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Neuro-fuzzy Approach for Short-term Electricity Price Forecasting Developed MATLAB-based Software

Neuro-fuzzy Approach for Short-term Electricity Price Forecasting Developed MATLAB-based Software Fuzzy Inf. Eng. (2011) 4: 339-350 DOI 10.1007/s12543-011-0089-2 ORIGINAL ARTICLE Neuro-fuzzy Approach for Short-term Electricity Price Forecasting Developed MATLAB-based Software M. Esfahani Received: 30 January 2011/ Revised: 27 July 2011/ Accepted: 16 October 2011/ © Springer-Verlag Berlin Heidelberg and Fuzzy Information and Engineering Branch of the Operations Research Society of China Abstract Bid and offer competition is a main transaction approach in deregulated electricity markets. Locational marginal prices (LMP) resulting from bidding com- petition determine electricity prices at a node or in an area. The LMP exhibits im- portant information for market participants to develop their bidding strategies. More- over, LMP is also a vital indicator for a Security Coordinator to perform market re- dispatch for congestion management. This paper presents a method using modular feed forward neural networks (FFNN) and fuzzy inference system (FIS) for forecast- ing LMPs. FFNN is used to forecast the electricity prices in a short time horizon and FIS to forecast the prices of special days. FFNN system includes an autocorrelation method for selecting parameters and methods for data preprocessing and preparing historical data to train the artificial neural network (ANN). In this paper, the histori- cal LMPs of Pennsylvania, New Jersey, and Maryland (PJM) market are used to test the proposed method. It is found that the proposed neuro-fuzzy method is capable of forecasting LMP values efficiently. In addition, MATLAB-based software is designed to test and use the proposed model in different markets and environments. This is an efficient tool to study and model power markets for price forecasting. It is included with a database management system, data classifier, input variable selection, FFNN and FIS configuration and report generator in custom formats. Keywords FIS · FFNN · Data pre-processing · Electricity price forecasting · Day- ahead energy market 1. Introduction There are two main transaction modes in a deregulated electric power industry, com- petitive bidding and bilateral contract. The competitive biddings are used in the fol- lowing markets: energy, spot, firm transmission rights and lastly ancillary service, M. Esfahani () Department of Electrical Engineering, Islamic Azad University, Khomeinishahr Branch, Esfahan, Iran e-mail: Mohammad.Esfahani@iaukhsh.ac.ir 340 M. Esfahani (2011) etc. The bilateral contract is adopted outside the competitive market (pool) for any two individual entities, buyer and seller. For either transaction mode, the electricity price information serves as an essential element for all entities to adjust their of- fers/bids and/or contract prices. Especially, LMP is one of the most popular modes for energy pricing in a competitive market. LMPs can reflect the electricity value at a node and may be discriminated at different nodes within a power network. The LMPs reveal important information, which is helpful to the market participants in develop- ing their bidding strategies. It is also a vital indicator for the Security Coordinator to mitigate the transmission congestion. LMPs reveal important information for both the spot market and the entities with bilateral contracts. In the past, some researchers employed the ANNs for short-term system marginal price (SMP) forecasting, mar- ket clearing price (MCP) and quantity (MCQ) forecasting. Moreover, autoregressive integrated moving average (ARIMA) and traditional time-series models are used to predict the next-day electricity prices. Neural network is the other method currently used for the price forecasting. Because the MCQ is irrelevant to the transmission con- straints, forecasting LMPs subject to transmission constraints is more difficult than forecasting MCPs. In this paper, a neuro-fuzzy method is proposed for forecasting the LMPs in the power market. The important information, including the historical data in a power market, e.g. PJM, is extracted first. On the other hand, it is found that the LMP values vary dramatically. Therefore, it is difficult to analyze the related data with tra- ditional techniques, for example, regression analysis. In this paper, the ANN is used to forecast the LMPs. In particular, the multi-layer perception (MLP) ANN is adopted because it is capable of modeling nonlinear and fast variations, as well as managing complicated input/output relations throughout the training processes with historical data [1, 2]. It is also found that the MLP is suitable for non-stationary time series forecasting, providing satisfactory results. Therefore, in this paper, all numerical data serve as inputs for the ANN for forecasting LMPs and fuzzy reasoning results are used to capture the power network events in ANN forecasted prices [10]. This paper is organized as follows: Section 2 introduces the applications of electricity price fore- casting. The PJM market data is described in Section 3. The problem formulation is described in Section 4. The proposed pre-processing and neuro-fuzzy systems are given in Section 5. Numerical results are given to show the utility of FFNN based on PJM data in Section 6. Mean absolute percentage error (MAPE) and root mean square error (RMSE) are used to evaluate the performance. The MATLAB-based software is introduced in Section 7 and finally the concluding remarks are provided in Section 8. 2. Application of Electricity Price Forecasting Price forecasting is commonly used to assist market participants’ bidding decision- making, portfolio allocation, and investment planning. Price forecasting is also useful to market operators, they can take advantage of forecasted prices to compute various indexes and measurements for market monitoring. 