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.
We develop a graph-theoretic algorithm for localizing the physical manifestation of attacks or disturbances in large power system networks using real-time synchrophasor measurements. We assume the attack enters through the electromechanical swing dynamics of the synchronous generators in the grid as an unknown additive disturbance. Considering the grid to be divided into coherent areas, we pose the problem as to localize which area the attack may have entered using relevant information extracted from the phasor measurement data. Our approach to solve this problem consists of three main steps. We first run a phasor-based model reduction algorithm by which a dynamic equivalent of the clustered network can be identified in real-time. Second, in parallel, we run a system identification in each area to identify a transfer matrix model for the full-order power system. Thereafter, we exploit the underlying graph-theoretic properties of the identified reduced-order topology, create a set of localization keys, and compare these keys with a selected set of transfer function residues. We validate our results using a detailed case study of the two-area Kundur model and the IEEE 39-bus power system.
In this paper we consider the problem of localizing disturbance inputs in first-order linear time-invariant (LTI) consensus networks using measurement-based graph-theoretic methods. We consider every node and edge of the network graph to be characterized with physical weights, and show that the resulting system dynamics can be represented in terms of an asymmetric Laplacian matrix Lm. Assuming the network graph to be divided into p coherent clusters, we next propose an input localization algorithm based on the properties of the weak nodal domains corresponding to the first p − 1 slow eigenvalues of Lm. The algorithm takes in sensor measurements of the states from selected nodes, runs a system identification routine to construct the input-output transfer matrix, and compares the signs of the residues of the component transfer functions to a nominal localization key to determine in which cluster(s) the disturbance input may have entered. We prove that for systems defined over a specific class of graphs, referred to as p-area complete graphs, the localization is unique. We also state the extension of this result for second-order synchronization networks. We illustrate the algorithms by applying them to large-scale power system networks.
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