The influence of wind energy market share on market clearing prices, wind park revenues and bid performance

Transcription

1 The influence of wind energy market share on market clearing prices, wind park revenues and bid performance Author: Sam Hartveld (321556) Coach: Prof. Wolfgang Ketter Co-reader: Dr. Jan van Dalen MSc Business Information Management Erasmus University Rotterdam, Rotterdam School of Management August 14, 2014 Abstract Wind energy presence has a strong influence on market clearing prices in day-ahead markets and imbalance prices. Considering the growing market share of wind energy the importance of this influence is increasing. When the influence on the Market Clearing Price (MCP) increases, this directly affects wind park revenues. This can be observed in both short-term day-ahead bids and long-term income. We present a model for wind gencos that optimizes bids in the day-ahead market by minimizing their imbalance costs. In this effort, the model takes into account the gencos influence on the MCP. This way a new perspective on wind park revenue forecasting is provided. Wind speed forecast data is used to calculate the influence of growing market shares of wind parks on their expected revenues. The expected revenues of wind gencos are then assessed in multiple market configurations in order to determine the influence of wind energy market share, wind speeds and imbalance prices on the expected revenue of wind gencos. Keywords: Wind Energy, Bid Strategy, Wind Park Size, Market Share, Renewables, Revenue Forecasting, MCP Forecasting Preface The copyright of the master thesis rests with the author. The author is responsible for its contents. RSM is only responsible for the educational coaching and cannot be held liable for the content. 1. Introduction Energy consumption and production patterns in todays environment are constantly in motion. New technologies are enabling consumers to become producers and the influence of renewable energy sources (or renewables) is increasing. Especially the influence of wind energy is growing because of its increasing market share in the US and many European markets. Wind energy has unique elements, which do not apply to traditional energy sources. These elements result in a special influence which wind energy have on energy prices and the profit of generating companies (gencos). Many bid strategies exist which aim to maximize profits of wind gencos assuming certain energy prices. At the same time, research has been done on the influence of wind energy on the market clearing price (MCP). This study takes the first steps into combining these research objectives. A model is proposed which predicts energy prices and determines optimal bids in the day-ahead market, taking into account the influence of wind energy. This information is used to assess how wind energy will influence the MCP and wind park profitability, when its output quantity on the market increases Differences between Energy Sources Before discussing the model, a general introduction in wind energy is provided. This paragraph covers the most essential differences between traditional, fossil fuels and wind energy. Four fundamental differences between the two sources exist. First, the earth contains a limited reserve of fossil fuels, whereas wind energy can be considered infinite. Also fossil fuels damage the environment by emitting greenhouse gasses, while wind energy uses the environment to generate energy in a sus- Preprint submitted to Energy Economics August 14, 2014

2 tainable manner. The third difference can be observed in the adjustability of the energy production quantity. Within a certain ramp-up rate, energy production plants using fossil fuels can increase or decrease its energy output. The only limitation here is the maximum/minimum capacity of the plant. Wind energy, however, is dependent on external factors, such as wind speed. This means that fossil fuels have the advantage that they can be used to adjust energy production according to demand, whereas wind energy cannot. A fourth difference lies in the cost structures of the energy sources. Both wind and fossil energy sources have high fixed costs. However, the variable costs (VC) of the energy sources differ fundamentally. The source of wind energy (wind) is free, which results in relatively low VC. The VC of fossil energy sources are higher, as they are dependent on the price of coal and other fossil fuels Influence of Renewables Renewable energy sources are dependent on external, uncontrollable circumstances. For wind energy the primary source of influence is wind speed. Wind speeds can change continuously and so does the energy output. Most energy is traded in the day-ahead market, which is between 12 and 36 hours before the actual energy delivery takes place. However, the problem is that wind speeds can only be reasonably predicted within a 4 hour forecast length. As a result, the connection of wind turbines to the electricity grid can potentially affect supply reliability and power quality (Chompoo-inwai et al., 2005). Fluctuating energy output can influence prices, because it results in peaks and shortages in supply. The dependency on wind speed speeds also poses an issue because of the required balance in the market. The imbalance prices, imposed by the TSO, have a major influence on wind park profitability; because errors in wind speed forecasts result in a lack of energy production. This in turn is penalized by the TSO. In the United States and in many Western European countries policies are made that stimulate the use of renewable energy sources. Hence, it can be expected that the share of energy coming from renewable sources will increase in the near future (Ketter et al., 2013). When the overall market share of wind parks will increase, the position of wind parks in the market is fundamentally different. Based on the influence of wind energy on the market, four differences from the current situation can be expected when the market share of wind power increases. The variability of the quantity of energy production on the grid is expected to increase, as the amount produced by more volatile energy sources increases. Secondly, 2 the amount of energy which is traded on the spot market will increase. Also, the increase in variability of production may result in more imbalances. Lastly, an increase in market share of wind gencos enables them to influence the MCP Increased Market Share of Wind Energy In this paper we propose a model that calculates the expected revenue of wind parks, while taking into account its influence on the MCP. Firstly, this provides us with insights in a wind parks influence on the MCP. Second, expected revenues can are optimized and assessed in multiple market configurations. Lastly, the performances of the bid strategies are compared. Initial expectations are that relative profit decreases, influence on MCP increases and the added value of bid optimizing strategies increases when wind energy market share increases. 2. Theoretical Background 2.1. Energy Markets There are three basic market structures in which energy can be sold: a pool-based market, contractual market and hybrid forms (Li et al., 2011). In a pool-based market suppliers and demanders place their bids and based on the supply and demand curves which result from those bids an energy price is determined. Energy on contractual basis is sold for a predetermined price which the involved parties agreed upon. Hybrid forms combine aspect of both markets. In this study a wind park genco is considered in a pool-based market. In a pool based market a TSO is responsible for balancing supply and demand. The energy pool market consists of three successive short-term trading floors: day-ahead market, adjustment market and the balancing market (Morales et al., 2010). The primary source of income of wind park genco is considered to be the energy traded on the day-ahead market. The only costs incurred in this energy trading are caused by imbalances in the grid. Gencos make real time decisions in order to optimize their performance and proper predictions help in this effort (Ketter et al., 2012). According to Pina et al. (2012) the intermittence of most renewable resources can create problems to electricity grids, when renewable energy provides a significant share of the energy mix. This increases the importance of role that the TSO has when the market share of renewables increases.

