Forecasting models for wind speed using wavelet, wavelet packet, time series and Artificial Neural Networks

Abstract

Wind speed forecasting is important for the security of wind power integration. Based on the theories of wavelet, wavelet packet, time series analysis and artificial neural networks, three hybrid models [Wavelet Packet-BFGS, Wavelet Packet-ARIMA-BFGS and Wavelet-BFGS] are proposed to predict the wind speed. The presented models are compared with some other classical wind speed forecasting methods including Neuro-Fuzzy, ANFIS (Adaptive Neuro-Fuzzy Inference Systems), Wavelet Packet-RBF (Radial Basis Function) and PM (Persistent Model). The results of three experimental cases show that: (1) the proposed three hybrid models have satisfactory performance in the wind speed predictions, and (2) the Wavelet Packet-ANN model is the best among them.

Introduction

Wind energy has developed fast in the world. Just in China, the current total capacity of wind farms is 25805.3 MW [1]. To use the increasing wind energy effectively and safely, high-precision wind speed predictions are desired [2].

In the last 2 years, some new works have been made to realize wind speed predictions. Cassola and Burlando [3] proposed a method using NWP and KF to predict wind speed. In their works, the KF was used to filter the outputs of the NWP to get accurate results. Zhang et al. [4] employed four improved adaptive coefficient methods by PSO to forecast wind speed. Their simulated results showed the PSO promoted the forecasting performance. Erdem and Shi [5] made a comparison of one-step predictions by ARIMA, decomposed ARIMA, VAR and restricted VAR for two wind observation sites in North Dakota, USA. Liu et al. [6] compared an ARIMA-ANN model with an ARIMA-Kalman in wind speed multi-step predictions. They did not use the ARIMA to make the wind speed predictions directly but adopted it to choose the best parameters for the ANN and Kalman components. Liu et al. [7] presented a hybrid ARMA–GARCH method to forecast a series of 7-year hourly wind speed data in Colorado, USA. The results showed the performance of the ARMA-GARCH was satisfactory. Bouzgou and Benoudjit [8] proposed a multiple architecture system for wind speed predictions. In their system, three classical methods (DRA, RBF and SVM) were included. Cao et al. [9] discussed the forecasting accuracy of univariate and multivariate ARIMA models with their RNN counterparts. Jiang et al. [10] examined a new method for very short-term wind speed forecasting using BT and SBM. Guo et al. [11] combined EMD and FNN to build a hybrid EMD-FNN model for wind speed predictions. They concluded the performance of the hybrid model was better than that of the single FNN. Salcedo-Sanz et al. [12] studied wind speed predictions by SVM in a Spanish wind farm. To improve the performance of the classical SVM, two new hybrid methods (EP-SVM and PSO-SVM) were proposed. Their results showed that the two hybrid models both had satisfactory predictions. Guo et al. [13] proposed a method based on BP and method of idea of eliminating seasonal effects to forecast wind speed. The hybrid method forecasted the daily average wind speed more accurate than the BP model without adjustment. Liu et al. [14] investigated the performance of TK model in wind speed predictions. In their research, the results displayed the TK was better than the ARIMA. Shi et al. [15] compared the performance of the ARIMA, ANN and SVM models in wind speed short-term predictions. Their results showed both of the performance of the hybrid ARIMA-ANN and ARIMA-SVM were better than those of the single ARIMA, ANN and SVM models. Haque et al. [16] presented a performance analysis of short-term wind speed predictions using SCMs formulated on the BPNN, RBFNN and ANFIS. The research results showed their proposed hybrid methods were successful. The hybrid ANFIS model improved up to 48% forecasting accuracy compared with the single ANFIS. Amjady et al. [17] designed a new HIFM model for wind speed forecasting considering the interactions of temperature and wind speed. The forecasting results based on some real data from Iran and Spain confirmed that the HIFM was effective. Salim et al. [18] proposed five different adaptive Neuro-Fuzzy wind predictors and compared their performance in the East Coast of Egypt. More works about wind speed predictions can be found in Refs. [19], [20], [21].

Based on the upper literatures, it can be found that: (a) most of the latest methods are proposed by using more than one forecasting approaches to get better performance; (b) the modeling theories used in those works can be classified as three kinds: statistical methods, physical methods and intelligent methods. Every kind of methods has their own advantages and disadvantages. For example, the statistical methods are simpler than the physical and intelligent methods but with lower accuracy; (c) when a new method is proposed, it should be seriously compared with some existing models to prove its contributions; and (d) besides the forecasting accuracy, the multi-step ahead capacity of models is also emphasized in wind speed predictions. Some similar conclusions can also be made by reviewing the literatures of wind power/load [22], [23], [24], [25], [26], [27], [28] and electricity price [29], [30], [31] predictions.

From the literatures [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], it can also be seen that in the wind speed predictions there are at least two kinds of effective ideas to possibly get high-precision results. One is to use the other methods to improve the forecasting capacities of the principal methods. After the necessary optimization, the principal methods could handle with the non-stationary wind speed data better. For instance, the PSO has been adopted to choose the best initial parameters of the SVM in the wind speed predictions [12]. In this kind, the other methods directly promote the forecasting performance of the principal methods. The other one is to utilize the other methods to decrease the forecasting difficulty of the original wind speed. For example, the EMD has been selected to decrease the non-stationary degree of the original wind speed in the wind speed predictions [11]. In this kind, the other methods do not directly promote the forecasting performance of the principal methods. In this study we would like to study the second classification. In signal decomposing fields, the WD [32] and the WPD [33] are generally recognized. In this paper, they are selected to build hybrid models with the representative one in intelligent methods-ANN and the classical one in statistical methods-ARIMA to predict three sections of wind speed data. Additional a comparison of the proposed hybrid methods and other important forecasting methods (including ANFIS, Neuro-Fuzzy, RBF and PM) will be provided.

This paper is organized as follows: Section 2 states the framework of this study; Section 3 demonstrates the computational steps of the proposed hybrid methods using a real section of wind speed data; Section 4 compares the proposed hybrid methods with other methods; and Section 5 provides additional two forecasting cases; and Section 6 concludes the results of this study.