Mathematical Problems in Engineering

Volume 2015, Article ID 278635, 7 pages

http://dx.doi.org/10.1155/2015/278635

## Short-Term Wind Speed Forecast Based on B-Spline Neural Network Optimized by PSO

Key Lab of Industrial Computer Control Engineering of Hebei Province, College of Electric Engineering, Yanshan University, Qinhuangdao 066004, China

Received 21 December 2014; Revised 24 March 2015; Accepted 7 April 2015

Academic Editor: Julien Bruchon

Copyright © 2015 Zhongqiang Wu 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

Considering the randomness and volatility of wind, a method based on B-spline neural network optimized by particle swarm optimization is proposed to predict the short-term wind speed. The B-spline neural network can change the division of input space and the definition of basis function flexibly. For any input, only a few outputs of hidden layers are nonzero, the outputs are simple, and the convergence speed is fast, but it is easy to fall into local minimum. The traditional method to divide the input space is thoughtless and it will influence the final prediction accuracy. Particle swarm optimization is adopted to solve the problem by optimizing the nodes. Simulated results show that it has higher prediction accuracy than traditional B-spline neural network and BP neural network.

#### 1. Introduction

Wind power is a kind of clean, free, and renewable natural resource. In wind power generation systems, the randomness and volatility of wind will affect the quality of power and the reliability of power system. Improving the prediction accuracy of short-term wind speed is of great significance for the real-time scheduling of power, reliability improving of power supply, and cost lowering of the wind power generation [1–3].

The common methods of wind speed forecasting include time series method, support vector machine (SVM) method, and wavelet analysis method. Time series method is adopted in [4, 5], making full use of the sample data and the prediction model is simple which can reduce the calculation time, but it does not take the correlation among the sample data into account, and the estimation of model orders is quite complicated. In [6, 7] SVM is adopted, SVM can make indivisible vector in low dimension space map into divided function in high dimension space by choosing appropriate kernel function, the generalizing ability is improved and the local minimization problem is solved, and it has higher prediction accuracy than time series method. The multiresolution analysis character of wavelet transform and the generalizing ability of SVM are combined to realize the short-term wind speed forecasting in [8]. The method can change the nonlinear phenomenon very well and improve the prediction accuracy, but the design process is rather complex.

In view of the various defects of prediction methods above in practical application, a prediction method based on B-spline neural network optimized by particle swarm optimization (PSO-BSNN) is proposed. Firstly, the wind speed data are used to calculate correlation integral function [9, 10] and prove that the discrete time series is chaotic. By phase space reconstruction [11, 12], the high dimension chaotic attractors are recovered. BSNN can change the division of input space and the definition of basis function flexibly [13, 14]. For any input, only a few outputs of the hidden layers are nonzero, so the outputs are simple and convergence speed is fast, but traditional method which divides the input space into linear space is thoughtless and will influence the final prediction accuracy. PSO is an intelligent search method. It has strong global search ability and is also easy to be realized [15–20]. It is used to optimize the nodes of BSNN. Simulated results show that PSO-BSNN has higher prediction accuracy than BSNN and BPNN.

#### 2. Phase-Space Reconstruction

A series of continuous sample data are collected from a field of wind farm in Colorado State. Set the sample interval of wind speed as 10 min; there will be 6 sample data in each hour. Let the 6 data be averaged; then the mean value of each hour is got. The discrete sample data of 10 days are recorded as . For better usage of nonlinear nature of neural network transfer function, the sample data are normalized into the interval , and the normalization formula can be expressed as follows:where is sample data, is minimum of all sample data, is the maximum of all sample data, is normalization data in the interval , and is the length of time sequence. The normalized wind speed is displayed in Figure 1.