Security Assessment of the French Transmission System Using Multi-Situation Methods

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IN

DEGREE PROJECT ELECTRICAL ENGINEERING,

SECOND CYCLE, 30 CREDITS ,

STOCKHOLM SWEDEN 2018

Security Assessment of the French Transmission System Using Multi- Situation Methods

LOUIS GARNIER

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

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Master Thesis Report

Security Assessment of the French Transmission System Using Multi-

Situation Methods

Date: September, 4^th 2017 – February, 23^th 2018 Student: Louis GARNIER

RTE Supervisors: Jérôme MAROT KTH Examiner: Lennart Söder KTH Supervisor: Elis Nycander

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ABSTRACT

Traditionally, the main sources of electricity production in the power system have been conventional power plants (using either nuclear fuel, coal, gas or oil). The power is transferred by the transmission system to the cities, where the distribution system ensures the link to the consumers. The power flows unidirectionally from the power plants to the centers of consumption. The Transmission System Operator (TSO) needs to make sure that these flows are in an acceptable range to provide security in the network. This is done by making studies in advance: the flows in the lines are given by the topology of the network and the consumption. By choosing one situation of the network and by forecasting the consumption, the flows can be predicted. This is how the studies have been conducted so far, thus the only varying parameter taken into account is the consumption.

In the recent years though, the situation has changed a lot. The rapid and widespread development of renewable energies such as wind power turbines and photovoltaic panels has complicated the studies. Today, the new sources of production are variable and need to be forecasted. Besides, they are connected to the network by multiple points. The power flows through the lines are more unpredictable compared to the previous situation with only conventional power plants. The studies conducted by the TSO for ensuring the security of the network need to evolve as well, and that is the topic of this Master Thesis. The multi-situation method studies many possible situations for the network and allows several parameters to vary at the same time. This leads to a better understanding of the power flows especially in areas with a lot of renewable generation. It can also help the TSO to forecast the possible security violations in the network, such as congestion on power lines. The purpose of this Master Thesis is to suggest a methodology for conducting a multi-situation study and point out its advantages compared to the conventional approach.

In order to validate the benefit of the multi-situation method, three different cases are studied. Each of the cases considers a different area in the west of France. Each of them has specific characteristics which makes the conventional method inappropriate. The results lead to the conclusion that the multi-situation approach can give useful information like the duration of congestions. It provides a more detailed analysis for the study thanks to this new point of view. The conventional method is very conservative: when the power flows are not known with precision, a precaution margin is chosen because the security is the primary concern. This often leads to over-dimension the network. The multi-situation approach is much more realistic and can be of great use for the TSO concerning some of the grid reinforcements. Money can be saved because the future power flows are known with better precision. On the other hand, the security of the network is reduced.

The conclusion of this thesis is to demonstrate that the two different approaches are not contradictory. In fact, they are complementary: the multi-situation method gives a new point of view and some useful information to add to the results of the conventional method. The overall outcome is a strong network study that assesses the possible congestions in the future.

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SAMMANFATTNING

Traditionellt har elproduktionen i nätet till största delen bestått av konventionella kraftverk, med användning av antingen kärnbränsle, kol, gas eller olja. Elen överförs av transmissionsnätet till städerna, där distributionssystemet sedan utgör länken till konsumenterna. Riktningen för eltransporten har varit från kraftverk till konsumtionscentrum.

Transmissionssystemoperatören (TSO) måste se till att dessa flöden hålls inom en acceptabel nivå för att upprätthålla driftsäkerheten i nätet. Detta görs genom studier på förhand: flödena på ledningarna bestäms av nätets topologi och elförbrukningen. Genom att välja en topologi för nätet och genom att prognostisera konsumtionen kan flödena förutsägas. Så här har studierna utförts hittills, den huvudsakliga variabla parameter som beaktats har varit förbrukningen.

Under de senaste åren har dock situationen förändrats. Den snabba utveckling av förnybara energikällor som vindkraft och solceller har gjort situationen för nätoperatörerna mer komplicerad. Idag är de nya produktionskällorna variabla och måste prognostiseras.

Dessutom är de mer geografiskt utspridda och anslutna till nätverket i flera punkter. Flödena på ledningarna är mer oförutsägbara jämfört med den tidigare situationen med endast konventionella kraftverk. De undersökningar som utförs av TSO för att säkerställa driftsäkerheten i nätet måste utvecklas, vilket är ämnet för detta examensarbete.

Multi-situations-metoden som används i detta arbete studerar många möjliga situationer för nätet och tillåter flera parametrar att variera samtidigt. Detta leder till en bättre förståelse av kraftflöden, särskilt i områden med mycket förnybar produktion. Det kan också hjälpa TSO att förutse möjliga säkerhetsöverträdelser i nätverket, t.ex. överbelastningar på kraftledningar.

Syftet med detta examensarbete är att föreslå en metod för att genomföra en studie med Multi- situationsmetoden och undersöka dess fördelar jämfört med det konventionella tillvägagångssättet.

För att undersöka fördelarna med Multi-situationsmetoden görs tre olika fall studier. Vart och ett av fallen avser ett område i västra Frankrike. Varje fall har specifika egenskaper som gör den konventionella metoden olämplig. Resultaten visar att multi-situationsmetoden kan ge användbar information som varaktighet av överbelastningar, vilket möjliggör mer detaljerad analys av nätsäkerheten. Den konventionella metoden är mycket konservativ: när effektflödena inte är kända med precision används en säkerhetsmarginal eftersom driftsäkerheten är den huvudsakliga målsättningen. Detta leder ofta till överdimensionering av nätet. Multi-situationsmetoden är mer realistisk och kan vara till stor nytta för TSO när det gäller att uppskatta behovet av nätförstärkningar. En bättre kännedom om framtida effektflöden möjliggör besparingar. Å andra sidan minskar nätets säkerhet.

