Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 351354, 13 pages

http://dx.doi.org/10.1155/2015/351354

## Short-Term Wind Speed Hybrid Forecasting Model Based on Bias Correcting Study and Its Application

School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

Received 27 October 2014; Revised 7 December 2014; Accepted 8 December 2014

Academic Editor: Pandian Vasant

Copyright © 2015 Mingfei Niu 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.

#### Abstract

The accuracy of wind speed forecasting is becoming increasingly important to improve and optimize renewable wind power generation. In particular, reliable short-term wind speed forecasting can enable model predictive control of wind turbines and real-time optimization of wind farm operation. However, due to the strong stochastic nature and dynamic uncertainty of wind speed, the forecasting of wind speed data using different patterns is difficult. This paper proposes a novel combination bias correcting forecasting method, which includes the combination forecasting method and forecasting bias correcting model. The forecasting result shows that the combination bias correcting forecasting method can more accurately forecast the trend of wind speed and has a good robustness.

#### 1. Introduction

Because of the global energy shortage, renewable energy has received increasing attention, just now. Wind power is one of the cleanest renewable energy sources that produces no greenhouse gases, has no effect on climate change, and produces little environmental impacts, and the energy generated from the wind has been well recognized as environmentally friendly, socially beneficial, and economically competitive for many applications [1]. As of now the effectiveness of wind speed forecasting is an important role in the scheduling of wind power. At present, these methods can be divided into two categories: statistical models and machine-learning models. Statistical models primarily use a time series approach and have been successfully applied for forecasting [2–7]. These models are based on the assumption that a linear correlation structure exists among time series values. Therefore, nonlinear patterns cannot be captured using these models. To overcome this limitation, machine-learning models have been used to improve nonlinear time series predictions (which primarily include artificial neural networks, support vector machines, heuristic algorithm, and fuzzy logic methods) [8–34].

In a nutshell, in the past decades, many computational intelligence techniques have been developed for short-term wind speed forecasting, for instance, support vector regression [15, 27, 35], support vector machine [26, 31, 33, 36], fuzzy model [21, 27], artificial neural networks [8, 9, 11, 13, 14, 20, 23–25, 28, 29], wavelet method [9, 34, 37], and heuristic intelligence algorithm: particle swarm optimization [37, 38], adaptive particle swarm optimization [17, 36, 39], chaotic particle swarm optimization [31], biogeography-based optimization [10], coral reefs optimization [16], gravitational search algorithm [19], and harmony search algorithm [16]. In the next section, we will detail the explanation of the previous work in the short-term wind speed prediction.

The remaining sections are arranged as follows. The related work will be brief description in Section 2. The preparation methods and main modeling process are described from Section 3 to Section 6. Section 7 forecasts the wind speed of Penglai using three wind farms and provides the forecasting results and analyses. Finally, the conclusion is presented in Section 8 and the future research in Section 9.

#### 2. Related Work

In the above references, Song et al. [5] employ a discrete-state Markov chain to model the nonlinear characteristic of the wind speed time series, and a Bayesian inference is applied to evaluate the parameters of the Markov-switching model. Finally, by comparison with other methods, this proposed method outperforms them. Liu et al. [9] present four important decomposing algorithms including wavelet decomposition, wavelet packet decomposition, empirical mode decomposition, and fast ensemble empirical mode decomposition, which are all adopted to realize the wind speed high-precision predictions. Salcedo-Sanz et al. [16] introduce a new hybrid coral reefs optimization and harmony search algorithm; this novel approach is utilized to obtain the best set of meteorological variables in the context of short-term wind speed forecasting, and the selection variable will be input to an extreme learning machine network. Experimental result shows that these proposed methods have good results when compared to other approaches. Wang et al. [17] proposed an optimization model to decide the rated power system and the capacity of a compressed air energy storage system in a power system with high wind power penetration. Moreno et al. [18] proposed a strategy including the uncertainty of involving market and wind power. Mondal et al. [19] solved economic dispatch problem in wind generation. In a nutshell, as the randomness of wind speed distribution, every prediction model owns some limitations.

In the short-term wind speed forecasting, because of ignoring of the secondary influence factors and correlations, every prediction model can generate prediction errors, which are the difference between the predicted value and the actual value, the main causes that forecasting method just considers the main factors, and many of the secondary factors are ignored. However, as the effect of the secondary factors, the forecasting bias may form a certain trend. Making allowance for these minor influence factors, the bias correction becomes important. The basic idea of forecasting bias correction is following. After forecasting by the prediction model and comparing with the actual wind speed, forecasting error is generated. Using suitable prediction model to forecast error, error correction can be got, which is used to modify the original forecasting result. The error correction prediction model expression is as follows: . is final forecasting value, is combination forecasting value, and is bias correction.

Nowadays, there are some error correction models [36, 40–42], such as the periodic extrapolation, vector error correction model, partial simulation approximate value, and Bayesian error correction model. But the relevant researches about the short-term wind speed and wind power error correction models are very rare. So this paper quotes bias correction model in short-term wind speed forecasting, thus, making wind power scheduling reasonable.

