奇异值分解结合均匀设计采样的半不变量法概率潮流计算
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摘要
在样本形成过程中半不变量法概率潮流(PLF-CM)计算可能遇到输入变量相关系数矩阵非正定的情况,此时常用的Cholesky分解不再适用。提出一种奇异值分解(SVD)结合均匀设计采样(UDS)的PLF-CM计算方法。通过SVD和UDS结合Nataf变换得到考虑相关性的随机变量样本,借助这些样本计算常规数值方法难以求解的部分输入变量的半不变量,利用SVD处理输入变量的协方差矩阵以准确计算输出变量的半不变量,采用Cornish-Fisher级数展开求得输出变量的概率分布。以改造后的IEEE 14节点测试系统为算例,验证了所提方法的快速性、有效性及对高渗透率新能源发电的适应性。
In the process of sample formation,the PLF-CM(Probabilistic Load Flow based on Cumulant Method) calculation may encounter the condition that the correlation coefficient matrix of input variables is non-positive definite,where the commonly used Cholesky decomposition is no longer applicable. A PLF-CM calculation method with the combination of SVD(Singular Value Decomposition) and UDS(Uniform Design Sampling) is proposed. The random variable samples with the consideration of correlation are obtained by the combination of SVD,UDS and Nataf transformation,which are used to calculate the cumulants of some input variables that are hardly be solved by the conventional numerical methods. The SVD is adopted to deal with the covariance matrix of input variables to accurately calculate the cumulants of output variables,and the probability distribution of output variables is obtained through Cornish-Fisher series expansion. The modified IEEE 14-bus test system is taken as an example to verify the rapidity,effectiveness,and adaptability of the proposed method to high permeability new energy power generation.
In the process of sample formation,the PLF-CM(Probabilistic Load Flow based on Cumulant Method) calculation may encounter the condition that the correlation coefficient matrix of input variables is non-positive definite,where the commonly used Cholesky decomposition is no longer applicable. A PLF-CM calculation method with the combination of SVD(Singular Value Decomposition) and UDS(Uniform Design Sampling) is proposed. The random variable samples with the consideration of correlation are obtained by the combination of SVD,UDS and Nataf transformation,which are used to calculate the cumulants of some input variables that are hardly be solved by the conventional numerical methods. The SVD is adopted to deal with the covariance matrix of input variables to accurately calculate the cumulants of output variables,and the probability distribution of output variables is obtained through Cornish-Fisher series expansion. The modified IEEE 14-bus test system is taken as an example to verify the rapidity,effectiveness,and adaptability of the proposed method to high permeability new energy power generation.
引文
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[18] 张里,刘俊勇,刘友波,等.计及风速相关性的电网静态安全风险评估[J].电力自动化设备,2015,35(4):84-89.ZHANG Li,LIU Junyong,LIU Youbo,et al.Static security risk assessment of power system considering wind speed correlation[J].Electric Power Automation Equipment,2015,35(4):84-89.
[19] CHEN Yan,WEN Jinyu,CHENG Shijie.Probabilistic load flow method based on Nataf transformation and Latin hypercube sampling[J].IEEE Transactions on Sustainable Energy,2013,4(2):294-301.
[20] GALICIA S.The real time data for wind speed of the Galician wind farm[EB/OL].(2016-04-01)[2017-05-20].http://www.sotaventogalicia.com/en/real-time-data/historical.
[2] 方斯顿,程浩忠,徐国栋,等.基于Nataf变换含相关性的扩展准蒙特卡洛随机潮流方法[J].电工技术学报,2017,32(2):255-263.FANG Sidun,CHENG Haozhong,XU Guodong,et al.A Nataf transformation based on extended quasi Monte Carlo simulation method for solving probabilistic load flow problems with correlated random variables[J].Transactions of China Electrotechnical Society,2017,32(2):255-263.
[3] 徐潇源,严正,冯冬涵,等.基于输入变量秩相关系数的概率潮流计算方法[J].电力系统自动化,2014,38(12):54-61.XU Xiaoyuan,YAN Zheng,FENG Donghan,et al.Probabilistic load flow calculation based on rank correlation coefficient of input random variable[J].Automation of Electric Power Systems,2014,38(12):54-61.
[4] 徐青山,黄煜,刘建坤,等.采用混合高斯模型及边缘变换技术的蒙特卡洛随机潮流方法[J].电力系统自动化,2016,40(16):23-30.XU Qingshan,HUANG Yu,LIU Jiankun,et al.Probabilistic load flow method using Monte Carlo simulation based on Gaussian mixture model and marginal transformation[J].Automation of Electric Power Systems,2016,40(16):23-30.
