EFuNN Based Forecasting of Electricity Price in Deregulated Market Scenario

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1 MIT International Journal of Electrical and Instrumentation Engineering, Vol. 3, No. 2, August 2013, pp EFuNN Based Forecasting of Electricity Price in Deregulated Market Scenario Jayashri Vajpai Associate Professor Electrical Engineering Department Faculty of Engineering, J.N.V. University, Jodhpur, Rajasthan, INDIA J.B. Arun Lecturer Teacher s Training Centre Government Polytechnic College Campus Jodhpur, Rajasthan, INDIA arun_jb@rediffmail.com ABSTRACT The electrical power industry is globally moving towards deregulation and open market operation. The electrical power is exchanged as a commodity and electricity price plays an important role in the process of exchange. Electricity price is primarily governed by the market supply and demand and the operating condition of transmission network. The market supply and demand is, in turn, affected by many factors, such as weather, economic situation, development planning, accidental failure, market designs, tariffs and other policies, pricing and bidding schemes, market power and gaming, etc. This problem involves modeling of chaotic or nonlinear dynamical time series, Neuro-fuzzy modeling techniques are hence harnessed for accurate results. The dynamic nature of these models allows incorporation of time varying characteristics of market and generation and embeds prior knowledge. The authors of this paper have hence applied evolving fuzzy neural network, an emerging neuro-fuzzy paradigm, for the modeling of spot price of electricity. The data from Spain for 2003 has been used for showing the effectiveness of the proposed technique. This forecasting methodology based on the evolving fuzzy neural networks and knowledge of time series of generation is expected to be useful for price bidding by generation companies and electricity retailers. Keywords: Electricity Market, Evolving Fuzzy Neural Networks, Neuro-Fuzzy Modeling, Power Market, Electricity Pricing, Time Series Modeling I. INTRODUCTION The deregulation of power sector has resulted in a paradigm shift from the centralised system approach to a competitive market. This has lead to the realisation of the importance of electricity price forecasting and further promoted a lot of research activity in the recent years. Power system planning and operation demands forecasting of electricity price over a wide variety of horizons such as hourly, daily average or monthly average. There is a need to forecast not only the general trend of this volatile market but also to predict the likely values of electricity prices one or two days ahead of trading. The stake holders in electricity price forecasting are the generation companies, the transmission companies, the distribution companies or retailers and the bulk consumers. Accurate forecasting leads to tremendous saving for all stake holders. Electricity price is primarily governed by the market supply and demand and the operating condition of transmission network. Further, the market supply and demand is affected by many factors, such as weather, economic situation, development planning, accidental failure, market designs, tariffs and other policies, pricing and bidding schemes, market power and gaming, etc. These factors influence the variations of electricity price and even slight change of any factor can lead to unpredictable variations of electricity price. The complex nature of dependence upon these factors and the randomness associated with the factors themselves results in a lot of uncertainty in the electricity prices. The uncertainty in the variations of electricity price makes its evaluation difficult. It is usually regarded as stochastic in nature and the probability theory and statistics is traditionally employed to investigate its distribution function and forecasting model. However, underlying order is found under the seemingly random behavior, that is, their processes are chaotic, not completely random and can be analyzed and forecasted successfully by using the chaos theory. It is extremely important to note that price forecasting involves modeling of nonlinear dynamical time series, which may sometimes be chaotic in nature. It is hence, necessary to apply adaptive and intelligent modeling techniques, such as neuro-fuzzy modeling for accurate results. The dynamic nature of these models allows incorporation of time varying characteristics of market and generation and embed prior knowledge. Neuro-fuzzy models are capable of adapting to the changing requirements of dynamic models. The authors of

