Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 9895639, 10 pages

http://dx.doi.org/10.1155/2016/9895639

## A Hybrid Model of EMD and PSO-SVR for Short-Term Load Forecasting in Residential Quarters

Department of Economics and Management, North China Electric Power University, Baoding 071003, China

Received 14 April 2016; Revised 14 October 2016; Accepted 23 November 2016

Academic Editor: Marco Mussetta

Copyright © 2016 Xiping Wang and Yaqi Wang. 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.

#### Abstract

Short-term load forecasting plays a vital role in the daily operational management of power utility. To improve the forecasting accuracy, this paper proposes a hybrid EMD-PSO-SVR forecasting model for short-term load forecasting based on empirical mode decomposition (EMD), support vector regression (SVR), and particle swarm optimization (PSO), also considering the effects of temperature, weekends, and holidays. EMD is used to decompose the residential electric load data into a number of intrinsic mode function (IMF) components and one residue; then SVR is constructed to forecast these IMFs and residual value individually. In order to gain optimization parameters of SVR, PSO is implemented to automatically perform the parameter selection in SVR modeling. Then all of these forecasting values are reconstructed to produce the final forecasting result for residential electric load data. Compared with the results from the EMD-SVR model, traditional SVR model, and PSO-SVR model, the result indicates that the proposed EMD-PSO-SVR model performs more effectively and more stably in forecasting the residential short-term load.

#### 1. Introduction

Considering that electricity cannot be stored, thus the accurate forecasting of electric load has a significant effect on reliability of power systems and the economic development of society. Particularly the short-term load forecasting plays a vital role in the daily operational management of power utility, such as energy transfer scheduling, unit commitment, and load dispatch [1, 2]. As an integral part of the daily operational management of power utility, accuracy prediction of the short-term electric load in residential quarters is of great significance to urban power network planning and the electric power market operating. The overestimation will raise the operating cost while underestimation will lead to electricity shortage [3]. Because of the limited capacities on the user side, the load characteristics have less smoothing effect. In addition, the residential load is influenced by many factors, such as holidays, weekends, and temperature [4, 5]. All of these factors lead to the load of residential quarters with more variability, higher randomness, and lower similarities in history load curves. Thus, the short-term load forecasting for residential quarters is a complex task and worthy of further studies.

In the literature, many researchers have proposed various methodologies to improve the short-term load forecasting accuracy during the past decades. These methods can be classified into two categories, namely, the classical statistical methods and artificial intelligence (AI) based algorithms. The classical statistical methods mainly include multiple regression [6], autoregressive integrated moving average (ARIMA) [7] or autoregressive moving average (ARMA) [8], and Kalman filter techniques [9]. Though these methods can provide some valuable improvements in terms of forecasting accuracy, most of these models are linear predictors, which have difficulties in forecasting the hard nonlinear behavior of electricity load series. To overcome the limitations of the linear models and account for the nonlinear patterns existing in real cases, AI techniques, such as artificial neural network (ANN) [10], fuzzy logic [11], and echo state network (ESN) [12], have been introduced into load forecasting. One of the most well-known models in the category of AIs is ANN, which is an effective way to deal with the complex nonlinear problem. However, the problems of ANN in overlearning, connection weight estimations, and the need of a large number of data pieces for system training make it difficult to apply for some short-term prediction. Considering support vector regression (SVR) employs the structural risk minimization principle to minimize an upper bound of the generalization errors, rather than minimizing the training errors used by ANNs, SVR is shown to be very resistant to the overlearning problem [13–15] and has been widely and successfully applied to many forecasting problems, particularly in terms of electric load forecasting. For example, Wang et al. [16] proposed a SVR model with the differential evolution (DE) algorithm to choose the appropriate parameters for the annual electric load forecasting of Beijing in China. Ceperic et al. [17] presented a generic strategy for short-term load forecasting based on SVR. Since the accuracy and stability of SVR largely depend on the selection of the kernel parameter and the penalty parameter, the parameter selection of SVR becomes a key problem. For now, the grid algorithm and the genetic algorithm are widely used in optimization methods, while the grid algorithm is time consuming and has poor performance. The genetic algorithm is less time consuming but has a troublesome operation [18]. Compared with both the grid algorithm and the genetic algorithm, particle swarm optimization (PSO) has some significant advantages, such as simple operation, good optimization performance, and quick convergence, and it does not require evolution operators such as crossover and mutation.

