Integration of regulation in Multi-Terminal Direct Current grids design

IN

DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2017 ,

Integration of regulation in Multi- Terminal Direct Current grids design

LÉO DALMAR

KTH ROYAL INSTITUTE OF TECHNOLOGY

EG230X Degree Project in Electric Power Systems, Second Cycle

Integration of regulation in

Multi-Terminal Direct Current grids design

L´eo Dalmar

Acknowledgements

I would like to thank, first of all, L´ea and my close family for their infinitely valu- able caring support. I would like to thank all people who provided their support to this project within SuperGrid Institute: Serge Poullain for his close guidance;

Bruno Luscan, for his contribution to the project proposal, Boussaad Isma¨ıl, for his

availability and his great help; Vincent Debusschere and Swann Gasnier, for their

reliable advises; and every single person who contributed to the good work atmo-

sphere. I would like to thank people at KTH involved in the project : Dina Khastieva

for supervising the project and providing valuable comments which helped me to

give a suitable form to the presentation of my work and Professor Mikael Amelin,

for having accepted to be the examiner of this master thesis.

Abstract

The supergrid denotes a transmission grid development option at European scale based on large power corridors enabling to transport electricity from large pro- duction centers (such as large o ffshore wind farms) to large consumption centers.

Technico-economic studies show that the development of supergrids could provide overall benefits in terms of : economic welfare, security of supply and integra- tion of renewables at European scale. However, some regulatory issues, such as non-harmonized financial regulatory models for grid investments and rules of co- ordinated operations among transmission system operators, are obstacles to real projects implementation. In consequence it is of interest for the designer of grid technologies to integrate regulation early in the design process. The overall ob- jective of the thesis it to propose a methodological approach enabling to integrate regulatory issues into design process. First, relevant regulatory issues are identified and classified. Second, a design method (method of technico-economic evaluation of grid technologies) which addresses selected regulatory issues is proposed. Last, the proposed design method is applied on a study case : the design of a power trans- mission corridor.

First regulatory issue identified thanks to literature is that current planning meth-

ods (methods of assessment of expansion projects) do not measure properly the

overall benefits of supergrids. As a result, they do not make possible the harmo-

nization of financial regulatory models and eventually the actual development of

supergrids. Second regulatory issue identified is the high uncertainty about future

operating rules for two reasons : some current rules are not applicable to supe-

grids operations and current security management methods are cost-ine fficient in

a context with several transmission system operators. A general alternative design

method consistent with future standard planning methods is chosen to address first

regulatory issue. That method is a risk-based cost minimization problem where an

optimal trade-o ff between technical costs and reliability costs is pursued by sim-

ulation of the power system. It relies on a probabilistic description of operating

conditions. The recommendation formulated regarding the second regulatory issue

is that the application of the general design method to particular cases requires a

case-per-case assessment of operating rules uncertainty. The case study illustrates

the application of the proposed design method. First, relevant operating mecha- nisms are identified (system reduction). Then, system cost functions are expressed based on the reduced power system representation. Additionally, simulation models are developed, implemented (on Python) and used to compare several power trans- mission corridor architectures.

In conclusion, a risk-based method consistent with standard planning methods

current development seems the most appropriate design method to be used and un-

certainty about future operating rules should be taken into account while applying

the general design method. The reports shows that such a risk-based method en-

ables to discriminate between technologies. As a result, it seems a suitable decision

tool for the supergrid designer.

Sammanfattning

Supern¨at betecknar ett alternativ f¨or utveckling av transmissionsn¨atet på en eu- ropeisk skala baserat på st¨orre kraftkorridorer som m¨ojligg¨or transport av elkraft från stora produktionscentra (som stora havsbaserade vindkraftparker) till stora kon- sumtionscentra. Utvecklingen av supern¨at skulle enligt tekno-ekonomiska studer kunna vara f¨ordelaktigt ur en ekonomisk synvinkel, smat f¨or leveranss¨akerhet och integration av f¨ornybar energi på en europeisk skala. Det finns dock frågest¨all- ningar kring regelverket, t.ex. brist på harminisering i finansiella regelverk f¨or n¨atin- vesteringar och koordinering mellan transmissionssystemoperat¨orer, som utg¨or hin- der f¨or att f¨orverkliga projekt. Det ¨ar d¨arf¨or av intresse vid utformningen av n¨at att ta h¨ansyn till regleringen tidigt i designprocessen. Den fr¨amsta måls¨attningen med detta examensarbete ¨ar att f¨oreslå en systematisk metod som g¨or det m¨ojligt att inte- grera regelverksfrågor i designprocessen. Till att b¨orja med identifieras och klassifi- ceras relevanta frågest¨allningar kring regelverket. D¨arefter f¨oreslås en designmetod (metoden f¨or tekno-ekonomisk utv¨ardering av n¨attekniker) som tar h¨ansyn till ut- valda regelverksfrågor. Till sist till¨ampas den f¨oreslagna metoden i en fallstudie:

design av en transmissionskorridor.

Den f¨orsta regelverksfrågan som identifieras i litteraturstudien ¨ar att de nu-

varande planeringsmetoderna (metoder f¨or utv¨ardering av utbyggnadsprojekt) inte

speglar den total nyttan med supern¨at. D¨arf¨or m¨ojligg¨or de ej en harmonisering

av de finansiella regelverken och den faktiska utbyggnaden av supern¨at. Den andra

regelverksfrågan som identifierats ¨ar att de framtida driftkostnaderna ¨ar h¨ogst os¨akra

av två sk¨al: vissa av de nuvarande reglerna går ej att till¨ampa på driften av supern¨at

och de nuvarande metoderna f¨or att hantera drifts¨akerheten ¨ar inte kostnadse ffek-

tiva i sammanhang då man har flera transmissionssystemoperat¨orer. F¨or att l¨osa det

f¨orsta problemet v¨aldes alternativ generell metod som ¨ar anpassad till framtida stan-

dardplaneringsmetoder. Metoden ¨ar ett riskbaserat kostnadsminimeringsproblem,

d¨ar en optimal avv¨agning mellan tekniska kostnader och tillf¨orlitlighetskostnader

s¨oks genom att simulera elsystemet. Metoden bygger på en stokastisk beskrivn-

ing av driftf¨orhållandena. Rekommendationen f¨or den andra frågan ¨ar att då den

generella metoden till¨ampas på ett specifikt fall så kr¨avs det en bed¨omning från fall

till fall av os¨akerheten i driftreglerna. Fallstudien illustrerar hur den f¨oreslagna de-

signmetoden kan till¨ampas. F¨orst identifierar relevanta driftmekanismer (systemre- duktion). D¨arefter uttrycks systemkostnasfunktionerna basxerat på den reducerade representationen av systemet. Dessutom utvecklas simuleringsmodeller, som im- plementeras (i Python) och anv¨ands f¨or att j¨amf¨ora flera utformningar av en trans- missionskorridor.

