A Graph-Theoretic Algorithm for Localization of Forced Harmonic Oscillation Inputs in Power System Networks

In this paper we consider the problem of localizing inputs in swing dynamic models of large power system networks in the form of forced oscillations with unknown amplitude and frequency. Such harmonic oscillations commonly result from internal failures of control actuators in synchronous machines, and are particularly dangerous because their frequency often lies in the range of the inter-area oscillation modes of the system, resulting in an unwanted sub-synchronous resonance phenomena. We first develop the concept of discrete nodal domains for second-order network dynamic systems, and relate these nodal domains to the residues of the system transfer function. Thereafter, we develop a graph-theoretic algorithm based on the magnitude as well as the sign of these residues that detects the location of the forced oscillation input. We simulate a 60-generator 4-area power system to illustrate the different steps of our algorithm.