A Graph Theoretic Algorithm for Forced Harmonic Input Localization in Large Power 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 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. This algorithm extends our recent work in [1] for first-order consensus networks to second-order oscillatory networks, and shows that if the system has a clustered topology resulting in two-time-scale behavior in the phase oscillations then one can accurately localize the cluster in which the resonance is initiated using the residues of the inter-area modes. Our discussion includes both undamped and weakly damped swing models. We simulate a 60-generator 4-area power system to illustrate the different steps of our algorithm.