Probabilistic Optimal Power Flow Considering the Dependence of Multiple Wind Farms Using Pair Diffusive Kernel Copula

As wind farms are commonly installed in areas with abundant wind resources, spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power. In this paper, a novel bivariate non-parametric copula, and a bivariate diffusive kernel (BDK) copula are proposed to formulate the dependence between random variables. BDK copula is then applied to higher dimension using the pair-copula method and is named as pair diffusive kernel (PDK) copula, offering flexibility to formulate the complicated dependent structure of multiple random variables. Also, a quasi-Monte Carlo method is elaborated in the sampling procedure based on the combination of the Sobol sequence and the Rosen-blatt transformation of the PDK copula, to generate correlated wind speed samples. The proposed method is applied to solve probabilistic optimal power flow (POPF) problems. The effectiveness of the BDK copula is validated in copula definitions. Then, three different data sets are used in various goodness-of-fit tests to verify the superior performance of the PDK copula, which facilitates in formulating the dependence structure of wind speeds at different wind farms. Furthermore, samples obtained from the PDK copula are used to solve POPF problems, which are modeled on three modified IEEE 57-bus power systems. Compared to the Gaussian, T, and parametric-pair copulas, the results obtained from the PDK copula are superior in formulating the complicated dependence, thus solving POPF problems.