2.1. Application to Market Participants Fuzzy Inf. Eng. (2011) 4: 339-350 341 Application of electricity price forecasting fall into three time horizons: Next-day or short-term (one day to one week) bidding strategies, medium-term (6 months to 1 year) portfolio decisions and bilateral-contract negotiations, long-term (beyond 1 year) planning. For various time horizons, the application of price forecasting is different. For the short-term time horizon, market participants use price forecasts to decide their bidding strategies so they can maximize their profits in the day-ahead markets or short-term forward markets. For the medium-term time horizon, suppliers and con- sumers use price forecasts to optimize the proportions of forward market and bilateral contracts in their asset allocations, price forecasts are also references in negotiations of bilateral contracts. For the long-term time horizon, facility owners use the long- term price trends to ensure recovery of investments in generation, transmission and distribution of the electricity [3-5]. 2.2. Applications to Market Operators Because the exercise of market power can increase the volatility of electricity prices, the analysis of energy market prices plays a key role in the monitoring of the par- ticipant behavior and market performance. Accurate price forecasts can be used to predict market monitoring indexes and measurements. Several market power indexes are commonly used, market participants use these indexes to measure the concentra- tion of market shares or to identify pivotal suppliers and in some cases to calculate the markup of prices over marginal costs (price-cost margin index) [6][7]. 3. Market, Energy and Climatic Data In a realistic market, there are generally market historical data available to the market participants and other users. For example, in the PJM market, there are day-ahead and real-time market data available. The day-ahead database contains following nu- merical data: • Hourly Nodal LMPs; • Hourly Zonal Load Data. nd th Fig. 1 illustrates the LMPs in Sidney bus (69kV) from February 2 through 6 , 2008 from day-ahead market. It is found that the LMPs vary in a wide range (about 50$ -100$ a day). Climatic data including daily temperature and humidity and etc. are correlated with load and electricity prices. Therefore, temperature data are used to capture the effect of temperature on the forecasting day and the day before forecasting day. Temperature data used in this model are the Minimum/Maximum/Average of each day [8]. From the generation point of view, both the day-ahead and real-time markets are affected by the energy availability and prices [9]. Therefore, following energy prices are used as extra market data: • Daily Gas Price Data (in the U.S.); • Daily Oil Price Data (in the U.S.); 342 M. Esfahani (2011) • Daily Coal Price Data (in the U.S.); 0 24 48 72 96 120 Hour nd th Fig. 1 Hourly day-ahead LMP in Sidney from Feb. 2 , 2008 to Feb. 6 , 2008 4. Problem Formulation LMP is the cost of supplying the next Mega Watt of load at a specific location, after considering the generation marginal cost, cost of transmission congestion, and losses. That is the marginal price of available resources to meet the load, subject to delivery constraints of the physical network. LMP is an efficient way of pricing energy supply when transmission constraints exist [10, 11]. In the day-ahead energy market, locational prices are the main goal of day-ahead electricity price forecasting in a grid environment,electricity prices are impacted by various factors like transmission congestions, supply-side decision-making, and mar- ket power exercises. The selection of input variables is important in order to achieve a high accuracy forecasting. Statistical methods forecast electricity prices by modeling the correlation behav- iors between the prices and the correlated factors. The correlated factors include his- torical prices from the financial forward market, historical loads and load forecasts, historical temperatures and temperature forecasts and transmission congestions from the physical grid. The degree of correlation is used for parameters selection in each calculation. By evaluating the correlation coefficients, the degree of correlated linear- ity can be investigated for each parameter. The selected parameters have correlation with r-value greater than 0.5. A day-ahead electricity price forecasting system is formulated. Its inputs are cor- related variables, and its outputs are hourly forecasted next-day prices. Significantly, correlated variables are historical prices of some hours on the previous day, demand loads of local zone of some hours on previous and forecast days, and temperature and energy prices of previous and forecast days. These variables must be included for accurate forecasting. System outputs (Day-ahead prices) in days and hours with contingency are ana- lyzed and edited by FIS. 5. Methodology LMP($/MWh) Fuzzy Inf. Eng. (2011) 4: 339-350 343 5.1. Preprocessing Data 1) Data Exclusion: To improve the training performance, the proposed method is included two data exclusion stages. First it replaces “out of range” training data with a proper limit for each input parameter in each hour and then it excludes training days having an outspread input (or output) parameter. Equation (1) shows the condition on th which the training day i should be ignored; std(X )>α∗ std X , (1) i,p k,p k=1 where: n: training period length; i: current analyzing day (record); p: input/output variables (24 hours); th X : amount of variable p at i record; i,p α: exclusion factor. If at least one parameter of training day meets above condition, it will be considered as a diffused training record and the model will remove this day from the training data. 2) Parameter Exclusion: To improve the predicting performance, this model uses an automatic correlation (AC) method for parameter selection. Because there are nu- merous input variables used in this model, this method is utilized before each training to select the best-correlated parameters [12, 13]. 