Analysis of the Dynamics and Topology Dependencies of Small Perturbations in Electric Transmission Grids

Abstract: Through an eigenanalysis of small perturbations, as typically done in small-signal stability studies, we intend to discover the underlying reasons that make those perturbations propagate in some way or another in the grid. To this end, we establish connections between the perturbations time-scale and topological metrics. Namely, the algebraic connectivity and the Fiedler vector of a generalized/weighted Laplacian matrix that depends on the stationary phase solutions of the system and is thereby inherently conditioned by the topology and the power distribution. Then, we aim to find out the isolated influence of topology on the perturbations when the network interacting agents have, in principle, opposite behaviors (i.e. producers and consumers). To do so, we study three networks: Small-world, Random, German grid. Furthermore, we tackle the effect of machine clustering on small perturbations and the influence of the network's average clustering coefficient on the intensity localization of the generalized Fiedler vector. Finally, we propose ways in which future (dynamic topology control) and existing (power system stabilizer) grid control strategies can adapt their response to comprehensively consider the topology and remote signals in the system.