پیش بینی کوتاه مدت سرعت باد با استفاده از فیلتر کالمن بدون بو مبتنی بر روش رگرسیون بردار پشتیبانی حالت فضا

Accurate wind speed forecasting is becoming increasingly important to improve and optimize renewable wind power generation. Particularly, reliable short-term wind speed prediction can enable model predictive control of wind turbines and real-time optimization of wind farm operation. However, this task remains challenging due to the strong stochastic nature and dynamic uncertainty of wind speed. In this study, unscented Kalman filter (UKF) is integrated with support vector regression (SVR) based state-space model in order to precisely update the short-term estimation of wind speed sequence. In the proposed SVR–UKF approach, support vector regression is first employed to formulate a nonlinear state-space model and then unscented Kalman filter is adopted to perform dynamic state estimation recursively on wind sequence with stochastic uncertainty. The novel SVR–UKF method is compared with artificial neural networks (ANNs), SVR, autoregressive (AR) and autoregressive integrated with Kalman filter (AR-Kalman) approaches for predicting short-term wind speed sequences collected from three sites in Massachusetts, USA. The forecasting results indicate that the proposed method has much better performance in both one-step-ahead and multi-step-ahead wind speed predictions than the other approaches across all the locations.

Green wind power is one of the promising renewable energy sources to substitute traditional coal and fossil fuel based power generation with mitigated carbon footprint and environmental impact. Due to its renewable nature and environmental friendliness, wind energy has received fast growing attention throughout the world and the utilization of wind power has increased dramatically over the past decade. For instance, the construction of new wind power generation capacity in the first three quarters of 2012 was 4728 MW in total and the cumulative wind power capacity in the United States was increased to 51,630 MW [1]. However, significant intermittency and stochastic fluctuation of wind speed pose great challenges to controlling wind turbines and optimizing wind farm operation towards reliable wind power generation [2]. Therefore, it is crucially important to accurately forecast wind speed so that the model based optimal control of wind turbines can be achieved with stabilized wind power output. Specifically, long-term wind speed forecasting is important for optimizing the site selection and production planning of wind farms, while short-term prediction is vital for controlling wind turbines and improving their power generation efficiency and life span [3], [4], [5] and [6]. In literature study, the methods developed for wind speed prediction can be divided into two main categories: physical model based approaches and statistical modeling methods. As one type of physical model based approaches, numerical weather prediction (NWP) techniques rely on a class of physical models with numerical parameters characterizing local meteorological and geographical properties such as temperature, atmospheric pressure, surface roughness and obstacles [7], [8] and [9]. Nevertheless, the prediction capability of NWP methods degrade significantly when the random uncertainty of weather conditions is strong. In practice, physical models are often utilized through integration with statistical modeling methods in order to combine the advantages of two different types of techniques while mitigate the restrictions of NWP methods [10], [11] and [12]. Since physical models alone may not well capture the stochastic nature of wind speed, statistical modeling methods are developed for wind speed prediction with some success. Different from physical models, statistical methods depend on historical wind speed data for dynamic predictions without prior knowledge of physical mechanism underlying wind speed pattern. Time-series models and artificial neural network (ANN) models are two main kinds of statistical modeling methods that have been used for wind speed prediction [13]. Among time-series modeling methods, autoregressive moving average (ARMA) models have gained substantial attention in predicting wind speed sequence and wind power output [14] and [15]. Several variants of ARMA models have been developed for forecasting wind speed and direction, including the simplified autoregressive (AR), autoregressive integrated moving average (ARIMA), ARMA or AR with exogenous input (ARMAX or ARX), fractional-ARIMA with the differencing parameter being a fractional number [16], [17] and [18]. However, AR, ARMA and ARIMA models require high model orders so as to accommodate stochastic variations of wind speed sequence. Furthermore, these time-series models are essentially linear so that they may not be well suited for characterizing the stochastic nature and uncertain dynamics of wind speed. Alternatively, ANN is a nonlinear modeling technique for wind speed prediction and it basically maps a random input vector into the corresponding random output scalar or vector through multi-layer network structure without presuming any physical relationship [19]. Heuristic algorithms such as genetic algorithm (GA) and particle swarm optimization (PSO) are employed to optimize parameters in ANN [20]. Moreover, geographic parameters can be incorporated into ANN model to predict the monthly average wind speed [21]. Another attempt is to design a generalized feed-forward type of ANN for predicting the probability density of annual wind speed based on the parameters of Weibull function [22]. So far, significant effort has been reported to develop different types of neural networks, improve the network structure, optimize the number of neurons and activation functions, and design network learning algorithms in order to conduct more accurate prediction [23], [24], [25], [26] and [27]. Though ANN techniques are capable of handling wind speed sequence with nonlinearity, its generalization ability is not guaranteed so that a well trained ANN model may lead to poor prediction performance for new observations. In addition