5.2. Neural Network In this paper, the FFNN is utilized to simulate the correlation between the LMP values and system conditions. Three modular forecasting systems including 24 FFNNs are presented for forecasting the LMP in an area for the use on weekdays, Saturdays and Sundays. In fact, each hour of the next-day price is forecasted by a single FFNN. In each FFNN, there are variable input neurons (more than 5 up to 83), three hidden layer neurons and a single output neuron. Selected input variables based on their correlation coefficients determine the number of input layer neurons. ANN reduced size in the proposed model decreases the calculation time and increases the forecasting system’s efficiency. 5.3. Fuzzy Inference System In this paper, FIS is utilized to capture the effect of transmission constraints and sys- tem contingencies on the next-day price forecasts. An FIS performs an input-output mapping based on fuzzy logic. Contingencies are not number-based data (as pre- sented in Section 3). FIS has four input and one-output variables. Forecasting days including contingencies will enable FIS, and normal forecasting days (without con- tingency) will not be analyzed by the FIS system. In another word, neural network 344 M. Esfahani (2011) forecasting results for normal days are the final results, while final results for con- tingency days are the FIS-edited results. Fig. 2 illustrates the proposed neuro-fuzzy system. Fig. 2 FIS-FFNN price forecasting system Period of time is one of FIS inputs (it is omitted in Fig. 2). Based on the regional conditions, hours in the next-day calculations can be divided to 7 sections. Fig. 3 Time membership functions Daytime section can be modeled for FIS by triangle or trapezoid membership func- tions, as illustrated in Fig. 3. Time sections are; “Early Morning”, “Morning”, “Noon”, “Afternoon”, “Evening”, “Night”, “Midnight”. Price at contingency hours in forecasting day will be determined by FIS system. Considering these hours, time membership function should be selected. The next input is forecasting day load for contingency hour. The FIS load input is included three triangle membership functions: “Low”, “Medium” and “High”. Load membership function limits will be selected adaptively by load limits in current hour during the training period. Contingency FIS input divided into 5 triangle membership functions: “Very Low”, “Low”, “Medium”, “High” and “Very High”. Contingencies belong to proper mem- bership function based on their importance. Fuzzy Inf. Eng. (2011) 4: 339-350 345 FIS output i.e. the final forecasted price at the current hour, is distributed by 3 membership functions: “Low”, “Medium” and “High”. Price membership function ranges will be selected adaptively, by price limits in current hour during the training period. Fig. 4 illustrates an example for FIS output membership functions [15, 16]. Fig. 4 Output price membership functions 6. Numerical Performance Since the PJM market is well recognized in the U.S and beyond, the forecasting sys- tem is tested using the data from the day-ahead energy market and system operations of PJM. The sampling period is January through December 2008 [4]. Two criteria are commonly used to evaluate the accuracy of price forecasting: RMSE and MAPE [2]. RMSE and MAPE are calculated, respectively, by; RMSE = (P − P ) , (2) actuali f orecasted i=1 P − P 100 actual f orecasted MAPE = , (3) N P actuali i=1 where N is the number of sample prices, and the terms P and P are f orecasted,i actual,i forecast and real prices respectively (i = 1, 2,··· , N). Because of the special behavior of the price in electricity markets, MAP-Error from Equation (3) is not suitable for price forecasting evaluations. In some cases, it will caused in unrealistic errors. Therefore, Equation (4) is a new method of using MAPE evaluation criteria. P − P 1  actual f orecasted MAPE = . (4) N P Average(actual) i=1 6.1. Price Forecasting Using the Proposed FFNN System 346 M. Esfahani (2011) The PJM system handles congestion through LMP. For the Dayton zone, the day- ahead LMPs are tested for all 52 weeks in 2008. Since nodal load data are not avail- able, all the load data are measured loads in PJM of zonal demands [9]. The FFNN forecast results for Saturday through Friday of a sample week at the above-mentioned period are separately forecasted and presented in Fig. 5 consecutively. nd th Fig. 5 Forecasted price by FFNN for Nov. 22 , 2008 to Nov. 28 , 2008. Numerical results of day-ahead price forecasting by FFNN, for the year 2008 are presented in Table 1. Table 1: FFNN results for day-ahead price forecasting in the year 2008. Weekday MAPE(%) RMSE($/MWh) Sunday 16.05% 8.03 Monday 14.88% 7.44 Tuesday 13.42% 6.53 Wednesday 11.74% 6.13 Thursday 11.60% 6.40 Friday 11.40% 5.78 Saturday 15.04% 7.03 6.2. Improvement by Fuzzy Inference, Transmission Constraints, US-holidays and Special Days The neuro-fuzzy approach deals with a combination of neural networks and fuzzy in- ference system to overcome the deficiencies of each technology when working stand alone. Fuzzy inference system described in Section 5 is utilized for special events and contingency days. The real-time and day-ahead database also comprises “trans- mission constraints” that include the linguistic description about contingency facili- ties and their corresponding occurrence times. For example, there is a contingency Fuzzy Inf. Eng. (2011) 4: 339-350 347 st description: 17:00-18:00h on May 31 , 2008 “Dayton 230KV 253A L/O DOOMS 500/230 TX#7 & BUS#6” which means that a transformer (500/230kV) contingency st occurred in Dayton at 17:00-18:00h on May 31 , 2008 and it caused a line (230kV) outage. In some cases, bus number and transformer location are included [6, 7, 9]. Nu- merical results of day-ahead price forecasting by FIS-FFNN are presented in Table Table 2: FIS-FFNN results for day-ahead price forecasting in the year 2008. Weekday MAPE(%) RMSE($/MWh) Sunday 15.86% 7.82 Monday 14.23% 7.06 Tuesday 12.43% 5.92 Wednesday 10.92% 6.09 Thursday 11.20% 6.12 Friday 11.92% 5.61 Saturday 14.21% 5.82 Load profile of a sample Thursday, a US-holiday (Thanksgiving Day) in the year 2008 is compared with the past and future Thursdays in Fig. 6. A sample result of the week including “Thanksgiving Day” is presented in Fig.7, which has a different load profile. Comparing results in Fig. 5 and this figure represents the improvement of the forecasting results specially for the sixth day of this period that encounters with thanksgiving day [14, 15]. Fig. 6 Load profile for “Thanksgiving Day” in Sidney bus in 2008 comparing with the past and future Thursdays. 