大电网可靠性评估的最优f散度重要抽样法  

Optimal f-divergence Based Importance Sampling for Composite Power System Reliability Evaluation

作　　者：赵渊[1] 刘祎 任和 程学渊 谢开贵[1] ZHAO Yuan;LIU Yi;REN He;CHENG Xueyuan;XIE Kaigui(State Key Laboratory of Power Transmission Equipment&System Security and New Technology(Chongqing University),Shapingba District,Chongqing 400044,China)

机构地区：[1]输配电装备及系统安全与新技术国家重点实验室(重庆大学),重庆市沙坪坝区400044

出　　处：《中国电机工程学报》2022年第14期5067-5078,共12页Proceedings of the CSEE

基　　金：国家杰出青年科学基金项目(51725701);国家自然科学基金项目(50977094)。

摘　　要：交叉熵重要抽样法基于KL距离(Kullback-Leibler divergence)实现了重要抽样概率密度函数(importance sampling probability density function,IS-PDF)参数的有效估计,显著提升了电网可靠性的蒙特卡洛仿真速度,但KL距离仅是更广义的f散度家族的一种距离形式,虽然有效但非唯一。为探讨f散度在重要抽样法中的实现方式,该文提出最优f散度重要抽样法,通过最小化零方差概率密度函数和IS-PDF之间的f散度,推导典型距离测度下IS-PDF的参数统一迭代更新表达式。因不同距离测度对应不同IS-PDF参数和重要抽样效率,为此,基于可靠性指标测试函数与似然比函数之积的方差最小化准则,提出f散度下的最优距离形式迭代优化确定方法。对IEEE-RTS79和IEEE-RTS96系统进行可靠性评估,结果表明该文方法能有效提高仿真效率,实现重要抽样法效率提升潜力的有效挖掘,对于大电网可靠性的快速评估具有重要的工程实用价值。By optimizing the parameters of the importance sampling probability density function(IS-PDF) based on Kullback-Leibler(KL) distance,the cross-entropy based IS method(CE-IS) can significantly accelerate Monte Carlo simulation of power system reliability.However,KL distance is only one form of the f-divergence family which generalizes some other common distances besides the well-known KL distance.To explore the implementation of f-divergence in IS method,this paper proposed an optimal f-divergence IS method(OFD-IS).By minimizing the f-divergence between the ideal zero-variance probability density function(ZV-PDF) and IS-PDF,the uniform iterative updating formulas of IS-PDF parameters under the typical distance measure were derived.By using the uniform formulas in the variance minimization of the product of reliability index test function and likelihood ratio function,an iterative optimization method to determine the optimal distance in f-divergence family was proposed.The reliability evaluation of IEEE-RTS79 and IEEE-RTS96 system shows that the OFD-IS method can effectively improve the simulation efficiency,further explore the potential of efficiency improvement of IS method,and it is of great practical value for the rapid reliability evaluation of composite power systems.

关 键 词：可靠性评估 重要抽样 最优f散度 方差最小化 

分 类 号：TM73[电气工程—电力系统及自动化]