Daniel Gómez

Piotr Dworakowski

Juan D Páez

Oriol Gomis-Bellmunt

Marc Cheah-Mane

Florent Morel

Jose Maneiro

Requirements for interconnection of HVDC links with DC-DC converters

Keywords: HVDC offshore grid, dc-dc converter, HVDC transmission, Modular Multilevel Converter (MMC), Line Commutated converter (LCC). I

The number of high voltage direct current (HVDC) links continue to increase over the years, most of them, for offshore applications or bulk power transmission over long distances. The present paper evaluates the possible development of a direct current (dc) grid in Europe given the present, and future, HVDC links. Eight potential cases for the interconnection between close links are suggested as starting scenario for a multiterminal network. The need of a dc-dc converter and its special requirements are evaluated in function of suggested interconnections. As an example, a case study is chosen to evaluate the behavior of an interconnection between line commutated converter (LCC) and voltage source converter (VSC) link using a front-to-front (F2F) isolated converter.

INTRODUCTION

High voltage direct current (HVDC) links have been taking place in the electrical transmission system for bulk power transmission over long distances, due to the absence of reactive power consumption on the line [START_REF] Wang | The advantages and disadvantages of using HVDC to interconnect AC networks[END_REF], low electrical losses and lower environmental impact related with the right of way (ROW) [START_REF] Oni | A review of LCC-HVDC and VSC-HVDC technologies and applications[END_REF]. Thanks to these benefits, a HVDC link can reduce the cost of a long line, compared to the high voltage alternate current (HVAC) link, after the called "break-even-distance".

The main use of HVDC links, in Europe, is for offshore applications, where the benefits of HVDC cables overcome those of the HVAC. This can be evidenced in Fig. 1 and 2 [START_REF]SGV world map[END_REF] with the number of HVDC lines installed and projected on the North Sea. The development of the HVDC technologies has opened the discussion for possible dc grid applications [START_REF]HVDC Grid Feasibility Study[END_REF], [START_REF] Jovcic | Feasibility of DC transmission networks[END_REF]. Particular challenges have been identified such as the interoperability, the system stability, the resilience, the fault management and the power flow control [START_REF] Barker | Requirements of DC-DC Converters to facilitate large DC Grids[END_REF]. Dc-dc converters are the elements that can help to solve the challenges increasing the controllability of the dc grid [START_REF] Adam | Review of DC-DC converters for multi-terminal HVDC transmission networks[END_REF].

For the development of future dc grids, two possible options may arise, either it is planned in advance, or it uses the already installed equipment to reduce the costs (case studied in this paper). The main inconvenient with this last scenario is the incapacity to interconnect two HVDC links of different characteristics without the use of an intermediary component (dc-dc converter) as the links have not been designed for multiterminal operation. The links may have different voltage levels, power rating, technology used, grounding, etc. Therefore, a dc-dc converter is needed for the interconnection of different already installed HVDC links.

The development of the dc grid is uncertain, but the role of the dc-dc converters has been already identified for the future multiterminal dc systems [START_REF] Adam | Review of DC-DC converters for multi-terminal HVDC transmission networks[END_REF]. This paper suggests possible applications for dc-dc converters in Europe (Section II) as initial scenarios of multiterminal dc systems. The applications are evaluated in function of the current situation of the HVDC links [START_REF] Entso-E | ENTSO-E Transmission System Map[END_REF] and the future projects in Europe [START_REF]ENERGY Projects of common interest -Interactive map[END_REF], [START_REF] Entso-E | TYNDP 2018 -Project Sheets[END_REF]. Even though these scenarios may not be realistic (missing detailed assessment), they can be used as a representative sample of the possible European dc grid and evaluate the requirements for the dc-dc converters. Section II details the identified requirements for the dc-dc converters depending on the suggested applications. Section IV, shows simulation results for a case study chosen to represent the general converter requirements. I).

I. APPLICATIONS

Currently, the transmission grid in Europe has 18 point-topoint links (P2P) IGBT-based, Voltage Source Converter (VSC) [START_REF] Barnes | VSC-HVDC Newsletter[END_REF], 20 P2P links thyristor-based [START_REF] Ms | HVDC Projects Listing[END_REF], Line Commutated Converter (LCC) and one link using both technologies in parallel (Skagerrak).

Based on Fig. 1, eight suggested dc-dc interconnections are presented in Table I and II. The interconnections were chosen by the lines proximity and number of countries and/or Transmission System Operators (TSOs) interconnected, assuming that the interconnection of different markets can be beneficial for the involved parties. Under these assumptions, two close links, interconnecting the same two countries and/or TSOs, are less interesting interconnection to assess because it would not increase the interconnected markets. Other evaluation criteria could lead to different conclusions e.g. a political analysis as the one presented in [START_REF] Dedecca | The integrated offshore grid in Europe: Exploring challenges for regional energy Fig.6. Simulations results for the interconnections between MMC link and a LCC link using a F2F as dc-dc converter: (a) Power on each MMC station, (b) Power transfer through the F2F (positive from LCC to MMC side), (c) Power in each LCC station, (d) voltages[END_REF], a detail evaluation studied in the PROMOTioN project [START_REF] Bhagwat | D7.4 Economic framework for a meshed offshore grid[END_REF], or an optimization approach in [START_REF] L'abbate | Development of HVDC offshore grids in the European system: long-term transmission expansion analyses[END_REF]. In general, a cost-benefit analysis [START_REF] Entso-E | 2nd ENTSO-E Guideline For Cost Beneft Analysis of Grid Development Projects FINAL -Approved by the European Commission[END_REF] evaluates the complete project impact in detail, but it is beyond the scope of this paper.

A. Existing HVDC links

Assuming the already installed links, 2 potential cases can be identified for the use of a dc-dc converter, presented in Table I. The first case is the intersection of the Baltic cable (Germany-Sweden) and the Kontek line (Germany-Denmark) shown in Fig. 2. The use of a dc-dc converter to interconnect both lines can increase the number of countries or transmission system operators (TSO) interconnected from 2, on each line, to 3 (Germany-Sweden-Denmark). In the second example, SwePol (Sweden-Poland)-NordBalt (Sweden-Lithuania), the cables do not cross each other, but their proximity makes the connection possible with extra cable segments (Fig. 1). The installation of the extra cables is feasible considering the repairing techniques known to date [START_REF] Heggås | A review of condition assessment methods for high voltage subsea power cables[END_REF], [START_REF] Worzyk | Submarine power cables: design, installation, repair, environmental aspects[END_REF].

B. Future interconnections

Including projects under construction and future HVDC links (Fig. 2, blue lines), six main examples for HVDC interconnection have been identified in Table II.

The potential interconnection 3, connects the lines under construction, Cobra Cable and NordLink. This dc-dc converter can increase the power flow between Netherlands, Denmark, Germany and Norway. The links have a crossing point to install the dc converter without the need of a cable extension. For the potential converters 4 and 5 (Table II), the interconnections Viking Link -NordLink and Viking Link -NorNed are suggested. As it is noticeable in Fig. 2, Viking Link, interconnecting UK-Denmark, cross the NorNed and NordLink creating a possible application for the dc-dc converter installation. If the two crossing points are used for the installation of dc-dc converters, the total interconnected system will have five countries as a dc multiterminal scheme around Viking Link (potential interconnection 9). The last 3 suggested interconnections (6, 7 and 8) do not have a crossing point to install the dc-dc converter but their proximity can increase the power flow in their respective zones. Suggested interconnection 6 can increase the interaction between UK-Belgium and Netherlands while potential interconnections 7 and 8, can increase the power flow flexibility inside Germany interconnecting the four TSO's market zones. Fig. 2, presents the North Sea power hub [START_REF] Entso-E | Project 335 -North Sea Wind Power Hub[END_REF], [START_REF]North Sea Wind Power Hub -Planning the Future Today[END_REF], a project presented to interconnect windfarms with Denmark, Germany and Netherlands. It will have a gradually increasing capacity up to 12 GW and it could be the first real implementation of a dc multiterminal system in the European region. Based on the North Sea power hub project, other locations for multiport dc converters (MPDCC) could be available for the interconnections between the windfarms and/or the neighboring countries. Fig. 2, shows the suggested locations for MPDCC 1 and 2. The MPDCC 1 is rather to interconnect the countries around, due to their proximity (UK-France-Belgium-Netherlands). This MPDCC 1, will, probably, need to adapt different dc voltages and grid topologies (in function of the projects on the region). MPDCC 2 shows a location close to the already installed HVDC lines for the windfarms in the north of Germany and it could help interconnect the four neighboring countries (Germany-Netherlands-Denmark-Norway). In this case, if the MPDCC 2 is used to interconnect the near windfarms, the required converter need to adapt medium voltage ratios [START_REF] Barker | Requirements of DC-DC Converters to facilitate large DC Grids[END_REF] (up to 1.9), different technologies and grid topologies (bipole, rigid bipole [START_REF] Hirsching | On control and balancing of MMC-HVdc links in rigid bipolar configuration[END_REF], symmetric monopole, asymmetric monopole). MPDCC are a possible option to interconnect the growing HVDC installations in the North Sea, but they are subject to more diverse requirements, more detailed evaluation must be done on this subject.

II. REQUIREMENTS FOR THE DC-DC CONVERTERS

Table I and II present the technical characteristics of the dc suggested interconnections, including the voltage ratio, the technology and the grid topology (grounding strategy) of each link. The following subsections explain why two HVDC links having a difference in, at least, one of these parameters require a dc-dc converter for their interconnection. Additional possible requirements, for the dc-dc converter, are included in the discussion.

A. Voltage ratio

Two dc systems with different voltage ratings cannot be interconnected without a dc-dc converter. This converter must adapt the voltage difference and ensure the security of the interconnected systems (e.g. high voltage should not appear on the low voltage side). The isolation requirements can increase with the relation between voltages, called voltage ratio.