348 M. Esfahani (2011) nd th Fig. 7 Forecasted prices by FIS-FFNN for Nov. 22 , 2008 to Nov. 28 , 2008 7. MATLAB-Based Software A MATLAB-based software is provided for modeling and analyzing different mar- kets. Proposed method is analyzed and tested by this comprehensive software. It is divided to nine main parts as follows: • Database and Data Preparing; • Data Query, Classification and Sub-models; • Data Exclusion Module; • Input Variables Module; • Neural Network Configuration; • Auto-Correlation Settings; • Fuzzy Module; • Simulation and Output Reports Module; • General Information Panel. A general view of the software is presented in Fig.8. Some capabilities of the provided software are as follow: • Multi-Type Database Compatibility; • Customized Weekday Sub-Models; • Data Analysis Possibility; • Data-Preprocessing with Different Methods; Fuzzy Inf. Eng. (2011) 4: 339-350 349 • Variable Selection Possibility; • Plot Output Results; • Export Output Results in Excel Database; Fig. 8 MATLAB-based price forecasting GUI 8. Conclusion An ANN forecasting system including FIS is proposed for the day-ahead electricity price forecasting in a deregulated environment. The model is based on an Automatic Correlation method and FFNN forecasting for weekdays, Saturdays and Sundays. The related factors, historical and forecasted loads, historical prices and environment temperatures are considered as the fuzzy reasoning is considered because of its ca- pacity in treating the linguistic description. In addition, some energy prices are con- sidered as external economic factors affecting generation costs and electricity prices. As a result, this forecasting system has the advantages of a high accuracy in a dereg- ulated market. Actual data from PJM website were used to show the applicability of the proposed method. 350 M. Esfahani (2011) Acknowledgements This research is supported by Dr. S. M. Moghaddas-Tafreshi, the Assistant Profes- sor at Power Engineering Department in Electrical Faculty of K.N.Toosi University of Technology. Author would like to thank referees and publisher for their helpful comments. References 1. Areekul P, Senju T, Toyama H, Chakraborty S, Yona A, Urasaki N, Mandal P, Saber A Y (2010) A new method for next-day price forecasting for PJM electricity market. International Journal of Emerging Electric Power Systems: Vol. 11: Iss. 2, Article 3 2. Niimura T (2006) Forecasting techniques for deregulated electricity market prices. IEEE Power Systems Conference and Exposition: 1-4244-0177-1: 51-56 3. Li G, Liu C C, Mattson C, Lawarree J (2007) Day-ahead electricity price forecasting in a grid envi- ronment. IEEE Transactions on Power Systems 22(1): 266-274 4. Capacity Adequacy Planning Department (2007) PJM Load/Energy Forecasting Model 5. Midwest ISO, FERC (2006) FERC filled joint and common market reports 6. Vahidinasab V, Jadid S, Kazemi A (2007) Day-ahead price forecasting in restructured power systems using artificial neural networks. Electric Power Systems Research, Vol. 78: Iss. 8: 1332-1342 7. PJM Incorporation (2008) Daily locational mariginal price database. PJM Electric Power Market 8. NCDC Corporation. National Climatic Data Center. U.S. Department of Commerce. 9. PJM Electric Distribution Companies (2008) Historical load data reports 10. Hong Y Y, Lee C F (2005) A neuro-fuzzy price forecasting approach in deregulated electricity mar- kets. Elsevier: Electric Power System Research: 151-157 11. Farhadi M, Moghaddastafreshi S M (2006) A novel model for short term load forecasting of Iran power network by using kohonen neural networks. IEEE ISIE2006: International Symposium on Industrial Electronics: 1726-1731 12. Moghaddastafreshi S M, Farhadi M (2007) Improved SOM based method for short term load forecast of Iran power network. Singapore: IEEE IPEC2007:Internatioanl Power Engineering Conference: 1377-1384 13. Moghaddastafreshi S M, Farhadi M (2007) Development of Iran daily load forecast software by kohonen and perception neural network algorithm based on thermal coefficients. Singapore: The 8th International Power Engineering Conference 14. Moghaddastafreshi S M, Farhadi M (2008) A linear regression-based study for temperature sensitiv- ity analysis of Iran electrical load, Chengdu: IEEE ICIT2008: Industrial Technology International Conference: 1-7 15. Effati S, Sadoghi H, Saberi Z (2007) A neural network model for solving stochastic fuzzy multi- objective linear fractional programs. Ferdowsi University of Mashhad, Iran: First Joint Congress on Fuzzy and Intelligent Systems: 1-8 16. Cheng C H, Chen T L, Teoh H J, Chiang C H (2008) Fuzzy time-series based on adaptive expectation model for TAIEX forecasting. Expert Systems with Applications 34: 1126-1132 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Fuzzy Information and Engineering Taylor & Francis

Neuro-fuzzy Approach for Short-term Electricity Price Forecasting Developed MATLAB-based Software

Fuzzy Information and Engineering , Volume 3 (4): 12 – Dec 1, 2011

Neuro-fuzzy Approach for Short-term Electricity Price Forecasting Developed MATLAB-based Software

Abstract

AbstractBid and offer competition is a main transaction approach in deregulated electricity markets. Locational marginal prices (LMP) resulting from bidding competition determine electricity prices at a node or in an area. The LMP exhibits important information for market participants to develop their bidding strategies. Moreover, LMP is also a vital indicator for a Security Coordinator to perform market re-dispatch for congestion management. This paper presents a method using modular feed...
