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The cross-entropy (CE) method can accelerate power system reliability evaluation effectively. An importance sampling (IS) based iterative parameter updating algorithm is usually used in CE optimization. However, the efficiency in capturing the concerned samples for parameter updating may be unsatisfactory, especially for a system with intrinsic nature of rare failure events. Besides, the stopping criterion of this iterative algorithm is usually determined subjectively, incurring insufficient or excessive parameter updating and a resultant higher computational burden of the entire simulation. To address the above two problems, a CE method based on subset simulation and minimum computational burden criterion is proposed. In CE optimization, the subset simulation combined with M-H sampling is adopted as an alternative to IS to effectively improve the efficiency of capturing desired samples for parameter updating at each iteration. Moreover, a novel quantitative stopping criterion is presented in such a way that the computational burden for the entire simulation is estimated and compared after each parameter updating iteration, and the optimal parameters corresponding to the minimum computational burden can be determined. The computational performance of the proposed method is validated by comparing the proposed approach with existing methods under several numerical tests including a realistic power system. [ABSTRACT FROM AUTHOR]

• A novel sparse density estimator named GCE is presented for dependence modeling. • A CE method using GCE is developed to get the IS-PDF of correlated RVs (CRVs) • Composite system reliability evaluation is greatly accelerated using IS-PDF of CRVs. Multivariate kernel density estimation (KDE) is powerful for dependence modeling, but producing a non-sparse probability density estimation model. To address this issue, a sparse density estimation technique termed as generalized cross-entropy (GCE) density estimator, is proposed to estimate the joint probability density function (PDF) of correlated random variables (RVs). Moreover, to effectively accelerate the composite systems reliability evaluation, a unified cross-entropy based importance sampling (CEIS) method accommodating both GCE and KDE density estimators is presented, and a creative CE optimization approach is also developed based on the composition sampling algorithm, through which the analytical updating rules of IS-PDF parameters can be derived even though GCE and KDE estimators do not belong to the exponential distribution family (EF). Compared to the KDE estimator, the GCE estimator encounters much less dimensionality difficulty in CE optimization due to the model sparsity merit, and consequently achieves more accurate IS-PDF parameters and better CEIS efficiency. The superiority of GCE estimator over KDE estimator in correlation modeling and CEIS is verified by several numerical tests. [ABSTRACT FROM AUTHOR]

• 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. [ABSTRACT FROM AUTHOR]

The uncertainties in reliability evaluation model are fundamentally classified into aleatory and epistemic types. Aleatory uncertainty arises from the intrinsic randomness associated with a physical system, such as components stochastic failure and repair process. Epistemic uncertainty, on the other hand, results from an incomplete or inaccurate scientific understanding of the underlying process, such as component reliability parameters uncertainty. It’s significant for risk based decision to distinguish the two kinds of uncertainties and quantify their impacts on reliability analysis. In literatures, most of papers focused on aleatory uncertainty, and only a few of them discussed the epistemic uncertainty. This paper is aimed to address uncertainty analysis of reliability indices considering the randomness of reliability parameters. Two goals are achieved in this paper. Firstly, the reliability indices are approximated through Taylor series with high efficiency after component parameters change, and its accuracy is compared with rerunning reliability evaluation. Secondly, to uncover the uncertainty propagation from input reliability parameters level to reliability evaluation output level, two methods, i.e. Taylor series Approximation and Monte Carlo simulation combined with nonparametric probability density estimation are proposed. Results obtained for the RBTS and IEEE-RTS79 power systems are presented and the validity of the proposed methods is verified. [ABSTRACT FROM AUTHOR]

• A nonparametric pair-copula construction is used to model multivariate correlation. • A uniform framework of nonparametric kernel density estimation is constructed. • A probability density function transformation method is proposed. • The conditional sampling method to generate correlated samples is depicted. • Reliability evaluation procedure considering multivariate dependence is detailed. The correlated variation of bus loads, wind powers, etc., has a significant impact on the power system operation risk. The construction of the accurate dependence model becomes vital in the field of power system reliability evaluation. Most currently used methods in estimating the multivariate joint probability density function (PDF) may encounter obstacles such as modeling accuracy and the curse of dimensionality, especially in the high-dimensional case. To address such problems, a nonparametric pair-copula construction (NPCC), which decomposes the joint PDF into a product of marginal PDFs and a set of bivariate copula (also called pair-copula) densities based on graph theoretic algorithm, is used in this paper to achieve an accurate modeling of the multivariate correlation. To construct a unified framework of nonparametric estimation, the marginal PDFs and the bivariate copula densities are both estimated in a data-driven mode. Moreover, a PDF transformation method is also proposed in estimating the bivariate copula densities, aiming to avoid the problem that the distribution range of the transformed variables in the pair-copula densities exceeds its feasible domain. The performance of the proposed NPCC is verified by a modified version of IEEE-RTS79 with complex correlation among bus loads and wind powers. [ABSTRACT FROM AUTHOR]