Gaussian Mixture Model for Multivariate Wind Power Based on Kernel Density Estimation and Component Number Reduction

Abstract: The Gaussian mixture model (GMM) is a powerful tool to establish the probability distributions of random variables in power system analyses. GMM can model arbitrary probability distributions by increasing the number of its Gaussian components, but the commonly used expectation-maximization (EM) algorithm fails to obtain accurate GMM for large component numbers, which limits the application of GMM to multivariate wind power modeling. In this letter, we first deduce the closed-form solutions to probabilistic power flow calculation with GMM, which validates the importance of large component numbers. Then, we propose a parameter estimation method for GMM with large component numbers by combining kernel density estimation (KDE) with the density-preserving hierarchical EM (DPHEM) algorithm. Finally, the proposed method is compared with EM-based GMM and Copula functions on actual wind speed data to validate its superiority in describing the details of probability densities of wind power.