Electricity Price Prediction Research Articles

Multivariate Exponential Smoothing and Dynamic Factor Model Applied to Hourly Electricity Price Analysis

Thanks to its very simple recursive computing scheme, exponential smoothing has become a popular technique to forecast time series. In this work, we show the advantages of its multivariate version and present some properties of the model, which allows us to perform a dynamic factor analysis. This analysis leads to a simple methodology to reduce the number of parameters (useful when the dimension of observations is large) via a linear transformation that decomposes the multivariate process into independent univariate exponential smoothing processes, characterized by a single smoothing parameter that goes from zero (white-noise process) to one (random walk process). A computer implementation of the expectation-maximization (EM) algorithm has been built for the maximum likelihood estimation of the models. The practicality of the method is demonstrated by its application to hourly electricity price predictions in some day-ahead markets, such as Omel, Powernext, and Nord Pool markets, whose forecasts are given as examples. This article has supplementary material online.

Model Predictive Control for Market-Based Demand Response Participation

In this study, we investigate the maximum possible profit for a commercial office building participating in New York’s Day-Ahead Demand Response (DADR) program. We formulate an optimal control problem, assuming perfect knowledge of future weather, occupancy, and day-ahead electricity price predictions to examine this potential benefit. Then, a practical control strategy based upon the framework of Model Predictive Control (MPC) is proposed, which enables a building to participate in the DADR program. The controller decides once every day, whether or not to participate in the Demand Response (DR) event, and then optimizes the electric consumption to increase savings. A simulation study is carried out using a building model extracted from an EnergyPlus model, real measured weather data, and real day-ahead spot market price data for New York. Savings in the range of 23% to 33% are reported.

A hybrid ARFIMA and neural network model for electricity price prediction

In the framework of competitive electricity market, prices forecasting has become a real challenge for all market participants. However, forecasting is a rather complex task since electricity prices involve many features comparably with those in financial markets. Electricity markets are more unpredictable than other commodities referred to as extreme volatile. Therefore, the choice of the forecasting model has become even more important. In this paper, a new hybrid model is proposed. This model exploits the feature and strength of the Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) model as well as the feedforward neural networks model. The expected prediction combination takes advantage of each model’s strength or unique capability. The proposed model is examined by using data from the Nordpool electricity market. Empirical results showed that the proposed method has the best prediction accuracy compared to other methods.

An Empirical Comparison of Alternate Schemes for Combining Electricity Spot Price Forecasts

In this paper we investigate the use of forecast averaging for electricity spot prices. While there is an increasing body of literature on the use of forecast combinations, there is only a small number of applications of these techniques in the area of electricity markets. In this comprehensive empirical study we apply seven averaging and one selection scheme and perform a backtesting analysis on day-ahead electricity prices in three major European and US markets. Our findings support the additional benefit of combining forecasts for deriving more accurate predictions, however, the performance is not uniform across the considered markets. Interestingly, equally weighted pooling of forecasts emerges as a viable robust alternative compared with other schemes that rely on estimated combination weights. Overall, we provide empirical evidence that also for the extremely volatile electricity markets, it is beneficial to combine forecasts from various models for the prediction of day-ahead electricity prices. In addition, we empirically demonstrate that not all forecast combination schemes are recommended.

Day-ahead electricity prices forecasting by a modified CGSA technique and hybrid WT in LSSVM based scheme

At the present time, day-ahead electricity market is closely associated with other commodity markets such as fuel market and emission market. Under such an environment, day-ahead electricity price forecasting has become necessary for power producers and consumers in the current deregulated electricity markets. Seeking for more accurate price forecasting techniques, this paper proposes a new combination of a Feature Selection (FS) technique based mutual information (MI) technique and Wavelet Transform (WT) in this study. Moreover, in this paper a new modified version of Gravitational Search Algorithm (GSA) optimization based chaos theory, namely Chaotic Gravitational Search Algorithm (CGSA) is developed to find the optimal parameters of Least Square Support Vector Machine (LSSVM) to predict electricity prices. The performance and price forecast accuracy of the proposed technique is assessed by means of real data from Iran’s, Ontario’s and Spain’s price markets. The simulation results from numerical tables and figures in different cases show that the proposed technique increases electricity price market forecasting accuracy than the other classical and heretical methods in the scientific researches.

