Machine Learning Applications for Load and Price

Machine Learning Applications for Load and Price Forecasting and Wind Power Prediction in Power Systems Michael Negnevitsky, Senior Member, IEEE, Paras Mandal, Member, IEEE, and Anurag K. Srivastava, Member, IEEE

Abstract— This paper reviews main forecasting techniques used for power system applications. Available forecasting techniques have been discussed with focus on electricity load and price forecasting and wind power prediction. Forecasting problems have been classified based on time frame, application specific area and forecasting techniques. Appropriate examples based on data pertaining to the Victorian electricity market, Australia and the PJM electricity market, U.S.A. are used to demonstrate the functioning of the developed neural network (NN) method based on similar days approach to predict hourly electricity load and price, respectively. The other important problem faced by power system utilities are the variability and non-schedulable nature of wind farm power generation. These inherent characteristics of wind power have both technical and commercial implications for efficient planning and operation of power systems. To address the wind power issues, this paper presents the application of an Adaptive Neural Fuzzy Inference System (ANFIS) to very short-term wind forecasting utilizing a case study from Tasmania, Australia. Index Terms— Adaptive neuro-fuzzy inference system (ANFIS), electricity market, intelligent systems, neural network (NN), short-term load forecasting, short-term price forecasting, very short-term wind power prediction.

is the fastest growing power generation sector in the world. However, wind power is intermittent. To be able to trade efficiently, make the best use of transmission line capability, and address concerns with system frequency in a re-regulated system, accurate very short-term forecasts are essential. This paper discusses the application of an adaptive neuro-fuzzy inference system (ANFIS) to forecasting a wind time series. The objective of this paper is to provide a brief overview of advancement in forecasting for power systems applications with focus on short-term load and price forecasting, and wind power prediction. The problems and various available techniques in these areas of forecasting are discussed. The rest of the paper is organized as follows. Section 2 provides classification of forecasting problems and methods associated with wind power, electric load and energy price based on time frame and applications. Case study results of short-term load and price forecasting, and very short-term wind power prediction are presented in Section 3. Section 4 presents the conclusion of this paper. II. C LASSIFICATION OF FORECASTING PROBLEMS AND

I. I NTRODUCTION

TECHNIQUES

ORECASTING is a vital part of business planning in today’s competitive environment. With an introduction of deregulation of power industry, many new challenges have been encountered by the participants of the electricity market. Forecasting of wind power, electric loads and energy price have become a major issue in power systems. Following needs of the market, various techniques are used to forecast the wind power, energy price and power demand. This paper presents short-term load forecasting results utilising a case study of the Victorian electricity market to demonstrate the functioning of the developed neural network (NN) model based on similar days (SD) method. Integration of NN and SD approach has also been applied to predict day-ahead electricity price in the PJM electricity market. In addition, the focus is on wind power prediction regarding which the authors describe very short-term wind power prediction utilising a case study from Tasmania, Australia. Wind power presently

In this section, we discuss about different forecasting problems and techniques in the area of electric load forecasting, energy price forecasting and wind power prediction.

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M. Negnevitsky and P. Mandal are with the School of Engineering, University of Tasmania, Hobart, Tasmania 7001, Australia (e-mail: [email protected], [email protected]). A. K. Srivastava is with the Department of Electrical and Computer Engineering, Mississippi State University, Mississippi State, MS 39762 USA (e-mail: [email protected]).

A. Load forecasting Load forecasting is a process to predict load for a future period. Application of load forecasting falls into different time horizons: long-term forecasting (from one year to ten years), medium-term forecasting (from several months to oneyear), short-term forecasting (from one-hour to one-week) and real-time or very short-term forecasting (in minutes). Long-term forecasts influence the decisions on generation and transmission planning, which is used for determining the economical location, type, and size of the future power plants. Medium-term load forecasts are necessary for generation and transmission maintenance, and also for fuel scheduling. Accurate short-term load forecasts are necessary for unit commitment an economic dispatch. Very short-term load forecasting is for minutes ahead and is used for automatic generation control (AGC) [1]-[3]. Load forecasting is however a difficult task. First, because the load series is complex and exhibits several levels of

