Bayesian Inference for Thermal Model of Synchronous Generator—Part I: Parameter Estimation

Abstract

Due to the increasing injection of intermittent power sources (solar+wind) into a common grid, dispatchable sources such as hydro power should be able to help reduce the variability in load and the variability in generation caused by the intermittent sources. A hydro generator should be able to operate short-term beyond its thermal capability limit. This requires the monitoring of internal temperatures in the hydro generator. In this paper, a thermal model of an air-cooled synchronous generator is presented, emphasizing the various aspects of parameter estimation and identifiability using Bayesian inference. Inferences are drawn from the posterior distributions of the parameters and initial conditions, dispersion (spreading) of particles and sampling efficiency, practical parameter identifiability, and model mismatch with experiments. Results show extremely narrow parameter distributions. It is early to generalize about the posterior distribution of air-related and metal-related parameters of the air-cooled synchronous generator based on the single experimental data presented here.INDEX TERMS Bayesian inference, model fitting, parameter estimation, parameter identifiability, synchronous generator, thermal model.

Markov Chain Monte Carlo Methods Applied to a Synchronous Generator Model

“…To conclude, the findings of this study improve on those of [1] -obtained for the same model using the same data and methodologies. The results indicate that employing MCMC, specifically the Metropolis and NUTS algorithm, is an effective way for producing best estimates of the unknown parameters of the thermal generator model.…”

“…We employ the same priors P (θ) used in [1]. For the initial states and unknown model parameters, truncated normal distributions are adopted, following common practice.…”

“…This entire process involves trial-and-error. When it comes to the priors for measurement noise variances, the conventional choice is the inverse gamma function; the same is chosen in [1]. Since the measurement magnitudes are comparable, the same prior is assumed for all measurement noise variances; comparable magnitudes in general is achieved by normalizing or standardizing the data.…”

“…Consequently, development of methods to assess and minimize the uncertainties associated with temperature monitoring becomes a central objective. Previous studies have dealt with state and parameter estimation for the generator model presented in [3]: in [1] the No-U-Turn Sampler (NUTS) [5] -a popular MCMC algorithm -is used. The posterior distributions of the parameters computed in that study, however, are extremely narrow, i.e., there is very little residual uncertainty.…”