Stochastic economic dispatch considering the dependence of multiple wind farms using multivariate Gaussian kernel copula

Abstract

Wind farms usually gather in areas with abundant wind resources. Therefore, spatial dependence of wind speeds among nearby wind farms should be taken into account when modeling a power system with large-scale wind power penetration. This paper proposes a novel non-parametric copula method, multivariate Gaussian kernel copula (MGKC), to describe the dependence structure of wind speeds among multiple wind farms. Wind speed scenarios considering the dependence among different wind farms are sampled from the MGKC by quasi-Monte Carlo (QMC) method, so as to solve the stochastic economic dispatch (SED) problem, for which an improved mean-variance (MV) model is established, which targets at minimizing the expectation and risk of fuel cost simultaneously. In this model, confidence interval is applied in the wind speed to obtain more practical dispatch solutions by excluding extreme scenarios, for which the quantile-copula is proposed to construct the confidence interval constraint. Simulation studies are carried out on a modified IEEE 30-bus power system with wind farms integrated in two areas, and the results prove the superiority of the MGKC in formulating the dependence among different wind farms and the superiority of the improved MV model based on quantile-copula in determining a better dispatch solution.