The voltage ratio is the relation between the voltage level of the links to be interconnected (VDC1/VDC2). Following the classification presented in [START_REF] Barker | Requirements of DC-DC Converters to facilitate large DC Grids[END_REF], only 2 of the presented examples (Tables I andII) have a medium voltage ratio (≥ 1.5). These are: SwePol -NordBalt (1.5) and COBRA Cable-NordLink (1.64). The rest of the examples lay within a small voltage ratio (≤ 1.5). The interconnection of small voltage ratio can be made with less constraints, with respect to the medium/high voltage ratio, as the interconnection might not need galvanic isolation [START_REF] Barker | Requirements of DC-DC Converters to facilitate large DC Grids[END_REF].

B. Technologies interconnection

The interconnection of different HVDC technologies is present in half of the examples. These interconnections can be interesting in the future of the European dc grid as HVDC links are (almost) evenly distributed between LCC and VSC. The main characteristics of each HVDC technology, important for their interconnection, are listed below.

The use of thyristors valves, in the LCC converters, force the dc current in a single direction, therefore the reversal power flow is made by changing the voltage in the HVDC line. In case of transients on the inverter ac side, LCC is susceptible to commutation failures, equivalent to a short circuit on the dc side. The LCC line can reverse the dc voltage to extinguish the arc, subject to a dc fault, thus, this technology can work in a P2P, using overhead lines, without the installation of dc circuit breakers (DCCB).

On the contrary, VSC uses IGBTs (with a diode in antiparallel), maintaining the voltage polarity unchanged. The power flow reversal is achieved by changing the current direction. The dc faults are cleared with ac circuit breakers, DCCB or full bridge submodules (FBSM) depending on the system stability, and/or protection, requirements.

For the interconnection of different technologies, [START_REF] Barker | Requirements of DC-DC Converters to facilitate large DC Grids[END_REF] suggests the use of a dc-dc converter with galvanic isolation, mainly for the commutation failures (equivalent to a dc fault) and the power reversal in LCC links (voltage polarity inversion).

C. P2P topology

The third technical parameter compared on Tables I and II, is the grounding strategy (topology). This is the most fluctuating parameter on the suggested cases. The P2P topology is a parameter in function of the needs and restrictions of each project. A bipole structure can be chosen to increase the availability after a dc fault, but to reduce the cost, the metallic return can be omitted to create a rigid bipole or a symmetrical monopole, reducing also the system availability. From this perspective, the link topology is not a parameter that can be standardized easily. Consequently, the future interconnections will, most likely, take care of this special requirement.

Two different grid topologies may have different transients during a given DC fault. E.g., a pole to ground fault in a bipole cable, may have a small impact in the healthy pole and the system can continue with partial operation after the fault. On the contrary, the same fault in a symmetric monopole can increase the voltage, in the healthy cable, up to 2 p.u. and loss the power flow capability until the equipment is repaired. These differences can increase the requirements for a dc-dc converter interconnecting different topologies, e.g. a degraded mode for faults on the bipole side and overvoltage capability in the symmetric monopole side.

D. Additional requirements

The dc-dc converter requirements may change in function of the application. A complete evaluation of the converter requirements is beyond the scope of this paper. Some additional requirements are listed below. Depending on the system control and protection strategy, different specifications for the dc-dc converter may be required. In function of the grid control strategy, the converter can be asked to work in power, voltage or droop control. This requirement may change for different grid operation points. The grid protection strategy can define the fault and post faults requirements of the converter. As it was mentioned in the previous subsection, the grid topology may change the transient behavior during a fault and also the possible system reconfiguration after the contingence.

The dc-dc converter can increase the power availability after a fault in a line. A system reconfiguration is possible, isolating the faulty side. The new system needs to optimize its operation in function of the system losses and the converter, lines and power ratings of healthy stations. This post-fault scenario may influence the design of the dc-dc converter specifying its power rating and degraded mode requirements.

General requirements of the converter must be taken into account, i.e., the capacity to isolate perturbations to keep system security and the need of galvanic isolation [START_REF] Barker | Requirements of DC-DC Converters to facilitate large DC Grids[END_REF]. The complete specifications may lead to an already exiting solution. The proper converter topology for each application can be evaluated based on the state of the art compiled in the literature [START_REF] Adam | Review of DC-DC converters for multi-terminal HVDC transmission networks[END_REF], [START_REF] Kish | On the emerging class of non-isolated modular multilevel DC-DC converters for DC and hybrid AC-DC systems[END_REF]- [START_REF] Schön | High power HVDC-DC converters for the interconnection of HVDC lines with different line topologies[END_REF] III. CASE STUDY In this section, a general scenario is proposed to represent each dc-dc converter requirements compared in the previous section (voltage ratio, technology and topology). The dc voltages are 800 kV/500 kV equivalent to a medium voltage ratio (1.6), similar to suggested interconnection 2 and 3 in Table I and II. The HVDC technologies being interconnected are LCC and VSC, modular multilevel converter (MMC), as interconnections 2, 5 and 6. The topologies are: a symmetric monopole (MMC link) and an asymmetric monopole (LCC link), shown in Fig. 3.

The MMC link is a symmetric monopole ±400 kV, 1 GVA, with a total cable length of 200 km. The cable was simulated with a wideband model from the Best paths project [START_REF] Paths | Best Paths, Transmission for sustainability[END_REF]. For simplicity, MMC1 and MMC2 are identical, as well as their respective ac systems (400 kVRMS L-L). MMC1 is set to control voltage and MMC2 is controlling power.

The LCC link, is an asymmetrical monopole of 12 pulses, 500 kV dc, 1 GVA, based on the Cigré HVDC benchmark, where the cable was simulated as a T model (series resistance, inductance and a capacitor to ground). The details of the cable, ac impedances and ac filters can be found in [START_REF] Szechtman | First benchmark model for HVDC control studies[END_REF]. The general parameters for each link are listed in Table III, the parameters are presented for the total length of 200 km in the case of the MMC link.

As the case study includes medium voltage ratio (1.6), different HVDC technology and different topology; following the recommendations from [START_REF] Barker | Requirements of DC-DC Converters to facilitate large DC Grids[END_REF], the dc-dc converter should have galvanic isolation. The MMC Front-to-front (F2F) is chosen, as it is a well-known converter in the literature that fulfill the requirements for this application. Fig. 4, shows the F2F in detail including half bridge submodules (HBSM) on the MMC link side and FBSM on the LCC side. The need of the FBSM is due to the voltage polarity change for the power reversal in LCC links. Switchgear is not considered in this paper, where the cables are mechanically disconnected and reconnected to keep the voltage polarity on the dc-dc converter while the LCC line voltage has been inverted, in that case HBSM can be implemented on the LCC side. The F2F converter is connected in the middle of both HVDC links as shown in Fig. 3. The general parameters of the F2F converter are presented in Table IV. The case study was implemented in Matlab-Simulink with a detailed LCC model and an arm average model for the MMC converters [START_REF] Freytes | On the modeling of MMC for use in large scale dynamic simulations[END_REF] shown in Fig. 5. The F2F converter using FBSM was implemented with the arm average model presented in [START_REF] Xinkai | Fast electromagnetic transient simulation models of full-bridge modular multilevel converter[END_REF]. More detailed models can be used to validate the control strategy or make fault simulations, but it is not the scope of this paper. The MMC (including the dc-dc converter) stations are controlled with an energy-based strategy presented in [START_REF] Páez | Study of the impact of DC-DC converters on the protection strategy of HVDC grids[END_REF], [START_REF] Shinoda | Energy difference controllers for MMC without DC current perturbations[END_REF]. The general energy control approach can be found in [START_REF] Zama | High dynamics control for MMC based on exact discrete-time model with experimental validation[END_REF]. The LCC is controlled based on the strategy presented in [START_REF] Jovcic | High voltage direct current transmission: converters, systems and DC grids[END_REF], keeping the inverter station in voltage control mode [START_REF]HVDC for beginners and beyond[END_REF]. The power flow through the dc-dc converter is limited to 300 MW due to stability issues discussed in [START_REF] Lu | Power flow control of interconnecting two LCCHVDC through front-to-front type DC/DC converter[END_REF]. Fig. 6 shows the power on each of the three parts of the system: the MMC side, the dc-dc converter and the LCC side. It is observed from Fig. 6a that the power is constant in MCC2 because that terminal controls power, while MMC1 controls the dc voltage and is subject to the F2F power variation. The power flow direction is changed on the MMC link at 5.5 s, from 600 MW to -600MW, taking the dc input as positive for power convention. Fig. 6c, shows the power variation on the LCC line starting with 800MW from LCC1 to LCC2 and around 7.2s the power flow direction is reversed. The voltage polarity variation can be observed in Fig. 6d. In this case, the roles of each LCC station are switched, such that LCC1 was initially operating as power control and LCC2 as dc voltage control (inverter). Then, after the voltage reversal, LCC1 controls dc voltage (inverter) and LCC2 controls power. Fig. 6b shows, the power flow through the F2F, where two sequences of positive-negative power between the HVDC links are tested. The first sequence at 3s and the second at 8s, after the power reversal in both sides.

The simulations demonstrate the feasibility of the F2F to interconnect HVDC links with different technologies, topology and/or voltage ratio, in normal operation, Further studies are needed for contingencies and the evaluation of the impact of the converter on the dc grid (control strategy, losses, stability, etc.).

The use of a transformer can isolate both dc sides avoiding undesired disturbances, but it is also the main constraint for the installation of a F2F in certain applications as the offshore dc grid. The transformer increases the space usage and the weight of the converter i.e. it increases the total installation cost. A first solution would be to increase the transformer frequency, decreasing its volume, but the implications are still subject of study. A second option is the study of new topologies without the use of an ac transformer as shown in [START_REF] Kish | On the emerging class of non-isolated modular multilevel DC-DC converters for DC and hybrid AC-DC systems[END_REF]. Further work must be done to evaluate the need and possible requirements of the transformer in a dc-dc converter.

