Analysis of Aggregated Wind Power Dependence Based on Optimal Vine Copula

Along with the rapid development of wind energy, a number of wind farms aggregate in the same region. It is necessary to consider the wind power dependence when analyzing aggregated wind farms. Aiming to the dependence of wind power, Copula function, which avoids the difficulty of constructing joint distribution function, is utilized for modeling dependence. Multivariate Copula functions, including Student t Copula, Gauss Copula and Archimedean Copula, is frequently used. However, traditional multivariate Copula functions assume that each pair of variables' correlation structures are the same, which is practically impossible, thus having limitation on precise and flexibility. Therefore, this paper adopts Vine-Copula to portray wind power dependence. Moreover, an optimal algorithm of choosing Vine is proposed. The modeling scheme is based on a decomposition of multivariate density into a cascade of pair copula, applied on original variables and on their conditional distribution functions. The case study uses several actual wind farms' operation data in Ningxia province of China for constructing both Vine-Copula and traditional multivariate Copula models. The result shows that the optimal Vine-copula that uses different Copula functions as building blocks can characterize the dependence of wind power more precisely and flexibly. At last, the proposed method is tested in the probabilistic load flow of an IEEE 118-bus system. The result shows the superiority of the proposed method.