计及输入变量相关性的有源配电网可靠性概率评估三点估计法
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摘要
为准确分析分布式电源出力的波动性和相关性对配电网可靠性的影响,提出一种计及随机变量相关性的有源配电网可靠性评估三点估计法。该方法利用Nataf变换处理输入变量之间的相关性,结合点估计法将有源配电网可靠性概率分析转化为确定性问题求解。首先在独立的标准正态变量空间中根据点估计法原理选取样本点;然后通过Nataf逆变换求取对应的原始变量空间的样本点,构造可靠性评估样本;最后采用故障模式后果分析法对样本进行可靠性计算,并将样本结果概率叠加得到配电网可靠性指标的概率分布信息。改进的IEEE RBTS-Bus6馈线F4系统算例结果表明,所提方法能够有效实现计及输入变量相关性的配电网可靠性评估,并且计算量小、计算速度快,具有良好的精度。
In order to make sure impact of fluctuation and correlation of distributed generation(DG) power on active distribution network reliability, a probabilistic reliability evaluation method based on three-point estimate method(3PEM) is proposed to consider correlation influence of random input variables. Nataf transformation is adopted to deal with correlation among variables and point estimation is used to transform probabilistic reliability analysis into deterministic problem for solving. Firstly, sample points were obtained with 3PEM in independent standard normal variable space. Then, corresponding sample points in original variable space were calculated with inverse Nataf transformation for reliability assessment. Finally, failure mode effect analysis(FMEA) method was adopted to calculate reliability samples and system reliability indexes of distribution network are obtained from probabilistic superposition of the sample results. Simulation results with modified IEEE RBTS-bus 6 feeder F4 system show that the proposed method can achieve probabilistic reliability evaluation of distribution network considering correlation of input variables effectively, efficiently and accurately.
In order to make sure impact of fluctuation and correlation of distributed generation(DG) power on active distribution network reliability, a probabilistic reliability evaluation method based on three-point estimate method(3PEM) is proposed to consider correlation influence of random input variables. Nataf transformation is adopted to deal with correlation among variables and point estimation is used to transform probabilistic reliability analysis into deterministic problem for solving. Firstly, sample points were obtained with 3PEM in independent standard normal variable space. Then, corresponding sample points in original variable space were calculated with inverse Nataf transformation for reliability assessment. Finally, failure mode effect analysis(FMEA) method was adopted to calculate reliability samples and system reliability indexes of distribution network are obtained from probabilistic superposition of the sample results. Simulation results with modified IEEE RBTS-bus 6 feeder F4 system show that the proposed method can achieve probabilistic reliability evaluation of distribution network considering correlation of input variables effectively, efficiently and accurately.
引文
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[16]杨欢,邹斌.含相关性随机变量的概率潮流三点估计法[J].电力系统自动化,2012,36(15):51-56.Yang Huan,Zou Bin.A three-point estimate method for solving probabilistic power flow problems with correlated random variables[J].Automation of Electric Power Systems,2012,36(15):51-56(in Chinese).
[17]孙若笛,谢开贵.计及风速-负荷相关性的配电网可靠性评估Monte Carlo模拟法[J].电力系统保护与控制,2012,40(18):12-18.Sun Ruodi,Xie Kaigui.Reliability evaluation of distribution networks using Monte Carlo method considering correlations between wind speed and load[J].Power System Protection and Control,2012,40(18):12-18(in Chinese).
[18]葛少云,张鑫,刘洪,等.基于点估计法的有源配电网概率可靠性评估[J].电力系统保护与控制,2014,42(12):91-100.Ge Shaoyun,Zhang Xin,Liu Hong,et a1.Active distribution network probabilistic reliability evaluation based on point estimation method[J].Power System Protection and Control,2014,42(12):91-100(in Chinese).
[19]赵渊,张夏菲,周家启.电网可靠性评估的非参数多变量核密度估计负荷模型研究[J].中国电机工程学报,2009,29(31):27-33.Zhao Yuan,Zhang Xiafei,Zhou Jiaqi.Load modeling utilizing nonparametric and multivariate kernel density estimation[J].Proceedings of the CSEE,2009,29(31):27-33(in Chinese).
