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

Performance Measures in Electric Power Networks under Line Contingencies