A fast and accurate sampler built on Bayesian inference and optimized Hamiltonian Monte Carlo for voltage sag assessment in power systems

Abstract

Sampling is recognized as one of the most time-consuming parts of Monte Carlo Simulations (MCS), especially for high-dimensional complex distributions. Therefore, efforts have been made on developing new techniques, or modifying existing ones to improve efficiency and accuracy of the simulations. There are sampling methods that have been explored by the power engineering community for many years, such as Importance Sampling (a Monte Carlo approximation), Metropolis-Hastings and Gibbs. On the other hand, a powerful method referred to as Hamiltonian Monte Carlo (HMC) has been successfully explored in different areas of science, but very little in power systems. This paper intends to further disseminate the qualities of HMC to the power systems community through a new HMC version for voltage sags studies, comprising a coefficient of variation for efficiency purposes and an optimization strategy to avoid manual fine-tuning of the integrator stepsize (usually a time-consuming task). It is verified through numerical experiments with small and large-port power systems that the average performance of the proposed algorithm is superior to other existing techniques for the problem of interest.