The impact of wind energy
on electricity spot prices
in the Netherlands
Jeroen Fidder
RijksUniversiteit Groningen
Faculty of Economics and Business
Master Thesis for Msc IE&B
Prof. Dr C.J. Jepma
The impact of wind energy on electricity spot prices in the Netherlands Jeroen Fidder1
Abstract
The rise of wind energy as the most prominent renewable resource in electricity generation in North-Western Europe is a fact. Its impact on electricity spot prices is the topic of this thesis.
Three hypotheses concerning the effects of wind energy on the electricity spot market will be tested: a) that prices at times of high electricity production due to wind energy availability would be lower, ceteris paribus, b) that this effect is most pronounced during the hours at which demand is greatest and that the marginal impact of extra generated MegaWatts of wind energy on electricity prices would decline -because of the shape of the supply curve- and c), that the effect of wind energy on electricity prices would become stronger as time progresses.
In line with the literature and a priori arguments, a time series model was employed that takes into account the specific patterns of electricity spot prices, the ARMAX model. By using data on electricity spot prices and wind energy production, 24 hourly time series were tested for every day during the period 01-01-2003 until 27-06-2007. The sign and form of the expected effect were confirmed as well as the expected hourly pattern. The hypothesis on the progression of the effect in time was, however, rejected.
After describing the developments affecting future developments of wind energy’s impact on electricity spot markets, research limitations and possible extensions have been pointed out.
The main conclusion of this thesis is that wind energy has been positive for consumers because it provides additional low-cost electricity supply, and reduces the ability to exercise market power by other electricity producers.
1
Contents
1. Introduction……… 3
2. Literature review………. 5
2.1 Electricity markets in Europe………. 6
2.2 Changing conditions in European electricity markets………. 7
2.3 The energy mix and wind energy……… 8
2.4 Effects of introducing wind energy.………... 11
3.1 Methodology: Modelling electricity spot prices ……… 15
3.2 The basic model……… 18
3.3 Diagnostics……… 20
3.4 Variables………. 23
3.5 Data………. 24
4.1 Testing the model and results………. 25
4.2 Normality of the residuals……….. 28
5. Discussion of results……….. 29
6. Wind energy’s market environment……… 31
7. Limitations and further research……….. 35
8. Conclusion……… 36
References………. 37
Appendix 1: Figures and tables……… 44
Appendix 2: Histograms and scatter plots for hours 4 and 16………. 48
1. Introduction
This master’s thesis has been written mainly for two reasons: Eneco Energy Trade’s (EET) desire to get wind energy’s effects on electricity prices investigated and my own interest in the economics of energy. The aim of this study is to analyze what the effect of the addition in ever increasing numbers of this new type of generation capacity has been on electricity markets. Taking into account the general concern for energy issues in the world as a result of rising prices and security of supply issues, the development of the electricity market is well worth studying both from a societal and an academic point of view. Electricity markets have been experiencing a turbulent period; the protection of public ownership has been replaced by the discipline of the competitive market place only a few years ago. Now that electricity has become a traded commodity and not a service encompassing everything from upstream generation to downstream delivery to consumers, new parties have emerged that all influence electricity prices.
Ten years ago, electricity was mainly generated by a number of asset types, such as power plants fuelled by natural gas and coal, nuclear plants, and hydrological energy. However, as concerns over the environment (notably the relation between carbon dioxide (CO2) emissions and global warming) have risen and dependence on carbon-based fuels became an item on the political agenda solutions have been sought in new means of power generation. Solar energy, wind energy and biofuels are amongst the most prominent new entrants, although numerous new techniques are also being looked into. After initial euphoria about these “renewable” resources some of their downsides are becoming apparent. Solar power is still expensive and its share of total power generated is very small. Biofuels are accused of being responsible for the rise of food and commodity prices and in their current form can only play a limited role. The installation of wind turbines has been under increasing scrutiny from nearby communities and offshore wind farms are only taking off slowly.
When wind energy is available however, the effect is the same as introducing a very cheap amount of additional production capacity which will always be utilized since its production is not storable. This suggests that prices should come down at times when wind energy is available in meaningful quantities, and both producers and consumers of electricity have experienced this2. Furthermore, since at times of relatively low availability of capacity market power can emerge -leading to higher prices- the effects should be highest at times of high demand. This leads to the hypotheses that will be tested: that wind energy has had negative effects on electricity spot prices, that these effects are most pronounced at times that prices are highest, and that these effects have grown larger during the years I have tested because of increases in installed generation capacity.
The results of the testing of the ARMAX model I constructed for this research confirm the first two hypotheses but fail to confirm the steady progress of the effects in time. The negative effects of wind energy on electricity spot prices imply that revenue is being gained by wind energy producers at the expense of electricity producers using conventional electricity generation assets. This could affect the amount of investment being used for these conventional assets in the future.
This thesis will start with an overview of electricity markets in general to get the reader acquainted with the specific environment and characteristics of these markets. I will first describe the process of liberalization and the changes that have profoundly affected the playing field for electricity market parties in the last decade. I will then proceed with the description of the changes in the mix of generation assets that provide us with electricity with a special emphasis on wind energy. After that I will provide some thoughts on how markets can be affected by these changes, leading up to the in three hypotheses. The next step is to test these hypotheses with a suitable model. I will provide a concise overview of electricity market modelling approaches and will argue which model is the most suitable for my purpose, an ARMAX model. Then I will briefly explain the model’s specific workings, and the variables and data I have used. The results of testing the model will be presented and discussed, as well as the implications for market parties. Finally, I will discuss the fast changing world of electricity and what role wind energy will likely play depending on the direction of these changes. A summary and conclusion will be presented in the final section.
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2. Literature review
Electricity markets have been receiving increasing political and academic attention. The main reasons are that energy consumption in general has been an increasingly hot topic during the last decade and the liberalization process of electricity markets that has been going on around the world. The broad energy consumption question, although inherently intertwined with the issues addressed in this thesis, is too broad and from an analytical point of view not relevant enough to be included here. This literature review will provide an overview of the way electricity markets in Europe function, and the changes that they are undergoing with a special emphasis on the energy mix. Finally, the most prominent change envisaged for the energy mix in the coming decade, the rising share of wind energy, is examined with respect to its impact on electricity markets and electricity prices.
The introduction of competition in a market –or rather a collection of independent markets dominated by state-owned monopolies with limited transparency and interconnection- has certainly lead to changes in its structure3. The process was set in motion in 1996 by Directive 96/92/EC which unbundled the production of electricity from its supply, in effect creating a good where there had been –ambiguously- an integrated service before4. In 2003, the process initiated by Directive 96/92/EC was accelerated and extended by Directive 2003/54/EC. This Directive demanded the complete liberalization of EU electricity markets before July 1st for wholesalers and consumers alike.
