Probabilistic optimal power flow considering dependences of wind speed among wind farms by pair-copula method

This paper aims at exploring the impacts of high dimensional dependences of wind speed among wind farms on probabilistic optimal power flow (POPF). Kernel density estimate method is employed to estimate probability distribution of wind speed. A joint probability distribution function of wind speed among wind farms is obtained by pair-copula method, which can use variational bivariate copula functions to, consider dependences of wind speed between two arbitrary wind farms and overcome the constraints of high dimensional copula function, not taking the mutual dependences of wind speed into account. Finally, the POPF calculation is operated by monte carlo simulation method under four cases to consider high dimensional dependences of wind speed among wind farms. Simulation results show that the impacts of dependences of wind speed on the POPF results exist and that cannot be ignored. Based on the pair-copula method to construct high dimensional dependences, the average relative errors Of POPF results is smaller than that by other methods. Besides, the distribution curve of output variables is also close to that obtained by using actual wind speed data. Under the case of high requirements for calculation accuracy, it is a feasible scheme for using pair-copula method to construct dependences of wind speed to calculate POPF. (C) 2016 Elsevier Ltd. All rights reserved.