Influence of ANN-based market price forecasting uncertainty on optimal bidding

INFLUENCE OF ANN-BASED MARKET PRICE FORECASTING UNCERTAINTY ON OPTIMAL BIDDING Jos´e L. Mart´ınez Ramos [email protected] Antonio G´omez Exp´osito [email protected] Jes´us Riquelme Santos [email protected] Alicia Troncoso Lora [email protected] Agust´ın R. Marulanda Guerra [email protected] Department of Electrical Engineering University of Sevilla Sevilla, Spain Abstract - In today’s deregulated markets, forecasting energy prices is becoming more and more important. In the short term, expected price profiles help market participants to determine their bidding strategies. Consequently, accuracy in forecasting hourly prices is crucial for generation companies (GENCOs) to reduce the risk of over/underestimating the revenue obtained by selling energy. In this paper, the influenceof the accuracy of ANN-based hourly energy price forecasting on the bidding strategy of GENCOs is assessed. First, a customized, recurrent Multilayer Perceptron is developed and applied to the 24-hour energy price forecasting problem, and the expected errors are quantified. Then, price profiles are used to compute the optimal bidding of realistic GENCOs, and the influence of forecasting errors on both the bidding strategies and the expected revenues is studied. Keywords - Artificial neural networks, energy price forecasting, competitive markets, optimal bidding 1 INTRODUCTION THE new competitive Spanish Electricity Market has been in operation since 1998, and it is mainly based on two separated day-ahead markets [7]: •The energy market, managed by the Market Operator (MO), where producers and consumers submit production and consumption bids (blocks of hourly energyand the correspondingprice in Euros/MWh). The MO produces a market-clearing price and sets of accepted production and consumption bids for every hour. Constraint management is subsequently performedby the System Operator (SO), taking also into account the scheduled bilateral contracts and adjusting the result of the energy market to avoid transmission congestion. Furthermore, additional markets for minor adjustments are also performed on an hourly basis. •The market for regulation reserves. Once the energy market and the subsequent constraint management procedure are finished, the SO establishes the requirements for operating reserves (an hourly band in MW up and down) that are needed for frequency control foreach of the 24hours of the followingday. The reserve market allocates the bands among the generators that are capable of providing secondary frequencycontrol by using generators’ up and down bids which include the offered band (MW) and the price (Euros/MW). A market for additional energy reserves (power that can be providedwithin 15 minutes for a period of two hours) is also performed. In this context, forecasting energy prices is extremely important. In the short term, expected price profiles, both in terms of energy and reserve prices, help market participants to determine their bidding strategies. Consequently, accuracy in forecasting hourly energy & reserve prices is crucial for generation companies (GENCOs) to reduce the risk of over/underestimating the revenue obtained by selling energy. The motivation of this paper is twofold: First, two customized Multi-layer Perceptrons are developedand applied to the 24-hour energy and reserve price forecasting problems, respectively, and the expected errors are quantified. Secondly, price profiles are used to compute the optimal bidding of several realistic GENCOs, and the influence of forecasting errors on both the bidding strategies and the expected revenues is presented. The objective is to compute the commitment schedule and the hourly generation profile of the GENCO in order to maximize the expected benefit from selling both energy and reserve to the corresponding markets [2]. 2 ANN-BASED MARKET PRICE FORECASTING As stated before, this paper is not aimed at developing the best market price forecasting technique, but to assess how relevant the forecasting errors are, so far as the benefits of a GENCO are concerned. The ANN approach has been chosen because of its successful performance in the load forecasting problem [3, 4]. Larger errors are expected in this case, however, as the influence of the load level on market clearing prices is only moderate, and other unpredictable factors play an important role in non-perfect oligopolistic markets. Usually, it is mandatory for GENCOs to provide the secondary regulation service, for which there is an additional income. Therefore, in order to prepare the day14th