With respect to the general picture, markets most studied in North-Western Europe are those liberalized earliest, the United Kingdom (UK) and the Nordic countries (Norway, Sweden & Finland). For an overview of status of liberalization in the EU, see table 1.
Nation Date of market liberalization
Belgium 2007 Denmark 2003 Finland 1998 France 2007 Germany 1999 Luxembourg 2007 Netherlands 2003 Norway 1993
3
Sioshansi 2001; Meeus, Purchala and Belmans 2005, Hirst and Kirby 2001 4
Sweden 1998
UK 1998
Table 1: liberalization dates in North-Western Europe5
Thus far, the creation of a European energy market has been coming along nicely, with, however, some nations performing better than others. The whole point of the liberalization in itself is to have EU consumers benefit from increased security of supply and greater efficiency in electricity sellers, leading to prices lower than what the ‘old’ system would have produced. Furthermore, the policy is aimed at furthering the general EU energy policy.
2.1 Electricity markets in Europe
The functioning of the world’s competitive electricity markets, i.e. the way prices come to be, is heavily influenced by the technical aspects of electricity and its grid. The impact of the non-storability of electricity is underlined in almost every body of literature studying electricity markets6. The direct impact of the fact that electricity is a good that cannot economically be stored is that the market where it is traded consists of a system in which demand and supply are perfectly equal at every moment in time. If this were not the case, the electricity system could not function properly. This is a direct consequence of the fact that for electricity to be useful for consumers, its supply has to be continuous and stable, since electrical grids operate within a very subtle margin of voltage fluctuation (maximum of 1.6%)7.
Equating the electricity supply to its demand is the task of Transmission System Operators (TSOs), such as TenneT in the Netherlands or ELIA in Belgium. This task amounts to the monitoring of the grid load and balancing it if necessary. The demand from consumers is redirected to retailers who in turn buy their electricity from producers or traders, or from the TSO if demand exceeds retailers’ expectations.
The total short-run demand for electricity is, by nature, hard to predict with precision. Quite some academic attention has been spent on the modelling of electricity demand from both residential and commercial consumers8 but a certain amount of unpredicted fluctuation cannot be eliminated. In this paper, demand is not endogenously modelled but taken as exogenous. Consumers receive periodic bills for their electricity use after it has been consumed
5
Kemfert, Lise & Ostling 2003 6
Geman and Roncoroni 2006 7
Mari, 2006 8
and in general pay at most two different fees, one for peak- and one for off-peak hours. This makes it hard for consumers to adapt their behaviour at times that spot prices would be a good reason to do so.
Suppliers meet their customers on three markets, making the electricity markets a sequence of markets9: the future/forward markets, the day-ahead (spot) market, and the imbalance (real-time) market. Forward prices for electricity have been studied to identify their risk premia10, the way they can be valuated11, and their relation to spot prices12. Spot prices in turn have been studied even more extensively, most probably because the spot market is (more) transparent than the forward markets since forward markets function through over-the-counter (OTC) contracts. Electricity spot markets have been studied to examine their components, such as the trajectorial and statistical properties13, the models used for their examination14, the way in which producers can set quantities to influence prices15, and the effectiveness of anti-gaming policies16. Literature on this market will be dealt with extensively in a later section. The market for real-time balancing has been examined with respect to its design and effectiveness17 and will also be commented upon in a later section.
2.2 Changing conditions in the European electricity markets
Besides the ‘simple’ restructuring of market players’ roles in the electricity market in Europe due to the liberalization process there are several other developments that have already changed the way these markets function and will do so in the near future even more. These developments are a.o. the interlinking of the previously independent national markets, the changes in the energy mix that supplies the EU’s electricity, and –related to that- the environmental and energy policies of the EU.
The linking up of markets is a profound change from the previously independent national networks. Although interconnector capacity has always existed, their function was more that of back-up system and less of a market development tool18. This has changed with the introduction of Regulation 1228/03 by the EU as a complement to the before mentioned
9
Glachant and Saguan 2005 10
Longstaff and Wang 2004, Bessembinder and Lemmon 2002 11
Burger et al. 2004 12
Eydeland and Geman 1998 13
Geman and Roncoroni 2004 14
Barlow 2002 15
Le Coq 2002 16
Boogert and Dupont 2005 17
Hirst and Kirby 2001, Glachant and Saguan 2005 18
Regulation 2003/54/EC. This regulation aims to ensure that interconnector capacity access is allocated by means of market-based principles. Furthermore, there has been the linking-up of spot markets19, namely the Finnish, Swedish and Norwegian markets which have become the Nordpool, whereas the Dutch (APX power NL), Belgian (BelPEX), and French (Powernext)electricity spot markets have been trilaterally linked. The latter three have also established links to the United Kingdom (UK) (APX power UK) and Nordpool markets. The coupling of the power markets of the Netherlands, France, Belgium, Luxemburg, and Germany has been planned for the 1st of January 2009 by all the parties involved, an would create a Central Western European (CWE) electricity region20.
The effect of the coupling of electricity spot markets was studied for the case of the Netherlands and Belgium21. It indicated that the behaviour of the largest producer in the market, i.e. whether a switch from price-taking to Cournot strategy was made, would determine the welfare effects of the coupling. The debate on investment in physical interconnector capacity has been carefully examined by a literature study22 and modelling of EU regulation effects23. Not being designed for commercial use, the interconnectors between the fully liberalized markets are suffering from congestion. “Congestion is particularly acute in the interconnectors linking Germany and Denmark, the Netherlands and Germany, the Netherlands and Belgium, Spain and France, France and Italy, and Italy and Austria.”24 The improvement of interconnector capacity is thus a serious issue at the political level, especially because the discussion on how this should be paid for and by whom is not yet concluded. Relevant possible implications of the market couplings and interconnector issue are discussed in the discussion section.
2.3 The energy mix and wind energy
The gradual changes in the mix of energy sources used for electricity generation are driven by both a political angle and a business angle. The political angle, embodied by both the EU and national governments, is driven by the issues of energy security and global warming. Both motives have resulted in the same course of action: the replacement of fossil fuels, especially the ones responsible for heavy CO2 emissions by “renewable” fuels, or at least fuels with less CO2 emissions. The business angle is affected by the utilization of incentive schemes
19
For an overview of spot markets in the EU, see Madlener and Kaufmann 2002 20
http://www.apxgroup.com 21
Hobbs and Rijkers 2005 22
Brunekreeft, Neuhoff, and Newberry 2004 23
Daxhelet and Smeers 2007 24
drawn up by governmental bodies and by the search for alternatives for increasingly expensive fossil fuels. Further thoughts with respect to the energy mix will be presented in the next section.