3 Market Clearing Price The energy market works like any commodity market with supply and demand curves which are used to determine a market price. However, the nature of the energy and its market structure make the market a bit more complicated. First, energy cannot be stored in large quantities. Also, in the energy market, market participants offer and demand large quantities of energy. Bids are placed in large blocks with a specific quantity and price. This results in intermittent rather than continuous supply and demand curves. The MCP is the price which lies between the ask price and the bid price which are closest to each other, before the ask price exceeds the bid price (Ott, 2003). More details about this can be found in the PowerTAC Specifications (Ketter et al., 2014). For pool-based markets two pricing mechanisms exist: Uniform Pricing (UP) and Pay as Bid (PAB). In UP every genco is paid the same amount, namely the Market Clearing Price (MCP) (Li et al., 2011). This implies that the bids of each individual supplier and demander influence the revenues of all other market participants. For the purpose of this study a UP pricing mechanism is assumed, hence MCP is considered the sell price for all energy in the market. Wind parks will always want to sell their energy, because their energy source (wind) cannot be stored. As a result wind parks are incentivized to always sell the maximum amount of energy that they can produce. This, combined with the low VC of wind parks, result in the fact that wind parks are incentivized to sell a maximum amount of energy against any price. The MCP is paid to all gencos, so the wind park will always get this price as well Bid Strategies This paragraph contains a discussion of bid strategies which are used by wind parks to maximize their expected revenue. Li et al. (2011) identified three different models which are used to achieve this goal: single genco optimization, game theory and agent-based Single Genco Optimization For wind gencos multiple sources of uncertainty can be identified that affect wind park profitability, among them are: the day-ahead market price, wind power generation and the imbalance price (Morales et al., 2010). The day-ahead price is the energy price for the dayahead market, wind power generation depends on wind speeds and the imbalance price is paid for energy shortages or surpluses. In order to maximize profits wind 3 park gencos use bidding strategies. This maximizes the revenue generation on the day-ahead market and minimizes the costs for imbalances. In this effort gencos constantly need to make a tradeoff between cost maximization and risk minimization (Ma et al., 2005). Optimization methods differ regarding auction methods and assumptions. Most methods consider a UP market (Ma et al., 2005; Matevosyan and Söder, 2006), others a PAB market (Rahimiyan and Mashhadi, 2007). Regarding prices most methods assume the genco has no influence on the market price and is price-taker (Ma et al., 2005; Matevosyan and Söder, 2006; Rahimiyan and Mashhadi, 2007). Others aim to use the influence of a genco on the MCP in order to optimize its income (de la Torre et al., 2002). However, de la Torre et al. (2002) did not do this considering a wind genco. Elements of the model by Matevosyan and Söder (2006) are used for the purpose of this study. Their method aims to minimize imbalance costs of wind gencos by using error scenarios. The errors between weather forecasts and actual wind speeds are used to predict potential future forecast errors. These errors influence imbalance costs of the genco. The most basic manner to bid for future energy production is by basing future energy production directly on weather forecasts. Henceforth, this is referred to as Direct Bids Matevosyan and Söder (2006) have shown that bids of their methodology are more profitable than direct bids. In this model power output scenarios are forecasted based on potential wind speed scenarios. The MCP and imbalance prices are then given and used to optimize the bid quantity Other Optimization Methods In game-theory models, equilibria are determined by combining the bid strategies of multiple gencos. This way gencos cannot influence their profit merely by influencing their own strategy. In agent based methods, market participants are modeled as adaptive agents. They are developed with bid preferences and strategies, they can use past experience to improve their future performance (Li et al., 2011). This paper proposes a single genco optimization method, so neither game-theory nor agent based methods are considered in this study Wind Park Influence on MCP Valenzuela and Wang (2011) have developed a probabilistic model to determine long-term probability distribution of MCPs. In their model Valenzuela and Wang (2011) state that one genco can have multiple bids on different price levels and quantities. This is directly related to the stepwise cost increase of traditional gencos.