seasonality: the load at a given hour is dependent not only on the load at the previous hour, but also on the load at the same hour on the previous day, and on the load at the same hour on the day with the same denomination in the previous week. Secondly, because there are many important exogenous variables that must be considered, specially weather related variables. Most forecasting models and methods have already been tried out on load forecasting, with varying degrees of success. Some of the models reported in literatures are multiplicative autoregressive models, dynamic linear or nonlinear models, autoregressive models, and methods based on Kalman filtering, Box and Jenkins transfer functions ARMAX models, optimization techniques, nonparametric regression. Several research works have been carried out on the application of artificial intelligence (AI) techniques to the load forecasting problem. Various AI techniques reported in literatures are expert systems, fuzzy inference, fuzzy-neural models, artificial neural network (ANN). Among the different techniques on load forecasting, application of NN technology for load forecasting in power system has received much attention in recent years. The main reason of NN becoming so popular lies in its ability to learn complex and nonlinear relationships that are difficult to model with conventional techniques [1], [2].

casting and long-term forecasting. Market participants need to forecast short-term (mainly one day-ahead) prices to maximize their profits in spot markets. Accurate medium term price forecasts are necessary for successful negotiations of bilateral contracts between suppliers and consumer. Long-term price forecasts influence the decisions on transmission expansion and enhancement, generation augmentation, distribution planning and regional energy exchange. Electricity price forecasting models include statistical and non-statistical models. Time-series models, econometric models and intelligent system methods are the three main categories of statistical methods. Non-statistical methods include equilibrium analysis and simulation methods. Methods based on time-series or NN is more common for electricity price forecasting due to their flexibility and ease of implementation. NN approach based on similar days has been proposed to forecast day-ahead prices in the PJM market [5], [6]. The time-series techniques are successful in the areas where the frequency of the data is low, such as weekly patterns, but they can be problematic when there are rapid variations and highfrequency changes of the target signal. Hence, there is a need of more efficient forecast tool capable of learning complex and non-linear relationships that are difficult to model with conventional techniques.

B. Price forecasting The main objective of electricity market is to maximize profits. Forecasting loads and prices in electricity markets are mutually intertwined activities, and error in load forecasting will propagate to price forecasting. Electricity price has its special characteristics. The main features that make it so specific are at least three. One of them is its non-storability of power, which implies that prices are strongly dependent on the power demand. Another characteristic is the seasonal behavior of the electricity price at different level (daily, weekly and annual seasonality) and the third one is related to the question of its transportability. Furthermore, electricity price can rise by tens of or even hundreds of times of its normal value showing one of the greatest volatilities among all commodities. Electricity cannot be transported from one region to another one because of existing bottle-necks or limited transportation capacity. Application of forecasting methods common in other commodity markets, can have a large error in forecasting the price of electricity [5]. In most competitive electricity markets, the hourly price series have the characteristics such as volatility, non-stationary properties, multiple seasonality, spikes and high frequency. These characteristics are due to events that may occur alternatively in a market. For instance, a price spike that is a randomized event can be caused by market power, and also by unexpected incidents such as transmission congestion, transmission contingency and generation contingencies. It can also be influenced by other factors such as fuel prices, generation unit operation costs, weather conditions, and probably the most theoretically significant factor, the balance between overall system supply and demand. Applications of electricity price forecasting fall into different time horizons: short-term forecasting, medium-term fore-

C. Wind power prediction One of the fundamental problems faced by power system operators is the variability and non-schedulable nature of wind farm power generation. These inherent characteristics of wind power have both technical and commercial implications for efficient planning and operation of power systems. Wind power prediction systems provide the information how much wind power can be expected at which point of time in the next few days. Wind power forecasting is one of the most critical aspects in wind power integration and operation. It is needed to estimate the long, medium, and short-term power production. The long-term forecast is required during the planning stage, while the medium and short-term forecasts are needed in the generation commitment and market operation. Long-term wind power forecasting is based on long term wind patterns, while medium and short-term forecasts are generally for a few days (depends on the market operation, generally between one and three days), and hours to a few minutes, respectively [7]. When considering the problem of wind power forecasting, a number of factors need to be considered. The first consideration is the prediction horizon or forecasting time frame of interest. The broad timescales can be considered as [8]: (i) Turbulence (1 second−30 minutes); (ii) Synoptic Scale in the Spectral Gap (30 minutes−6 hours); (iii) Synoptic Scale (6 hours−7 days); and (iv) Climatic Scale (months to years). A wind forecasting time scale of less than 30 minutes is referred to as the turbulence time scale or more generally as the very short-term time scale. Various studies have been conducted on power fluctuations from large wind farms and their effects on power system operations. Large ramp variations in the very short-term time scale can have significant impacts on both power system security and (depending on the bidding and dispatch inter-