IV. CONCLUSION

The present and future European transmission grid includes the use of HVDC transmission lines, most of them for offshore applications. The growing number of HVDC links has opened the discussion about a possible, future dc grid. This paper presented the possibility to interconnect two or more existing HVDC links as a starting point for the development of dc multiterminal systems.

The suggested interconnections need the installation of a dc-dc converter to adapt, at least, the voltage, the HVDC technology and/or grounding topology. Among these three requirements, the most common will be the interconnection between different grounding topologies as the grounding depends on the needs of each project and it is difficult to standardize. The interconnection of different technologies can be a requirement by even distribution number of LCC and VSC links in Europe. Finally, the voltage ratio will not represent a limitation for the dc-dc converter as, most of the HVDC links in Europe have similar operating voltages, leading to a small voltage ratio transformation. Section IV, presents the simulation results for the interconnection between a LCC and a VSC (MMC) link. The need of FBSM, on the LCC side of the dc-dc converter, is mandatory for the power reversal (voltage polarity change) if a specialized switchgear is not used. For LCC with unidirectional power flow the FBSM are necessary only if the dc-dc converter control strategy is affected by the impact of the dc faults on LCC side leading to instability.

The need of galvanic isolation is recommended for most of the dc-dc converter applications, but it leads to higher cost and volumes, especially critical in offshore applications, which represent the majority in Europe. Further studies must be done to evaluate the alternatives of the dc-dc converter without ac transformer that fulfil the system requirements (stability, reliability, fault blocking capability, power management, security, etc.). The impact of the dc-dc converter on the grid control strategy, the response in contingencies and system reconfigurations are left for future research studies.

Fig. 1 .

 1 Fig. 1. HVDC already installed links (magenta), the dashed lines are those in construction. Future projects (blue) in Europe including the North Sea Power Hub and potential interconnection 2 (TableI).

Fig. 2 .

 2 Fig. 2. Possible locations for dc-dc converters suggested in Table I and II and the dc Hub in the North Sea. Multiport dc converter (MPDCC) 1 (red circle) interconnecting UK-France-Nederland and Belgium. MPDCC 2, interconnecting Germany-Nederland-Denmark and possibly Norway.

Fig. 3 .

 3 Fig. 3. System studied. MMC line (top), LCC line (bottom), interconnection using a F2F dc-dc converter isolated (middle).

Fig. 4 .

 4 Fig. 4. dc-dc converter (MMC F2F) used for the case study. The high voltage side (MMC link) has HBSM while the low voltage side (LCC link) has FBSM.

Fig. 5 .

 5 Fig. 5. Arm average model used for the MMC and F2F converter, where mu and ml are the modulation indexes.

TABLE I .

 I POTENTIAL INTERCONNECTIONS GIVEN THE CURRENT HVDC INSTALLATIONS

	Potential interconnection	Link 1		Link 2	Voltage ratio	Technology	Topology (grounding)	Countries / TSO	Comments
	1	Baltic Cable 450kV -600MW (Sweden -Germany)	Kontek 400kV -600MW (Germany -Denmark)	1.13	LCC -LCC	Asymmetric monopole (both lines)	3	Crossing point available
	2	SwePol 450kV -600MW (Sweden -Poland)	NordBalt 300kV -700MW (Sweden -Lithuania)	1.5	LCC-VSC	Asymmetric monopole -Bipole	3	No crossing point.
		TABLE II.	POTENTIAL INTERCONNECTIONS INCLUDING FUTURE HVDC PROJECTS
	Potential interconnection	Link 1		Link 2	Voltage ratio	Technology	Topology (grounding)	Countries / TSO	Comments
	3	COBRA Cable ±320kV -700MW (Netherlands -Denmark)	NordLink 525kV -1400MW (Germany -Norway)	1.64	VSC -VSC	Symmetric monopole -Rigid Bipole	4	Crossing point available
	4	NordLink 525kV -1400MW (Germany -Norway)	Viking link 400-500kV -1000-1400MW (Denmark -UK)	1.31 -1.05 VSC -VSC	Rigid Bipole -Bipole	4	Crossing point available
	5	Viking link 400-500kV -1000-1400MW (Denmark -UK)	NorNed 450kV -700MW (Norway -Netherlands)	1.11 -1.13	VSC -LCC	Bipole -Symmetric monopole	4	Crossing point available
	6	Nemo Link 400kV -1000MW (Belgium -UK)		BritNed 450kV -1000MW (UK -Netherlands)	1.13	VSC -LCC	Symmetric monopole -Bipole	3	No crossing point
	7	SuedLink 2000 MW (Germany)	SuedOstLink ≥ 2000 MW (Germany)	Unknown	Unknown	Unknown	3	No crossing point.
	8	Ultranet 380 kV 2000 MW (Germany)	SuedLink 2000 MW (Germany)	Unknown	VSC -Unknown	Unknown	2	No crossing point.
	9	Viking -NordLink -NorNed (UK-Denmark -Germany -Norway -Netherlands)	1.05 -1.31	VSC -LCC -VSC	Bipole -Rigid Bipole -Symmetric monopole	5	Two crossing points available for 2 dc-dc converters

TABLE III

 III

	.	PARAMETERS DC-DC CONVERTER
	Parameter		High Voltage	Low Voltage
			side (MMC)	side (LCC)
	AC frequency		150 Hz
	AC impedance (R, L) referred	80 m Ω, 40 mH
	to High voltage side
	Tranformer voltage ratio		800kV Δ/Y 500kV
	Arm resistance		1 Ω	0.626 Ω
	Arm inductance		50 mH	39 mH
	Capacitance per SM (Fig. 4)	3 mF	4.5 mF
	Number of submodules per arm	500	313
	Equivalent capacitance (Fig. 5)	6 µF	14.4 µF

TABLE IV

 IV

	.	PARAMETERS LINES AND CONVERTER STATIONS
	Parameter	Link 1 (MMC)	Link 2 (LCC)
	Total cable resistance	1.1 Ω	5 Ω
	Total cable inductance	600 mH	0.2 H
	Total cable capacitance	48.4 µF	26 µF
	AC frequency		50 Hz	50 Hz
	AC impedance (R, L)	80m Ω, 0.5mH	~3.7 Ω,~151mH
	Arm resistance		1 Ω	--
	Arm inductance		50 mH	--
	Capacitance per SM	8mF	--
	Number of submodules	500	--
	per arm
	Equivalent capacitance	16 µF	--
	DC smoothing reactor	--	0.5968 H

ACKNOWLEDGMENT

This work has been supported by a grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" Program (ANE-ITE-002-01).


Nathan Evans
email: nathan.evans@supergrid-institute.com

Piotr Dworakowski

Mohammed Al-Kharaz

Sneha Hegde

Elie Perez

Florent Morel

Cost-performance framework for the assessment of Modular Multilevel Converter in HVDC transmission applications

Keywords: cost-performance assessment, offshore wind, transmission, HVDC, MMC, VSC, power transformer, submodule, IGBT, film capacitor, cost-benefit analysis, LCOE, OEM. I

This article proposes a methodology of Cost-Performance Assessment (CPA) enabling the efficient cost evaluation required for the Cost-Benefit Analysis (CBA). The proposed method is applied for the Modular Multilevel Converter (MMC) in offshore wind high voltage direct current (HVDC) transmission. Thanks to the developed model, an analysis of submodule voltage rating is performed demonstrating the interest of this methodology in the evaluation of new technologies for HVDC transmission. The analysis shows that increasing the submodule (SM) voltage could lead to savings in the MMC cost and weight.

INTRODUCTION

The Cost-Benefit Analysis (CBA) allows to evaluate the interest of projects of future investments and to compare different solutions [START_REF] Gasnier | Technical and economic assessment tool for offshore wind generation connection scheme: Application to comparing 33 kV and 66 kV AC collector grids authors[END_REF] - [START_REF] Lakshmanan | Assessment of collection systems for HVDC connected offshore wind farms[END_REF]. A CBA is often expressed in monetary terms where the cost is calculated taking into account the investment and operational cost and the benefit may take into account the socioeconomic welfare. This forms one of many criteria identified in the ENTSO-E guidelines document [START_REF] Entso-E | Guideline for Cost Benefit Analysis of Grid Development Projects[END_REF]. The choice of HVDC transmission for offshore wind farms results in fact from the CBA considering the cost of the link and offered benefits like the reduced energy cost [START_REF] Wang | The advantages and disadvantages of using HVDC to interconnect AC networks[END_REF].

The modular multilevel converter (MMC) has become the reference in HVDC transmission where the Voltage Source Converters (VSC) are required [START_REF] Lesnicar | An innovative modular multilevel converter topology suitable for a wide power range[END_REF], [START_REF] Jesus | HVDC Connection of Offshore Wind Parks : VSC vs LCC with STATCOM[END_REF]. To investigate opportunities for innovation in this area, a power electronic cost-performance analysis should be carried out.

The energy cost is usually measured thanks to the Levelized Cost of Energy (LCoE). Power converters, such as the MMC, contribute substantially to the LCoE of the HVDC transmission connection of offshore wind farms. Given that a power converter of this type, in the class of 600-1000 MW, can cost several tens of million euros, detailed cost modelling can help to identify and understand valuable areas of innovation for researchers, original equipment manufacturers (OEMs) and 1 st tier manufacturers alike. This article, therefore, proposes a methodology of Cost-Performance Assessment (CPA) which enables this cost evaluation required to be made and used as input for a complete CBA. The CPA does not evaluate the whole benefit, though it is a powerful tool in the comparison of alternative solutions. It may also provide a basis for design optimization studies.