Avslutningsvis, den l¨ampligaste designmetoden f¨orefaller att vara en riskbaserad metod i enlighet med den nuvarande utvecklingen inom standardplaneringsmetoder.

Dessutom b¨or os¨akerhet om framtida driftregler tas i beaktning då den generella de-

signmetoden till¨ampas. Rapporten visar att en sådan riskbaserad metod g¨or det

m¨ojligt att s¨arskilja tekniska l¨osningar. F¨oljaktligen f¨orefaller metoden vara ett

l¨ampligt beslutsverktyg vid design av supern¨at.

Contents

Acknowledgements iii

Abstract v

Sammanfattning vii

Introduction 1

1 Background and literature review . . . . 1

2 Motivation of the project within SuperGrid Institute . . . . 3

3 Objectives . . . . 4

1 Regulation and coordination in MTDC grids 5 1 General link between regulation and design . . . . 5

2 Reference planning method choice . . . . 8

3 Reference planning method application . . . . 12

2 Reliability management method for MTDC architectures evaluation 15 1 Architectures Evaluation Problem (AEP) principle . . . . 15

2 Security issues in AEP . . . . 16

3 System cost function in AEP . . . . 17

4 Formulation and application approach of AEP . . . . 19

3 Transmission corridors architectures : System reduction and models development 21 1 Context and objectives . . . . 21

2 System reduction . . . . 23

3 System power functions . . . . 30

4 System cost functions . . . . 34

5 System states graph models . . . . 37

6 System states stochastic generation model . . . . 41

4 Transmission corridors architectures : Models implementation and sim-

ulation results 43

1 Simulation set-up . . . . 43 2 Test architecture simulation . . . . 45 3 AEP application . . . . 52

Conclusion 61

1 Summary . . . . 61 2 Perspectives and limits . . . . 63

Bibliography 66

Appendix 67

I Graph Theory and maximum flow algorithm . . . . 67

List of Figures

1.1 Transmission grid activities . . . . 6

1.2 Transmission grid objectives . . . . 9

1.3 Synergies at Sea project infrastructure . . . . 13

3.1 DC vs AC power transmission investment costs (from [1]) . . . . . 22

3.2 Symmetrical monopole . . . . 25

3.3 Symmetrical monopole nominal mode . . . . 25

3.4 Grounded bipole . . . . 26

3.5 Grounded bipole nominal mode . . . . 26

3.6 Bipole MR . . . . 27

3.7 Bipole MR nominal mode . . . . 27

3.8 Bipole MR in degraded state (one HV cable unavailable) . . . . 28

3.9 Model structure . . . . 38

3.10 Symmetrical monopole nominal graph . . . . 39

3.11 Virtual-converter edge . . . . 39

3.12 Converter-cable edge . . . . 40

3.13 Cable-cable edge . . . . 40

3.14 Symmetrical monopole degraded graph . . . . 40

3.15 Grounded bipole nominal graph . . . . 41

4.1 Minimal feasible n in P

variation range - m =3 . . . 45

4.2 Simulation process flowchart . . . . 46

4.3 Architecture graph : NetworkX Viewer screenshot . . . . 47

4.4 Operating power P

distribution . . . . 49

4.5 Maximal power P

distribution . . . . 49

4.6 Power duration curves . . . . 50

4.7 Total energy transfer E

repartition over 100 simulation cycles . . 51

4.8 Architectures compared . . . . 53

4.9 Non-oriented graph example . . . . 67

4.10 Graph notions . . . . 68

List of Tables

3.1 Nominal maximal flow extended expression . . . . 29

3.2 Solution installed capacity expression . . . . 29

3.3 Architecture unit index . . . . 30

3.4 Nominal dimensioning N-1 maximal power transfer . . . . 33

4.1 Components reliability data . . . . 44

4.2 Architectures total energy transfers comparison . . . . 52

4.3 Preventive actions cost functions numerical values . . . . 54

4.4 Availability numerical values . . . . 54

4.5 Availability di fferences between redundant and minimal architectures 55 4.6 E ffect of N-1 criterion - Coefficient α

numerical values . . . . . 55

4.7 N-1 criterion e ffect differences between redundant and minimal ar- chitectures . . . . 56

4.8 Architecture cost functions numerical values . . . . 57

4.9 C function value di fferences between redundant and minimal archi- tectures . . . . 57

4.10 Total system cost functions numerical values . . . . 58

Introduction

1 Background and literature review

The supergrid is often seen as a solution to achieve o fficial European objectives out- lined in the third Energy Package relating to the massive integration of renewables.

Supergrids rely on High Voltage Direct Current (HVDC) technologies based on Voltage Source Converters (VSC). Voltage ratings reach more than 500 kilovolts.

Moreover, VSC are suitable for multi-terminal (MT) applications such as the super- grid because they deliver a constant DC voltage. The supergrid is then a concept of MT HVDC grid

. Moreover, VSC enable the control of power flows by controlling current. That is a technical advantage that could make possible bulk power transmis- sion from remote production centers to load centers without causing supplementary congestion in AC system. Nevertheless, there are also technical challenges such as system protection. Indeed, for this issue, there are new speed requirements due to fast fault propagation in low impedance DC systems. That is an example of tech- nical challenges among others. Furthermore, there are regulatory obstacles to be overcome.

A general identification of some regulatory obstacles is made in [2]. Several questions are raised: who should operate the grid? Which financial regulatory model should be used for investments? The lack of clear and uniform rules are an obstacle to power system stakeholders coordination and eventually supergrid achievement. Technical challenges are identified separately in the paper. Concern- ing supergrid concept applications, o ffshore grids are typical. They consist in the connection of several o ffshore wind farms to shore. The North Sea Grid project study ([3]) and a study sponsored by European Commission about “regulatory mat- ters concerning the development of the North Sea o ffshore energy potential” ([4]) investigate regulatory barriers for di fferent offshore grid real projects. The latter study uses an approach which consists of three steps:

- listing barriers : E.g. support schemes, grid access responsibility, priority grid

1In the study, we generally talk about Multi-Terminal Direct Current (MTDC) grids.

connection, etc;

- splitting barriers into two categories: barriers addressed at European level and barriers not addressed;

- proposing new regulation implementation plan.

Regulatory issue is tackled on the case-per-case basis in the two latter studies.