However, several previous studies [19, 20] using PSO-SVR model for short-term load forecasting usually directly applied the original electric load data to construct forecasting models. Because of the nonlinearity and nonstationarity in residential load data, it is difficult to describe the moving tendency of electric load and to improve the forecast accuracy. To establish a suitable and effective forecasting model, the original data features of the residential short-term electric load need to be fully considered and analyzed. Despite the wavelet transform (WT) becoming a de facto standard for the analysis of nonlinear and nonstationary signals, the time consuming for computing and failure in achieving fine resolutions in both time domain and frequency domain simultaneously present a major barrier for the analysis of short-term load time series. Therefore, empirical mode decomposition (EMD), as a special adaptive and direct data processing method developed especially for dealing with nonlinear and nonstationary data, is used to decompose the original load data into a set of intrinsic mode function (IMF) components and one residue, which can improve the accuracy of forecasting [21–23]. As EMD can decompose data into a number of independent components, some researchers developed several kinds of hybrid forecasting methods by combining EMD with forecasting models to achieve better performance in various fields of signal processing, short-term electric loading, and traffic engineering [24]. For example, Wang et al. [25] proposed a novel model of EMD and Elman neural network to forecast wind speed and concluded that the proposed model was suitable for wind speed prediction. Chen et al. [26] proposed an EMD approach combined with an artificial neural network for tourism demand forecasting. Zhu et al. [27] presented a hybrid method based on EMD and SVM for short-term electronic load forecasting. To date, short-term load forecasting in residential quarters still remains insufficiently researched in the literature.

Considering the nonlinear and nonstationary characteristics of residential electric load data and the divide and conquer principle, a novel hybrid model based on the EMD and the PSO-SVR is proposed to forecast short-term load in residential quarters in this paper. EMD is used to decompose the electric load data into a number of intrinsic mode function (IMF) components and one residue; then SVR is constructed to forecast these IMFs and residual value individually. In order to gain optimization parameters of SVR, PSO is implemented to automatically perform the parameter selection in SVR modeling. Then all of these forecasting values are reconstructed to produce the final forecasting result for residential electric load data. The proposed model is compared with the single SVR, the hybrid models of EMD-SVR and PSO-SVR, and it is shown that the EMD-PSO-SVR model performs more effectively and more stably and yields more accurate results.

The rest of this paper is organized as follows: Section 2 describes EMD, SVR, and PSO methodologies. Section 3 presents the detailed modeling steps of the EMD-PSO-SVR model. Section 4 presents the numerical results from real data and compares the performance of the proposed hybrid model with other alternative models. Section 5 draws the conclusion of this article.

#### 2. Methodology

##### 2.1. Empirical Mode Decomposition

EMD, first proposed by Huang et al. [28], is a novel empirical analysis tool used for processing nonlinear and nonstationary datasets. The main idea of EMD is to decompose the nonlinear and nonstationary time series into a sum of several simple intrinsic mode function (IMF) components and one residue with individual intrinsic time scale properties. Each IMF represents a kind of natural oscillatory mode and has to satisfy the following two conditions: in the whole data series, the number of extreme values and the number of the zero crossings must either be equal or differ at the most by one; at any point, the average of the envelope constructed by the local minimum values and maximum values is zero [29–33].

Let be a given original short-term load time series; then the detailed steps of EMD calculation can be described as follows [34].

*Step 1. *Determine all the local extremes of the original electrical load series .