2 MIT International Journal of Electrical and Instrumentation Engineering, Vol. 3, No. 2, August 2013, pp this paper have hence applied evolving fuzzy neural networks an emerging neuro-fuzzy paradigm for the modeling of spot price of electricity. The data from Spain for 2003 has been used for showing the effectiveness of the proposed technique. This forecasting methodology based on the evolving fuzzy neural networks and knowledge of time series of generation is expected to be useful for price biding by generation companies. II. STATE OF ART IN ELECTRICITY PRICE FORECASTING The effective price forecasting methods employ the following two major approaches: time series and simulation approaches. The former is based on the historical data of market prices, while the latter is an extension of traditional production costbased optimization approach. The simulation approach is based on the modeling of power system equipment and their cost information. In order to cover various possibilities, such as equipment failure, Monte-Carlo type stochastic simulations are often employed. The simulation methods can be computationally intensive because of the requirement of large amount of data on existing equipment. They would be effective if used by market operators and regulators who have an authority of collecting precise equipment and operational information. The time series approaches, include, linear regression-based models and non-linear heuristic models. Stochastic models are also used for time series data, but they are focused on valuing options, not on forecasting prices. Regression-based models include auto-regressive moving average (ARMA) models, its extension, auto-regressive integrated moving average (ARIMA) models and their variants. While these models aim at modeling and forecasting the changing price generalized autoregressive conditional heteroskedasticity (GARCH) aim at modeling the volatility of prices [1]. Diongue et al. have investigate conditional mean and conditional variance forecasts using a dynamic model following a k-factor GIGARCH process to provide the analytical expression of the conditional variance of the prediction error [2]. The have applied this method to the German electricity price market for the period August 15, 2000 December 31, 2002 and tested spot prices forecasts until one month ahead forecast. The forecasting performance of the model outperforms the SARIMA-GARCH benchmark model using the year 2003 as the out of sample. Non-linear heuristic models are mostly based on soft computing techniques. Soft computing is a consortium of emerging methodologies; viz., Fuzzy logic, neural networks and genetic algorithms. The first is primarily concerned with imprecision of data and information, the second with learning and the third with optimization. The implementation of soft computing is based on the exploitation of the tolerance for imprecision, uncertainty and partial truth to achieve tractability, robustness and low cost solution. The artificial neural networks (ANN), are capable of representing nonlinear input-output data relations with a structure of internal connections. Other heuristic models, fuzzy systems or evolutionary computation are often applied to extend the data feature representation capability of either regression-based or ANN models. In many applications, it is advantageous to exploit the synergism of these methods by using them in combination rather than alone. Examples of combined use include neuro-fuzzy, neurogenetic, genetic-fuzzy and neuro-fuzzy-genetic systems. Recent attempts aim at including the forecasts of confidence intervals of prices. A useful account of the electric price forecasting technique develop over the last two decades has been presented by Niimura [1]. The main focus of this survey is the study of methods of forecasting electrical energy prices on a pool-style energy forward market (typically, one-day ahead). The general procedure of price forecasting is summarized and factors to be considered have been discussed. They have concluded that although several useful tools for forecasting prices exist, every market is different. Therefore, there is no universal tool for price forecasting. It is hence recommended to pick one or more suitable tools for a specific market and the desired target for practical applications. Contreras et al. have presented a study of time series based methods for short-term demand and price forecasting i.e., ARIMA, dynamic regression and transfer function methodologies [3]. They have concluded that demand forecasting is best performed using time series procedures, Artificial Intelligence and combinations of several methods. Relevant conclusions are drawn on the effectiveness and flexibility of the considered techniques. In another paper Contreras et al. have proposed a method to predict next-day electricity prices based on the ARIMA methodology [4]. ARIMA techniques are used to analyze time series and in the past, have been mainly used for load forecasting, due to their accuracy and mathematical soundness. A novel technique to forecast day-ahead electricity prices based on the wavelet transform and ARIMA models has been presented by Conejo et al. [5]. The historical price series is decomposed using the wavelet transform and the future values are forecast using properly fitted ARIMA models. In turn, the ARIMA forecasts alongwith the inverse wavelet transform, allow reconstructing the future behavior of the price series and therefore forecasting prices. Garcia et al. have provided an approach to predict next-day electricity prices based on the Generalized Autoregressive Conditional Heteroskedastic (GARCH) methodology empirical results from the mainland Spain and California deregulated electricity-markets are discussed [6]. Chongqing et al. have presented the methodology of joint analysis of power system reliability and market price considering the uncertainties of load forecasts [7]. A stochastic load model is established to describe the uncertainty of future system load. Nogales et al. have provided two accurate and efficient price forecasting tools based on time series analysis: dynamic regression and transfer function models [8].

