Impact of German Renewable Energies on the Spot Prices of the French- German Electricity Markets

Impact of German Renewable Energies on the Spot Prices of the FrenchGerman Electricity Markets Bich-Thuy Doan Degree project in Electric Power Syste...
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Impact of German Renewable Energies on the Spot Prices of the FrenchGerman Electricity Markets

Bich-Thuy Doan

Degree project in Electric Power Systems Second Level, Stockholm, Sweden 2013

XR-EE-ES 2013:004

IMPACT OF GERMAN RENEWABLE ENERGIES ON THE SPOT PRICES OF THE FRENCH-GERMAN ELECTRICITY MARKETS by Bich-Thuy Doan

A thesis submitted to the Royal Institute of Technology of Stockholm in partial fulfilment of the requirements for the degree of Master of Science

Supervisors: Serge LESCOAT (INDAR Energy) & Mohammad R. Hesamzadeh (KTH) Examiner: Mohammad R. Hesamzadeh

Department of Electric Power Systems, School of Electrical Engineering Kungliga Tekniska Högskolan, Stockholm, Sweden & INDAR Energy, Paris, France December 2012

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Abstract Thanks to growing environmental concerns, renewable energies take a higher and higher share of electricity generating portfolios. In Germany particularly, the installed capacity of wind and solar plants has increased continuously for the past ten years. Given the principle of the merit-order dispatch, a greater use of wind and solar power allows the electricity spot prices to drop significantly. However, wind and sun are both intermittent resources, and this leaves great room for uncertainties on prices. As a consequence, prices become much more dependent on the weather conditions and show greater volatilities, making hedging much more difficult. At the same time, the mechanism of market coupling in the Central West Europe (France, Germany, Benelux) goes toward a harmonization of prices. As such, the cross-border interconnections play a decisive role in the electricity pricing. This paper deals with the actual influence of the interconnections between France and Germany on electricity spot prices when renewable energies are added to the energy mix. A model of a French-German market is made in order to see the impact of an increasing penetration of renewable energies on spot prices. The wind and solar generations are modelled using artificial neural networks, ANN. Multiple linear regression is employed to model the French and German loads. The cross-border interconnections are modelled based on the capacity allocations published by RTE (the national French grid operator) and finally the French and German prices are modelled with a GARCH process to study the volatilities. The study is made for three different scenarios: the reference scenario, with a penetration of renewable energies as seen in 2012, a 2020 scenario, with a penetration of renewable energies as predicted in 2012, and a 2020 scenario with increased interconnection capacities between France and Germany. Running the models shows that a higher penetration of renewable energies lowers spot prices in average, but introduces price spikes that did not exist beforehand. On short periods of observation, the volatility seems to decrease, but on longer periods, the spikes increase the volatility. Also, increasing the interconnection capacities does make the prices converge, but to a certain extent only. Finding fitting hedging strategies becomes more delicate when prices vary with such uncertainty. The study could be more developed (by extending it to the whole European continent) in order to get a more accurate vision of how energy markets will look like in a few years. However, it must be understood that the future scenarios depend on many variable factors, and no mathematical model is able to capture all those factors accurately.

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Abstrakt Till följd av en växande miljöproblematik blir förnybara energikällor en allt högre andel av dagens elproduktion. I Tyskland framförallt, har den installerade kapaciteten av vindkraft och solenergi ökat kontinuerligt under de senaste tio åren. En ökad användning av vindkraft och solenergi resulterar i en avsevärd prissänkning av elspotspriserna, detta med meritorderprincipen i åtanke. Dock är vind och sol intermittenta resurser, vilket resulterar i en stor osäkerhet kring priserna. På grund av detta blir priserna mer beroende av väderförhållanden och visar större volatilitet, vilket gör risksäkring mycket svårare. Samtidigt rör sig mekanismen för marknadskoppling i Västcentrala Europa (Frankrike, Tyskland, Benelux) mot en harmonisering av priserna. De gränsöverskridande sammanlänkningarna spelar på så vis en avgörande roll i elprissättningen. Denna uppsats behandlar det faktiska inflytande sammanlänkningarna mellan Frankrike och Tyskland har på elspotspriserna, när förnybara energikällor blir en del av energiproduktionen. För att se effekterna av en ökning av förnybara energikällor på spotpriser, görs en fransk-tysk marknadsmodell. Vinkraft and solenergi modelleras med artificiella neurala nätverk, ANN. Multipel linjär regression används för att modellera den franska och tyska förbrukningen. De gränsöverskridande sammanlänkningar skapas baserat på de kapacitetsanslag som publicerats av RTE (den nationella franska nätoperatören) och de franska och tyska priserna modelleras slutligen med hjälp av en GARCH process för att studera volatiliteten. Studien är gjord för tre olika scenarion: referensscenariot, med en ökning av förnybara energikällor som vi sett 2012, ett 2020 scenario, med en ökning av förnybar energi som förutspåtts 2012, och ett 2020 scenario med ökad sammankopplingskapacitet mellan Frankrike och Tyskland. Dessa modeller visar att en ökning av förnybara energikällor sänker spotpriser i genomsnitt, men introducerar pristoppar som inte existerade tidigare. Under korta observationsperioder verkar volatiliteten minska, men under längre perioder så ökar pristopparna volatiliteten. Ökad sammanlänkningskapacitet gör dessutom att priserna konvergerar, men endast i en viss utsträckning. Att hitta passande risksäkringsstrategier blir känsligare när priserna varierar med sådan osäkerhet. Studien kunde utvecklats vidare (genom att utvidga den till hela den europeiska kontinenten) för att få en mer rättvisande bild av hur energimarknaderna kommer att se ut om några år. Det måste emellertid förstås att framtidsscenarierna beror på många rörliga faktorer, och ingen matematisk modell har förmågan att exakt fånga alla dessa faktorer.

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Acknowledgement

I would like to express my gratitude to several people without whom the writing of this thesis would not have been possible. First, I would like to give my special thanks to my family, particularly G. NGUYEN and N. DELAUNAY, for supporting me every day throughout the whole thesis writing. I would also like to thank L. SÖDER, professor at the Electric Power Systems division at KTH, who, through his excellent lectures, gave me the will to start a thesis in this department. I would not have gone far without my supervisor at INDAR Energy, S. LESCOAT, and his advice and counselling, his suggestions and ideas. His knowledge on energy markets and financial markets came as a great support for my work. My thanks also go to Y. KOCHANSKA and D. POSE from INDAR Energy, for allowing me to work in their company in the best conditions possible. Several other people contributed as well to the progress of the thesis, one way or another. Among them, I wish to thank R. KATZ, M. ISSERLIS and S. KHOU from POWERNEXT for giving me access to valuable data which I would not have been able to obtain otherwise. I would like to thank M. THIOLLIERE, vice-president of the CRE (Commission de Régulation de l’Energie), for his time and useful references. My thanks also go to M. DHAUSSY and J-B. BART from EDF R&D for giving me the opportunity to gather more information for my thesis. And finally, I would like to thank M. GUIHOT from Supélec, for helping me in data gathering and various other things, including her reading recommendations.

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Table of contents Table of figures .......................................................................................................................... 8 Table of tables ............................................................................................................................ 9 Introduction .............................................................................................................................. 10 1 Renewable energies on the France-Germany market ....................................................... 12 1.1 Environmental policies and consequences on wind and solar penetration .............. 12 1.1.1 Reduction of CO2 emissions ............................................................................. 12 1.1.2 Investments in renewable energies ................................................................... 13 1.1.3 Support schemes for renewable energies ......................................................... 14 1.1.4 Penetration of wind and solar power ................................................................ 16 1.2 French and German generation and consumption .................................................... 18 1.2.1 Generation portfolios........................................................................................ 18 1.2.2 Consumption profiles ....................................................................................... 20 1.3 Supplying customers ................................................................................................ 21 1.3.1 Intermittency of wind and solar power............................................................. 21 1.3.2 Keeping power balance .................................................................................... 22 1.4 Impact on the France-Germany market .................................................................... 23 1.4.1 Pricing system in a perfect market ................................................................... 24 1.4.2 Structure of the markets ................................................................................... 27 1.4.3 Comparison of prices ....................................................................................... 30 1.4.4 French and German interconnections ............................................................... 31 1.4.5 Spot prices future evolution ............................................................................. 32 2 Existing methods of analyses ........................................................................................... 35 2.1 Preliminary observations .......................................................................................... 35 2.2 Marginal cost model and multiple linear regression ................................................ 35 2.3 Power flow solution ................................................................................................. 38 2.4 Statistical analysis .................................................................................................... 41 2.5 Impact on European cross-border transmission ....................................................... 43 3 Econometrical analysis ..................................................................................................... 47 3.1 Preliminary observations .......................................................................................... 47 3.2 Description of the France-German market model to compute prices ...................... 52 3.3 Modelling of intermittent energies ........................................................................... 54 3.3.1 Wind production modelling ............................................................................. 55 3.3.2 Solar production modelling .............................................................................. 58 3.4 Modelling of the load ............................................................................................... 59 3.5 Market simulation procedure and results ................................................................. 63 3.6 Modelling of the spot prices ..................................................................................... 66 3.6.1 Mean-reverting jump diffusion models ............................................................ 66 3.6.2 ARCH/GARCH models ................................................................................... 68 3.7 Discussions ............................................................................................................... 78 4 What can be expected in the future? ................................................................................ 79 References ................................................................................................................................ 82 Appendices ............................................................................................................................... 86

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Table of figures Figure 1.1: Avoidance of greenhouse gases emissions in Germany in 2011 ........................... 13 Figure 1.2: Investment in renewable facilities in Germany in 2011 ........................................ 13 Figure 1.3: Production from renewable energies in France and Germany............................... 16 Figure 1.4: Wind and solar productions in France and Germany ............................................ 17 Figure 1.5: Installed wind capacity in France and Germany .................................................... 17 Figure 1.6: Installed photovoltaic capacity in France and Germany........................................ 18 Figure 1.7: French installed capacity in 2011 .......................................................................... 19 Figure 1.8: German installed capacity in 2011 ........................................................................ 19 Figure 1.9: Monthly load in France and Germany since 2009 ................................................. 20 Figure 1.10: Daily consumption profile in France and Germany............................................. 21 Figure 1.11: Planned and actual wind production in Germany ................................................ 22 Figure 1.12: Pricing system in a perfect market ....................................................................... 25 Figure 1.13: Day-ahead prices in France and Germany ........................................................... 27 Figure 1.14: Calendar 13 prices in France and Germany ......................................................... 28 Figure 1.15: Shares of the French power exchange Powernext ............................................... 29 Figure 1.16: Shares of the German power exchange EEX ....................................................... 30 Figure 1.17: Difference between French day-ahead prices and German ones ......................... 31 Figure 1.18: Variations of day-ahead prices in France and of transmissions from Germany to France ....................................................................................................................................... 32 Figure 1.19: Illustration of higher marginal costs to cover for start-up costs .......................... 33 Figure 2.1: Illustration of marginal cost model ........................................................................ 36 Figure 2.2: System marginal cost with and without renewable generation ............................. 36 Figure 2.3: Variation of spot price with wind power penetration ............................................ 41 Figure 2.4: Probability density of spot prices for different wind power penetration ............... 42 Figure 2.5: EUPowerDispatch model....................................................................................... 43 Figure 3.1: German spot prices versus production of renewables ........................................... 47 Figure 3.2: French spot prices versus production of renewables ............................................. 48 Figure 3.3: Studied time series ................................................................................................ 49 Figure 3.4: Diagram of the simplified France-Germany market .............................................. 52 Figure 3.5: MLP Network ........................................................................................................ 55 Figure 3.6: Forecast values of wind production using ANN.................................................... 57 Figure 3.7: Linear fit between forecast and expected values of wind production ................... 57 Figure 3.8: Forecast values of solar production using ANN .................................................... 58 Figure 3.9: Linear fit between the forecast and expected values of solar production .............. 59 Figure 3.10: German temperature, humidity and consumption profile .................................... 60 Figure 3.11: French temperature, humidity and consumption profile...................................... 60 Figure 3.12: June 2012 consumption in France and Germany ................................................. 61 Figure 3.13: Modelled and actual French load ........................................................................ 62 Figure 3.14: Modelled and actual German load ....................................................................... 62 Figure 3.15: Modelled prices in the 2012 scenario .................................................................. 63 Figure 3.16: Modelled prices in the 2020 scenario .................................................................. 65 Figure 3.17: Modelled prices in the 2020 scenario with double capacities ............................. 65 Figure 3.18: Modelled French and German spot prices with mean-reverting jump diffusion . 68 Figure 3.19: Price volatilities in all the scenarios .................................................................... 76

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Table of tables Table 1.1: Overall French targets concerning the share of renewable energies ....................... 14 Table 1.2: Overall German targets concerning the share of renewable energies ..................... 15 Table 1.3: Market system example .......................................................................................... 24 Table 1.4: Summary of LMP results in a multi-area market .................................................... 26 Table 2.1: Multiple linear regression coefficients for Spotbase............................................... 37 Table 2.2: Nodal prices for 24 buses ........................................................................................ 40 Table 2.3: Spot price and wind power of each year ................................................................. 42 Table 2.4: Results of the dispatching ....................................................................................... 44 Table 3.1: ADF test for German spot prices ............................................................................ 50 Table 3.2: ADF test for French spot prices .............................................................................. 51 Table 3.3: ADF test for renewable production ......................................................................... 51 Table 3.4: Granger causality test results .................................................................................. 51 Table 3.5: Marginal costs per plant type .................................................................................. 53 Table 3.6: Regression coefficients for the French load ............................................................ 61 Table 3.7: Regression coefficients for German load ................................................................ 62 Table 3.8: Mean prices in the three scenarios .......................................................................... 66 Table 3.9: Coefficients of the mean-reverting jump diffusion ................................................. 67 Table 3.10: Residuals sum of squares from the Box-Cox transformation ............................... 71 Table 3.11: Autocorrelation and partial correlation coefficients of the raw series .................. 71 Table 3.12: ADF test result for trend and constant .................................................................. 72 Table 3.13: ADF test result with constant only ........................................................................ 72 Table 3.14: ADF test result with no trend nor constant ........................................................... 72 Table 3.15: ADF test result after differencing ......................................................................... 73 Table 3.16: AR(1) model results for German spot prices ........................................................ 73 Table 3.17: ARCH model results for German spot prices in the 2012 case............................. 74 Table 3.18: ARCH model results for French spot prices in the 2012 case .............................. 74 Table 3.19: ARCH model results for German spot prices in the 2020 case............................. 75 Table 3.20: ARCH model results for France spot prices in the 2020 case............................... 75 Table 3.21: ARCH model results for German spot prices in the 2020 case with doubled capacities .................................................................................................................................. 75 Table 3.22: ARCH model results for French spot prices in the 2020 case with doubled capacities .................................................................................................................................. 76

