Support Vector Regression Method for Wind Speed Prediction Incorporating Probability Prior Knowledge

Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2014, Article ID 410489, 10 pages http://dx.doi.org/10.1155/2014/410489 Research Article Support Vector Regression Method for Wind Speed Prediction Incorporating Probability Prior Knowledge Jiqiang Chen,1,2 Xiaoping Xue,1 Minghu Ha,2 Daren Yu,3 and Litao Ma2 1 Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China School of Science, Hebei University of Engineering, Handan 056038, China 3 School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China 2 Correspondence should be addressed to Xiaoping Xue; Received 3 December 2013; Accepted 20 January 2014; Published 4 March 2014 Academic Editor: Huaiqin Wu Copyright © 2014 Jiqiang Chen 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. Prior knowledge, such as wind speed probability distribution based on historical data and the wind speed fluctuation between the maximal value and the minimal value in a certain period of time, provides much more information about the wind speed, so it is necessary to incorporate it into the wind speed prediction. First, a method of estimating wind speed probability distribution based on historical data is proposed based on Bernoulli’s law of large numbers. Second, in order to describe the wind speed fluctuation between the maximal value and the minimal value in a certain period of time, the probability distribution estimated by the proposed method is incorporated into the training data and the testing data. Third, a support vector regression model for wind speed prediction is proposed based on standard support vector regression. At last, experiments predicting the wind speed in a certain wind farm show that the proposed method is feasible and effective and the model’s running time and prediction errors can meet the needs of wind speed prediction. 1. Introduction Wind power is a clean, renewable energy that will play an increasingly important role in the future electricity supply [1]. Unfortunately, due to the stochastic and nonstationary nature of wind, the wind power is variable and uncontrollable. It is difficult to maintain the balance between the supply and the demand of electricity, which is required by the electricity system [2]. Wind speed prediction is a key point in the management of wind farms because it is directly related to the power produced by each of the farm’s turbines, so it is usually the base of wind power forecasts, and it is necessary to increase the accuracy of the wind speed prediction for the effective use of wind energy. At present, there are mainly two kinds of wind speed prediction methods. One is based on the physical model, and the other is based on historical data. The prediction methods based on physical model often use the numerical weather prediction (NWP) data for wind speed prediction [3, 4]. Wind speed prediction methods based on NWP do not focus on the speed of a farm’s turbines but on the speed of a region. Thus, it needs to solve the problem of how the wind speed of a region is mapped to the wind speed of a certain wind generator. Wind speed prediction methods based on historical data predict the wind speed by using correlations among the initial data. In 2008, Louka et al. [5] improved wind speed forecasts for wind power prediction using Kalman filtering. In 2012, Cao et al. [6] presented a comparative analysis of the wind speed prediction accuracy of univariate and multivariate ARIMA models with their recurrent neural network counterparts. In 2013, Woods et al. [7] developed a method to produce synthetic time series of wind power at several locations based on a measured time series of wind speed from a reference site, and so on. In the 1990s, Vapnik et al. [8, 9] proposed support vector machines (SVMs), including support vector classifications (SVCs) and support vector regressions (SVRs). SVMs focus on the statistical learning problems for small size samples by solving a convex quadratic optimization problem and can solve the local minimization problem which cannot 2 be avoided by the neural network algorithm. SVMs use a kernel function to map the data in original space to a high dimensional feature space and then solve the nonlinear decision problem in high dimensional space. Thus, SVMs can successfully solve the problem of dimension disaster and have good generalization ability. However, the standard SVMs focus on historical data and cannot incorporate prior knowledge into learning process, which may causes the generalization ability of the standard SVMs to decrease. Therefore, in 2009, Guan et al. [10] proposed a modified method that incorporated prior knowledge into cancer classification based on gene expression data to improve accuracy. In 2011, Zhang et al. [11] proposed a fully Bayesian methodology for generalized kernel mixed models, which are extensions of generalized linear mixed models in the feature space induced by a reproducing kernel. In 2012, Liu and Xue [12] focused on designing a new class of kernels to incorporate the prior information into the training process of support vector regressions. Currently, SVMs have received extensive attention and are attracting more and more scholars to study from different views [13–22]. In 2011, Zhou et al. [23] presented a systematic study on fine tuning of LS-SVM model parameters for one-step ahead wind speed prediction, and Ortiz-Garcı́a et al. [24] proposed an improvement to an existing wind speed prediction system using banks of regression support vector machines for a final regression step in the prediction system. However, for the problem of wind speed prediction in practice, there is much prior knowledge. For example, the wind speed has a certain probability distribution in a season or in a day, and the probability distribution can be estimated with historical wind speed data. As the probability distribution can provide much more information about the wind speed, it is necessary to incorporate it into the wind speed prediction. Also, in a wind farm, the output wind speed V at a fixed time 𝑡 is the mean value V of many measured values V𝑘 (𝑘 = 0, 1, . . . , 𝑙) during a certain period of time Δ𝑡. Assume that Vmax = max𝑘 {V𝑘 } and Vmin = min𝑘 {V𝑘 }, then the larger the Vmax − Vmin is, the more the fluctuation of wind speed during the period of time Δ𝑡 is. Conversely, the smaller the Vmax − Vmin is, the less the fluctuation of wind speed during the period of time Δ𝑡 is. Nevertheless, the mean value V does not provide this prior knowledge at all. Therefore, in order to decrease the wind speed prediction errors, it is necessary to find a way to incorporate this prior knowledge in the wind speed prediction. However, the present methods for wind speed prediction often used the historical win (...truncated)