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

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.