Abstract：Accurate wind farms’ output prediction possesses a vital part in the security and the economy research when wind farm connecting to the power grid.Considering that there often exists output correlation between adjacent wind farms, a novel method based on the Copula function and the kernel estimation theory is proposed to analysis wind farms’ output correlation.Firstly, the kernel estimation Copula function is derived by the Copula function and the nonparametric kernel density estimation theory.Then, the empirical Copula function is replaced by the kernel estimation Copula to analysis the correlation of wind farms’ output.Unlike the empirical Copula function, the kernel estimation Copula is a continuous function, and can effectively eliminate the parameter hypothesis error.Moreover, using the kernel estimation Copula can reduce the complexity and calculated amount of parameter estimation in principle.The actual output of wind farms in North China is chosen as an example.The wind farms’ output model based on the kernel estimation Copula and the empirical Copula function are connected to the IEEE30 node test system to calculate the power flow.The results show that the correlation model of wind farms’ output established by the kernel estimation Copula function is closer to the actual data model, and the two calculation results are consistent.
徐玉琴,陈坤,李俊卿,聂暘. Copula函数与核估计理论相结合分析风电场出力相关性的一种新方法[J]. 电工技术学报, 2016, 31(13): 92-100.
Xu Yuqin ,Chen Kun ,Li Junqing,Nie Yang. A New Method Analyzing Output Correlation of Multi-Wind Farms Based on Combination of Copula Function and Kernel Estimation Theory. Transactions of China Electrotechnical Society, 2016, 31(13): 92-100.
[1] 陈妮亚,钱政,孟晓风,等.基于空间相关法的风电场风速多步预测模型[J].电工技术学报,2013,28(5):15-21. Chen Niya,Qian Zheng,Meng Xiaofeng,et al.Multiste pahead wind speed forecasting model based on spatial correlation and support vector machine[J].Transactions of China Electrotechnical Society,2013,28(5):15-21. [2] 曲正伟,王京波,王云静,等.考虑运行风险约束的风电场群准入容量分析[J].电网技术,2014,38(7):1861-1866. Qu Zhengwei,Wang Jingbo,Wang Yunjing,et al.Analysis on acceptable capacity of wind farm group considering operation risk constraints[J].Power System Technology,2014,38(7):1861-1866. [3] 张颖超,郭晓杰,叶小岭,等.一种短期风电功率集成预测方法[J].电力系统保护与控制,2016,44(7):90-95. Zhang Yingchao,Guo Xiaojie,Ye Xiaoling,et al.An integrated forecasting method of short-term wind power[J].Power System Protection and Control,2016,44(7):90-95. [4] 吴巍,汪可友,韩蓓,等.基于 Pair Copula 的随机潮流三点估计法[J].电工技术学报,2015,30(9):121-128. Wu Wei,Wang Keyou,Han Bei,et al.Pair Copula based three-point estimate method for probabilistic load flow calculation[J].Transactions of China Electrotechnical Society,2015,30(9):121-128. [5] 甘迪,柯德平,孙元章,等.基于集合经验模式分解和遗传-高斯过程回归的短期风速概率预测[J].电工技术学报,2015,30(11):138-147. Gan di,Ke Deping,Sun Yuanzhang,et al.Short-term wind speed probabilistic forecasting based on EEMD and coupling GA-GPR[J].Transactions of China Electrotechnical Society,2015,30(11):138-147. [6] 田中大,李树江,王艳红,等.基于小波变换的风电场短期风速组合预测[J].电工技术学报,2015,30(9):112-120. Tian Zhongda,Li Shujiang,Wang Yanhong,et al.Short-term wind speed combined prediction for wind farms based on wavelet transform[J].Transactions of China Electrotechnical Society,2015,30(9):112-120. [7] 李剑楠,乔颖,鲁宗相,等.大规模风电多尺度出力波动性的统计建模研究[J].电力系统保护与控制,2012,40(19):7-13. Li Jiannan,Qiao Ying,Lu Zongxiang,et al.Research on statistical modeling of large-scale wind farms output fluctuations in different special and temporal scales[J].Power System Protection and Control,2012,40(19):7-13. [8] 蔡德福,石东源,陈金富.基于Copula理论的计及输入随机变量相关性的概率潮流计算[J].