Estimation of optimal number of components in Gaussian mixture model-based probabilistic load flow study

Gaussian mixture approximation (GMA)-based probabilistic load flow (PLF) is an efficacious approach for quantifying the uncertainties associated with non-Gaussian and discrete input random variables (RVs). GMA approximates these input RVs by an equivalent weighted finite sum of Gaussian components. Expectation maximization (EM) algorithm is a well-established approach to estimate the parameters of the mixture components. The critical aspect is to know a priori the optimal number of components approximating the non-Gaussian distributions. The estimation of optimal number of parameters is essential because the parameters with inappropriate components may not evaluate the mixture model accurately. This paper adopts a cluster distortion function-based approach to determine the optimal number of mixture components. The k-means clustering result pertaining to that optimal number is then used for EM initialization. PLF using multivariate-GMA is performed on two IEEE test systems, considering various types of input RVs and their multiple correlations.