Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 740490, 14 pages

http://dx.doi.org/10.1155/2015/740490

## Research and Application of a New Hybrid Forecasting Model Based on Genetic Algorithm Optimization: A Case Study of Shandong Wind Farm in China

^{1}School of Statistics, Dongbei University of Finance and Economics, Dalian 116025, China^{2}Department of Statistics, Florida State University, Tallahassee, FL 32306-4330, USA

Received 16 October 2014; Revised 19 December 2014; Accepted 20 December 2014

Academic Editor: Reza Jazar

Copyright © 2015 Ping Jiang 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

With the increasing depletion of fossil fuel and serious destruction of environment, wind power, as a kind of clean and renewable resource, is more and more connected to the power system and plays a crucial role in power dispatch of hybrid system. Thus, it is necessary to forecast wind speed accurately for the operation of wind farm in hybrid system. In this paper, we propose a hybrid model called EEMD-GA-FAC/SAC to forecast wind speed. First, the Ensemble empirical mode decomposition (EEMD) can be applied to eliminate the noise of the original data. After data preprocessing, first-order adaptive coefficient forecasting method (FAC) or second-order adaptive coefficient forecasting method (SAC) can be employed to do forecast. It is significant to select optimal parameters for an effective model. Thus, genetic algorithm (GA) is used to determine parameter of the hybrid model. In order to verify the validity of the proposed model, every ten-minute wind speed data from three observation sites in Shandong Peninsula of China and several error evaluation criteria can be collected. Through comparing with traditional BP, ARIMA, FAC, and SAC model, the experimental results show that the proposed hybrid model EEMD-GA-FAC/SAC has the best forecasting performance.

#### 1. Introduction

Wind, as a kind of environmentally friendly, economically competitive, and socially beneficial energy, has become the most widely used renewable energy resource all over the world. Particularly in China, the majority of energy sources are fossil fuels such as coal, oil, and natural gas, but rapid economic growth and decrease of fossil fuel reserves compel China to find out alternatives. Wind energy with more advantages including low cost of power generation, high degree of industrial maturity, and good physical and social environmental impact becomes the first choice of renewable energy sources in China [1]. Owing to the volatility and chaotic characteristics of wind speed, grid interconnection of wind farms has been a difficult and challenging task. However, in order to ensure the safe operation of the grid, the accuracy of wind speed forecasts plays a vital role in calculating the spinning reserve capacity of grid security forewarning management in wind grid. Therefore, it is necessary to forecast wind speed accurately. Generally speaking, there are two kinds of wind speed forecasts in terms of time span. One is long-term wind speed forecast, which is crucial for the sitting and sizing of wind power application [2, 3]. It is helpful for wind risk evaluation. The other is short-term wind speed forecast, which is significant to improve the efficiency of wind power generation systems [4, 5]. The time scale of short-term forecasting range is from some seconds to minutes, hours, or several days. It can help the daily and intraday spot market, system management, and maintenance scheduling [6].

Many researchers have made efforts to develop good wind speed forecasting approaches including statistical methods, physical methods, physical-statistical models, artificial intelligent methods, and some other new hybrid methods. Statistical methods include autoregressive integrated moving average (ARIMA) model and generalized autoregressive conditional heteroskedasticity (GARCH) model. Kavasseri and Seetharaman [7] used f-ARIMA model to forecast wind speed of four sites in North Dakota on the day-ahead and two-day-ahead horizons. Liu et al. [8] found that ARMA-GARCH (-M) models could improve the modelling sufficiency of mean wind speed as the height increases. Physical methods, like weather research forecasting model (WRF) and mesoscale models, combine multiple physical considerations and provide good forecasting accuracy. WRF model was evaluated by González-Mingueza and Muñoz-Gutiérrez [9] through different parameterization options in Peru to minimize the uncertainty of wind speed forecast. Janjai et al. [10] evaluated wind energy potential of Thailand using an atmospheric mesoscale model and a geographic information system (GIS) approach. The experimental performance presented areas in the south had high wind energy potential. For physical-statistical methods, WRF results can usually be considered as input variables, combined with observed historical data, to train the system based on statistical theories [11]. Recently, some hybrid approaches based on artificial intelligence techniques have been proposed to forecast wind speed and have got good forecasting effects. Guo et al. [12] developed a hybrid model for wind speed prediction based on the empirical model decomposition (EMD) and feed-forward neural network (FNN). Wang et al. [13] applied a combined epsilon-SVR forecast model based on the history data series eliminating the seasonal variation to make short-term prediction. Pourmousavi Kani and Ardehali [14] applied artificial neural network (ANN) and Markov chain (MC) to propose a new hybrid ANN-MC model for short-term wind speed forecast. Guo et al. [15] proposed a hybrid seasonal autoregression integrated moving average and least square support vector machine (SARIMA-LSSVM) model to predict the mean monthly wind speed in Hexi Corridor. Wang et al. [16] used another new combined forecasting method including the seasonal ARIMA forecasting model, the seasonal exponential smoothing model, and the weighted support vector machines to make short-term prediction.