*Step 2. *Calculate the upper envelope , which can be derived by connecting all the local maxima using a cubic spline line. Similarly, the lower envelope also can be obtained. And then the average envelope based on the upper and lower envelopes can be calculated as

*Step 3. *Calculate the first difference between the original series data and the mean envelope :

*Step 4. *Check whether satisfies the two requirements of IMF. If is an IMF, then is denoted as the first IMF and replaced with the residue :Otherwise, if is not an IMF, replace with and repeat Steps 2-3 until the termination criterion is satisfied. For convenience, we use the standard deviation (SD) as the termination criterion and it is defined as where is the length of the signal; represents the number of iterative calculations and is the terminated parameter, which is usually determined according to the actual application. According to [2], is assumed in the range of 0.2 to 0.3 in this paper.

After the EMD calculation, the original time series data can be decomposed into summing up all the IMF components and a residue as follows:where () is the IMF in different decomposition and is the residue after numbers of IMFs are derived. By this process, each IMF is independent and specific for expressing the local characteristics of the original time series data.

##### 2.2. Support Vector Regression

SVR, an extension of support vector machine (SVM), is a machine learning method based on statistics, which was proposed by Drucker et al. [35]. The basic idea of the method can be described as follows. Assuming that a set of data , where is a -dimensional input vector and is a corresponding target output. Define a nonlinear mapping function to map the input data into the high dimensional feature space. Then in the high dimensional feature space, there theoretically exists a linear function to formulate the nonlinear relationship between input and output data. Such a linear function, namely, SVR function, can be defined aswhere and are the coefficients that can be adjusted. The empirical risk is defined as follows:where is called insensitive loss function, it is utilized to obtain an optimum hyperplane which divides the training data into two linearly separable subsets with maximum separation distance. In fact, SVR is an optimizing problem in whose objective function is:

The first term of (8) measures the flatness of the function. The second term penalizes training errors of and by using the insensitive loss function. specifies the trade-off between the empirical risk and the model flatness. Training errors above are denoted as while below - are denoted as . After solving the optimization problem the parameters vector of (6) can be found as in the following:where and are the Lagrangian multipliers, which are obtained by solving a quadratic program. Finally, the SVR regression function is obtained: where is called Kernel function and must satisfy Mercer’s theorem (Vapnik, 1995 [13]). In the feature space, the kernel function can be described as .

Among the three typical kernel functions, that is, Gaussian radial basis function (RBF), polynomial function, and linear function, the Gaussian RBF is the most widely used kernel function. It can be defined as , where denotes the width of the RBF. Considering that the RBF kernel is not only easy to implement, but also a proper tool for dealing with nonlinear problems, we thus employ the RBF kernel in this study.

##### 2.3. Particle Swarm Optimization

PSO is a population-based stochastic optimization algorithm proposed Kennedy and Eberhart [36]. Inspiration for optimization procedure is found in social behaviors of bird groups and fish schools. In a PSO system, each particle is a potential solution in searching hyperspace with a randomized velocity for the optimal position to land. When the search is complete, the best position of the system can be found by adjusting the direction of each particle towards its own best location and towards the best particle of the swarm at each generation.

In this study, PSO is used to optimize the parameters in the SVR model. The detailed description is listed as follows.

*Step 1 (data preparation). *Input original data for forecasting.

*Step 2 (particle initialization). *Initialize a population of particles with random positions and velocities in the hyperspace.

*Step 3. *It is to train the SVR model with training samples data and to evaluate each particle fitness value of PSO for the SVR.

*Step 4. *The velocity and position of each particle are updated until the stopping condition is satisfied.

*Step 5. *Build and retrain the SVR forecasting model based on the optimal parameters.

#### 3. The Proposed EMD-PSO-SVR Model

As mentioned above, the residential electric load data series has the typical characteristics of higher nonlinearity and nonstationary, which leads to insuperable difficulties in the load forecasts. For this reason, the proposed EMD-PSO-SVR model is employed according to the principle of decomposition and ensemble. The framework of an EMD-PSO-SVR model is demonstrated in Figure 1.