A New Recursive Dynamic Factor Analysis for Point and Interval Forecast of Electricity Price

The functional principal component analysis (FPCA) is a recent tool in multivariate statistics and it has been shown to be effective for electricity price forecasting. However, its online implementation is expensive, which requires the computation of eigen-decomposition at each update. To reduce the arithmetic complexity, we propose a recursive dynamic factor analysis (RDFA) algorithm where the PCs are recursively tracked using efficient subspace tracking algorithm while the PC scores are further tracked and predicted recursively using Kalman filter (KF). From the latter, the covariance and hence the interval of the forecasted electricity price can be estimated. Advantages of the proposed RDFA algorithm are the low online complexity, and the availability of the prediction interval thanks to the KF framework. Furthermore, a robust extension is proposed to tackle possible non-Gaussian variation. Finally, the RDFA algorithm can be extended to predict electricity price in a longer period using a multi-factor model by capturing trends in different time horizon. Experimental results on the New England and Australian datasets show that the proposed RDFA approach is able to achieve better prediction accuracy than other conventional approaches. It thus serves as an attractive alternative to other conventional approaches to forecast electricity price and other related applications because of its low complexity, efficient recursive implementation and good performance.

Optimal Energy Management of Wind-Battery Hybrid Power System With Two-Scale Dynamic Programming

This study is concerned with the optimal energy management for a wind-battery hybrid power system (WBHPS) with local load and grid connection, by including the current and future information on generation, demand, and real-time utility price. When applying typical dynamic optimization schemes to such a problem with a single time scale, the following dilemma usually presents: it is more beneficial to plan the (battery) storage setpoint trajectory for the longer horizon, while prediction of renewable generation, utility price, and load demand is more accurate for the shorter term. To relieve such conflict, a two-scale dynamic programming (DP) scheme is applied based on multiscale predictions of wind power generation, utility price, and load. A macro-scale dynamic programming (MASDP) is first performed for the whole operational period, based on long-term ahead prediction of electricity price and wind energy. The resultant battery state-of-charge (SOC) is thus obtained as the macro-scale reference trajectory. As the operation proceeds, the micro-scale dynamic programming (MISDP) is applied to the short-term interval based on short-term three-hour ahead predictions. The MASDP battery SOC trajectory is used as the terminal condition for the MISDP. Simulation results show that the proposed method can significantly decrease the energy cost compared with the single scale DP method.

Solar feed-in tariffs and the merit order effect: A study of the German electricity market

Abstract This study investigates the merit order effect (MOE) of the recent years' implementation of solar power in Germany. Market clearing electricity prices and production levels are compared for the years 2009–2011, and a model for the relationship between the electricity price and price sensitive electricity production is developed and applied to predict electricity prices in Germany from July 2010 to July 2011 with and without solar electricity generation (SEG). The results show that the SEG has caused a 7% reduction in average electricity prices for this period. The average daily maximum price and daily price variation are also found to decrease, by 13% and 23%, respectively. When taking the MOE into account the net consumer's cost of the solar feed-in tariff (FIT) system is found to be 23% less than the charge listed in the electricity bill. The German FIT policy for solar power has been subject to considerable public debate, and a common argument brought up in disfavor of the system is the high cost for the consumers. In this study we demonstrate the importance of including the MOE when evaluating the total costs and benefits of the FIT policy mechanism.

A proposed grey model for short-term electricity price forecasting in competitive power markets

In order to improve the performance of traditional grey models for short-term electricity price prediction in competitive power markets, a novel grey model, named PGM(1,2,a,b), is proposed in this paper. In the proposed model, the reference sequence is determined with correlation method. Furthermore, considering the limitation of the least square method (LSM), particle swarm optimization algorithm (PSO) is adopted to identify the parameters instead of LSM. To demonstrate the superiority of the proposed model, public available data coming from Nordpool, California, and Ontario power markets were used for training and testing. Simulation results show that the proposed model is capable of forecasting short-term electricity price efficiently and accurately.

Day-ahead electricity price forecasting by a new hybrid method

Electricity price forecasting has become necessary for power producers and consumers in the current deregulated electricity markets. Seeking for more accurate price forecasting techniques, this paper proposes a new hybrid method based on wavelet transform (WT), autoregressive integrated moving average (ARIMA) and least squares support vector machine (LSSVM) optimized by particle swarm optimization (PSO) to predict electricity prices. The proposed method is examined by using the data from New South Wales (NSW) of Australian national electricity market. Empirical testing indicates that the proposed method can provide more accurate and effective results than the other price forecasting methods.

