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

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, a parameter estimation method for GMM with large component numbers is proposed based on kernel density estimation (KDE) and the improved density-preserving hierarchical EM algorithm. Then, the closed-form solution to probabilistic power flow (PPF) calculation is derived based on piecewise linearization and GMM, which validates the importance of large component numbers. Finally, the proposed uncertainty modeling method is compared with EM-based GMM, Copula functions, KDE, k-nearest neighbors and block neural autoregressive flow on actual wind speed data to validate its superiority in describing the details of probability densities of wind power. PPF calculation is performed to show the efficiency and accuracy of the proposed uncertainty analysis method.