Optimal energy bidding for renewable plants: A practical application to an actual wind farm in Spain

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by Elsevier in Renewable Energy, Vol. 175 , on September 2021, available at: https://doi.org/10.1016/j.renene.2021.05.054 Copyright 2021 Elsevier. En idUS Licencia Creative Commons CC BY-NC-ND * Corresponding author. email: javierser[email protected] Optimal Energy Bidding for Renewable Plants: A Practical 1 Application to an Actual Wind Farm in Spain 2 3 Lázaro Endemaño Ventura, Javier Serrano González*, Juan Manuel Roldán Fernández, Manuel Burgos 4 Payán and Jesús Manuel Riquelme Santos 5 6 Department of Electrical Engineering, Universidad de Sevilla 7 8 Escuela Superior de Ingenieros, Av. de los Descubrimientos S/N, 41092, Sevilla - SPAIN 9 10 11 Abstract 12 13 Finding an optimal bidding strategy for a wind farm in the electricity market is not straightforward due to 14 the wind variability. This issue is becoming more relevant as renewable plants are more exposed to 15 market signals. Considering the characteristics of the European markets, operators must submit the energy 16 bidding between 12-36 hours ahead the actual delivery time. This bidding can be adjusted later in any 17 session of the intraday markets, but sometimes this is not enough to reduce significantly the deviation 18 risk. This paper presents a practical application of a method to analytically calculate the optimal bidding 19 of a wind power plant, based on the maximisation of the income function. The results show that, given the 20 characteristics of the deviation markets in Spain, the optimal bidding strategy depends essentially on the 21 deviation of the system. The proposed technique has been tested and validated in a real application by 22 considering actual data for energy production and forecasts for an operating wind farm in Spain, as well 23 as real market deviations and prices provided by the Spanish system and market operators; analysing the 24 advantages of the proposed optimal bidding strategy over the most plausible option, based on bidding the 25 forecasted energy. 26 Keywords: electricity balancing markets, electricity day-ahead market, wind power bidding, wind 27 energy 28 29 30 2 Nomenclature 31 WFO: Wind Farm Operator WF: Wind Farm VPP: Virtual Power Plant PPA: Power Purchase Agreement PDF: Probability Density Function SCADA: Supervisory Control and Data Acquisition MEC: Ministry of Economy and Competitiveness DK: Denmark UK: The United Kingdom US The United States DAM: Day Ahead Market IM: Intraday Market RTM Real Time Market BM: Balancing Market BS: Balancing Services t: Dispatching Time k: Lead Time Ef(t): Production forecast for hour (t) Ep(t): Energy output for hour (t) Eb(t): Energy bid for hour (t) F(Eb): Probability of producing an energy output less or equal to Eb B: Expected income λ: Day-ahead market price β: Probability of a positive system´s deviation 𝑪𝒑 +: Cost of a positive deviation being positive the deviation of the system 𝑪𝒑 −: Cost of a negative deviation being positive the deviation of the system 𝑪𝒏 +: Cost of a positive deviation being negative the deviation of the system 𝑪𝒏 −: Cost of a negative deviation being negative the deviation of the system u: Generation Unit s: Market Session z: Regulation Zone b: Bid Block i: International Interconnection NBEUD: Net balance of assigned energy upward and downward of the balancing services AEIMUu,s: Assigned energy upward by the imbalance management procedure AEIMDu,s: Assigned energy downward by the imbalance management procedure AETERUu: Assigned energy by tertiary reserve upward AETERDu: Assigned energy by tertiary reserve downward AESECUz: Assigned energy by secondary reserve upward AESECDz: Assigned energy by secondary reserve downward EIIBi,b: Energy imported EEIBi,b: Energy exported MPDAM: Marginal price of the day-ahead market WAPU: Weighted average price of the energies upward on the imbalance management, secondary and tertiary reserve. WAPD: Weighted average price of the energies downward on the imbalance management, secondary and tertiary reserve. 1. Introduction 32 The main challenge for the participation of wind energy plants in a liberalized market is the variable 33 behaviour of wind speed. In Europe, the European Commission's new legislative package on the rules for 34 the functioning of the internal electricity market aims at moving towards a market design that facilitates 35 the integration of renewables into an electricity system with an increasing presence of variable generation 36 3 sources. However, the current design of most European markets requires generators to submit their bids 37 on the day-ahead market (DAM) around 24 hours in advance, a lead time in which forecast uncertainty 38 about actual production by wind generators is still high. For example, to participate in the Iberian DAM 39 (the Spanish and Portuguese electricity markets are integrated into a single Iberian market, which is also 40 part of the Internal European electricity market), it is necessary to submit a bid 12-36 hours prior to the 41 actual dispatching time [1]. This bidding could be adjusted later in the intraday market (IM), but even in 42 this market the wind farm operators (WFO) must send their bids 3-14 hours before. These are lead times 43 in which wind forecasts still have a relatively high degree of uncertainty, which implies a certain level of 44 risk associated with the participation of wind plants in electricity markets, as deviations from the bid are 45 penalized. This represents a difficult situation for wind farms to participate in liberalized electricity 46 markets under the same conditions as conventional generators. 