For its part, the e-Highway 2050 project ([5]) has a di fferent approah: the super- grid is seen as one possible grid development option at European scale among other options. Indeed, it explores several grid development options by 2050. On the par- ticular issue of regulation, it proposes a “governance model of the European trans- mission network with cross-border impact”, as well as an implementation roadmap ([6]). Governance issues are split into five categories:

- transmission network expansion design;

- ownership of new transmission capacity with a cross-border impact;

- financing of investments;

- allocation of costs of grid development;

- technical and market operation of transmission networks and related system services.

The target governance model developed by e-Highway 2050 project is integrated, detailed and seeks to be comprehensive: a large amount of notions and mechanisms, interrelated each others and complex are included.

In this manner, literature highlights that regulatory issues have an obvious influ- ence on actual power system development. Regulatory issues specific to supergrids are outlined in general terms in [2]. They are confirmed and detailed in surveys based on real o ffshore grid projects ([3], [4]). An opposite approach of regulatory issues (not specific to supergrids, comprehensive and integrated) is proposed by e- Highway 2050 project ([5],[6]).

The purpose of this thesis is not to propose solutions to solve regulatory issues.

Rather, it is to understand to what extent regulatory issues should be taken into

account at grid design level. Therefore the overall challenge is to draw the link

between regulatory issues and grid design activity. However, existing literature is

either too specific (project-based surveys) or too complex (e-Highway 2050 gover-

nance model) to draw that link. Therefore, a prerequisite for the study is a high-level

understanding of regulations interactions. That working phase was a process of:

- Identification of relevant documents such as: o fficial documents (regulations, recommendations), technical documents (scientific papers and institutional technical reports about regulatory mechanisms) and European projects deliv- erables (including e-Highway 2050 project);

- Identification of the mechanisms involved in regulatory issues mentioned pre- viously;

- Synthesis of findings.

It should be noted that all documents cannot be comprehensively listed in this report. Nevertheless, conclusions of chapters 1 and 2 are the results of the synthetis- ing e fforts.

2 Motivation of the project within SuperGrid Insti- tute

The project was performed at SuperGrid Institute, using their human and material resources. It was designed to meet specific objectives defined prior to the project within the institute.

SuperGrid Institute carries out research and development on future power trans- mission systems based on a combination of alternating current (AC) and direct cur- rent (DC) transmission technologies. The research is focused on MT HVDC grids for o ff-shore or continental transmission. In particular the research program “Ar- chitectures of the supergrid” aims to provide functional requirements for HVDC grid components. The latter outputs are integrated in other research programs de- sign studies of grid components. One of the objectives of the program is to per- form technico-economic evaluations (hereafter evaluations) of supergrid architec- ture principles (hereafter architectures) such as grid topologies (meshed or radial) or grid technologies (AC or DC). Architectures are compared by mean of a cost- benefit analysis (hereafter CBA). Previous activities within the research program

“Architectures of the supergrid” identified drivers (for) and barriers (against) the

achievement of the supergrid. On the one hand, benefits mentioned in the previous

paragraph were identified as drivers while regulatory issues were simply identified

as barriers. Hence the need to understand the link between regulatory issues and

SuperGrid Institute design activity.

3 Objectives

The overall objective of the thesis project (hereafter study or project) is to propose a methodological approach enabling to explicitly integrate regulatory elements into a design method, i.e. a method of technico-economic evaluation of supergrid tech- nologies. That overall objective can be subdivided into three sub-objectives listed below :

1) Identify, classify and select suitable regulatory issues (first chapter)

2) Propose a design method which addresses identified regulatory issues (second chapter)

3) Illustrate the proposed design method on a study case: the design of a trans- mission corridor (third chapter and fourth chapter)

As mentioned above, the main objective of the thesis relates to the establish-

ment of the link between grid design activity and regulatory issues. As a result, the

study case aims to provide an insight about how to applicate the design method to a

particular design case. Then, a lot of simplifying assumptions are made.

Chapter 1

Regulation and coordination in MTDC grids

1 General link between regulation and design

1.1 European regulation

Definition and complexity

The term regulation can designate the action of controlling something by means of rules as well as the rule itself. Both definitions are relevant for European power sys- tem applications. Indeed an independent national regulatory authority is designated in each member state as required in Article 35(1) of Directive 2009 /72/EC of the European Commission. Generally, national regulatory authorities have a power of:

decision, approval and authorisation at national level although their roles are di ffer- ent from country to country. They act together with (among other actors) national transmission system operators (TSOs hereafter) to develop national rules relating to transmission grids. Other stakeholders intervene in the rules evolutions process at European level: the European Commission (EC), the Agency for the Cooperation of Energy Regulators (ACER) and the European Network of Transmission System Operator for Electricity (ENTSO-E) are the predominant ones. As a result, there exists a massive amount of o fficial texts both at national and European levels. But the complexity of regulation is also due to the evolution dynamics that is a highly uncertain process.

Main legal grounds

The third energy package (2009) gathers regulations and directives aiming to foster

completion of an internal energy market (electricity and gas) within the European

Union. Regarding electricity market, it includes:

- Regulation (EC) 713 /2009 of the European Parliament and the council of 13 july 2009 establishing an Agency for the Cooperation of Energy Regulators (ACER);

- Regulation (EC) 714 /2009 on the conditions for access to the network for cross-border exchanges in electricity;

- Directive 2009 /72/EC concerning common rules for the internal market in electricity.

Network codes that ensue from the third energy package are continuously evolv- ing. They are jointly developed mainly by national transmission system operators through ENTSO-E and the ACER. They are eventually published by the European Commission. We don’t list network codes in this document.

Last, regulation (EC) 347 /2013 (TEN-E regulation) on guidelines for trans- European energy infrastructure completes the legal grounds of a pan-European power system development.

1.2 European regulation application

Transmission grids activities

A simple classification of transmission grid activities is proposed on figure 1.1. The application of European regulation is then detailed for each activity field.

Figure 1.1: Transmission grid activities

Planning

Transmission grid planning is a task performed at several levels and by di fferent

actors. At European level, ENTSO-E is tasked by the European Commission “to

adopt a non-binding Community-wide ten-year network development plan [. . . ],

including a European generation adequacy outlook every two years [7]. The cor- responding report (hereafter TYNDP) edited by ENTSO-E aims to provide a pro- active approach for grid development by making forecasts on future demand and generation. It assesses “candidates” projects identified in six regional investment plans by mean of a standard CBA ([8]) as required by the European Commission in TEN-E regulation. The TYNDP is developed in parallel of national development plans published by national TSOs. Following the TYNDP, the European Commis- sion establishes a list of Projects of Common Interest (hereafter PCIs) that is “part of the latest available 10-year network development plan for electricity, developed by ENTSO for electricity” ([9]). Projects must however fall under certain criteria stated in TEN-E regulation to be eligible to the list of PCIs. The PCIs get from this procedure an advantageous legal status in the next stages of development.