The cost-performance indicators of power converters are discussed in Section II. The modelling methodology is outlined in Section III. An MMC case study is highlighted and its analysis is outlined in Section IV. An analysis of a SM voltage variation is given in Section V. Finally, the conclusions and perspectives are given in Section VI.

II. COST-PERFORMANCE INDICATORS OF POWER CONVERTERS

The LCoE takes into account the investment and operating cost and the amount of energy produced:

 LCoE = ∑ 𝐼 𝑡 +𝑂 𝑡 +𝐹 𝑡 (1+𝑟) 𝑡 𝑛 𝑡=1 ∑ 𝐸 𝑡 (1+𝑟) 𝑡 𝑛 𝑡=1

 

where:

It investment cost at year t Ot operating cost at year t Ft fuel cost of year t (zero for wind power) Et produced energy at year t r discount rate n number of years during which the system is exploited.

The investment cost, also named the Capital Expenses (CapEx), is related to the purchase of the converter and converter station components, installation, commissioning, construction, and decommissioning. The investment cost should take into account at least the costs incurred due to:  Engineering -involving all the project design activities,  Production -taking into account the cost of subsystem/ system assembly,  Component purchase -based on the amount paid for acquiring a given component.

The Operating Expenses (OpEx) are related to the converter power loss during operation, and the converter maintenance costs during its operational lifetime. It is considered in [START_REF] Kolar | Performance trends and limitations of power electronic systems[END_REF], [START_REF] Hillers | Systematic comparison of modular multilevel converter topologies for battery energy storage systems based on split batteries[END_REF] that at least the following costperformance indicators shall be considered when evaluating and designing a power converter:  Converter cost structure,  Size and weight,  Power loss,  Reliability.

The following subsections give details on these indicators and explains why the investment cost for offshore wind is highly sensitive to both weight and volume while the power converter operating cost is sensitive to both power loss and also reliability.

A. Converter cost structure

The cost structure of the power conversion equipment is different for every manufacturer as the supply chain strategy varies between them. Taking the CapEX as an example, one manufacturer can produce its own IGBT power module, thus involving engineering/production/component cost, whereas another can buy a ready product, thus incurring the component cost only.

B. Converter Size and Weight

The size and weight of the converter and the station equipment influence the civil works required for their installation. These two parameters also have an indirect impact on the investment cost especially when installing the converter on a platform, which is the case in Offshore Wind Farms (OWF) [START_REF] Volov | Transformers for Offshore Wind Platforms: Expected Problems and Possible Approaches[END_REF] - [START_REF] Toshon | Estimation of Power Density of Modular Multilevel Converter Employing Set Based Design[END_REF].

C. Converter Power Loss

The power loss has an impact on the converter design and cooling management [START_REF] Jones | Calculation of power losses for MMCbased VSC HVDC stations[END_REF] as well as the energy produced [START_REF] Ladoux | Comparative study of variant topologies for MMC[END_REF]. For example, the typical 1% of power loss in 1GW converter station stands for up to 88TWh of energy loss per year, which is equivalent to approximately 4 million euros (using an energy price of 44€/MWh [START_REF] Rte | Données de marché[END_REF]).

D. Converter Reliability

The reliability of power converter impacts the HVDC transmission downtime and repairs, influencing the operating cost and the energy produced [START_REF] Entso-E | Improving HVDC System Reliability[END_REF] - [START_REF] Najmi | High reliability capacitor bank design for modular multilevel converter in MV applications[END_REF].

III. THE PROPOSED MODELLING APPROACH OF MMC STATIONS IN HVDC

A. The MMC In offshore wind farm HVDC transmission systems, the VSC represents the reference case for power conversion in this environment because of its ability in active and reactive power handling (four quadrant operation) and its black-start capability [START_REF] Sellick | Comparison of HVDC Light (VSC) and HVDC Classic (LCC) site aspects, for a 500MW 400kV HVDC transmission scheme[END_REF]. Of the family of VSC, the MMC (Fig. 4) offers [START_REF] Lesnicar | An innovative modular multilevel converter topology suitable for a wide power range[END_REF], [START_REF] Van Hertem | HVDC Grids: For Offshore and Supergrid of the Future[END_REF]:

 Synthesis of a sinewave with low harmonic distortion at low switching frequencies, allowing a reduction in filter requirements and power losses,  Modularity in structure that allows easy adaptation to different voltage and power levels, enabling a reduction in costs associated with engineering, production, and component,  Hardware redundancy which allows uninterrupted operation under component failure, leading to an increase in converter operational time.

B. The CPA Modelling Approach

The modelling approach to cost-performance assessment must take into account the amount of available information in the function of power converter Technology Readiness Level (TRL) which varies from 1-9. At TRL1 (converter conceptualization stage), only a rough CPA can be performed with a limited precision. Whereas, at TRL5 (converter prototype development stage) a detailed CPA is possible with a sufficient precision required for product development.

Two modeling approaches are possible: the bottom-up approach and the top-down approach. In the bottom-up approach (Fig. 2), the power converter system is divided into several subsystems which are further divided to obtain lower level of components such as IGBT, capacitors etc. The data of the individual component are aggregated together at the lower level to obtain the data of the higher level.

Bottom-up approach

System -Modular Multilevel Converter [ABB]

Subsystem -MMC submodule [Siemens] Component -IGBT pack [Mitsubishi]
Fig. 2. Cost-performance modelling approach -bottom-up (images taken from [START_REF] Billmann | Modular Multilevel Converters: State of the Art and Future Progress[END_REF])

In the top-down approach (Fig. 3) there is the high-level data that is aggregated and anonymized. This high-level data is often published by authorities or consulting companies. The high-level data is not sufficient in the CPA of new technologies as we do not know the system breakdown structure and the component share in the overall CPA, but this data can provide a benchmark for the results of a costperformance assessment.

In this article the bottom-up approach is proposed for model development, more adapted to low-TRL studies, whilst the top-down approach is proposed for model validation, which can be used at both low-and moderate-TRL stages in power converter development. Both are based on a power converter station breakdown structure. Fig. 3. Cost-performance modelling approach -top-down (typical HVDC station costs [START_REF] Russo | Design of a Power Transformer and HVDC Transmission System[END_REF] and typical power transfomer costs [START_REF] Black | Capital costs for transmission and substations[END_REF]) For a complete cost-performance analysis, of the station components to which the cost-performance parameters have a non-negligible sensitivity should be included. For example, the MMC SM component requirements will have a big impact on the station cost, the footprint and also the station weight.

C. Converter Component Breakdown Structure

The converter component breakdown structure, based upon power converter structure and component information published in the literature [START_REF] Toshon | Component Level Decomposition Approach to Develop Selection Metrics for Shipboard Power Converter Systems[END_REF] offers the hierarchical tree structure allowing to identify the elementary components. Each low-level component is associated with the cost-performance indicators presented in the Section II. The higher level is simply calculated using algebraic operations based on lower level data. The breakdown depth can be adjusted according to the required precision. The raw data of elementary components is gathered in a database which is the heart of the CPA.

D. Converter CPA Model Implementation

The model can be implemented in any programming or computational environment. The authors have successively utilized Excel, Python and MATLAB. Excel offers the easiest and fastest implementation but does not allow an easy traceability and configuration management. Python has particular interest because of the way that it handles matrices and also in the fact that it is an open-source language. MATLAB requires a larger initial investment but comes with powerful programming and interface functionalities.

The model inputs are at least the converter station voltage and power, and the parameters are related to the technology such as SM voltage or IGBT used (see Fig. 4). Thanks to the database for each component (used to store information about component price, size, reliability, etc.) the cost-performance indicators are calculated and further aggregated in the converter breakdown structure. The results present the overall system cost-performance. Eventually an optimization algorithm can be added allowing to adjust the parameters, thus optimizing the converter design.

Inputs and parameters

Results

Database

E. Statement of hypothesese

Given the potential complexity of the CPA model, it is important to well define the assumptions that are made within the model. Here in the following case study, for example, it is assumed that the energy storage in the MMC is fixed according to its power rating.

F. Parameter Sensitivty Analysis

Once the model has been constructed, it is ready to be evaluated. The main aim of this evaluation is to make a study of the effects that varying the model inputs can have on the cost-performance parameters.

IV. MODULAR MULTILEVEL CONVERTER CASE STUDY

This technology is dominant within Offshore Wind Farm (OWF) HVDC connections and is the reference for HVDC transmission stations in the class of 600-1000 MW [START_REF] Menke | 2nd Generation DC Grid Access for Large Scale Offshore Wind Farms[END_REF].

A. MMC Model Inputs and Parameters

Out of the existing and operational projects of this class, BorWin 2 provides an excellent example in that it is both recent and has had sufficient enough data published about it to be used to form the inputs of a case study (TABLE I).

B. MMC Component Breakdown Structure

A component breakdown structure of the converter station should include the following components: power converter; HVDC transformers; cooling system; protection; filtering; auxiliary systems; and, the platform. The important CPA parameters to assess here would be the station equipment electrical power densities, by volume and by weight, because of the sensitivity in the offshore environment to these two parameters; the individual contribution to the overall cost of the station by the transformers (~10-15 million euros, assuming two 600 MVA transformers in parallel [START_REF] Black | Capital costs for transmission and substations[END_REF]), the platform, and the protection system are significant enough to be studied in their own right.

For the sake of brevity it is only the MMC arm components that are studied in this paper (see Fig. 5). The contribution to the overall cost and weight of the converter station of the MMC modules makes them an important aspect of a CPA. For example, the component cost breakdown of the MMC power converter shows that the largest contribution to the weight of the MMC arm is found to be made by the MMC modules (Fig. 6, left). Also, the largest contribution to the estimated arm cost comes from the module (Fig. 6, right). Therefore, the SM components are studied here in more detail.

