Parameter Estimation in Ill-conditioned Low-inertia Power Systems

TL;DR

This paper addresses the challenge of estimating parameters in low-inertia power systems with ill-conditioned models, proposing a direct least-squares approach on the swing-equation model that improves estimation reliability.

Contribution

It introduces a novel least-squares estimation method for ill-conditioned power system models, overcoming failures of standard state-space approaches and analyzing the impact of network topology.

Findings

Standard models fail for low-inertia systems.

The proposed method improves parameter estimation accuracy.

Network connectivity influences estimation susceptibility.

Abstract

This paper examines model parameter estimation in dynamic power systems whose governing electro-mechanical equations are ill-conditioned or singular. This ill-conditioning is because of converter-interfaced power systems generators' zero or small inertia contribution. Consequently, the overall system inertia decreases, resulting in low-inertia power systems. We show that the standard state-space model based on least squares or subspace estimators fails to exist for these models. We overcome this challenge by considering a least-squares estimator directly on the coupled swing-equation model but not on its transformed first-order state-space form. We specifically focus on estimating inertia (mechanical and virtual) and damping constants, although our method is general enough for estimating other parameters. Our theoretical analysis highlights the role of network topology on the parameter estimates of an individual generator. For generators with greater connectivity, estimation of the associated parameters is more susceptible to variations in other generator states. Furthermore, we numerically show that estimating the parameters by ignoring their ill-conditioning aspects yields highly unreliable results.