Construction

Once a project belongs to the PCIs list, its implementation procedure is subject to certain rules set out in the third energy package that provides a framework for rights and duties of di fferent actors within the procedure: project promoters, national reg- ulation authorities (NRAs), ACER, national TSOs and public. The permit granting process is among the procedures relating to the implementation of a project of com- mon interest. That procedure is rather complex and requires the coordination of national stakeholders (NRAs, TSOs). TEN-E regulation provides the legal frame- work for coordination between national stakeholders, the rules for public participa- tion and the time constraints at each procedure stage. Note that national regulation applies within the European framework, increasing stakeholders interactions com- plexity.

We put aside the construction phase in this study. Indeed, although permitting procedures may be facilitated by some design choices for social and environmental acceptability reasons in particular, these aspects are not investigated.

Operation

Schematically, network codes define operational rules: on the market side, on the

grid side and at the border. The European power system gets more and more inter-

connected and consequently more complex. In addition, the power system develop-

ment follows technical and technological advances. As a result, European network

codes evolve rapidly. But specific national rules generally apply. Grid architectures

must obviously comply with the di fferent operational constraints, which already

naturally play a major role in grid design activity.

1.3 European regulation limits

In the description of European regulation that runs transmission grid activities (sec- tion 1.2), the predominance of national decisions was emphasized. As a result, European legal grounds previously presented (section 1.1) are not su fficient to un- derstand current and future interactions between grid actors, for at least two reasons.

On the one hand, miscellaneous national practices play a major role in transmission grid activities and worth being studied as well. On the other hand, today’s regulation will evolve in a way that is not fully predictable. Hence the di fficulty to go beyond the identification regulatory barriers that “only” highlights the di fference between national regulatory logics.

1.4 Link between regulation and design

Power system planning activity consists in selecting future expansion projects while power system design consists in selecting technologies that compose these projects.

Eventually there exists a close link between these activities. As a result, the method of technico-economic assessment of technologies (design method) must be con- sistent with the standard method of technico-economic assessment of expansion projects, i.e. standard planning method. Hence the need of a standard planning method as a reference for the design method to be used.

2 Reference planning method choice

2.1 Problem statement

An obvious choice would be the standard CBA ([8]), i.e. the current standard plan- ning method, mentioned in previous section. However, the features of the stan- dard CBA are partly responsible of the absence of harmonized financial regulatory model, identified as a regulatory barrier in the introduction. The choice of another reference planning method to overcome this regulatory barrier is the challenge of this section. First, we introduce the notion of inapppropriate regulation to qualify standard CBA. Then we explain why standard CBA is inappropriate. Addition- ally, we explain why standard CBA features make impossible the development of an harmonized financial regulatory model. Last, we present briefly the alternative reference planning method chosen.

2.2 Inappropriate regulation definition

Rules that are applicable in their current form to MTDC grids can be inappropriate,

meaning that they are unfit to fulfil MTDC grid e fficiency objectives. Grid objec-

tives are the common ground beyond the di fferent approaches of regulation from country to country that result from a complex process of successive interpretations of these objectives implying political and social visions on the energy resource. A schematic representation of grid objectives is given on figure 1.2. Each objective meaning is detailed in next paragraphs.

Figure 1.2: Transmission grid objectives

Economic e fficiency

Over the last decades, the power sector has been “deregulated” : it has been moving from a vertically-integrated market where central decisions were made towards a competitive and trade-oriented integrated European market. In the deregulated con- text, economic e fficiency is a microeconomic notion. Indeed the assumed optimal economic e fficiency is reached if, in a given system state, it is impossible to im- prove an individual’s welfare without downgrade any other’s. Such a system state is said Pareto e fficient. From that point, the two following fundamental theorems of welfare economics drive the deregulated electricity markets design ([10]).

First theorem : Any competitive equilibrium leads to a Pareto e fficient allocation of resources.

Second theorem : Any e fficient allocation can be attained by a competitive equi- librium, given the market mechanisms leading to redistribution.

Indeed, the overall objective of electricity markets design is to reach a fair and

Pareto-e fficient state of the system. Fairness is based in that particular context on a

vision of society relating to redistribution of resources. Electricity markets regula-

tion is the legally binding translation of that idea.

Sustainability

Sustainability is a wide concept first defined in the Brundtland report ([11]) pub- lished in 1987 by the World Commission on Environment and Development of the United Nations Organization, to characterize a development that “meets the needs of the present without compromising the ability of future generations to meet their own needs”. Sustainability suggests to assess political, social and environmental e ffects that can not be transmitted by market prices. Thus, regulation should aim at ensuring sustainability despite market inablity to address externalities. For instance, emissions of carbon dioxyde (CO

) is an externality that is adressed through the promotion of renewable energy sources ([12]). Essentially, the corresponding reg- ulation pushes for support instruments that have a direct impact on market equilib- rium. In short, regulation addresses sustainability through electricity market design.

Electricity market design is already at an advanced level of maturity although the rules that are applied are still di fferent from country to country. Schematically, electricity market design tackles the double objective of economic e fficiency and sustainability, as explained in section 2.2. In that framework, economic e fficiency is measured by social-economic welfare and sustainability is assessed through ex- ternalities indicators such as CO

emissions.

Reliability

Reliability is defined in general terms in [13] as “the overall ability of the system to perform its function”. Reliability in a power system can be subdivided according to its di fferent functions. On the one hand, any power system must be able to “respond to dynamic or transient disturbances arising within the system”. That ability refers to the security of the system. On the other hand, any power system must “satisfy the consumer load demand and the system operational constraints” thanks to “the existence of su fficient facilities”. That ability corresponds to the system adequacy.

System security can be seen as an operational constraint so that the two notions are inseparable. Furthermore, securtiy is strongly linked to system stability, that can be subdivided into three categories [14]: rotor angle stability, frequency stability and voltage stability. The translation of that idea in regulation are standard reliability management methods (RMM).