C. MMC Component Modelling

Thin film metallized polypropylene film (MPPF) capacitors are the reference technology for the MMC SM due to their low cost, low loss and stability in wide temperature and frequency range [START_REF] Tang | Capacitor Selection for Modular Multilevel Converter[END_REF]. Consequently, this technology is represented in the case study model. The data stored in the CPA database for the film capacitor includes a model of the capacitor mass as a function of its energy storage and a model of the capacitor cost as a function of capacitor mass and has been taken from manufacturer datasheets. The weight model is valid for capacitors with a rated current of 250A rms.

The total weight of the capacitors in the submodule can be found by:

𝑤𝑡 𝑐𝑎𝑝,𝑠𝑚 (𝑊 𝑠𝑚 ) = 𝑛 𝑐𝑝 (3.57𝑊 𝑠𝑚 + 5.92) [𝑘𝑔] (2)
where 𝑛 𝑐𝑝 is the number of capacitors in parallel and 𝑊 𝑠𝑚 is the submodule energy storage value in kJ. The cost of the total required capacitance can be found by [START_REF] Lakshmanan | Assessment of collection systems for HVDC connected offshore wind farms[END_REF].

𝑐𝑜𝑠𝑡 𝑐𝑎𝑝 (𝑤𝑡 𝑐𝑎𝑝 ) = 40𝑤𝑡 𝑐𝑎𝑝 [€]

(3)

The IGBT used in MMCs in HVDC applications can range in voltage from 3.3-6.5 kV [START_REF] Gong | A 3.3kV IGBT module and application in modular multilevel converter for HVDC[END_REF], [START_REF] Wang | IGBT technology for future high-power VSC-HVDC applications[END_REF]. There is a number of suppliers of IGBT power modules (PM). For this study, a model of the IGBT PM weight, 𝑤𝑡 𝐼𝐺𝐵𝑇,𝑠𝑚 , has been fitted to components in this voltage range. This model is a function of the derated breakdown voltage of the IGBT, 𝑉 𝑑𝑒𝑟𝑎𝑡𝑒𝑑 , which has the following relationship with the IGBT breakdown voltage, 𝑉 𝐵𝑟 :

𝑉 𝑐𝑒𝑙𝑙 = 𝑉 𝑑𝑒𝑟𝑎𝑡𝑒𝑑 = 0.56 × 𝑉 𝐵𝑟 [𝑉] (4)
where 𝑉 𝑐𝑒𝑙𝑙 is the MMC submodule voltage. The IGBT PM weight is modelled by [START_REF] Wang | The advantages and disadvantages of using HVDC to interconnect AC networks[END_REF].

𝑤𝑡 𝐼𝐺𝐵𝑇,𝑠𝑚 (𝑉 𝑐𝑒𝑙𝑙 ) = 0.9 × 10 -3 𝑉 𝑐𝑒𝑙𝑙 -0.43 [𝑘𝑔] (5)

The cost model fitted to IGBT data is expressed in the form of [START_REF] Lesnicar | An innovative modular multilevel converter topology suitable for a wide power range[END_REF].

𝑐𝑜𝑠𝑡 𝐼𝐺𝐵𝑇.𝑠𝑚 (𝑉 𝑐𝑒𝑙𝑙 ) = 1.27𝑉 𝑐𝑒𝑙𝑙 -960 [€] (6)
The MMC loss model utilises the loss and characterisitcs commonly found in the component datasheet. Reliability calculations in a static form use the component failure-in-time (FIT) rate, which can also be found in the component datasheet. Neither parameters are calculated in this paper and so these models are not detailed.

V. RESULTS OF A SUBMODULE VOLTAGE VARIATION

STUDY

The following section presents the results of a study on the variation of the submodule voltage. This analysis is interesting when evaluating the use of new technologies, as Silicon Carbide (SiC).

A. MMC Submodule Cost-Performance Assessment Hypothesis

In the analysis made in the following CPA, the main hypothesis held is that the minimum global energy storage requirement of the MMC is fixed, the value of which is chosen based upon the maximum permissible fluctuation in the submodule dc voltage. The energy stored within the MMC converter is normally expressed as a function of the active power transfer requirement [START_REF] Ilves | On Energy Storage Requirements in Modular Multilevel Converters[END_REF].

According to [START_REF] Merlin | Cell capacitor sizing in multilevel converters: cases of the modular multilevel converter and alternate arm converter[END_REF], for an MMC that employs sinusoidal pulse-width modulation (SPWM) [START_REF] Ladoux | Comparative study of variant topologies for MMC[END_REF] the expected figure, when the converter is operating in a worst-case scenario (that is to say ac grid voltage is 0.9pu and the phase shift between the grid voltage and grid current 𝜑 =90º) the total energy stored in the MMC should be 39kJ/MVA or 21kJ/MVA, for triplen harmonic injection. Assuming that the latter control approach is used in the model in this case study, a value of 21kJ/MVA is chosen.

The assumptions that are made in [START_REF] Merlin | Cell capacitor sizing in multilevel converters: cases of the modular multilevel converter and alternate arm converter[END_REF] are also made here. That is to say that the capacitor voltage ripple is fixed at 10%. Furthermore, that the operation of the MMC is considered in steady state only, that the energy stored in the inductors in the converter is neglected, and that the storage in the MMC in ratio with the apparent power S is given as in [START_REF] Jesus | HVDC Connection of Offshore Wind Parks : VSC vs LCC with STATCOM[END_REF].

B. Power Converter Electro-Technical Model

To identify the number of parallel capacitors required in the submodule bank of capacitors, 𝑛 𝑐𝑝 , an expression of the rms current is required. The SM capacitor bank will be subjected to currents with frequencies at the line frequency and double the line frequency [START_REF] Errigo | Assessment of the Impact of Split Storage within Modular Multilevel Converter[END_REF]. The rms value can be found by evaluating [START_REF] Kolar | Performance trends and limitations of power electronic systems[END_REF]. . Using (8) to calculate the capacitor rms current, the number of parallel required capacitors to ensure that the value of rated current for the capacitor model is not exceeded, 𝑛 𝑐𝑝 = 3.

Using the relationship between capacitance, voltage and energy applied at the submodule level, we can define the total energy storage requirement of the SM in each arm of the MMC as in [START_REF] Volov | Transformers for Offshore Wind Platforms: Expected Problems and Possible Approaches[END_REF].

𝑊 𝑎𝑟𝑚,𝑚𝑖𝑛 = 1 2 𝑛 𝑠𝑚,𝑎𝑟𝑚 𝑛 𝑐𝑝 𝐶 𝑐𝑎𝑝 𝑉 𝑐𝑒𝑙𝑙 2 [𝐽] (10)
where 𝑛 𝑠𝑚,𝑀𝑀𝐶 is the number of submodules in the three phases of the MMC and, 𝐶 𝑐𝑎𝑝 , is the capacitance of the individual capacitors used in the capacitor bank model and 𝑛 𝑐𝑝 is the number of capacitors in parallel. The number of SM is normally expressed as in [START_REF] Nakanishi | High Power Density Design for a Modular Multilevel Converter With an H-Bridge Cell Based on a Volume Evaluation of Each Component[END_REF], where 𝑘 𝑟 is the coefficient used to add redudancy to the number of SM in the MMC here (𝑘 𝑟 = 1.1). 𝑛 𝑠𝑚,𝑎𝑟𝑚 = 𝑘 𝑟 2 × 𝑉 𝐷𝐶 𝑉 𝑐𝑒𝑙𝑙 [START_REF] Nakanishi | High Power Density Design for a Modular Multilevel Converter With an H-Bridge Cell Based on a Volume Evaluation of Each Component[END_REF] Substituting [START_REF] Volov | Transformers for Offshore Wind Platforms: Expected Problems and Possible Approaches[END_REF] and ( 11) into [START_REF] Hillers | Systematic comparison of modular multilevel converter topologies for battery energy storage systems based on split batteries[END_REF] and rearranging this equation into a function of the cell voltage gives [START_REF] Toshon | Estimation of Power Density of Modular Multilevel Converter Employing Set Based Design[END_REF].

𝑉 𝑐𝑒𝑙𝑙 = 10 × 10 -3 𝑆 𝐶 𝑐𝑎𝑝 𝑉 𝐷𝐶 [𝑉] (12)

C. Parameter Sensitivity Analysis

Once the models of the components have been defined, the sensitivity of the CPA parameters to variation of input values can be made. In this cost-performance assessment, the submodule voltage was varied to see the impact that this would have on the MMC arm cost and weight.

D. Results

In Fig. 7 and Fig. 8, the impact of the variation of the SM voltage can be seen on the MMC arm cost and weight, respectively. The results indicate that there is a sensitivity in these two parameters to an increase in the SM cell voltage.

As can be seen in those figures, with the case study input data taken from TABLE I, the increasing the voltage class of the IGBT could yield decreases in both the cost and weight of the MMC arm. Therefore, the impact of this on the weight and volume should be carefully monitored. The CPA is essential in the evaluation of new technology concepts. It can be applied in the study of innovative HVDC converter topologies, such as the Series Bridge Converter [START_REF] Amankwah | The Series Bridge Converter (SBC): A hybrid modular multilevel converter for HVDC applications[END_REF], which seems an interesting candidate to challenge the MMC. Moreover, it can provide important information for the cost-benefit analysis allowing to evaluate the interest of DC-DC converters [START_REF] Páez | Overview of DC-DC Converters Dedicated to HVdc Grids[END_REF] for HVDC transmission. The CPA requires an expert knowledge on the analyzed system and a solid component database. Extended with an optimization algorithm it becomes a powerful tool in the new product development.

To explore further the costs and benefits of increasing this voltage, the reliability, the power loss, and the submodule size should be introduced to the model. The positive impact that reducing the number of submodules could have on the reliability of the MMC would be interesting to study further. On the other hand, the increase in the cell voltage may also lead to increased IGBT failure, due to cosmic ray effects, and so there may be an optimal point to be located between reliability and the cell voltage.