47 The existing literature on the impact of weather forecast of renewable plants on DAMs participation is 48 extensive. The authors would like to refer to [2–4] for a thorough review on this subject. Ahmed et al. 49 presented in [2] a very deep analysis of forecasting of different aspects of power systems such as 50 forecasting in renewable power dispatch, forecasting for energy storage systems, impact of forecasting 51 uncertainties in energy markets, forecasting in reserve size estimation, etc. Jónsson et al. [3] describe the 52 impact of wind power forecasts on the electricity markets. WFs are considered as price maker in that 53 work, considering its potential effects on prices in areas where wind power has a high penetration and 54 share a considerable amount in the generation mix. The influence of wind power forecast in prices is 55 analysed in the Western Danish price area (DK-1) of Nord Pool´s Elspot market. The authors 56 demonstrated that the ratio between the forecasted wind power generation and the forecasted load has a 57 strong association with the spot prices. Zhang et al. [4] surveyed the state-of-art methods and new 58 developments in wind power probabilistic forecasting. In that work, the forecasting methods are classified 59 into three categories in terms of uncertainty representation: probabilistic forecast, risk index forecast, and 60 space time scenario forecast. The authors stated that the two main sources of uncertainty in wind power 61 forecast are the variability in wind speed and wind-to-power curves. The three aforementioned papers 62 conclude that the uncertainty on the forecast of wind power production increasingly affect not only the 63 market prices. Facing the difficulty of reducing this uncertainty in its own way, one solution would be the 64 hybridization. Some authors have investigated on the potential of hybridizing wind farms with other type 65 of technologies in order to increase the participation of wind farms in deregulated electricity markets. 66 Mengxuan Lv. et al. [5] presented a review on optimal dispatch of VPP and the optimal bidding of this 67 kind of plants has been explored. Dhillon et al. analysed in [6] the operation in deregulated markets and 68 balancing services of a hybrid wind-pumped storage plant. This type of plant could help to increase the 69 wind power penetration in the electric power systems due to its maturity and large storage capacity. In 70 this same line of research Moghaddam et al. [7] presented a two-stage stochastic programming model 71 based on profit maximisation for the participation in the day-ahead for a combined wind-hydro system. 72 The results obtained by the authors highlight the importance of the chosen penalty market mechanism in 73 the optimal supply strategy by renewable generators. Laia et al. [8] presented also a combined bidding 74 strategy for WFs and thermal units by means a stochastic mixed-integer linear programming approach, 75 4 showing the potential of the proposed method to maximize the income obtained through the joint 76 participation of both technologies in the market. 77 WF aggregation would be another feasible solution to increase its benefits by mitigating forecasts 78 uncertainty. Authors in [9,10] have explored this possibility. Baeyens et al. analysed in [9] the benefits of 79 a coalitional bidding of a group of WF in a two-settlement market. The option of bidding in DAM and 80 real time markets (RTM) is considered as well. The imbalance prices are modelled as random non- 81 negative variables. Three different strategies are proposed by Guerrero-Mestre [10] in order to calculate 82 the optimal bidding of a group of WF: (i) each WF offer their energy separately, (ii) each WF offer their 83 energy separately but imbalances are compensating among the WF, and (iii) all WF makes a joint offer to 84 the DAM market. The problem is modelled as a stochastic mixed integer linear programming. 85 Conditional value at risk is included in the objective function as well as the sum of the expected profit. 86 Other solution to increase the incomes of a wind farm in liberalized markets is adjusting the bids as 87 close as the time to produce the energy. Of course, not all markets have the same characteristics. This 88 bidding strategy has been analysed in [11–13]. In [11] Usaola and Moreno consider the bids made in the 89 day ahead market, and the uncertainty in the power production to adjust the bid in the IM market. In this 90 way, improving the active power forecast could reduce the penalties incurred in. The authors also 91 explored the uncertainty in prices, considering two types of probability density functions (Normal, and 92 Gamma). Three different approaches were considered to calculate the IM offer: (i) participation in the IM 93 is not allowed (worst scenario, whose results are taken as a reference for comparison with the remaining 94 scenarios), (ii) participation in the IM is allowed and the best forecast available is bid in the IM, in this 95 case the revenues are 0.8% higher than the worst scenario and (iii) participation in the IM is allowed and 96 the bid in the IM is based on the proposed approach by authors considering the uncertainties of the wind 97 power forecast, in this case the obtained revenues were 8.5% higher than the worst case. Additionally, 98 authors also analysed the behaviour of the proposed approach by using also a forecasting tool for the IM 99 prices, the revenues obtained in this case were 0.3% higher than the worst scenario. The authors stated 100 that have faced high difficulties to predict the imbalance prices. Therefore, they have multiply by a fix 101 factor the monthly average of the DAM in order to calculate the imbalance prices. In [12] Usaola and 102 Angarita also considered the imbalance costs, by following a similar approach as in [11], but analysing 103 different theoretical prices for buying and selling energy in the balancing market (BM). These prices were 104 calculated by multiplying the DAM prices by a factor and considering the influence on the revenues when 105 varying this factor. The results obtained ranged between 4.26% and 7.83% of improvement when buying 106 price were higher than the selling price. When buying price were lower than selling price, the revenues 107 obtained were between -3.93% and 30.85% higher than the reference scenario. In [13] Bueno et al. 108 focused on the calculation of the IM bid analysing in detail the IM prices. The formulation of this paper is 109 based on the formulation in [11]. The authors have concluded that the uncertainties in the IM prices 110 makes not possible to use forecasted values of this variable to improve de revenues due to the high 111 volatility of this variable, then they have considered perfect information. Imbalance prices have been 112 calculated by multiplying the DAM price by a fixed factor. 113 A different approach was presented by Holttinen in [14] by analysing the influence of the wind power 114 generation forecast and the lead time to submit the bid. On one side, different time horizons to make the 115 5 bid were analysed. On the other hand, two scenarios are studied: (i) individual WF bidding or (ii) 116 aggregated bidding in case of being more than one WF. The method was applied in the Nordpool 117 electricity market in the Nordic Countries. 