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Introduction Nowadays, sustainable development has been fairly accepted and encouraged by most countries over environmental concerns such as CO2 and other greenhouse gases emissions. Because of those concerns, renewable energies have been promoted for the past decade now and a focus has been put on wind and solar generations. Those two energies present several aspects which make them all the more attractive: they are inexhaustible, not polluting and require no production cost (there are however installation costs). For those reasons, most countries have seen their wind and solar installed capacities grow continuously. In the European Union, according to EurObserv’ER barometers, Germany and France are leading countries in both the wind and solar areas: in 2010, Germany ranked first with over 27 GW (respectively 17 GWp1) of installed wind (respectively solar) capacity. France ranked third for wind power with over 6 GW and fourth for solar power with 335 MWp. Environmentally speaking, that continuous growth is very beneficial but one has to wonder about the economic impact of an increasing penetration of renewable energies in the energy mixes. Supporters of wind and solar energies claim that electricity prices on the market will drastically go down since it doesn’t cost anything to produce electricity from wind and the sun. However, that reasoning works only if we consider that the country which produces the green energy doesn’t import or export power with any other country. In reality, this is not the case. In Central West Europe, a market coupling exists between France, Germany and the Benelux. The market coupling has been helping electricity prices to converge through cross-border interconnections, making more expensive areas become cheaper and vice-versa. One of the objectives of this paper is therefore to study the role of the cross-border interconnection between France and Germany in the making of the electricity prices. Another problem with wind and solar energies is that they are intermittent resources, i.e. no one can control when the wind will blow or when the sun will shine. This causes problems when it comes to deliver power to the consumers. For example, if there is suddenly no sun nor wind, conventional plants2 have to be started immediately to produce electricity. Since it has a cost to produce electricity with those plants, the prices can climb up very quickly. And the higher the penetration of renewables is, the more meteorological uncertainties are introduced. If electricity prices depend on those uncertainties, it can be seen that the prices will be subject to a high volatility. Therefore, the second objective of this paper is to study the impact of a higher penetration of renewables in Germany on the electricity prices volatility in both France and Germany. In order to carry out those objectives, a model of the France-Germany market is made. The model will take into account the renewable generation, the loads and the interconnection capacity. In order to model those items, a lot of data must be collected: histories of wind and solar generations, of French and German loads, of temperatures, wind speeds and atmospheric pressures in specific locations, and a history of French and German electricity prices. Simulations of the market will be run with various levels of renewables in order to get a price curve and a fitting model for the prices will be found in order to study the volatility.

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Wp: W att-peak: measure of nominal power of photovoltaic cells. We call “conventional plants” all the plants that produce electricity with non-intermittent resources (nuclear, gas, coal etc.) 2

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The paper is divided into three main parts. The first part gives the current state of electricity generation in France and Germany, with a focus on wind and solar generations. It also explains the problem of supplying the customers with electricity and introduces the notion of intermittency. A general background of the France-Germany market is also given, in order to understand the basic concepts of electricity pricing. The second part of the paper gives a literature review where some previous work on the area is presented. The literature includes papers that give preliminary results on the impact of wind or solar power on electricity prices, but in very specific conditions. The last part is the econometrical analysis that is performed to model the FranceGermany market. First, the intermittent energies are modelled with artificial neural networks, then the loads are modelled using multiple linear regression, the cross-border interconnection is modelled based on the methods of capacity allocations given by RTE 3 and the prices are modelled with two processes: mean-reverting jump diffusion and ARCH/GARCH.

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RTE: Réseaux de Transport d’Electricité, the national French grid operator.

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1 Renewable energies on the France-Germany market This first part will describe the environmental policies that have been elaborated in order to promote an increasing integration of renewable energies in electricity production in European countries. Those policies have naturally a consequence on the renewable production farms and we will focus more particularly on wind and solar farms in France and Germany. We will describe both countries’ consumption profile and generation capacities to introduce the notion of power balance (generation should equal consumption at any time) and see how the introduction of wind and solar energies affects this power balance. Finally, we will have a first overview of the France-Germany market to understand the effects of wind and solar energies on the determination of spot prices.

1.1 Environmental policies and consequences on wind and solar penetration Several directives have been issued by the EU to promote the development of renewable energies. From the “Renewable Electricity Directive”4 and the “Biofuels Directive”5, it is stated that the EU should reach a share of 21% in electricity generation through renewable energies by 2010 and a share of 5.75% in transport. However, those targets weren’t met by most Member States and brought about the adoption of a new directive in 2009, the “Renewable Energy Directive”6, setting new objectives such that the EU should reach a share of 20% of renewable energies by 2020[1]. In this part an overview of France and Germany’s current progress in term of reducing CO2 emissions is given, then a quick description of those countries’ investments in renewable energies is made. In a third part, the national support schemes to promote the use of renewable energies are detailed and finally the consequences on wind and solar penetration are described.

1.1.1 Reduction of CO2 emissions The main problem, as far as environment is concerned, is the reduction of CO2 and other greenhouse gases emissions. In that area, both France and Germany have achieved positive results: from 2010 to 2011, the estimated amount of CO2 that was emitted dropped by 19.8%, going from 34.2 million tons to 27.4 million tons[2]. This can be explained by a higher use of nuclear power, but also of wind and solar power. On the German side, it has been estimated that the avoidance of CO2 emissions amounted to 82.1 million tons in 2011[3]. Figure 1.1 shows the part of renewable energies in the avoidance of greenhouse gases emissions in electricity generation. The total amount is 87.3 million tons, with 15.5 million tons from hydropower, 34.2 million tons from wind power, 24.7 million tons from biomass and 12.9 millions tons from photovoltaic cells.

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Directive 2001/77/EC of 27 September 2001 on the promotion of electricity produced from renewable energy sources. 5 Directive 2003/30/EC of 8 May 2003 on the promotion of the use of biofuels or other renewable fuels. 6 Directive 2009/28/EC of 23 April 2009 on the promotion of the use of energy from renewable sources.

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Figure 1.1: Avoidance of greenhouse gases emissions in Germany in 2011 (source: AGEE-Stat[3])

1.1.2 Investments in renewable energies In 2011, Germany invested a total of 22.9 billion euros in the construction of renewable energies, from which 17.9 billion euros come from wind and solar power. As can be seen on Figure 1.2, the most significant investment has been in photovoltaic facilities with 15 billion euros. In comparison, France invested 4.1 billion euros in renewable energies, from which 3.6 billion euros come from solar power. The high investments in photovoltaics don’t mean that a huge amount of PV cells have been installed; they come from the fact that the construction cost is much higher than for any other power sources, renewable or not. 16000

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Figure 1.2: Investment in renewable facilities in Germany in 2011 (source: AGEE-Stat[3])

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1.1.3 Support schemes for renewable energies Given the costs of implementing wind and solar facilities, it is necessary for governments to give incentives to producers in order to promote a higher integration of those green energies, in order that electricity prices don’t skyrocket. This part will focus on the national action plans of France and Germany for their renewable energies policies. France: After the “Grenelle Environment Forum” held in 2007, a working group was formed to establish a reference scenario in order to achieve the target of 23% of renewable energies in electricity production. The adopted strategies combine tariff regulations, incentives and communication campaigns. French targets are displayed in Table 1.1 (the share of energy from renewable resources in 2005 was 9.6% as a base for comparison): Share of energy from renewable resources in the gross final energy consumption in 2020 Expected total adjusted energy consumption in 2020 Expected quantity of energy from renewable resources corresponding to the 2020 target

23% 155 268 ktoe7 35 711 ktoe

Table 1.1: Overall French targets concerning the share of renewable energies (source: MEEDDM)

France offers subsidies that fit with to the level of maturity of renewable energies sectors. For mature technologies such as hydropower and onshore wind turbines, the subsidy guaranteeing a return on investment by protecting investors from electricity price fluctuations. However, for less mature technologies such as photovoltaics, the incentives aim at reducing the initial investments. To support electricity production from renewable energies, electricity distributors such as EDF have the obligation to purchase electricity with renewable origins. The obligation to purchase is usually run on a duration of 15 to 20 years. In the case of onshore wind power, for the wind farm to benefit from the obligation of purchase, it is necessary for the wind farm to be located in a Wind Power Development Area (ZDE). Those areas are specific locations which have been acknowledged as fitting to have wind farms built on. For offshore wind power, the procedure is different as the turbines don't have to be located in a ZDE, and their development is ensured mainly with calls for tenders. In the case of photovoltaic power, the owner of the solar facility must apply to get a certificate that gives the right to benefit from the obligation of purchase. However, since April 2009 and in order to simplify procedures, solar installations with less than 250 kW of power rating are exempt of such certificates. Another way to prompt a higher penetration of renewable energies is to make national calls for projects. Those projects are entrusted to the CRE (Commission de Régulation de l’Energie). Examples of projects have been: construction of onshore wind farms or construction of photovoltaic centres in each French region. 7

Toe: tonne oil equivalent. 1 toe = 11 630 MWh

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In order to guarantee the production of electricity from renewable origin, the EU has implemented the RECS (Renewable Energy Certificate System) certificates. The RECS are managed by each country separately by a single agency (Observ'ER in France). Producers must send a request to the agency to receive the certificates; the latter are allocated after the agency has obtained proof that the producer has indeed produced green power[4]. Germany: The base for German policy is the Renewable Energy Act (Erneuerbare-EnergienGesetz, EEG). An interesting fact to notice is that in 2010, an amendment has been made in the photovoltaics in order to adjust compensation rates and to double the target for the yearly volume of solar power. In a similar way to France, Germany's targets are displayed in Table 1.2 below (the share of energy from renewable resources in 2005 was 5.8% as a base for comparison): Share of energy from renewable resources in the gross final energy consumption in 2020

18,00%

Expected total adjusted energy consumption in 2020

197 178 ktoe

Expected quantity of energy from renewable resources corresponding to the 2020 target

35 492 ktoe

Table 1.2: Overall German targets concerning the share of renewable energies (source: BMU)

Strangely enough, it can be noticed that Germany's target of share of renewable energies is lower than in France. However, Germany assumes that the 18% will be achieved through national measures only, without any help from the other Member States. But in the electricity field only, the target set by the EEG is more ambitious: a minimum of 30% share of electricity should come from renewable energies by 2020. As Germany is a federal state, each state has its own set of measures to promote renewable energies penetration, especially in the wind power field. In a more general way, Germany applies the principle of feed-in tariffs: the plant operator receives it from the grid operator whose network he supplies. The measure is obligatory, i.e. the EEG compels the grid operators to give compensation for electricity from renewable resources. A special requirement must be met by photovoltaic facilities in order to receive the feed-in tariff: they must be registered at the Federal Grid Agency in a system register. The amount of the tariff depends on the renewable source and on the technologies use. For example, in the case of wind power, offshore turbines receive a higher compensation than onshore turbines as the technology required to install offshore turbines is more complex. If Germany keeps following its current trend of growth, it is estimated that plants generating from renewable energies will reach an installed capacity of 111 GW by 2020 and will represent 38.6% of the gross consumption of electricity. The most significant investments will be done in solar and wind power, following the trend that will be described in the next part. Conjectures forecast an installed capacity of solar power of 51 753 MW and an installed capacity of 35 750 MW and 10 000 MW of onshore and offshore wind power, respectively[5]. For more complete information on support schemes in France and Germany, the reader can refer to [4] and [5].

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1.1.4 Penetration of wind and solar power As a direct consequence of all the aforementioned support schemes, and in relevance to the present study, the evolution of the power production from renewable resources in France and Germany from 2001 to 2011 is described in this part. On Figure 1.3, all kind of renewable energies are considered: wind, solar, hydropower, biomass and waste. Figure 1.4 however shows the production from wind and solar energies only. It can be observed that French production from renewable energies has been following a rather flat trend, remaining in a tunnel of production between 60 000 and 80 000 GWh. Germany’s production has however been growing steadily to reach 122 TWh in 2011. This represents 20% of the total gross electricity consumption in Germany. As far as wind and solar energies are concerned, Figure 1.4 shows the clear difference between both countries: while France's production barely reaches 14 TWh in 2011, Germany's production peaks at 65 TWh. Still, both countries present growing penetrations of wind and solar energies, illustrating the efficiency of the environmental support schemes. From this observation, it can be seen that the impact of renewable energies will come mainly from the German side. However, a focus on the evolution of installed capacity of wind (Figure 1.5) and solar (Figure 1.6) farms shows a continual growth in both countries, reflecting the will to integrate more and more of those energies. Photovoltaic (PV) cells have been installed in France only since 2006 with 4 MW capacity, and 7 MW in 2007. When comparing wind to solar power, one can see that the growth of solar installed capacity is much more significant than that of the wind, especially in Germany. Renewable production in France and Germany since 2001

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Figure 1.3: Production from renewable energies in France and Germany (source: RTE[2], AGEE-Stat[3])

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Figure 1.4: Wind and solar productions in France and Germany (source: RTE[2], AGEE-Stat[3])

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Figure 1.5: Installed wind capacity in France and Germany (source: RTE[2], AGEE-Stat[3])

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Figure 1.6: Installed photovoltaic capacity in France and Germany (source: RTE[2], AGEE-Stat[3])

It can be seen that the general trend of evolution for the wind installed capacity is logarithmic, while the solar installed capacity is more exponential. The discrepancy between French and German figures is reflected directly on the generation portfolio of each country, as it will be seen in the next part.

