A Gaussian mixture approach to model stochastic processes in power systems

Abstract

Probabilistic methods are emerging for operating electrical networks, driven by the integration of renewable generation. We present an algorithm that models a stochastic process as a Markov process using a multivariate Gaussian Mixture Model, as well as a model selection technique to search for the adequate Markov order and number of components. The main motivation is to sample future trajectories of these processes from their last available observations (i.e. measurements). An accurate model that can generate these synthetic trajectories is critical for applications such as security analysis or decision making based on lookahead models. The proposed approach is evaluated in a lookahead security analysis framework, i.e. by estimating the probability of future system states to respect operational constraints. The evaluation is performed using a 33-bus distribution test system, for power consumption and wind speed processes. Empirical results show that the GMM approach slightly outperforms an ARMA approach.