A new feature selection algorithm and composite neural network for electricity price forecasting

In a competitive electricity market, the forecasting of energy prices is an important activity for all the market participants either for developing bidding strategies or for making investment decisions. In this paper, a new forecast strategy is proposed for day ahead prediction of electricity price, which is a complex signal with nonlinear, volatile and time dependent behavior. Our forecast strategy includes a new two stage feature selection algorithm, a composite neural network (CNN) and a few auxiliary predictors. The feature selection algorithm has two filtering stages to remove irrelevant and redundant candidate inputs, respectively. This algorithm is based on mutual information (MI) criterion and selects the input variables of the CNN among a large set of candidate inputs. The CNN is composed of a few neural networks (NN) with a new data flow among its building blocks. The CNN is the forecast engine of the proposed strategy. A kind of cross-validation technique is also presented to fine-tune the adjustable parameters of the feature selection algorithm and CNN. Moreover, the proposed price forecast strategy is equipped with a few auxiliary predictors to enrich the candidate set of inputs of the forecast engine. The whole proposed strategy is examined on the PJM, Spanish and Californian electricity markets and compared with some of the most recent price forecast methods.

Neural-wavelet Approach for Short Term Price Forecasting in Deregulated Power Market

This paper proposes designing a model using artificial neural network (ANN) and wavelet techniques to increase the accuracy of short term price forecast in the electricity market. The prior electricity price data are treated as time series. They are decomposed into several wavelet coefficient series using the wavelet transform technique known as Discrete Wavelet Transform (DWT), while the forecast model is based on wavelet multi-resolution (MR) decomposition. The wavelet coefficient series are used to train the artificial neural network and used as the inputs to the ANN for electricity price prediction. The Scale Conjugate Gradient (SCG) algorithm is used as the learning algorithm for the ANN. To get the final forecast data, the outputs from the ANN are recombined using the same wavelet technique. The model was evaluated with electricity price data of New South Wales Australia for the year 2008. Empirical results indicate that the WT-ANN combination model improves the price forecasting accuracy.

Econometric Estimation of Spatial Patterns in Electricity Prices

Information about the spatial structure of the transmission grid is relevant to understanding and predicting electricity prices, but this information has not been incorporated into empirical models of electricity prices in the literature. We propose the use of spatial econometric panel methods, discuss their formal characteristics in the context of electricity price data, and provide an application to a panel of PJM price data. Our econometric model includes a simple representation of the transmission system, and provides information about the effect of system constraints on the extent of electricity market integration. Empirical results confirm the existence of spatial patterns in electricity prices and illustrate their impact on estimation, forecasting, and interpolation.

Application of a new hybrid neuro-evolutionary system for day-ahead price forecasting of electricity markets

In this paper, a new forecast strategy is proposed for day-ahead prediction of electricity prices, which are so valuable for both producers and consumers in the new competitive electric power markets. However, electricity price has a nonlinear, volatile and time dependent behavior owning many outliers. Our forecast strategy is composed of a preprocessor and a Hybrid Neuro-Evolutionary System (HNES). Preprocessor selects the input features of the HNES according to MRMR (Maximum Relevance Minimum Redundancy) principal. The HNES is composed of three Neural Networks (NN) and Evolutionary Algorithms (EA) in a cascaded structure with a new data flow among its building blocks. The effectiveness of the whole proposed method is demonstrated by means of real data of the PJM and Spanish electricity markets. Also, the proposed price forecast strategy is compared with some of the most recent techniques in the area.

Design of input vector for day-ahead price forecasting of electricity markets

In new deregulated electricity market, price forecasts have become a fundamental input to an energy company’s decision making and strategy development process. However, the exclusive characteristics of electricity price such as non-stationarity, non-linearity and time-varying volatile structure present a number of challenges for this task. In spite of all performed research on this area in the recent years, there is still essential need for more accurate and robust price forecast methods. Besides, there is a lack of efficient feature selection technique for designing the input vector of electricity price forecast. In this paper, a new two-stage feature selection algorithm composed of modified relief and mutual information (MI) techniques is proposed for this purpose. Moreover, cascaded neural network (CNN) is presented as forecast engine for electricity price prediction. The CNN is composed of cascaded forecasters where each forecaster is a neural network (NN). The proposed feature selection algorithm selects the best set of candidate inputs which is used by the CNN. The proposed method is examined on PJM, Spanish and Ontario electricity markets and compared with some of the most recent price forecast techniques.