1.2 French and German generation and consumption In this part, the French and German productions from renewable energies are included in their global portfolio, in order to see the share of renewable in both countries’ energy mixes. Then the load profiles are described to introduce the problem of supplying the load. We will see later that the integration of wind and solar powers have an impact on global supply, thus on the electricity prices.

1.2.1 Generation portfolios While French generation rests mainly on nuclear power, German generation finds its biggest share in thermal plants (coal, lignite and gas). Germany’s plan to phase out its nuclear production after the incident of Fukushima in March 2011 has brought about significant changes in the country’s energy mix. At the end of 2011, France had an installed capacity of 126 GW, including 63 130 MW of nuclear, 27 790 MW of thermal, 25 400 MW of hydropower, 6 640 MW of wind power, 2 230 MW of solar power and 1 270 MW of other renewable resources.

18

1% 2%

Nuclear

5%

Thermal Hydropower Wind PV

20%

Other renewables 50%

22%

Figure 1.7: French installed capacity in 2011 (source: RTE[2])

On its side, Germany had an installed capacity of 162 GW. The energy mix in Germany is a bit more diversified, with a main share of thermal production. With eight nuclear power plants which have been shut down, only nine remain in function, making the nuclear share fall to 12% of the total installed capacity. In 2010, it represented 22% of the installed capacity. The share of wind and solar powers represents however 27% of the capacity, against 7% in France.

6%

12%

10%

Nuclear Thermal Pumped storage Run-of-the-river Seasonal storage

17%

Wind Solar 42%

2%

Others

4% 7%

Figure 1.8: German installed capacity in 2011 (source: EEX{1})

19

1.2.2 Consumption profiles On one hand is generation, on the other hand is the consumption (or load). In order to know how much generation power should be dispatched, it is necessary to have a fair idea of how the load looks like. Despite the fact that loads follow a stochastic behaviour, a global periodicity can still be observed, especially if a separation is made during a year between winter and summer. As can be seen on Figure 1.9, in winter, the load is much higher since there is a strong need for heating while in summer, there is a significant drop in consumption. (In some other countries such as the US, it is the opposite due to a high use of air conditioning.)

60000

Consumption (GWh)

55000

50000

Germany France Average summer Ge

45000

Average summer Fr Average winter Ge

40000

Average winter Fr

35000

2012/4

2012/1

2011/10

2011/7

2011/4

2011/1

2010/10

2010/7

2010/4

2010/1

2009/10

2009/7

2009/4

2009/1

30000

Figure 1.9: Monthly load in France and Germany since 2009 (source: ENTSO-E{1})

When comparing with German yearly load, one can notice that the difference between winter load and summer load is not as pronounced as in France, meaning that the German consumption profile can be considered more ‘constant’ than the French one. The regular pattern that can be observed on a yearly basis can also be observed on a daily basis (Figure 1.10). Again, the profiles of both countries are similar, with a maximum load at lunch and dinner time. In theory, the knowledge of those profiles should be enough to determine the necessary generation that needs to be dispatched. In reality, operators must take into account other factors while forecasting the load. These factors are[6]: -

Overall economic activities and population Weather conditions Price of electricity (so called price-sensitive loads) Technological improvements of the energy end use

Predicting each of these factors involves uncertainties in the power delivery equation.

20

80000 75000

Consumtion (MW)

70000 65000 60000

Germany France

55000 50000 45000

01 :0 0: 00 03 :0 0: 00 05 :0 0: 00 07 :0 0: 00 09 :0 0: 00 11 :0 0: 00 13 :0 0: 00 15 :0 0: 00 17 :0 0: 00 19 :0 0: 00 21 :0 0: 00 23 :0 0: 00

40000

Figure 1.10: Daily consumption profile in France and Germany (source: ENTSO-E{1})

Does this mean that if somehow, the load could be predicted accurately, there would be no delivery problem? The answer is no, as it will be seen in the next part, for there is not only uncertainties on the determination of the load, but also on the generation. And the main reason for those uncertainties is the integration of wind and solar powers in the generation mix. This will be seen in the next part.

1.3 Supplying customers The fundamental characteristic of electricity is that once it is generated, it can’t be stored, i.e. it must be delivered to consumers for immediate use. This implies that at any given time, generation must equal consumption. It is therefore necessary, at any given time, to be able to forecast the value of the load. It will be seen in this part that the integration of wind and solar powers in the grid adds an intermittent factor to the equation; this intermittency has to be taken into account when supplying customers. The intermittency of wind and solar powers is illustrated in this part, in order to understand the problems it poses to calculate the required generation and see how it could impact electricity prices.

1.3.1 Intermittency of wind and solar power As one cannot control when wind should blow or when the sun should shine, operators can only rely on models to forecast the production of wind or solar farms. Those models can be relatively simple or more complex, but in any case they cannot ensure a complete accuracy in the results and errors are necessarily introduced. In the case of solar power, the errors may

21

be narrower as there is usually a peak at midday and no sun at night. In the case of wind power, distribution profiles of wind speed have been developed but the errors with the actual wind production can vary from a site to another. Daily data over a month has been collected from the EEX database in order to illustrate that fact. The data represents the planned production and actual production of wind power in Germany in June 2011. 18 000 16 000

Production (MW)

14 000 12 000 10 000

Actual production Planned production

8 000 6 000 4 000 2 000

12 /0 6/

20

12 28

/0 6/

20

12 24

/0 6/

20

12 20

/0 6/

20

12 16

/0 6/

20

12 12

08

/0 6/

20

12 20 /0 6/ 04

01

/0 6/

20

12

0

Figure 1.11: Planned and actual wind production in Germany (source: EEX{2})

The calculation of the correlation coefficient gives a result of 0.92, which isn’t too bad, but which could be improved. Quite often, it can be noticed that the actual production is lower than the planned production, which means that more conventional units have to be quickly dispatched to serve the load. In the next part we will see how this can affect generation.

1.3.2 Keeping power balance System operators are in charge of keeping balance between production and generation through scheduling, real-time dispatch and regulation processes. The dispatching is done in such a way that it minimizes electricity price while maximizing reliability towards the customers. As seen above, the traditional strategy is to first dispatch the lowest-cost units, and then supply the remaining load with more expensive units. Normally, when the supply is only conventional (i.e. non intermittent generators), those actions are based on deterministic models of expected load and generation. Following the aforementioned strategy, wind and solar units should be dispatched first as their production costs are very low (no energy costs and very low operating costs). It means that whenever wind and solar resources are available, they should be dispatched immediately by the system operators. However, the problem of wind and solar powers is that their generations can’t be controlled as they depend solely on meteorological parameters. As seen before, even if 22

models can be drawn to forecast expected wind and solar productions, there will always be an error on the estimations that will induce errors on the planned generation. These intermittent generations have an impact on several generation operations[6]: -

Frequency control: normally, when balance between generation and load is kept, the frequency of the grid is constant (it is equal to 50 Hz in France and Germany). However, if there is a load increase (or generation decrease), the frequency will drop and vice-versa. When the frequency is no longer equal to 50 Hz, units must either be dispatched (if there is a load increase) or stopped (if there is a load decrease). This is called frequency control. It can be easily seen that wind and solar units can’t participate to frequency control as their dispatching can’t be controlled.

-

Ramping rate: ramping rate represents how quickly a unit can change its output. With a higher penetration of intermittent units in the grid, the apparent rate of change of the load is likely to increase. Indeed, it is very possible for the load to increase while the intermittent generation decreases, or vice versa. Therefore the ramping rates of conventional units have to increase in order to compensate for the apparent rate of change of the load.

-

Unloadable generation: unloadable generation is the amount of generation that can be quickly backed down in case of a decrease in load. Normally, with conventional units, operators don’t bother with unloadable generation: they simply trip a generator to reduce production. Now, in order to use wind and solar powers to their maximum output, conventional units must be able to back down quickly if there is a decrease in load. The backing down cannot be done by tripping a generator anymore because the unit may be needed again shortly after being tripped.

-

Operating reserve: the reserve is used to face unexpected changes in load or generation. To determine the amount of operating reserve, the operators need to be able to predict load or generation variation on the short term. The predictions can be quite unreliable when intermittent units are taken into account, and therefore more operating reserves must be available to keep a margin. However, keeping an operating reserve is expensive.

Those impacts have a consequence on the balance regulation costs: they get higher as more conventional units are required to regulate the possible imbalances in the power system. Therefore it can be seen that uncertainty in wind and solar productions forecasts induces uncertainty in the final price that the consumers have to pay.

1.4 Impact on the France-Germany market This part will use the information given previously on intermittent resources and uncertain generation to describe how electricity prices are influenced. The explanation of the pricing system in a perfect market is first detailed, then the French and German markets are described in order to understand concretely how spot prices are determined and finally a comparison of prices between France and Germany is shown.

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1.4.1 Pricing system in a perfect market Single-area market: A perfect market is a market where all the participants are assumed not to hold any dominating market power, i.e. none of them can influence the price of the commodities that are bought or sold (so called 'price takers'). A perfect market also means perfect information, which means that all the participants have full knowledge of the prices and quality of the products. In such a market, the pricing system to determine electricity spot prices is simple: it is a bidding system. Each supplier offers a bid to the power exchange, stating what capacity he can dispatch and at what price. Normally the price corresponds to its marginal cost. Then the power exchange will sort all the received bids in the merit order, i.e. by ascending prices. It means that the units will be dispatched in that order. For simplicity's sake, let's assume that the load to be supplied is not price-sensitive, that is to say it is a constant load. The price of electricity is then equal to the marginal cost of the most expensive unit that had to be dispatched. Let's take an example to illustrate the principle, where all marginal costs are kept constant for simplicity reasons (in reality, that is not the case: every extra MW that is produced costs more than the previous one; that cost is called the incremental cost). Let's assume a system where the suppliers are as listed in the following table: Generating units

Capacity (MW)

Marginal cost (€/MWh)

Wind turbine

100

3

Hydro plant

300

5

Coal plant

500

40

Natural gas plant

200

55

Table 1.3: Market system example

The values in the table are arbitrary and are given solely as an example. Now assume a load of 800 MW. The wind turbine and the hydro plant will be dispatched first as they have the lowest marginal cost. When combined, both of them give a generation of 400 MW. The coal plant is then dispatched in order to supply the 400 remaining MW. The electricity price will therefore be 40 €/MWh. Now assume that the load is 1000 MW. Like in the previous case, the wind turbine and the hydro plant will be dispatched first, then the coal plant, giving a combined generation of 900 MW. To supply the missing 100 MW, the natural gas plant needs to be started up and therefore the electricity price will now be 55 €/MWh. An easy way to determine the spot price is to plot both the supply and demand curves, as shown in figure 1.15. The price is the intersection of both curves. This method is called the Locational Marginal Pricing (LMP) method.

24

Figure 1.12: Pricing system in a perfect market

The spot price here is the one we will focus on through this thesis, and should not be mistaken with the intraday prices which are prices defined every hour due to readjustments during day. Multiple-area market: The main point of the thesis is to study the prices in both France and Germany, knowing that those countries are linked via a cross-border interconnection. In that case, the LMP method is slightly different compared to a single-area market, in order to take into account the interconnection. Two main situations can occur while considering a multiple-area market: congestion or no congestion. An example is used to illustrate those situations. Consider two areas: area A and area B. The data for both areas are displayed in the following tables: Generating units in area A

Capacity (MW)

Marginal cost (€/MWh)

Incremental cost (€/MWh/MW)

Plant A1

50

0

0

Plant A2

70

5

0.01

Plant A3

20

7

0.01

Plant A4

100

20

0.01

Generating units in area B

Capacity (MW)

Marginal cost (€/MWh)

Incremental cost (€/MWh/MW)

Plant B1

80

0

0

Plant B2

30

4

0.01

Plant B3

50

9

0.01

Plant B4

70

18

0.01

Load in area A (MW)

Load in area B (MW)

200

95

Transmission capacity between areas A and B (MW) 70

25

An incremental cost has been added to better show the impact of interconnections on prices. The new formula function to calculate the prices becomes: P(G)=MC+G*IC, where P is the price, G is the generation, MC is the marginal cost and IC is the incremental cost. If there was no interconnection between areas A and B, plants A1, A2 and A3 would produce at their maximum capacities and plant A4 would produce 60 MW in order to meet the demand in area A. Plant B1 would produce at its maximum capacity and plant B2 would produce 15 MW in order to meet the demand in area B. The price in area A would be 20+60*0.01=20.6€/MWh and the price in area B would be 4+15*0.01=4.15€/MWh. The fact that there is actually an interconnection means that cheap power can flow from area B to area A. In that case, the price in area A will decrease (because it will produce less power) and the price in area B will increase (because it will produce more power). The equilibrium is reached when the prices are equal in both areas. In that case, the multiple-area market can be considered a one-area market. In our example, the equilibrium is reached when plants A1, A2, A3, B1 and B2 produce at their maximum capacity and B3 produces 45 MW (in order to meet the demand of both areas A and B). The price for both areas A and B would be 9+45*0.01=9.45€/MWh. For this to be possible, area B should produce and transfer 60 MW more than if there was no interconnection. The transmission capacity between A and B is 70 MW, which means there is no congestion and it is possible to transfer the 60 MW. Now assume that the transmission capacity is only 30 MW. It means that area B can only transfer as much, and there is congestion. In that case, plants A1, A2 and A3 produce at their maximum capacities and plant A4 produces 30 MW. Plants B1 and B2 produce at their maximum capacities and plant B3 produces 15 MW. The price in area A is 20+30*0.01=20.3€/MWh and the price in area B is 9+15*0.01=9.15€/MWh. A summary is given in Table 1.4: Case No interconnection No congestion Congestion

Price in area A (€/MWh) 20.6 9.45 20.3

Price in area B (€/MWh) 4.15 9.45 9.15

Table 1.4: Summary of LMP results in a multi-area market

It can be seen that there is a benefit from importing cheap power provided that the capacity of the transmission line is big enough. As said at the beginning of this part, this system works in a perfect market. In reality, there is no such thing as a perfect market, and the way to determine electricity prices isn't so easy, because of market power and imperfect information. In that case, forecasting prices becomes a more difficult exercise. However, even if the market is assumed to be perfect, it can be seen that the integration of wind and solar powers makes the determination of prices rather difficult as no supplier can bid with 100% accuracy a certain amount of MW from their wind or solar farm. Theoretically, the prices should drop since wind and solar powers have extremely low marginal costs. But the wind and solar productions can vary at any time, changing the supply curve and therefore the electricity prices. The consequence is that the prices have to face a greater volatility than when the production is made only by conventional units. That volatility will have to be taken

26

into account while modelling the impact of wind and solar powers on the France-Germany market.