[20]Liu P L,Der K A.Multivariate distribution models with prescribed marginals and covariances[J].Probabilistic Engineering Mechanics,1986,1(2):105-112.
[21]Hill G W,Davis A W.Generalized asymptotic expansions of Cornish-Fisher type[J].The Annals of Mathematical Statistics,1968,39(4):1264-1273.
[22]王杨,万凌云,胡博,等.基于孤岛运行特性的微电网可靠性分析[J].电网技术,2014,38(9):2379-2385.Wang Yang,Wan Lingyun,Hu Bo,et a1.Isolated island operating characteristics based analysis on reliability of microgrid[J].Power System Technology,2014,38(9):2379-2385(in Chinese).
[23]Billinton R,Jonnavithula S.A test system for teaching overall power system reliability assessment[J].IEEE Transactions on Power Systems,1996,4(11):1670-1676.
[2]康龙云,郭红霞,吴捷,等.分布式电源及其接入电力系统时若干研究课题综述[J].电网技术,2010,34(11):43-47.Kang Longyun,Guo Hongxia,Wu Jie,et a1.Characteristics of distributed generation system and related research issues caused by connecting it to power system[J].Power System Technology,2010,34(11):43-47(in Chinese).
[3]沈鑫,曹敏.分布式电源并网对于配电网的影响研究[J].电工技术学报,2015,30(1):346-351.Shen Xin,Cao Min.Research on the influence of distributed power grid for distribution network[J].Transactions of China Electrotechnical Society,2015,30(1):346-351(in Chinese).
[4]罗奕,汪隆君,王钢.计及分布式电源出力相关性的微电网发电系统可靠性评估[J].电力系统自动化,2014,38(12):34-38+80.Luo Yi,Wang Longjun,Wang Gang.Reliability assessment of microgrid generation system considering output correlation of distributed generators[J].Automation of Electric Power Systems,2014,38(12):34-38+80(in Chinese).
[5]王昌照,汪隆君,王钢,等.分布式电源出力与负荷相关性对配电网可靠性的影响分析[J].电力自动化设备,2015,35(6):99-105.Wang Changzhao,Wang Longjun,Wang Gang,et a1.Impact of distributed generation output and load correlation on distribution network reliability[J].Electric Power Automation Equipment,2015,35(6):99-105(in Chinese).
[6]万国成,任震,吴日昇,等.混合法在复杂配电网可靠性评估中的应用[J].中国电机工程学报,2004,24(9):92-98.Wan Guocheng,Ren Zhen,Wu Risheng,et a1.Hybrid method for the reliability evaluation of the complex distribution system[J].Proceedings of the CSEE,2004,24(9):92-98(in Chinese).
[7]田洪迅,袁蓉,赵渊.含分布式电源的配网可靠性概率计算[J].电网技术,2013,37(6):1562-1569.Tian Hongxun,Yuan Rong,Zhao Yuan.Computation of probability distribution for reliability indices of distribution system containing distributed generation[J].Power System Technology,2013,37(6):1562-1569(in Chinese).
[8]赵华,王主丁,谢开贵,等.中压配电网可靠性评估方法的比较研究[J].电网技术,2013,37(11):3295-3302.Zhao Hua,Wang Zhuding,Xie Kaigui,et a1.Comparative study on reliability assessment methods for medium voltage distribution network[J].Power System Technology,2013,37(11):3295-3302(in Chinese).
[9]卢晶晶,赵渊,赵勇帅,等.含分布式电源配电网可靠性评估的点估计法[J].电网技术,2013,37(8):2250-2257.Lu Jingjing,Zhao Yuan,Zhao Yongshuai,et a1.A point estimation method for reliability evaluation of distribution network with distributed generation[J].Power System Technology,2013,37(8):2250-2257(in Chinese).
[10]黄辉,王淳,王宁,等.基于开关特性的配电网可靠性等效叠加评估算法[J].电网技术,2016,40(10):3163-3168.Huang Hui,Wang Chun,Wang Ning,et al.Equivalent Superposition Algorithm for Distribution Network Reliability Evaluation Based on Switch Characteristics[J].Power System Technology,2016,40(10):3163-3168(in Chinese).