Slutsatsen av detta arbete är att de två metoderna inte är motstridiga. I själva verket komplementerar de varandra: multi-situationsmetoden ger en ny synvinkel och bör beaktas tillsammans med resultaten av den konventionella metoden. Tillsammans möjliggör de en mer fullständig nätstudie som bedömer eventuella överbelastningar i framtiden.

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ACKNOWLEDGEMENTS

I would first like to thank my supervisor at KTH Elis NYCANDER for answering my questions and my examiner Lennart SÖDER for supervising my thesis.

I would also like to thank the operation center of RTE in Nantes, especially Sylvie MANGEL and Jérôme VIDON who accepted me into their team.

I am thankful to all the employees that I have met, for welcoming me and for their cheerfulness. It helped me to work efficiently during my time at RTE.

Finally, I would like to express my gratitude to my supervisor at RTE Jérôme MAROT for his guidance, his support and his confidence for the whole duration of the project.

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ABBREVIATIONS - NOMENCLATURE

AC: Alternative Current DC: Direct Current

ENTSO-E: European Network of Transmission System Operators

Imap: « Intensité Maximale Admissible en régime Permanent » - Ampacity PTDF: Power Transfer Distribution Factors

R&D: Research and Development

RTE: « Réseau de Transport d’Electricité » - French Transmission System Operator

SEDRE: « Service Etude et Développement du Réseau Electrique » - National R&D department of RTE

TSO: Transmission System Operator

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1. INTRODUCTION

1.1. Background

The electricity supply chain is identical in almost every country of the world. It can be divided into three parts as shown in Figure 1. First, the electricity is produced by the power plants (using either nuclear fuel, coal, oil or renewable energies). The power is then transferred to the cities by the transmission network. The first substation transformer raises the voltage in order to decrease the losses during the long distance that separates the plants from the cities. The second substation transformer lowers the voltage before the distribution network that transports the electricity to the end consumers.

Figure 1: Electricity supply chain [1]

In France there is only one Transmission System Operator (TSO) which is RTE. It operates the 100 000 km of lines that separate the production from the distribution system.

There are five levels of voltage in the transmission network: 400kV, 225kV, 150kV, 90kV and 63kV. The missions of RTE are to maintain the power balance between the supply and the demand at every moment and also provide all customers with economical and reliable electricity. In order to do that, the transmission system is meshed: that means, that there are always several ways for the electricity to flow from one point of the network to another. If an electrical line were to shut down, the supply would still be provided.

The distribution network is owned almost entirely by Enedis which is a customer of RTE.

The voltage varies between 20kV and 220V, the legal value in France for domestic use.

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Unlike the meshed transmission system, the distribution system is said to have a radial structure. That means, that there is only one path for the electricity to flow to each customer.

For the rest of the report we will be focusing mostly on the transmission network.

As shown in Figure 1, the electricity supply chain is unidirectional. The power flows in one direction from the production in the left to the final consumer in the right. But this representation is not completely accurate. First, not all consumers are supplied by the distribution network: the big industries with a high consumption (like papermaking) are plugged directly to the transmission system. Secondly, the production is not connected at the same level of voltage. The nuclear and thermal power plants which produce the most are linked to the 400kV lines but wind farms may be connected at 225kV or 90kV. Some of the wind turbines are not even linked with the transmission system, they deliver their power directly on the distribution lines.

These particularities were not taken into account before because the installed capacity of renewable energies was too small compared to the conventional power plants. The effect on the power flows was neglected. But this situation is currently changing: In 2007 Europe set up a “2020 package” which describes the climate and energy targets for the year 2020. There are three key targets:

 20 % cut in greenhouse gas emissions (from 1990 levels)

 20% of renewable sources in the energy mix

 20% improvement in energy efficiency

These objectives have huge consequences on RTE because it affects directly the transmission network. First, the goal of 20% of renewable energies in the total mix led to the rapid development of wind power and solar power in France. As shown in Figure 2, an average of 1GW of wind power is connected to the grid each year since 2007 which corresponds to 500 new wind turbines. This amount of power is equivalent to a nuclear unit.

The same phenomenon is witnessed for the photovoltaic panels (+ 800 MW on average each year since 2010). That means, that these new sources cannot be neglected as before but their consequences have to be taken into account.

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Figure 2: Connection of wind power to the grid [2]

The figure 3 displays the installed capacity of all energy sources for the month of January 2018. The share of renewable energies in the total mix is 37% whereas the share of nuclear is only 48%. It seems that the strategy adopted by the country for the last ten years has been successful, especially concerning the rapid development of wind power and solar power which were almost nonexistent before 2005. Besides, the share of conventional thermal power plants has been decreased significantly in the last decade in order to achieve the first target of the “2020 package”: the 20% cut in the gas emissions.

Figure 3: Installed capacity January 2018 in MW [3]

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Nevertheless, the previous point of view in not realistic because we focused only on the installed capacity. The truth is less cheerful. Figure 4 displays the total energy mix for the month of January 2018 in France. In fact, the nuclear holds the major part of the production with 72%. The share of renewable energies is only 21%. The explanation lies in the fact that, for the same installed capacity, renewable energies cannot produce the same amount of energy as nuclear or thermal power plants. It is not a matter of production costs because renewable sources are always the first in the merit order list. The reason is that their production depends on external factors like the wind, the sun or the rain. Unlike the nuclear or the thermal power plants which can be easily controlled to produce more or less electricity, the renewable sources cannot be managed by RTE. As we can see in Figure 4, despite the rather important installed capacity of wind and solar power, they do not produce so much energy during the month of January. The capacity factor of wind power during the month is 38% and for the solar power it is only 5%. It is not much for the photovoltaic panels because we have considered only one month during the winter so the capacity factor is at its lowest.

