Electric Load Forecast Using Combined Models with HP Filter-SARIMA and ARMAX Optimized by Regression Analysis Algorithm

Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 386925, 14 pages http://dx.doi.org/10.1155/2015/386925 Research Article Electric Load Forecast Using Combined Models with HP Filter-SARIMA and ARMAX Optimized by Regression Analysis Algorithm Cui Herui, Peng Xu, and Mu Yupei School of Economics and Management, North China Electric Power University, Baoding 071003, China Correspondence should be addressed to Peng Xu; Received 20 July 2015; Accepted 10 November 2015 Academic Editor: Akemi Gálvez Copyright © 2015 Cui Herui et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Electric load in summer has a significant cyclical trend with temperature effects. In general, the parameters of the SARIMA and the SMA turn out to be nonsignificant in most cases. To address this issue, the hybrid time series model is utilized to extract the spectrum sequences with different frequencies. The original electric load series are first decomposed into the trend sequence “G” and the cycle sequence “C.” After that, a revised ARMAX model is proposed to deal with the two divided sequences. Finally, the combined models are tested by case study. The case study on electric load forecast in one city from China shows that the proposed model outperforms other four comparative models in terms of prediction accuracy. It proves that the combined model proposed by the authors is more accurate than those based on a single forecasting method. 1. Introduction Load forecast is mainly used to predict power load in the next few days [1, 2], which plays an important role in the modern electricity Demand Side Management (DSM). Accurate forecast on short-term electric load is a crucial element to the dynamic operations of Advanced Electricity Demand Side Management (EDSM) and Advanced Power Information Systems (APIS) in improving the efficiency and the safety of power grid. To a certain extent, mediumterm power load is affected by seasonal factors, summer temperature, and consumption peaks due to unexpected cases. In general, high temperature in summer may form a high “air conditioning load.” With the rise of temperature, air conditioning load increases as well. Temperature data fluctuate widely in summer. Electric load also changes a lot with temperature. Theoretically, it is difficult to forecast mutable data, such as summer air conditioning load. To address this problem, this paper proposes the combined model with HP Filter-SARIMA and ARMAX model optimized by regression analysis algorithm. Over the past decade, many forecasting methods have been put forward, such as time series, gray model, SVM, and artificial neural networks (ANN) [3]. Azadeh et al. explored seasonal fluctuation and nonlinearity in forecasting based on the fuzzy system and data mining techniques to analyze monthly electricity demand in Iran. This model is established on well developed statistical theories to show explicit relationships between input data and outputs. However, the SARIMA model does not perform well when electric power deviates greatly from the normal weekly pattern. It cannot react under abnormal load conditions before the flow deviation is detected [4]. Hamzacebi and Es predicted annual electricity consumption by the optimization GM(1, 1) model, which is more effective in analyzing the long-term trend but has less effect in seasonal variation [5]. Zhu et al. used the HP filter to decompose the GDP sequence into the tendency item and the cyclical item [6]. He et al. also took advantage of the HP filter in energy price analysis to study the synchronization between the markets home and abroad [7]. Zhang et al. employed four improved adaptive coefficient approaches optimized by particle swarm optimization (PSO) to forecast daily mean wind speed, the simulated results of which showed that the PSO obtained an observable improvement in forecasting performance [8]. Guo et al. proposed a modified EMD-FNN model by combining 2 empirical mode decomposition (EMD) with the ensemble learning paradigm of feedforward neural network (FNN), which had better accuracy than that based on the basic FNN and unmodified EMD-FNN [9]. The multivariate ARIMAX model is hypothesized to improve the one-step-ahead forecasting accuracy of the univariate SARIMA model. Bierens and Broersma used the ARMAX model to study the relation between unemployment and interest rate. They found that the relationship is not confined only to the Netherlands; but it holds for USA, Canada, Japan, Germany, UK, and France [10]. Bordignon et al. analyzed combined versus individual forecasts for British electricity price prediction. It is found that combined forecasts are more accurate than or at least equivalent to individual ones [11]. Yan and Chowdhury adopted a hybrid midterm forecasting model based on the combination of both least squares support vector machine (LSSVM) and autoregressive moving average with external input (ARMAX) modules to forecast electricity market clearing price (MCP). It is shown that the proposed hybrid model can improve forecasting accuracy compared with the forecasting model using a single LSSVM [12]. Wang et al. proposed a two-stage model in estimating value-at-risk (VaR) based on ARMAXGARCHSK and extreme value theory (EVT). It is shown in the empirical analysis that the ARMAX-GARCHSK-EVT model can rapidly reflect the most recent and relevant change of electricity prices, with accurate forecasts of VaR at all confidence levels, thereby presenting better dynamic characteristics [13]. Yang et al. proposed a new evolutionary programming (EP) approach to identify the autoregressive moving average with exogenous variable (ARMAX) model for hourly load demand forecasts from one day to one week ahead. The developed EP based load forecasting algorithm is verified by different types of data for Taiwan Power (Taipower) system and substation load as well as temperature values [14]. Huang et al. proposed a new particle swarm optimization (PSO) approach to identify the autoregressive moving average with exogenous variable (ARMAX) model for load forecasts. It is indicated by the testing results that the proposed PSO has the characteristic of high-quality solution, superior convergence, and shorter computation time [15]. Wangdi et al. adapted ARIMAX model to determine predictors of malaria in the coming month. ARIMAX model is an extension of ARIMA modeling in an attempt to predict the malaria cases using the climatic factors and the number of cases in the previous month. The predictors in the model include the number of cases in the previous month, mean maximum and minimum temperature, relative humidity, and rainfall lagged in a month. It is shown by test results that prediction accuracy has been greatly improved [16]. The above forecasting methods ha (...truncated)