Performance Measures in Electric Power Networks under Line Contingencies

TL;DR

This paper extends the analysis of ${ m H}_2$-norm based performance measures in power networks to include line perturbations, revealing their dependence on network topology and load, with validation through numerical simulations.

Contribution

It introduces a theoretical framework for line perturbations in power networks, previously limited to nodal perturbations, and analyzes their impact on performance measures.

Findings

Performance measures depend quadratically on load on the faulted line.

Dependence varies with whether the line connects active or passive buses.

Numerical results agree with theory for longer fault durations in high-inertia systems.

Abstract

Classes of performance measures expressed in terms of ${\cal H}_2$-norms have been recently introduced to quantify the response of coupled dynamical systems to external perturbations. So far, investigations of these performance measures have been restricted to nodal perturbations. Here, we go beyond these earlier works and consider the equally important, but so far neglected case of line perturbations. We consider a network-reduced power system, where a Kron reduction has eliminated passive buses. Identifying the effect that a line fault in the physical network has on the Kron-reduced network, we find that performance measures depend on whether the faulted line connects two passive, two active buses or one active to one passive bus. In all cases, performance measures depend quadratically on the original load on the faulted line times a topology dependent factor. Our theoretical formalism being restricted to Dirac-$\delta$ perturbations, we investigate numerically the validity of our results for finite-time line faults. We find good agreement with theoretical predictions for longer fault durations in systems with more inertia.