A graph-theoretic algorithm for disturbance localization in large power grids using residue estimation

Abstract

In this paper we consider the problem of localizing unknown disturbances in large power systems using a measurement-based graph theoretic method. We first show that the aggregate electro-mechanical model of the power system, under certain assumptions, can be analyzed analogously to a generic n th -order asymmetric networked dynamic system. Considering that the network exhibits a clustering structure leading to slow and fast eigenvalues, we propose an input localization method based on the properties of the weak nodal domains corresponding to the first p dominant slow eigenvalues. In particular, we prove that for systems defined over p-area complete graphs the input localization is unique. We provide simulation results to illustrate our algorithm.

A graph-theoretic algorithm for localization of forced harmonic oscillation inputs in power system networks

“…This result was used in [2] without proof. The following corollary extends Corollary 5.1 if the output of (17) is x 1 (t).…”

“…The first results state that the residues are symmetric and the nodal domains of v k and w k are identical despite the asymmetry in L m [2]. …”

“…Using these facts, the next lemma describes the sign pattern of R i kl [2]. Lemma 4.2: Let v i be an eigenvector of L m corresponding to λ i .…”

“…In our previous work [2], we described a method of using nodal domains to localize impulsive inputs in firstorder consensus networks. We briefly recall those results here before extending the method to second-order networks in the form of (5) which are perturbed by a forced harmonic input.…”

“…In our recent paper [2] we developed a related localization method for first-order consensus networks using the concept of nodal domains of clustered graphs that result in certain sign patterns in the residues of a system's transfer function. Compared to the first-order models studied in [2], the network models in this paper are, instead, coupled second-order oscillators which have complex eigenvalues and eigenvectors, and therefore, complex residues. When the swing dynamics of the system exhibit a coherency structure leading to a two time-scale behavior in the phase angle oscillations, the algorithm can be naturally extended to localize forced harmonic inputs.…”