The current rating of the IGBT pack should also be introduced as a variable in further modelling work and its isolation material should be modelled as voltage-dependent. Additionally, the thryistor model should be given as a function of voltage.

Given the impact that the control system can have on the operation of the converter, the effect of using nearest level modulation (NLM) on the cell capacitor sizing should be studied further. A comparison between the MMC and the twolevel series connected VSI may also have interest in being made.

Fig. 1 .

 1 Fig. 1. MMC converter station line diagram with major station equipment (SM = submodule)

Fig. 4 .

 4 Fig. 4. Cost-performance model implementation

Fig. 5 .

 5 Fig. 5. The MMC arm component breakdown structure. The IGBT and capacitor weight and cost models are considered functions of the SM cell voltage; all other components are modelled as constants

Fig. 6 .

 6 Fig. 6. The percentage contributions of MMC arm components to the arm weight (left of figure) and to the arm cost (right of figure) with Vcell = 2.5 kV (Vbr = 4.5 kV)

Fig. 7 .Fig. 8 .

 78 Fig. 7. The relative weight of the MMC arm with different IGBT voltage classes

TABLE I .

 I BORWIN2 OFFSHORE STATION CASE STUDY INPUT DATA[START_REF]Fact Sheet: BorWin2 HVDC Platform[END_REF]

	Parameter	Variable	Value	Unit
	Rated power	P	800	MW
	AC voltage	Vac	155	kV
	DC voltage	Vdc	±300	kV
	DC current	Idc	1320	A
	IGBT breakdown voltage	Vbr	4.5	kV

ACKNOWLEDGMENT

This work was supported by a grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" Program (ANE-ITE-002-01).


Florian Errigo

Laurent Chédot

Pascal Venet

Ali Sari

Piotr Dworakowski

Florent Morel

Assessment of the Impact of Split Storage within Modular Multilevel Converter

Keywords: HVDC, Modular multilevel converter, Energy storage system, Topological analysis

The introduction of Renewable Energy Sources (RES) and the electricity market liberalization have pointed out the need to upgrade the current electricity transmission network. High Voltage Direct Current (HVDC) transmission system is potentially the key. Recent advances in power electronics have allowed the introduction of power converters in power system applications as the Modular Multilevel Converter (MMC). In the same perspective, grid scale Energy Storage Systems (ESSs) have broadly appeared. The dual purposing to combine both systems can provide a completely new solution. Even though each submodule (SM) within modular converter can have its own ESS, decreasing the number of energy storage submodules (ES-SMs) may be required to reduce the cost. This paper deals with the opportunities to introduce split storage into an MMC. The analysis is focused on the internal energy exchange to maintain the proper function of the converter by using circulating current. Analysis shows that, SM capacitor voltage ripple or semiconductors load are greatly influenced by additional circulating current injection. This study helps to design embedded ESSs in the converter to provide new function like ancillary services for power system operation. Finally, a simulation of an MMC with ESS confirms analytical calculations.

I. INTRODUCTION

Energy policies are playing a more and more important role in the improvement of the power transmission network since states have gathered in a collective effort to develop green electricty [START_REF]Com (2011) 112 -A roadmap for moving to a competitive low carbon economy in 2050[END_REF]. A massive introduction of Renewable Energy Sources (RES) is expected in the future energy mix. Similarly, the shift from an integrated model to an unbundled model for electricity companies with the opening of the electricity market has imposed new considerations as there is no central organization responsible for the provision of the electrical energy [START_REF] Kirschen | Fundamentals of power system economics[END_REF]. Although competition is expected to benefit the whole economy, the complexity of the electricity market will inevitably require more interconnections to build a well connected area. The needs to upgrade the existing transmission system is stronger than ever.

HVDC transmission system has been receiving an increasingly interest for the supply of the electrical energy at high voltage over long distances [START_REF] Fairley | DC versus AC: The second war of currents has already begun [in my view[END_REF]. The technology has gained acceptance with the Modular Multilevel Converter (MMC) milestone [START_REF] Lesnicar | An innovative modular multilevel converter topology suitable for a wide power range[END_REF]. Thanks to its modular structure, it can easily adapt to high voltage and power levels.

The previously explained issues impose more stress on the transmission grid. Maintaining system stability is harder. Flexible mechanisms are required to cope with unforeseen outages and unpredictable demand. Energy Storage Systems (ESSs) are considered as a main enabling solution to face new challenges entailed by the ongoing transition.

In regard to the above mentioned, the association of both systems seems a promising solution. The idea to divide massive storage into smaller blocks within each submodule (SM) of a multilevel converter was initiated in [START_REF] Maharjan | A transformerless energy storage system based on a cascade multilevel PWM converter with star configuration[END_REF] in a Cascaded H-Bridge (CHB) converter. Because most of the time, multilevel converters are considered to only connect an ESS to the grid, MMC topology have been less investigated. However, the purpose to increase the attractiveness of the MMC by providing grid support in addition to power transfer function was introduced in [START_REF] Vasiladiotis | Modular Multilevel Converters with Integrated Split Battery Energy Storage[END_REF] and has since then attracted much interest both in industry and academia over the last years [START_REF] Kawakami | Development of a 500-kW modular multilevel cascade converter for battery energy storage systems[END_REF]- [START_REF] Konstantinou | A hybrid modular multilevel converter with partial embedded energy storage[END_REF].

It is generally assumed that all the SMs are connected to an ESS unit. However, the main advantage of the converter is that energy is stored in the SMs between the ac and dc grid. The internal stored energy can be freely controlled. This new degree of freedom allows to maintain the energy balance even with a not regular storage allocation by utilizing circulating currents. It is usually done at the cost of higher semiconductor load [START_REF] Henke | Balancing of modular multilevel converters with unbalanced integration of energy storage devices[END_REF]. However no information on capacitor voltage ripple, which is prevailing to determine the size of a SM, or simulation results have been provided. Currently, one of the few solutions for the enhancement of MMC converters for HVDC transmission was lately brought by [START_REF] Judge | Modular multilevel converter with partially rated energy storage with intended applications in frequency support and ancillary service provision[END_REF] where each arm comprises only a fraction of SMs with an ESS.

To a certain extent, reducing the number of energy storage submodules (ES-SMs) require to oversize components. But it is not straightforward and some configurations permit more flexibility. The main contribution of this paper is to give an analysis and a simulation model of an MMC with split ESS that can be used to design a converter with storage services. For instance, the relation between the power transfer, capacitor voltage ripple and arm currents are analysed.

The outline of this paper is as follows. Section II recalls the MMC fundamentals. This is followed by an analysis on the internal power flow of the converter. A comparison among five configurations where ESS is unevenly distributed within the converter is presented in Section III. In Section IV, analytical results are validated by simulations. Finally, Section V concludes the presented comparison. An MMC (Fig. 1) is composed of three phase legs (Subscript a,b,c), each with an upper and a lower arm (Superscript u,l). Each arm comprises a set of SMs. In this paper the most popular structure is assumed, a half-bridge cell. Each SM has two switches and a floating dc capacitor. By controlling the proportion of SMs inserted or bypassed in the respective arms, it is possible to generate a controlled staircase voltage waveform at the ac output of the converter. For preliminary considerations, arm voltage and current equations are reminded in (1), ( 2), (3), (4). Only one MMC leg is taken into account, x (x ∈ {a, b, c}), because it can be easily extended to a three-phase system by adjusting the phase shift.

II. MODULAR MULTILEVEL CONVERTER

i u x (t) = I dc 3 + I acx 2 sin(ωt -φ) + i circx (t) (1)
i l x (t) = I dc 3 - I acx 2 sin(ωt -φ) + i circx (t) (2)
v u x (t) = V dc 2 -V acx sin(ωt) (3)
v l x (t) = V dc 2 + V acx sin(ωt) (4)
Each arm conducts a dc component, I dc , equally split from the dc side and half of the ac output current, i ac (t), with I ac the maximum peak value and φ the phase shift of the grid current from the grid voltage. To perform properly, an MMC needs a power balance between the dc and ac sides but also an adequate arm energy balancing. During normal operation, the internal energy is evenly shared among all the arms. But in case of unbalance, balancing currents, the so called "circulating currents" are induced, i circx (t). Those currents allow an horizontal power transfer between phase legs and a vertical power transfer within a single leg to keep the converter balanced. They are at least comprised of a dc component, I dc circx , and an ac component at the line frequency, i ac circx (t) with ψ the phase shift of the circulating current from the grid voltage, to enable power to be transferred among arms [START_REF] Maharjan | A transformerless energy storage system based on a cascade multilevel PWM converter with star configuration[END_REF]. They have no impact on the grids and remain internal to the converter. Consequently, the sum of the circulating currents in the three phase legs is null [START_REF] Vasiladiotis | Modular Multilevel Converters with Integrated Split Battery Energy Storage[END_REF].

i circx (t) = I dc circx + I ac circx sin(ωt -ψ) (5) i circa (t) = -i circ b (t) -i circc (t) (6)

B. Internal power flow

The ac and dc grids are coupled through arm dynamics. The arm behavior can be decomposed into two decoupled ac and dc voltage sub-systems that can be controlled independently [START_REF] Shinoda | Virtual capacitor control: Mitigation of DC voltage fluctuations in MMC-based HVDC systems[END_REF]. SM capacitors are always charged/discharged with modulated dc and ac currents. Their voltage, u u,l cx (t), which reflects the energy stored, is permanently kept close to a reference value. Because the evolution of the arm energy depends on the power exchanged, the average power into the arm equals to zero over one period. Suggesting that SM capacitors energy will not deviate. To analyse the energy variation in the arms, the instantaneous power is given by:

p u x (t) = v u x (t)i u x (t) (7) p l x (t) = v l x (t)i l x (t) (8)
Substituting (1), ( 2), (3), ( 4) into ( 7), ( 8), the time average of the power in the arms are as follow:

p u x = V dc I dc 6 - V ac I ac cos(φ) 4 - V ac I ac circx cos(ψ) 2 (9)
+ V dc I dc circx 6 p l x = V dc I dc 6 - V ac I ac cos(φ) 4 + V ac I ac circx cos(ψ) 2 (10)
+ V dc I dc circx 6
The first two terms on the right side of ( 9), [START_REF] Soong | Evaluation of emerging modular multilevel converters for BESS applications[END_REF], depict the power balance between the ac and dc grids. The remaining terms represent the power exchange within the converter due to the ac and the dc component of the circulating currents.