1.4.2 Structure of the markets When talking about the market, a difference must be made between the short-term (or day-ahead) market, and the long-term market. Spot prices correspond to prices on the dayahead market. It is called day-ahead because the prices are set on the previous day for the next day. Figure 1.13 shows the day-ahead prices in France and Germany since 2008. It can be seen that they present a high volatility, with prices ranging globally from 5€/MWh to 135€/MWh. This is easily explained with the fact that there are several factors influencing the prices on the short term: meteorological conditions which can change abruptly, sudden failure of generating plants, unexpected increase in load etc. For example, the high French peak (612€/MWh) is due to a bad timing in the market coupling with Switzerland while the negative German peak (-139€/MWh) is due to an excess of generation, and the consumers had to be paid to consume electricity.

300,00 250,00 200,00

€/MWh

150,00 100,00

Germany France

50,00 0,00 -50,00 -100,00

01/05/2012

01/01/2012

01/09/2011

01/05/2011

01/01/2011

01/09/2010

01/05/2010

01/01/2010

01/09/2009

01/05/2009

01/01/2009

01/09/2008

01/05/2008

01/01/2008

-150,00

Figure 1.13: Day-ahead prices in France and Germany (source: Powernext)

As seen before, adding the intermittency of wind and solar powers is going to increase this volatility even more. On term market, there are several types of contracts, (derivatives): month-ahead, quarter and calendar. Quarters represent three months and are numbered: Quarter 1 represents January, February and March; Quarter 2 represents April, May and June and so on. A calendar represents a year. Actors buying those types of contract buy or sell electricity for a delivery on the next month (month-ahead), the next trimester or the next year. Those contracts

27

aim at reducing the risks taken by the market actors, and especially to limit the volatility of the prices. Figure 1.14 shows the Calendar 13 prices in France and Germany. Calendar 13 means that electricity traded on that contract will be delivered in 2013. 55 54 53

€/MWh

52 France

51

Germany

50 49 48

02/10/2012

02/09/2012

02/08/2012

02/07/2012

02/06/2012

02/05/2012

02/04/2012

02/03/2012

02/02/2012

02/01/2012

47

Figure 1.14: Calendar 13 prices in France and Germany (source: Reuters)

It can be seen that the volatility is much lower, with prices ranging globally from 48€/MWh to 54€/MWh. The longer span of time is the main factor in reducing the prices volatility, as they are calculated over an average of spot prices[7]. French market: Since 2000, the organization of the French electricity network is split in two: the production and retailing part is supervised by EDF (Electricité de France) while the transmission part is managed by RTE (Réseaux de transport d’électricité). Previously, both production and transmission was the sole responsibility of EDF. The deregulation of electricity market has forced France to open its market to competition, which happened in several steps from 1999 where 30% of the market was open, to 2007 where 100% of the market was open. In 2001, Powernext, the French power exchange, was founded. Several branches of Powernext are launched almost every year such as Powernext Day-ahead, Powernext Carbon (spot market for CO2 allowances) or Powernext Intraday (for electricity to be delivered on the French hub). At the end of 2008, Powernext Day-ahead and Powernext Intraday have been transferred to a common platform, EPEX Spot SE, dealing with the markets in France, Germany, Austria and Switzerland.

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German market: On the German side, deregulation started in 1998. At that time, in Germany, there were eight generation companies. Following the deregulation, some companies merged and others were acquired by foreign companies, reducing their number to four: RWE and VEW merged into RWE then Preussen Elektra and Bayernwerk merged to E.ON. HEW, VEAG and BEWAG merged to the Swedish Vattenfall Europe and the French EDF bought a major part of EnBW[8]. In 2000, Germany’s first power exchange, Leipzig Power Exchange (LPX), was created. During the same year, a second power exchange was started: the European Energy Exchange (EEX). Both power exchanges then merged in 2002 into EEX. As said earlier, EEX entered in close cooperation with the French Powernext through the joint venture EPEX Spot SE. The shares of the French and German power exchanges can be summarized in Figure 1.15 and Figure 1.16. ECC (European Commodity Clearing AG) is the central European clearing house for exchange and OTC transactions in power, natural gas, emission rights and coal. EMCC GmbH (European Market Coupling Company) is a company which deals with the congestion management at the German-Danish border. Store-x GmbH (Storage Capacity Exchange) is a platform for secondary trading in storage capacities for natural gas, and Trac-x GmbH (Transport Capacity Exchange GmbH) is a platform for natural gas transport capacities. To summarize the current situation of the France-Germany market, the trades are realized mainly on two common platforms: EPEX Spot SE (common power spot exchange based in Paris) and EEX Power Derivatives GmbH (common power derivatives exchange based in Leipzig).

Figure 1.15: Shares of the French power exchange Powernext (source: Powernext)

29

Figure 1.16: Shares of the German power exchange EEX (source: EEX)

1.4.3 Comparison of prices As seen before, the “renewable effect” comes mainly from the German side. The question then is how will this affect the prices in France? First, data on day-ahead prices in France and Germany is collected. Figure 1.17 shows the difference between French day-ahead prices and German ones. It can be seen that the gap is usually positive in winter and negative in summer (the darker curve represents the real fluctuations in the price difference, while the lighter curve represents a mobile average, given for more clarity). This can be explained by the fact that in winter, the demand in electricity is very high in France (as shown on Figure 1.9) and the nuclear production cannot cover it all. As a result, more expensive units must be dispatched. In summer however, the demand is much lower than in Germany, and the nuclear production can cover a much higher part of the load. There are noticeable spikes during winter 2009-2010 and 2010-2011 due to successive waves of cold in France. February 2012 has been particularly cold too, which can be clearly seen on the graph. If a closer look is given to the graph, it can be noticed that the spread in prices difference is quite large until 2010 while it is much narrower afterwards. It happened that on November 9th 2010, the market coupling of the Central West Europe (CWE, which includes France and Germany) was launched. As a result, spot prices started converging, hence the smaller spread in prices difference. As explained in 1.4.1, the fact that prices converge means that the power produced in each country is distributed all over the CWE in order to level the prices.

30

100

Difference (€/MWh)

80 60 40 20 0 -20

01/07/2012

01/04/2012

01/01/2012

01/10/2011

01/07/2011

01/04/2011

01/01/2011

01/10/2010

01/07/2010

01/04/2010

01/01/2010

01/10/2009

01/07/2009

01/04/2009

01/01/2009

01/10/2008

01/07/2008

01/04/2008

01/01/2008

-40

Figure 1.17: Difference between French day-ahead prices and German ones (source: Powernext)

This means that the interconnections between France and Germany play a major role in determining electricity prices, and that the German production has an impact in France. The point afterwards will be to see how a higher penetration of wind and solar powers in the grid can influence the prices in both France and Germany through their interconnections.

1.4.4 French and German interconnections “Market coupling mechanisms allow the optimization of the allocation process of crossborder capacities thanks to a coordinated price formation mechanism, taking into account orders placed by the members of different exchanges.” (Source: EPEX Spot SE). The launch of market coupling in the CWE in November 2010 has allowed prices to converge between France and Germany (among other countries) by using available cross-border transmission capacities for power exchange. Allocation of transmission capacity is made through implicit auctioning, meaning that the transmission capacity is used to integrate the spot markets of the various countries. Data about the utilization of transmission capacities on the France-Germany interconnection was collected from RTE in order to pinpoint a relation between transmission and price. The variation of day-ahead prices in France was calculated every day as well as the variation of the volumes transmitted from Germany to France. The result is plotted on Figure 1.18.

31

40 000

150

Transmission from Germany to France

100

Price

30 000 20 000 50

0

0

€/MWh

MW

10 000

-10 000 -50 -20 000 -100 -30 000

28/05/2012

21/05/2012

14/05/2012

07/05/2012

30/04/2012

23/04/2012

16/04/2012

09/04/2012

02/04/2012

26/03/2012

19/03/2012

12/03/2012

05/03/2012

27/02/2012

20/02/2012

13/02/2012

06/02/2012

30/01/2012

23/01/2012

16/01/2012

09/01/2012

-150 02/01/2012

-40 000

Figure 1.18: Variations of day-ahead prices in France and of transmissions from Germany to France (source: RTE{1}, Powernext)

It can be often seen that, globally, when the price variation is negative, the transmission variation is positive and vice versa. It means that when transmission from Germany to France rises, day-ahead prices in France drop. Most likely the conclusion that can be drawn is that France imported cheaper power than its nuclear power from Germany, and the only cheaper power that exists in Germany is wind and solar power. Therefore the import of renewable power to France has a certain impact on day-ahead prices. There are mismatches on the graph, and those mismatches are due to various factors such as sudden weather changes, unexpected nuclear plants breakdowns, congestions or the timing when the data was acquired. Indeed, the day-ahead prices are set on the previous day for the next day based among other things on the weather forecasts, and the transmission capacities are then allocated through bids. Unexpected occurrences can change the actual transmissions; this shows that spot prices are influenced by many other external factors.

1.4.5 Spot prices future evolution As it can be seen in the previous parts, several factors influence spot prices and the introduction of renewable energies introduce variations of those factors, making it difficult to know for certain if the general trend of spot prices will be bearish or bullish. In this part we will make a summary of the various factors and their impact on spot prices. Bearish factors: Wind and solar energies have no marginal cost, making wind and solar farms a priority to dispatch. This dispatching will put aside units with higher marginal costs, making spot prices go down. Also, since wind and solar energies will be used first, it means that the demand in other fuels such as oil, gas or coal will decrease. If the demand decreases, the price of those fuels will decrease as well, which will lower the marginal costs of those units.

32

Bullish factors: They come mainly from the intermittency of wind and the sun. When those resources aren’t enough, conventional units must be dispatched for shorter periods of time than without intermittent units. It means that the start-up costs of the conventional units won’t be optimized, and the marginal costs will increased to cover for the start-up costs as shown in Figure 1.19:

Figure 1.19: Illustration of higher marginal costs to cover for start-up costs (source: [9])

Another factor that may tend to increase prices is the increased variability of the demand towards flexible resources such as gas[9]. To face the growing variability, more storage facilities and flexible production facilities have to be built, and the plants’ operating costs can go up. The fact that the demand in those fuels gets lower and more variable erases the scale economies in operating the plants, thus driving the prices higher.

Conclusion In an environment where European (and global) policies prompt producers to install more and more renewable units, it is relevant to start wondering about the impact they can have on the electricity market. Through subsidies, taxes and other incentives, investments have been made in both Germany and France (though much less in the latter), especially for photovoltaic cells. As such, both countries have seen their generation portfolio change to include more production from wind and solar power. The evolution of the generation portfolio has an impact on the way the demand is supplied, for the reason that wind and the sun are intermittent resources and introduce a factor of uncertainty. Meteorological conditions cannot be controlled, and therefore generation from those resources becomes stochastic. Under those conditions, the volatility of spot prices becomes higher, which means that prices can very well face a sudden increase, for example if it is a cloudy and non-windy day. When only conventional generators are used, those uncertainties can be overlooked as system operators simply need to request more (respectively less) generation from a unit when the load is higher (respectively lower) than the forecasts. When including wind and solar power, operators aren't even certain of the dispatched generation as meteorological conditions may suddenly change. Therefore it is much more difficult to decide in real time the capacity to dispatch and it results in higher costs for maintaining balance from the operators. Those costs will eventually have an impact on spot prices.

33

Now, as mentioned earlier, the main supplier of renewable energies is Germany (with a share of 27% of its installed capacity versus 7% in France). Therefore it can be wondered how the German production can influence the French prices. For France and Germany, spot prices are decided on a common power exchange, EPEX Spot SE. The decision to merge the electricity markets of both countries in a common platform is in accordance with the policy of market coupling which aims at harmonizing electricity prices in the Central West Europe. The launch in November 2010 of the market coupling in CWE has started making prices converge though they still aren’t completely harmonized as transmission capacities are limited. Still, a closer look shows a general trend between transmissions from Germany to France and spot prices in France: the latter tend to drop when the transmissions increase. Therefore the exportations to France do have an impact on French prices. In any case, several factors must be considered in order to study the impact of wind and solar powers on prices with as much accuracy as can be. Those factors can for example be: stochastic behaviour of the weather, unexpected generation faults, stochastic behaviour of the demand, future environment policies or energy regulation laws. Various methods have already been suggested to model the generation of a power system with and without renewable energies, and other methods have been developed to model the load and determine the electricity price. The next part will review some of those methods and analyze the obtained results.

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2 Existing methods of analyses This part will present four papers. The three first papers describe different approaches that have been used in order to study the impact of renewable generation on spot prices. The first paper suggests simple methods in order to illustrate the general trend taken by prices when wind and solar generations is used, while the second paper gives a more detailed and quantitative model through an optimization problem to find electricity prices in a nodal system. The third paper makes observations on the relationship between wind power and spot prices (and notably prices volatility), based on historical data. The fourth paper is very recent. It studies the impact of renewable energies in neighbouring countries in 2025. This is of great interest as the scope of the present thesis is to study the impact of the German production not only in Germany, but also in France.