3 MIT International Journal of Electrical and Instrumentation Engineering, Vol. 3, No. 2, August 2013, pp Lin et al. have proposed that the accuracy of system marginal price (SMP) is important for bidding of generation companies [9]. Electrical load, historical value of SMP corresponding time and tendency of current SMP are regarded as three main influencing factors in estimating the next value of SMP. A recurrent neural network has been introduced to forecast the SMP, because it has an ability of mapping the dynamic power market. The genetic algorithm is used to obtain by combining binary encoding and real encoding. The methodologies discussed above have been applied mainly to Spain and California market. Dondo and El-Hawary have successfully shown how uncertainties in bus loads and/or the unavailability of sufficient information on system loading levels can be modeled using fuzzy based rules [10]. It can be concluded that the fuzzy approach provides a narrow range of real time electricity prices. The defuzzification rules allow the fuzzy electricity rates to be successfully converted to their crisp values. Warland et al. have addressed the problem of forecasting tariffs for the electricity market in power system with a considerable share of hydropower [11]. They have concluded that introduction of dynamic point tariffs for pricing of power transmission can result in considerable savings in losses and thus increase the social welfare. The example presented in this paper indicates potential savings in the range of 1 2% of optimal losses. A two-regime model with a Gaussian distribution in the spike regime has been developed by Bierbrauer et al. Furthermore, for short and medium-term periods the results obtained for German EEX Power market underpin the frequently stated hypothesis that electricity futures quotes are consistently greater than the expected future spot, a situation which is denoted as contango [12]. An intelligent time series model based on the Simultaneous Perturbation Stochastic Approximation (SPSA) and an error compensator has been developed by Ko et al. The SPSA based intelligent model is applied to predict the electricity market price in the Pennsylvania New Jersey Maryland (PJM) electricity market [13]. Chen et al. have developed a novel non-parametric approach for the modeling and analysis of electricity price curves by applying the manifold learning methodology. Locally Linear Embedding (LLE). The prediction method based on manifold learning and reconstruction has been employed to make shortterm and medium term price forecasts. This method not only performs accurately in forecasting one-day-ahead prices, but also has a great advantage in predicting one-week-ahead and one-month-ahead prices over other methods. The forecast accuracy is demonstrated by numerical results using historical price data taken from the Eastern U.S. electric power markets [14]. Weron and Misiorek compared the accuracy of 12 time series methods for short-term (day-ahead) spot price forecasting in auction-type electricity markets in an empirical paper. The methods considered include standard autoregression (AR) models and their extensions spike preprocessed, threshold and semiparametric autoregressions (i.e., AR models with non-parametric innovations) as well as mean-reverting jump diffusions. The methods are compared using a time series of hourly spot prices and system-wide loads for California, and a series of hourly spot prices and air temperatures for the Nordic market. They have found evidence that (i) models with system load as the exogenous variable generally perform better than pure price models, but that this is not necessarily the case when air temperature is considered as the exogenous variable; and (ii) semiparametric models generally lead to better point and interval forecasts than their competitors, and more importantly, they have the potential to perform well under diverse market conditions [15]. A three-layer BP (Back-Propagation) model has been designed by Xu and Nagasaka to train the historical data, then it was tested to predict both demand and price of electricity for Queensland electricity market of Australia [16]. Chogumaira and Hiyama have developed an artificial neural network, ANN, based approach for estimating short-term wholesale electricity prices using past price and demand data. The objective is to utilize the piecewise continuous nature of electricity prices on the time domain by clustering the input data into time ranges where the variation trends are maintained. Due to the imprecise