vals involved) on trading in deregulated electricity markets. The importance of achieving the best possible wind power forecasting accuracy in the very short-time scale is thus of paramount importance during significant large ramp events or periods of high volatility in wind farm power output [8]. In addition, wind power − electric power generated from wind kinetic energy − possesses unique characteristics and attributes that differentiate it from fossil-based electric power. Unlike fossil- based power, where the rate of energy throughput is completely controllable, wind power is intermittent, variable, and non-dispatchable. Indeed, wind generation could vary according to diurnal heating and cooling patterns or suddenly increase with a storm front. Without an energy storage system, wind energy being converted into electric power has to be consumed immediately. As a result, the economic value of wind generation is dependent on the relative synchronized timing of the wind and load patterns. During the on-peak period of the day, the production of wind generation commands a high value. While during off-peak periods, wind generation may provide very little value or could even be curtailed when there is no load to serve. Furthermore, wind power generation does not lend itself readily to participate in the traditional generation scheduling process where controllable generators are scheduled to meet a variable load. Generation scheduling process with wind power must take into account the variability and intermittency characteristics. Therefore, certain power system resources must be allocated separately to hedge against unavailability and variability of wind power during a low or no wind condition. These additional reserves increase the overall generation costs [8]. Several techniques have been identified for wind forecasting. These techniques can be categorized into numeric weather prediction (NWP) methods, statistical methods, methods based upon NNs, and hybrid approaches. Numerical weather prediction (NWP) based techniques are well established for wind parameter forecasting with a prediction horizon of several hours or more. NWP methods could be the most accurate technique for short-term forecasting. However, in general, statistical, NN methods, or several advanced hybrid methods based on observations perform more accurately over the very short-term forecast range. In general, forecasting techniques for very short-term wind power prediction use recent historical data as inputs to suitably structured models. These techniques include the simple persistence approach, classical linear statistical models such as Moving Average (MA), Auto-Regressive Moving Average (ARMA) and the Box-Jenkins approach based on AutoRegressive Integrated Moving Average (ARIMA) or seasonally adjusted ARIMA models, also known as SARIMA models. The statistical time series and NN methods are mostly aimed at short-term predictions. Typical time series models are developed based on historical values. They are easy to model and capable to provide timely prediction. In several predictions, they use the difference between the predicted and actual wind speeds in the immediate past to tune the model parameters. The advantage of the NN is to learn the relationship between inputs and outputs by a non-statistical approach.

Fig. 1. Six hour ahead load forecasting (Monday, September 01−Sunday, September 07, 2003).

III. C ASE S TUDY R ESULTS The case study results presented in this paper mainly focus on short-term load and price forecasting, and very short-term wind power prediction. The results are based on the authors’ published works. A. Load forecasting results The previous works done by authors in the area of shortterm load forecasting are found in [2], [4] where the authors have proposed NN technique based on SD method. SD method adopts the information of the days being similar to that of the forecast day. According to similar days method, selection of similar load days corresponding to forecast day is performed by adopting the Euclidean norm equation [2]. Euclidean norm with weighted factors is used to evaluate the similarity between a forecast day and searched previous days. The smaller the Euclidean, the better the evaluation of similar days. Short-term load forecasting was carried out based on different time frames, e.g., [4] deals with several-hour-ahead electric load forecasting in which authors have presented oneto-six hour ahead load forecasting using NNs using the case study of Victorian electricity market. The actual and forecast load curves for six-hour-ahead load forecasting are presented in Fig. 1 where we can observe an improved accuracy in forecasting as the MAPE value by using NN (1.30%) is better compared to SD approach (1.74%). It is also to be noted that one to six hour ahead load forecast errors (MAPE) range from 0.56% to 1.30% in reference [4]. Another work on next day load curve forecasting was presented in reference [2] where the authors have proposed load forecasting using hybrid correction method, which is a combination of NN and fuzzy logic using the case study of Okinawa Electric Power Co., Japan. Reference [2] contributes to day-ahead load forecast methodology, especially as it shows how to reduce neural network forecast error over the test period by 23% through the application of fuzzy logic correction, which can be observed in Fig. 2.

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Fig. 2. Forecasting results (Monday, July 21, 1997: Substitute holiday). (a) Forecasted load curves [MW], (b) forecast error [%].