118 The short-term energy markets participation is analysed in [15–18]. In [15] Pinson et al. presented a 119 methodology to determine the optimal strategy based on modelling the bidding sensitivity against 120 balancing costs generation forecasts. The authors calculated and compared the market value using 121 different forecast methods and the associated bids using different optimization algorithms. Four methods 122 for predicting the imbalance costs were analysed and compared with perfect forecasts in the Dutch 123 electricity pool. They have obtained an 16.41% of improvement with respect to the Persistent method in 124 the best of the cases. Bathurst et al. [16] applied Markov Probabilities to determine the best bidding 125 strategy for a WF in the UK. They showed the effect of market closure delay and forecast window length 126 on imbalance costs of the WF. A method to minimize the imbalance costs was presented by Matevosyan 127 and Söder in [17]. Stochastic programming (a mixed integer algorithm) is used to generate optimal bids of 128 wind energy generation for short-term markets. Forecasting errors of WF output energy are considered as 129 stochastic parameters. The author Afshar et al [18] developed an optimal bidding strategy based on a bi- 130 level approach optimised by a Particle Swarm Optimisation algorithm, the authors modelled the punitive 131 effect of trading in balancing market by considering the prices of this market as a factor of the day-ahead 132 market prices. Then the optimal offer for the balancing market is calculated. The results were tested in the 133 three-bus test system and the IEEE 24-bus test system. 134 Finally, with regard to analytical approaches based on the probability density function (PDF) of energy 135 forecasts to optimise the bidding strategy, Morales et al. presented in [19] a method to determine the 136 optimal trading strategies for renewable energy plants in electricity markets. That work presented optimal 137 strategies to participate in the DAM and BMs considering both deterministic and stochastic prices. The 138 relation between these both markets is analysed in order to make arbitrage between them, that is that the 139 optimal bid in the (BMs) is normally influenced by the bid made in the DAM. However, it should be 140 mentioned that the results presented are based on a conceptual approach and not on a numerical one. 141 Authors in [20,21] have gone a step further making a detailed analysis for different scenarios on the 142 optimal bidding subject. Analytical results using Great Britain market data has been presented by Dent et 143 al. in [20]. The authors considered different scenarios to calculate the optimal bidding. They have only 144 taken into account the WF production and the real-time prices which are in fact related to DAM prices. 145 Markets with a single and double imbalance prices are analysed. The influence of the conventional 146 generation in the bid is analysed when the wind farm production and the real time prices are correlated. In 147 [21], Bitar et al. has presented an analysis of different problems regarding the optimal bidding and the 148 influence of forecasting uncertainties with the market prices. In the paper the possibility of adjusting the 149 bidding in the IM is considered. Additionally, the authors proposed of installing a small thermal plant 150 along with the WF to cope with its negative imbalance. In this way they have analysed the role of the 151 reserve margin in power systems with a high penetration of renewable energy. Empirical results have 152 been calculated using aggregated data of 14 WF in the US. 153 One of the most recent papers on the present subject was published by Li and Park in [22]. In this 154 paper the optimal bidding in the DAM and the RTM (real time market) are calculated. The authors have 155 6 considered different variables with uncertainties: RTM wind power generation, DAM locational marginal 156 prices (LMPs) (the paper used real data in the PJM market in the U.S. where each node of the system 157 have different prices depending on the state of the system and other variables), RTM LMPs and deviation 158 penalty rates (a single-price deviation is considered in the analysis and this price is the same for every 159 hour in the same day). Two PDF have been used in this work: (i) the PDF of historical actual wind power 160 generation, and (ii) the PDF of wind power prediction errors. This variable has been modelled by the beta 161 distribution function to represent RTM wind power generation distribution. The authors concluded that 162 when using the PDF of wind power prediction errors, they obtain a 6.7% more revenue compared with the 163 obtained when use the PDF of historical actual wind power generation and 3.7% when used the PDF of 164 wind power generation prediction errors compared with bidding the forecasted wind power generation. 165 The work presented in the present paper advances the current state of the art by introducing an 166 approach based on the analysis of actual energy production forecasts, which enables identifying the 167 associated uncertainty thorough the PDFs and establishing a method for the analytical optimization of the 168 WF’s expected income. According to the knowledge of the authors, this work would be the first to 169 propose an analytical approach which considers the daily market price and four deviation prices, whose 170 dependence has been modelled according to a new variable that takes into account the system deviation. 171 This formulation allows a realistic approach to obtain the optimal bidding strategy under the existing 172 market structure in the Iberian system (Spain and Portugal). 173 Another important point is that the performed analysis demonstrates that the optimal offer is strongly 174 influenced by the deviation of the system, which as mentioned above, is explicitly introduced for the first 175 time in the formulation presented in this paper. 176 The method proposed in this work also introduces a real practical advantage for WFOs (both in the 177 case of planned plants as well as in the case of plants already in operation), since it is based on the 178 analysis of data that are fully accessible for the WFOs themselves, such as energy production forecasts 179 (usually provided by weather forecasting companies), as well as actual production data. This means that 180 the WFOs can increase its income from energy market participation without the need to incur additional 181 costs or expenses. Therefore, the proposed paper presents an important advantage over those previously 182 stated as it is based on information readily available to the WFOs. 183 After this brief introduction, the paper is organized as follows. Section II provides a general overview 184 of the proposed approach. Section III presents the problem formulation. The test cases and results are 185 presented in Section IV and conclusions are discussed in Section V. 186 2. Methodology overview 187 WFOs are paid for the energy produced at a variable price according to the spot market in case of 188 merchant projects or most commonly at fixed price either by a public support scheme or through a 189 corporate Power Purchase Agreement (PPA). There are different types of PPAs that are out of the scope 190 of this paper, the authors would like to refer to references [23,24] for further details on this topic. 