Combination of moment-matching, Cholesky and clustering methods to approximate discrete probability distribution of multiple wind farms

This study focuses on approximating a reduced discrete probability distribution (RDPD) of wind power from the original discrete probability distribution (ODPD), consisting of a large number of observed original scenarios (OSs), to relieve the burden of solving stochastic programs of wind power generation. The proposed method, namely, the MMCC method, aims to achieve high approximation accuracy and computational efficiency by combining an improved moment-matching (MM) method with the clustering (C) method and the Cholesky decomposition (CD) method. First, the C method is used to reduce the number of OSs by minimising the space distance between the reduced scenarios (RSs) and the OSs. Next, the CD method is used to rectify the correlation of the RSs to satisfy that of the ODPD. Finally, the RS probabilities are optimally determined by the MM method in order to minimise the stochastic features (first four moments and correlation matrix) between the RDPD and the ODPD. Simulations of RDPD approximation for three wind farms with 10, 20, 40, 60, 80, and 100 scenarios were carried out using the Latin hypercube sampling, importance sampling, C, moment-matching-clustering (MMC), and MMCC methods. The results showed that the MMCC method exhibits the best performance in terms of capturing the features of the ODPD.