PSCC, Sevilla, 24-28 June 2002 Session 07, Paper 1, Page 1 ahead bid, an estimation of prices for this complementary service must be available, in addition to energy prices. The study reported in this paper is based on the hourly Spanish energy and secondary regulation prices recorded from January 2001 to August 2001. As weekends and holidays constitute separate cases, only data correspondingto working days have been retained and analyzed. Figures 1 and 2 show the hourly averages and standard deviations (s.d.) of both prices for the working days of March 2001, in cents of Euro per kWh and cents of Euro per kW respectively. Average spot prices larger than 2 cent/kWh take place during the morning and evening peak hours (10am-2pm and 8-10pm respectively). Except for a few valley hours, the s.d. of this price exceeds 20% of the mean value, reaching even 40% at 8pm and 9pm. Note that the s.d. of regulation market price is, in relative terms, much higher than that of the energy market price, which means that this factor is less predictable. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 1 5 9 13 17 21 Hours cent/kWh Mean Mean + S.D. Mean - S.D. Figure 1: Hourly average of spot market prices for March 2001. 0 1 2 3 4 5 6 1 5 9 13 17 21 Hours cent/kW Mean Mean + S. D. Mean - S. D. Figure2: Hourly average of secondary regulation prices for March 2001. Figure 3 represents the energy prices for two selected days of March 2001. The significant differences in the prices of the peak hours can not be explained by a change in the demand profile, probably revealing market power mechanisms. 0 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hours cent/kWh Thursday-1st Friday-30th Figure 3: Evolution of energy prices for two days of March 2001. 2.1 Structure of the ANN A brief description of the ANN adopted in this work is provided in this section (the reader interested in ANN background is referred to [5] and [6]). An ANN is composed of a certain number of perceptrons organized by layers. Each perceptron has several inputs and a single output, whose value is a non-linear function of the inputs. Each perceptron’s input is affected by a weighting factor, which must be determined during the training phase. Usually, an ANN is composed of three layers (input, hidden and output), where the outputs of a layer feed the inputs of the next layer. The two main steps involvedin the use of an ANN are: •Determining its topology, which basically consists of defining the number of perceptrons in the intermediate hidden layer. •Obtaining the input weighting factors for a given non-linear function (training process). According to authors’ previous experience, it is decided to feed the ANN with a shifting window of prices comprising 24 hours. This means that the input layer is composed of 24 perceptrons. As far as the number of output perceptrons is concerned, two possibilities have been evaluated [6]: a) A single output whose value is dictated by the previous 24 hours. Under this scheme, very popular in load forecasting, the window is shifted one hour each time. b) Twenty four outputs corresponding to the prices of a whole day, whose values are determined by those of the previous day. This implies that the window is shifted 24 hours each time. Test results have shown better accuracy for scheme b), which is the only one considered in the sequel [6]. In order to fully define the ANN, it is necessary to determine the number of perceptrons in the intermediate layer and the numberof days required for the training process. Figure 4 shows, for 12, 24 and 36 neurons in the hidden layer, the average forecasting errorin the energy price 14th PSCC, Sevilla, 24-28 June 2002 Session 07, Paper 1, Page 2 corresponding to the working days of February 2001, a representative month, versus the number of days used to train the ANN. As can be noted, 20 days are sufficient to train the ANN, the number of neuronsnot being so important. Similar conclusions are reached forthe ANN devoted to forecasting the spinning reserve price. For the results presented below, 24 and 12 neurons in the hidden layer have been used to forecast the spot market energy and reserve service prices, respectively, and the actual prices of the 20 previous days are used to train the ANNs to predict the next day. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 5 10 15 20 25 30 35 40 45 Days Error (cent/kWh) n12 n24 n36 Figure 4: Average forecasting error in the energy price. 