Empirical mode decomposition (EMD), widely adopted in many different fields [17–19], is a data adoptive method for analyzing nonlinear and nonstationary data. However, EMD may not function properly if the data does not meet certain conditions. Therefore, noise is introduced during the decomposition process to prevent mode mixing from contaminating the information embedded in IMFs [20]. This noise-assisted EMD method is named ensemble empirical mode decomposition (EEMD) [18]. Wind is an intermittent energy which means that there exists large variability due to temperature, humidity, pressure, and weather conditions [21]. Based on the above features, this work first employs EEMD method to eliminate high frequency fluctuant parts of ten-minute wind speed. For the sake of improving the forecasting precision, optimized hybrid models need to be developed. A hybrid model including first-order adaptive coefficient forecasting method (FAC) and second-order adaptive coefficient forecasting method (SAC) is proposed in this paper. In addition, the genetic algorithm (GA) is a highly parallel, stochastic, and adaptive optimization technique on the basis of biological genetic evolutionary mechanisms. Its performing operation is similar to natural selection, crossover, and mutation to get the final optimization results after repeated iterations [22].

The structure of this paper is as follows. Section 2 refers to our contribution of the paper. Section 3 introduces relative methods including ensemble empirical mode decomposition (EEMD), genetic algorithm (GA), first-order adaptive coefficient forecasting method (FAC), and second-order adaptive coefficient forecasting method (SAC). In Section 4, experimental simulation and evaluation of forecasting performance can be described in detail. Finally, Section 5 concludes this work.

#### 2. Our Contributions

We propose an intelligent optimized hybrid model EEMD-GA-FAC/SAC based on the EEMD, GA, and FAC/SAC model which have several advantages. To begin with, as an intermittent energy, wind is vulnerable to the impact of temperature, humidity, pressure, and weather conditions, causing its characteristic of nonstationary and high frequency. It is necessary to develop methods of eliminating the interference information that would be well practical in application. Second, through the performance of experimental simulation results, it is obviously illustrated that the proposed hybrid model EEMD-GA-FAC/SAC is suitable for the current research. Second, ten-minute wind speed data is nonlinear and nonstationary. The EEMD-GA-FAC/SAC model can effectively eliminate high frequency inference signals and determine the optimal weight parameters of FAC and SAC model. Third, in order to select the most suitable weight coefficients for the hybrid model, GA is applied to determine the weight parameters of FAC or SAC. Finally, from the case study it can be concluded that the MAPE, MRE, and MAE of the proposed EEMD-GA-FAC/SAC model are smaller than the ones of the EEMD-FAC/SAC, FAC/SAC, BP, and ARIMA model. To sum up, the hybrid model EEMD-GA-FAC/SAC has good forecasting quality and high forecasting accuracy. For the above reasons, the proposed hybrid model EEMD-GA-FAC/SAC is more effective and adaptive to improve the forecasting accuracy than traditional BP, ARIMA, FAC, and SAC model.