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Fuzzy Inf. Eng. (2011) 4: 339-350 DOI 10.1007/s12543-011-0089-2 ORIGINAL ARTICLE Neuro-fuzzy Approach for Short-term Electricity Price Forecasting Developed MATLAB-based Software M. Esfahani Received: 30 January 2011/ Revised: 27 July 2011/ Accepted: 16 October 2011/ © Springer-Verlag Berlin Heidelberg and Fuzzy Information and Engineering Branch of the Operations Research Society of China Abstract Bid and offer competition is a main transaction approach in deregulated electricity markets. Locational marginal prices (LMP) resulting from bidding com- petition determine electricity prices at a node or in an area. The LMP exhibits im- portant information for market participants to develop their bidding strategies. More- over, LMP is also a vital indicator for a Security Coordinator to perform market re- dispatch for congestion management. This paper presents a method using modular feed forward neural networks (FFNN) and fuzzy inference system (FIS) for forecast- ing LMPs. FFNN is used to forecast the electricity prices in a short time horizon and FIS to forecast the prices of special days. FFNN system includes an autocorrelation method for selecting parameters and methods for data preprocessing and preparing historical data to train the artificial neural network (ANN). In this paper, the histori- cal LMPs of Pennsylvania, New Jersey, and Maryland (PJM) market are used to test the proposed method. It is found that the proposed neuro-fuzzy method is capable of forecasting LMP values efficiently. In addition, MATLAB-based software is designed to test and use the proposed model in different markets and environments. This is an efficient tool to study and model power markets for price forecasting. It is included with a database management system, data classifier, input variable selection, FFNN and FIS configuration and report generator in custom formats. Keywords FIS · FFNN · Data pre-processing · Electricity price forecasting · Day- ahead energy market 1. Introduction There are two main transaction modes in a deregulated electric power industry, com- petitive bidding and bilateral contract. The competitive biddings are used in the fol- lowing markets: energy, spot, firm transmission rights and lastly ancillary service, M. Esfahani () Department of Electrical Engineering, Islamic Azad University, Khomeinishahr Branch, Esfahan, Iran e-mail: Mohammad.Esfahani@iaukhsh.ac.ir 340 M. Esfahani (2011) etc. The bilateral contract is adopted outside the competitive market (pool) for any two individual entities, buyer and seller. For either transaction mode, the electricity price information serves as an essential element for all entities to adjust their of- fers/bids and/or contract prices. Especially, LMP is one of the most popular modes for energy pricing in a competitive market. LMPs can reflect the electricity value at a node and may be discriminated at different nodes within a power network. The LMPs reveal important information, which is helpful to the market participants in develop- ing their bidding strategies. It is also a vital indicator for the Security Coordinator to mitigate the transmission congestion. LMPs reveal important information for both the spot market and the entities with bilateral contracts. In the past, some researchers employed the ANNs for short-term system marginal price (SMP) forecasting, mar- ket clearing price (MCP) and quantity (MCQ) forecasting. Moreover, autoregressive integrated moving average (ARIMA) and traditional time-series models are used to predict the next-day electricity prices. Neural network is the other method currently used for the price forecasting. Because the MCQ is irrelevant to the transmission con- straints, forecasting LMPs subject to transmission constraints is more difficult than forecasting MCPs. In this paper, a neuro-fuzzy method is proposed for forecasting the LMPs in the power market. The important information, including the historical data in a power market, e.g. PJM, is extracted first. On the other hand, it is found that the LMP values vary dramatically. Therefore, it is difficult to analyze the related data with tra- ditional techniques, for example, regression analysis. In this paper, the ANN is used to forecast the LMPs. In particular, the multi-layer perception (MLP) ANN is adopted because it is capable of modeling nonlinear and fast variations, as well as managing complicated input/output relations throughout the training processes with historical data [1, 2]. It is also found that the MLP is suitable for non-stationary time series forecasting, providing satisfactory results. Therefore, in this paper, all numerical data serve as inputs for the ANN for forecasting LMPs and fuzzy reasoning results are used to capture the power network events in ANN forecasted prices [10]. This paper is organized as follows: Section 2 introduces the applications of electricity price fore- casting. The PJM market data is described in Section 3. The problem formulation is described in Section 4. The proposed pre-processing and neuro-fuzzy systems are given in Section 5. Numerical results are given to show the utility of FFNN based on PJM data in Section 6. Mean absolute percentage error (MAPE) and root mean square error (RMSE) are used to evaluate the performance. The MATLAB-based software is introduced in Section 7 and finally the concluding remarks are provided in Section 8. 