Tommaso Coletta

Tommaso Coletta, Philippe Jacquod

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-$δ$ 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.

Tommaso Coletta, Philippe Jacquod

We investigate the dependence of transmission losses on the choice of a slack bus in high voltage AC transmission networks. We formulate a transmission loss minimization problem in terms of slack variables representing the additional power injection that each generator provides to compensate the transmission losses. We show analytically that for transmission lines having small, homogeneous resistance over reactance ratios ${r/x\ll1}$, transmission losses are generically minimal in the case of a unique \textit{slack bus} instead of a distributed slack bus. For the unique slack bus scenario, to lowest order in ${r/x}$, transmission losses depend linearly on a resistance distance based indicator measuring the separation of the slack bus candidate from the rest of the network. We confirm these results numerically for several IEEE and Pegase testcases, and show that our predictions qualitatively hold also in the case of lines having inhomogeneous ${r/x}$ ratios, with optimal slack bus choices reducing transmission losses by ${10}\%$ typically.