These values mean, that for 62% of the time, the wind turbines are not producing any power, whereas nuclear plants can generate electricity at any time (except for maintenance reasons).

Figure 4: Energy mix of January 2018 in GWh [3]

To summarize, the “2020 package” established by Europe has led to the rapid development of renewable energies in the French network, in both installed capacity and energy produced. This phenomenon is enhanced by the closure of thermal power plants in order to reduce the gas emissions. Even some of the nuclear reactors are planned to be shut down in the coming years for security reasons (new rules have been set up after the Fukushima accident). The energy transition is real and it will become more and more important in the future so the TSOs like RTE need to be prepared.

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In addition to this first phenomenon another great change is happening on the French network, it concerns the last point of the “2020 package”: the energy efficiency. The last key target aims to improve by 20% the energy efficiency of the devices plugged to the network.

This has a strong impact on the total consumption as shown in Figure 5. Since the beginning of electricity, there has always been more and more consumers connected to the network and they were eager to consume more and more power. The total consumption has always increased until the year 2008. For the last decade, the French electricity consumption has been stagnating and has even slightly decreased (around 485 TWh a year). There are two main reasons to explain this unprecedented situation. First, the economic crisis of 2009 has weakened the country and its development. Many companies have indeed shut down their high electricity-consuming factories. The second reason is the consequence of the “2020 package” set up by Europe in 2007 concerning the energy efficiency. Many devices have been improved and changed in domestic houses (fridge, light bulbs) and that led to a reduction of the consumption. Despite the natural population growth, the total consumption in France is not forecasted to increase in the near future.

Figure 5: Total consumption in France since 1973 [4]

The transformation of the French electricity network has already begun and it will continue in the coming years. It will change from a vertical model, where the power flows unidirectionally from the conventional plants to the cities, to a horizontal model where multiple sources are connected throughout the network. The conventional sources (nuclear and thermal) can be easily managed by RTE to change their production in order to face an imbalance between the supply and the demand. The new renewable sources are not that flexible, they generate electricity according to the weather, that makes extremely hard for RTE to forecast their production and therefore to control them. The power flows are also completely changed in this new model. Before, they were unidirectional but now they can

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flow in both ways according to the wind and the sun. One of the missions of the TSO is to ensure the security of the network which means that at every moment the current in the lines and the voltages at the buses should be kept below the security limits. This is done during operation (real time) but also in advance by making studies: the power flows and voltages are forecasted and RTE verifies that they are in an acceptable range. This is called planning. In the following of this report, we will focus mainly on the long-term studies which happen at least six months before the real time. Until now, these studies have always been conducted with a “deterministic approach”.

The deterministic approach consists in studying only a few situations which are considered as the worst ones in terms of congestions on the network. Typically they are based on the consumption: in winter, a lot of domestic houses switch their heating on, so the current through the lines of the network reach a high value. If the currents are high, it is more likely to have congestions because some lines will be too loaded compared to their transport capacity.

The classic points studied are displayed in Table 1. The worst situation is a week day of January at 7pm. It is winter so the consumption is high and the daily peak happens at 7pm when most people get back from work and switch their devices on at home. June 4am is the point when the consumption has its lowest value: in the middle of the night during summer.

The currents through the lines are very low so they are unlikely to be congested. Nevertheless, this situation is still studied in particular for the voltage security. When the consumption is low, the voltage tends to increase and RTE needs to control the voltage everywhere in the network. There could be other situations studied like the middle season peak or off-peak, some particular days like public holidays or national day. Every time there is a risk that the consumption reaches a higher value than the winter peak, it has to be studied.

January 7pm June 4am April 10am

Winter peak demand Summer off-peak Middle season peak demand Table 1: Classic points for the deterministic studies

The consumption for the all year lies between the winter peak and the summer off-peak.

RTE studies these two situations and design the network based on these worst cases. In that way the TSO is sure that for all the other situations the network is secured. That is the concept of the deterministic method: analyzing only the worst situations to be sure that it will suit all the other cases as well.

This approach has proven to be very successful in the past before the development of renewable energies. As described previously, the electric system before 2005 was vertically integrated: the power flowed unidirectionnaly from the production plants to the cities. By forecasting the consumption the current through the lines could be known in advance and therefore the congestions could be anticipated. The only varying parameter was the

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consumption, the power flows were directly proportional to it. Studying only the winter peak and the summer off-peak was enough to ensure the security of the network for all the other situations. But today the electric system is totally different, it is horizontally integrated. The consumption is no longer the only unknown parameter. The production of all renewable sources can no longer be neglected, so parameters like the wind, the sun and the rain have to be taken into account as well. The power flows still depend on the consumption but also on the weather. Another new parameter to consider in the studies is the trade with other European countries which has been developed in the recent years. France has many connections with its neighbors like Spain, Italy, UK, Germany, Belgium and Switzerland. The power can flow freely through these connection lines and disrupt the border regions. We are not focusing on these interconnections in this Master thesis because the region studied lies in the west of France where the trade with others countries has a limited influence.

All these new parameters affect the power flows and thereby make the work of RTE harder to forecast the possible congestions. The winter peak and the summer off-peak are still serious situations but they may not be the worst cases anymore. For example if we consider another point for which the consumption is lower than the winter peak: the current through the lines is lower as well so it is less likely for the congestions to appear. But the wind production may also be different between the two cases. This can create new congestions which may not be anticipated if only the winter peak is studied. RTE is still basing its studies on a deterministic approach but new variants are added in order to take into account the multiplication of parameters. The new situations studied are displayed in Table 2.

