Classes of performance measures expressed in terms of ${\mathcal H}_2$ -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. 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.

中文翻译：

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线路意外情况下电网的性能指标

绩效指标的类别以 $ {\ mathcal H} _2 $ 最近引入了-范数来量化耦合动力系统对外部扰动的响应。到目前为止，对这些性能指标的研究仅限于节点扰动。在这里，我们超越了这些较早的著作，并考虑了同样重要但至今被忽略的线扰动情况。我们考虑一种减少网络的电源系统，在这种系统中，减少Kron消除了无源总线。确定物理网络中的线路故障对减少Kron的网络的影响，我们发现性能度量取决于故障线路是连接两个无源总线，两个有源总线还是将一个有源总线连接到一个无源总线。在所有情况下，性能指标都取决于故障线上原始负载乘以拓扑相关因子。 $ \ delta $摄动，我们在数值上研究了有限时间线故障的结果的有效性。对于惯性比的均匀阻尼，我们发现与具有较大惯性的系统中更长的故障持续时间的理论预测吻合良好，为此，网络的本征模很难激发。