191 Taking into account the maturity of the wind technology, it is increasingly common that the incentives 192 and support schemes are reduced or even totally eliminated in places with high penetration of variable 193 7 renewable generation. This is leading to the increasing trend of wind projects to sign a PPAs or to 194 participate in the DAM. In other words, this is leading to an increasing integration of renewable 195 technologies into the markets at a global scale. 196 The WFO must consider different variables in order to calculate the energy bid for the DAM. In a first 197 stage of the problem, the WFO knows the energy forecast. Making a bid with exactly this value is the 198 approach most commonly adopted by WFO, but this may entail some penalties due to forecast 199 uncertainty. 200 The methodology proposed in this paper takes into consideration a realistic approach based on 201 identifying the uncertainty related to energy forecasts. To this end, it is proposed to identify the 202 probability density functions (PDFs) of the WF actual production for a given energy production forecast 203 (corresponding to a certain lead time). This identification of the PDFs is carried out by analysing the 204 forecast historical data during a previous training period. This work has been developed using hourly 205 wind production forecasts based on meteorological models, provided by a specialized company in wind 206 energy forecasting to the WFO of an actual Spanish WF. As shown in Figure 1, the aforementioned PDFs 207 are inputs to the module for calculating the expected income function, along with additional input data 208 including the energy production forecast for the hour under analysis, the DAM price, the system deviation 209 (i.e., if the electrical system has surplus or deficit of generation) as well as the deviation costs that are 210 calculated according to Spanish regulations, as explained below in Section III.A. 211 All these inputs are used to determine the expected income function (explained below in Section III) 212 that subsequently allows the identification of the optimal energy bidding amount (assuming, as it happens 213 in most energy markets, that WFs are price-takers, i.e., their bids are made at zero price) by an analytical 214 optimization approach. The process described in Figure 1 is repeated sequentially for each delivery period 215 (usually 1 hour in the Iberian market, as in most European markets). Thus, for each hour and a given lead 216 time, the first step of the proposed approach is to determine analytically (as detailed later in Section 3) the 217 optimal value of the cumulative probability function for which the expected income is maximized as a 218 function of the DAM and BS prices as well as the system deviation. Once this optimal value of the 219 cumulative probability function is determined, the next step is the numerical identification through the 220 PDF of the value corresponding to the optimal bid energy. 221 Additionally, it is important to note that the proposed procedure can be applied indistinctly for 222 different time frames, depending on the lead times provided by the forecasting companies, and for any 223 different session of the market (i. e. DAM or IM, etc.). 224 Finally, it is worth mentioning that the method proposed in this paper focuses on the development of a 225 new approach which is intended to be the core of a complete integrated optimization bidding tool 226 including also the forecast of DAM and BS prices. This work introduces a novel approach to the 227 analytical calculation of the optimal bidding strategy based on the DAM price plus the four BSs prices 228 depending on the system deviation and the historical behaviour of energy forecasts made on the actual 229 production of WFs. Therefore, forecasts about market prices and the behaviour of system deviations are 230 beyond the scope of this paper. In this way, it is possible to analyse the improvement potential of the 231 proposed algorithm and the effect of energy production uncertainty (information which is fully available 232 to WFOs) on the optimal bidding strategy. 233 8 234 235 Figure 1. Flowchart of the proposed approach 236 3. Problem Formulation 237 At certain instant, 𝑡𝑜, the WFO needs to make a bid in the DAM for the hour 𝑡. In order to do this, the 238 WFO receives a production forecast, 𝐸𝑓(𝑡), with a certain lead time, k = t-to, (please, note that for the 239 sake of simplicity the lead time has not been included in the nomenclature of the following formulation). 240 However, for the hour t, the WF will eventually generate an energy output 𝐸𝑝(𝑡). Therefore, depending 241 on the energy bid, 𝐸𝑏(𝑡), and the actual energy output for hour t, the WFO will have more or less 242 penalties/incomes for the deviations. Therefore, the aim of the method presented on this paper is to 243 maximize the total income from the participation in both the DAM and the BSs. 244 With this aim, the probability of producing an energy output, Ep, greater than or equal to the bidding 245 energy, Eb, is described in (1) or, otherwise, in (2). 246 247 1−𝐹(𝐸𝑏)=∫ 𝑓(𝐸𝑝)𝑑𝐸𝑝 ∞ 𝐸𝑏=𝑝𝑟𝑜𝑏(𝐸𝑝≥𝐸𝑏) (1) 248 𝐹(𝐸𝑏)=∫ 𝑓(𝐸𝑝)𝑑𝐸𝑝 𝐸𝑏 −∞ =𝑝𝑟𝑜𝑏(𝐸𝑝≤𝐸𝑏) (2) 249 where 𝑓(𝐸𝑏) is the probability of producing an energy output 𝐸𝑏. 250 The expected income, B, for a certain scheduling period, t, can be described by (3). 