电力系统保护与控制,2013,41(20):13-19. Cai Defu,Shi Dongyuan,Chen Jinfu.Probabilistic load flow considering correlation between input random variables based on Copula theory[J].Power System Protection and Control,2013,41(20):13-19. [9] 蒋程,刘文霞,张建华,等.含风电接入的发输电系统风险评估[J].电工技术学报,2014,29(2):260-270. Jiang Cheng,Liu Wenxia,Zhang Jianhua,et al.Risk assessment of generation and transmission systems considering wind power penetration[J].Transactions of China Electrotechnical Society,2014,29(2):260-270. [10]杨洪明,王爽,易德鑫,等.考虑多风电场出力相关性的电力系统随机优化调度[J].电力自动化设备,2013,33(1):114-120. Yang Hongming,Wang Shuang,Yi Dexin,et al.Stochastic optimal dispatch of power system considering multi-wind power correlation[J].Electric Power Automation Equipment,2013,33(1):114-120. [11]Papaefthymiou G,Kurowicka D.Using Copula for modeling stochastic dependence in power system uncertainly analysis[J].IEEE Transactions on Power Systems,2009,24(1):40-49. [12]蔡菲,严正,赵静波,等.基于Copula理论的风电场间风速及输出功率相依结构建模[J].电力系统自动化,2013,37(17):9-16. Cai Fei,Yan Zheng,Zhao Jingbo,et al.Dependence structure models for wind speed and wind power among different wind farms based on Copula theory[J].Automation of Electric Power Systems,2013,37(17):9-16. [13]Faugeras O P.A quantile-copula approach to conditional density estimation[J].Journal of Multivariate Analysis,2009,100(9):2083-2099. [14]Gardes L,Girard S.Nonparametric estimation of the conditional tail copula[J].Journal of Multivariate Analysis,2015,137(4):1-16. [15]侯亚楠.Copula函数的估计及其应用[D].武汉:华中科技大学,2013. [16]Johan S.Hybrid copula estimators[J].Journal of Statistical Planning and Inference,2014,160:23-34. [17]Nelsen R B.An introduction to copulas[M].New York:Springer,2006. [18]任洲洋,颜伟,项波,等.考虑光伏和负荷相关性的概率潮流计算[J].电工技术学报,2015,30(24):181-187. Ren Zhouyang,Yan Wei,Xiang Bo,et al.Probabilistic power flow analysis incorporating the correlations between PV power outputs and loads[J].Transactions of China Electrotechnical Society,2015,30(24):181-187. [19]缪鹏彬,余娟,史乐峰,等.基于改进非参数核密度估计和拉丁超立方抽样的电动公共客车负荷模型[J].电工技术学报,2016,31(4):187-193. Miao Pengbin,Yu Juan,Shi Lefeng,et al.Electric public bus load model based on improved kernel density estimation and latin hypercube sampling[J].Transactions of China Electrotechnical Society,2016,31(4):187-193. [20]Epanechnikov V A.Nonparametric estimation of a multivariate probability density[J].Theory of Probability and its Applications,1969,14(1):153-158. [21]Qin Zhilong,Li Wenyuan,Xiong Xiaofu.Estimating wind speed probability distribution using kernel density method[J].Electric Power Systems Research,2011,81(12):2139-2146. [22]Bouezmarni T,Rombouts J V.Nonparametric density estimation for multivariate bounded data[J].Journal of Statistical Planning and Inference,2010,140(1):139-152. [23]潘雄,王莉莉,徐玉琴,等.基于混合Copula函数的风电场出力建模方法[J].电力系统自动化,2014,38(14):17-22. Pan Xiong,Wang Lili,Xu Yuqin,et al.A wind farm power modeling method based on mixed Copula[J].Automation of Electric Power Systems,2014,38(14):17-22. [24]季峰,蔡兴国,王俊.基于混合Copula函数的风电功率相关性分析[J].电力系统自动化,2014,38(2):1-5. Ji Feng,Cai Xingguo,Wang Jun.Wind power correl-ation analysis based on hybrid Copula[J].Automation of Electric Power Systems,2014,38(2):1-5. [25]Longla M.On mixtures of copulas and mixing coefficients[J].Journal of Multivariate Analysis,2015,139:259-265. [26]黎静华,文劲宇,程时杰,等.考虑多风电场出力 Copula 相关关系的场景生成方法[J].中国电机工程学报,2013,33(16):30-36. Li Jinghua,Wen Jinyu,Cheng Shijie,et al.A scene generation method considering copula correlation relationship of multi-wind farms power[J].Proceedings of the CSEE,2013,33(16):30-36. [27]杨希.Copula函数的选择方法与应用[D].济南:山东科技大学,2010.
2016, Vol. 31 