2. Application of Electricity Price Forecasting Price forecasting is commonly used to assist market participants’ bidding decision- making, portfolio allocation, and investment planning. Price forecasting is also useful to market operators, they can take advantage of forecasted prices to compute various indexes and measurements for market monitoring. 2.1. Application to Market Participants Fuzzy Inf. Eng. (2011) 4: 339-350 341 Application of electricity price forecasting fall into three time horizons: Next-day or short-term (one day to one week) bidding strategies, medium-term (6 months to 1 year) portfolio decisions and bilateral-contract negotiations, long-term (beyond 1 year) planning. For various time horizons, the application of price forecasting is different. For the short-term time horizon, market participants use price forecasts to decide their bidding strategies so they can maximize their profits in the day-ahead markets or short-term forward markets. For the medium-term time horizon, suppliers and con- sumers use price forecasts to optimize the proportions of forward market and bilateral contracts in their asset allocations, price forecasts are also references in negotiations of bilateral contracts. For the long-term time horizon, facility owners use the long- term price trends to ensure recovery of investments in generation, transmission and distribution of the electricity [3-5]. 2.2. Applications to Market Operators Because the exercise of market power can increase the volatility of electricity prices, the analysis of energy market prices plays a key role in the monitoring of the par- ticipant behavior and market performance. Accurate price forecasts can be used to predict market monitoring indexes and measurements. Several market power indexes are commonly used, market participants use these indexes to measure the concentra- tion of market shares or to identify pivotal suppliers and in some cases to calculate the markup of prices over marginal costs (price-cost margin index) [6][7]. 3. Market, Energy and Climatic Data In a realistic market, there are generally market historical data available to the market participants and other users. For example, in the PJM market, there are day-ahead and real-time market data available. The day-ahead database contains following nu- merical data: • Hourly Nodal LMPs; • Hourly Zonal Load Data. nd th Fig. 1 illustrates the LMPs in Sidney bus (69kV) from February 2 through 6 , 2008 from day-ahead market. It is found that the LMPs vary in a wide range (about 50$ -100$ a day). Climatic data including daily temperature and humidity and etc. are correlated with load and electricity prices. Therefore, temperature data are used to capture the effect of temperature on the forecasting day and the day before forecasting day. Temperature data used in this model are the Minimum/Maximum/Average of each day [8]. From the generation point of view, both the day-ahead and real-time markets are affected by the energy availability and prices [9]. Therefore, following energy prices are used as extra market data: • Daily Gas Price Data (in the U.S.); • Daily Oil Price Data (in the U.S.); 342 M. Esfahani (2011) • Daily Coal Price Data (in the U.S.); 0 24 48 72 96 120 Hour nd th Fig. 1 Hourly day-ahead LMP in Sidney from Feb. 2 , 2008 to Feb. 6 , 2008 4. Problem Formulation LMP is the cost of supplying the next Mega Watt of load at a specific location, after considering the generation marginal cost, cost of transmission congestion, and losses. That is the marginal price of available resources to meet the load, subject to delivery constraints of the physical network. LMP is an efficient way of pricing energy supply when transmission constraints exist [10, 11]. In the day-ahead energy market, locational prices are the main goal of day-ahead electricity price forecasting in a grid environment,electricity prices are impacted by various factors like transmission congestions, supply-side decision-making, and mar- ket power exercises. The selection of input variables is important in order to achieve a high accuracy forecasting. Statistical methods forecast electricity prices by modeling the correlation behav- iors between the prices and the correlated factors. The correlated factors include his- torical prices from the financial forward market, historical loads and load forecasts, historical temperatures and temperature forecasts and transmission congestions from the physical grid. The degree of correlation is used for parameters selection in each calculation. By evaluating the correlation coefficients, the degree of correlated linear- ity can be investigated for each parameter. The selected parameters have correlation with r-value greater than 0.5. A day-ahead electricity price forecasting system is formulated. Its inputs are cor- related variables, and its outputs are hourly forecasted next-day prices. Significantly, correlated variables are historical prices of some hours on the previous day, demand loads of local zone of some hours on previous and forecast days, and temperature and energy prices of previous and forecast days. These variables must be included for accurate forecasting. System outputs (Day-ahead prices) in days and hours with contingency are ana- lyzed and edited by FIS. 5. Methodology LMP($/MWh) Fuzzy Inf. Eng. (2011) 4: 339-350 343 5.1. Preprocessing