## 1 Introduction
However, it was concluded in [24] that the performance of multivariate Archimedean copulas deteriorates drastically if the number of wind and load sites increases. The deficiency cannot be overcome by simply using a mixture of multiple Archimedean copula functions. Hence, researches on the pair copula method, which specializes in high dimension dependence construction, have been developing rapidly. The pair copula method is capable of representing a complex multivariate correlation structure as the product of multiple bivariate conditional copula functions, each of which can be chosen from any copula function family individually. The method greatly improves the flexibility and accuracy of the multivariate dependence modeling [25]. In recent years, there have been researchers introducing the pair copula into the optimal planning and reliability assessment of power systems, whose graphical structure is called C-vine structure [26; 27]. C-vine copulas are suitable for cases where there is a dominant variable among all the correlated random variables (RV). For instance, if the wind speed at one site is relatively highly related with the wind speed and load at all other sites, C-vine will exhibit satisfactory efficiency and precision. Using the joint PDF of load and wind speed, we can evaluate the CC of wind energy based on the calculation of reliability indices. In the context of high reliability of power systems, various methodshave been developed to accelerate the process of reliability assessment, among which the CE-IS method is a most popular one [28; 29]. By combining CE-IS and the secant method, we can obtain a complete algorithm for CC evaluation. However, there are drawbacks in this algorithm. Firstly, GMM fails to consider the higher-order statistics of the marginal PDFs, which may result in an excessive number of components. Secondly, C-vine copulas need the existence of a dominant RV. Otherwise, its performance declines greatly. Thirdly, the traditional CE-IS method assigns one RV to every conventional unit or wind turbine generator (WTG) to represent its working state, while too many RVs hinder the performance of CE-IS. To solve the first and second problems, we develop a method of constructing a joint PDF by combining SNMM with D-vine copulas. SNMM owns superiority over GMM by considering higher-order statistics, which enables it to capture features of the PDFs with fewer components [30]. D-vine copulas are introduced to link the marginal PDFs fitted by SNMM to form an integral joint PDF. The D-vine structure needs no dominant RV, and can thus be applied to more general situations [31]. As for the drawback of CE-IS, we seek to improve it by offering a dimension reduction (DR) idea. The newly developed method is called DRCE-IS. The DR idea is implemented by using binomial and trinomial distributions to group two-state and three-state generators, which reduces discrete RVs. DRCE-IS is then designed to accommodate the two distributions to fulfil the speed-up of the power system reliability assessment. On the basis of the SNMM, D-vine copulas and DRCE-IS, we can obtain reliability indices rapidly and precisely, offering necessary information for the secant method to further evaluate the CC of each wind farm. The rest of the paper is organized as follows. Section 2 details the process of SNMM for marginal PDF construction. Section 3 describes the basic ideas of pair copulas and D-vine structure. In Section 4, the DRCE-IS method is presented with SNMM and D-vine copulas integrated; the pre-simulation and main simulation stages are detailed. Section 5 discusses the concept and procedures of the secant method. Numerical tests are performed and discussed in Section 6. The conclusions are summarized in Section 7.