The alternative (non-hydro) fuel that is the most prominent new entrant at the moment in North-Western Europe is wind energy25. Being available in many locations, emitting no operational CO2, and with free fuel, wind turbines are a growing source of electricity in Europe. As wind power is producing a progressively larger (but bounded) portion of European electricity, there is a possibility of seeing this change in the energy mix reflected in electricity spot prices. However, it first needs to be clarified what distinguishes the addition of wind power from adding a new conventional plant to the system.
Wind energy is energy produced by wind turbines, either as a single unit or a whole farm with currently up to 60 turbines. The harnessing of wind power is very old and the basic idea as not changed that much since the first wind mills were used to grind wheat or regulate water levels. Wind is obstructed by a turbine shaped in such a way that, as it “catches” wind, it turns and drives an axle which in turn drives a generator that converts the kinetic energy into electrical energy. The turbines have been growing larger and larger in terms of height, rotor diameter and production capacity. The production capacity (as measured by yearly produced output in kilowatt-hours (kWh)) of a turbine is determined by the average yearly wind speeds at its location, its efficiency, and its rotor diameter26. The production capacity of a turbine is approximately quadrupled if the rotor diameter is doubled, making turbines with bigger rotors attractive. Rotor diameters can become as large as 126 meters at the moment and production capacity as high as five MW27.
The costs of building a wind turbine depend largely on the rotor diameter; further variables that influence costs include its height, the base structure, grid connection, and the transformer. Yearly costs are mostly maintenance and insurance costs. Offshore wind projects are always more expensive than onshore projects because of added construction costs. Prices for onshore projects are about 1.100-1.300 Euros/kW whereas offshore turbines can cost as much as 2.500 Euros/kW. Prices for wind projects have risen sharply in the past few years because of higher demand and more expensive input materials such as steel and copper28.
25
Without subsidies profitable projects would be very scarce around the world with only a few places with very high wind speeds being able to offer competitive returns29. Costs at the moment are about 5 Eurocents/kWh for wind whereas coal comes at 4 and natural gas at 4,5 Eurocents/kWh. It is, however, quite an effective hedge instrument against rising energy prices as its production costs are fixed and known. Building the turbines has been attractive because of the subsidies attached to the electricity they produce, their fixed costs, and also because of the good PR value they represent. The turbines and wind farms are owned and exploited by individual parties (such as farmers or companies), collective parties, project developers, and electricity producers. The government target for installed (or allocated) production capacity is 4.000 MW onshore in 2012 and about 700 MW offshore in 201030.
“Wind power production is characterized by variations on all time scales: seconds, minutes, hours, days, months and years. Even the short-term variations are to some extent unpredictable.”31 The specific intermittent character of wind is a relatively unfamiliar phenomenon for many electricity producers and traders. Where a producer can exercise a fair degree of control over the output of conventional generation methods by simply feeding more or less fuel into the system (within technical boundaries), this is impossible with wind, except for having the turbine go off-line32. Targets for production do therefore not exist; the aim is basically to get the turbines to produce as much energy as possible at any time. Production does follow a specific pattern with higher average wind speeds during the winter than during the summer and higher average wind speeds during the daytime than during the nighttimes.
The intermittent nature of wind itself directly affects the production of electricity from wind. In a study on hourly wind power variations in the Nordics, Holttinen found that wind turbines spread over the whole Nordic region produce an average mean of 25.1% of their maximum power over the years 2000-2002 (A random single wind turbine was found to produce between 0.0 and 105.0% of its maximum capacity). The median, however, was 22.4% and the minimum and maximum average were 1.2 and 86.5%, respectively. The standard deviation in the study was found to be about 30% of capacity for a single turbine.
This intermittency in itself can of course be overcome by adjusting the supply of electricity from conventional sources to complement wind production profiles33. However, this is hindered by another characteristic of wind energy: its limited predictability. Although
29 http://home.wxs.nl/~windsh/basics.html 30 http://nwea.trialversion.nl/node/95 31 Holttinen 2004a, p. 173 32
Bathurst and Strbac, 2001 33
forecasting abilities have improved tremendously over the course of the years, predictions are still imperfect and even a common standard for model performance does not exist34. This is not to say that progress has ceased and it can be expected that further improvements will appear35, so the prediction error can be expected to decrease somewhat more. The prediction error itself can be smoothed out for a whole nation or a region as Holttinen shows36, although whether or not this is of any help for an individual power producer remains to be seen (whereas the advantages for a TSO are more obvious). The way in which forecasting errors influence prices will be taken up in a following section.
Another influence on the accuracy with which wind power can be predicted is the time span between the forecast and the actual moment that production has to be realized. Wind speeds are stochastic, the predictions of which get worse as the period from the moment of forecasting gets longer37. For the day-ahead market bids have to be subjected several hours in advance with different ‘gate closures’ for the different countries examined at the moment this paper was written. This results in selling different amounts of electricity than a producer can actually deliver, and leading to extra costs on the regulating market (which is more expensive than the normal market). It also implies however that the unpredictability in itself has no influence on the day-ahead price.
2.4 Effects of the introduction of wind energy
The economical literature on wind energy is not large, but growing as data and other information is becoming available. With respect to the technical integration of wind-generated electricity, empirical evidence seems to indicate that large amounts of wind energy can be integrated in grid systems38. Studies on this subject, although of interest are, however, not part of the scope of this paper. Economical integration has been studied quite a lot, where integration is taken to be an understanding of how wind energy should be priced and thus becoming a useful and understood electricity source. The treatment of surplus production of electricity by wind farms39, the revenues produced by wind farms under different systems40, electricity market operation from wind producers’ view41, combining wind- and hydro power to
34
Costa et al., 2007, private correspondence with Dr. Holttinen May 2008 35 Barthelmie et al. 2008 36 Holttinen 2004a 37 Holttinen 2004b 38 Soens 2005 39
Lund and Münster 2003 40
Angarita-Márqueza, Hernandez-Aramburob, Usaola-Garcia 2007 41
gain on the spot market,42 and the use of geographic dispersion of wind farms in a portfolio43 ,have been looked into. However, a specific examination of wind production’s effects on spot prices has, to my knowledge, not yet been carried out.
