考虑相关性变量的电网可靠性评估交叉熵法  

An Efficient Cross-entropy Method for Reliability Evaluation of Composite Systems With Correlated Random Variables

作　　者：赵渊[1] 陈嘉[1] 谢开贵[1] 赖仲谋 胡家勤 ZHAO Yuan;CHEN Jia;XIE Kaigui;LAI Zhongmou;HU Jiaqin(State Key Laboratory of Power Transmission Equipment Technology(Chongqing University),Shapingba District,Chongqing 400044,China)

机构地区：[1]输变电装备技术全国重点实验室(重庆大学),重庆市沙坪坝区400044

出　　处：《电网技术》2025年第4期1551-1561,共11页Power System Technology

基　　金：国家自然科学基金项目(52177071)。

摘　　要：交叉熵法可显著加速电网可靠性评估,但往往聚焦于独立随机变量,若将其拓展至相关性变量可进一步提升加速性能。为有效获取相关性变量的重要抽样密度函数以实现其重要抽样,针对相关性建模中广泛使用的核密度估计模型(kernel density estimation,KDE)开展了交叉熵优化研究。因KDE模型不属于指数分布家族,传统交叉熵优化难以实施,故利用复合抽样算法特点提出了新颖的直接交叉熵优化方法,推导出KDE模型最优权重参数的解析表达式。因权重参数数量级较小,直接优化易导致准确性退化,故基于子集模拟思想进一步提出间接交叉熵优化方法,将较小的权重参数优化转换成较大的条件概率优化,提升了优化准确性。通过MRTS79和MRTS96可靠性测试系统的评估分析,验证了所提方法在含相关性变量电网可靠性评估中的高效加速性能。The cross-entropy method(CEM)can greatly speed up power system reliability evaluation but is mainly focused on the importance sampling(IS)of independent random variables(RVs).The performance of CEM can be improved if CEM can accommodate the IS of correlated RVs.This paper investigates the cross-entropy optimization method(CEOM)for the widely used kernel density estimation(KDE)model to address this issue.To obtain the optimal importance sampling density function(IS-DF)of correlated RVs,which KDE,a direct CEOM,models to achieve the optimal weight parameters of KDE is developed based on the characteristic of the composition sampling algorithm and the analytic updating rules of optimal weight parameters are derived.Second,to address the problem that the accuracy of the direct CEOM may degrade as the KDE’s weight parameters are usually very small,an indirect CEOM is presented,where the optimization of small weight parameters is converted into the optimization of large conditional probabilities.Finally,the performance of the proposed method is verified by the reliability evaluation of MRTS79 and MRTS96 test system.

关 键 词：相关性随机变量 核密度估计 交叉熵法 复合抽样 可靠性评估 

分 类 号：TM721[电气工程—电力系统及自动化]