4 In their model block bids are based on the Marginal Costs (MC) of the output of the respective block. Besides that they assume that wind gencos always bid the lowest price, as wind parks have the lowest MC (Valenzuela and Wang, 2011). This methodology is used to determine expected MCPs and related imbalance prices. 3. Research Objectives Many studies have been performed on wind park profitability optimization bid strategies (Li et al., 2011; Ma et al., 2005; de la Torre et al., 2002); most of them focus on their dependency on wind forecasts and their position in the market. Studies exist on the influence on wind energy on MCP (Valenzuela and Wang, 2011; Sensfuß et al., 2008). However, we found no studies that combine these aspects in order to determine expected wind park revenues when they are able to influence the MCP. In this paper we present a model which predicts wind park revenues based on wind forecast, taking into account the wind parks influence on the MCP. First, the influence of wind park size on the MCP is assessed, then the expected revenues are calculated. This way the influence of the size of a wind park on its own profitability can be assessed. Lastly, accuracy of bidding strategies are evaluated by comparing expected revenues with actual optimal revenues. Figure 1 provides an overview of the relation between the variables in the model which we propose. In this chapter we elaborate how our research objectives relate to the variables and indicated relations. In chapter 4 we provide a detailed explanation of the model and the content of the relations. Paragraph 4.5 contains the details of the values of the independent variables that apply to our analysis MCP Influence An increase in wind energy will result in a fundamental shift in the structure of the energy market and the behavior of energy prices. Today, the key role of fossil fuel gencos in the energy market gives them strong influence on energy prices. However, with the growing availability of renewable energy it can be expected that the influence of renewable energy gencos will increase. This shift in the market power balance can be expected to have an impact on the MCP. Prior studies have had the relation between wind energy and the MCP as their primary focus (Valenzuela and Wang, 2011). This relation is part of our study as well; it is represented in the relation between Forecasted Quantity and Market Clearing Price. 4 Research Question 1. What effect does the market share of wind energy have on Market Clearing Prices? In some countries (e.g. Germany and Denmark) wind market shares are growing (Blanco, 2009), resulting in a considerable effect on MCP. The increasing amount of wind parks stresses the importance of a better understanding of prices patterns arising from wind energy influence, because these patterns are becoming more apparent. This objective is achieved by assessing the MCP for multiple wind speeds considering a certain wind park size. The wind speed is manipulated by adjusting the wind forecast. We then compare the MCP curves of multiple wind park sizes to determine the influence of wind park sizes. The wind park size is manipulated by adjusting the amount of turbines Expected Wind Park Revenue In this study a model is proposed which calculates optimal bids, while taking into account the wind parks influence on MCP. These optimal bids are determined by maximizing the expected revenues following from a bid. The expected revenue is influenced by the bid quantity (which is being maximized), the MCP, the imbalance price and the surplus/shortage which follows from the expected energy quantity and the bid. The second goal is to assess the influence of wind speeds on expected revenue. This provides us insight in what the expected revenue is for a specific wind speed forecast. The outcomes are highly relevant for short term revenue expectations in, for example, the day-ahead market. The influence of wind speeds is assessed by calculating the expected revenue for different wind speeds, keeping all other variables constant. Subsequently, the amount of turbines is adjusted in order to analyze the influence of the wind energy market share. Research Question 2. How is the expected revenue of wind parks influenced by the market share of wind energy in the energy market? The next topic of interest is the long term implication of the differences in expected revenues of the assessed wind park sizes. This provides us with an insight in the relation between the revenues and sizes of wind parks and enables us to assess profitability of wind parks in future energy markets. It impacts currently existing wind parks, but also has implications for future investments in wind energy. This objective is achieved by calculating the expected revenue of the different wind park sizes. Then, past wind speed data is used as an expectation for future wind behavior. The expected revenue is divided by the amount of turbines in the wind park in order to

5 Figure 1: Variable Overview provide a clear view on the profitability of turbines for given wind park sizes. Research Question 3. How are long term revenues of wind parks influenced by the market share of wind energy in the energy market? 3.3. Bid Performance Fundamental aspects of the bid method are derived from the methodology of Matevosyan and Söder (2006). The bid strategy is proven to result in better results than direct bids. In this study we assess the performance of the method as well. We compare the actual revenue which we receive with the optimal revenue which could have been received; this is defined as the bid performance. The bid performance indicates the value of the bid method in practice. If a bid closely represents actual optimal bids, it provides wind gencos with a better tool to optimize their bids and predict their revenues. Additionally, if the model performs well, it can be implemented in smart market simulations in order to improve their quality (Bichler et al., 2010). First, the actual revenue following from our optimized bid, considering actual wind speeds and market situations, is calculated. The actual revenue of the genco is compared with the best revenue which could have been achieved, having perfect information about actual wind speeds, to determine the bid performance. Also, the bid performance of the actual revenue which would have been received with direct bids is calculated and used as a benchmark. 5 Research Question 4. What is the bid performance of our bid method compared to direct bids and bids with perfect information? 4. Model 4.1. Bidding Strategy to Minimize Imbalance Costs This paragraph contains a discussion of the model which is simulated for the purpose of this study. It combines aspects of the models of Matevosyan and Söder (2006) and Valenzuela and Wang (2011). The relevant concepts of both models are explained in detail and their relation to this study is elaborated on. The aim is to provide a knowledge base which is required in order to understand the following methodology. Matevosyan and Söder (2006) developed a model that optimizes the energy bid amount based on given wind speed behavior, forecasts and market clearing prices. It assumes that wind parks have no variable costs and hence maximize profits by minimizing the imbalance costs on the spot market. Valenzuela and Wang (2011) also assume that wind parks have no variable costs. They assumed a given supply distribution in an effort to determine the long term effect of wind energy on MCP. This model contains a series of steps in which aspects of both models are combined. The model is depicted in figure 2. Table 1 contains a concise explanation of each step. After that, they are discussed more in to detail. For each