Electricity producers already observed negative effects44 of wind energy on electricity spot prices, as have large consumers45. Wind energy producers are actually charged a penalty fee of a certain percentage of the spot price by traders. Theoretically, every extra MegaWatt (MW) of wind electricity could shift the merit order one MW to the right leading to a lower equilibrium price (see figure A1 in the Appendix). The merit order in which different sources of generation are called into action depends on their marginal costs (see figure A2 in appendix 1). These marginal costs are reflected in the APX prices, being much higher at “peak” hours than during “off-peak” hours, with massive peaks not being uncommon (see figure A3 in appendix 1). The prices are determined by an auction system in which suppliers and buyers have the time until 11:00 in the morning to submit their bids for every individual hour of the following day (0:00-1:00,…, 23:00-24:00). The resulting “bid-ladders” are then fitted and their intersection with demand determines the clearing prices and volumes for all market players. Buyers’ price elasticities are commonly extremely low and can therefore be assumed to have a negligible impact on APX price formation46.
To illustrate the rationale behind the merit order, consider the following: nuclear power has lower marginal costs than coal-generated and will thus be used to satisfy demand before a coal plant will be fired up, which in turn gets called into service before a gas-fired plant. The fact that wind comes at zero marginal costs and its lack of fuel usage earns it a place at the very start of this merit order of generation. The shape of the merit order is more or less a “hockey stick”47, with two thirds (the “baseload” part) of the electricity provided at comparable cost levels. The final third of generation is provided at fast rising marginal costs, leading to an almost exponential rise of the price curve with the dearest generation offered at more than six times the average. The availability of wind, should it have enough clout, could push the curve to the right to such an extent that higher generation-cost units will fail to be “hit” by the APX bidding ladder and cause the price to drop in a non-linear fashion.
42
Angarita-Márqueza, Usaola-Garcia 2006 43
Drake and Hubacek 2007 44
Private conversation with M. Tellman of Eneco Energy Trade, March 2008. 45
Presentation at Akzo Nobel’s Rotterdam Chlor-Alkali plant by Harmen Kruijt of Akzo Nobel May, 2008. 46
Escribano et al. 2002 47
We have to keep in mind, however, that wind can still be considered a marginal player most of the time48 and total wind energy production might simply not carry enough weight to significantly influence the price. Furthermore, there could be oligopolistic behavior by other producers withholding generation capacity from the APX. It would in principle be possible for producers to withhold conventional power to maintain high prices in times of higher wind-generated electricity supply.
There are four reasons to disregard the latter behavioral aspect: Firstly, the technical nature of most plants makes it more cost-efficient for them to keep producing power at a constant level49, which is a clear incentive to bid for the generation contract. Furthermore extreme price volatility leads to a situation where it is all but impossible to determine the amount of capacity to withhold in order to maximize profits. Secondly, especially since the coupling of the APX to the French and Belgian markets it has become harder to manipulate the system50. However, interconnectors do not have enough capacity to be an efficient market adjustment tool at the moment. Thirdly, competition in the Netherlands looks most like “strategic entry deterrence through capacity choice”51. This implies that competition is discouraged by maintaining generation capacities in such amounts that a new entrant would not be able to cover its investment costs.
Investment decisions in renewables are distorted by government subsidies and public image effects, however, and the extra capacity is introduced disregarding the normal pattern. Finally, there are no suitable ways for me to measure the exercising of market power in the electricity market in order to dampen the price responses on increasing wind power supply. The following hypotheses will be tested.
Hypothesis 1: Wind energy has exercised a negative effect on the APX price in the sample period.
Given the shape of the supply curve the effects of wind energy, should they be significant, should be most pronounced in the peak hours52 since the price volatility is largest then. This is due to the fact that the extra wind-MWs would make it harder for the “really igh-cost generation threshold” to be reached. Technically, the peak hours could still depend on higher order generation sources, which cannot be substituted for by inflexible coal-fired plants.
48
See figure A4 and table A1 in appendix 1 49
M. Hol, ENECO Energy Trade, interview March 2008 and Green 2001 50
See www.apxgroup.com for a review of price convergence after market coupling. 51
Woerd et al. 2004 52
However, they could be substituted for by cheaper peak hour CCGTs should they be in a suitable generation “range”, i.e. one that allows more flexibility.
Another reason for expecting the effects to more visible during peak hours is that most wind energy is produced during the daytime and actually resembles the load curve to some extent (see figure A4 and A5 in Appendix 1). This is because during the daytime the sun causes the thermal effects that in their turn cause the wind to blow.
So, if at a peak hour a lot of wind-generated electricity would be available, it could show up more pronounced in prices than during off-peak hours. However, the extent to which this (cheaper) source will be present in practice and to what extent the unpredictable wind energy is bid in is unclear53. This leads the the following hypothesis:
Hypothesis 2: Wind energy has larger effects on APX prices at peak hours than at off-peak hours during the sample period.
This effect, if present, could become more pronounced as the years progress and installed wind capacity increases. The more wind power there is in the system, the less likely the higher bids onto the APX will be hit, either causing the producers of higher-order generation capacity to bid lower or demanded capacity to be completely fulfilled by lower-order (cheaper) capacity. Either way, it could be perfectly possible that the negative influence of wind has been growing in the sample period. On the other hand, there could be learning effects as producers learn how to deal with larger wind volumes, or the way wind is used in the market has not been consequent, i.e. more MWs were sold OTC. Finally, average annual wind speeds have not been constant during the sample years54. This ambiguity can be tested by means of the following hypothesis.
Hypothesis 3: Negative effects of wind energy on APX prices have become larger every year during the sample period.
53
Although the unpredictability itself cannot affect the APX, under predicted wind power has to be bought at unfavorable prices at the intra-day or imbalance market, causing potential downward bias in bidding strategy.
54
3.1 Methodology: Modeling electricity spot prices
To test for the presence of the hypothesized effect, a model for electricity prices that incorporates the production of wind energy has to be constructed. Electricity spot price modeling is a relatively new phenomenon, since before the liberalization electricity prices purely reflected generation costs and government policies55. A number of characteristics electricity prices exhibit have been explored in the literature56:
• Mean reversion
• Multi-scale seasonality (intra-day, weekly, seasonal) • Erratic price spikes with fast mean reversion
• Non-normality of the distribution (positive skewness and leptokurtosis) • Excessive time-varying volatility (annualized values 200% or more)
These aspects should be taken into account as much as possible in my analysis. The models that have already been used in electricity price analysis can be subdivided into six classes57: cost-based, equilibrium, artificial intelligence-based (AI), quantitative, fundamental, and statistical.