2.1 Preliminary observations A few remarks should be made on the studied literature. First, a closer look on the data used in the various papers shows that different time steps are used. In the first paper, the data is averaged on a monthly basis, which doesn’t reflect the volatility of a daily spot price. In the second paper, the time step that is chosen is the hour, therefore the data is generated hourly to give one final price per node. The third paper which presents interesting results does not give the detail of the data that were used. Instead it only gives year-averaged results and therefore one has to be careful as for how the calculations were made. As a summary, all those papers only give a unique price at a certain date, which doesn’t allow us to study the impact of the volatility of intermittent resources on the volatility of spot prices. The fourth paper is a particular case, as it tries to compute expected values of load and generation in 2025. Another point is that none of the three first papers (the oldest) study the impact of renewable generation on another country. The first paper considers a package of countries as a single country (with no transmission limitations) while the two other papers consider the impact within the country where the production comes from. The last paper which actually deals with cross border transmissions was submitted in June 2012; this shows that studies in that area have started only a short time ago and are therefore still recent and under development.

2.2 Marginal cost model and multiple linear regression In [10], Obersteiner and Redl study the impact of renewable energy sources (RES-E, excluding hydropower) on the EEX Spot market, first by using a marginal cost model and then a multiple linear regression. Marginal cost model: In accordance to the dispatching strategy of merit order (the lowest-cost units must be dispatched first), the supply curve and the demand curve are drawn. Adding generation by renewable energies is equivalent to a decrease in demand. This is translated on the supply-

35

demand graph by a shift of the demand curve to the left (Figure 2.1). As a consequence, the spot price (determined by the intersection of both curves) is lowered.

Figure 2.1: Illustration of marginal cost model (source: [10])

The assessment of the EEX spot prices is made by considering that Germany, Austria, Switzerland and France (called the Central European submarket and composed of the four countries that share their markets on EEX Spot market) are not subject to cross-border transmission capacity bottlenecks and therefore the spot price is the same for all those countries. The system’s marginal cost when including renewable generation is then plotted and compared with the marginal cost with no renewable generation. The results are displayed on Figure 2.2. The dashed curve represents the cost with no renewable generation while the plain curve represents the cost with renewable generation.

Figure 2.2: System marginal cost with and without renewable generation (source: [10])

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As the load-burden is lessened due to the renewable generation, the marginal prices decrease (quantitatively, the decrease amounts to 9%). This marginal cost model is very simple, and omits various factors such as the intermittency of the RES-E, volatility of the demand or transmission capacity limits. Still, it gives an idea of the price trend. In order to confirm that trend, Obersteiner and Redl use a second method, empirical this time, in order to model the influence of various parameters on the spot prices: multiple linear regression. Multiple linear regression: The main hypothesis is to assume that spot prices are also influenced by the generation costs of conventional plants. Therefore the following linear regression is suggested: ln( Spotbase)  b1  b2 ln(GRES )  b3 ln( MCCCGT )  b4 ln( MCHC )

(2.1.)

where ln represents the natural logarithm, Spotbase is the monthly average of spot prices, GRES is the generation in RES-E, MCCCGT is the marginal cost of CCGT and MCHC is the marginal cost of hard coal plants. bi (i=1…4) are the parameters of the linear regression model, to be determined. The least squares method8 is used to determine them and the results are given in Table 2.1:

b1 b2 b3 b4 R²

15,02 -1,42 0,71 -0,02 0,70

Table 2.1: Multiple linear regression coefficients for Spotbase (source: [10])

The negative sign for b2 is sensible and confirms the fact that a higher renewable generation lowers the spot prices. In the same way, a positive sign for b3 is normal as a higher use of CCGT increases the spot prices. However, what is noticeable is the impact of hard coal plants: it is negligible and in fact, it even seems to make prices go down (though slightly). This strange fact could be due to insufficient data used for the least squares method. What should be noticed though is that the CCGT have a much bigger influence on prices than coal plants.9 The regression coefficient R² shows that the relation between the logarithm of the spot prices and the other aforementioned factors isn’t exactly close to linear, but still gives coherent results. One of the main problems that was raised in the previous part of the thesis was the stochastic nature of renewable sources (wind and solar). It was shown that it has an impact on spot prices through the amount of load burden the renewables can relieve from conventional plants. But it can actually be a burden itself if there is a sudden shortage of wind or sun. Obersteiner and Redl offer two simple ways to model and illustrate the bearish trend of spot prices but the stochastic aspect was neglected. In the first model (marginal cost model) it is not taken into account at all while in the second model it was taken into account but only in an empiric way, from sole observations of past data. No method was suggested to model the 8

See appendix A. It must be noted that those calculations were made in 2006-2007, at a time where it was more profitable to run gas plants than coal plants. Today in 2012, the trend is clearly the opposite: coal plants are much more profitable than gas plants (in an era where CO2 emissions are supposed to be cut down…) 9

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volatility of renewable sources. In their paper, Obersteiner and Redl actually discuss the effect of limited predictability of wind power by calculating the accuracy of previous forecasts and comparing it with the imbalance costs on the same periods. They show that the imbalance costs are reduced with more accurate forecasts. But the main problem of volatility remains. It can be seen in their comparison that in order to assess spot prices as accurately as possible, it is necessary to be able to forecast wind and solar productions as accurately as possible. For that purpose, several methods exist to model the stochastic volatility of wind and solar productions. The next model that is going to be described includes such considerations.

2.3 Power flow solution Zhao, Wang, Goel and Ding suggest in [11] a model for each of the following points: wind generation, solar generation and load in Singapore. An Optimal Power Flow problem is then formulated and solved in order to get nodal prices in a power system with a given number of nodes and buses. Using a nodal system has the advantage of representing customers’ preferences. A node has a certain price and a certain reliability, and therefore the customers can choose to pay a higher price to get a certain reliability, or to neglect it to a certain extent for a lower price. The customer’s behaviours have in turn an impact on the nodal prices. Model of wind generation: A time step of an hour is used to generate a series of hourly wind speeds. The output power of the wind turbines is then determined based on the wind speeds. The series of wind speeds SWt at time t is given by: SWt  t   t * yt

(2.2.)

where μt is the hourly mean wind speed and σt is the hourly standard deviation. yt is a time series built on an ARMA (autoregressive moving average) model as follows: p

q

i 1

j 1

yt   i yt i  at    j at  j

(3.1.)

where Φi and θj are the autoregressive and moving average parameters of the model, and at is a white noise, normally distributed and centred in 0. Its variance σa2 has to be determined along with the ARMA parameters. The power output then depends on the wind turbine design parameters. Let Vcut-in, Vr and Vcut-out be the turbine cut-in speed, rated speed and cut-out speed respectively. The power output Pw(t) at time t is given by: 0  Pw (t )  ( A  B  SWt  SWt 2 ) Pr P  r

0  SWt  Vcut in or Vcut out  SWt Vcut in  SWt  Vr

(2.3.)

Vr  SWt  Vcut out

where A and B are determined with Vcut-in, Vr and Vcut-out.

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Model of solar generation: The power output of photovoltaic cells depends on the solar radiation, which in turn depends on the meteorological conditions. In this model, the “peak sun hours” are used to calculate the power output. The peak sun hours represent the number of hours the sun should have to shine on a PV cell at its peak value to obtain the same amount of radiations that the PV cell would actually receive during the whole day. The peak sun hour at hour t is given by: PH (t )  I C (t ) /1

(2.4.)

where Ic(t) is the average hourly solar radiation at hour t (expressed in kWh/m²). Let ηs be the efficiency of the PV cells and Pm their rated power. The power output is given by: Ps (t )  PH (t ) * Pm * s

(2.5.)

Customer behaviour and load: Two assumptions are made to model the customer behaviour: the first one is that the customer wants to minimize their electricity costs, and the second one is that the system operator wants to minimize the load curtailment. This is summarized with the following function: Min  t  C ( D tj  D t 0 )   tj D tj

(2.6.)

where Dtj is the demand at time t in a state j, Dt0 is the equilibrium demand at time t in a normal state, C(Dtj – Dt0) is the cost of the load curtailment and ρtj is the electricity price at time t in a state j. The load is deduced by minimizing that function through the Reliability Test System (RTS) that has been developed by IEEE. Formulation of the Optimal Power Flow (OPF) problem: Nodal prices are calculated through the formulation of the OPF problem which wants to minimize the total generation cost and the load curtailment cost. This is expressed with:

Min f   Cg ( Pgtj , Qgtj )   Cltj (Pl tj , Qltj ) gG

lL

(2.7.)

where G is the set of generating units, L is the set of buses, Pgtj and Qgtj are the active and reactive powers of generating unit g at time t in a state j, ΔPltj and ΔQltj are the active and reactive power curtailments of the load on bus l at time t in a state j. The function is subjected to power flow constraints, generating unit limits, voltage limits, load curtailment limits and transmission line power flow limits. Also, the wind and solar units should be dispatched first to meet the demand, and only after are the conventional units dispatched. The OPF problem is then solved through the Lagrange function10 Ltj and the following prices are calculated: nodal price in a normal state and expected nodal price in case of outages. The results are displayed in Table 2.2: 10

See appendix B.

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Without renewable generation With renewable generation Bus 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Nodal price Expected nodal Nodal price Expected nodal in normal price in case of in normal price in case of state outages state outages 50,98 202,4 50,05 51,09 204,3 50,14 50,31 211,9 49,71 51,51 191,7 50,7 51,01 181,2 50,28 54,85 254,2 53,87 48,4 45,58 48,09 49,67 77,18 49,36 50,45 190,9 50,05 50,02 169,8 49,69 51,16 217 50,74 51 246,3 50,58 50,49 227,9 50,19 50,89 232,3 50,47 48,99 228 48,54 49,12 228,8 48,69 48,08 225,8 48,65 47,77 224,9 48,34 49,38 231,1 48,98 49,12 231,9 48,75 47,6 224 47,16 46,31 218,4 45,87 48,78 231,9 48,43 50,41 229,5 49,84 Table 2.2: Nodal prices for 24 buses (source: [11])

166,9 168 171,1 159,1 152 200,5 45,19 71,22 158,2 143 180,4 176,8 190,4 193,7 190,8 191,5 189,7 189,1 193,1 193,8 188,5 185 194,2 187,7

From the table of results, it can be seen that during a normal state, the prices are very slightly lower with renewable generation, but it’s not very noticeable. However, in a state of outage, when prices can skyrocket, the impact of renewable generation is much more visible as the price drop is more significant. This is explained by the fact that a higher share of the load is supplied by renewable production. This second study shows the positive impact on prices of a higher penetration of wind and solar energies in the generation mix. Of course, those results depend on the level of wind and solar resources. The results won’t be the same in a country with almost no sun or wind than in a very sunny or windy country. Also, this study has only considered one scenario of generation. To be more complete, the calculations should be done with different wind and solar generations and different loads in order to really see the stochastic aspect of the intermittent energies. Still, this study is interesting as it gives models to generate wind and solar data. The wind model will be more specifically used in the econometrical part of this thesis. The paper is also interesting from the customers’ point of view as the model developed here is a nodal model which gives the customers a choice as for how they want to be supplied (higher prices but higher reliability and vice versa). The introduction of renewable energies adds its own

40

contribution to how the nodal prices and reliabilities evolve and therefore gives the customers more choices, which illustrates the concept of a deregulated market. The nodal feature of the system that was used could be compared with several interconnected countries; however the whole transmission aspect is not detailed explicitly and doesn’t bring any enlightenment on how the generation in a node can affect the prices in another node. That problem is also part of the main problems that were raised in the previous part of the thesis.

2.4 Statistical analysis In [12], Hu, Chen and Bak-Jensen draw the relationship between wind generation in Denmark and several types of prices: spot prices, up-regulation prices and down-regulation prices. However, we will focus here on the spot prices only. First, the authors plot the variation of average spot price with wind power penetration in order to show a relationship between wind power and spot prices. The result is displayed in Figure 2.3

Figure 2.3: Variation of spot price with wind power penetration (source: [12])

What is noteworthy is not the fact spot prices decrease with wind penetration (it has already been shown in the previous papers), but that the variation is not linear. This means that the linear regression made in [10] is not quite accurate, and that we have to find another relation between spot prices and penetration of renewables. Then an observation is made on the spot prices and wind generation every year. Data history comes from Western Denmark. The mean values and standard deviations are given for each year in Table 2.3:

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Spot price (DKK/MWh) Wind power (MW) Standard Standard Mean value Mean value deviation deviation 2004 214,3 49,8 555,1 504,8 2005 277,4 127,3 573,4 511,4 2006 329,5 99,3 526,9 485,4 2007 241,4 179 635 565,2 2008 420,7 150,7 591,1 555 Table 2.3: Spot price and wind power of each year (source: [12]) Year

Now we have something interesting. First, we notice that the higher the mean value of wind production is, the higher its standard deviation is. This means that the more wind power is produced, the more volatility it introduces. We also notice a rather important fact: the higher the mean value of wind production is, the higher the standard deviation of spot prices is. This illustrates the fact that a higher penetration of wind makes spot prices more volatile. Finally, the authors plot the probability density of spot prices for different wind power penetration. The results are displayed in Figure 2.4:

Figure 2.4: Probability density of spot prices for different wind power penetration (source: [12])

What can be noticed is that the probabilities to have peak spot prices and null spot prices are higher as the percentage of wind penetration gets high. This supports the fact that high wind penetrations induce high variations of spot prices. Still, the values of the peaks are lower as the percentage of wind penetration is higher.

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In summary, the main interest of [12] is that it gives an effective first proof that an increasing penetration of wind power in the grid will increase the volatility of spot prices. The main problem of this paper is that the methodology used was not detailed, and of course the problems of solar penetration and transmission to another country are not mentioned either.

2.5 Impact on European cross-border transmission This paper[15] has been published in June 2012, partly by people from the Joint Research Centre (JRC) Institute for Energy and Transport (IET), which is an institution of the European Commission. In this paper, Brancucci Martínez-Anido, Vries and Fulli use a dispatch model of Europe to model the interconnections and see the effects of increasing renewable energies penetration in 2025. The model that is used is called EUPowerDispatch and has been developed by the JRC. It represents the 32 European countries as 32 nodes, and uses optimization to minimize the costs of dispatching. The inputs and outputs are described in Figure 2.5:

Figure 2.5: EUPowerDispatch model (source: European Commission)

Consumption is modelled based on data from 2010 by assuming that overall consumption will increase by 30% from 2010 to 2025. Generation is modelled in each country for each type of production and operational constraints are put on the plants (for example, nuclear plants are constrained between 70% and 100% of their available power). For wind generation, an hourly time series was created by averaging and interpolating existing data on onshore and offshore wind power outputs. For solar generation, a noteworthy point is the lack of available data since the photovoltaic branch is still little developed. For that reason, the installed capacity has been considered equally distributed within a country.