2.2 Results About two months of the available period (January - February 2001) are used in several experiments to find out and tune the best ANN topology, while the remaining material (March-August 2001) is devoted to check the forecasting errors and to perform the market simulations of the second part of the paper. Figure 5 presents the absolute value of the error of the forecasted spot market prices for the two days of March 2001 leading to the largest and smallest average errors. 0 0.5 1 1.5 2 2.5 3 1 3 5 7 9 11 13 15 17 19 21 23 Hours Error (cent/kWh) Friday 23 Monday 12 Figure 5: Absolute value of the error of the forecasted energy prices. Figure 6 shows the hourly average of the forecasted energyprices corresponding to March 2001, as well as the resulting predictionerrors (obtainedby differencewith the actual prices of figure 1). Note that the forecasting errors are larger during peak hours. Figure 7 provides the same information for the price of the reserve service. 0 0.5 1 1.5 2 2.5 3 3.5 1 4 7 10 13 16 19 22 Hours cent/kWh Errors Forecasted Figure 6: Hourly average of the forecasted energy prices (March 2001). 0 0.5 1 1.5 2 2.5 3 3.5 4 1 4 7 10 13 16 19 22 Hours cent/kW Errors Forecasted Figure 7: Hourly average of the forecasted reserve prices (March 2001). Finally, tables 1 and 2 present the average and s.d. of actual prices, the average of forecasting errors and the maximum errors for Spring and Summer seasons. For the spot market price, the average error ranges from 12% (Summer) to 15% (Spring) of the hourly average price. As expected, the larger the s.d. of prices the higher the average forecasting error. Note that regulation price errors are rather high, obviously due to the influence of external factors such as unit failures on the reserve market. Daily Prices (cent/kWh) Average s. d. Average Maximum real price absolute errors errors March-May 2.2588 0.7801 0.3464 2.671 June-August 3.5482 1.0597 0.428 2.0736 Table 1: Forecasting errors for the energy prices. Frequency Regulation Service (cent/kW) Average s. d. Average Maximum price absolute errors errors March-May 0.7965 0.9864 0.5309 5.12 June-August 0.5986 0.4471 0.4916 4.49 Table 2: Forecasting errors for the reserve prices. 14th PSCC, Sevilla, 24-28 June 2002 Session 07, Paper 1, Page 3 3 OPTIMAL BIDDING OPTIMIZATION PROBLEM After obtainingthe forecasted energy andreserveprice profiles, the GENCO must determine the optimum commitment and hourly generation schedule in order to maximize the expected benefit from selling both energy and spinning reserve. In this paper, perfect competition is assumed, and, in consequence, no GENCO has the possibility of modifying the market clearing prices. After computing the optimal hourly generation scheduling based on the forecasted prices, the GENCO may choose to offerthe scheduled energy at zero price to ensure that the offer will be accepted, or to offer the energy at marginal cost, as Game Theory recommends. If the GENCO has market power, the optimization problem must reflect its capability to modify the market-clearing prices by controlling the total amount of energy and reserve offered [8]. The optimal generation scheduling problem can be posed as a mixed-integer linear programming model as proposed in [2], allowing complex operating costs to be modeled, e.g., non-convex cost functions and exponential start-up and shut-down costs, along with operating constraints such as ramp limits. 3.1 Objective Function The total benefit of a GENCO over a 24-hour scheduling period, given the energy and spinning reserve hourly prices, λtand µtrespectively, is defined by BT= 24 X t=1 λt·Pt+µt·(Pt−Pt)(1) − {C(Pt)·Ut+UC(St)·Yt+DC ·Zt} where Ptis the average generated power at hour t,C(Pt) is the operating cost, Ptis the available maximum power at hour t,Stis the number of hours the thermal unit has been shut-down at the end of hour t,UC(St)is the startup variable cost, DC is a shut-down fixed cost, Ut,Ytand Ztare 0/1 variables which are equal to one if the thermal unit is committed at hour t, started-up or shut-down at the beginning of hour t, respectively. 3.2 Constraints The maximization of the objective function is subject to the following constraints (t= 1,...,24): •Upper and lower generation limits: Pm·Ut≤Pt≤PM·Ut(2) •Maximum up and down ramps: Pt= min {PM·(Ut−Zt+1) + SD ·Zt+1, Pt−1+RU ·Ut−1+SU ·Yt}(3) Pt= max {Pm, Pt−1−RD ·Ut}(4) wherePtis the minimumgeneratedpower at hourt, PMand Pmare the maximum and minimum power of the thermal unit, RU and RD are the maximum up and down ramps, SU and SD are the maximum start-up and shut-down ramps, respectively. •Minimum up and down times: (Xt−1−UT )·(Ut−1−Ut)≥0(5) (St−1−DT )·(Ut−Ut−1)≥0(6) where Xtis the number of hours the thermal unit has been on at the end of hour t, and UT and DT are the minimum up and down times. •Logic constraints: Yt−Zt=Ut−Ut−1(7) Yt+Zt≤1(8) Xt= [Xt−1·(1 −Yt) + 1] ·Ut(9) St= [St−1·(1 −Zt) + 1] ·(1 −Ut)(10) The above model is solved by using the CPLEX optimization module under GAMS [1]. 