Data 1) Data Exclusion: To improve the training performance, the proposed method is included two data exclusion stages. First it replaces “out of range” training data with a proper limit for each input parameter in each hour and then it excludes training days having an outspread input (or output) parameter. Equation (1) shows the condition on th which the training day i should be ignored; std(X )>α∗ std X , (1) i,p k,p k=1 where: n: training period length; i: current analyzing day (record); p: input/output variables (24 hours); th X : amount of variable p at i record; i,p α: exclusion factor. If at least one parameter of training day meets above condition, it will be considered as a diffused training record and the model will remove this day from the training data. 2) Parameter Exclusion: To improve the predicting performance, this model uses an automatic correlation (AC) method for parameter selection. Because there are nu- merous input variables used in this model, this method is utilized before each training to select the best-correlated parameters [12, 13]. 5.2. Neural Network In this paper, the FFNN is utilized to simulate the correlation between the LMP values and system conditions. Three modular forecasting systems including 24 FFNNs are presented for forecasting the LMP in an area for the use on weekdays, Saturdays and Sundays. In fact, each hour of the next-day price is forecasted by a single FFNN. In each FFNN, there are variable input neurons (more than 5 up to 83), three hidden layer neurons and a single output neuron. Selected input variables based on their correlation coefficients determine the number of input layer neurons. ANN reduced size in the proposed model decreases the calculation time and increases the forecasting system’s efficiency. 5.3. Fuzzy Inference System In this paper, FIS is utilized to capture the effect of transmission constraints and sys- tem contingencies on the next-day price forecasts. An FIS performs an input-output mapping based on fuzzy logic. Contingencies are not number-based data (as pre- sented in Section 3). FIS has four input and one-output variables. Forecasting days including contingencies will enable FIS, and normal forecasting days (without con- tingency) will not be analyzed by the FIS system. In another word, neural network 344 M. Esfahani (2011) forecasting results for normal days are the final results, while final results for con- tingency days are the FIS-edited results. Fig. 2 illustrates the proposed neuro-fuzzy system. Fig. 2 FIS-FFNN price forecasting system Period of time is one of FIS inputs (it is omitted in Fig. 2). Based on the regional conditions, hours in the next-day calculations can be divided to 7 sections. Fig. 3 Time membership functions Daytime section can be modeled for FIS by triangle or trapezoid membership func- tions, as illustrated in Fig. 3. Time sections are; “Early Morning”, “Morning”, “Noon”, “Afternoon”, “Evening”, “Night”, “Midnight”. Price at contingency hours in forecasting day will be determined by FIS system. Considering these hours, time membership function should be selected. The next input is forecasting day load for contingency hour. The FIS load input is included three triangle membership functions: “Low”, “Medium” and “High”. Load membership function limits will be selected adaptively by load limits in current hour during the training period. Contingency FIS input divided into 5 triangle membership functions: “Very Low”, “Low”, “Medium”, “High” and “Very High”. Contingencies belong to proper mem- bership function based on their importance. Fuzzy Inf. Eng. (2011) 4: 339-350 345 FIS output i.e. the final forecasted price at the current hour, is distributed by 3 membership functions: “Low”, “Medium” and “High”. Price membership function ranges will be selected adaptively, by price limits in current hour during the training period. Fig. 4 illustrates an example for FIS output membership functions [15, 16]. Fig. 4 Output price membership functions 6. Numerical Performance Since the PJM market is well recognized in the U.S and beyond, the forecasting sys- tem is tested using the data from the day-ahead energy market and system operations of PJM. The sampling period is January through December 2008 [4]. Two criteria are commonly used to evaluate the accuracy of price forecasting: RMSE and MAPE [2]. RMSE and MAPE are calculated, respectively, by; RMSE = (P − P ) , (2) actuali f orecasted i=1 P − P 100 actual f orecasted MAPE = , (3) N P actuali i=1 where N is the number of sample prices, and the terms P and P are f orecasted,i actual,i forecast and real prices respectively (i = 1, 2,··· , N). Because of the special behavior of the price in electricity markets, MAP-Error from Equation (3) is not suitable for price forecasting evaluations. In some cases, it will caused in unrealistic errors. Therefore, Equation (4) is a new method of using MAPE evaluation criteria. P − P 1  actual f orecasted MAPE = . (4) N P Average(actual) i=1 6.1. Price Forecasting Using the Proposed FFNN System 346 M. Esfahani (2011) The PJM system handles congestion through LMP. For the Dayton zone, the day- ahead LMPs are tested for all 52 weeks in 2008. Since nodal load data are not avail- able, all the load data are measured loads in PJM of zonal demands [9]. The FFNN forecast results for Saturday through Friday of a sample week at the above-mentioned period are