6 phase it will be stated what data is required and which methods are applied. RMS E measured for given values ofα,β andσ z. The resultingα,β andσ z provide a curve for RMS E ARMA, which matches the RMS E measured values as closely as possible. Thereby it provides the best possible representation of the measured past error events. The measured events in this model are represented by the RMS E measured values. There is one value for the RMS E measured for every forecast length (k). The RMS E measured values can be found in AppendixA. The RMS E ARMA follows a curve which is calculated with formula (3), where (4) applies when k = 0, (5) applies when k=1, and (6) when k> 1: Figure 2: Graphical representation of the model Determination of statistical behavior of wind speed forecast errors The goal of this phase is to determine the statistical behavior of wind speed forecast errors. It is a pattern in which forecast errors are expected to occur in the future and is based on past wind speed forecasts and actual wind speeds. The statistical behavior of forecast errors is represented in parametersα,β, andσ z. The manner in which these parameters are used is discussed in section The parameters are calculated in a Root Mean Square Error (RMSE) calculation of an Auto Regressive Moving Average (ARMA) formula, this will be discussed later in this section. The RMSEs of errors in past forecast data are used to determine RMS E measured values. Errors from past predictions follow from the data set which is provided by the PowerTAC platform and originates from the KNMI (KNMI, 2010). The RMSE Auto Regressive Moving Average (ARMA) is used to match the RMS E measured values, with formula (1): where, minq(α,β,σ z ) (1) Q(α,β,σ z )=Σ K k=1 [RMS E measured (k) (2) RMS E ARMA (k)] 2 The goal here is to minimize the value of Q, where Q represents the difference in between RMS E ARMA and 6 σ(x(k))= V(k) (3) V(0) = 0 (4) V(1)= σ 2 z (5) V(k)= σ 2 z (α 2(k 1) + (1+β 2 + 2αβ)Σ k.1 i 1 αi 1 ) (6) Where: k=the forecast length andα,β andσ z are dependent variables, which are calculated in the effort of minimizing Q as explained in formula (1). In this formulaσ(x(k)) represents the RMS E ARMA values Determination of wind speed error scenarios With the parametersα,β andσ z from the abovementioned RMS E ARMA curve the wind speeds error scenarios can be determined. Formula (7) is used to create the scenarios. where, X i (t)= αx i (t 1)+Z(t)+βZ(t 1) (7) X(0)= 0 Z(0) = 0 And, X i (t)=wind speed forecast error in t hour forecast and Z(t)=arandom Gaussian variable for hour t (with standard deviation=σ z and mean= 0). It can be observed thatαrepresents the degree to which an error correlates with the preceding error value, β represents the degree to which the error correlates with the random value of the preceding timeslot andσ z determines the standard deviation of the random variable. The scenarios are created by generating values Z(t) until the desired forecast time has been reached. Each value X(t) represents a possible wind speed error at hour t. For each X(t) only one Z(t+1) is generated. This results in a probability tree, where t=0 is the source of

7 Phase no. Title Description 1 Determination of statistical behavior Based on wind speed forecast error data, parametersα,β and of wind speed forecast σ z are determined. 2 Determination of wind speed error Wind speed error scenarios are determined, based on theα,β scenarios andσ z which represent the natural behavior of the wind speed errors. 3 Calculation of wind speed scenarios Wind speed scenarios are calculated based on the wind speed error scenarios, with the same probabilities. 4 Calculate wind park power output The wind speed is obtain from the aforementioned scenarios, for the given wind speeds based on these, wind park power output is determined. 5 Determination of MCP The MCP is required to determine the optimal bids and is based on given market structure. 6 Solving optimization problem to The final step is to minimize the imbalance costs and determine the optimal bid consequently maximize the wind park s expected profit. Table 1: Bidding strategy pase outline every scenario. At higher values of t, there is only one outcome possible for X(t+1). A scenario is defined as a series of consecutive nodes from X(0) to X(T), where T is the maximum value of t. For the purpose of this study T = 24. This method of scenario creation is based on the method by Söder (2004). An infinite amount of scenarios can be created. For the purpose of this study we created 1000 scenarios per optimization. Each scenario is created randomly and has the same likelihood of occurrence; hence they have equal probability values. Figure 3: Graphical representation of ten error scenarios, T= Calculation of wind speed scenarios The wind speed scenarios are calculated by summing the wind speed forecast and the forecast error scenario. This is represented in formula (8): V i (t)= V f (t)+x i (t) (8) 7 Where V i (t)= Wind speed at hour t for one scenario (wind speed scenario), V f (t)= Wind speed forecast at hour t and X i (t) = Wind speed forecast error for one scenario. By adding the wind speed forecast to each error scenario, the error scenario is transformed to a wind speed scenario. A forecast is given for a value t. So for every value t the same forecast value is used. As a result a wind forecast of value of t is transformed into a series of potential wind speed values for a value of t. The amount of wind speed equals the amount of error scenarios. The error scenarios are repeatedly used for multiple forecasts. This can be done because the values represent the natural behavior of the wind for the specific region and hence apply in one location for all points in time (assuming no major changes in the environment). Each wind speed scenario has a probability which equals the probability of the corresponding error scenario. Hence all wind speed scenarios have equal probabilities Calculate wind park power output from given wind speeds This step involves the transformation from wind speed into electrical energy. For each wind speed there is a corresponding power output per turbine. The power transformation values are provided in paragraph The size of the wind park is determined here; the output per turbine is multiplied time the amount of wind turbines. The total power output is calculated per scenario. The potential scenarios of energy output are used in twofold: first it is used to determine corresponding MCP and second it is used as input variable in the calculation of the optimal bid value. Both are discussed in the following steps.