4 TEST RESULTS The optimization model described in the former section is used in conjunctionwith the ANN-based forecasted prices to assess the benefits of two different GENCOS, whose main parameters are shown in table 3. Fuel costs have been scaled so that the incremental cost of generators equals the average market price and half the average price, respectively. Start-up costs are functions of the time the generator have been shut-down, with time-constants of 2 and 12 hours. Finally, start-up and shut-down ramp rates have been equalled to the normal up and down ramp limits, and no minimum up or down time constraints have been imposed. The results reported below refer to March 2001, considered a representative month. Economical data GENCO C(Pt)UC (Euros/h) (Euros) Gas-turbine 594.58 + 29 ·Pt6541.7·(1 −e − St 2) Coal-fired 359.5 + 14.5·Pt12588.6·(1 −e − St 12 ) Technical data GENCO PmPMRU RD (MW) (MW/h) Gas-turbine 100 350 350 350 Coal-fired 100 350 50 50 Table 3: GENCOs main technical and economical data. 4.1 Case A: Conventional coal-fired generator This unit takes several hours to fully start up and its fixed cost is high. However, its variable cost is about one half of the average market clearingprice. In past regulated markets, this would have been a base unit usually working at rated power. 14th PSCC, Sevilla, 24-28 June 2002 Session 07, Paper 1, Page 4 Figure 8 compares the total daily benefits obtained with forecasted prices with those that would have been obtained if actual prices had been known in advance. The monthly average difference is 7.7%, the largest deviation taking place on March 12 (please note that, as weekends are excluded from the analysis, this is day #8 in the figures). As shown in figure 5, this is also the day leading to the largest energy price forecasting error. Note that the benefit obtained with perfect information is always larger than or equal to the profit achieved from forecasted prices. This is not the case, however, when profits are analyzed at the hourly frame, because the objective function considers the daily period as a whole. Figure 9 represents the hourly profit based on forecasted prices (right) and the scheduled energy (left) on March 1. Except for the valley hours, the unit maximizes its profit at rated power. Another exception arises at 7pm, when the income from the regulation service is so high that it is better for the unit to reduce the scheduled power. In order to assess the influence of the reserve income on the optimal bidding strategy, the experiment is repeated by ignoring this term in the objective function. As shown in figure 10, the profit decreases during some valley hours and at 7pm, in spite of the increased generated energy. However, this kind of units are not significantly influenced by this income component, as the profit reduction for the scheduling shown in figure 10 is only 2%. -20000 0 20000 40000 60000 80000 100000 120000 140000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Day Profit (Euros) Profit with forecasted prices Profit with actual prices Figure 8: Total daily benefit of the coal-fired generator. 0 100 200 300 400 1 3 5 7 9 11 13 15 17 19 21 23 Hour Energy (MWh) -12000 -10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 10000 12000 14000 Profit (Euros) Energy Profit Figure 9: Hourly benefits and scheduled energy of the coal-fired unit. 0 100 200 300 400 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hour Energy (MWh) -12000 -10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 10000 12000 14000 Profit (Euros) Energy Profit Figure 10: Hourly benefits and scheduled energy of the coal-fired unit. Reserve incomes not considered. 4.2 Case B: Gas-turbine generator This is a fast-acting, high averagecost unit whose optimal bidding strategy is quite differentfrom that of Case A. Figure 11, the counterpart of 8, shows that the profit attained with forecasted prices is very similar to that obtained if exact prices were available the day before, except for days #8, 13, 14, and 15. As discussed in Case A, unexpectedly high energy price forecasting errors are responsible for this deviation on March 12 (day #8). However, the large profit gap observed on days #13 to #15 is fully attributable to the extremelyhigh uncertainty that took place in the reserve price during these days. This is confirmed by the fact that the net income is nearly indistinguishable from the one