2.3 Standard CBA inappropriateness

According to the previous definition, current standard planning method is inap-

propriate because it is unfit to promote the development of supergrids despite their

ability to pursue grid objectives. One reason is the lack of integration between long-

term reliability management methods (RMM) and the standard CBA mentioned previously. Indeed adequacy (long-term reliability) is managed through studies per- formed at national level. Adequacy studies consist in assessing if the power system was able to meet the load demand over a past long period. Adequacy studies guide the planning process at national and regional level but are separated from the method of technico-economic assessment of candidate expansion projects, i.e. the standard CBA. An integrated method is all the more necessary in the context of supergrids because the role of supergrids in the power system is unclear. Indeed it is not sure if the benefit of the MTDC grid relates to its ability to bring flexibility to neigh- bouring AC systems or if it should be operated close to the security limits so that socio-economic benefit relating to market integration is maximal.

2.4 Challenge for the standard planning method

The study [4] identifies the distribution of costs, benefits and financial risk of trans- mission investments as the main challenge for the development of MTDC grids.

That means that a “fair” investment costs repartition is a prerequisite for MTDC grids development. But what is “fair”? First, cost repartitions mechanisms should take into account MTDC grids specificities: high investment costs and risks due to technological uncertainties that may have a deterrent e ffect on investors. For in- stance, anticipatory investments that are needed to enable the MTDC grid to get op- timally expanded require financial risk mitigation mechanisms. However, purely fi- nancial mechanisms are not relevant in this study. Second, the existing cross-border cost allocation mechanism should evolve in order to fit with the multi-country con- text of MTDC grids. That aspect is relevant in this study because it poses a double challenge for standard planning method according to e-Highway 2050 project vi- sion ([6]). On the one hand, the standard CBA should be able to quantify economic benefits of the di fferent stakeholders or groups of stakeholders. On the other hand it should be able to quantify cost components that cannot be allocated to a specific stakeholder : reliability costs. Thus, the standard planning method should be able to identify and measure reliability costs for the purpose of a fair repartition of invest- ments costs. In conclusion, the e-Highway 2050 vision does not explicitly put into question the standard CBA as a method but confirms the need of more integration between the standard CBA and reliability management for the purpose of develop- ing an harmonized financial regulatory model.

We identify standard CBA inappropriateness as our first regulatory issue be-

cause it is the translation of the regulatory issue identified in the introduction : the

absence of harmonized financila regulatory model for investments. In order to over-

come this issue, we choose an alternative reference planning method.

2.5 Alternative reference planning method

The deficit of integration of planning methods motivated the European project GARPUR

, whose main objective is to “design, develop, assess and evaluate such new reliability criteria to be progressively implemented over the next decades at a pan-European level, while maximising social welfare”. The long-term risk-based reliability management approach proposed in [16] in the framework of the project strives to become the standard way to assess reliability in expansion projects, i.e.

the future standard planning method. We choose that approach as the reference planning method.

3 Reference planning method application

3.1 Problem statement

The unrealistic representation of operating conditions is one deficit of the current CBA highlighted in [17]. Indeed, particular operating conditions are tested. In gen- eral, these are worst-case conditions such as peak load situations. That is why the reference planning method aims to represent operating conditions in a more realistic way. Indeed, a probabilistic description of events and disturbances is used. There- fore, a wide range of operating conditions with their corresponding probabilities are covered.

However, there are di fferent sources of uncertainty about future operating rules.

That is identified as our second regulatory issue in link with design activity be- cause it causes the absence of hamonized model of coordinated operations between national transmission system operators, identified as a regulatory barrier in the in- troduction. One of the objectives of this section is to present that sources of un- certainty. We first introduce the notion of inapplicable regulation for two sources of uncertainty : the legal conflicts in existing regulation and the lack of network codes. Then we reuse the notion of inappropriate regulation for the last source of uncertainty: current standard security management methods deficit.

3.2 Inapplicable operating rules

For legal or technical reasons, some rules presented in the general context of trans- mission grids activities (section 1.2) can be inapplicable in the MTDC grids context.

Indeed, MTDC grids have several singular features. Amongst them :

1Generally Accepted Reliability Principle with Uncertainty modelling and through probabilistic Risk assessment, [15]

- their size :some infrastructures may cross several borders, particularly o ff- shore infrastructures;

- the emerging nature of technologies;

- the fastness of electrical phenomena due to low impedances.

Legal conflicts

Legal issues are conflicts between existing rules. We illustrate it by an example: the Synergies at Sea project. The project infrastructure between o ffshore wind farms respectively belonging to British and dutch national systems is schematically repre- sented on figure 1.3.

Figure 1.3: Synergies at Sea project infrastructure

The project feasibility study highlights a legal conflict between two existing rules of congestion management :

- the obligation of allocating capacity through implicit market coupling auc- tions applicated to interconnectors according to commission regulation (EU) 2015 /1222 establishing a guideline on capacity allocation and congestion management;

- the priority dispatch rule for RES applicated to wind farms connection lines according to the directive (EU) 2009 /28/EC (art. 16(2)).

The infrastructure represented on figure 1.3 can be considered as an intercon- nector or a wind farm connection line. Indeed, an interconnector is defined in reg- ulation 714 /2009 (art.2 (1)) as “a transmission line which crosses or spans a border between Member States and which connects the national transmission systems of the Member States.”. For its part the definition of a wind farm connection line is a transmission line that connects a wind farm to the national transmission system of a member state.

Therefore, there is a legal conflict in the current regulatory framework that

should be removed in the future in regulation by clearly qualifying these hybrid

o ffshore grid infrastructures. Pending that regulatory evolution, the legal conflict

causes uncertainty about future e ffective operating rules.

Lack of network codes

The network code commonly referred as HVDC network code sets out rules of connection of HVDC systems and rules at the interfaces with other systems (AC systems in particular) but nothing about operations within the HVDC system itself.

Indeed, physical phenomena are strongly di fferent in DC grids than in AC grids. For instance, due to the nature of electrical lines (direct current and low impedance), the propagation of a disturbance is faster and fault-currents never cross zero. In conse- quence, the constraints on control and protection systems are specific. A working group of the European Committee for Electrotechnical Standardization

currently addresses system aspects of HVDC grids in a view of developing standards for functional specifications of several of these system aspects ([18]). Pending new ef- fective network codes, that causes uncertainty about future e ffective operating rules.

3.3 Inappropriate standard security management methods

Power system operations are driven by security rules formulated in network codes.

In particular, the N-1 criterion (“the rule according to which the elements remaining in operation within a TSO’s control area after occurrence of a contingency are capa- ble of accommodating the new operational situation without violating operational security limits” ([19]) is widely used to manage security.

However, the N-1 criterion has several drawbacks. First, it is conservative be- cause it is applied by each TSO within its control area and with a limited coor- dination with others. As a result, large reliability margins are kept by TSOs due to the increasing uncertainty caused by RES penetration and the multi-area nature of operations. That leads to cost-ine ffective operations ([20]). Paradoxically, cost- e ffectiveness has been the main driver for European electricity market deregulation.

