@article{nudell_nabavi_chakrabortty_2015, title={A Real-Time Attack Localization Algorithm for Large Power System Networks Using Graph-Theoretic Techniques}, volume={6}, ISSN={["1949-3061"]}, DOI={10.1109/tsg.2015.2406571}, abstractNote={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 electro-mechanical 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.}, number={5}, journal={IEEE TRANSACTIONS ON SMART GRID}, author={Nudell, Thomas R. and Nabavi, Seyedbehzad and Chakrabortty, Aranya}, year={2015}, month={Sep}, pages={2551–2559} }
 @article{nudell_chakrabortty_2015, title={Graph-Theoretic Methods for Measurement-Based Input Localization in Large Networked Dynamic Systems}, volume={60}, ISSN={["1558-2523"]}, DOI={10.1109/tac.2015.2398911}, abstractNote={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.}, number={8}, journal={IEEE TRANSACTIONS ON AUTOMATIC CONTROL}, author={Nudell, Thomas R. and Chakrabortty, Aranya}, year={2015}, month={Aug}, pages={2114–2128} }
 @inproceedings{boker_nudell_chakrabortty_2015, title={On aggregate control of clustered consensus networks}, DOI={10.1109/acc.2015.7172204}, abstractNote={In this paper we address the problem of controlling the slow-time-scale dynamics of clustered consensus networks. Using time-scale separation arising from clustering, we first decompose the actual network model into an approximate model, and define the controller at every node as the sum of two independent state-feedback controls, one for the fast dynamics and another for the slow. We show that the slow controller is identical for every node belonging to the same cluster, indicating that only a single aggregate slow controller needs to be designed per area. This reduces the computational complexity of the design significantly. Applying results from singular perturbation theory, we show that when these individual controllers are implemented on the actual network, the closed-loop response is close to that obtained from the approximate models, provided that the clustering is strong. The design procedure is demonstrated by a simulation example.}, booktitle={2015 american control conference (acc)}, author={Boker, A. M. and Nudell, T. R. and Chakrabortty, Aranya}, year={2015}, pages={5527–5532} }
 @inproceedings{nudell_chakrabortty_2014, title={A graph-theoretic algorithm for localization of forced harmonic oscillation inputs in power system networks}, DOI={10.1109/acc.2014.6859401}, abstractNote={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.}, booktitle={2014 american control conference (acc)}, author={Nudell, T. R. and Chakrabortty, Aranya}, year={2014}, pages={1334–1340} }
 @inproceedings{nudell_chakrabortty_2013, title={A graph-theoretic algorithm for disturbance localization in large power grids using residue estimation}, booktitle={2013 american control conference (acc)}, author={Nudell, T. R. and Chakrabortty, A.}, year={2013}, pages={3467–3472} }