8 The wake effect is an attribute of wind farms related to the decrease in downstream airflow in wind farms. As the air passes through the wind turbine rotor disc, downwards airflow streams are reduced. This results in disturbed, reduced wind speeds for wind mills that are positioned behind other turbines (Matevosyan and Söder, 2006). However, this effect is not taken into account in this model as the shapes of the wind farms are undetermined Determination of market clearing prices For the purpose of this study the influence of the wind park energy output on the MCP and consequently the profitability of the wind park are assessed. In order to achieve this goal the energy output of the wind park is used as input value in the MCP calculation. This calculation is performed as explained in paragraph 4.3. The imbalance price is determined by the TSO. Hence it is dependent on the market in which the genco is operating. The imbalance price is difficult to predict, because of its many dependencies on conditions in the market. However, the price is influenced by factors which can be modeled; this is further elaborated on in paragraph Optimize bid In the final phase in this methodology the optimal bid quantity is determined. The optimal bid is the bid which is expected to result into the largest profit. This is calculated for every forecasted point in time. Given the fact that the only costs taken into account are the imbalance costs, this is done by minimizing the expected imbalance costs. The revenue is calculated as follows. First the expected revenue, based on the bid is calculated, this is the spot price (P sp i ) times bid quantity (Q w b ). Then the expected imbalance costs added to this. The imbalance costs are the imbalance price (P imb i ) times the absolute difference between the scenario power output (Q w i ) and the bid quantity (Q w b ). The imbalance price changes when the bid quantity exceeds the scenario power quantity. However the difference between the quantities must remain absolute, because the imbalance price will determine whether the consequence will have a negative or positive value. As the MCP is based on the scenario quantity and the imbalance price on MCP, it follows that for every scenario there is a different quantity, spot price and imbalance price. Given the fact that each scenario has an equal probability, it follows that the revenue is maximized by determining the optimal bid quantity (Q w b ), which results in the highest average pay-off considering all scenarios. This results in equation (9): 8 Zt= t max[avg(p sp i Q w b + Pimb i abs(q w i Q w b ))] (9) Where: Zt w = Revenue of wind park genco at hour t, P sp i = Spot price for scenario i, Q w b = Quantity of power bid to the market, P imb i = Imbalance price, Q w i = Wind park power output quantity prediction for scenario i Notations All notations are explained throughout the paper, table 2 is included to provide an overview of all used variables in the model. Notation t T k K l Notation α,β andσ z Z(t) X i (t) V f (t) V i (t) Q(v) P w t Q w t Zt w P s i p P imb i Q w i Q b b P i, j Q i, j 4.3. MCP Calculation Indices and numbers Definition Hour of prediction Maximum value of t Forecast length Maximum value of k Position in merit order Variables Definition Parameters used to illustrate error behavior of wind Random Gaussian variable with standard deviationσ z for hour t Wind speed forecast error for scenario i Wind speed forecast at hour t Wind speed at hour t for scenario i Power generated for wind speed V Bid price of genco W at hour t Bid quantity of genco W at hour t Revenue of genco W at hour t Spot price for scenario i Imbalance price for scenario i Wind park quantity for scenario i Wind park bid quantity Bid price of genco i in block j Bid quantity of genco i in block j Table 2: Notations As explained in section the MCP is the price at which supply and demand meet. In this method a demand curve is taken as given. The supply at the other hand is based on the cost structures of different energy sources in the market.