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The variable production costs (which are to be minimized by the model) comprise variable maintenance, operational costs, fuel costs and CO2 taxes. The latter has been set at 22€/ton11. The computation of those costs is not described in details. For the transmission capacities, EUPowerDispatch defines each interconnection between the 32 countries by its maximum transfer capacity in 2025. The capacities are calculated based on the ENTSO-E’s Ten-Year Network Development Plan. Transmission losses are included, and are proportional to the square root of the geographical areas, which implies higher losses between two big countries than between smaller countries. Once all the inputs have been defined, the authors compare a base case scenario to three other ones called A, B and C. In scenario A, the renewable capacity is double compared to the base case. In scenario B, the cross-border transmission network from 2010 is used (i.e. no new transmissions are added). In scenario C, assumptions from both scenarios A and B are considered. Results of the simulations are displayed in Table 2.4:

Table 2.4: Results of the dispatching (source: [15])

On all four scenarios, it can be noticed that solar curtailment is never needed. In the base case scenario, there is no need for wind curtailment either, which means that the planned cross-border transmission network for 2025 should be sufficient for the planned wind and solar capacities. When keep the same amount of renewables but using the transmission network of 2010 (scenario B), it can be noticed that the need for wind curtailment is very small, but the percentage of load not served isn’t null anymore, which means that extra transmission capacity is actually needed to ensure load supply. Unsurprisingly enough, in scenarios A and C (where the amount or renewables is doubled) the percentage of wind curtailment increases significantly. It is the highest when the transmission network of 2010 is kept (scenario C) and this illustrates clearly the need to have higher transmission capacities in order to serve the entire load. The impact of transmission capacities on spot prices isn’t described directly but it can be easily understood that limited transmission capacities result in wind curtailment, which in return results in an increased use of higher-cost productions. Therefore spot prices should be higher with insufficient transmission capacities. That is however an aspect which is not developed in the paper, but it must be noted that it is the only relevant one that actually studies the relationship between increasing renewable generation capacities and cross-border transmission capacities.

11

As of today, the price of a carbon ton is around 8€/t.

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Conclusion The literature review in this part has introduced several ways of determining spot prices while integrating generation from renewable sources. The first one, the easiest, is to calculate the spot price through the marginal cost of the generating units. It is a very simple and graphic model that assumes that the supply and demand curves are known accurately and that no external factor can influence those curves. Some questions that can be raised are the following: how were the marginal costs obtained for the CCGT and the hard coal plants? If it is through time series, how much data is there and how reliable is it? It must be understood that when doing regressions, the accuracy of the results depend greatly on the accuracy of the data. The second approach is to model the relation between spot prices, renewable generation and conventional generation costs with a multiple linear regression. That method is empirical as it is based on past data, and the results show that even if a linear relation doesn’t work too badly, there may be better ways to model the impact of renewables on spot prices. Furthermore, the paper was written at a time when the penetration of renewable energies wasn’t as high as it is nowadays, and doesn’t take into account the high uncertainties that are introduced because of the intermittent nature of wind and solar energies. The resulting volatility of spot prices is therefore neglected. The third method is much more detailed as it considers a nodal system and offers a model for each of the following points: wind generation, solar generation and demand. An OPF problem is formulated and optimization through a Lagrange function is used in order to solve the problem. Optimization problems are quite popular when it comes to modelling the impact of renewables penetration on nodal systems. In [13] and [14], objective functions under constraints are built in order to study the impact of solar penetration. The main difference is the system that is used in each paper, and the markets they work on: PJM (Pennsylvania-Jersey-Maryland) for [13] and Singapore for [14]. The optimization approach looks quite exhaustive and gives a significant comparison of nodal prices with and without renewable generation, but still doesn’t illustrate the price volatility in regard of a higher penetration of renewables. Furthermore, the country that is studied in that paper is Singapore, where the level of sun radiations is much higher than in France or Germany. Also, the modelling of solar production in Singapore is much simpler for two reasons: the size of the country, and the fact that is a quasi-equatorial country. In such a small country, the solar radiation can be considered homogeneous all over the area. In Germany, the photovoltaic outputs in Hamburg are not the same as in Munich, and therefore the modelling would be much more complex. The fourth method described in the third paper actually shows some results about prices volatility in regards of wind penetration in Western Denmark, based on historical data. Even though the paper doesn’t give an analytical methodology, it is one of the rare which actually gives some observations on the topic. The main problem, which has been pinpointed several times already, is the origin and the processing of the data. In this kind of research, it is quite difficult to find public long time series data which are exploitable. The wind industry is well developed now in Germany, but the solar industry is still at its beginnings, which makes data availability quite scarce, especially on the photovoltaic technology that is used.

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All in all, the results given by the three first papers converge to a single conclusion: the introduction of renewable energies lowers spot prices. Finally, the last paper introduces the notion of cross-border interconnections in the integration of renewable energies. A model was developed to represent the interconnections between all 32 countries of Europe and then simulations were run with different levels of renewables production and transmission capacities. What has to be noted is that the model was developed by the JRC which is an institution of the European Commission and the research was made by people from that institution, for that institution. By belonging to the JRC, access to data is quite easier, provided that they exist. As it was said for the solar area, it is still under development and therefore not many countries offer data on the photovoltaic production. Even Germany which is one of the most advanced countries in the area can barely offer any data. On the content of the paper itself, several assumptions were made. First, the scenarios make a projection to 2025 and all the inputs of the models are forecasts of the situation in 2025. The forecasts are based on today’s conjectures and policies for the future; however, by 2025, the probability for new changes in environmental policies to occur isn’t zero. Unexpected events can also suddenly change some countries’ policies about their generation portfolios (e.g. Germany’s decision to shut down its nuclear reactors after the Fukushima incident). And is setting the carbon price at 22€/t a legitimate decision? What impact on the consumption would an economic crisis have? Also, it was assumed that all the solar installations were equally distributed within the area of each country. As it was mentioned in the second paper, that assumption may not be reasonable for big countries. Finally, the link between the cross-border interconnections and the electricity spot prices isn’t established per se, but the paper can be a good base if a link between the wind curtailment and spot prices can be drawn. From the available literature, several general problems can be raised: first, no relevant paper was found about France since there are barely any available statistics about renewable generations there. The main reason of that lack of data is the fact that renewable energies are still new in France, even if the country plans to develop its farms more and more in the coming years. Moreover, all the studies based themselves on past data to determine a future price, which means that they don’t take into consideration the fact that renewables have a higher and higher penetration in some countries’ energy mixes, such as Germany. This poses a problem when we know that environmental policies prompts countries to increase production from renewable resources and we want to know the actual impact in the future. It also means that so far, there isn’t any model which gives an actual correlation of wind and solar penetration with spot prices, and no model to illustrate the consequences of growing intermittent generation on the volatility of spot prices. To summarize, the question that can be raised is: while knowing the proportion of renewable production in Germany on a certain day, is it possible to model out the price curve for the next day and its impact in France?

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3 Econometrical analysis It has been seen in the previous parts that in order to obtain a spot price for electricity, numerous factors must be taken into account. However, considering all of them at the same time would greatly increase the complexity of the study. Therefore it is necessary to choose only those relevant to the thesis’ topic. The main factors that will be considered here are: the wind production in Germany, the solar production in Germany, the consumption curves in both France and Germany and the transmission capacities between France and Germany. All those factors are modelled in the next sections in order to be used in the final model of the France-Germany market. What has to be remembered, though, is that even if this paper focuses only on France and Germany, those countries are still connected to other European countries as well. But the French and German markets being the most liquid, it is a reasonable assumption to consider them separately from the rest of Europe. Several simulations will be performed: a first simulation will be done with values that are representative of 2012. The main goal of that simulation is to validate the hypotheses and simplifications made in the model. Then a second simulation is made with demand and offer values that could be representative of 2020. A final simulation is done by increasing the interconnection capacities to see the impact that German renewables have on France.

3.1 Preliminary observations This section will give a first, qualitative overview of the relationship between the German production in renewables and spot prices in France and Germany, since 2010. The scatter plots on Figure 3.1 and Figure 3.2 show a negative correlation between prices and renewable production. 80 70

Spot price (€/MWh)

60 50 40 30 20 10 0 0

5 000

10 000

15 000

20 000

25 000

Production (MW)

Figure 3.1: German spot prices versus production of renewables (sources: EEX Transparency{1}, EPEXSpot{1})

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140

Spot price (€/MWh)

120 100 80 60 40 20 0 0

5000

10000

15000

20000

25000

Production (MW) Figure 3.2: French spot prices versus production of renewables (sources: EEX Transparency{1}, EPEXSpot{1})

It is less obvious in France, which lets us think that the cross-border transmissions between both countries do play a role in the spot prices. For example, if the transmission line is congested, then less “low-cost” power can flow from Germany to France, and therefore the impact on French prices will be lesser. On the other hand, a high transmission capacity will allow prices to converge via the market coupling mentioned in the first part of this thesis. Now we know that the higher the production of renewables, the lower the spot prices. The next question that can be asked is how this knowledge is going to help in studying the further impact of renewables on spot prices. In order to find out whether or not it is legitimate to try and predict a price curve based on the production of renewables, a Granger causality test is performed. Given two sets of time series Yt and Zt, the Granger causality test is used to determine whether Zt could be useful to forecast Yt or vice-versa. We define the two information sets as follows: p

p

i 1

i 1

p

p

i 1

i 1

Yt    iYt i   i Z t i  t Zt    i Zt i    iYt i  t

(3.1.)

where p is the lag order, αi, βi, γi, δi are regressive coefficients.

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It can be said that Zt Granger-causes Yt if the coefficients βi are significantly different from 0. In the same way, Yt Granger-causes Zt if the coefficients δi are significantly different from 0. The significance is usually calculated through the F-statistic. The Granger causality isn’t a real causality per se, as in a series doesn’t cause another series to happen. It is only a measure of how much a series can be used to predict the values of another series. The test is performed using Eviews. The time series that are tested are the German spot prices, the French spot prices and the German production in renewables (wind and solar). The prices were taken on Epexspot while the productions were taken on EEX Transparency. Some pieces of data were missing and therefore the series were readjusted to match the missing data. Also, only weekdays have been considered since spot prices are always lower during weekends (the consumption is lower), independently of the production. Weekends have therefore been removed in order not to take into account the effect of the consumption. Naturally the test could have been run separately with weekends as well, but we assume that the results obtained for weekdays are valid for weekends as well since wind and sun don’t blow and shine depending on the day of the week.

25 000

140 120

20 000 100 15 000

80

60

10 000

40

Renewable production German spot price French spot price

5 000 20 0

0 1 41 81 121 161 201 241 281 321 361 401 441 481 521 561 601 641

Figure 3.3: Studied time series (sources: EEX Transparency{1}, EPEXSpot{1})

Testing for stationarity: the Augmented Dickey-Fuller test (ADF test): Most existing statistical tests – including the Granger causality test – require the series to be stationary. Before modelling anything, it is therefore necessary to check that the time series Yt is stationary. A time series can be called stationary if its mean and variance don’t vary with time. If it is not stationary, then the non-stationarity must be removed before any further analysis can be done. There are two types of non-stationarity: trend stationarity and difference stationarity. A process Yt is said to be trend stationary (TS) if it can be written as:

49

Yt  f (t )  Zt

(3.2.)

where f(t) is a function of time and Zt is a stationary process. On the other hand, a process Yt is said to be difference stationary (DS) of order d if it can be written as: (1  B ) d Yt  Z t

(3.3.)

where B is the lag operator and Zt is a stationary process. The process to remove the nonstationarity isn’t the same depending on whether the series is TS or DS. As such, it is essential that the non-stationarity is correctly identified. Several tests exist, and the one that will be used here is the Augmented Dickey-Fuller (ADF) test, which aims at finding a unit root in the following three regressions: p

Yt  Yt 1     t   i Yt i   t

Trend and constant:

(3.4.)

i 1

p

Yt  Yt 1     i Yt i   t

Constant:

(3.5.)

i 1

p

Yt  Yt 1   i Yt i   t

No trend nor constant:

(3.6.)

i 1

The null hypothesis that has to be tested is: H0 :   0

(3.7.)

If this hypothesis is accepted, it means that there is a unit root and that the series is nonstationary. The significance of the test is assessed with the Student’s statistic (or t-statistic). The result ttest of the T-statistic that is obtained for the unit root test must be compared to the relevant critical values tcrit given by the Student tables. If ttest 1.97 and 5.13 > 1.97. This means that the coefficients are significantly different from 0 and an AR(1) seems like a good model to go along with. Moreover, the absolute value of the inverted AR root is lesser than 1, which is a condition for stationarity of the model. It is actually the best model as all the other models which were tested give t-statistics that are superior to 1.97. Therefore we keep the AR(1) model. Now we find the fitting ARCH/GARCH model. The most common models are the ARCH(1), ARCH(2) and GARCH(1,1). The best fit was found with an ARCH(1). Results are given in Table 3.17:

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Dependent Variable: GERMAN Method: ML - ARCH (Marquardt) - Normal distribution Date: 11/29/12 Time: 16:41 Sample (adjusted): 1/02/2012 6/29/2012 Included observations: 180 after adjustments Convergence achieved after 21 iterations Presample variance: backcast (parameter = 0.7) GARCH = C(3) + C(4)*RESID(-1)^2 Variable

Coefficient

Std. Error

z-Statistic

Prob.

