A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables

The traditional cumulant method (CM) for probabilistic optimal power flow (P-OPF) needs to perform linearization on the Karush–Kuhn–Tucker (KKT) first-order conditions, therefore requiring input variables (wind power or loads) varying within small ranges. To handle large fluctuations resulting from large-scale wind power and loads, a novel P-OPF method is proposed, where the correlations among input variables are also taken into account. Firstly, the inverse Nataf transformation and Cholesky decomposition are used to obtain samples of wind speeds and loads with a given correlation matrix. Then, the K-means algorithm is introduced to group the samples of wind power outputs and loads into a number of clusters, so that in each cluster samples of stochastic variables have small variances. In each cluster, the CM for P-OPF is conducted to obtain the cumulants of system variables. According to these cumulants, the moments of system variables corresponding to each cluster are computed. The moments of system variables for the total samples are obtained by combining the moments for all grouped clusters through the total probability formula. Then, the moments for the total samples are used to calculate the corresponding cumulants. Finally, Cornish–Fisher expansion is introduced to obtain the probability density functions (PDFs) of system variables. IEEE 9-bus and 118-bus test systems are modified to examine the proposed method. Study results show that the proposed method can produce more accurate results than traditional CM for P-OPF and is more efficient than Monte Carlo simulation (MCS).