9 Establishing the supply curve Valenzuela and Wang (2011) state that each energy source has a different cost structure and that the prices differ for each capacity level. In this model it is assumed that there are 10 energy sources. It is assumed that each genco operates one energy source to produce energy; hence the cost structure of a genco is based on the energy source it uses. Gencos have given capacities which are divided into a set of blocks. Each genco has a different cost structure, in which prices increase in per capacity block. This is the result of decreasing efficiency of power plants when output increases. So for a capacity block a genco i can bid a quantity Q (limited to maximum capacity of the block) for price P at capacity block j. Bids are ordered based on price (lowest prices offered first). This results in a merit order in which multiple gencos offer multiple bids, resulting from the capacity blocks. Table 3 contains an example of the merit order. Eventually the merit order determines the supply curve, with the lowest values being served first and highest latest. Table 3: Block bids for Q i, j and P i, j Merit Order Quantity and Price 6 Q 3,2 P 3,2 5 Q 2,3 P 2,3 4 Q 2,2 P 2,2 3 Q 3,1 P 3,1 2 Q 2,1 P 2,1 1 Q 1,1 P 1,1 Table 3: Merit Order MCP determination The demand curve is determined in the same manner as the supply curve, but the other way around: Block asks in a merit order with the highest ask price coming first and lowest coming last. The supply and demand block bids move toward each other until they intersect. As a result price P i, j, that corresponds with quantity Q i, j which offers the final quantity before the supply price exceeds the demand price, is the MCP Influence of wind energy MC of fossil fuel gencos increase with quantity, whereas the MC of renewable gencos do not (Soleymani et al., 2007). A wind park places one bid offering all its energy for a price lower than the lowest fossil fuel genco, because it is assumed it has no variable costs; wind parks always are first in the merit order. Hence, its offer increases market supply and thereby moves the supply curve to right. An increase in supply increases 9 the total market size and decreases the MCP, assuming the demand remains constant Imbalance price determination The imbalance price is an instrument which is used by a TSO to incentivize gencos to provide accurate forecasts of the amount of energy which is going to be provided to the market (Ketter et al., 2014). It is used to fine gencos which do not provide the amount energy which has been bid in at the bidding phase (Morales et al., 2010). The imbalance price always is related to the MCP of the corresponding point in time. This is the case, because in order to fine a genco a potential revenue stream must be lower than the MCP or a fine must exceed the MCP. The imbalance price changes depending on two aspects: the balance in the market and the balance of the genco. The balance in the market is explains whether the TSO has a surplus or shortage of energy on the grid for a given hour t. When the balance in the market is negative, the TSO has a shortage; the suppliers deliver less energy than predicted or demand is higher than expected. Vice versa, when the balance is positive, the TSO faces a surplus; supply is higher than predicted or demand is lower than expected. The balance of the genco for an hour t depends on its actual energy output and bid energy quantity. In the optimization the energy output of a scenario is taken as the actual energy output, because it is assumed that this is a potential actual amount of energy that the genco can produce for a given wind speed. The balance of the genco is negative in a situation in which a bid quantity exceeds the actual quantity, because it cannot deliver the promised amount of energy. Alternatively the balance is positive, when the genco actual amount of energy exceeds the bid the genco, because it can deliver more than initially promised. This means that the genco balance changes the moment that the bid energy quantity exceeds the power quantity in the scenario. This results in four potential situations, which are explained in table 4. The imbalance price is linked to the MCP. The downward regulating price mostly has a value between 0% and 100% of the MCP and sometimes exceeds the MCP. The upward regulation price can move up to high percentages of the MCP. This is the case because when the TSO has a high negative balance it needs to provide strong financial incentives to punish or reward to gencos that cause or solve that imbalance. In the dayahead bidding stage the gencos do not know whether the market balance will be positive or negative. In case the gencos would be aware of the balance in the market this would result in unrealistic bidding behavior because of the resulting imbalance prices. (e.g. when a negative

10 No. Market Genco Description Imbalance Balance Balance Price 1 Negative Positive The market required more energy and the genco can offer this. Regular trading MCP takes place, so energy exceeding the bid is sold at MCP. 2 Negative Negative The market requires more energy, but the genco does not live up to its promise < 100 of of delivery. The genco receives a penalty over the size of the shortage for not MCP delivering when it is required. This penalty can be any percentage of the MCP. This percentage is manipulated to study its influence. (Known as upward regulation price) 3 Positive Positive The TSO has excess energy; the genco can deliver more than initially expected. 0% of MCP The genco will be able to sell its surplus against a tariff which is lower than the MCP. (Known as downward regulation price) 4 Positive Negative The TSO has excess energy; the genco delivers less than expected. As a result - MCP the shortage is the part of the initial bid, which cannot be met. This part of the sale does not occur, but besides that the genco is not fined. The shortage is deducted from the bid. Table 4: Imbalance price possibilities balance is given then a genco would always bid 0, because it would always have a positive balance and sell its energy for MCP.) Hence the market balance will be randomly assigned to all scenarios in the simulation Data In this section contains a concise elaboration on the variables which are used in the model and the sources of the related data Wind speed forecast We used wind speed forecasts of the city of Rotterdam, which originate from the Royal Dutch Meteorological Institute, KNMI (KNMI, 2010). The data set contains forecasts with a forecast length of up to 24 hours. 24 forecasts are provided for every hour of every day in the year Forecast error behavior Hourly wind forecasts and actual wind speeds of a specific location are required in order to determine the forecast error behavior. In addition to the forecasts, the actual wind speeds in Rotterdam of every hour of every day in the year 2009 have been provided by the KNMI as well. As discussed in paragraph 4.1.1, the forecast error behavior is represented by parameters :α,β andσ z. The values resulting from the Rotterdam data set are as follows:α=1.0248,β= andσ z = Amount of turbines This variable is manipulated based on the requirements of the research objectives. In this study its values 10 range between 100 and 2000, with respective markets share of 2.5% and 25.1% Turbine efficiency The power performance curve of a GE 1.5s wind turbine has been used. It assumes an air temperature of 20 C and an air density of 1.225kg/m 3. Table 5 provides the turbine output in kw for the corresponding wind speeds. The output values of wind speeds between the wind speed values in the table are calculated as a weighted average of the corresponding outputs. Wind Speed Power Wind Speed Power (m/s) (kw) (m/s) (kw) Table 5: Power Performance Curve Data Supply& demand bids The market is assumed to be stable. This means that bids are set and not changing over time. The only changing bid is the one by the wind genco, which is determined in this model. Characteristics of the supply bids are based on the IEEE reliability test system (Grigg et al., 1999). Demand bids are set at random values, which are in line with the supply bids in terms of quantities and price levels. Supply and demand bids are provided in AppendixB.