Cost-based models estimate prices on the basis of production costs but ignore bidding strategies, making them unsuitable for today’s markets. Furthermore, finding out the marginal costs of the generation assets in the Netherlands today is very difficult because such knowledge can be considered confidential. One such model has been successfully employed to measure market power in the UK, using a data set with direct measures of marginal costs58. The conclusion was that prices were indeed affected by market power, although not to the extent oligopolistic theory predicted. The reasons for this could be entry deterrence combined with fear of regulatory actions, resulting in a price somewhere between pure oligopoly and competitive pricing.
Equilibrium approaches compensate for this lack of market power incorporation, but have the major disadvantage that complete information on market participants has to be known or assumed upfront. For an extensive overview of equilibrium approaches, see Ventosa et al., 2005. This paper explains in great detail the workings of this class of models and recognizes that the short-term modeling suffers from the lack of complete information on market party behavior. They state that equilibrium approaches are most suitable for medium term price
55
Bunn and Karakatsani 2003, Knittel and Roberts 2005 56
Bunn and Karakatsani 2003 57
Overview from Misiorek et al 2006 58
predictions, which is not of interest when trying to find out the relationship between wind energy production and spot prices.
The AI models are difficult to use and as already has been proven in the literature59, there are serious problems with the successful implementation of AI-models in general. These models employ computer programs to gain insight into processes that can be thought of as mimicking biological behavior (such as interplay of market players and their environment). The complexities of this class of models and their bad track record have ruled out their use in this research.
Fundamental methods use functional associations between physical and economic drivers of the price of electricity (such as environmental conditions and fuel prices), making this class of models highly suitable for the analysis of the effect of wind (being a potential fundamental driver) on the APX price. The fundamental approach has been used to model the relationship between electricity and natural gas futures prices60. The findings of this paper indicate that there is a relationship between electricity- and gas consumption and their respective prices. However, gas prices are not nearly as volatile as wind production and availability does not differ over the course of the day, making its effect stable throughout the day and eliminating the intra-day variation effects. Incorporating the fundamental approach in a statistical or quantitative model, however, would make intuitive sense.
Quantitative models are mainly used to evaluate derivatives and manage risk and describe the main characteristics of electricity prices, not their driving forces. This reduces the electricity price formation to a mere stochastic process, which cannot take the influence of wind into account. Statistical approaches have proven to be a good way of modeling the electricity spot price in combination with afore mentioned fundamentals. Extensive comparisons of various tests can be found in Misiorek et al. 2006, Knittel and Robberts 2001, Weron and Misorek 2005, Escribano et al. 2002, and Cuaresma et al. 2004. All these papers have in common that they test various datasets of power exchange prices using models that incorporate the mean-reverting tendency, the time-varying mean, and time-varying volatility.
Knittel and Roberts (2001) analyze electricity prices in a Californian district around the summer of 2000 using various models. They employ an EGARCH model, a mean-reverting process model, a varying mean model, jump-diffusion process models (one time-dependent), and an ARMAX model, in order of correctness in predicting future prices. None of
59
Conejo et al. 2005a 60
these models were really satisfactory with respect to their predicting value for valuation purposes.
Escribano et al. (2002) test the mean-reverting properties and the unit root using various tests for prices of power exchanges in Argentina, Australia, New Zealand, Nordpool, and Spain. They firmly conclude that the electricity prices are indeed mean-reverting and that there is no unit root process but that the data are stationary. Furthermore, they stress the added value of a GARCH component to take care of the heteroskedasticity in their data.
Cuaresma et al. (2004) test various mean-reverting models for the Leipzig power exchange, also including a jump component to explain price spikes. They find the mean-reversion terms to be highly explanatory and find that the jump component improves forecasting performance. Another important point raised is the superior performance of consecutive hourly modeling when compared to the modeling of continuous days.
Weron and Misiorek (2005) also test various mean-reverting models but include an explanatory variable, load (which is a good proxy for demand). They conclude that the addition of the explanatory variable reduces errors when forecasting, and this explains part of the price forming process. The integrated models, used to remove possible non-stationarity, all perform worse than the standard ones when measuring their weekly prediction errors.
Misiorek et al. (2006) find, in contrast to earlier studies, that non-linear mean-reverting models (both with and without explanatory variables) produce better forecasting results in terms of weekly errors than linear ones. They provide an overview of increasingly sophisticated models to maximize forecasting performance for the Californian Power Exchange. Again, the explanatory variable and GARCH term improve the fit of the model.
A fundamental model alone would not be able to capture certain aspects of electricity prices that are well established in the literature such as their tendency to revert to their mean. Statistical models by themselves, on the other hand, are unable to take into account explanatory variables and a combination of the two would thus make sense. A good example of this would be the approach taken by Contreras et al. (2003) who model electricity prices with the explanatory variables load and hydro power production. They conclude that the explanatory variables are useful in explaining price variations.
Weighing this latter approach against the alternatives, I think that employing this statistical-fundamental hybrid model is most suitable for the testing of my hypotheses. The major potential drawback is that this class of models is aimed at forecasting short-term electricity price changes. However, the parameter estimators the model yields are, if significant and unbiased, useful indicators of the direction and size of the effects of the explanatory variables on the price changes.
3.2 The basic model
As already stated, the basic aim of the model to be used is to determine the relationship between wind-generated electricity produced at a certain hour and the APX price at that hour. The most suitable way to perform basically any analysis of APX prices would be to model the separate hours of days as 24 separate time series, because at the moment of bidding the prices for all 24 hours are set and no new information is added that could influence the prices61. Another approach would be to take the daily average price62, but this is less suited for the type of analysis I would like to perform. The intra-day variation of wind-generated electricity means that wind production levels will differ at various hours and influences will vary throughout the day. Losing the information captured in the hourly levels would thus be wasteful.
The data are presented as a series of consecutive daily measurements over single hours, or time series. Time series analysis is often used in research into commodity and financial products’ price series. The biggest difference between these “normal” goods and electricity is the lack of possibility of storage which eliminates the convenience yield principle (holding a commodity instead of a forward contract) and thus leads the spot price process to reflect most of power’s fundamental properties63. Electricity has, like other commodities, a
61
Huisman, Huurman and Mahieu, 2007 and private conversation with Dr. Huisman, April 2008 62
Mugele et al., 2005 63
mean-reverting tendency to a level dictated by marginal costs and characterized by seasonality64.
Time series data in general have two traits that can make analysis difficult: firstly, the way the series “behaves” can be either stationary or non-stationary. This should always be checked, since analysis using non-stationary series can lead to spurious results. The second trait is the dependency of prediction errors on their past values, or serial correlation. This can be the case when there is variables that have influence on the dependent variable (but which are not modeled) whose effects persist over some time. Checks for structural breaks in the series should also always be made when using time series data65.