Horizontal power transfer: The circulating current contains a dc component. It is common to each arm of an individual phase leg. So, the upper and lower arm act in the same manner by injecting (or consuming) power ( 9), [START_REF] Soong | Evaluation of emerging modular multilevel converters for BESS applications[END_REF]. Due to [START_REF] Vasiladiotis | Modular Multilevel Converters with Integrated Split Battery Energy Storage[END_REF], a power transfer between legs is feasible.

Vertical power transfer: Arm currents within a leg are in opposition of phase (1), [START_REF] Kirschen | Fundamentals of power system economics[END_REF]. By utilizing an alternating current common to a leg, [START_REF] Maharjan | A transformerless energy storage system based on a cascade multilevel PWM converter with star configuration[END_REF], a power transfer between the upper and the lower arm is possible ( 9), [START_REF] Soong | Evaluation of emerging modular multilevel converters for BESS applications[END_REF]. The optimal power transfer is done when it is phase aligned with one of the two arms. This freedom to control the dispersion of the internal energy allows unequal ESS integration. In this paper, if an MMC arm has energy ES-SMs, all their capacitors are connected to an ESS unit through a dc-dc converter, see Fig. 2. This configuration allows a full decoupling of the energy management of the ESS from the capacitor voltage and to optimize the design of the solution. In the following section, the case where all MMC modules have an ES-SM and the cases depicted in Fig. 3 will be studied. A term P u,l ESS must be added to ( 9), ( 10) for arms with ES-SMs. It stands for the additional average power provided into the SM capacitors of the respective arms by the ES-SMs.

C. Analysis on submodule capacitor ripples

Since the arm currents are not identical with split ESS, the change in current imposes more stress on semiconductors [START_REF] Henke | Balancing of modular multilevel converters with unbalanced integration of energy storage devices[END_REF]. Similarly, the rectified current that flows across the SM toward the capacitor, i u,l smx , will change, see Fig. 2. It can be simply expressed in [START_REF] Trintis | A new modular multilevel converter with integrated energy storage[END_REF], with m u,l x (t), the sinusoidal modulation function, and M the modulation index. Note, this approach does not consider the switching contribution.

i u,l smx (t) = m u,l x (t)i u,l x (t) (11)
m u,l x (t) = 1 2 ± M 2 sin(ωt) M = 2 V ac V dc
Similarly, this examination considers a steady state operation mode of the converter. It supposes the circulating currents are calculated in a way that it balances the direct current necessary for the power exchange. Then, a unity power factor is assumed. By substituting (1), ( 2) into [START_REF] Trintis | A new modular multilevel converter with integrated energy storage[END_REF], the evolution of the current that flows towards the SM capacitors, i u,l smx , is derived. It is composed of a dc component which equals zero in steady state without any grid disturbances. Otherwise SM capacitors energy will drift. The remaining terms are intrinsic oscillations at the line frequency and twice the line frequency. For a sake of clarity, they were simplified into two trigonometric functions [START_REF] Errigo | Optimal supercapacitor pack sizing for modular multilevel converter with integrated energy storage system[END_REF].

ĩu,l smx (t) = (a u,l 1 ) 2 + (b u,l 1 ) 2 sin ωt -arctan b u,l 1 a u,l 1 + (a u,l 2 ) 2 + (b u,l 2 ) 2 sin 2ωt -arctan b u,l 2 a u,l 2 ĩu smx (t)                            a u 1 = - I dc M 6 + I ac cos(φ) 4 - I dc circx 2 + I ac circx cos(ψ) 2 b u 1 = I ac sin(φ) 4 + I ac circx sin(ψ) 2
a u 2 = I ac M sin(φ) 8 + I ac circx sin(ψ) 4 b u 2 = - I ac M cos(φ) 8 - I ac circx M cos(ψ) 4 (12) ĩl smx (t)                            a l 1 = I dc M 6 - I ac cos(φ) 4 + I dc circx 2 + I ac circx cos(ψ) 2 b l 1 = - I ac sin(φ) 4 + I ac circx sin(ψ) 2
a l 2 = I ac M sin(φ) 8 - I ac circx sin(ψ) 4 b l 2 = - I ac M cos(φ) 8 + I ac circx M cos(ψ) 4
In this paper, the assumption that all the ripples are buffered by the SM capacitor is made. Consequently, the current that flows through the SM capacitors, ĩu,l cx , is given as follows [START_REF] Konstantinou | A hybrid modular multilevel converter with partial embedded energy storage[END_REF].

ĩu,l smx (t) = ĩu,l cx (t) (13) īu,l smx = i es (t)
The values of the ac and dc currents can be calculated as a function of the ac and dc powers and considering the power flow within the converter [START_REF] Henke | Balancing of modular multilevel converters with unbalanced integration of energy storage devices[END_REF]. Then the circulating currents were deduced from ( 9), [START_REF] Soong | Evaluation of emerging modular multilevel converters for BESS applications[END_REF].

P ac = P dc + P ess (14)
Because capacitor voltage ripple is a driving factor for determining the size of the SM capacitor, an estimation is provided by integrating [START_REF] Errigo | Optimal supercapacitor pack sizing for modular multilevel converter with integrated energy storage system[END_REF]. In Fig. 4, capacitor current and voltage waveforms are shown during normal inverter operation. The derived equation indicated that the SMs of each arm experience various voltage ripple if an uneven power distribution occurs.

III. UNBALANCED STORAGE INTEGRATION

This section provides a comparison among five configurations, where ESS is differently assigned within the MMC, using the derived relations of Section II. The values of the circulating currents are calculated using ( 9), [START_REF] Soong | Evaluation of emerging modular multilevel converters for BESS applications[END_REF]. It investigates the impact on the arm currents and SM capacitor sizes in the arms with and without ES-SMs, see Fig. 5 and Fig. 6. A 1 GW converter is considered [START_REF] Peralta | Detailed and averaged models for a 401-level MMC-HVDC system[END_REF]. In inverter mode, the dc power is kept constant while the power injected by the ESS, P ess , varies from zero to the nominal power of the converter according to the deviation in AC power. By the same way in rectifier mode, the ac power is unchanged. A positive (reciprocally a negative) value of P ESS means the ES-SMs have to generate (reciprocally absorb) power.

A. Integrating ESS in one or two legs

Connecting ESS to one leg (orange lines) rather than to two legs (yellow lines) leads to higher peak and RMS currents in the phase with ES-SMs. No matter the operating point of the converter, the phases without ES-SMs have the same behaviour. Therefore, yellow and orange lines are mixed up. The explanation is made for one phase.

Considering phase a has ES-SMs, a power transfer between individual phase legs is required. The dc part of the circulating current is used to transfer energy, I dc circx . Because the power injected in phase a must be evenly distributed among arms, the standard legs b and c receive an equal amount of power (i.e I dc circ b = I dc circc = -I circa /2). Note those currents only cause a positive or negative dc offset depending on the legs. In rectifier mode, the phases without ES-SMs experience no change. The ac input power remains fixed and the circulating current compensates the changes in dc current from the dc bus to maintain the dc component in each individual phase leg constant. As a result, capacitor voltage ripple also does not change.

When increasing the power the ESS has to absorb in inverter mode, standard phase legs have less contribution. The dc offset leads to a zero current in these phases while all the dc current from the dc grid, I dc , must be supported by the phase with ES-SMs.

B. Integrating ESS in one side of the converter

By integrating ESSs in one side of the converter (purple line), the power transfer within each leg is done by the ac part of the circulating current, i ac circx (t). A phase shift of ψ = 180 • is assumed to maximise the power transfer without any residual reactive power ( 9), [START_REF] Soong | Evaluation of emerging modular multilevel converters for BESS applications[END_REF].

Considering an inverter mode, if the ac output rises (P ESS > 0), the ac component of the arm current increases. However, the circulating ac current is phase aligned with the top arms and in opposition with the bottom arms. Those currents tend to add each other in the upper arms and cancel them in the lower arms. If the ac power decreases (P ESS < 0), the dc current that power SMs from the dc grid is unchanged and is still equally distributed among the phase legs. But, in the lower side, the circulating current compensates the missing part of the ac current. It explains why the arms without ES-SMs expect no changes in this mode. Finally, it also decreases the RMS current in the upper side before returning to nominal value when the whole input power is absorbed. Even though capacitors voltage ripple follows a same trend, the voltage deviation is more important. A value close from zero is also observed for P ESS ≈ -0.35 p.u. It corresponds to a situation where the intrinsic oscillations of the converter and the extra oscillations induced by the circulating current erase each other in SM capacitor current, [START_REF] Errigo | Optimal supercapacitor pack sizing for modular multilevel converter with integrated energy storage system[END_REF] In rectifier mode, the lower arms have to be considered now. Roles are reversed. With increasing P dc (i.e P ESS ), the additional circulating ac current leads to a slight drop in upper arm RMS current and a decrease in capacitor voltage ripple. However, it is counterbalanced in the lower arms without ES-SMs. The additional circulating ac current is added to the existing arm ac component and so increases the resulting RMS arm current and capacitor voltage ripple magnitudes.