Consumption Wind Sunshine Rainfall Border trades Seasons

Maximum Maximum Maximum Maximum Maximum Winter

Minimum Minimum Minimum Minimum Minimum Spring

Importer/Exporter Summer Fall Table 2: Some variants studied by the deterministic method

The deterministic approach considers all the extreme values of the parameters that affect the power flows in order to find the worst case. Before, it was only the consumption that was studied (maximum and minimum) for two seasons (winter and summer). Today the number of situations has increased exponentially because the power flows are now depending on numerous parameters. Of course not all the situations are studied in practice, it depends on the area. If there are no photovoltaic panels in the region there is no use of adding the two variants for maximum and minimum solar production.

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1.2. Objectives

As described previously, the aim of the deterministic approach is always to study the worst situation possible. Before, it was quite easy: the two cases were the maximum and minimum of the consumption. Now it is far more complicated because of the increased number of parameters that need to be taken into account. For the winter, the worst case is often a situation of high consumption with no wind power, no solar power, no hydro power and with no trade with others countries. All the parameters that cannot be predicted are chosen at their worst value. In that case, RTE is sure that the situation that will occur in practice will be covered by the study. The deterministic approach is very conservative and secured because all the congestions are anticipated. Nevertheless this method has its limit.

The situation studied does not correspond to a realistic situation. The worst case is chosen to be the January peak at 7pm. Besides that, the wind and solar power are set to zero. It is extremely unlikely that at this specific hour there is no wind and sun at all. Finally the study highlights several congestions that are unlikely to appear in real life.

In order to match more precisely to what happens in practice, the Research and Development Department has come up with a new approach for the studies, called the multi- situations method. It consists in studying, not only a few situations, but a lot of them. Unlike the deterministic method, the worst case is not considered, all the different situations are studied. That means, that all the parameters can vary at the same time and take any possible values. With the deterministic approach the wind and the sun are set to specific values whereas with the multi-situations approach they are based on measured time series from previous years. Of course it takes more time to study numerous situations than only a few of them. This is one drawback of this approach: it is far more complicated and time-consuming to conduct a multi-situation study. Nevertheless, it matches more with the real life and the possible congestions are known with better precision. The aim of this Master Thesis is to suggest a methodology to conduct a multi-situation study and explain its benefits and advantages compared to the deterministic approach. This report presents three different cases for which the conventional method shows its limits and is unable to resolve the new problems raised by the energy transition. The multi-situation, on the other hand, can give useful information and is more suitable in the current context. The three examples have been chosen on purpose because they are representative of present situations that RTE encounters and for which the conventional method is not sufficient. The ultimate goal for the TSO is to better assess the possible congestions in the future by forecasting the power flows more precisely.

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1.3. Software

The need for the multi-situation approach came as a result of the rapid development of wind power and photovoltaic panels in France in the recent years. The deterministic method was unable to deal with the uncertainty of these new parameters. The security of the network was still provided but the solutions applied were significant and not always necessary because the real congestions were not known with precision. This method is now considered too much conservative. The national R&D department of RTE, called SEDRE, developed three softwares to answer this need. They all present their specific characteristics but they are all based on the multi-situation approach. Basically, they run a DC load flow on a delimited area for a high number of simulations.

 PTDF: it is suited for the study of the 400kV network and also for the interconnections with the others countries.

 Assess: it is used for the 400kV network as well but it is more orientated for grid reinforcements. With this software, it is possible to run an optimized power plow.

 Inod: it is suited for regional network mostly 90kV and 225kV. This Master Thesis focuses only this particular software because it is the most appropriate for the cases studied.

These three softwares have been developed in 2015 but there is no final version yet. They are constantly evolving depending on feedback they receive. For now, it is not used much mainly because it is new and unknown for most people. Only a handful of experts in SEDRE can conduct a multi-situation study.

The last software mentioned in this report is Convergence, it is the current tool used by RTE for both planning and operation. It will be described in more detail in section 2.

Table 3 summarizes the main differences between the software:

Software Used for Type of load flow

Associated with

Characteristics

PTDF Planning DC load flow Multi-

situation 400 kV network

ASSESS Planning DC load flow Multi-

situation 400kV network Optimisation

Inod Planning DC load flow Multi-

situation

Regional network Convergence Planning and

Operation AC load flow Deterministic Considers the entire network Table 3: Features of the different softwares

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1.4. Disposition

The report is structured in the following way: Chapter 1 presents the introduction and describes the background and objectives of this Master Thesis. The deterministic approach is explained in Chapter 2 and illustrated with two examples. Chapter 3 depicts the multi- situation method, its advantages and its drawbacks. The comparison of the two approaches is discussed in Chapter 4. Finally the conclusion closes this report in Chapter 5.

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2. THE DETERMINISTIC APPROACH

2.1. Principle of the deterministic approach

The deterministic method is a way that the TSO has used to conduct its studies so far. It consists in examining only a few situations considered as the “worst cases” in terms of the consumption. The winter peak is often chosen because the consumption is at its highest value.

Then all the uncertain parameters like the wind, the sun are set to their extreme values in order to worsen the situation even more. In that way the power flows in the lines reach their maximal value and the TSO needs to check if they are in an acceptable range or find solutions otherwise.

RTE like all the other TSOs in Europe is subjected to the “N-1” criterion. The definition given by the agency of European TSOs (ENTSO-E) is the following:

“N-1” criterion: The rule according to which elements remaining in operation after a fault of one element within TSO’s control area must be capable of accommodating the new operational situation without exceeding operational security limits.