I will now explain how the model is built up from the start, beginning with the mean-reverting component. This typically leads to a basic model such as the one in Misiorek et al. 2006: t h t h t
B
P
P
=
ρ
(
)
+
ε
0
<
ρ
<
1
(1) WhereP
th is the APX price at hour h on day t,ρ
(B
)
is a backward shift operator, i.e.ρ
(
B
)
=
1
−
ρ
1B
+
...
+
ρ
pB
p andε
t is the error term at day t i.i.d. with zero mean66. This is a simple AR(p) model, of which the determination of the order will be treated later on.The series also move within a certain bandwidth which is caused by seasonal influences, which requires a moving average component leading to an ARMA (p,q) model,
t t h h t
B
Pt
B
P
=
ρ
(
)
+
θ
(
)
ε
+
ε
−
1
<
θ
<
1
(2)Where
θ
(B
)
is the backward shift operator, i.e.θ
(
B
)
=
1
+
θ
1B
+
...
+
θ
qB
q which determines the speed with which the price diverges from the previous average.The next step will be to adapt the general ARMA to incorporate explanatory (X) factors. This type of model is usually called ARMAX67 or transfer function approach68 models and has already been used for looking at the influence of load data and temperatures. These are both
64
Geman and Roncoroni, 2006 65
Hill et al., 2001 66
Misiorek et al., 2006 67
Misiorek et al. 2006, Weron and Misiorek 2005, Knittel and Roberts 2001, Knittel and Roberts 2005 68
explanatory factors that influence the electricity price and on which traders have no influence and producers can be assumed to have, on average, similar expectations. This also goes for the variable I would like to include. Wind production cannot be called into service but will simply be there or not, but the amount of wind energy provided can roughly be estimated by all market parties. As mentioned in the previous section, the ARMAX models have outperformed the other ones in comparative tests with ARIMA and ARIMA-E (ARIMA with load variable) in earlier papers69. This leads to the following model:
t h t h t t h h t
B
Pt
B
W
P
=
ρ
(
)
+
θ
(
)
ε
+
Λ
+
+
ε
(−
1
<
θ
<
1
,0
<
ρ
<
1
) (3)The inclusion of fundamental variables does not always lead to spectacular improvements of the analysis of the prices70 but it should be most suitable tool for the analysis of exogenous variables such as wind energy. It has to be said that there are many other factors that (potentially) influence the electricity price and could be introduced into the model. However, my goal is to determine whether there is a relation between wind energy and the APX price. Furthermore and of more importance, the introduction of more variables linked to electricity prices trough elaborate economic ties would make the model too complicated.
The model now takes into recognizes all the factors mentioned earlier (mean reversion, multi-scale seasonality, non-normality of the distribution, excessive time-varying volatility) with the exception of the spikes. Procedures to model spikes are the construction of a regime-switching component71 or component that models the spikes as a sinoidal process72. However, I think the occurrence of price spikes is influenced by the availability of wind energy so trying to include probabilistic means of explaining them would take away some of the explanatory power of my wind energy variable. Hence, I choose not to model the spikes separately.
3.3 Diagnostics
The ARMA-type models assume normally distributed errors, which cannot be taken for granted and the literature suggests that heteroskedasticity could pose a problem73. I will thus test for the presence of heteroskedasticity with a method used a lot in time series analysis, testing for ARCH effects in the squared residuals. The ARCH test was devised by Engle in 1982
69
Misiorek et al. 2006, Nogales et al. 2002, Knittel and Robert 2005 70
Nogales and Conejo, 2006 71
See for example Huisman and Mahieu 2003 72
See for example Cuaresma et al. 2004 73
and was adapted to GARCH by Bollershev in 1986. GARCH stands for Generalized AutoRegressive Conditional Heteroskedasticity74 and is used to denominate the relationship between the variance and error terms, using their past values to forecast the next value. GARCH errors can be seen by examining residual graphs, and show up as clusters of errors. These clusters are caused by turbulent periods in which the model itself functions less well because of external events (such as for example extreme heat causing plant output to drop).
The easiest way to check for the presence of a GARCH process is to look at a correlogram of the squared residuals. Whereas the errors will be uncorrelated, the squared errors show clear signs of autocorrelation when a GARCH process is present. The process of adding ARCH and GARCH terms follows the same procedure as the AR and MA terms, respectively.
A final test could be made concerning the endogeneity of the load, which is in effect the quantity demanded and supplied. As already stated and following amongst others Bunn and Karakatsani (2004) I assume demand to be inelastic and thus exogenous in the short term. Supply however could pose a problem since in theory producers can withhold capacity when wind energy is available to maintain higher prices. In practice, this will not likely be the case75. When wind energy is sufficiently present, the possibility for exercising of market power greatly diminishes since there will be enough parties with spare capacity at low marginal costs to make strategic behavior less attractive. Furthermore, it is impossible to expose ex ante the quantities supplied by all parties and at specific marginal costs so as to discover whether or not capacity bids have been uncompetitively low. Looking at market power would be the next plausible option.
There is actually no single proven way to measure the exertion of market power in electricity markets although various approaches have been successful. Input and production costs can be compared76, but the lack of data availability makes it impossible for me to use this approach. Conventional measures of market power such as the Herfindahl-Hirschman index are also not useful because they fail to take into account some important aspects of electricity as a commodity as mentioned above77. An important aspect is that the possibility to exercise market power is time varying with available generation capacity78. Fabra and Toro (2005) find evidence for the Spanish market that there is indeed collusion between the two firms that have
74
Bollershev 1986 75
Private conversation with W. Graveland, analyst at Eneco Asset Management 76
Wolak 2003, Wolfram 1999, Borenstein et al. 2002 77
Stoft 2002 78
a de facto duopoly in the Spanish electricity market. They use a Markov regime-switching model (i.e. a model that allows transition between two “states” of the market by means of a Markov probability matrix) to prove this, although they also find periods of intense price wars with mark-ups below marginal costs. The construction as well as the collection of marginal cost structure data needed for the calibration of such a model is beyond the scope of my research.
A standard test for endogeneity –the Hausman test- is to measure the correlation between the residuals of the series and the suspected explanatory variable. Should there be correlation between the two, the regression assumption of no correlation is violated leading to a biased least squares estimator. However, it is well known that variations in the quantities demanded dictates movements of the price to such a great extent that their general behavior is basically those of twins, as can be seen in the figure below. The figure shows prices (dotted line, $/MWH) and quantities (straight line, MW) as traded on the Pennsylvania New Jersey Maryland (PJM) market. Variation of the load does correspond with variation in the price but it cannot be proven that this is connected to suppliers responding to sudden drops in prices by adjusting demand.