11 Imbalance price volatility The imbalance price level is relevant for the upward regulation market, when the genco has a shortage. The volatility of the imbalance price is represented as a multiplier of the MCP. For the Dutch market we calculated the difference between the average MCP between December 2013 and May 2014, provided by the APX- Group (2014), with the average upward regulating price, provided by TenneT (2014). This resulted in a multiplier of The downward regulation price had been set to 0. We assumed that energy could not be sold when it was not bid on the dayahead market. This assumption has been made because our data showed the downward regulation price is unpredictable and hence it did not fulfil our entry requirements. less. In this situation the lowest priced buyer is willing to paye74.00 and the total served market moves from 1031MWh to 1181MWh. This increase can be explained by the fact that there was more demand for the price of e51.09/mwh, but a lack of supply. Subsequently, we assessed a 1000 turbine wind park; this park has a market share of 15.9%. The market share is not linearly related to the amount of turbines, because of the difference in genco output, the different market sizes and wind speeds in the given region. A more detailed elaboration on the relation between the amount of turbines and the market share is provided in AppendixC. Figure 4 illustrates the market shares of wind parks for its corresponding amount of turbines. 5. Results This section contains a discussion of the findings related to our research objectives. First, this relation between wind energy market share and the MCP is discussed. Subsequently, an analysis is performed on the effect of different wind speeds on the hourly wind park revenues. This is done for multiple wind park sizes, in order to illustrate how revenues differ when wind energy market shares increase. The results provide an indication of the expected revenues for different wind speeds, but it does not take into account the wind speeds that actually occur within a specific region. In order to provide a realistic indication of wind park revenues over different situations we assess the actual wind behavior for a specific region. These are then used in order to determine the revenue per wind turbine for multiple wind market shares. Another factor influencing the expected revenue is the imbalance prices in a market. An overview of multiple imbalance price scenarios is provided to indicate its influence. Lastly, we assess how accurate our revenue predictions are as compared to the optimal revenues for multiple forecast lengths Wind park size influence on MCP In this section we discuss how the wind park size influences the MCP; in this analysis we take into account how wind speeds affect this relation. First, we assessed the MCP for a wind park with 100 turbines (market share 2.5%). In this situation the MCP ise51.09/mwh for all wind speeds. The market price is constant, because of the fact the small market share: even when providing full output to the market (150MW) the genco is unable to supply to buyers which are willing to pay 11 Figure 4: Wind park market share The 1000 turbine park shows a fundamentally different pattern than the 100 turbine park. Due to its 1500MW capacity the wind park is able to offer energy to energy to buyers which are willing to pay less. With a wind speed of 0 m/s (and an output of 0MWh) the MCP is e51.09/mwh. However, when wind speeds is 14m/s the MCP drops to e22.92/mwh. This is due to the low priced wind energy, which serves buyers who are willing to pay less. The MCP moves in a pattern which is determined by the matching ask and bid prices for different energy output levels. The market size moves between 1031MWh and 2493MWh, with wind speeds of 0m/s and 14m/s respectively. The market size increases with 1462MWh, instead of the 1500MWh which could initially be expected, because of the gencos that are no longer willing to offer energy to the market for this low MCP. Figure 5 provides a comparison of the MCP development for the two wind park sizes.

12 Turbines t=10 t=100 t=200 t=300 t=400 t=500 t=600 t=700 t=800 t=900 t=1000 Market share 0.3% 2.5% 4.7% 6.6% 8.4% 9.9% 11.3% 12.6% 13.8% 14.8% 15.9% w=0 e 0 e 0 e 0 e 0 e 0 e 0 e 0 e 1 e 1 e 0 e 0 w=1 e 0 e 1 e 1 e 2 e 2 e 3 e 4 e 5 e 5 e 7 e 5 w=2 e 1 e 6 e 11 e 16 e 21 e 26 e 30 e 39 e 44 e 52 e 44 w=3 e 3 e 32 e 66 e 96 e 131 e 152 e 191 e 223 e 269 e 296 e 311 w=4 e 15 e 151 e 314 e 457 e 614 e 749 e 939 e 1,101 e 1,284 e 1,406 e 1,499 w=5 e 43 e 428 e 883 e 1,313 e 1,746 e 2,141 e 2,665 e 3,170 e 3,568 e 3,841 e 4,342 w=6 e 88 e 879 e 1,784 e 2,685 e 3,555 e 4,379 e 5,383 e 6,171 e 7,073 e 7,597 e 8,640 w = 7 e 148 e 1,503 e 3,034 e 4,514 e 6,015 e 7,317 e 8,962 e 10,381 e 11,643 e 12,818 e 14,169 w = 8 e 228 e 2,311 e 4,568 e 6,523 e 8,848 e 11,005 e 13,463 e 14,849 e 16,342 e 18,161 e 20,356 w = 9 e 344 e 3,459 e 6,842 e 10,155 e 