Análise crítica do Monte Carlo hamiltoniano na avaliação de afundamentos de tensão - REIS, Diogo de Jesus Fonseca (2021)
Voltage sags are one of the main power quality problems, able to cause significant financial losses to industrial consumers. One way of assessing voltage sags is through the SARFI-X index (System Average RMS Frequency Index). This index is a measure of the number of voltage sags with remaining RMS magnitude inferior to the specified percentage value X (p.u.). Monte Carlo Simulation (MCS) is one of the most used methods to obtain this index, regardless of its high computational cost. It is presented in this work an introduction to Hamiltonian Monte Carlo (HMC) sampling of highdimensional model spaces on probabilistic assessments of voltage sags in power systems. It is shown that the proposal mitigates adverse effects of the standard Metropolis-Hastings (MH) sampling algorithm, such as low acceptance rates, randomwalk and slow convergence, by surrogating simple updates for momentum variables (typical independent Gaussian distributions) with Metropolis updates, where a new state is proposed by computing a trajectory through the solution of the Hamiltonian’s equations of motion. The proposed state can be distant from the current state and still present a high probability of acceptance. This procedure avoids the slow exploration of the state space that occurs when Metropolis updates are performed, leading to a fast exploration of the distribution. It is verified through test-systems that the Hamiltonian Monte Carlo sampler mitigates the difficulties of the Metropolis-Hastings (MH) algorithm. The results may encourage its use in other probabilistic power systems problems.