U max ). By convention, a marge of 5% may be used:

Once the initial specification for each surge arrester is defined as shown in equation [E-3], the SIPL will be used as the main reference for the characterisation of the surge arresters. Therefore, through the known ratio between the SIPL and the U c of each arrester, the value of SIPL can be estimated as shown in equation