separately forecasted and presented in Fig. 5 consecutively. nd th Fig. 5 Forecasted price by FFNN for Nov. 22 , 2008 to Nov. 28 , 2008. Numerical results of day-ahead price forecasting by FFNN, for the year 2008 are presented in Table 1. Table 1: FFNN results for day-ahead price forecasting in the year 2008. Weekday MAPE(%) RMSE($/MWh) Sunday 16.05% 8.03 Monday 14.88% 7.44 Tuesday 13.42% 6.53 Wednesday 11.74% 6.13 Thursday 11.60% 6.40 Friday 11.40% 5.78 Saturday 15.04% 7.03 6.2. Improvement by Fuzzy Inference, Transmission Constraints, US-holidays and Special Days The neuro-fuzzy approach deals with a combination of neural networks and fuzzy in- ference system to overcome the deficiencies of each technology when working stand alone. Fuzzy inference system described in Section 5 is utilized for special events and contingency days. The real-time and day-ahead database also comprises “trans- mission constraints” that include the linguistic description about contingency facili- ties and their corresponding occurrence times. For example, there is a contingency Fuzzy Inf. Eng. (2011) 4: 339-350 347 st description: 17:00-18:00h on May 31 , 2008 “Dayton 230KV 253A L/O DOOMS 500/230 TX#7 & BUS#6” which means that a transformer (500/230kV) contingency st occurred in Dayton at 17:00-18:00h on May 31 , 2008 and it caused a line (230kV) outage. In some cases, bus number and transformer location are included [6, 7, 9]. Nu- merical results of day-ahead price forecasting by FIS-FFNN are presented in Table Table 2: FIS-FFNN results for day-ahead price forecasting in the year 2008. Weekday MAPE(%) RMSE($/MWh) Sunday 15.86% 7.82 Monday 14.23% 7.06 Tuesday 12.43% 5.92 Wednesday 10.92% 6.09 Thursday 11.20% 6.12 Friday 11.92% 5.61 Saturday 14.21% 5.82 Load profile of a sample Thursday, a US-holiday (Thanksgiving Day) in the year 2008 is compared with the past and future Thursdays in Fig. 6. A sample result of the week including “Thanksgiving Day” is presented in Fig.7, which has a different load profile. Comparing results in Fig. 5 and this figure represents the improvement of the forecasting results specially for the sixth day of this period that encounters with thanksgiving day [14, 15]. Fig. 6 Load profile for “Thanksgiving Day” in Sidney bus in 2008 comparing with the past and future Thursdays. 348 M. Esfahani (2011) nd th Fig. 7 Forecasted prices by FIS-FFNN for Nov. 22 , 2008 to Nov. 28 , 2008 7. MATLAB-Based Software A MATLAB-based software is provided for modeling and analyzing different mar- kets. Proposed method is analyzed and tested by this comprehensive software. It is divided to nine main parts as follows: • Database and Data Preparing; • Data Query, Classification and Sub-models; • Data Exclusion Module; • Input Variables Module; • Neural Network Configuration; • Auto-Correlation Settings; • Fuzzy Module; • Simulation and Output Reports Module; • General Information Panel. A general view of the software is presented in Fig.8. Some capabilities of the provided software are as follow: • Multi-Type Database Compatibility; • Customized Weekday Sub-Models; • Data Analysis Possibility; • Data-Preprocessing with Different Methods; Fuzzy Inf. Eng. (2011) 4: 339-350 349 • Variable Selection Possibility; • Plot Output Results; • Export Output Results in Excel Database; Fig. 8 MATLAB-based price forecasting GUI 8. Conclusion An ANN forecasting system including FIS is proposed for the day-ahead electricity price forecasting in a deregulated environment. The model is based on an Automatic Correlation method and FFNN forecasting for weekdays, Saturdays and Sundays. The related factors, historical and forecasted loads, historical prices and environment temperatures are considered as the fuzzy reasoning is considered because of its ca- pacity in treating the linguistic description. In addition, some energy prices are con- sidered as external economic factors affecting generation costs and electricity prices. As a result, this forecasting system has the advantages of a high accuracy in a dereg- ulated market. Actual data from PJM website were used to show the applicability of the proposed method. 350 M. Esfahani (2011) Acknowledgements This research is supported by Dr. S. M. Moghaddas-Tafreshi, the Assistant Profes- sor at Power Engineering Department in Electrical Faculty of K.N.Toosi University of Technology. Author would like to thank referees and publisher for their helpful comments. References 1. Areekul P, Senju T, Toyama H, Chakraborty S, Yona A, Urasaki N, Mandal P, Saber A Y (2010) A new method for next-day price forecasting for PJM electricity market. International Journal of Emerging Electric Power Systems: Vol. 11: Iss. 2, Article 3 2. Niimura T (2006) Forecasting techniques for deregulated electricity market prices. IEEE Power Systems Conference and Exposition: 1-4244-0177-1: 51-56 3. Li G, Liu C C, Mattson C, Lawarree J (2007) Day-ahead electricity price forecasting in a grid envi- ronment. IEEE Transactions on Power Systems 22(1): 266-274 4. Capacity Adequacy Planning Department (2007) PJM Load/Energy Forecasting Model 5. Midwest ISO, FERC (2006) FERC filled joint and common market reports 6. 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Journal

Fuzzy Information and EngineeringTaylor & Francis

Published: Dec 1, 2011

Keywords: FIS; FFNN; Data pre-processing; Electricity price forecasting; Day-ahead energy market

References