Graph-theoretic model reduction of oscillation propagation in spatially distributed power system networks

In this paper we consider continuum models of large distributed power systems defined over dynamic equivalent clusters, and derive a model reduction method to illustrate how oscillations can propagate from one cluster to another in the form of equivalent frequency waves depending on the topology of their interconnections. Previous results in [1], [2] have modeled such electromechanical waves mostly for two-area radial transfer paths (or, equivalently for a two-node line graph) by representing the swing dynamics in terms of partial differential equations (PDEs). Our results extend this approach to a network of areas connected by equivalent transfer paths, and defines an equivalent Sturm-Liouville eigenvalue equation for the entire network. We show that depending on the network topology the solutions of this eigenvalue problem can be significantly different from those for the individual paths. Simulation results for several representative power system network structures confirm our hypothesis.