This is how the network is secured for the planning: first all the power flows must be in an acceptable range in normal operation (N state). Besides, the electric system must afford to lose its larger unit of production or any lines (N-1 state). During its studies RTE needs to simulate the loss of any element in the network and still find solutions to keep the power flows in the security limits. The strategies examined during the planning are mainly topology modifications (activating breakers or shunts). The re-schedule of production or load shedding can happen but only in real-time for very critical situations since it is very expensive. It is not an option considered in the long-term studies because it is the last recourse that the TSO has to resolve a congestion.

There are different types of studies run by the TSO: long-term studies or short-term studies. They examine the network sustainability for the coming year, the coming month, the coming week and the coming day. Of course, the closer we are to the real time, the more precision we have on the forecasted consumption and weather so it is easier to choose a value for these parameters. On the other hand, if the study is done for the coming year, the wind power and sun power are totally unknown whereas the consumption can be anticipated with quite a good accuracy. According to the deterministic method, they need to be set to their extreme levels in order to analyze the worst case. Since these parameters cannot be known, the worst is assumed whether or not it is a realistic situation.

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All the studies conducted by RTE are based on a software called Convergence. This is a simulation program that models the entire French transmission network (the voltage from 63kV to 400kV). It contains all the sources of production (almost 10000) and nodes of consumption (almost 7000) connected to the transmission system. All the lines operated by RTE are displayed (almost 10000) as well as the shunt capacitors and reactances. This software is constantly updated (every five minutes) to keep a realistic picture of the grid. It is indeed continuously changing according to new connections, loss of a line, outages.

The 400kV lines and nodes are displayed in red, the green represents the 225kV. The yellow is used for the 90kV and the purple for the 63kV. The black lines are disconnected from the network at the time when the picture was taken.

Figure 6: Display of the French west region in Convergence

Convergence is the most precise tool for conducting studies on the network. It is based on a true situation but all the parameters (consumption, production at every node) can be changed manually afterwards. The lines can be disconnected or re-connected as wished. This program is very useful to validate the “N-1” criterion: we can simulate the loss of any line and examine the new power flows after this fault. If they are not within the security limits, we can change the topology of the network in the software and see if this resolves the issue. This is done by activating breakers to change the power flows and activating shunts to modify the voltages.

Basically, Convergence performs a load flow calculation for the entire French transmission network according to the desired assumptions. As a result, all the power flows through the lines and the voltages at every node are displayed for the specific simulated situation. In that way, it is very easy to identify which element does not respect the “N-1” criterion, and is therefore susceptible to jeopardize the entire network.

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2.2. Theory for load flow calculations

The load flow method is at the center of this Master Thesis because all the softwares used are based on it. This process is very useful for computing the voltages and power flows in a given network.

For the rest of this report, we will consider the following representation for the lines in the electric system (Figure 7). It is a rather accurate model, called the “π-equivalent model”. All the variables are expressed in per-unit.

Figure 7: π-equivalent model of the lines

Let

̅̅̅̅ ̅

̅̅̅̅ √

The power through this line can be expressed as:

̅̅̅̅ ̅̅̅̅ ( ̅̅̅̅ ̅ )

With,

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and are respectively the real part and the imaginary part of the complex power ̅̅̅̅.

They are called active and reactive powers and they depend on the voltage magnitude and phase angle of the two buses.

In an electrical network, the power can be generated and consumed at many different locations. We consider now, a system with N buses where a generator and a load can be connected at each bus as shown in Figure 8. The bus k is linked with the others buses by N electrical lines.

Figure 8: Representation of the bus k

Kirchoff’s current law gives:

̅ ̅ ∑ ̅

By taking the conjugate of this equation, and multiply it with the bus voltage, the same equation stands for the complex power:

̅ ̅ ∑ ̅

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̅ is the generated complex power at bus k.

̅ is the consumed complex power at bus k.

̅ is the complex power flow from bus k to bus j.

The power balance at bus k must hold both for the active and reactive part of the previous expression. That means:

{

∑

Let and be the net generation of active and reactive power at bus k. They are assumed constant.

and are the active and reactive powers through the line kj. As described previously, they depend on the voltage magnitude and phase angles of the two buses.

We have 2N equations to describe the system but there are four variables of interest at each bus: the net active and reactive power and , the voltage magnitude , and the voltage phase angle . There are therefore 4N unknown variables for only 2N equations. The system is not solvable.

It is necessary to specify two quantities at each bus in order to reduce the number of unknown variables.

 For the buses with pure load demand, we often know the active and reactive powers consumed. That means, that and are known. The unknown variables are then, and . It represents a system bus where the power consumption can be considered to be independent of the voltage magnitude.

These specific buses are called “PQ buses” because the active and reactive powers are specified.

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 On the contrary, the generators connected to the system often have a voltage regulating device, which makes the magnitude of the voltage almost constant at the bus, and independent of the net reactive power generation. Then, it is easier to specify the net active power generation and the voltage magnitude: and are known whereas and are still unknown.

These specific buses are called “PU buses” because the active power and the voltage magnitude are specified.

 If a load and a generator are connected at the same bus, it can either be a “PQ bus” or a “PU bus” depending on the characteristics of the generator and the load.

At this point, two comments must be made:

 The first one concerns the active powers: it is not possible to specify P at every bus.

Thus, it is necessary to choose a bus as a “reference bus” where the net active power generation is unknown. Since P is allowed to vary at this bus, a generator must be present.

 The second comment is related to the voltage phase angles: only the difference between them appear in the equations. That means, that we can add the same constant to every phase angle without changing the system. This, since the phase angles are only relative to one another and not absolute. The voltage phase angles must then, be given as an angle in relation to a reference angle. The “reference bus” also plays this role.

To conclude, it is necessary to add a “reference bus” also called “slack bus”, where the voltage magnitude and phase angle are known whereas the active and reactive powers are unspecified.