251 252 𝐵(𝐸𝑏)=𝜆∙𝐸𝑏+𝛽∙𝐶𝑝 +∫ (𝐸𝑝−𝐸𝑏)∙𝑓(𝐸𝑝)∙𝑑𝐸𝑝+ ∞ 𝐸𝑏 𝛽∙𝐶𝑝 −∫ (𝐸𝑏−𝐸𝑝)∙𝑓(𝐸𝑝)∙𝑑𝐸𝑝+ 𝐸𝑏 −∞ (3) (1−𝛽)∙𝐶𝑛 +∫ (𝐸𝑝−𝐸𝑏)∙𝑓(𝐸𝑝)∙𝑑𝐸𝑝+ ∞ 𝐸𝑏 DAM and BS price forecasts Calculation of optimal energy bidding For every hour, t, and a given lead time, k Income calculation Analytical calculation of cumulative distribution function value for optimal energy bidding, System deviation forecast Probability density function for energy forecasted and lead time, k Identification of optimal the energy bidding, , by means the probability density function of forecasts Energy produced forecast, Ef Ef 15 Conventional approach 59788 883786 44735 689821 Proposed approach 63797 927158 56105 813252 Theoretical maximum 63797 927158 63797 927158 419 Figure 6 shows the hourly income obtained through the proposed methodology and through the 420 conventional approach based on bidding the forecasted energy. As can be seen in Table 2, the proposed 421 methodology improves the income in comparison to the conventional approach. The total income using 422 the proposed methodology during the first two weeks of the period under study would be 63797€, while 423 by using the conventional approach the income would be 59788 €. This means a 6.7% of improvement 424 obtained by the proposed strategy. Extending the period of analysis to the whole second half of 2016, the 425 total income achieved through the proposed approach would be 927158 €, whereby the conventional 426 approach would obtain 883786 €, which is a 4.9% of improvement. Figure 6 also shows the theoretical 427 maximum income (represented by the blue circles) that would be possible to achieve if the energy 428 forecasts were perfect (i.e., under this approach the bids are exactly the actual generated energy, 429 represented by the black line in Figure 5). It is interesting to note that the proposed strategy achieves the 430 theoretical maximum possible for all hours in the entire period analysed (the second half of 2016). These 431 results show the great potential of the proposed method to maximize the WF income. The proposed 432 strategy achieves the theoretical maximum and simplifies, for the Spanish case, the variables to be taken 433 into account to make the bid, reducing it only to the system's deviation. This is due to the price structure 434 of BS in the Spanish system, which, as detailed in the following lines, leads to the optimal supply to be 435 independent of the energy forecast, as well as of market prices; depending only on whether the entire 436 system has a deficit or surplus of generation. 437 Additionally, it can also be seen how in some hours the income obtained through the conventional 438 approach is negative, this situation occurs mainly in those cases where the plant bided a certain energy in 439 the DAM, but eventually the real production of the plant was lower than forecasted or even zero. 440 441 442 Figure 6. Comparison of hourly income between the proposed approach and the conventional approach 443 16 consisting on bidding the forecasted energy for Case 1. 444 445 Figure 7. Comparison of hourly bidding strategies between the proposed approach and the conventional 446 approach consisting on bidding the forecasted energy for Case 1. 447 448 Figure 7 shows a comparison between the bids made by the two approaches analysed. As can be seen, 449 the conventional approach consists simply of bidding the available forecasted energy for the 450 corresponding lead time (in this case 24 h), whereas the bids made using the proposed approach consist of 451 bidding either zero energy or energy equal to the plant's nominal power. This is a consequence of the 452 price structure of the DAM and the BS in Spain. As can be seen in Figure 4, in the Spanish markets, the 453 equality 𝜆=−𝐶𝑝 − is true for every hour. This means that when the system deviation is positive (i.e., 454 𝛽=1) the value of 𝐹(𝐸𝑏 ∗), obtained through equation (6), is equal to 1. The consequence is that in this 455 case the optimal strategy consists in bidding the nominal power of the WF, independently of the PDF of 456 the energy forecasts and of the levels reached by the prices of DAM and BS. In the same way, the 457 following relationship is also fulfilled for all hours in the Spanish market: 𝜆=𝐶𝑛 +, this implies that for all 458 hours when the system deviation is negative (i.e., 𝛽=0), the value of 𝐹(𝐸𝑏 ∗) is null, which makes the 459 optimal bid in this case to be also null. 460 In summary, with the current price structure in the Spanish markets it is possible to establish an 461 optimal strategy based only on predicting the behaviour of the system deviation and bidding zero energy 462 (or, in practical terms, the minimum allowed volume to be entitled to participate in the DAM and BS 463 according to the Iberian market regulation) in the case of a negative system deviation or the maximum 464 energy of the plant in the case of a positive system deviation. This is because the price formation of the 465 BS in the Iberian/Spanish market does not always penalize generators (including renewable plants) for 466 their deviations. Spanish market rules only penalize generators when their deviations are contrary to the 467 system. When the deviations are favourable to the system, even though the actual production of the 468 generator differs (in excess or defect) from the energy committed for that hour, the generator is not 469 penalized for its deviation. This could have important consequences from the point of view of energy 470 policies, because in the transition towards a highly decarbonized system, with high penetration of variable 471 technologies, it could be convenient that every market agent were fully responsible for the deviations 472 17 produced over their committed generation or demand. Renewable generator could be especially 473 concerned with this new regulation approach, since when their actual productions did not exactly match 474 the scheduled amounts, they would result penalized, even when their deviations were favourable to the 475 system. 476 4.1.1 Sensitivity analysis 477 The objective of this sensitivity study is to analyse in a more realistic way the real applicability of the 478 proposed approach to obtain the optimal bid for a wind farm. To this end, instead of considering the 479 prices of the DAM and BS as previously known at the time of making the bid, the uncertainty of the 480 forecast of these prices has been modelled by adding a random noise by means a normal variable (it 481 should be noted, however, that the relationships between the different prices currently in force in the 482 Spanish markets, i.e., 𝜆=−𝐶𝑝 − and 𝜆=𝐶𝑛 + as mentioned above, have also been taken into account in this 483 sensitivity analysis), which allows emulating the behaviour of the estimates provided by the prices 484 forecasting algorithms. Likewise, the existing uncertainty in the forecast of the electricity system 485 deviation has also been modelled by adding an error probability on this variable for every hour of the 486 studied period. In this way, the sensitivity analysis proposed in this section consists of analysing the 487 percentage improvement obtained by the proposed methodology compared to the classical approach 488 consisting of bidding the forecasted energy. 