Due to the randomness of wind speed, the former forecasting models have their own limitations. It is because of the volatility of the wind speed; firstly, this paper proposes a combination of a linear model and two nonlinear models: double exponential smoothing method (*DES*), backpropagation of particle swarm optimization artificial neural network (*PSO-BPANN*), and Elman artificial neural network (*Elman-ANN*). The inputs of* PSO-BPANN* and* Elman-ANN* consist of historical wind speed data and residual errors of the* DES* model. Then the combined weight will use adaptive particle swarm optimization algorithm (*APSO*) to optimize. The combination model can more accurately forecast short-time wind speed. The reasons of wind speed forecasting errors are analyzed; then, the empirical orthogonal function model will be error correction. Making use of this model, main variables can be extracted, and error correction model is built by the empirical orthogonal function regression method. Some advantages are that the main variables are determined by the properties of wind speed series itself, but not prior artificial regulation, and can reflect the actual wind speed data basic structure, and expansion equation converges fast. Finally, combination bias correcting forecasting model is presented. In order to check the validity of the model, the case study will be analyzed in detail.

Generally speaking, in this research, our main contribution is that we set up the combination bias correction forecasting model in the short-term wind speed forecasting, which consists of double exponential smoothing (*DES*),* PSO-BP* artificial neural network, and* Elman* artificial neural network and, finally, adaptive particle swarm optimization algorithm (*APSO*) to optimize the combination weights. Forecasting error can be corrected by the empirical orthogonal function, which can be used in variables analysis and regression forecasting for wind speed prediction bias and correcting wind speed prediction result. In this paper, the ten-minute wind speed data from three wind farms in Penglai of Shandong province in China were used as examples to evaluate the performance of the proposed approach. To avoid volatility due to the* PSO-BP*, Elman, and* PSO* optimization algorithm, all of the simulations were repeated 50 times prior to averaging. As time goes on, more wind speed information will be obtained, more accurate wind speed characteristic will be derived by forecasting models, and the new information on the wind speed is absorbed by this combination bias correction model. Therefore, the performance of this combination bias correction model will be accurate and stable.

#### 3. Combination Forecasting Model

Due to the random features of wind speed, the nonlinear characteristics are significant. So the combination forecasting consists of a linear model and two nonlinear models; then the combined weight will use adaptive particle swarm optimization algorithm (*APSO*) to optimize. Three models theories are as follows.

##### 3.1. Wind Speed* DES* Model

Exponential smoothing technique used to forecast wind speed is comparatively simple. It only needs a single wind speed series. It can be divided into single exponential smoothing method (*SES*), double exponential smoothing method (*DES*), cubic exponential smoothing method (*CES*), and so on. The main steps of exponential smoothing method used to forecast wind speed include modeling and calculating the consequence of exponential smoothing, determining the smoothing coefficient of , and forecasting. Because* DES* is based on single exponential smoothing values and is more accurate than the single exponential smoothing method, it can better reflect the linear characteristic of wind speed. So this paper uses* DES*. The procedure is as follows.

###### 3.1.1. Modeling and Calculating the Consequence of Exponential Smoothing

The* DES* is modeled by the wind speed data, and the expression is as follows:

The* DES* model is similar to the double moving average method (*DMA*); first of all, on the base of the sequence of the single exponential smoothing (smoothing coefficient ),and calculating the consequence of second exponential smoothingwhere the initial value and , , .

###### 3.1.2. Determining the Smoothing Coefficient and Forecasting

A sequence of the single exponential smoothing is relative to data migration or lag effect, and a sequence of the double exponential smoothing is relative to lag effect, otherwise. Under certain conditions, such as large enough, especially is close to 1, and two lags are equal. Among them, the smoothing coefficient can be optimized via analyzing the wind speed forecasting error. Just for the sake of smooth sequence, can be small enough. If it is used to predict, when the original wind speed volatility is not obvious, can get smaller or get bigger, in order to make the smoothing sequence reflect the changes of the wind speed data.

Through calculation we get the intercept and slope of the prediction linearFinally, prediction model is as follows:

##### 3.2. Wind Speed* PSO-BP* Neural Network Prediction Model

In order to solve the nonlinear features of wind speed, artificial neural network (*ANN*) methods have been proposed.* ANN* is able to give better performance in dealing with the nonlinear relationships among their input variables [35]. The conventional backpropagation algorithm (*BP*) is successfully applied to complex nonlinear problems. However, using BP method needs the following; the transfer function of each neuron must be different. Moreover, it has been proven that gradient techniques are slow to train and are sensitive to the initial guess which can possibly be trapped in a local minimum [43].

To overcome these shortcomings, the paper introduces particle swarm optimization algorithm (*PSO*) to optimize the* BP* network to solve the wind speed forecasting problem. The* PSO* algorithm is applied to the neural network in the training phase, to obtain a set of weights that will minimize the error function in competitive time. Weights are progressively updated until the convergence criterion is satisfied. The objective function to be minimized by the* PSO* algorithm is the predicted error function [37].

Figure 1 shows the flow process of* PSO*-*BPANN* forecasting model [38].