Second, the N-1 criterion covers by definition only N-1 situations, putting aside rare threatening events of wide extent occuring in N-k (k > 1) situations. Adequacy studies measure the aggregated consequences of service interruptions due to secu- rity limits violations over a defined period and disclose long-term cost-ine fficiency.

Hence the challenge for the European power system integration: moving to- wards cost-e fficient multi-area operations while maintaining an acceptable level of system security. In consequence, security management methods are likely to evolve in the future. That causes uncertainty about future operating rules as well.

2CENELEC Technical Committee TC8X Working Group WG06 “System Aspects of HVDC Grids”

Chapter 2

Reliability management method for MTDC architectures evaluation

In this chapter, we go into the detail of the design method we propose. That method is a long-term reliability management method based on the planning approach pro- posed by the European project GARPUR. We propose a general cost-minimization problem with the following main features :

- applicability to di fferent design cases;

- integrability with a Cost-Benefit Analysis (CBA);

- capability to promote overall positive e ffects of MTDC grids by a trade-off between costs and improved reliability.

1 Architectures Evaluation Problem (AEP) principle

1.1 AEP compact mathematical formulation

We propose a general risk-based RMM formulated as a simple constrained cost- minimization problem by 2.1 and 2.2. The long-term RMM is a planning decision tool in the GARPUR framework. Then the set of feasible decisions is a set of candi- date investment projects. As explained in chapter 1, it is possible to apply the plan- ning method approach to architectures evaluation by changing the decisions nature.

In the design problem, the set of feasible decisions is a set of feasible architectures A.

minimize

A

z (2.1)

subject to P (E) <  (2.2)

Where :

A : Set of feasible architectures z : Objective function

P : Probability function E : Event

 : Tolerance level

The main idea is to simulate the architecture behaviour in the power system over its life span (typically a couple of decades) in order to sum in the same function (the objective function z) costs of di fferent natures. The costs in question can be capital or operational. They can be direct - for instance due to electrical losses - or indirect.

That is specifically in the latter category that reliability costs fall under. Indeed the total cost function z should reflect the impact of the architecture on the whole power system.

We interpret the probabilistic constraint in section 2 and we detail the composi- tion of objective function z in section 3.

2 Security issues in AEP

2.1 Security constraint

The AEP constraint (2.2) relates to security management (short-term RMM). Events E correspond to security limits violations. Hence a prerequisite for the problem resolution : that security limits be clearly defined, i.e. either known or assumed (see section 2.2). The following definition is used for security limits : physical limits beyond which service interruptions (or customer interruptions) occur somewhere in the power system. Ideally, security limits violations should be completely avoided.

In that case, perfect security would lead to a perfect long-term reliability. In reality, the power system can not be 100% reliable. Therefore, security limits violations rarely occur in the power system. Then the role of short-term RMM is to limit the probability level of security limits violations, i.e. to set a tolerance level for such events. That is expressed by  in constraint 2.2. That constraint is reformulated by 2.3.

P security limits violations
<  (2.3)

2.2 Security management

There is a clear lack of network codes applicable to MTDC grids as explained in first chapter. In that highly uncertain context about security limits, the following two-step approach is proposed :

1. Risk (security threat) identification on a case-per-case basis 2. Security limits assumption

The most widespread security management method consists in completely elim- inating the risk of security limits violations following a single contingency prede- fined in a set of contingencies. That is the N-1 criterion. Mathematically, the N-1 criterion can be expressed by 2.4. For the sake of clarity, N − k refers to system states following k simultaneous contingencies. Consequenctly, N − 0 refers to the normal state of operations.

P security limits violations
= 0 ∀ N − 0, N − 1 (2.4) Therefore, in the AEP theoretical framework, the N-1 criterion application is a means to set the tolerance level . That is expressed by 2.5.

 = X

k>1

P (N-k) P security limits violations | N − k

(2.5)

3 System cost function in AEP

3.1 Service interruptions cost

In case of security limits violations, service interruptions occur somewhere in the power system : some end-customer are disconnected from the grid. Disconnections are characterized by a cumulative cost function (service interruptions cost function) that is part of the objective function z. That function is noted S IC : A

7→ sic

(where A

∈ A). S IC function aggregates all singular service interruption events over the period considered.

Estimating S IC function is a hard task out of scope of this study. However, the general expression of the function is given by 2.6.

S IC = ENS × VOLL (2.6)

Where :

ENS : Energy Not Served (MWh)

VOLL : Value of lost load ( e/MWh)

There exist methods of calculation of quality of supply indices such as the en- ergy not served (ENS ). Furthermore, the value of lost load (VOLL) depends on internal and external factors. Internal factors refer to the type of loads that are shed (E.g. households, industry, commercial services) and their location (E.g. country, economic region). External factors refer to the time (E.g. season, hour of the day) and environmental conditions (E.g. weather, temperature).

The main idea is that S IC function should capture the “real” cost of security limits violations consequences on end-customers in presence of the MTDC grid.

Indeed, on the one hand, security limits violations caused by the MTDC grid are prone to a ffect the whole power system behaviour, leading to service interruptions in AC systems. By modelling cascading sequence caused by such security limits violations, the involuntary load shedding and the ensuing energy not served can be estimated. On the other hand, security limits violations occuring in AC systems should be studied as well. In that way, the capability of MTDC grid to bring flexi- bility to AC systems and consequently to limit service interruptions is captured by the S IC function.

To conclude: if only security limits violations caused by the MTDC grid itself are studied, the design problem outputs is likely to promote architectures that dis- turb the least the well functioning of AC systems. On the contrary, if only security limit violations that occur in AC systems are also considered, the design problem will find a balance between : “disturbing the less” and “support the more” AC sys- tems.

3.2 Security cost

The second term of the objective function is a cost function relating to security management divided into :

1. the corrective cost function relating to corrective security management.

2. the preventive cost function relating to preventive security management.

Corrective cost

Corrective actions refer to the mechanisms, activated either automatically or man-

ually in reaction to a disturbance in the power system, aiming at avoiding service

interruptions. Redispatching of power flows over transmission lines and voluntary

load shedding are two examples of such corrective actions. Corrective actions are characterized by a cumulative cost function (corrective cost function). That function is noted CC : A

7→ cc

(where A

∈ A). The CC function estimation is challenging since corrective mechanisms involve AC systems behaviour.

Similarly to the S IC function estimation issue, the CC function value depends on the extent of the corrective actions considered. Indeed, some MTDC architec- tures, thanks to controllable converters for example, are prone to “help” AC sys- tems in post-disturbance state. As a result, AC systems would avoid triggering their proper corrective procedures. In order to capture the entire spectrum of e ffects of the MTDC grid, AC systems corrective actions should be modelled as well.

