Electric Load Forecasting Based on Statistical Robust Methods

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, NO. 3, AUGUST 2011
Electric Load Forecasting Based on Statistical Robust Methods
Yacine Chakhchoukh, Member, IEEE, Patrick Panciatici, Member, IEEE, and Lamine Mili, Senior Member, IEEE
Abstract—In this paper, the stochastic characteristics of the electric consumption in France are analyzed. It is shown that the load time series exhibit lasting abrupt changes in the stochastic pattern, termed breaks. The goal is to propose an efficient and robust load forecasting method for prediction up to a day-ahead. To this end, two new robust procedures for outlier identification and suppression are developed. They are termed the multivariate ratio-ofmedians-based estimator (RME) and the multivariate minimumHellinger-distance-based estimator (MHDE). The performance of the proposed methods has been evaluated on the French electric load time series in terms of execution times, ability to detect and suppress outliers, and forecasting accuracy. Their performances are compared with those of the robust methods proposed in the literature to estimate the parameters of SARIMA models and of the multiplicative double seasonal exponential smoothing. A new robust version of the latter is proposed as well. It is found that the RME approach outperforms all the other methods for “normal days” and presents several interesting properties such as good robustness, fast execution, simplicity, and easy online implementation. Finally, to deal with heteroscedasticity, we propose a simple novel multivariate modeling that improves the quality of the forecast. Index Terms—Outliers, robustness, SARIMA models, shortterm load forecasting.
I. INTRODUCTION HE electric load forecasting is a major endeavor carried out on a daily basis by RTE, a company that manages and operates the electric power transmission system in France. It helps RTE to make important decisions regarding the security and reliability of the French electric power transmission system. There is a very extensive literature on all three load forecasting problems, namely long-term, medium-term, and shortterm load forecasting. The reader is referred to [1]–[4] for a general review of the proposed methodologies and techniques. This paper is mainly concerned with short-term load forecasting. The
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Manuscript received May 05, 2009; revised October 18, 2009, April 01, 2010, May 19, 2010, and July 19, 2010; accepted August 12, 2010. Date of publication October 28, 2010; date of current version July 22, 2011. Paper no. TPWRS00292-2009. Y. Chakhchoukh was with RTE, DMA-Gestionnaire du Réseau de Transport d’Electricité and L2S-Laboratoire des Signaux et Systèmes (CNRS-University Paris-Sud XI-Supélec), Paris, France, and is now with the Signal Processing Group at the Institute of Telecommunications, Technische Universität Darmstadt, Darmstadt, Germany (e-mail: ychakh@spg.tu-darmstadt.de). P. Panciatici is with RTE, DMA, 78005 Versailles cedex, France (e-mail: patrick.panciatici@). L. Mili is with the Bradley Department of Electrical and Computer Engineering, Virginia Tech, NVC, Falls Church, VA 22043 USA (e-mail: lmili@vt. edu). Color versions of one or more of the figures in this paper are available online at . Digital Object Identifier 10.1109/TPWRS.2010.2080325
methods proposed in the literature to address this problem consist of heuristic techniques, statistical methods, and artificial intelligence-based techniques. Examples of the latter include fuzzy logic approaches, neural networks [5], or expert systems [6]. As for the statistical methods, they are usually classified as nonparametric [8], semiparametric, and parametric approaches. The latter may be based on a variety of methodologies, including linear regression; exponential smoothing [9]; stochastic time series [9], [10]; structural models; and state space models [11]. RTE has developed for more than 15 years a short-term load forecasting method that makes use of seasonal autoregressive integrated moving average (SARIMA) models. The method consists of the following steps. The load time series is first corrected from the influence of the weather by using a regression model, where the exploratory variables are the temperature and the nebulosity recorded in few selected cities and towns in France. The nebulosity is a measure of the cloud cover in real time. It influences the electricity consumption since it plays an important role in electric lighting consumption. The resulting adjusted series encompasses a general growth trend and several major cycles (daily, weekly, seasonal, yearly, etc.). Regarding the daily load curves, they can be classified in different groups corresponding to weekends, working days, non-working days, public holidays, and some special days. Furthermore, the load time series exhibit lasting abrupt changes in the stochastic pattern, termed breaks, for example due to public holidays and the transition periods between holidays and normal days. To illustrate the occurrences of these breaks, let us consider the load demand from Friday, April 27, 2007 to Monday, June 1, 2007, which are displayed in Fig. 1(a). We notice in this figure that there are several breaks appearing during the following time periods: Tuesday, April 30 and May 1; Monday, May 7 and Tuesday, May 8; Thursday, 17 and Friday, May 18, 2007 (approximately from observation 145 to 241, 481 to 577, and 961 to 1057). Interestingly, May 1, 8, and 18 are public holidays in France. Because the breaks do not follow the general pattern of the time series, they detrimentally affect the classical statistic approaches. To improve the robustness of the parametric forecasting methods, we may resort to a robust statistical estimation or a diagnostic approach. Good diagnostic techniques achieve robustness via outlier detection and hard rejection, resulting in missing values in the load time series. By contrast, robust methods accommodate outliers by bounding their influence on the estimates, yielding no missing values, which may be an advantage in some applications. In the robust statistical literature, there are numerous robust estimation methods that have
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