C. Integrating ESS in one arm

This situation is a combination of a power transfer among phase legs and between arms within the phase with ES-SMs. Both the dc and the ac part of the circulating current are needed. However, no vertical power transfer must occur in the phase legs b, c which contain no ES-SMs. By controlling the circulating current in these phases in quadrature with the respective lower and upper arm voltages, only reactive power can be transferred whilst ( 6) is still respected [START_REF] Henke | Balancing of modular multilevel converters with unbalanced integration of energy storage devices[END_REF].

Results show that this configuration increases significantly the current and voltage ripple values as in the arm with ES-SMs as in the opposite arm (black line) or the remaining legs (black dotted line) without ES-SMs. Large circulating currents are required. It is also the case where the load distribution differs the most within the converter. Fig. 8 represents the SM capacitor currents within the MMC arms when only one arm is equipped with ES-SMs. It clearly shows this disparity. To verify the previous analysis, an MMC reduced order average model with a storage function was developed in Matlab/Simulink [START_REF] Antonopoulos | On dynamics and voltage control of the modular multilevel converter[END_REF]. Each MMC arm is represented by an ideal SM with an equivalent capacitor. It is assumed that all the SM capacitors are strictly identical. Consequently, the voltage at its terminal, Σu u,l cx , is the sum of all the SM capacitor voltages. All the SMs are modelled by means of a state variable model with an ESS connected to it that behaves as a current source. This latter can be activated or not depending on the required configuration. The dc and the ac grids are modelled as ideal voltage sources.

This model allows to decouple the MMC into two ac and dc sub-systems that can be controlled independently. The low level control of the MMC, which aims to select the SMs that should be inserted to synthesize the desired arm voltage, is not taken into account [START_REF] Zama | A comparative assessment of different balancing control algorithms for modular multilevel converter (MMC)[END_REF]. Only the high level control is considered. An overview of the control scheme is depicted in Fig. 9. The control structure is based on an inner and an outer loop.

The inner loop regulates the grid currents within the converter. Considering that an MMC is a 3-phase system from the ac point of view, the regulation of the ac currents is achieved in a dq rotating frame using a Phase Lock Loop (PLL) to follow the grid voltage. While the dc current are controlled in a classical stationary frame. The outer loop helps to control the inputs of the inner layer but also the total internal energy stored, W M M C . In order to regulate the energy distribution within the converter, three different energy controllers are implemented.

Global energy management: An MMC can be seen as an energy buffer whose the energy variation is driven by the power mismatch between the dc and ac side [START_REF] Judge | Modular multilevel converter with partially rated energy storage with intended applications in frequency support and ancillary service provision[END_REF]. A controller focus on the overall energy content is needed to compensate the error before the energy level becomes unsatisfactory. Phase energy balancing control: As stated before, the internal energy stored should be well distributed among the six arms. Consequently, each leg must firstly store one third of the total energy. A controller is required to ensure adequate energy level among legs and enable horizontal power transfer.

Inter-arm energy balancing control: During one period the upper and lower arm inherently exchange energy. However, the energy deviation between the two arms must remain zero. To maintain the power balance within each individual phase leg, a second controller is necessary to allow vertical power exchange between the upper and the lower arm.

Finally, it has been chosen to regulate the desired energy level of the MMC by adjusting the ac power and let the dc power track its reference.

Because of the cascaded control structure of the converter, the inner loop must be faster than the outer loop to have enough time to converge. The different PI controllers have been designed to ensure this minimum response time and make the two loops dynamically independent. More details on the model and the control variables are available in [START_REF] Shinoda | Virtual capacitor control: Mitigation of DC voltage fluctuations in MMC-based HVDC systems[END_REF]. An additional loop was added to control the power exchanged by the ES-SMs. On the basis of a measure of the equivalent SM capacitor voltage, Σu u,l cx , plus the power mismatch between the dc and ac grids, a current reference is provided to the dc-dc converter.

Table I gives specifications of the MMC converter. Simulations results (Fig. 10) are those of an MMC with only the upper arm of phase a equipped with ES-SMs (Fig. 3(c)) in inverter mode. This configuration has been chosen to show the aptitude of the converter to achieve both vertical and horizontal power transfer. A 100 MW energy storage power is considered. During the simulations, SM voltage is properly controlled around a mean value of 1600 V as shown Fig. 10(d)(e). The converter is able to follow the change of operating point (Fig. 10(a)). At normal load condition, the converter is well balanced and no circulating current is required. As a results arm currents (and capacitor voltage ripple) are strictly identical among arms.

An example of an MMC in overload operation is shown from t = 3s to t = 6s. The converter compensates an increase of power at the ac side. During this time interval, the arm current in the upper arm in phase a, i u a , increases more than others but there is also a slight rise in the remaining legs as observed Fig. 10(b). As the overall arm currents goes up, the voltage ripple on the SM capacitors changes. The peak to peak deviation becomes more significant in the upper arm with ES-SMs, u u ca , and less restrictive in the opposite arm, u l ca (Fig. 10(d)(g)).

Then, from t = 9s to t = 12s, the converter has to absorb an excess of power via the ES-SMs. During this cycle, the RMS current in the arm with storage function drops, i u a (Fig. 10(b)(h)) just as the capacitor voltage ripple, u u ca (Fig. 10(d)(i)). It can be noted that the current in the opposite arm increases, i l a , just like the capacitor voltage ripple, u l ca . While the remaining legs keep a behavior close as in normal operation mode. In a general manner, the MMC performs as expected Fig. 5. Fig. 11 shows the comparison of the capacitor voltage obtained by the simulation in the upper arm of phase a during overload condition and the one derived analytically in the previous section. As it can be observed, the estimated waveform matches with the simulation. The previously derived analytic expressions have been validated for all the case studies. These formulae can help for designing an MMC with ESSs in a future work.

V. CONCLUSION AND OUTLOOKS

In this paper, the integration of split storage within an MMC for ancillary services have been discussed. The concept of using circulating currents to ensure the proper energy balancing of the converter have been described. Simulation results have been presented to demonstrate its feasibility and to validate the theoretical analysis. The worst case, when only one arm of the converter is equipped with ES-SMs, has been chosen to demonstrate the feasibility.

It has been shown that RMS arm currents and capacitor voltages become the limiting factors when trying to reduce the number of SMs with ESSs. A one size fits all solution does not exist. Selecting the right configuration mainly depends on the application but above all of the power conversion system that will be implemented between the ESS unit and the SM capacitor.

However, it can be judicious to try to avoid the use of circulating current. And certainly, the concept of an arm with a fraction of SMs [START_REF] Judge | Modular multilevel converter with partially rated energy storage with intended applications in frequency support and ancillary service provision[END_REF] can be interesting. Nonetheless, it causes additional challenges such as the need of SMs with different capacitors sizes because of different energy deviations experienced.

Fig. 1 .

 1 Fig. 1. Three-phase Modular Multilevel Converter topology with half bridge SM

Fig. 2 .

 2 Fig. 2. Structure of an Energy Storage Submodule (ES-SM)

Fig. 3 .Fig. 4 .

 34 Fig. 3. MMC with ESS connected to (a) one side, (b) one leg, (c) one arm of the converter (Note an MMC with two ES-SMs legs is not depicted because is very similar to operating an MMC with one ES-SMs leg)

Fig. 5 .

 5 Fig. 5. RMS arm current, Capacitor voltage ripple in the converter assuming unequal ESS distribution -Inverting dc Power

-

Figure. 7 Fig. 7 .

 77 Fig. 7. Submodule capacitor current for an MMC with ES-SMs in the upper side of the converter and P ESS = -0.35 p.u during inverter operation

Fig. 8 .

 8 Fig. 8. Submodule capacitor current for an MMC with ES-SMs in the upper arm of phase a of the converter and P ESS = 0.2 p.u during inverter operation

Fig. 9 .

 9 Fig. 9. General schematic diagram of the high level control scheme for a MMC with ESSs

Fig. 10 .

 10 Fig. 10. Modular Multilevel Converter with ESSs connected to the upper arm in phase A. From top to bottom : (a) Difference between the AC and DC side powers. (b) Upper arm currents. (c) Lower arm currents. (d) Upper arm SM voltages. (e) Lower arm SM voltages. (f) Zoom on lower arm currents. (g) Zoom on lower arm SM voltages (h) Zoom on upper arm currents. (i) Zoom on upper arm SM voltages

Fig. 11 .

 11 Fig. 11. Comparison of the estimation of the capacitor voltage with simulation results

) without ES-SMs -Capacitor voltage ripple

							Arm(s) with ES-SMs -RMS current
			4					ESS in all the SMs
	(p.u)	3					ESS in one leg ESS in two leg
	Current	1 2					ESS in one side ESS in one arm
			-1 0	-0.8	-0.6	-0.4	-0.2	0	0.2	0.4	0.6	0.8	1
								P ESS (p.u)
							Arm(s) without ES-SMs -RMS current
			4
	(p.u)	3
	Current	1 2
			-1 0	-0.8	-0.6	-0.4	-0.2	0	0.2	0.4	0.6	0.8	1
								P ESS (p.u)
						Arm(s) with ES-SMs -Capacitor voltage ripple
	(p.u)	1.5
	ripple		1
	Voltage	0.5
			-1 0	-0.8	-0.6	-0.4	-0.2	0	0.2	0.4	0.6	0.8	1
								P ESS (p.u)
						Arm(s
	(p.u)	1.5
	ripple		1
	Voltage	0.5
			-1 0	-0.8	-0.6	-0.4	-0.2	0	0.2	0.4	0.6	0.8	1
								P ESS (p.u)

ACKNOWLEDGMENT

This work was supported by a grant overseen by the French National Research Agency (ANR) as part of the "Investissements d Avenir" Program (ANE-ITE-002-01).