Preventive cost

Preventive actions refer to the way the system is operated in normal state in order to mitigate security limits violation risk. The preventive cost function is noted PC : A

7→ pc

(where A

∈ A). The application of a security criterion such as the N-1 criterion is an example of preventive action. Preventive actions have a strong link with the security constraint. As it was explained in section 2.2, the N-1 criterion sets a tolerance level  for security limits violations. The preventive cost function (PC) measures the cost of applying preventive risk management measures

.

3.3 Architecture cost

The architecture itself has a corresponding cost function (architecture cost) that can be seen as the output of a CBA where the costs mentioned previously (service inter- ruptions cost and security cost) are excluded. That cost function accounts the fol- lowing factors (among others) : capital expenditure (hereafter CAPEX), electrical losses or environmental cost. The architecture cost function, noted AC : A

7→ ac

(where A

∈ A), is the last term of the objective function z.

4 Formulation and application approach of AEP

4.1 AEP detailed mathematical formulation

According to sections 2 and 3, the architectures evaluation problem (AEP) can be formulated by 2.7 and 2.8.

1The N-1 criterion remains the paradigmatic security management method today. However, GARPUR project explore different short-term reliability management (security management) meth- ods, including a risk-based method like the one from which the design problem is adapted.

minimize

A

S IC + CC + PC

| {z }

Security cost

+AC (2.7)

subject to P security limits violations
<  (2.8)

4.2 AEP application approach

We propose a cost-minimization problem that is general enough to be applicable to di fferent design cases. Indeed, for each design case, the following steps of the application approach are di fferent :

- Description of candidate architectures - Identification of relevant operating issues - Identification of relevant security issues - Identification of relevant preventive actions - Identification of relevant corrective actions

- Identification of relevant involuntary load shedding mechanisms

Moreover, the problem we propose is integrable with a multi-criteria CBA. In- deed, the CBA output is seen as a term of the problem objective function.

Several scientific barriers were highlighted for the application of the general problem we propose. First, the identification of security threats that could lead to involuntary load-shedding situations requires a deep understanding of cascading mechanisms: in the MTDC grid itself but also in adjacent AC grids (national AC grids). Second, the application of the problem requires corrective actions modelling (voluntary load shedding, redispatching, etc.) and service interruptions cost estima- tion that relate to AC systems behaviour. These issues are are rather critical because the understanding of AC system behaviour enable to capture the “real” e ffect of MTDC grids on power system reliability. In particular : the positive e ffect brought by ancillary services o ffered by MTDC grids to support AC systems. They are not tackled in detail in this thesis.

The study case presented in chapter 3 illustrates the application approach but

makes a lot of simplifying assumptions in order to bypass scientific barriers men-

tioned above.

Chapter 3

Transmission corridors

architectures : System reduction and models development

1 Context and objectives

1.1 Transmission corridors in the supergird context

Transmission corridors are the basic bricks of all target grids proposed within e- highway2050 project ([5]) development scenarios. The regions they connect and their capacity are outputs of the long-term planning methodology developed in the framework of the project ([21]) for each scenario. Transmission corridors objectives may be di fferent : enabling the transport of hydro and wind power from the North Sea region to continental Europe or ensuring southern Europe (Spain, Portugal) security of supply, among other objectives. Di fferent technologies and strategies may be used for transmission corridors achievement. Multi-terminal DC solutions (MTDC) is one of the technological options mentioned in [22]. In particular, point- to-point solutions (MTDC elementary brick) are considered.

1.2 Transmission corridors technologies

Transmission corridors are characterized by their long distances - hundreds to thou-

sands of kilometers - and high capacities - several gigawatts. Distances are much

higher than the critical power transmission distance (often estimated equal to a cou-

ple of hundreds of kilometers) above which high voltage direct current (HVDC)

transmission solutions are more economical than high voltage alternating current

(HVAC) transmission ones in terms of investment cost. That justifies (among other

arguments) the use of HVDC solutions. When looking through the investment cost

detail, DC terminals are more expensive than AC terminals due to high cost of AC /DC converters. However, DC cables are more economical than AC cables (per kilometer). Hence the critical power transmission distance, illustrated on figure 3.1.

That critical distance is di fferent for overhead lines and subsea lines : it is a couple of hundreds kilometers for overhead lines and approximately 50km for subsea lines.

We consider in this study distances above that latter critical distance. That is one of the reason why we do not consider AC cables in this study.

Figure 3.1: DC vs AC power transmission investment costs (from [1]) Furthermore, HVDC long distance power transmission solutions provide sev- eral operational pros including power flow control capabilities and reduced electri- cal losses. Therefore, HVAC solutions are disregarded in this chapter.

Three HVDC solutions are studied : 1. the symmetrical monopole 2. the grounded bipole

3. the bipole with a metallic return path (bipole MR) They are described in detail in section 2.2.

1.3 Study case objectives and chapter focus

The overall objective of the study case is to apply the general architectures evalu-

ation problem (AEP) presented in chapter 2 to the particular case of transmission

corridors architectures design in chapter 3.

The objective of this chapter is to demonstrate the application approach pre- sented in section 4.2 to end-up with an expression of system cost functions and suitable simulations models.

First, relevant operational drivers are identified for the simulation (section 2).

Then, system cost functions are formulated based on simulation outputs (sections 3 and 4). Eventually, we propose simulation models enabling to achieve the simula- tion features presented before (sections 5 and 6).

2 System reduction

The application approach presented in chapter 2 consists in reducing the power system for architectures simulations by :

- identifying relevant operating mechanisms (security issues, preventive mech- anisms, corrective mechanisms and service interruptions mechanisms);

- describing architectures accordingly.

2.1 Simulation operating conditions

Power transfer issues

The main function of a power transmission corridor is to transmit power from one zone of the power system to another zone

. Therefore, we focus in this study on two operating issues that may impact the power transfer over the transmission corridor :

1. the transmission corridor components unavailability

2. the security risk in case of large instantaneous power transfer variation over the transmission corridor

The two operating issues are linked with architectures components failure. On the one hand, a component unavailability is the consequence of the component fail- ure in post-failure system state. Then, if one or several architecture components are unavailable in a given system state, the maximal power transfer over the transmis- sion corridor may be limited. The corresponding power limit (first power limit) is further detailed in section 3.1. On the other hand, the power variation is the instan- taneous consequence of component failure. For AC stability reasons that are not

1The two zones are assumed to be two different price zones

detailed here, the power transfer variation after a component failure (possibly after reconfiguration of the power transfer) is identified as a security threat. Therefore, we set a maximal power transfer variation that is the security limit above which there is a security limit violation. We note the maximal power transfer variation M and we assume that it is the security threat we consider in the problem. The applica- tion of the N-1 criterion (preventive mechanism) in the corresponding system state may limit the power transfer as well. The corresponding power limit (second power limit) is further detailed in section 3.1.

