A Novel Probabilistic Optimal Power Flow Model With Uncertain Wind Power Generation Described by Customized Gaussian Mixture Model

A novel probabilistic optimal power flow (P-OPF) model with chance constraints that considers the uncertainties of wind power generation (WPG) and load is proposed in this paper. An affine generation dispatch strategy is adopted to balance the system power uncertainty by several conventional generators, and thus the linear approximation of the cost function with respect to the power uncertainty is proposed to compute the quantile (which is also recognized as the value-at-risk) corresponding to a given probability value. The proposed model applies this quantile as the objective function and minimizes it to meet distinct probabilistic cost regulation purposes via properly selecting the given probability. In particular, the hedging effect due to the used affine generation dispatch is also thoroughly investigated. In addition, an analytical method to calculate probabilistic load flow (PLF) is developed with the probability density function of WPG, which is proposed to be approximated by a customized Gaussian mixture model whose parameters are easily obtained. Accordingly, it is successful to analytically compute the chance constraints on the transmission line power and the power outputs of conventional units. Numerical studies of two benchmark systems show the satisfactory accuracy of the PLF method, and the effectiveness of the proposed P-OPF model.