Enhanced Cross Entropy Method for Composite Power System Reliability Evaluation

Abstract

Cross entropy method (CEM) can effectively accelerate the reliability evaluation of power system. It is mainly utilized to conduct importance sampling (IS) on discrete component state variables and independent or fully correlated continuous variables. To carry out IS on continuous variables with complicated correlation, this paper proposes an enhanced CEM (ECEM) that addresses the following two problems: the first one is the probabilistic modeling of the joint probability density function (PDF) for the correlated continuous variables, and the second one is the IS on the modeled joint PDF. For the first one, a Gaussian mixture model (GMM) is utilized to estimate the original joint PDF of correlated continuous variables. For the second one, the parameters of the GMM based joint PDF are optimized directly by a direct-updating-rule based method (DURM) to obtain the optimal IS-PDF. Furthermore, as an alternative to DURM, a Nataf transformation based method (NTM) is also presented to distort the parameters of the GMM-based joint PDF indirectly. Compared with NTM, which is suitable for normal copula correlation, DURM has a much wider application scope without any restriction on the correlation type. Finally, an improved unbiased estimator for the reliability index is presented to further accelerate ECEM. Test studies on RTS79 and MRTS with wind farm verify the effectiveness of ECEM.