[11]李蕊,李跃,郭威,等.分布式电源接入对配电网可靠性影响的仿真分析[J].电网技术,2016,40(7):2016-2021.Li Rui,Li Yue,Guo Wei,et al.Simulation Analysis of the Influence of Distributed Generation on the Reliability of Distribution Network[J].Power System Technology,2016,40(7):2016-2021(in Chinese).
[12]韦婷婷,王主丁,寿挺,等.基于DG并网运行的中压配网可靠性评估实用方法[J].电网技术,2016,40(10):3006-3012.Wei Tingting,Wang Zhuding,Shou Ting,et al.A Practical Reliability Assessment Method of Distribution Systems With Grid Connected DGs[J].Power System Technology,2016,40(10):3006-3012(in Chinese).
[13]史清芳,徐习东,赵宇明.电力电子设备对直流配电网可靠性影响[J].电网技术,2016,40(3):725-732.Shi Qingfang,Xu Xidong,Zhao Yuming.Effects of Power Electronic Devices on DC Distribution Reliability[J].Power System Technology,2016,40(3):725-732(in Chinese).
[14]韩海腾,高山,吴晨,等.基于Nataf变换的电网不确定性多点估计法[J].电力系统自动化,2015,39(7):28-34.Han Haiteng,Gao Shan,Wu Chen,et a1.Uncertain power flow solved by multi-point estimate method based on Nataf transformation[J].Automation of Electric Power Systems,2015,39(7):28-34(in Chinese).
[15]李洪双,吕震宙,袁修开.基于Nataf变换的点估计法[J].科学通报,2008,53(6):627-632.Li Hongshuang,LüZhenzhou,Yuan Xiukai.Point estimate method based on Nataf transformation[J].Science in China Press,2008,53(6):627-632(in Chinese).
[16]杨欢,邹斌.含相关性随机变量的概率潮流三点估计法[J].电力系统自动化,2012,36(15):51-56.Yang Huan,Zou Bin.A three-point estimate method for solving probabilistic power flow problems with correlated random variables[J].Automation of Electric Power Systems,2012,36(15):51-56(in Chinese).
[17]孙若笛,谢开贵.计及风速-负荷相关性的配电网可靠性评估Monte Carlo模拟法[J].电力系统保护与控制,2012,40(18):12-18.Sun Ruodi,Xie Kaigui.Reliability evaluation of distribution networks using Monte Carlo method considering correlations between wind speed and load[J].Power System Protection and Control,2012,40(18):12-18(in Chinese).
[18]葛少云,张鑫,刘洪,等.基于点估计法的有源配电网概率可靠性评估[J].电力系统保护与控制,2014,42(12):91-100.Ge Shaoyun,Zhang Xin,Liu Hong,et a1.Active distribution network probabilistic reliability evaluation based on point estimation method[J].Power System Protection and Control,2014,42(12):91-100(in Chinese).
[19]赵渊,张夏菲,周家启.电网可靠性评估的非参数多变量核密度估计负荷模型研究[J].中国电机工程学报,2009,29(31):27-33.Zhao Yuan,Zhang Xiafei,Zhou Jiaqi.Load modeling utilizing nonparametric and multivariate kernel density estimation[J].Proceedings of the CSEE,2009,29(31):27-33(in Chinese).
[20]Liu P L,Der K A.Multivariate distribution models with prescribed marginals and covariances[J].Probabilistic Engineering Mechanics,1986,1(2):105-112.
[21]Hill G W,Davis A W.Generalized asymptotic expansions of Cornish-Fisher type[J].The Annals of Mathematical Statistics,1968,39(4):1264-1273.
[22]王杨,万凌云,胡博,等.基于孤岛运行特性的微电网可靠性分析[J].电网技术,2014,38(9):2379-2385.Wang Yang,Wan Lingyun,Hu Bo,et a1.Isolated island operating characteristics based analysis on reliability of microgrid[J].Power System Technology,2014,38(9):2379-2385(in Chinese).
[23]Billinton R,Jonnavithula S.A test system for teaching overall power system reliability assessment[J].IEEE Transactions on Power Systems,1996,4(11):1670-1676.