#### 3. Relative Methods

##### 3.1. Ensemble Empirical Mode Decomposition (EEMD)

Empirical mode decomposition (EMD) is an adaptive and efficient approach that is used to decompose nonlinear and nonstationary signals into a series of meaningful IMFs and one residual trend from high frequency to low frequency [23, 24]. However, the mode mixing problem is the most important shortcoming of EMD, which indicates either a single IMF consisting of signals of dramatically disparate scales or a signal of the same scale appearing in different IMF components, and usually intermittency of analyzing signal [25]. In order to eliminate the mode mixing phenomenon and get the actual time-frequency distribution of the seismic signal, a new approach called ensemble empirical mode decomposition (EEMD) was proposed [26, 27]. The aim of EEMD is to add white noise to the data, which distributes uniformly in the whole time-frequency space, and make the bits of signals of different scales be automatically designed onto proper scales of reference established by the white noise [25]. The detailed description of the algorithm of EEMD is as follows [24].

*Step 1. *Initialize the number of ensemble and the amplitude of the added white noise, with .

*Step 2. *Perform the th trial on the signal added with white noise:(a)add a white noise series with the given amplitude to the investigated signal
where represents the th added white noise series and indicates the noise-added signal of the th trial;(b)decompose the noise-added signal into several IMFs by the EMD method, where denotes the th IMF of the th trial and is the number of IMFs;(c)if then go to step (a) with . Repeat steps (a) and (b) again and again, but with different white noise series each time.

*Step 3. *Calculate the ensemble mean of the trials for each IMF:

*Step 4. *Report the mean of each of the IMFs as the final IMFs.

##### 3.2. Genetic Algorithm (GA)

The genetic algorithm (GA), a famous metaheuristic algorithm, can follow the natural evolution processes. The GA starts at defining optimization variables, objective functions, and control parameters [28]. Generally speaking, the GA begins by creating a random population which composes of a certain number of individual solutions indicated by “chromosomes”, and the “chromosomes” contain all the genes (i.e., variables) and are involved in each possible solution. The chromosomes are evaluated based on the “objective function,” which is the expected objective of the problem [29]. The brief procedure can be seen in the following way [30, 31].

*Step 1. *Randomly generating the initial population.

*Step 2. *Computing and saving the fitness function for each individual in the population. The individual fitness function can be defined as ; is the objective function.

*Step 3. *Section operation: the fitness value in the population can take part in this operation on the basis of probabilities. Define selection probabilities of each individual while maintaining the proportionality. In the selection operation, the members of the population with better fitness value can participate several times, while the members with worse value may be removed for the sake of getting a larger fitness average. Next, we can generate offspring.

*Step 4. *Crossover operation: it allows an exchange of the design characteristics between two mating parents. This operation is done by selecting two mating parents in which two random places are selected on each chromosome string and the strings between these two places among the mates are exchanged.

*Step 5. *Mutation operation: the aim is to search the minimum solution and keep population diversity and avoid the premature convergence phenomenon. It is invoked with a low probability at a randomly selected site on the chromosomal string of the randomly chosen design. The operation consists of a switching of a 0 to 1 or vice versa.

##### 3.3. First-Order Adaptive Coefficient Forecasting Method (FAC)

The aim of the first-order adaptive coefficient forecasting method (FAC) [32, 33] is to correct the coefficient values constantly on the basis of changes in data, thus making forecasting results the best. The forecasting equation is as follows:

The solution of is given below. If there is a system error during a particular forecasting time (it means all the values are positive or negative), should be larger. When the forecasting value is relatively smaller, that is, , we can make larger so as to increase according to (3). When the forecasting value is relatively larger, that is, , we can also make larger in order to decrease . In other words, the larger the system error is, the larger the value is. If there is not a system error, that is, values of are alternately positive and negative and absolute values of are relatively smaller, thus can remain unchanged. How to measure the system error? We can give measure methods in the following way.

Supposing that is a constant (), we can make exponentially weighted average for the forecasting errors before time : can reflect the situation of the forecasting system errors; when , Thus, based on (4) and (5) the recursive calculative formula of can be got as follows: In order to make , let when , In a similar way, the recursive calculative formula of can be obtained:

In order to satisfy the above requirements, let . Figure 1 shows the calculation procedure of first-order adaptive coefficient forecasting method.