Risk constrained stochastic economic dispatch considering dependence of multiple wind farms using pair-copula

With higher and higher penetration of wind power into power systems, dependence among the wind speeds of different wind farms should be considered when modeling the wind power outputs. In this paper, a novel pair copula method is applied to formulate the dependence of multiple wind farms. A large number of stochastic scenarios, in which the complicated dependence of multiple wind farms are considered, are generated to represent the uncertainties of wind power based on quasi-Monte Carlo (QMC) simulations. To find an optimal dispatch solution, a risk constrained mean-variance (MV) model is constructed for the stochastic economic dispatch (SED) problem. The MV model considers economic cost and economic risk under the uncertainties of wind power simultaneously, among which economic risk is calculated by means of least variance of fuel cost. Moreover, with the probability density function (PDF) obtained for fuel cost, a predefined level of confidence interval is proposed to improve the MV model to acquire more practical dispatch solutions. For solving the multi objective SED problem, group search optimizer with multiple producers (GSOMP) is employed in this paper. The effectiveness of the proposed pair-copula method and the improved MV model are validated via numerical simulations with a modified IEEE 30-bus system.