489 Figure 8 shows the results obtained in the sensitivity analysis performed for this case, varying the error 490 in predicting the deviation of the system in the range 1%-10%. The results obtained correspond to the 491 average values obtained after 10 executions of the proposed algorithm (thus mitigating the random 492 component in the presentation of results) during the entire period analysed in this Case 1 (i.e., the second 493 half of 2016). Furthermore, this analysis has been reproduced also considering the error in the prices of 494 the DAM and the BS, varying within the range of 2%-10%. As can be seen, the results obtained are not 495 affected by the error introduced in the prices. This is due to the fact that in this case the relations between 496 the prices of the DAM and the existing BS in the Iberian market are fulfilled, which leads to that, as 497 explained above, the optimal bid is independent of the prices and only depends on the direction of the 498 deviation of the system. On the other hand, it can also be noted, the virtually linear dependence of the 499 percentage of improvement depending on the error introduced in the deviation of the system. For low 500 values of the error in the system deviation, the percentage of improvement is similar to that obtained in 501 the ideal situation where the system deviation is assumed to be known beforehand. However, as the 502 system deviation error increases, the percentage of improvement gradually decreases. This figure allows 503 to draw an important conclusion, since the potential of the tool proposed in this work is directly linked to 504 the accuracy of the techniques for predicting the behaviour of the system deviation: assuming that the 505 typical error of the forecast tools is between 5 and 8%, the potential of improvement that would be 506 obtained by means of the approach proposed in this work would be within the range of 1-2.5%, which 507 shows its viability in realistic conditions. 508 18 509 Figure 8. Sensitivity analysis to forecast error in DAM and BSs prices and system deviation for Case1. 510 4.2 Case 2 511 In this second test case, an alternative price structure of the BS is proposed so that in all cases 512 deviations of the renewable plant from the scheduled energy are penalized. In this way, the aim is now to 513 analyse an alternative scenario corresponding to a future possible market rules that would penalise any 514 kind of deviation, even when those deviations are favourable to the system. In this case, the following 515 assumptions are proposed to establish the basic rules for the formation of prices corresponding to the BS: 516 (i) If a power plant has a positive deviation and the system deviation is also positive, the 517 deviation produced by the plant does not benefit the system and therefore the plant will not 518 receive any remuneration for the additional energy injected, apart from the 519 scheduled/dispatched in the DAM, i.e.: 𝐶𝑝 +=0. 520 (ii) If the plant has a negative deviation and the system deviation is also negative, the deviation 521 again negatively impacts the system so that the plant will no longer receive the market price 522 for the unsupplied energy and will additionally be responsible for acquiring such energy 523 deficit for the system at the double of the wholesale market price. In this way, 𝐶𝑛 −=−2𝜆. 524 (iii) If the generator deviation is positive and the system has a generation deficit, the system is 525 benefited from the plant deviation, so it is proposed that the plant should receive a price 526 slightly lower than the DAM price, because its deviation introduces a disturbance that should 527 be penalized. In this case, it is proposed that the retribution received is penalized in a linear 528 manner, based on the ratio between the total generation deficit and the total energy of the 529 system in each hour, reaching a maximum penalty of 10% over the DAM price for the 530 maximum value of the aforementioned ratio during the second half of 2016. 531 1 2 3 4 5 6 7 8 9 10 Error in the system deviation variable, β, (%) 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Prices error = 2% Prices error = 4% Prices error = 6% Prices error = 8% Prices error = 10% Improvementpercentage (%) 19 (iv) If the power plant deviation is negative and the system has excess generation, the deviation 532 introduced by the plant favours the system again. In this case it is proposed to slightly 533 penalize the plant following an approach completely analogous to the previous assumption. 534 Based on these rules, the hourly prices of the BS have been obtained as shown in Figure 9. 535 536 Figure 9. Proposed modified hourly prices of BS for Case 2 for the first two weeks of the analysed period. 537 538 Figure 10 shows the comparison between the hourly income obtained through the two proposed 539 approaches. It can be seen how the proposed strategy improves the income obtained for most of the hours 540 of the two weeks under study. It can also be seen how the frequency and severity of negative income 541 increases for certain hours, as a result of the greater penalties introduced in the prices of BS. As it can be 542 inferred from Table 2, the improvement ratio of total revenues obtained through the methodology 543 proposed in this second case is of 26.4% for the first two weeks of the second half of 2016 and 19.6% 544 considering the second complete second half of the year. These values are significantly higher than those 545 of Case 1, due again to the greater penalty of the cost of the deviations for the plant considered in this 546 case. Additionally, the blue dots show the theoretical maximum hourly income if the energy forecasts 547 were perfect (i.e., the forecasts were exactly the same as the energy finally generated). In this case the 548 proposed strategy does not reach the theoretical maximum, since in this situation the prices of the BS lead 549 the bidding strategy to be dependent on the accuracy of the energy forecast. This means that during the 550 first two weeks of the analysed period, the proposed strategy reaches revenues that are 12.1% below the 551 theoretical maximum, while for the entire second half of the year the revenues obtained would be 12.3% 552 lower than the theoretical maximum. 553 Figure 11 shows the comparison between the bids for each of the hours. In this case, the hourly volume 554 of energy bid using the proposed methodology is usually different from zero or from the plant's rated 555 capacity, because the price structure of the BS considered in Case 2 leads to values of 𝐹(𝐸𝑏 ∗) different 556 from zero or one, which implies that the expected income function, depending on the energy bid, has a 557 maximum that can take on any value within the range between 0 and the plant's nominal power. 