B. Price forecasting results The price forecasting result presented in this paper is based on the authors previous work to forecast day-ahead electricity price in the PJM market using NN model integrated with SD method [5]. In the developed price prediction method, dayahead electricity price is obtained from the neural network that modifies the price curves obtained by averaging selected number of similar price days corresponding to forecast day, i.e., two procedures were analyzed: 1) prediction based on averaging prices of similar days and 2) prediction based on averaging prices of similar days plus neural network refinement. The developed multi-layer feed-forward NN model was trained and tested using the data (from January 1, 2004 to May 31, 2006) derived from the PJM electricity market. Sets of data include hourly price and load data. Figure 3 shows the day-ahead price forecasting results for January 20, 2006. The forecast results obtained from the proposed NN are quite close to the actual LMP values. The prediction behavior of the proposed NN technique for this day is very appropriate with a daily mean absolute percentage error (MAPE) of only 6.93%, which is much lower than that

obtained using the similar days (SD) approach (13.90%). Figure 4 shows the weekly price forecasts during February 17, 2006, which is typically a low demand week. These forecasts are based on day-ahead and have been represented for a week. As it can be seen from Fig. 4 that the forecast results obtained from the proposed NN are close to the actual LMP values. Also, it can be observed that when price spikes appear, our model does not forecast price jumps as in last three days of this week. The weekly MAPE obtained from the NN approach is 7.66%, which is much lower than that obtained using the similar days method (12.80%). Daily and weekly MAPE values obtained from the selected day and week show that the NN technique outperforms the direct use of similar days method. C. Wind power prediction results The case study presented in [7] used a wind site in Tasmania as the data set, providing a 21-month time series in steps of 2.5 min. This was to be the forecast period as well. The application of a particular type of hybrid intelligent system called an Adaptive Neuro-Fuzzy Inference System (ANFIS) to very short term wind power prediction was investigated.

compared to persistence. Apart from the overall performance improvement for the entire test period, it was observed that the ANFIS model provided significantly better predictions than persistence for certain periods in the time series when the wind farm power output was rapidly increasing or decreasing. IV. C ONCLUSIONS

Fig. 5. Chart of prediction errors for various systems, tested over a period of eight months on a wind site in Tasmania, Australia.

This paper presented applications of machine learning techniques for forecasting loads and prices, and short-term wind power prediction in power systems. A brief overview and general background of different approaches and developments were discussed. The paper also underlined major challenges related to wind power prediction. The importance of forecasting loads and prices including their characteristics was discussed. The results of several case studies were presented and discussed. It was demonstrated that machine learning techniques could be applied to forecasting problems in power systems. R EFERENCES

Fig. 6. Snapshot of ANFIS model performance for 5 minute ahead wind power prediction at a US wind farm.

In order to optimize the performance of the ANFIS system, multiple architectures should be evaluated using the same data set [7]. A persistence model was also developed for comparison. Persistence is presently an industry benchmark for very short-term wind forecasting and so is the most indicative assessment. The ANFIS model was developed in several different formats. The ANFIS model design is flexible and capable of handling rapidly fluctuating data patterns [9], [10]. This was to highlight the usefulness of intermediary splines through data for very short-term forecasting. The results are shown in Fig. 5. The chart also includes the results from the persistence model. A useful comparison is available through considering the persistence results and the ANFIS model with no spline. The ANFIS model shows some improvement, in the order of 5%. In the case study as reported in [7], [9], a suitable ANFIS model configuration was found to provide an overall performance improvement of more than 8% over the industry standard persistence approach for five minute ahead predictions. Fig. 6 shows the snapshot of the ANFIS model performance

