1. Introduction
Electric power is a clean and efficient energy which plays an increasingly vital role in our daily life. Compared with traditional energy such as natural gas, coal and oil, electric power is more suitable and efficient for the requirement of environment-friendly society. In the field of power system planning, the accuracy of electric load forecasting is of great importance for energy generating capacity scheduling and power system management [
1,
2]. An overestimation may waste many energy resources and significantly improve the operational costs, and an underestimation will decrease the reliability of the power system and cannot meet the requirement of electricity utilization [
3]. Therefore, accurate electric load forecasting is essential and significant for power systems. However, because the electric load series is affected by many complicated influencing factors, it is really a challenging job to accurately predict the electric load.
Over the past several decades, various interesting models for the electric load forecasting have been established, and they can be generally divided into the following two types. The first type is the multi-factor forecasting method, which needs to search the causal relationships between different influencing factors and forecasting values [
4]. The other one is time series forecasting method which is based on the historical series. As is mentioned above, the electric load series is affected by various complicated and nonobjective factors which are very difficult to be controlled in practical application and, consequently, it is a very challenging job to establish an accurate forecasting model by utilizing the multi-factor forecasting method. Based on the above considerations, lots of researchers turn to utilizing the time series forecasting method to forecast electric load [
5]. Compared to multi-factor forecasting method, the time series forecasting method is much easier and quicker. The most frequently and widely used time series forecasting models can be further divided into the following three subcategories: statistical models; machine learning models, and; hybrid models [
6]. As for the statistical models, the auto-regressive moving average (ARMA), auto-regressive integrated moving average (ARIMA), generalized autoregressive conditional heteroskedasticity (GARCH), vector auto-regression (VAR), and Kalman filters methods are widely used in the electric load forecasting areas. For example, Pappas et al. [
7] established an ARMA model for short-term electric load forecasting, and the results showed the good performance of the proposed model. Kavousi-Fard and Kavousi-Fard [
8] proposed a new hybrid model based on ARIMA for short-term load forecasting. Takiyar et al. [
9] developed a GARCH-based hybrid model for short-term electric load forecasting. Garcia-Ascanio and Mate [
10] utilized VAR-based interval time series model to forecast electric load forecasting. Takeda et al. [
11] developed an ensemble model based on Kalman filter for short-term electric load forecasting, and the experiment indicated that the predicting accuracy of the proposed model is obviously better than that of the present state-of-the-art models.
With the fast development of machine learning method, many of them have been widely used in various forecasting issues, such as artificial neural network (ANN), extreme learning machine (ELM) and support vector machine (SVM). Yolcu et al. [
12] developed a new ANN model based on both linear and nonlinear structures for time series predicting. Gutierrez-Corea et al. [
13] focused on the usage of ANN in short-term global solar irradiance forecasting. Li et al. [
14] proposed a novel model based on modified artificial bee colony (MABC) and ELM for short-term electric load forecasting, and the experimental results showed that the proposed hybrid model owned the best forecasting ability with comparison to the other benchmark models adopted in their paper. Zhou et al. [
15] developed a hybrid model based on SVM for short-term wind speed forecasting. Chen and Lee [
16] established a weighted least square support vector machine (LSSVM) model based on learning system for time series forecasting, and the experimental results demonstrated the effectiveness of the proposed model.
By integrating the advantages of different single forecasting models, hybrid forecasting models generally performs better than the single forecasting models and therefore are widely used in many forecasting areas. For example, Liu and Shi [
17] proposed an ARMA-GARCH model for predicting short-term electricity prices. Voyant et al. [
18] developed an original technique to forecast global radiation based on a hybrid ARMA-ANN model for numerical weather forecasting. Ismail et al. [
19] developed a hybrid self-organizing maps (SOM)-LSSVM model combining SOM and LSSVM for time-series predicting, and the experiment in the paper showed that SOM-LSSVM outperforms the single LSSVM model. Even though the hybrid model performs better than the single forecasting model, they still cannot effectively deal with the nonlinear and nonstationary characteristics associated with majority of time series in practical life. Therefore, many researchers have integrated various data preprocessing techniques into the forecasting models in order to effectively decrease the forecasting errors. The most widely used data preprocessing techniques includes empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), wavelet packet transform (WPT) and variational mode decomposition (VMD). Liu [
20] predicted short-term wind speed by a hybrid model combining wavelet transform (WT) and SVM optimized by genetic algorithm, and the simulation results demonstrated that the proposed hybrid model is more efficient than the other comparison models adopted in their paper. Wang et al. [
21] developed a hybrid forecasting model based on WPT, particle swarm optimization (PSO), simulated annealing (SA), phase space reconstruction (PSR) and LSSVM for multi-step ahead wind speed forecasting, and the case studies showed that the proposed model outperformed all the other comparison models. Zhang et al. [
22] investigated the usage of WT-LSSVM model in the time series forecasting of fair-weather atmospheric electric field, and the experimental results showed that the proposed WT-LSSVM model is a superior method compared to the single LSSVM and ANN model. Wang et al. [
23] developed a two-layer decomposition model for multi-step ahead electricity price forecasting, where VMD is specifically applied to decompose the high frequency sub-signals generated by fast ensemble empirical mode decomposition (FEEMD), and the experimental results illustrated the superior performances of the proposed model. For more details on different forecasting models, the reader can refer to the references [
24,
25,
26], among others.