nature of cluster boundaries a fuzzy inference technique is employed to handle data that lies at the intersections. Application of this model to the Australian New-South Wales electricity market data shows considerable improvement in performance compared with approaches that regard price data as a single continuous time series, achieving MAPE of less than 2% for hours with steady prices and 8% for the clusters covering time periods with price spikes [17]. Korniichuk has proposed a model for forecasting extreme electricity prices in real time (high frequency) settings. This model has ability to forecast electricity price exceedances over very high thresholds, where only a few (if any) observations are available. The model can also be applied for simulating times of occurrence and magnitudes of the extreme prices. A copula with a changing dependence parameter has been employed for capturing serial dependence in the extreme prices and the censored GPD for modeling their marginal distributions. An approach based on a negative binomial distribution has been proposed for modeling times of the extreme price occurrences. The model has been applied to electricity spot prices from Australia s national electricity market [18]. The authors of this paper have applied a new neurofuzzy modeling technique i.e., EFuNN for electricity price forecasting in the deregulated market. III. PROBLEM FORMULATION AND THE PROPOSED METHODOLOGY The basic concepts explained above can be applied for forecasting of the average cost of electric energy on daily

4 MIT International Journal of Electrical and Instrumentation Engineering, Vol. 3, No. 2, August 2013, pp basis. A standard database for the problem of this type along with results of forecasting by Fuzzy Wang-Mendel Model method is available on the internet for electric price forecasting for Spain in 2003 [19]. This dataset has 365 patterns with 6 inputs and one output. The inputs are the energy produced (in kwh) in Spain, for every day of the The data is available for the following categories: (1) Hydraulics, (2) Nuclear, (3) Coal (cob coal, importing coal, black and brown Lignite), (4) Fuel (fuel-oil and fuel/gas), (5) Gas and (6) Special regimen (Eolithic, solar, hydraulics minicentrals, minicentrals, etc). The output is the average per unit cost in Euros in the spot market. This application presents the design of an adaptive neurofuzzy system based on Kasabov s Evolving Fuzzy Neural Network (EFuNN) model [20]. EFuNN is a neuro-fuzzy structure that can evolve to learn the relational mapping existing between the input-output data pairs. It has five layers of neurons, viz., input layer, fuzzy input membership functions layer, rule node layer, fuzzy output membership functions layer and output layer as shown in Fig. 1. The evolving process begins with no rule nodes prior to learning and all of them are created during the evolving process. The nodes representing membership functions, the fuzzy rule neurons and connection weights can be modified during learning. Each input variable is represented by a group of spatially arranged fuzzy input layer neurons to represent a fuzzy quantisation of this variable, using different types of membership functions. The EFuNN can evolve very fast because it uses one pass training based on unsupervised reinforcement learning [21]. If the corresponding variable values for a given input vector values do not belong to any of the existing ones to a degree greater than membership threshold, new fuzzy input or output neurons can be created during the adaptation phase of an EFuNN. Fig. 1: An Evolving Fuzzy Neural Network Structure The initial values for the system parameters include number of membership functions, sensitivity threshold S and error threshold E. The process of learning commences with setting the first rule node to memorize the first example (x, y) W 1 (r 1 ) = x f and W 2 (r 1 ) = y f (1) The process is continued over presentations of input output pairs (x, y). The local normalized fuzzy distance D between x f and the existing rule node connections W 1 and the activation A 1 of the rule node layer is calculated. Then the closest rule node r k to the fuzzy input vector x f is found so that the input vector is in the receptive field of this rule node. The learning rules of EFuNN can be summarized as follows: If A 1 (r k ) < S (sensitivity threshold ) create a new rule node for (x f, y f ) Else, find the activation of the fuzzy output layer A 2 = W 2 * A 1 (1- D (W 1, x f ))) and the output error E rr = y y / N out If E rr > E create a new rule node to accommodate the current example (x f, y f ) Else, update W 1 (r j ) and W 2 (r j ) according to W 1 (r j ) = W 1 (r j ) + l 1 * ( W 1 (r j ) - x f ) (2) W 2 (r j ) = W 2 (r j ) + l 2 * (A 2 - y f ) * A 1 (r j ) (3) where l 1 and l 2 learning rates of rule nodes. Algorithm The basic steps in the EFuNN algorithm are shown below: 1. Propagate the current input vector through the network. 