558 𝜆 𝐶𝑛 + 𝐶𝑝 +−𝐶𝑛 − −𝐶𝑝 − 024 48 72 96 120 144 168 192 216 240 264 288 312 336 Hour 0 20 40 60 80 100 120 €/MWh 20 559 Figure 10. Comparison of hourly income between the proposed approach and the conventional approach 560 consisting on bidding the forecasted energy for Case 2. 561 562 563 Figure 11. Comparison of hourly bidding strategies between the proposed approach and the conventional 564 approach consisting on bidding the forecasted energy for Case 2. 565 566 Finally, Figure 12 shows the improvement ratio obtained between the proposed and conventional 567 approaches for Case 2 depending on the forecast lead time. As it was expected, the proposed 568 methodology obtains a greater improvement as the forecast lead time increases, since the forecasts are 569 more accurate as they are closer to the energy delivery time, which reduces the deviations uncertainty. It 570 should also be noted that the improvement ratio corresponding to the usual lead times for participation in 571 the day ahead market (between 12 and 36 hours) is around 17-18%, which will presumably enable even 572 significant improvement margins to be obtained in the case of implementing a complete optimal bidding 573 tool including also the forecast of prices in the DAM and BS. 574 21 575 Figure 12. Improvement ratio of the proposed methodology versus the conventional bidding strategy 576 depending on the forecast lead time for Case 2. 577 4.2.1 Sensitivity analysis 578 Figure 13 shows the results of the sensitivity analysis performed on Case 2. In this analysis, the 579 relationships mentioned above for this case between the different prices of the DAM and the BS have 580 been considered and subsequently modified by introducing a random error to each of them. Likewise, as 581 in the previous section, an error has also been considered on the variable for estimating the deviation of 582 the electrical system. 583 As can be seen in the figure, under the considerations introduced in the sensitivity analysis of this 584 second case, the percentage of improvement depends on both the error in estimating the direction of the 585 system deviation, as well as the error considered in the prices of DAM and BS. In a similar way to what 586 happened in Case 1, the dependence of the percentage improvement on the error in the system deviation 587 is almost linear (for the same value of error in the prices of DAM and BS). On the other hand, as the error 588 in the estimation of the prices of DAM and BS increases, the percentage of improvement obtained 589 through the proposed methodology is also progressively reduced. As an example, for a typical error in the 590 estimation of prices and the deviation of the system of about 5-8%, the percentage range of improvement 591 obtained would be about 5-10% (the lower edge corresponding to an error of 8% in the estimation of 592 prices and direction of the deviation, while the upper edge would correspond to an error of 5%), which 593 again highlights the potential of the proposed methodology to a price scenario such as the one proposed in 594 this second test case. 595 596 0 5 10 15 20 25 30 35 40 Forecast lead time (hours) 13 14 15 16 17 18 19 20 Improvementpercentage (%) 22 597 Figure 13. Sensitivity analysis to forecast error in DAM and BSs prices and system deviation for 598 Case2. 599 4.3 Results discussion 600 The results shown in these case studies highlight the applicability of the proposed method in a realistic 601 environment. In fact, all the data considered in Case 1 proceeds from a real application, in which both the 602 production data and the forecast data for different lead times correspond to an existing wind farm. 603 Likewise, the remaining variables involved in the problem (i.e., the hourly price of the DAM and the four 604 hourly prices of the BSs, as well as the direction of the system's deviation) have been taken from the 605 actual results provided by the Spanish System Operator. The results of the first case study show that the 606 improvement potential that the proposed methodology would have over the classical approach based on 607 bidding the forecasted energy for the corresponding lead time is around 4.9% for the whole period 608 analysed. However, it is worth mentioning that this first analysis considers that the prices of DAM and 609 BS, as well as the deviation of the system are known beforehand, so it is also essential to analyse the 610 influence of the errors associated with the forecasting techniques of these variables. For this reason, a 611 sensitivity analysis to these errors has also been carried out, showing that for a typical range of error in 612 the forecast of the system's deviation of 5-8%, the proposed methodology would allow an increase in 613 profit of 1-2.5%. 614 It is also very interesting to note that the proposed approach shows that under the current price 615 structure of the Iberian market, the optimal bid only depends on the direction of the deviation of the 616 electricity system, which implies that when implementing the approach proposed in this paper, operators 617 can establish their bid on only one variable subject to uncertainty (the system deviation), which greatly 618 simplifies the optimal bidding strategy. 619 1 2 3 4 5 6 7 8 9 10 Error in the system deviation variable, , (%) 0 2 4 6 8 10 12 14 16 18 Improvementpercentage (%) Prices error = 2% Prices error = 4% Prices error = 6% Prices error = 8% Prices error = 10% 23 Likewise, an alternative price scenario has been proposed in the second case study, increasing the 620 responsibility from an economic point of view of the deviations produced by the generation units with the 621 objective of emulating a possible price structure in a scenario of high penetration of variable energy 622 sources. This second case study shows even greater potential for improving the proposed methodology 623 over the classic approach that would achieve 19.6% under the assumption that prices and system 624 deviation are previously known. However, the sensitivity analysis carried out on this second case 625 including price uncertainty and system deviation shows that a range of improvement through the 626 proposed methodology between 5-10% for errors within the range of 5-8% in the previously mentioned 627 variables. 628 The potential for improvement achieved through the proposed methodology is in line with those 629 documented in other previous works. However, it should be noted that the results are not directly 630 comparable, since our work is the first to formulate the problem analytically through the price of the 631 DAM plus the four existing prices in the BSs which in turn depend on the direction of the system 632 deviation, as is currently the case in the Spanish system. 