to time-series and ANN models, support vector regression (SVR) method has been applied to predict wind speed through a nonlinear kernel function based predictive model within high-dimensional feature space [28], [29] and [30]. As opposed to ANN method, SVR approach effective overcomes the drawbacks of model over-fitting and poor generalization. Thus it has desired characteristics such as global optimal solution and strong generalization capability. However, SVR technique itself does not have strong capacity to handle system uncertainty and stochastic nature. More recently, different types of statistical methods are integrated to enable more accurate and reliable wind speed prediction. For instance, wavelet analysis is employed to decompose original time-series of wind speed into different sub-series and then combined with improved time series method (ITSM) to forecast wind speed and wind power generation [31]. Nevertheless, the way of decomposing wind series can be quite empirical so that the optimal prediction performance is obtained by ad-hoc. Meanwhile, ARIMA model is applied to build the state-space formulations for Kalman filter based wind speed sequence estimation and update [32]. Nevertheless, Kalman filter relies on the basic assumption of Gaussian disturbance, which may not hold for actual wind speed sequence. In addition, Markov chain (MC) is attempted to modify the predicted horizons of ANN method according to long-term patterns of wind speed data so as to avoid the over-fitting issue of ANN model in short-term wind speed forecasting [33]. However, dividing the wind speed variation into different states for MC is arbitrary and lack of systematic feature. Typically, a hybrid model tends to yield more accurate prediction results than a single kind of method. On the other hand, a proper integration of different types of statistical modeling techniques to obtain the optimal prediction performance is not a trivial task. In addition to physical and statistical models, spatial correlation model provides an alternate way for wind speed prediction. Different from statistical approaches that only take into consideration the historical wind speed measurements, spatial correlation models use the cross-correlation information of wind speed between different geographic locations. Based on the assumption that wind speed measurements in neighboring sites are correlated, the wind speed data at neighboring sites are employed to predict the local wind speed sequence [34] and [35]. Moreover, a local recurrent multi-layer network model is employed to carry out wind speed and power forecasting by considering spatial correlation [36]. Another attempt to predict monthly average wind speed is achieved by a ANN model with resilient propagation, which obtains prediction by using the wind speed in neighboring sites termed as reference stations [37]. Similarly, a spatial correlation model based on prognostic method with exergy analysis is proposed to predict time-series of wind speed [3]. Spatial correlation models are advantageous in wind speed prediction among multiple wind farms that are geographically close to each other. However, extremely large number of wind speed measurements from multiple related sites are needed for developing the spatial correlation models. In this article, a novel hybrid predictive modeling approach is proposed by integrating unscented Kalman filter with support vector regression based nonlinear state-space model framework in order to enhance the capacity of handling stochastic and dynamic uncertainty as well as minimize the errors of multi-step-ahead wind speed forecasting. First, support vector regression is employed to formulate a kernel function based nonlinear state-space model structure. Then, unscented Kalman filter instead of regular Kalman filter is adopted to conduct recursive state estimation on the SVR based nonlinear state-space model with strong stochastic uncertainty. Further, the wind speed sequence is predicted from the UKF driven SVR model. In this way, the integrated SVR–UKF approach can mitigate prediction errors by well accounting for the stochastic and dynamic nature of wind speed. The remainder of the article is organized as follows. Section 2 gives preliminaries on ANN, AR and AR-Kalman based wind speed prediction methods. In Section 3, SVR and UKF techniques are integrated to form the novel SVR–UKF approach for short-term wind speed prediction. The presented SVR–UKF approach is applied to wind speed forecasting of three different locations and its performance is compared with that of the SVR, AR-Kalman, AR and ANN approaches for both one-step-ahead and multi-step-ahead predictions in Section 4. The conclusions of this paper are summarized in Section 5.

In this study, a novel hybrid modeling method is proposed for short-term wind speed prediction by integrating nonlinear support vector regression based state-space model with unscented Kalman filter based dynamic state estimation. The presented approach first builds a nonlinear support vector regression model in order to formulate the state-space framework for characterizing wind speed sequence. Then unscented Kalman filter is adopted to dynamically update states with random uncertainty within state-space formulations so that the future wind speed can be more precisely predicted. Since the dynamic state is recursively updated in the proposed SVR–UKF approach, the stochastic uncertainty and fluctuations of wind speed can be better accounted for by the presented method than the traditional strategies. The proposed SVR–UKF method is demonstrated to be capable of predicting short-term wind speed with high accuracy through its comparison with the conventional ANN, AR, AR-Kalman and SVR approaches. The better performance of SVR–UKF method in both one-step-ahead and multi-step-ahead wind speed predictions in different locations indicates its considerably improved reliability and robustness. Future research may further explore the wind power prediction from different kinds of wind turbines and then develop the predictive model based control and optimization strategies for wind farm operation.