The following table (Table 4) summarizes the different type of buses considered:

Bus type Number Known variables Unknown variables

Slack bus 1 U,θ

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PU bus (generator) M ,θ

PQ bus (load) N-M-1 U,θ

Table 4: Bus types for load flow calculation

The previous system with the 2N equations was the following:

{

∑

We consider now, only the equations on interest:

 For the PQ buses, the equations on both the active and reactive power.

 For the PU buses, only the equations on active power.

Then, the number of equations for the new system is equal to:

These equations involve the following variables: the voltage magnitude and phase angle at each bus, and . Nevertheless, these quantities are known for the “slack bus” and for the

“PU buses”, the voltage magnitude is specified.

Then, the number of unknown variables is equal to:

This new system is solvable because it contains as many unknown quantities as the number of equations. However, its resolution is not easy because the expressions of the power flows through a line include squared voltages as well as trigonometric expressions. This system can be solved numerically by using the Newton-Raphson method for instance.

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The resolution of this system gives the voltage magnitude and phase angle at every “PQ buses” and “PU buses”. Since these quantities are already known at the slack bus, we have access to the voltage at every node of the network.

The last step consists in using these new quantities in the M+2 equations not used until now, to determine:

 The net reactive power generation at every “PU bus”.

 The net active and reactive power generation at the slack bus.

Once the entire system is resolved, the power flow through the lines, the losses and any other useful information can be easily deduced.

The most common calculation of the grid flows is the AC power flow. However, an AC power flow is computationally heavy and sometimes we do not need that level of details.

Therefore, a simplified version of the AC power flow can be used to run quick computations with less accuracy on the results. This is called the DC power flow which consists in linearizing the AC equations.

The active power transported by an AC line was:

For the DC load flow, we assume the following:

 Line resistances are negligible compared to line reactances ( ).

 The voltage amplitude is the same for all buses (in per-unit).

 Voltage angle differences between neighboring nodes are small ( ) Then, the previous AC equation can be linearized:

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∑

This system is a lot easier to solve than the AC one because there are only N equations and they are all linear. The voltage angle is known at the slack bus whereas the active power is unknown. For all the other buses, P is known and the unknown variable is θ.

2.3. Power flow congestion

2.3.1. Description

The first mission of RTE is to ensure the security of the network. The TSO should constantly monitor the power flows and keep them in the safety limits. The ampacity of an electric line is the maximum amount of current that can be safely carried through it. In fact, this limit is just an image of the safety distance between the line and objects that are located under it. The more current is transported through a line, the warmer it will get. This leads to a dilatation of the line and its possible interaction with objects below. Every line has its own safety distance and therefore ampacity, according to its voltage, its length, its composition but also the environment. For the transmission lines (high voltage) the safety distance is usually three meters as shown in Figure 9.

Figure 9: Safety distance for high voltage lines

A crucial idea to understand with ampacity is the fact that, the maximal current transported by the line is not restrained by technical limitations but it is mainly restricted by environmental issues. Since the dilatation of the line is the major problem here, the outside temperature affects the ampacity. When there are some wind and low temperatures, the line is colder so its dilatation is reduced. Hence, it is possible to transport more current before it

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reaches the safety distance. On the contrary, during summer, the dilatation effect is worsened and as a matter of fact, the ampacity is reduced.

RTE makes the distinction between three seasons to determine the ampacity of the lines:

 During winter, the ampacity is at its higher value.

 During middle season, the ampacity is at medium value.

 During summer, the ampacity is at its lower value.

Each line has thereby three security limits according to the current season. It is an important parameter to take into account during the studies. In winter for instance, the consumption is higher and so are the power flows but the lines can similarly transport more current because their ampacity is higher.

The power flow congestion occurs when the current through a line reaches the security limit (ampacity). Then, the line is automatically disconnected from the grid after a certain period of time and the power flows through the surroundings lines. This can create a chain reaction that leads to a total blackout if the “N-1” criterion was not respected. Otherwise, the network can afford to lose this line without huge consequences. RTE needs to anticipate the possible power flow congestions and verify that the “N-1” criterion is still respected in order to avoid this kind of situation.

2.3.2. Case study: Brittany

In this part, an example of power flow congestion is described with the software Convergence. The main goal is not to produce any accurate results but mainly to understand how a deterministic study is conducted.

The region chosen for this example is Brittany, it lies in the west of France. We can display the transmission network in this area with Convergence as shown in Figure 10. The purpose here is to study the security of Brittany’s power supply.

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Figure 10: Transmission network in the west of France

The first important fact to notice about Brittany is that, there are no major sources of production located there. The power comes mainly from two plants: the nuclear plant of Flamanville in Normandy and the thermal plant of Cordemais in Pays de la Loire. The currents flow unidirectionnaly from these sources to the west part of Brittany through three 400kV lines, as shown in Figure 10. Brittany is a very vulnerable region for the power supply, it is often qualified as an “electric antenna”. This term describes an area with a high consumption but no production. RTE needs to make sure that Brittany can still be supplied if a fault occurs on one of the three main lines which provide electricity in the region. That is what we are going to simulate now.

In order to examine the security of Brittany’s power supply, we consider a situation with a high consumption. The date chosen is the 19/09/2017 at 12h45, the total consumption in France is 57205 MW whereas the power consumed in Brittany reaches 3000 MW. To emphasize the region’s behavior as an electric antenna, we increase the consumption by 500MW (+16%) in the area. In order to keep the balance between the supply and the demand in this situation, the production needs to increase by the same amount of power. Hence, the two plants of Flamanville and Cordemais are chosen to change their production. In this way, the situation is worsened compared to what happened in practice. In the studies, the consumption is often increased manually by 10%. That allows the TSO to have a certain margin in the eventuality of a bad forecast.