2. Find the highest activated rule node (the winner). 3. IF the maximum activation is less than the sensitivity threshold, add a node. ELSE evaluate the error between the calculated and the desired outputs. 4. IF the error over the desired output is greater than the error threshold, add a node. ELSE update the weights of the connections to the winning node. 5. Repeat for each training vector. The EFuNN has been applied successfully in a large number of applications for modeling and classification of complex relational data. It has been particularly successful for modeling of chaotic time series [22], [23], [24], [25]. The authors have now applied EFuNN for electric price forecasting. IV. RESULTS The dataset has 365 samples of datasets in all and 90% of these, i.e., 329 days datasets are used as training samples. The remaining 10% (36 Days) are used as testing samples. The governing parameters for the price modeling by EFuNN are found out by a method of experimentation and selection. The final parameter values used for EFuNN are as follows: Number of membership functions = 3 Sensitivity Threshold = 0.9 Error Threshold = 0.1 The actual and the forecasted values of electricity prices are shown in Fig. 2 and the error is shown in Fig. 3. Ten out of the test data along with their forecasted values are shown in Table I. The mean square error for this application was found to be This can be compared with the algorithm applied

5 MIT International Journal of Electrical and Instrumentation Engineering, Vol. 3, No. 2, August 2013, pp by Keel which is based on Fuzzy Wang-Mendel Model and gives mean square error as 0.30 on the same dataset, when 90% of data is used for training and 10% for testing [19]. However, EFuNN model does not require such a lot of data for training. Even when only 20% of data is used for training and 80% for testing, the mean square error is Hence, it can be concluded that EFuNN can be effectively used for the forecasting of electricity price in spot market. Fig. 2: Actual and Forecasted values of Electricity Price V. CONCLUSION This paper presents a neuro-fuzzy forecasting model to predict electricity prices based on time series analysis. The EFuNN model yields an error of 0.2 which is accurate enough to be used by producers to prepare their corresponding bidding strategies. However, the Spanish market shows volatility and hence unpredictability, due to a high proportion of outliers and a lesser degree of competition. Moreover, during peak hours the Spanish market shows even higher dispersion. This fact causes more uncertainty in periods of high demand, producing less accurate forecasts. Further, it can be pointed out that the ARIMA models to predict hourly prices in the electricity markets of Spain needs 5 hours to predict future prices [4], as opposed to the a few seconds needed by the EFuNN model. Hence, the proposed technique can also be used for on-line applications. The authors are presently engaged in the refinement of EFuNN modeling by determining the optimal values of the governing parameters with the help of genetic algorithm. Moreover, in the future, effort will be made for improving the model, by addressing influencing factors such as special treatment for weekend data (calendar effect) and the inclusion of exogenous variables (water storage, weather, etc.). The accuracy of forecasts by the proposed model is expected to be even better in the future, when new regulatory frameworks and the introduction of long-term contracts will hopefully change the behavior of day-ahead markets. Their impact on prices is still unknown and it is a relevant and important subject for future research work. REFERENCES Fig. 3: Error in Forecast of Electricity Price [1] T. Niimura, Forecasting Techniques for Deregulated Electricity Market Prices Extended Survey, in Proc. Power Systems Conference and Exposition, PSCE 06, 2006 IEEE PES Oct Nov , pp S.No. Hydraulics* Nuclear* Coal* Fuel Oil* Table I: Data, Actual and Forecasted Prices Gas* Special regimen* Actual Price in Euro Forecasted Error in Euro * Energy produced (in kwh) in Spain, for every day of the 2003.

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