Spatio-temporal oscillation monitoring in spatially distributed power system networks using energy functions

In this paper we consider continuum models of power system networks divided into clusters, and present a model reduction method to derive the analytical expressions for frequency waves propagating from one cluster to another depending on the network topology. Previous results have modeled such electromechanical waves mostly for two-area radial transfer paths, i.e., for two-node line graphs. Our results extend this approach to a network of areas connected by equivalent transfer paths by defining an equivalent Sturm-Liouville eigenvalue equation for the clustered network. We derive analytical expressions for the equivalent damping and power spectrum of this eigenvalue problem, as well for the spatio-temporal kinetic and potential energy functions that may used for transient stability assessment of the clustered network model following a disturbance.