C AR(1)

40.33469 0.387961

1.672305 0.075600

24.11922 5.131782

0.0000 0.0000

3.817348 2.597056

0.0001 0.0005

Variance Equation C RESID(-1)^2

27.0692 0.129158

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.127836 0.112969 11.98280 25271.42 -699.6213 8.598938 0.000023

Inverted AR Roots

.39

41.40812 0.216325

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

40.51680 12.72299 7.818014 7.888969 7.846783 1.922480

Table 3.17: ARCH model results for German spot prices in the 2012 case

The t-statistic has been replaced with the z-statistic as the estimations for an ARCH/GARCH process are asymptotic and are assumed to follow approximately a normal distribution, so the critical value is changed to 1.96. The French spot prices are then treated with the same procedure. We find that the best fit is also an ARCH(1) model. The results are displayed in Table 3.18: Dependent Variable: FRENCH GARCH = C(4) + C(5)*RESID(-1)^2 Variable

Coefficient

Std. Error

z-Statistic

Prob.

C AR(1) MA(1)

49.85108 0.464249 0.425645

1.209353 0.068252 0.062724

41.22127 6.801941 6.785957

0.0000 0.0000 0.0000

9.889512 11.03740

0.0000 0.0000

Variance Equation C RESID(-1)^2

27.17812 0.095730

2.748176 0.008673

Table 3.18: ARCH model results for French spot prices in the 2012 case

A first observation can already be made before we start modelling the prices found in the 2020 scenario. The constant C of the variance equation in the German case is much higher than in the French case, which already gives us an observation on the difference of volatility

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between a country which relies on renewables and a country which does not. Now we model the prices in the 2020 scenario. The statistics are given in Table 3.19 and Table 3.20: Dependent Variable: GERMAN GARCH = C(4) + C(5)*RESID(-1)^2 Variable

Coefficient

Std. Error

z-Statistic

Prob.

C AR(1) MA(1)

28.95197 0.938626 -0.731741

3.538616 0.029991 0.074600

8.181722 31.29699 -9.808796

0.0000 0.0000 0.0000

9.187454 3.228192

0.0000 0.0000

Variance Equation C RESID(-1)^2

41.45073 0.150131

7.123925 0.122238

Table 3.19: ARCH model results for German spot prices in the 2020 case Dependent Variable: FRANCE GARCH = C(4) + C(5)*RESID(-1)^2 Variable

Coefficient

Std. Error

z-Statistic

Prob.

C AR(1) MA(1)

45.91550 0.808068 0.069447

1.991215 0.060380 0.069920

23.05904 13.38298 3.993235

0.0000 0.0000 0.0000

8.164435 4.701581

0.0000 0.0000

Variance Equation C RESID(-1)^2

21.69177 0.163304

2.656861 0.034734

Table 3.20: ARCH model results for France spot prices in the 2020 case

Finally, we model the prices in the 2020 scenario with doubled capacities. Results are given in Table 3.21 and Table 3.22: Dependent Variable: GERMAN GARCH = C(5) + C(6)*RESID(-1)^2 + C(7)*RESID(-2)^2 Variable

Coefficient

Std. Error

z-Statistic

Prob.

C AR(1) AR(2) MA(1)

31.46896 -0.300339 0.494490 0.980758

1.787444 0.070685 0.067218 0.012081

17.60557 -4.248976 7.356479 81.18028

0.0000 0.0000 0.0000 0.0000

5.813851 3.834478 2.345343

0.0000 0.0040 0.0190

Variance Equation C RESID(-1)^2 RESID(-2)^2

37.19642 0.089721 0.140604

8.117928 0.107518 0.187863

Table 3.21: ARCH model results for German spot prices in the 2020 case with doubled capacities

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Dependent Variable: FRENCH GARCH = C(3) + C(4)*RESID(-1)^2 Variable

Coefficient

Std. Error

z-Statistic

Prob.

C AR(1)

43.68584 0.830414

1.908898 0.047367

22.88537 17.53141

0.0000 0.0000

8.084580 4.195469

0.0000 0.0000

Variance Equation C RESID(-1)^2

22.67186 0.157750

2.804333 0.037600

Table 3.22: ARCH model results for French spot prices in the 2020 case with doubled capacities

Most of the models are ARCH(1) processes except for German prices in the last scenario where the fitted model is an ARCH(2). The volatility is represented by the standard deviation. Therefore the standard deviation equations that were found are plotted on MATLAB and displayed on Figure 3.19: 120 100

Volatility

80 60 40 20 0 1

10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181

German 2012

French 2012

German 2020

French 2020

German double capacity

French double capacity

Figure 3.19: Price volatilities in all the scenarios

Now from the observations, a few visible conclusions can be drawn: first of all, the volatilities of the 2012 scenario are the lowest and do no present any volatility spikes. The volatility of German prices in both the 2020 scenarios (with and without doubled capacities) is higher by about 20% in average compared with the 2012 scenario. It can be noticed that, without the doubled capacities, the German volatility is somehow slightly higher than with doubled capacities. This could be explained by the fact that adding interconnection capacities with France helps “level” prices a bit since the volatility is more “split” over the two countries. The impact of higher renewable output on French prices without the doubled capacities is close to none, but when the capacities are doubled, higher volatility spikes appear, confirming the fact that France “takes” a part of Germany’s volatility. Still, the average French volatility remains quite unchanged, but as pinpointed earlier, the impact on 76

the prices themselves was not that big, even after doubling the capacities. This shows that in order from France to benefit from the “green effect”, the amount of available transmission capacities plays a central role. The model developed here takes into account the interconnections between France and Germany only, but it has to be reminded that the market coupling that was launched in the Central West Europe introduces many more connections with other neighbouring countries such as Belgium or Spain (which also possesses big wind farms). Modelling volatilities with ARCH/GARCH models allow us to obtain time-varying volatilities, but depending on the period over which the volatility is calculated, the variance equation could change a lot. A simple observation of Figure 3.16 shows that, if we take the bits between the price spikes, the variations of prices in the 2020 case are smaller than in the 2012 case, which could make us think that volatility should be therefore lower as well, but that is mainly because of the weekly pattern: on weekdays, prices are much higher than on weekends. The point of introducing more renewables is to make those weekdays prices lower. What makes the volatility high is the recurrence of price spikes. That is one of the reasons why the choice was made to model a six-month long series.

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3.7 Discussions The topic of the thesis was to study the impact of a significant increase of renewable penetration from the German side, and particularly on the French prices. For that purpose, an algorithm was developed based on the Locational Marginal Pricing method. The inputs used were: loads, generations and interconnection capacities. The loads were modelled through multiple linear regressions, while wind and solar productions were modelled through artificial neural networks. Several scenarios were considered in order to compare the statistics of the spot prices that were obtained. The first scenario was the reference scenario, based on 2012 figures. The second scenario considered figures of renewable productions and loads in 2020. The last scenario also considered increased interconnections in 2020. In order to run our model efficiently, several statistical series had to be collected. Data collection and processing was the most important task to carry out the simulations. A lot of effort was put on the collection in order to get the most accurate data possible; however, data availability has proved to be limited at times. The lack of necessary figures was compensated with extrapolations and statistical processing in the most rigorous way possible, but compromises had to be made at the cost of lesser accuracy (monthly data instead of daily data, for instance). Still, when no extrapolations could be done (for instance, for the modelling of the photovoltaic production without any data about the solar irradiation), the results still proved satisfactory. One more point which rendered data collection more difficult was the fact that France and Germany are big countries on European scale, and those territories cannot be considered uniform from two main points of view: the weather and the locations of wind and solar farms. In our study, we picked only a few sites that we believe are representative of the country. In order to obtain more accuracy in the electrical output, a complete listing of all the wind and solar farms along with extended relevant weather data. Results for the first scenario allowed us to validate the hypotheses made about the choices of the input values. The other results showed that when there is an increase of renewable production in Germany but with no additional interconnections, prices decrease greatly in Germany only, but high spikes can be observed from time to time. The peaks are globally lower, except for those spikes. When more interconnection capacities are added, the impact on France is more visible and prices converge better. Globally, the results obtained are in accordance with what was expected (namely, that prices go down when more renewables are introduced). However, doubling the interconnection capacities only helped to decrease French prices by around 6.7%, which means that to have a significant impact, the capacities must be much more developed. The model we developed gave price curves for various scenarios while taking into account a limited number of factors, but the sensible results that were obtained show that the choice of factors was pertinent. Moreover, it is a model that uses meteorological factors to predict prices, which is not the conventional way to model prices (mean-reverting jump diffusion, etc.). However, in order to study the impact of renewable energies, it is not possible to ignore weather aspects, for they are the origin of the intermittency.

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4 What can be expected in the future? The main motivation for choosing the topic is based on the hypothesis that German renewables will have an impact not only on the German’s market, but also on the French one. The goal of this thesis was to study in more details that impact on French prices. A literature review was carried out to gather relevant information on that topic. Based on that literature, it was observed that, though a lot of research has been made about price modelling, most of them are purely statistical and do not take enough into account the actual multiple factors that drive prices. Therefore we chose to form a Locational Marginal Pricing model that takes into account several of those factors. For simplicity purposes, hypotheses were defined and tested for validation. Running the model on different scenarios gave the following results: with interconnection capacities at our current level, the impact of German renewable on French prices is not too obvious, and even when doubling the capacities, the impact remains lower than expected. Also, even if electricity prices are lower in average when there are more renewables, the price volatility is greater, which introduces a higher risk for price spikes. From those observations, it can be seen that increasing the level of renewables may have some positive impacts, but it also brings about negative consequences which are described in the next paragraphs. Furthermore, those consequences raise but one question: can the 2020 scenario projected by the ENTSO-E in [35] actually happen? Talks about energy transition have been ceaseless for the past few years and prompt countries to shift from carbon-emitting resources to greener resources. In Germany, the transition wants to be more radical than in any other countries, with a complete nuclear phaseout by 2022 and with an energy mix that relies on renewable energies at 80% by 2050[37]. Following that line of thought, it is easy to see that several major problems arise on technical, economic and financial aspects. From the technical point of view, Germany’s decision also affects its neighbouring countries. The high level of intermittency on the German grid will have non-negligible impacts on foreign operators and will make the task of keep the balance between demand and offer much more difficult. On the mid-term, it becomes obvious that Germany will have to rely on fossil fuels (coal and lignite) anyway to ensure that the balance is kept. As of now, new coal plants are still built and 12GW of extra capacity could be installed by 2030. Also, the national grid also has to be developed in order to deliver power throughout the country, from the wind and solar farms to the consumers. Obviously, the development of the electrical grid as well as the funding of the new installations will have a heavy cost to support. It was stated earlier that building photovoltaic farms is still not profitable at all and the government must give a lot of subsidies to encourage calls to tender. In the middle of the economic crisis that Europe is currently facing, those subsidies are most likely to be cut. Also, current environmental policies are not encouraging enough to deter electricity production from coal. Coal remain a really cheap resource, and the price of European carbon emission permits is in a current range of 6-8€/t while it should be at 20€/t at least in order to be efficient. Finally, the growing competition coming from Asia is constantly adding pressure on European photovoltaic manufacturers. It is the same crisis that makes German consumers less inclined to get green power at any cost. The extra costs of the energy transition will mainly be billed on the end consumers.

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At the end of 2010, extra costs to support renewable energies amounted to 244€/MWh for the end consumer (compared to 129€/MWh in France). By 2025, the costs could reach 400€/MWh and recent polls have shown that the consumers are not so ready to pay that much anymore[37]. On the French side, recent talks have been undergoing about nuclear phase-out as well, but the main difference with Germany is that French production relies on nuclear at around 75% (around 20% in Germany). The figure is supposed to drop to 50% by 2025, but as France still refuses to make use of non-conventional gas, the only replacements for nuclear are renewable energies. Around 30.4GW of installed capacity is projected for 2020. However, given the current installed capacities of wind and photovoltaic farms (around 8GW), it can be seen that the goal is not realistic. All those uncertainties about the future generation mixes make hedging quite tricky for a portfolio manager. Assuming that more renewables are introduced, traders will assume a higher volatility of spot prices. Naturally, spot prices cannot be hedged, but the month-ahead and year-ahead contracts can. As those contracts are partly based on spot prices, their volatility will also increase, though not as much as for spot prices. Taking the current month as reference, traders can anticipate the next months and cover themselves accordingly. The problem arises when all traders start anticipating the impact of the future installation of a wind or solar farm. Taking positions based on how volatile one thinks the forward curve will be can actually lead prices to be more volatile than what they should have been. Therefore it can be seen that current models of prices are maybe not the best ones to forecast electricity prices that take into account renewable energies, because renewable energies are parameters which are highly variable and thus unreliable to predict forward curves. We have introduced in this thesis a model of prices that takes into account meteorological factors via an ANN modelling of intermittent sources. During this study, no paper was found about price forecasts which explicitly include meteorological factors. On the long-term, it can be interesting to wonder about a potential rupture with the current pricing models; namely consider a way to take into account the evolution of generation portfolios. The example of Fukushima is an illustration of such a rupture, where Japan and Germany decided to drastically change their generation portfolios by phasing out their nuclear plants. In our case, the rupture could lead to relinquishing the intermittency of the renewable production on the grid by compelling the producers to place bids on the markets. Naturally, this would imply investing more to be able to predict the weather accurately, and it would imply more risks for the producers, but it would also give them a responsibility on the grid’s safety. Another point is, forward prices are not based solely on spot prices, but also on various other factors, including the exercise of market power. In all the above study, we have used the hypothesis of perfect competition, which will never be the case in reality. Finally, there remains the problem with cross-border interconnections. The model developed here takes into account France and Germany only since high volumes are traded between those two countries, but the approximation holds to a certain extent only. For more accurate results, the interconnections with the other neighbouring countries should be taken into account, but at that point, data collection becomes much more difficult, and the computation would take much longer (it took MATLAB a total of several dozen hours to compute all the prices in 3.5). Paper [15] (presenting a model of the European grid) gives an idea of the required resources to carry out a simulation with more than two countries. The European Commission plans to increase the capacities and build new connections in order to cope with an increased penetration of renewables. The main idea is to increase power transfers to ensure that consumers will have electricity even if there is no wind and no sun at some point. The impact of the increased transmission capacities (especially the new

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connections planned between the Nordic countries and Central Europe, and between Southern Europe and Central Europe) will probably change the direction of some power flows, according to ENTSO-E[38]. For example, if power can’t be transferred directly from German to France, it could flow from Germany to Belgium, and then from Belgium to France. In that case, the necessity to consider the whole European continent to study electricity prices becomes more obvious. Another point of improvement can be inserting the ATC calculations into the algorithm instead of using ATC histories. Interconnection capacities are indeed not completely allocated before the power dispatching. Normally, bids to obtain capacity are made after the power pools received the power bids from each producer and then an optimization program runs to dispatch the available power through the available interconnections to obtain the lowest spot prices possible. In our case, the computation would most certainly take too much time. In the same way, the dispatching of the hydro power could be modelled with a separate optimization function (taking into account the storage levels and the evolution of electricity prices in order to decide whether to actually store the water or store it for later). One last point: for the 2020 simulation, electricity generation costs were assumed to be on the same level as in 2012. That is an assumption that can neither be confirmed nor rejected as those costs depend partly on fuel prices and it is not possible to predict accurately the evolution of those prices eight years before. Still, the present paper wants to focus on the statistics of the prices and not on the values of the prices themselves. Consequently, even if generation costs were modified, it would not change the conclusion on the increasing volatility of spot prices. However, it must not be forgotten that there are plenty of other factors to take into consideration. Predicting the future with so many variables becomes a not so easy task. However, this topic is a current topic of concern which is subject to a lot of studies, and even though predicting the future is not so obvious, companies are still willing to have a good idea of possible scenarios which can occur in the future.