Figure 1, PJM market demand and prices (Source: Fezzi 2007)
The dependent variable,
P
th, is the value of the APX. It will be log-transformed to achieve a more stable variance79 and improve on a potential lack of dispersion of the data. The usefulness of such a transformation is disputed in Knittel and Robberts (2005) because, as they argue, the problem with forecasting lies in the kurtosis, not the skewness. The distribution of the data however is such that a log-transformation is needed to attain a more suitable distribution (as measured by the Jarque-Bera statistic) for regression analysis. The original data distributions and their transformations can be found in the Appendix for hours 4 and 16.The first term(s) in the equation,
ρ
(B
)
, is (are) a simple statistical measure(s) that describe(s) the speed at which the series reverses to its mean and is very common when dealing with autocorrelated time series. The reason the series can be assumed to be autocorrelated and mean reverting is very straightforward; the fundamental values of the price do not change very rapidly but some deviation will eventually occur due to the existence of supply disruption or unexpected surges in demand. The former can also go accompanied by market power of higher merit-order generation sources which can start up when prices suddenly spike. The determination of the order p will be explained shortly.The second term(s),
θ
(B
)
, is (are) the value(s) of the way in which the average tends to move around. Electricity prices as a whole were probably (weakly) stationary during the time frame I am considering (01-01-2003 until 27-06-2007), but due to seasonality and other variables that influence the price and are serially correlated the mean tends to move around during the year. Higher prices will, on average, prevail during the winter in the Netherlands (due to increased use of lighting, heating and cooking is mostly done by using natural gas) and lower prices during the summer. The determination of the order q will be explained shortly.The first explanatory variable, load, is a variable that signals demand and is often mentioned and also used80 as an explanatory variable in electricity prices. This variable should have significant explanatory power and will thus improve the fit of the model and will also serve as a way of checking whether the model performs as expected. I expect the effect of the load to be significant and positive at all times, and on average higher during off-peak than during peak hours. I expect this because variations in prices are explained by load variations to a higher extent during hours in which plants run at baseload capacity. Since price elasticities are so low I assume exogeneity. That is, prices are driven by demand and demand not by prices. The exact value used will be the load at hour h on day t. It will be denominated by the
79
Weron and Misiorek 2005. 80
term
Λ
ht in the model. The data will be used in log-transformed form for the same reasons as for prices.The second explanatory variable, hourly wind production, will be used to check for the influence of wind production on the spot price of electricity. The data’s values will be the amount of wind energy expected to be produced in the Netherlands in MW per hour, denoted by the symbol
W
th. The exogeneity of wind is defendable as prices of electricity do not affect wind speeds and will not be tested as well. The data will be log-transformed for the same reason as for prices. The original data distributions and their transformations can be found in Appendix 1.3.5 Data
This section will give a short overview of data I used for the basic model. The data all span from the 1st of January 2003 until the 28th of June 2007, making for 39.336 observations for 24 hours or 1639 observations in total.
- Hourly APX prices: Single-round bidding prices that denote the hourly spot price of electricity for all market parties on the Amsterdam Power Exchange. The data comes from ENECOGEN, the EET database, which receives this data automatically from the APX group. The series has been transformed to take daylight savings into account81. Extremely high prices that could be considered outliers have not been removed because these should be negatively affected by wind energy production and are an important aspect of the electricity market.
- Load data: Load data for the Netherlands are assumed to be unknown or at least not publicly accessible. As a measure of load I have chosen to take the load for the Dutch Province of Utrecht (situated in the middle of the Netherlands) multiplied by a factor of 3.5. The load data for Utrecht come from the ENECOGEN database and the multiplier is commonly used by the analysts at Eneco82. The series has also been transformed to take daylight savings into account.
81
In line with other literature (Huisman and Mahieu 2003, Miriorek et al. 2006) the “missing value” at 3:00 AM on the last sunday in March is replaced by the arithmatic average of the two adjacent hours and the “extra value” at 3:00 AM on the last sunday in October is deleted.
82
- Wind volumes: Wind production volumes from EET’s portfolio, which is geographically nicely dispersed through the Netherlands. The portfolio begins with a 5% share of total wind capacity in 2003 and ends with a 20% share in June 2007. I use the electricity production as given by EET in the period as a proxy for national production. National production figures are not (publicly) available on an hourly level. I compensate the lacking volume by calculating the monthly wind volume produced in the EET portfolio as a percentage of CBS-reported monthly production, then multiplying EET’s hourly volumes by the reciprocal of the monthly percentage. The series has been modified to take daylight savings into account. Furthermore, all the negative values have been substituted for by 1. Negative values make no sense in the model and cannot be log-transformed but do occur in real life when turbines go off-line.
4. Testing the model and results
Testing for stationarity of the series, the Augmented Dicky-Fuller test rejects the null hypothesis of a unit root process in the data at a 95% confidence interval for all hours for all the time series. This is also in line with most of the literature83 as well as common sense since prices can only rise and fall to a limited extent, which can not be caused by a unit root process. Rejecting a unit root process for prices and wind energy production is important since regressions using non-stationary time series are known to yield possibly spurious results84. The results as given are thus for the log-transformations of the three series for price, load, and wind production without differencing. Structural breaks were not detected.
The model itself is built on the basis of estimator performance. This implies that the maximum of autocorrelation will have to be removed without using too many ARMA terms as these also reduce correlation that could be caused by the explanatory variables. Autocorrelation was examined in correlograms for the Partial AutoCorrelation Function (PACF) and the AutoCorrelation Function (PAC). Also, the squared residuals’ correlograms were examined to detect heteroskedasticity. The final models used for the various hours can be found in the appendix. Most of the off-peak hours were simple ARMAX(2,1) structures with GARCH(1,1) component whereas peak hours exhibited a weekly pattern demanding the addition of Seasonal AR (SAR) terms at their seventh lag as well as a Moving Average term at lag seven. The GARCH term that was needed was kept constant at (1,1) although some autocorrelation sometimes emerged at very high lags such as 20. After estimation of a linear model, which
83
Robinson 2000 and Escribano et al. 2002 84
confirmed the negative relationship between wind energy and APX prices at all hours between 11 and 22 and at hour 01 the expected exponential relationship was tested. These results were again significant for the peak hours and all had the right sign. The variable load was always highly significant and always had the right sign. A summary of the estimators is given below; the Eviews-output is presented in Appendix 3.