obtained with exact prices, when exact prices are adopted for the regulation service only (third series in figure 11). -20000 0 20000 40000 60000 80000 100000 120000 140000 1 3 5 7 9 11 13 15 17 19 21 Day Profit (Euros) Profit with forecasted prices Profit with actual prices Profit with forecasted market and actual regulation prices Figure 11: Total daily benefit of the gas-turbine generator. As in Case A, the scheduledenergyand profit achieved with forecasted prices on March 1 is shown in figures 12 and 13, with and without consideration of the income arising from the reserve service, respectively. Unlike in Case A, the profit difference between both situations is very important. When the objective function takes into account the regulation service income (figure 12), the unit is dispatched most of the time at minimum power. Only at peak hours does the energy price justify maximum power. Note 14th PSCC, Sevilla, 24-28 June 2002 Session 07, Paper 1, Page 5 that the net income is negative from 4 to 7 am, in spite of which the unit is not shut-down. The total profit in this situation is 40300 Euros. 0 100 200 300 400 1 3 5 7 9 11 13 15 17 19 21 23 Hour Energy (MWh) -12000 -10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 10000 12000 14000 Profit (Euros) Energy Profit Figure 12: Hourly benefits and scheduled energy of the gas-turbine unit. 0 100 200 300 400 1 3 5 7 9 11 13 15 17 19 21 23 Hour Energy (MWh) -12000 -10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 10000 12000 14000 Profit (Euros) Energy Profit Figure 13: Hourly benefits and scheduled energy of the gas-turbine unit. Reserve incomes not considered. When the regulation service income is ignored in the optimization model, the unit starts up only at 9am, and the total profit reduces to 10000 Euros. This suggests that about 3/4 of the net profit for this unit is due to the reserve income. Therefore, in cases like this, the uncertainty in the reserve clearingprices may have a significant influence on the overall profit. 5 CONCLUSIONS This paper addresses the influence of the accuracy of ANN-based hourly energy price forecasting on the bidding strategy of GENCOs. First, two customized Multilayer Perceptrons have been applied to the 24-hour energy and reserve price forecasting problems, respectively, using real data of the Spanish energy and reserve markets. For the energymarket price, the average errorranges from 12% (Summer) to 15% (Spring) of the hourly average price, errors being much higher in the reserve price forecasting, as expected. Secondly, forecasted price profiles have been used to compute the optimal bidding of two realistic GENCOs, a coal-fired generator and a gasturbine plant, and the influence of forecasting errors on both the bidding strategies and the expected revenues have been presented. ACKNOWLEDGMENTS The authors would like to acknowledge the financial supportof the Spanish DGES undergrants PB97-0719and DPI2001-2612. REFERENCES [1] A. Brooke, D. Kendrick and A. Meeraus, “GAMS: A user’s Guide, Release 2.25”, The Scientific Press. San Francisco. 1996. [2] J. M. Arroyo and A. J. Conejo, “Optimal Response of a Thermal Unit to an Electricity Spot Market”, IEEE Trans. on Power System, Vol. 15, pp. 10981104. 2000. [3] R. Lamedia, A. Prudenzi, M. Sforna, M. Caciotta, V. Orsolini Cencellli, “A Neural Network Based Technique for Short-Term Forecasting of Anomalous Load Periods”, IEEE Trans. on Power System, Vol. 11, pp. 1749-1755. 1996. [4] A. S. Alfuhaid and M. A. El-Sayed, “Cascaded Artificial Neural Network for Short-Term Load Forecasting”, IEEE Trans. on Power System, Vol. 12, pp. 1524-1529. 1997. [5] M. El-Sharkawi and D. Niebur, “Tutorial course on Artificial Neural Networks with Applications to Power Systems”, IEEE Catalog Number 96, Tp 1120, 1996. [6] J. Riquelme, J.L. Mart´ınez, A. G´omez and D. Cros Goma, “Possibilities of Artificial Neural Networks in Short-Term Load Forecasting”, Proceedings of the IASTED International Conference Power and Energy Systems. pp. 165-170, Marbella, Spain. September 2000. [7] A. Canoyra, C. Ill´an, A. Landa, J.M. Moreno, J.I. P´erez Arriaga, C. Sall´e and C. Sol´e, “The Hyerarchical Market Approach to the Economic and Secure Operation of the Spanish Power System”, Bulk Power System Dynamic and Control IV, August 2428, Santorini, Greece. [8] A. J. Conejo, J. Contreras, J.M. Arroyo and S. de la Torre, “Optimal Response of an OligopolisticGenerating Companyto a Competitive Pool-Based Electric Power Market”, To appear in IEEE Trans. on Power System. View publication statsView publication stats 14th PSCC, Sevilla, 24-28 June 2002 Session 07, Paper 1, Page 6