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References [1] European Commission, “Renewable Energy: Progressing towards the 2020 target”, Communication from the Commission to the European Parliament and the Council, December 2011 [2] RTE, “Bilan électrique 2011”, 2012 (Can be found on http://www.rtefrance.com/uploads/Mediatheque_docs/vie_systeme/annuelles/Bilan_electrique/RTE_bilan_el ectrique_2011.pdf) [3] Bundesministeriums für Umwelt, Naturschutz und Reaktorsicherheit (BMU), “Development of renewable energy sources in Germany 2011”, 2012 (Can be found on http://www.erneuerbareenergien.de/files/english/pdf/application/pdf/ee_in_deutschland_graf_tab_en.pdf) [4] Ministère de l’Ecologie, de l’Energie, du Développement Durable et de la Mer (MEEDDM), “National action plan for the promotion of renewable energies 2009-2020”, 2009 (Can be found on http://ec.europa.eu/energy/renewables/action_plan_en.htm) [5] Federal Republic of Germany, “National renewable energy action plan in accordance with Directive 2009/28/EC on the promotion of the use of energy from renewable sources”, 2009 (Can be found on http://ec.europa.eu/energy/renewables/action_plan_en.htm) [6] Yih-Huei Wan, Brian K. Parsons, “Factors Relevant to Utility Integration of Intermittent Renewable Technologies”, National Renewable Energy Laboratory, U.S. Department of Energy, 1993 [7] Commission de Régulation de l’Energie (CRE), “The Electricity Market” (Can be found on http://www.cre.fr/en/markets/wholesale-market/the-electricity-market#section3_2) [8] Müsgens, F., “Market Power in the German Wholesale Electricity Market”, EWI Working paper Nr 04.03, 2004 [9] Eurelectric, “Integrating intermittent renewable sources into the EU electricity system by 2020: challenges and solutions”, 2010 [10] Carlo Obersteiner, Christian Redl, “Electricity Spot Markets and Renewables – A Feedback Analysis”, Energy Economy Group (EEG), Vienna University of Technology, 2007 [11] Qian Zhao, Peng Wang, Lalit Goel, Yi Ding, “Impacts of Renewable Energy Penetration on Nodal Price and Nodal Reliability in Deregulated Power Systems”, IEEE, 2011 [12] Weihao Hu, Zhe Chen, Birgitte Bak-Jensen, “The Relationship between Electricity Price and Wind Power Generation in Danish Electricity Markets”, IEEE, 2010 [13] Jeremy Lin, “Potential Impact of Solar Energy Penetration on PJM Electricity Market”, IEEE, 2011

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[14] Qian Zhao, Peng Wang, Yi Ding, Lalit Kumar Goel, “Impacts of Solar Power Penetration on Nodal Prices and Nodal Reliability”, IEEE, 2010 [15] Carlo Brancucci Martínez-Anido, Laurens de Vries, Gianluca Fulli, “Impact of Variable Renewable Energy on European Cross-Border Electricity Transmission”, European Commission, Joint Research Centre, Institute for Energy and Transport, TU Delft, 2012 [16] Wei, W.W.S., “Time Series Analysis: Univariate and Multivariate Methods”, AddisonWesley, Redwood City, 1990 [17] Tommaso Proietti, Helmut Lütkepohl, “Does the Box-Cox transformation help in forecasting macroeconomic time series?”, MPRA, n°32294, July 2011 [18] Peiyuan Chen, “Stochastic Modeling and Analysis of Power System with Renewable Generation”, Aalborg University, Department of Energy Technology, January 2011 [19] Régis Bourbonnais, Michel Terraza, “Analyse des séries temporelles”, Dunod, 2004 [20] Ektor Sotiropoulos, “Modeling of German Electricity Load for Pricing of Forward Contracts”, Swiss Federal Institute of Technology (ETH), June 2012 [21] Zaid Mohamed, Pat Bodger, “Forecasting Electricity Consumption: A Comparison of Models for New Zealand”, University of Canterbury, Department of Electrical and Computer Engineering [22] N. Amral, C.S. Özveren, D. Kind, “Short Term Load Forecasting using Multiple Linear Regression”, University of Abertay Dundee, UPEC, 2007 [23] Panagiotis A. Dafas, “Estimating the parameters of a mean-reverting Markov-switching jump-diffusion model for crude oil spot prices”, 2004 [24] R. Weron, M. Bierbrauer, S. Trück, “Modeling electricity prices: jump diffusion and regime switching”, Elsevier, 2003 [25] R. Weron, “MRJD_MLE: MATLAB function to estimate parameters of a MeanReverting Jump-Diffusion (MRJD) process using maximum likelihood” and “MRJD_SIM: MATLAB function to simulate trajectories of a Mean-Reverting Jump-Diffusion (MRJD) process” (can be found at http://ideas.repec.org/c/boc/bocode/m429010.html and http://ideas.repec.org/c/boc/bocode/m429008.html) [26] Abdelmoula Dmouj, “Stock Price Modelling: Theory and Practice”, Amsterdam Faculty of Science, 2006 [27] Christophe Barraud, “Etude du cours boursier de l’action Exxon Mobil”, Université Paris Dauphine, 2008 [28] Maitha H. Al Shamisi, Ali H. Assi, Hassan A. N. Hejase, “Using MATLAB to Develop Artificial Neural Network Models for Predicting Global Solar Radiation in Al Ain City – UAE”, Engineering Education and Research Using MATLAB, Dr. Ali Assi (Ed.), ISBN: 978953-307-656-0, InTech, 2011 (can be found on:

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http://www.intechopen.com/books/engineering-education-and-research-using-matlab/usingmatlab-to-developartificialneural-network-models-for-predicting-global-solar-radiation-in-al) [29] Juan J. Flores, Mario Graff, Hector Rodriguez, “Evolutive Design of ARMA and ANN Models for Time Series Forecasting”, Universidad Michoacana de San Nicolas de Hidalgo, 2012 [30] RTE, “Calcul des capacités d’échanges transfrontaliers d’énergie électrique : méthodologie commune appliquée par RTE aux divers horizons prévisionnels”, 2010 (can be found on: https://clients.rtefrance.com/htm/fr/offre/telecharge/Methode_de_Calcul_de_Capacite.pdf) [31] RTE, “Structure of the Allocation of Capacity among different Timeframes on the France-Germany border”, October 2012 (can be found on: http://clients.rtefrance.com/htm/an/offre/telecharge/FRDE_Structure_for_allocation_of_capacity_between_timeframes_V1.0.pdf) [32] Lennart Söder, “Electricity Market Analysis, EG2060 L2”, Kungliga Tekniska Högskolan, 2012 [33] International Energy Agency (IEA), Nuclear Energy Agency (NEA), Organization for Economic Co-operation and Development (OECD), “Projected Costs of Generating Electricity”, OECD Publications, 2010 [34] Shane Rourke B.E., “Locational Marginal Pricing of Electricity”, National University of Ireland, Department of Electronic and Electrical Engineering, Faculty of Engineering and Architecture, University College Dublin, November 2003 [35] ENTSO-E, “Scenario Outlook and System Adequacy Forecast 2011-2025”, 2010, ENTSO-E AISBL [36] DB Climate Change Advisors, “The German Feed-in Tariff for PV: Managing Volume Success with Price Response”, Deutsche Bank Group, May 2011 [37] Etienne Beeker, Clélia Godot, “La transition énergétique allemande est-elle soutenable ?”, La note d’analyse n°281, Centre d’Analyse Stratégique, September 2012 [38] ENTSO-E, “ENTSO-E Report System Adequacy Forecast 2010-2025”, 2010, ENTSO-E AISBL

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Statistical references: EEX{1}: http://www.transparency.eex.com/en/Statutory%20Publication%20Requirements%20of%20th e%20Transmission%20System%20Operators/Power%20generation/Installed%20generation% 20capacity%20%E2%89%A5%20100%20MW EEX{2}: http://www.transparency.eex.com/en/Statutory%20Publication%20Requirements%20of%20th e%20Transmission%20System%20Operators/Power%20generation/Expected%20wind%20po wer%20generation ENTSO-E{1}: https://www.entsoe.eu/resources/data-portal/consumption/ RTE{1}: http://clients.rtefrance.com/lang/fr/visiteurs/vie/interconnexions/all/capa_util.jsp?codePays=ALL RTE{2}: https://clients.rte-france.com/lang/fr/visiteurs/vie/prod/realisation_production.jsp Wunderground{1}: http://www.wunderground.com/history/ Epexspot{1}: http://www.epexspot.com/en/market-data/auction IEA{1}: http://www.iea.org/stats/prodresult.asp?PRODUCT=Electricity/Heat

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Appendices

Appendix A: Least Squares Method for linear regression This appendix describes the Least Squares Method (LSM) used when trying to fit a linear model to a set of data. Here a single linear regression model is used for simplicity, but it can be generalized to a multiple linear regression. Given two vectors of data y = (y1, y2,…,yn) and x = (x1,…,xn), we want to find two coefficients a and b such that y = ax+b and we want those coefficients to realize a ‘best fit’, i.e. we want the quantity y – (ax+b) to be as close to 0 as possible. For that purpose, the LSM is often suggested for it is easy to compute. The error ε(a,b) is defined as: n

 (a, b)   ( yi  (axi  b)) 2 i 1

This error should be minimized in regard of the coefficient a and b, which means that the following set of equations should be solved:  E  a  0   E  0  b Developing the equations gives: n  n  yi  a  xi  bn  i 1 i 1  n n n  x y  a x2  b x   i i n i  i 1 i 1 i 1

Solving the above linear system gives the values of a and b which realize the best fit. In order to know if the model found is actually good (i.e. if y and x can be considered to have a linear relation), the correlation coefficient R is calculated as follows: n

R

 ( x  x)( y  y) i 1

i

i

n

n

i 1

i 1

 ( xi  x)2  ( yi  y)2 A correlation coefficient close to 1 indicates a good model while a correlation coefficient close to 0 shows that a linear model is probably not the best relation between x and y.

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Appendix B: Lagrange multipliers The method of Lagrange multipliers is used to solve optimization problems with constraints. To explain the method, we will consider two variables and one constraint, but this can be generalized. The problem we want to solve is: minimize f ( x, y ) subject to h( x, y )  0

The constraint h(x,y) defines a curve on which we have to stay in order to fulfil the constraint. Now moving along the curve will likely make f(x,y) increase or decrease. Since we want to minimize f, we have to find an extremum of f. At the extremum, the curve defined by f(x,y) is tangential to the constraint curve because it is only at that point that any differential movement on the constraint curve will yield a gradient vector of f that is equal to 0. This means that the tangent vector of h and the tangent vector of f are parallel. As the gradient vectors are perpendicular to the tangent vectors, it also means that the gradient vectors of h and f are parallel, i.e. there exist a constant λ such that: f ( x, y)  h( x, y)

λ is called the Lagrange multiplier and represents the fact that the gradients of f and h don’t have necessarily the same length. We define the Lagrangian function L(x,y,λ) as follows: L( x, y,  )  f ( x, y)   h( x, y)

Minimizing the Lagrangian gives the solution to the constrained problem. The minimization is done by solving this equation: f ( x, y)  h( x, y)  0

That is to say: f h  x   x  0  h  f 0   y  y  f h 0     

Not all optimization problems have two variables and one constraint. The generalization of the Lagrangian is given below: m

L( x1 ,..., xn )  f ( x1 ,..., xn )   i hi (x1 ,..., xn ) i 1

This will yield a system of n+m equations with n+m unknowns. It has to be noted that the system is not necessarily linear.

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Appendix C: Information criteria Akaike Information Criterion (AIC): The AIC is a criterion used to select a model among several possible models. It does not tell if the selected model is actually good or not, it simply tells that it is the best one among all the models. The calculation of the AIC returns a value for each model, and the choice is made based on the following criterion: the best model is the one with the lowest AIC. The calculation of the AIC is: AIC  2k  2ln( ) where k is the number of parameters of the model and θ is the maximized likelihood function of the model. It can be seen that the AIC gets higher as the number of parameters increases and therefore it discourages overfitting, i.e. adding too many parameters in order to increase the goodness of a fit. Bayesian Information Criterion or Schwarz Criterion (BIC): The BIC is another criterion that used to select the best model among existing models. Like the AIC, it is based on the likelihood function of the models, and returns a value per model. Again, the best model is the one presenting the lowest value of BIC. The calculation of the BIC is: BIC  2ln( )  k ln(n)

where k is the number of parameters of the model, θ is the maximized likelihood function of the model and n is the number of observations of the series (sample size).

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