Performance Measures in Electric Power Networks Under Line Contingencies

Classes of performance measures expressed in terms of <inline-formula><tex-math notation="LaTeX">${\mathcal H}_2$</tex-math></inline-formula>-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-<inline-formula><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> perturbations, we investigate numerically the validity of our results for finite-time line faults. For uniform damping over inertia ratios, we find good agreement with theoretical predictions for longer fault durations in systems with more inertia, for which eigenmodes of the network are harder to excite.