Correlation Characteristic Analysis for Wind Speed in Different Geographical Hierarchies
As the scale of wind power bases rises, it becomes significant in power system planning and operation to provide detailed correlation characteristic of wind speed in different geographical hierarchies, that is among wind turbines, within a wind farm and its regional wind turbines, and among different wind farms. A new approach to analyze the correlation characteristics of wind speed in different geographical hierarchies is proposed in this paper. In the proposed approach, either linear or
... her linear or nonlinear correlation of wind speed in each geographical hierarchy is firstly identified. Then joint sectionalized wind speed probability distribution is modeled for linear correlation analysis while a Copula function is adopted in nonlinear correlation analysis. By this approach, temporal-geographical correlations of wind speed in different geographical hierarchies are properly revealed. Results of case studies based on Jiuquan Wind Power Base in China are analyzed in each geographical hierarchy, which illustrates the feasibility of the proposed approach. In general, correlation coefficients  were applied to measure the degree of correlation of targets. The Pearson coefficient is commonly used as a measure of the linear dependence of variables. Applying it to the wind energy field,  presented a two-stage model for wind speed series considering autocorrelation and cross-correlation based on Pearson coefficient. However, the Pearson correlation coefficient only describes linear correlations but cannot cope with nonlinear correlation problems. Alternatively, Copula theory has recently been applied to wind speed and wind power as a way of modeling nonlinear dependence structures. A rank correlation coefficient  , namely the Spearman coefficient was extensively utilized to measure nonlinear correlation of wind speed. Reference  proposed to evaluate the fit of a class of Copulas-Archimedean Copulas to model wind speed correlation. Reference  separated multivariate wind speed time series into dependence structure modeled by Copulas and subsequently utilized an ARMA model to represent each univariate time series. However, the tail correlation of wind speed among wind farms, which commonly exists in the wind speed joint distribution, has attracted less attention. Against the background of Jiuquan in northwest China, where the biggest 10 GW wind power base is under construction, the need to further investigate the interrelationship among wind turbines within the wind farm as well as among wind farms within the wind site persists is driven by the facts of their geographical adjacency and randomness in wind energy. This paper addresses the analysis for correlation characteristics of wind speed in different geographical hierarchies that is, among wind turbines, within the wind farm and its wind turbines, and among wind farms. According to the linear or nonlinear correlation condition in each geographical hierarchy, the use of the Pearson coefficient for linear correlations, and Spearman and tail coefficients for nonlinear correlations were judged, respectively. In this paper, the proposed approach is to analyze the correlation characteristics of wind speed quantitatively and qualitatively based on data from the Wind Speed Dataset of the Gansu Wind Power Technology Center, China. The correlation characteristic analysis in different geographical hierarchies will provide detailed correlation information to improve the accuracy of wind speed or power prediction. It is implemented to evaluate the wind unit siting and wind farm planning, especially for China's concentrated wind power integration. They is certainly high interest in production probability simulation, which contributes to power system planning and risk assessments. We note that while in this work the proposed approach is applied to the Gansu Wind Power Base, it can be easily extended to other cases in different regions. The remainder of the paper is organized as follows: Section 2 introduces the linear correlation analysis including joint sectionalized wind speed probability modeling and linear correlation coefficient for correlation measurement. In addition, nonlinear correlation analysis including Copula theory and its nonlinear correlation coefficients are given in Section 3. The proposed methodology for analysis of the correlation characteristics of wind speed in different hierarchies is described in Section 4. Case studies on the correlation characteristics of wind speed among wind turbines, among wind farm and its wind turbines, and among wind farms are discussed in Section 5. Conclusions are given in Section 6. Linear Correlation Analysis Correlations can be classified as linear correlations and nonlinear correlations. Linear correlations, which refer to a straight line correlation between two variables, characterize the degree of correlation to which larger wind speed x values go with larger speed y values and smaller x values go with smaller y values in the paired wind data sets. In this section, the method to establish a joint sectionalized wind speed probability distribution will be introduced. The joint sectionalized probability distribution is appropriate for linear correlations in a qualitative way. Then, the Pearson coefficient that can be used to quantitatively measure the linear correlation between the individual values of wind speed series at different locations.