633 5. Conclusions 634 The growth in the participation of WFs in the liberalized electricity markets has brought an important 635 challenge due to the variability of the wind energy production and forecasts uncertainty. This work has 636 proposed a novel method to calculate the optimal bidding strategy for a WF by an analytical 637 maximization of the expected income function, depending on the energy bidding. The proposed method is 638 easy to implement in both already operational or planned WFs, since it is based on data that every WFO 639 has available from its SCADA system and from the energy production forecasts needed to participate in 640 the market. Therefore, the implementation of the methodology does not require any additional investment 641 and only consists of modifying the bidding strategy. Likewise, the proposed method is also easily 642 adaptable to different organized markets other than the Spanish system, and its implementation can be 643 extended to other variable renewable technologies, such as solar photovoltaic. 644 The potential of the proposed approach has been validated by using actual forecast and production data 645 from a real 28 MW WF located in Spain. The proposed methodology is based on the initial validation of a 646 novel approach by the analytical optimization of the problem. To this end, all the variables involved in 647 calculating the actual income of a WF have been considered in the formulation, such as DAM prices, as 648 well as the four prices of BS depending on overall deviation of the electricity system. The initial 649 validation of the proposed methodology shows a great potential for improvement in revenues with respect 650 to the conventional bidding strategy based on bidding the forecasted energy. 651 Two test cases have been analysed, the first test case considers actual data for both the plant generation 652 and forecasts, as well as realistic hourly DAM and BS price data of the Spanish system. However, in the 653 case of Spanish BS, the price formation structure leads to the fact that the WF can establish an optimal 654 supply strategy based solely on the deviation of the electricity system, which could lead to an increase in 655 the system's balancing needs, affecting to the operation of the whole system. Therefore, the analysis of a 656 second case is proposed, by considering modified prices of the BS so that in all cases WFs are responsible 657 24 for their deviations, which could be more appropriate in a future scenario of greater renewable penetration 658 in the electricity system. The methodology proposed in the present work has demonstrated to be 659 satisfactory with a noticeable range of improvement in the income for all the cases analysed. 660 Additionally, the analysis carried out on a real case in the Iberian market provides important 661 conclusions from the point of view of energy policies, since the current design of BS in Spain does not 662 penalize all deviations produced by generators, which in future can lead to inefficient management of the 663 whole electricity system. This is especially important in a scenario of high penetration of renewables, 664 such as that foreseen in the Spanish National Energy and Climate Plan , which foresees by 2030 a 74% 665 share of renewables in the electricity system doubling variable renewable energy sources' current installed 666 capacity from approximately 30 GW at present to a total of 90 GW by 2030. 667 Acknowledgments 668 This work was partially supported by the Spanish MEC - Ministerio de Economía y Competitividad 669 (Ministry of Economy and Competitiveness), co-funded by the European Commission (ERDF - European 670 Regional Development Fund) under grant ENE2016-77650-R, as well as by the European Commission 671 under grant SI-1778/12/2018. This work was also partially supported by grants US-1265887, Red 672 CYTED 718RT0564 and CERVERA program for Outstanding Research Centers CER-20191019. 673 References 674 [1] OMIE, Daily and Intraday Electricity Market Operating Rules, 2014. 675 [2] A. Ahmed, M. Khalid, A review on the selected applications of forecasting models in renewable 676 power systems, Renewable and Sustainable Energy Reviews. 100 (2019) 9–21. 677 https://doi.org/10.1016/j.rser.2018.09.046. 678 [3] T. Jónsson, P. Pinson, H. Madsen, On the market impact of wind energy forecasts, Energy 679 Economics. 32 (2010) 313–320. https://doi.org/10.1016/j.eneco.2009.10.018. 680 [4] Y. Zhang, J. Wang, X. Wang, Review on probabilistic forecasting of wind power generation, 681 Renewable and Sustainable Energy Reviews. 32 (2014) 255–270. 682 https://doi.org/10.1016/j.rser.2014.01.033. 683 [5] M. Lv, S. Lou, B. Liu, Z. Fan, Z. Wu, Review on power generation and bidding optimization of 684 virtual power plant, in: Proceedings - 2017 International Conference on Electrical Engineering and 685 Informatics: Advancing Knowledge, Research, and Technology for Humanity, ICELTICs 2017, 686 Institute of Electrical and Electronics Engineers Inc., 2018: pp. 66–71. 687 https://doi.org/10.1109/ICELTICS.2017.8253242. 688 [6] J. Dhillon, A. Kumar, S.K. Singal, Optimization methods applied for Wind-PSP operation and 689 scheduling under deregulated market: A review, Elsevier Ltd, 2014. 690 https://doi.org/10.1016/j.rser.2013.11.009. 691 [7] I.G. Moghaddam, M. Nick, F. Fallahi, M. Sanei, S. Mortazavi, Risk-averse profit-based optimal 692 operation strategy of a combined wind farm-cascade hydro system in an electricity market, 693 Renewable Energy. 55 (2013) 252–259. https://doi.org/10.1016/j.renene.2012.12.023. 694 [8] R. Laia, H.M.I. Pousinho, R. Melíco, V.M.F. Mendes, Bidding strategy of wind-thermal energy 695 producers, Renewable Energy. 99 (2016) 673–681. https://doi.org/10.1016/j.renene.2016.07.049. 696 [9] E. Baeyens, E.Y. Bitar, P.P. Khargonekar, K. Poolla, Coalitional Aggregation of Wind Power, 697 IEEE Transactions on Power Systems. 28 (2013) 3774–3784. 698 https://doi.org/10.1109/TPWRS.2013.2262502. 699 [10] V. Guerrero-Mestre, A.A.S. de la Nieta, J. Contreras, J.P. Catalao, Optimal bidding of a group of 700 wind farms in day-ahead markets through an external agent, IEEE Transactions on Power Systems. 701 31 (2015) 2688–2700. 702 [11] J. Usaola, M.Á. Moreno, Optimal bidding of wind energy in intraday markets, in: 2009 6th 703 International Conference on the European Energy Market, EEM 2009, 2009. 704 https://doi.org/10.1109/EEM.2009.5207179. 705