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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]

In this paper, an optimal reliability allocation (ORA) model of ±800 kV ultra-high voltage direct current (HVDC) transmission system is proposed. The model intends to provide the means to determine the availability requirements of components in the bidding process of ±800 kV ultra HVDC transmission projects. In this model, the component availability is optimized based on the prespecified system reliability. The objective function is composed of the component investment cost and the operation and maintenance cost. The ORA is formulated as a constrained nonlinear programming problem, and the genetic algorithm (GA) is used to find its solution. An improved dagger sampling (IDS) method is proposed to evaluate the reliability of ultra HVDC systems, and a bisection method is used to generate the initial population of the GA. An actual ultra HVDC project is used to conduct the case study. Results show that the proposed ORA model can minimize the component investment, operation, and maintenance costs, while achieving optimal allocation of the system reliability index to obtain the availability of components. In addition, the impact of the component spare on the ORA result is investigated. Performance comparison on the sampling efficiency of the IDS method and the direct Monte Carlo sampling method is also presented. [ABSTRACT FROM AUTHOR]

Wind turbine power converter system (WTPCS) is a crucial device in a wind energy conversion system. This paper presents the new failure rate models and a reliability evaluation technique for the (WTPCS) considering effects of wind speeds, which can be named by the multistate probability analysis method. The case studies on the WTPCS of a 2 MW wind turbine with a permanent magnet synchronous generator are conducted using wind speed data at Lauwersoog and Valkenburg wind sites in Holland. The results indicate that reliability of the WTPCS is affected significantly by variations of wind speed and the rated wind speed of wind turbine. The effectiveness of the proposed method is demonstrated by examples. [ABSTRACT FROM AUTHOR]

Abstract: Power system component failures can generally be classified into two categories: repairable random failures and aging failures. An essential step in power system reliability evaluation is the calculation of component unavailability. The paper presents a new model for calculating the unavailability due to aging failures using the normal distribution. It is based on the strictly mathematical derivation and can be used more easily with high accuracy compared to the traditional model. An example of seven generating units and two test systems of the RBTS and the IEEE-RTS were used to demonstrate effectiveness of the proposed model and its applications in power system reliability evaluation. [Copyright &y& Elsevier]

• The proposed multi-state model prevents the underestimation of reliability level caused by two-state failure model. • The proposed model can accurately evaluate the reliability index, which better reflects the multiple operation states. • Different TES strategies will lead to different operation decisions and reliability results of CSP plants. • The SF size and the TES capacity are positively correlated with the system reliability level. But the system reliability index tends to be stable when the SF size and the TES capacity are large. This paper proposes a multi-state reliability evaluation model for the concentrated solar power (CSP) plant considering partial function failure. Firstly, the component functions and components' consequences of random failure of CSP plants are analyzed. Core components affecting the output of CSP plants are selected. The CSP plant is divided into three subsystems: the heat collection, the heat exchange, and the power generation subsystems, according to the component function. Each subsystem is equivalent to a two-state component. Thus, an 8-state Markov model of CSP plant is established. The CSP plant can be operated in a partial function failure state as thermal energy storage (TES) or generation, depending on the functions of solar-heat and heat-electricity conversion. On this basis, the 8-state model can be simplified to a 4-state model by combining the partial function failure states of the same effect. Finally, the 4-state model is applied to the sequential Monte Carlo simulation for the reliability evaluation of power systems containing CSP plants. Two TES strategies are considered in the simulation: One is based on solar field (SF) average output, another is designed to satisfy the load preferentially. The proposed model is tested on the modified RBTS/IEEE RTS systems to verify the effectiveness. [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]