An efficient cross-entropy method addressing high-dimensional dependencies for composite systems reliability evaluation

• Published in: International journal of electrical power & energy systems 2024-06, Vol.157, p.109857, Article 109857
• Main Authors: Zhao, Yuan, Chen, Jia, Liu, Linhua, Cheng, Xueyuan, Xie, Kaigui, Hu, JiaQin, Wang, Qi
• Format: Article
• Language: English
• Subjects: Cross entropy; Dimension reduction; Multivariate correlation; Reliability evaluation; Sparse density estimation
• ISSN: 0142-0615
• DOI: 10.1016/j.ijepes.2024.109857

•The cross-entropy (CE) method addressing high-dimensional dependencies is explored.•A CE method termed as CE-DRDM is developed from dimension reduced dependence model.•An improved hierarchical disaggregate structure is proposed to enhance CE-DRDM.•A novel CE optimization is used to derive the analytic formula of IS-PDF parameter.•A novel sparse density estimator is used to reduce the number of IS-PDF parameter. Cross-entropy (CE) based importance sampling (IS) accelerates the reliability evaluation of power system greatly, but is mainly focused on the CEIS of independent random variables (RVs) or low-dimensional correlated RVs (CRVs). To extend the CE method to high-dimensional CRVs while avoiding the “curse of dimensionality” in optimizing a high-dimensional IS probability density function (IS-PDF), an efficient CE method termed as CE-DRDM, is developed from a dimension-reduced dependence model (DRDM). First, based on the DRDM’s original hierarchical disaggregate structure (HDS), the CE-DRDM which conducts the CEIS for a single aggregate RV rather than the high-dimensional CRVs is proposed. Second, to solve the issue that the performance of CE-DRDM may degrade in the case of high penetration of renewable energy, the CE-DRDM is enhanced by improving the DRDM’s HDS, and then a novel CE optimization method is proposed, through which the analytical updating formulas of IS-PDF parameters can be derived. Thirdly, the CE-DRDM is further enhanced by using a sparse density estimator, based on which the number of IS-PDF parameters needed to be optimized in the CE optimization reduces greatly, and consequently the optimization accuracy improves accordingly. Finally, the validity of CE-DRDM is verified by several numerical cases with high-dimensional dependencies.