13,252 e 16,110 e 18,956 e 21,811 e 23,879 e 26,335 e 28,867 w = 10 e 443 e 4,338 e 9,217 e 12,547 e 16,464 e 20,077 e 23,306 e 25,922 e 28,764 e 29,985 e 32,705 w = 11 e 568 e 5,899 e 11,568 e 16,383 e 21,376 e 25,279 e 29,541 e 33,958 e 36,603 e 36,583 e 32,840 w = 12 e 684 e 6,948 e 13,533 e 18,401 e 24,679 e 28,607 e 34,563 e 40,412 e 42,160 e 39,047 e 32,547 w = 13 e 742 e 7,458 e 14,673 e 20,027 e 26,078 e 31,792 e 36,906 e 43,130 e 41,097 e 36,029 e 33,612 w = 14 e 762 e 7,548 e 14,610 e 20,407 e 25,769 e 31,656 e 37,643 e 41,690 e 39,284 e 31,966 e 33,857 Turbines t=1100 t=1200 t=1300 t=1400 t=1500 t=1600 t=1700 t=1800 t=1900 t=2000 Market share 17.1% 18.2% 19.3% 20.3% 21.2% 22.0% 22.8% 23.8% 24.6% 25.1% w=0 e 0 e 2 e 1 e 1 e 1 e 1 e 1 e 0 e 1 e 1 w=1 e 7 e 11 e 8 e 11 e 12 e 12 e 11 e 6 e 16 e 11 w=2 e 59 e 66 e 67 e 75 e 83 e 83 e 92 e 71 e 110 e 113 w=3 e 357 e 404 e 421 e 449 e 462 e 532 e 561 e 513 e 617 e 670 w=4 e 1,672 e 1,906 e 1,890 e 2,112 e 2,200 e 2,485 e 2,595 e 2,636 e 2,941 e 3,123 w=5 e 4,722 e 5,240 e 5,196 e 5,912 e 6,221 e 6,794 e 7,168 e 7,317 e 7,970 e 8,591 w = 6 e 9,188 e 10,216 e 10,022 e 11,831 e 12,190 e 13,392 e 14,079 e 14,298 e 15,221 e 16,238 w = 7 e 15,218 e 16,599 e 16,174 e 18,802 e 19,238 e 21,152 e 21,749 e 22,703 e 23,564 e 24,518 w = 8 e 21,868 e 23,559 e 22,327 e 25,275 e 25,793 e 26,931 e 29,543 e 28,759 e 30,354 e 31,510 w = 9 e 30,023 e 32,253 e 29,764 e 34,234 e 34,068 e 33,765 e 32,888 e 32,148 e 31,392 e 31,241 w = 10 e 30,534 e 30,019 e 26,096 e 27,871 e 30,601 e 29,700 e 30,438 e 29,574 e 27,748 e 25,787 w = 11 e 30,878 e 32,144 e 29,448 e 34,020 e 31,891 e 29,256 e 26,063 e 23,932 e 23,023 e 20,638 w = 12 e 34,538 e 35,514 e 32,937 e 38,570 e 31,781 e 25,344 e 24,203 e 22,645 e 20,748 e 20,040 w = 13 e 35,620 e 36,519 e 35,019 e 41,266 e 25,302 e 24,437 e 23,072 e 22,169 e 19,912 e 20,413 w = 14 e 35,503 e 37,113 e 35,058 e 40,229 e 23,819 e 25,071 e 23,130 e 22,364 e 19,865 e 20, Table 6: Expected revenue for multiple wind park sizes

13 Figure 5: Influence of wind speed on MCP 5.2. Wind park size influence on expected revenues Where other studies have taken the MCP as given (Matevosyan and Söder, 2006), we are now able to assess the expected revenue given the wind parks influence on MCP. Again we use a 100 turbine and a 1000 turbine wind park to illustrate the relation between wind park size and revenues Wind speeds and expected revenue Considering a 100 turbine wind park, we observe an almost linear relation between the expected revenue and the amount of energy produced. The reason for this is that the MCP remains constant. The only deviation from this is the anticipation for potential imbalance penalties. Intuitively, one would expect that a wind park which has 10 times this size also has 10 times the revenue. However, this is not the case. The expected revenue of a 1000 turbine park is heavily influenced by its effect on the MCP. With a wind speed of 5m/s the average expected revenue of a 100 and 1000 turbine wind park ise and 4, respectively. This is where the downward trend starts. At wind speed 12m/s the average expected revenue of a 100 and 1000 turbine wind park is e7, and e32, respectively. Here the 1000 turbine wind park only makes 464% of the 100 turbine wind park, where 1000% would be expected. This trend is comparable with the trend of the MCP. The relative expected revenue decreases when wind park sizes increase because of the negative effect of wind park size on the MCP and the increased imbalance risk to which the wind park is exposed. Table 6 provides an overview of the expected hourly revenues of wind parks with different sizes for wind speeds of 0 until 14 m/s. Figure 6 provides an overview of the revenue of a 1000 turbine wind park as a percentage of a 100 turbine wind park, it also includes the percentage of 10 times a 100 turbine wind park as a benchmark. 13 Figure 6: Revenue comparison of t = 10* 100 and t = Market share and expected revenue Knowing the expected revenues of wind parks for different wind speeds and wind park sizes, we now analyzed them with actual wind forecasts. First, we analyzed the distribution of wind speed forecasts of one month in The likelihood of occurrence for each wind speed can be found in Appendix C. Taking this wind speed distribution into account we analyzed the expected revenue per turbine while manipulating the market share of the wind park. As could be expected from the previous paragraph, the revenue per turbine is negatively related with the market share. With a market share of 2.5% and 15.9% the revenue per turbine is e12.92 and e9.38 respectively. Figure 7 illustrates the relation between market share and revenue per turbine. In this graph the revenue per turbines of a 10 turbine wind park is used as an index. Table 7 provides the revenue per turbines in absolute terms. Figure 7: Revenue per turbine with average revenue per turbine of 10 turbine park as benchmark