Performance Measures in Electric Power Networks under Line Contingencies

Classes of performance measures expressed in terms of H2-norms have been recently introduced to quantify the response of coupled dynamical systems to external perturbations. For the specific case of electric power networks, these measures quantify for instance the primary effort control to restore synchrony, the amount of additional power that is ohmically dissipated during the transient following the perturbation or, more conceptually, the coherence of the synchronous state. So far, investigations of these performance measures have been restricted to nodal perturbations. Here, we go beyond 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 metrics depend on whether the faulted line connects two passive, two active buses or one active to one passive bus. In all cases, performance metrics depend quadratically on the original load on the faulted line times a topology dependent factor. Our theoretical formalism being restricted to Dirac-δ 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.