A Bayesian Approach for Parameter Estimation with Uncertainty for Dynamic Power Systems

TL;DR

This paper presents Bayesian methods to estimate parameters and their uncertainties in dynamic power systems, demonstrating their effectiveness on a 9-bus grid and analyzing factors affecting performance and efficiency.

Contribution

It introduces adjoint-based and stochastic spectral Bayesian approaches for dynamic power system parameter estimation and uncertainty quantification, including generator inertias.

Findings

Methods accurately estimate parameters and uncertainties.

Performance depends on measurement frequency and noise.

Approaches are computationally efficient for small systems.

Abstract

We address the problem of estimating the uncertainty in the solution of power grid inverse problems within the framework of Bayesian inference. We investigate two approaches, an adjoint-based method and a stochastic spectral method. These methods are used to estimate the maximum a posteriori point of the parameters and their variance, which quantifies their uncertainty. Within this framework we estimate several parameters of the dynamic power system, such as generator inertias, which are not quantifiable in steady-state models. We illustrate the performance of these approaches on a 9-bus power grid example and analyze the dependence on measurement frequency, estimation horizon, perturbation size, and measurement noise. We assess the computational efficiency, and discuss the expected performance when these methods are applied to large systems.