Linear wind
Squared wind
hour: Load
Wind
S.E.
hour: Load
Wind
S.E.
0
0.985* n.s.
-
0
1,021* n.s.
-
1
1,174* -0.007*
0,002
1
1,171* -0.000359*
9.23E-05
2
3,197* n.s.
-
2
4,068* n.s.
-
3
2,593* n.s.
-
3
2,598* n.s.
-
4
2,964* n.s.
-
4
2,963* n.s.
-
5
2,629* n.s.
-
5
2,654* n.s.
-
6
3,028* n.s.
-
6
3,028* n.s.
-
7
2,341* n.s.
-
7
2,353* n.s.
-
8
2,150* n.s.
-
8
2,153* n.s.
-
9
1,346* n.s
-
9
1,744* -0.000352**
0.000165
10
1,305* n.s.
-
10
1,574* n.s.
-
11
1,545* -0,005*
0,002
11
1,543* -0.000338*
0.000103
12
1,272* -0,006*
0,002
12
1,275* -0.000338*
8.62E-05
13
1,212* -0,007*
0,002
13
1,213* -0.000330*
0.000121
14
1,158* -0,006*
0,002
14
1,159* -0.000309*
0.000114
15
1,387* -0,008*
0,002
15
1,387* -0.000375*
0.000111
16
1,460* -0,012*
0,001
16
1,457* -0.000716*
9.51E-05
17
1,459* -0,013*
0,001
17
1,458* -0.000759*
9.62E-05
18
0,845* -0,006*
0,001
18
0,857* -0.000363*
6.50E-05
19
0,999* -0,005*
0,002
19
0,701* -0.000210*
0.000100
20
0,804* -0,005*
0,002
20
0,815* -0.000323*
8.22E-05
21
0,797* -0,004**
0,002
21
0,805* -0.000289*
8.59E-05
22
1,551* -0,004*
0,001
22
1,542* -0.000238*
5.06E-05
23
1,051* n.s.
-
23
1,051* n.s.
-
Coefficient significance levels: *=0,01 **=0,05, n.s.=not significant
Table 2, explanatory variable estimator coefficients
volatility wind energy’s influences are the highest as can be seen in Figure A8a and A8b in the Appendix.
The third hypothesis stated that the effects of wind energy on APX prices should increase every year as additional power is added. For all hours that have shown to be significantly affected by wind power this difference was tested using yearly dummies with 2003 as the base year. The coefficients should all be negative since average wind speeds in 2004-2007 were all higher than in 2003 and more wind power was installed85. However, the tests yield ambiguous results. For the year 2004, all but hour 18 have significant results with the expected sign. For 2005, three hours have significant results with the right sign and for 2006 only one hour show significant results but with the wrong sign. Finally, for 2007 the hours up until 17 show positive results, all with the right sign, although the later hours show no significant effects. Hypothesis three is thus rejected and wind energy’s effects have not been growing steadily during the sample period.
2004 2005 2006 2007 1 -0.010926* n.s. n.s -0.016735* 9 -0.012538* n.s. n.s. -0.033918* 11 -0.020534* n.s. n.s. -0.034914* 12 -0.020909* -0.006802** n.s. -0.016868* 13 -0.026133* n.s. 0.014702* -0.024144* 14 -0.023629* n.s. n.s. -0.030889* 15 -0.022658* n.s. n.s. -0.034883* 16 -0.031868* n.s. n.s. -0.052266* 17 -0.031704* n.s. n.s. -0.050751* 18 n.s. -0.005770* n.s. n.s. 19 -0.009356* n.s. n.s. n.s. 20 -0.008731** n.s. n.s. n.s. 21 -0.010212** n.s. n.s. n.s. 22 -0.012041* -0.005955* n.s. n.s.
Coefficient significance levels: *=0,01 **=0,05, n.s.= not significant Table 3, yearly progression of wind energy effects
An explanation for these results could be that during the years 2004 and 2007 volatility has been notably lower than in 2005 and 2006, as can be seen in Figure 2. The base year, 2003, has been very volatile so the reason for the insignificance of the two years could be simply that the conditions were similar to 2003 in terms of price variance. If a complex system such as the electricity market is very volatile, smaller influences such as wind energy could fail to make a large footprint. Periods of high variance are an indication of less well functioning markets, i.e. there is more room for market power and less competitive pricing. This does not mean that wind did not have a growing influence but that the conditions were such that these influences
85
were swamped by other, maybe larger forces at work and are thus not detected as more influential. 0 0,5 1 1,5 2 2,5 3 3,5
Figure 2, yearly variability APX prices 2003-2007, sample average = 1 4.2 Normality of the residuals
The regression that tested the hypotheses was done on the basis of the assumption that the errors are normally distributed. Since the dependent variable is not normally distributed and there is still some correlation this assumption is possibly violated. After inspection of the histograms of the residuals as produced by Eviews I can quite surely state that the errors are not normally distributed. The high kurtosis leads to high Jarque-Bera statistics. The skewness is not really a problem and the histogram indeed looks like a stretched out bell shape, which is a clear sign that there is a serious problem with the estimators. To deal with this, I could change the functional form or remove values to attain a better distribution of the residuals. Instead of using a log-log functional form I could use a linear component but this should yield even poorer results because of the distribution of the original data (skewness problems). After testing this for two hours this was confirmed. The use of a reciprocal would not suit the expected effect either and should not be used in this case.
took this into account since I did not succeed in removing all the autocorrelation from the model.
5. Discussion of results
The first and second hypotheses were validated by the model, whereas the third hypothesis could not be accepted on the basis of the results. The results in general do offer clues on where the electricity market is heading for if wind energy reaches the penetration rate governmental organizations and other interest groups envisage at the moment. In the whole of North Western Europe, plans to add additional wind farms on ever larger scales are being realized. Targets exist for a tripling of capacity in the Netherlands alone, to a total of 6 GW of installed capacity. To what extent these targets are attainable depends mostly on political decisions, notably building permits for the turbines and subsidy policies.
The results suggest that the impact of the addition of wind power on APX prices could be large. Should the market environment remain unchanged save for the addition of the extra wind energy, the market probably becomes less volatile. This is because a lot of the wind energy added is offshore in large wind farms which produce a much more stable and less intermittent flow of electricity than current wind parks do. Furthermore, the mere addition of production capacity will ensure that the threshold at which high-cost generators are called into action is reached less often, even at lower wind speeds. Finally, the new wind turbines are able to continue operation at higher wind speeds which less advanced models could not. At wind speeds at which production would be highest the turbines would be taken off-line to ensure that they would not be destroyed.
