@article{anderson_chakrabortty_2014, title={PMU placement for dynamic equivalencing of power systems under flow observability constraints}, volume={106}, ISSN={["1873-2046"]}, DOI={10.1016/j.epsr.2013.08.002}, abstractNote={In this paper we develop two graph-theoretic algorithms for placing Phasor Measurement Units (PMUs) in a multi-area power system network with the objective of identifying its dynamic equivalent model. The system is considered to be divided into clusters of synchronous generators and loads, with each area connected to other sets of areas through designated transmission networks. We first show that in order to derive the equivalent line parameters connecting the different areas we must have PMUs placed at the minimum vertex cover of the bipartite graphs formed between every pair of node-sets arising from the boundary buses of these areas. Considering further that the number of tie-lines observable from any given PMU is constrained by an upper limit, we derive two sets of algorithms to compute the sub-optimal minimum cover, first for a bipartite graph and then for any general topology. The respective algorithms are referred to as CONPLAC and CONITPLAC. Results are illustrated using a IEEE 34-bus system pointing to the robustness of the proposed algorithms against time-varying network topology. Finally, we present statistical analyses to describe how the final set of chosen PMU locations and the computational time of these algorithms depend on network size, complexity and measurement constraints.}, journal={ELECTRIC POWER SYSTEMS RESEARCH}, author={Anderson, Joel E. and Chakrabortty, Aranya}, year={2014}, month={Jan}, pages={51–61} }
 @inproceedings{anderson_chakrabortty_2012, title={A minimum cover algorithm for PMU placement in power system networks under line observability constraints}, DOI={10.1109/pesgm.2012.6345002}, abstractNote={In this paper we develop a graph-theoretic PMU placement algorithm for multi-area power system networks with the objective of identifying a dynamic equivalent model for the system. The system is considered to be divided into clusters or areas of synchronous generators, with each area connected to other sets of areas through designated transmission networks. The buses in the system are accordingly divided into two types, namely - boundary buses of the areas and boundary buses of the transmission networks. We first show that in order to derive the equivalent line parameters connecting the different areas we must have PMUs placed at the minimum vertex cover of the bipartite graphs formed between every pair of node-sets arising out of the boundary buses of the areas and those of the corresponding transmission networks they are connected to. Considering further that the number of tie-lines observable from any given PMU is constrained by an upper limit, we derive an algorithm to compute the sub-optimal minimum cover for the multi-area system. The method is illustrated via a 4-6 bipartite network, as well as with two small examples from the WECC system. Statistical analyses of the algorithm are also presented describing how the final set of chosen PMU locations as well as the computational time needed to run the algorithm are dependent on the size, complexity and measurement constraints of the network.}, booktitle={2012 IEEE Power and Energy Society General Meeting}, author={Anderson, J. E. and Chakrabortty, Aranya}, year={2012} }
 @inproceedings{anderson_chakrabortty_2012, title={Graph-theoretic algorithms for PMU placement in power systems under measurement observability constraints}, DOI={10.1109/smartgridcomm.2012.6486054}, abstractNote={In this paper we develop two graph-theoretic PMU placement algorithms for multi-area power system networks with the objective of identifying a dynamic equivalent model for the system. We first show that to derive the equivalent line parameters connecting the different areas we must have PMUs placed at the minimum vertex cover of the bipartite graphs formed between every pair of node-sets arising out of the boundary buses of the areas. Considering further that the number of tie-lines observable from any given PMU is constrained by an upper limit, we derive an algorithm to compute the sub-optimal minimum cover, first for a bipartite graph and then for any general topology. We illustrate our results using a IEEE 34-bus model.}, booktitle={2012 IEEE Third International Conference on Smart Grid Communications (SmartGridComm)}, author={Anderson, J. E. and Chakrabortty, Aranya}, year={2012}, pages={617–622} }