Markov Chain Monte Carlo Methods Applied to a Synchronous Generator Model

Abstract

Markov Chain Monte Carlo (MCMC) approaches are widely used for tuning model parameters to fit process measurements. While modern probabilistic programming languages (PPLs) such as Stan, PyMC, and Turing have made it easier to implement efficient MCMC samplers, configuring them for high dimensional and multi-modal parameter distributions remains a challenging task. In Pandey and Lie (2022), the No-U-Turn Sampler (NUTS) was employed via Turing to estimate parameters of an air-cooled synchronous generator model using real-world experimental data, but the produced posterior distributions were excessively narrow. The present study extends the findings in Pandey and Lie (2022) by producing more realistic parameter estimates using the same data. To accomplish this, the study first reviews the basics of MCMC; it offers some general advice for choosing appropriate settings for MCMC to ensure successful estimation, as well a discussion of the impact of measurement data on the computation of posteriors. The study then implements the simple classical MCMC technique, Metropolis, from scratch to estimate the generator model parameters, providing more insight into MCMC — its fundamental process and terminology. Finally, the knowledge gained is applied to select appropriate settings for NUTS — implemented via Turing —that yield more accurate parameter estimates.