An Effort to Optimize Similar Days Parameters for ANN-Based Electricity Price Forecasting

This paper presents a sensitivity analysis of similar days (SD) parameters to increase the accuracy of artificial neural network (ANN) and SD-based short-term price forecasting. Work presented in this paper is an extended version of previous works done by the authors to integrate ANN and SD method for predicting electricity price. The focus here is on sensitivity analysis of SD parameters while keeping the parameters same for ANN to forecast hourly electricity prices in the Pennsylvania-New Jersey-Maryland (PJM) (regional transmission organization in northeast America) electricity market. Several cases are simulated by choosing (a) two, (b) three, (c) four, and (d) five SD parameters to calculate the norm. In addition, sensitivity analysis has been carried out by changing the time framework of SD (d = 15, 30, 45, 60) and the number of selected similar price days (N = 5, 10). From sensitivity analysis, it is identified that the optimized mean absolute percentage error (MAPE) is obtained using case-c with d = 30 and N = 10. MAPE of reasonably small value, along with forecast mean square error and mean absolute error of around 2$/MWh and 1$/MWh, is obtained for the PJM data, which has correlation coefficient of determination (R2) of 0.7758 between load and electricity price. Numerical results show that forecasts generated by the developed ANN model based on the optimized case are accurate and efficient.

Multi-step ahead forecasts for electricity prices using NARX: A new approach, a critical analysis of one-step ahead forecasts

The prediction of electricity prices is very important to participants of deregulated markets. Among many properties, a successful prediction tool should be able to capture long-term dependencies in market’s historical data. A nonlinear autoregressive model with exogenous inputs (NARX) has proven to enjoy a superior performance to capture such dependencies than other learning machines. However, it is not examined for electricity price forecasting so far. In this paper, we have employed a NARX network for forecasting electricity prices. Our prediction model is then compared with two currently used methods, namely the multivariate adaptive regression splines (MARS) and wavelet neural network. All the models are built on the reconstructed state space of market’s historical data, which either improves the results or decreases the complexity of learning algorithms. Here, we also criticize the one-step ahead forecasts for electricity price that may suffer a one-term delay and we explain why the mean square error criterion does not guarantee a functional prediction result in this case. To tackle the problem, we pursue multi-step ahead predictions. Results for the Ontario electricity market are presented.

Sensitivity analysis of neural network parameters to improve the performance of electricity price forecasting

This paper presents a sensitivity analysis of neural network (NN) parameters to improve the performance of electricity price forecasting. The presented work is an extended version of previous works done by authors to integrate NN and similar days (SD) method for predicting electricity prices. Focus here is on sensitivity analysis of NN parameters while keeping the parameters same for SD to forecast day-ahead electricity prices in the PJM market. Sensitivity analysis of NN parameters include back-propagation learning set (BP-set), learning rate (η), momentum (α) and NN learning days (dNN). The SD parameters, i.e. time framework of SD (d=45 days) and number of selected similar price days (N=5) are kept constant for all the simulated cases. Forecasting performance is carried out by choosing two different days from each season of the year 2006 and for which, the NN parameters for the base case are considered as BP-set=500, η=0.8, α=0.1 and dNN=45 days. Sensitivity analysis has been carried out by changing the value of BP-set (500, 1000, 1500); η (0.6, 0.8, 1.0, 1.2), α (0.1, 0.2, 0.3) and dNN (15, 30, 45 and 60 days). The most favorable value of BP-set is first found out from the sensitivity analysis followed by that of η and α, and based on which the best value of dNN is determined. Sensitivity analysis results demonstrate that the best value of mean absolute percentage error (MAPE) is obtained when BP-set=500, η=0.8, α=0.1 and dNN=60 days for winter season. For spring, summer and autumn, these values are 500, 0.6, 0.1 and 45 days, respectively. MAPE, forecast mean square error and mean absolute error of reasonably small value are obtained for the PJM data, which has correlation coefficient of determination (R2) of 0.7758 between load and electricity price. Numerical results show that forecasts generated by developed NN model based on the most favorable case are accurate and efficient. Copyright © 2008 John Wiley & Sons, Ltd.

Electricity price forecasting through transfer function models

Forecasting electricity prices in presentday competitive electricity markets is a must for both producers and consumers because both need price estimates to develop their respective market bidding strategies. This paper proposes a transfer function model to predict electricity prices based on both past electricity prices and demands, and discuss the rationale to build it. The importance of electricity demand information is assessed. Appropriate metrics to appraise prediction quality are identified and used. Realistic and extensive simulations based on data from the PJM Interconnection for year 2003 are conducted. The proposed model is compared with naïve and other techniques.