Although VMD has been utilized in many forecasting issues such as forecasting of wind power [
27] and financial time series [
28], the advantages of VMD have not been confirmed in the electric load forecasting area. Based on the above considerations, this paper aims to establish an ensemble model combining VMD and an improved ELM for short-term electric load forecasting. The process of the proposed model can be summarized into the following three steps: first, VMD is used to decompose the original electric load series into a set of components with different frequencies in order to effectively decrease the stochastic fluctuation characteristics; then, each component is forecasted using the ELM model whose initial weights and thresholds between the input layer and hidden layer are optimized by DE algorithm; finally, the ultimate forecasting series of electric load is obtained by aggregating the forecasting value of each component. Two real-world electric load series collected from New South Wales (NSW) and Queensland (QLD) located in Australia are used to test the effectiveness of the proposed ensemble model.
Based on aforementioned researches, the main novelties and contributions of this paper can be summarized to the following four aspects: (1) VMD technique is firstly applied to preprocess the electric load series in order to improve the overall forecasting accuracy; (2) VMD technique is combined with machine learning methods to develop a novel ensemble model for short-term electric load forecasting; (3) DE algorithm is employed to optimize the initial weights and thresholds of ELM in order to improve its function approximation ability; (4) the effectiveness of the proposed model is also examined by comparing with the forecasting models combining different decomposition techniques such as EMD and WT.
The rest of this paper is organized as follows.
Section 2 firstly describes in detail the fundamental methods used in the paper, and then develops the hybrid VMD-DE-ELM model.
Section 3 provides the data source and preprocessing results.
Section 4 is the empirical study where the performance evaluating criteria, parameter settings and experimental results are presented.
Section 5 concludes the paper.
3. Data Description and Preprocessing
In this paper, two half-hour electric load series collected from NSW and QLD [
34] are adopted to test the effectiveness of the proposed model. In Australia’s electricity market, there are 48 observation data points every day, which means the time gap of observation values is half an hour. In this paper, each electric load series contains 1488 observation data points (from 1 January 2017 to 31 January 2017), see
Figure 2. Moreover, in each case, the 1st–1200th observation points are taken as training sets, and the rest, the 1201st–1488th observation points, are taken as testing sets. The descriptive statistics of the two electric load series is shown in
Table 1.
As is shown in
Table 1, the mean of electric load series of NSW is 8588.11, and the minimum value and maximum value of electric load series of NSW is 5767.31 and 13947.70, respectively. It is obvious that the maximum value of electric load series of NSW is larger than twice of the minimum value, which illustrates that the electric load series of NSW owns notable stochastic fluctuation characteristic. In QLD, the mean of electric load series is 7025.13, and the minimum value and maximum value of electric load series is respectively 5254.92 and 9357.09. The stochastic fluctuation characteristic of electric load series of QLD is also obvious. In addition, it should be noted that all numerical experiments in this paper are coded in MATLAB R2010a.
In order to make the forecasting results own more practical significance, this paper adopts multi-step ahead electric load forecasting. Compared with one-step ahead forecasting, multi-step ahead forecasting can supply more information for electricity market participants. Since multi-step ahead forecasting has to deal with many other additional complications such as the accumulation of errors, increased uncertainty and reduced accuracy [
35], it is therefore more difficult to obtain precise forecasting results. This paper aims to propose an ensemble model for electric load forecasting over different horizons. Different horizons have different practical meanings. For instance, as for the half-hour data source, four-step ahead represents two-hour ahead, eight-step ahead represents four-hour ahead, and twelve-step ahead represents six-hour ahead. Furthermore, as shown in
Figure 3, we take four-step ahead forecasting as an example to clearly interpret the multi-step ahead forecasting process. As shown in
Figure 3, in the training process, the input and output datasets of DE-ELM model for four-step ahead forecasting are respectively
and
, and in the testing process, the input and output datasets of DE-ELM model are respectively
and
.