Spectral Analysis of Synchronization in a Lossless Structure-Preserving Power Network Model

This paper considers the synchronization and transient stability analysis in a simple model of a structure-preserving power system. We derive sufficient conditions relating synchronization in a power network directly to the underlying network state, parameters, and topology. In particular, we provide a spectral condition based on the algebraic connectivity of the network and a second condition based on the effective resistance among generators. These conditions build upon the authors' earlier results on synchronization in network-reduced power system models. Central to our analysis is the reduced admittance matrix of the network, which is obtained by a Schur complement of the network's topological admittance matrix with respect to its bus nodes. This network-reduction process, termed Kron reduction, relates the structure-preserving and the network-reduced power system model. We provide a detailed graph-theoretic, algebraic, and spectral analysis of the Kron reduction process leading directly to the novel synchronization conditions.