Impact on architectures simulation

In order to tackle the power transfer issues mentioned above, we :

- generate components failures and repairing events over the simulation period - calculate first and second power limits in each system state

Then we use this information to calculate some relevant power functions: the maximal power transfer and the secure power transfer. Eventually, system cost functions are deduced from power functions.

Now that operating mechanisms involved in the simulation are known, we de- scribe technologies power transfer issues in a view of describing architectures by parameters in a suitable way for simulations.

2.2 Technologies power transfer issues

Terminology and assumptions

A simplistic representation of each technology is used : all DC terminal compo- nents (AC and DC filters as well as switchyards, transformers and converter valves) are aggregated. The resulting component on all representations and models is called

“converter”. We describe operating modes of the HVDC solutions, di fferent if com- ponents are available or not. The terminology below is used.

Nominal mode : Operating mode with all components available (all converters and cables)

Degraded modes : Operating mode with at least one component unavailable

For each technology, the nominal operating mode (or nominal mode) and some

degraded operating modes (degraded modes) are described. Indeed, only degraded

modes involving cable(s) failure(s) are described. The ones involving converter(s)

failure(s) (converter(s) unavailable) are not described for the sake of simplicity.

Symmetrical monopole operations

Figure 3.2: Symmetrical monopole

For the symmetrical monopole (figure 3.2), each terminal is composed of a single converter with a mid-point grounded (not represented on figure 3.2) between posi- tive voltage polarity ( +V

) and negative voltage polarity (−V

).

We study the nominal mode. Assume that the power flows from AC

to AC

(red arrows direction on figure 3.3 that illustrates nominal mode operations).

Figure 3.3: Symmetrical monopole nominal mode

Given the current I and the voltage magnitude V

, the active power flow P

over the symmetrical monopole is given by 3.1.

P

= (+V

· I) + (−V

· −I ) = 2V

I (3.1) We study the degraded modes. If any component of the symmetrical monopole (converter or cable) is unavailable, the power cannot flow over the symmetrical monopole. It is expressed by 3.2.

P

= 0 (3.2)

Grounded bipole operations

Figure 3.4: Grounded bipole

For the grounded bipole (figure 3.4), each terminal is composed of two converters between which there is the grounding point. The upper DC cable is at the positive voltage polarity ( +V

) while the lower DC cable is a the negative voltage polarity (−V

).

We study the nominal mode. Assume that the power flows from AC

to AC

. The nominal mode is illustrated on figure 3.5.

Figure 3.5: Grounded bipole nominal mode

Given the current I and the voltage magnitude V

, the power flow P

over the grounded bipole is given by 3.3.

P

= (+V

· I) + (−V

· −I ) = 2V

I (3.3) We study the degraded modes. If any component of the grounded bipole is un- available, the power cannot flow. Indeed, it is assumed that ground is not a suitable current return path. It is expressed by 3.4.

P

= 0 (3.4)

Bipole with metallic return path (MR) operations

Figure 3.6: Bipole MR

The bipole MR (figure 3.6) has a structure similar to the grounded bipole, except that a low voltage cable (MR) is added between the two terminals mid-points. The metallic return can serve as a current return path in certain degraded modes.

We study the nominal mode. Assume that the power flows from AC

to AC

. The nominal mode is illustrated on figure 3.7.

Figure 3.7: Bipole MR nominal mode

Given the current I and the voltage magnitude V

, the power flow P

over the bipole MR is given by 3.5.

P

= (+V

· I) + (−V

· −I ) = 2V

I (3.5)

We study the degraded modes. In case of unavailability of one cable (HV cable),

a non-zero power can still flow. In that mode, the power flows through the remaining

cable. The return current passes through the metallic return. That degraded mode is

illustrated on figure 3.8.

Figure 3.8: Bipole MR in degraded state (one HV cable unavailable)

Given the current I and the voltage magnitude V

, the power flow over the bipole MR is expressed by 3.6.

P

= V

· I (3.6)

In case of unavailability of the MR, the solution is equivalent to a grounded bipole. The power flow over bipole MR is expressed by 3.7.

P

= 2V

· I (3.7)

In case of unavailability of the two HV cables or one HV cable and the metallic return, the power cannot flow. It is expressed by 3.8.

P

= 0 (3.8)

2.3 Architectures parameters

Design assumption

In section 2.1, the power transfers in any mode (nominal or degraded) are expressed as a function of the current I and the DC voltage magnitude V

, without consider- ing any power limitation. Yet, the power is limited due to :

- the converters power rating (same for all converters in a given solution), noted P

;

- the cables thermal limit (same for all cables in a given solution), expressed by I

, upper limit of current I (see for instance figure 3.3).

As a first step, we make a simplifying design assumption enabling to reduce the number of descriptive parameters.

Based on the notion of nominal maximal flow defined below, we fix the relation

between P

and I

.

The nominal maximal flow is the upper limit of the power transfer over a given transmission solution in nominal mode, considering power limitations. The follow- ing notations (only for nominal mode) are used :

p

: Power limitation due to converters power rating p

: Power limitation due to cables thermal limit

The power limitations are expressed in table 3.1 for each solution in nominal mode.

Solution p

p

Symmetrical monopole P

2V

I

Bipole MR 2P

2V

I

Grounded bipole 2P

2V

I

Table 3.1: Nominal maximal flow extended expression

The resulting nominal maximal flow p

for each solution is then expressed by 3.9.

p

= min 

p

, p



(3.9) For each technology, cables and converters are chosen such that in nominal mode neither converters nor cables are more limiting. That is expressed by 3.10.

p

= p

(3.10)

As a result, the nominal maximal flow p

(architecture unit installed capac- ity) is expressed by 3.11, i.e. as a function of the converters power rating P

only.

Nominal maximal flows for all solutions are summed up in table 3.2.

p

= p

(3.11)

Solution p

Symmetrical monopole P

Bipole MR 2P

Grounded bipole 2P

Table 3.2: Solution installed capacity expression

The maximal flow in any degraded mode of any technology is limited by power converters rating and cable thermal limits as well as on component(s) unavailability.

Thanks to the design assumption, the degraded maximal flow can be expressed as a

function of P

. All expressions ensue from solutions operating modes.