[1] H. S. Hippert, C. E. Pedreira, and R. C. Souza, “Neural networks for short-term load forecasting: A review and evaluation,” IEEE Trans. on Power Syst., vol. 16, no. 1, pp. 44−55, Feb. 2001. [2] T. Senjyu, P. Mandal, K. Uezato, and T. Funabashi,“Next day load curve forecasting using hybrid correction method,” IEEE Trans. on Power Syst., vol. 20, no. 1, pp. 102−109, Feb. 2005. [3] M. Shahidehpour, H. Yamin, and Z. Li, Market operations in electric power systems: forecasting, scheduling, and risk assessment. John Wiley & Sons, Inc., New York, 2002. [4] P. Mandal, T. Senjyu, and T. Funabashi,“Neural networks approach to forecast several hour ahead electricity prices and loads in deregulated market,” Energy Conversion and Management, vol. 47, Issues 15−16, pp. 2128−2142, Sep. 2006. [5] P. Mandal, T. Senjyu, N. Urasaki, T. Funabashi, and A. K. Srivastava, “A novel approach to forecast electricity price for PJM using neural network and similar days method,” IEEE Trans. on Power Syst., vol. 22, no. 4, pp. 2058−2065, Nov. 2007. [6] P. Mandal, A. K. Srivastava, M. Negnevitsky, and J.-W. Park, “Sensitivity analysis of neural network parameters to improve the performance of electricity price forecasting,” International Journal of Energy Research, vol. 33, no. 1, pp. 38−51, Jan. 2009. [7] C. W. Potter and M. Negnevitsky, “Very short-term wind forecasting for Tasmanian Power Generation,” IEEE Trans. on Power Syst., vol. 21, no. 2, pp. 965−972, May 2006. [8] M. Negnevitsky and P. Johnson, “Very short term wind power prediction: A data mining approach,” in Proc. IEEE Power and Energy Soc. General Meeting, pp. 1−3, Pittsburgh, USA, 2008. [9] P. Johnson, M. Negnevitsky, and K. M. Muttaqui, “Short-term wind power forecasting using adaptive neuro-fuzzy inference systems,” in Proc. Australian Universities Power Engineering Conference (AUPEC), Perth, Western Australia, 2007. [10] M. Negnevitsky, Artificial Intelligence: A Guide to Intelligent Systems. Second Edition, Addison Wesley, 2005.

V. B IOGRAPHIES Michael Negnevitsky (M’95-SM’07) received the B.S.E.E. (Hons.) and Ph.D. degrees from the Byelorussian University of Technology, Minsk, Belarus, in 1978 and 1983, respectively. Currently, he is Chair Professor in Power Engineering and Computational Intelligence and Director of the Centre for Renewable Energy and Power Systems at the University of Tasmania, Hobart, Australia. From 1984 to 1991, he was a Senior Research Fellow and Senior Lecturer in the Department of Electrical Engineering, Byelorussian University of Technology. After arriving in Australia, he was with Monash University, Melbourne, Australia. His interests are power system analysis, power quality, and intelligent systems applications in power systems. Dr. Negnevitsky is a Chartered Professional Engineer, Fellow of the Institution of

Engineers Australia. He is also Member of CIGRE AP C4 (System Technical Performance) and CIGRE AP C6 (Distribution Systems and Dispersed Generation), Australian Technical Committees, and CIGRE Working Group JWG C1/C2/C6.18 (Coping with Limits for Very High Penetrations of Renewable Energy), International Technical Committee.

Paras Mandal (SM’05-M’06) received his B.E. degree in Electrical and Electronics Engineering from Kuvempu University (now under Visveswariah Technological University), India in 1998; M.E. degree in the field of Energy, Economics and Planning from Asian Institute of Technology, Thailand in 2002; and Ph.D. degree from the University of the Ryukyus, Japan in 2005. He is presently a research fellow in the School of Engineering at the University of Tasmania, Hobart, Australia. From Nov. 2005 to July 2007, he was a JSPS postdoctoral fellow at the University of the Ryukyus. Then, he worked in the School of Engineering, Yonsei University, Seoul, South Korea as a Research Professor till January 2008. His research interests include application of artificial intelligence techniques to electricity load and price forecasting, power system modeling and power system deregulation. Dr. Mandal is a member of IEEE Power and Energy Society. Dr Mandal is a recipient of several awards and serves as a reviewer for IEEE Transactions on Power Systems, international journals and conferences.

Anurag K. Srivastava (SM’01-M’05) received his Ph.D. degree from Illinois Institute of Technology (IIT), Chicago, in 2005, M. Tech. from Institute of Technology, India in 1999 and B. Tech. in Electrical Engineering from Harcourt Butler Technological Institute, India in 1997. He is working as an Assistant research professor at Mississippi State University since September 2005. Before that, he worked as a research assistant and teaching assistant at IIT, Chicago, and as a Senior Research Associate in Electrical Engineering Department at the Indian Institute of Technology, Kanpur, India as well as a Research Fellow at Asian Institute of Technology, Bangkok, Thailand. His research interest includes power system security, power system deregulation, power system modeling, and artificial intelligent application in power system. Dr. Srivastava is a member of IEEE, IET, IEEE Power and Energy Society, ASEE, Sigma Xi and Eta Kappa Nu. He is a recipient of several awards and serves as a reviewer for IEEE Transactions on Power Systems, international journals and conferences.