[5] 吴晨曦,文福拴,陈勇,等.含有风电与光伏发电以及电动汽车的电力系统概率潮流[J].电力自动化设备,2013,33(10):8-15.WU Chenxi,WEN Fushuan,CHEN Yong,et al.Probabilistic load flow of power system with WFs,PVs and PEVs[J].Electric Power Automation Equipment,2013,33(10):8-15.
[6] USAOLA J.Probabilistic load flow with correlated wind power injections[J].Electric Power Systems Research,2010,80(5):528-536.
[7] 石东源,蔡德福,陈金富,等.计及输入变量相关性的半不变量法概率潮流计算[J].中国电机工程学报,2012,32(28):104-113.SHI Dongyuan,CAI Defu,CHEN Jinfu,et al.Probabilistic load flow calculation based on cumulant method considering correlation between input variables[J].Proceedings of the CSEE,2012,32(28):104-113.
[8] 黄煜,徐青山,卞海红,等.基于拉丁超立方采样技术的半不变量法随机潮流计算[J].电力自动化设备,2016,36(11):112-119.HUANG Yu,XU Qingshan,BIAN Haihong,et al.Cumulant method based on Latin hypercube sampling for calculating probabilistic power flow[J].Electric Power Automation Equipment,2016,36(11):112-119.
[9] 刘宇,高山,杨胜春,等.电力系统概率潮流算法综述[J].电力系统自动化,2014,38(23):127-135.LIU Yu,GAO Shan,YANG Shengchun,et al.Review on algorithms for probabilistic load flow in power system[J].Automation of Electric Power Systems,2014,38(23):127-135.
[10] 张润楚,王兆军.均匀设计抽样及其优良性质[J].应用概率统计,1996(4):337-347.ZHANG Runchu,WANG Zhaojun.Uniform design sampling and its fine properties[J].Applied Probability,1996(4):337-347.
[11] 方斯顿,程浩忠,徐国栋,等.基于 Nataf 变换和准蒙特卡洛模拟的随机潮流方法[J].电力自动化设备,2015,35(5):38-44.FANG Sidun,CHENG Haozhong,XU Guodong,et al.Probabilistic load flow method based on Nataf transformation and quasi Monte Carlo simulation[J].Electric Power Automation Equipment,2015,35(5):38-44.
[12] HYV?RINE A,OIA E.Independent component analysis:algorithms and applications[J].Neural Networks,2000,13(4-5):411-430.
[13] XIAO Q.Evaluating correlation coefficient for Nataf transformation[J].Probabilistic Engineering Mechanics,2014,37(4):1-6.
[14] 刘苏琴.考虑风电机模型的电力系统随机潮流计算[D].南京:东南大学,2007.LIU Suqin.Probabilistic load flow in power systems containing wind farms[D].Nanjing:Southeast University,2007.
[15] 刘立士.半不变量的概率组合性质[D].沈阳:东北大学,2006.LIU Lishi.The probabilistic and combinatorial characteristics of the cumulants[D].Shenyang:Northeastern University,2006.
[16] 郭效军,蔡德福.不同级数展开的半不变量法概率潮流计算比较分析[J].电力自动化设备,2013,33(12):85-90.GUO Xiaojun,CAI Defu.Comparison of probabilistic load flow calculation based on cumulant method among different series expansions[J].Electric Power Automation Equipment,2013,33(12):85-90.
[17] 胡泽春,王锡凡.基于半不变量法的随机潮流误差分析[J].电网技术,2009,33(18):32-37.HU Zechun,WANG Xifan.Error analysis of the probabilistic load flow based on cumulant method[J].Power System Technology,2009,33(18):32-37.
[18] 张里,刘俊勇,刘友波,等.计及风速相关性的电网静态安全风险评估[J].电力自动化设备,2015,35(4):84-89.ZHANG Li,LIU Junyong,LIU Youbo,et al.Static security risk assessment of power system considering wind speed correlation[J].Electric Power Automation Equipment,2015,35(4):84-89.
[19] CHEN Yan,WEN Jinyu,CHENG Shijie.Probabilistic load flow method based on Nataf transformation and Latin hypercube sampling[J].IEEE Transactions on Sustainable Energy,2013,4(2):294-301.
[20] GALICIA S.The real time data for wind speed of the Galician wind farm[EB/OL].(2016-04-01)[2017-05-20].http://www.sotaventogalicia.com/en/real-time-data/historical.
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