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At this point, the network is stable, all the power flows lay within the security limits. This is called the N-state because everything is still connected to the grid. The next step consists in disconnecting one of the three main lines 400kV that provide electricity in Brittany and examine the consequences on the network. It is called the “N-1” state because one element has been removed. The 400kV lines are often very loaded, so when they are suddenly disconnected, all the power flows through the surroundings lines (225kV, 90kV) which have a lower ampacity. This situation can create serious congestions, especially in a very fragile region like Brittany, where all the power is delivered by just a few lines.

The 400kV line between Domloup (Rennes) and Plaine-Haute (Côtes d’Armor) is disconnected in Convergence to simulate a fault. The consequence is the power flow congestion of the 225kV line between Belle Epine (Rennes) and La Rance, as shown in Figure 11. The values written on the lines stand for the active power transported.

Figure 11: State of the network after the fault

Figure 12 displays the characteristics of the 225kV line Belle Epine – La Rance. The current transported by it reaches 833A whereas the ampacity (Imap) of the line is only 795A in summer. That means an overloading of almost 5%. This example illustrates the

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vulnerability of Brittany’s power supply: when the consumption in the area is high, the lines which deliver the power produced outside the region, are very loaded as well. Thereby, if a fault occurs, there is a rather good probability that the smaller lines become congested.

In this case, the “N-1” criterion is not respected because the loss of one element (the 400kV line) creates congestions. The next step would have been to find solutions to overcome this issue but this will not be described in this Master Thesis.

This is how the major part of the studies is conducted in order to verify the security of the network: the loss of every element is simulated (lines, power plants, transformers, etc). If that creates any congestion, RTE needs to come up with answers in order to guarantee an operational network despite the fault. If the study is for the long-term, the actions that RTE can take are mainly modifications of the network topology by using breakers or activating shunts. If this happens during operation, RTE can re-schedule the production in order to solve the congestion.

Figure 12: Characteristics of the congested line

If we wanted to produce an even more detailed study, we should have taken into account the small-scale production of renewable energies in Brittany. The rule consists in setting all the uncertain production at zero (in that case) in order to worsen the situation to the maximum. This can be done in Convergence because all the small-scale production is

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represented in the software even if they are not connected directly to the transmission system.

Here, a production inside the region will improve the situation because the lines will deliver less power from outside. Despite the unknown wind power production, the study will cover all the possible values and the TSO will not be surprised in real time. However, this assumption considers that all the wind turbines in Brittany are stopped at this particular hour when the consumption is maximal. That seems extremely unlikely to happen in practice. This issue is the main topic of this Master Thesis.

2.4. Overvoltages

2.4.1. Description

This second example deals with a completely different problem that exists in the grid.

RTE needs to monitor the power flows but also the voltages at every node of the network. As described previously, there are four levels of voltages in the transmission system (400kV, 225kV, 90kV and 63kV). Nevertheless, the voltage may differ a little around these values (in the range of 10% approximately). A lower voltage or a higher voltage can cause serious injuries to the network, and especially to the transformers which have been designed for a certain level of voltage. The protections will disconnect automatically some elements of the grid if the voltage goes beyond the safety limits. Therefore, it is an important parameter for the TSO to control and examine in the studies. In this part, we will focus only on high voltages caused by reactive power generation.

To understand the link between overvoltages and reactive power, we have to go back to the expression of the complex power transported by a line. As described in chapter 2 about the

“theory for load flow calculations”, the power through a π-equivalent line can be written as:

̅̅̅̅ ̅̅̅̅ ( ̅̅̅̅ ̅ ) With,

For high voltage lines (U>70kV), the line resistance can be neglected compared to the line reactance. That means, . Besides, we assume that the voltages ̅̅̅̅ and ̅ are in phase ( ). This implies that the active power flow is very small.

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( )

This equation shows that if the difference in voltage magnitude between the ends of the line is small, it will generate reactive power.

To conclude, when the active power flow is low, overhead lines and especially cables generate reactive power. This injection of reactive power will increase the voltages and may even cause overvoltages.

In real life, this is a serious situation for the TSO. It is the reason why RTE includes the summer off-peak in its studies. The situation considered is a summer night of June at 4h, when the global consumption reaches its lowest value. The active power flows through the lines are then minimal, and consequently, the voltages tend to increase and reach the safety limits. This situation is worsened by the presence of renewable energies and especially wind turbines connected to the grid. As described in the introduction, these new sources are called

“decentralized production” because they deliver power to the network by multiple points.

They are located almost everywhere in the country in contrast with the conventional power plants which are rather centralized. The consequence is a diminution of the active power flows and then, an increase of the voltages. Besides, these renewable sources do not participate to the voltage control by absorbing reactive power. The conventional power plants, on the other hand, have this useful asset. They can easily adapt their production or consumption of reactive power as needed. It does not cost any money and RTE can use this lever to secure the voltages in the network.

2.4.2. Case study: Poitou-Charentes

To illustrate this issue of overvoltages, this part describes the example of the region Poitou-Charentes and especially the substation 225kV of Fléac which is often subjected to this kind of problem. Fléac is located between two centers of consumption (the cities of Angoulême and Niort), as shown in Figure 13. The power consumed by these cities is an important parameter to consider for the study of this substation because it has a direct impact on the power flows and voltages. Not far from Fléac, a lot of wind turbines have been constructed in the recent years, especially in the area circled in blue. Today, there is almost 200MW of wind power there, and it is expected to increase in the future. What we want to

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demonstrate with this example is that, during off-peaks periods, a high production of wind power can create overvoltages.

Figure 13: Transmission network in Poitou-Charentes

First, we consider a situation with low consumption. The date chosen is the 24/09/2017 at 5h. The global consumption in France is 34000MW. At this state (N-state) all the power flows and voltages are within the security limits. The substation of Fléac has a voltage of 243kV, it must not exceed 245kV.

The next step consists in increasing the wind power production of the blue area to the maximum. That means that every wind turbine produces now at installed capacity. Of course, the conventional production should be reduced by the same amount of power to keep the balance in the network.

This simulation leads to several overvoltages in 225kV substations and especially in Fléac, as shown in Figure 14. The new voltage is 246.2kV, whereas the security limit is set to 245kV.

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Figure 14: Overvoltages in several 225kV substations

This overvoltages issue is a serious problem to consider for the TSO, just as important as the power flows congestions. But these two problematics have very different causes. Power flows congestions often happen when the consumption is rather high and a line is suddenly disconnected. Overvoltages, on the other hand, occur when the consumption is low and the wind turbines produce a lot.

This second part of the report describes the deterministic approach by the studies of two cases: Brittany and Poitou-Charentes. Each region well illustrates an important issue of the grid: overcurrents and overvoltages. For both cases, the method was quite similar: first, we base the study on a real network situation. Then, we change manually some parameters according to what we are looking for. The unknown variables are usually set to their extreme levels to cover all possible situations that can occur during real time.

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3. THE MULTI-SITUATION APPROACH

3.1. Principle of the multi-situation approach

The deterministic method is not suitable for the studies with many varying parameters.

When we analyzed the Brittany’s power supply for instance, we assumed that every wind turbine in the region was stopped for the situation of high consumption. If there was any solar panel or interconnection in Brittany, we would have done the same for any varying parameter.

In the end, the network state is not credible. The more unknown variables we have, the more assumption we need to take and consequently, the less realistic the studied situation becomes.

For the Poitou-Charentes region, we concluded that the substation of Fléac is subjected to overvoltages when the wind power production is maximal in the area, during off-peak periods. But does that really happen in practice? How many hours in a year? The deterministic approach cannot answer these questions because it focuses only on one scenario for which the combination of assumptions is the most unfavorable.

The first idea that was developed to let several parameters vary at the same time in the studies, consisted in probabilistic methods based on the Monte-Carlo simulations. The technique was very simple: consider numerous networks situations with random values for the parameters (consumption, wind, sun, etc). After several load flow calculations, it gave a scope of the possible values that the power flows could take. The number of situations considered had to be huge in order to examine all the possible scenarios that could happen. The drawback of this method is that, it did not take into account the correlation between the parameters.

Now, the approach has evolved a little, the probabilistic aspect has been completely removed but the principle remain similar. It is called the “multi-situation” method. As its name indicates, it consists in studying numerous different network situations contrary to the deterministic method which focuses only on a handful of them. Unlike considering one scenario and one value for the production and consumption at each bus, the multi-situation method uses a sequence of values for the different parameters. Typically, a series of 8760 values is chosen for each variable, one for each hour in a year. In this way, we have 8760 different network situations with, for each of them, one value of production and consumption at each bus. After computing 8760 load flow calculations (one for each scenario), we examine the 8760 possible values of the power flows. This scope of values is just a picture of what the power flows could be according to the fluctuations of the grid parameters. The main idea with this method is to let the different variables change and not fix them to extreme levels.

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The 8760 values are not chosen randomly as they were with the Monte-Carlo simulations.

Now, they come directly from historic records. In fact, RTE stores the details of all the production and consumption at each bus of the network, for each hour, for the last ten years.

This makes very easy to create the sequences for a multi-situation study. For example, Figure 15 displays the wind power production in France for the year 2015. We use this kind of sequence but specified for each bus of the network.

Figure 15: French 2015 wind power production in MW

The benefit of using these series of historic values is double: first, we let the several parameters vary at the same time instead of fixing them to a certain value. Secondly, we keep the correlation that can exist between some variables because all the sequences are based on the same year. The consumption and the production from renewable sources do not seem to be correlated, but in fact, they have in common the same source of uncertainty: the outside weather. During winter, for instance, the consumption is rather high, mainly due to domestic heating. Similarly, during winter, it is also windier so the wind production is higher as well.

The opposite can be said concerning the solar production: rather low in winter and high in summer. By taking random values with the Monte Carlo simulations, we completely lose this dependency between the parameters. That is why the multi-situation approach has been chosen over the probabilistic method.

Another advantage offered by these sequences of values, is to keep the temporal consistency of the network. The values are not randomly distributed in the series, they are listed in chronological order. The power flows determined after the load flow calculations will

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keep this consistency. In that way, it is possible to characterize congestions with a concept of duration: how many hours in a year this line reaches its ampacity? How often? During which seasons? This duration factor was totally absent with the deterministic approach because only one situation was studied.

To summarize:

The multi-situation method allows several parameters to vary at the same time,

 Consumption

 Production from renewable sources: wind, solar, hydraulic

 Trades with other countries

And this, for a large number of simulations:

 8760 for one year

 It is also possible to consider several years

The benefits of this approach are numerous:

 Characterized congestions with the concept of duration, occurrence and severity

 Understand which combination of parameters leads to such congestion

 Better evaluate the efficiency of the solutions found to overcome the congestions

However, the aim is not to replace the deterministic method by a multi-situation approach but mainly to add this new component in order to produce a strong network study, that combines the two techniques. The multi-situation has also important drawbacks. The most significant is the fact that, all the calculations are done in active power only. The reactive power is not considered at all, which means that the overvoltages issues cannot be studied.

This choice does not come from any technical limitations but from pure calculation issue: it takes too much time to run the 8760 load flows in both active and reactive power. Yet, this feature is planned to be added in the near future but in this report, we assume the voltages to be constant and that the reactive power has a limited impact on the power flows.