Grid Monitoring: Bounds on Performances of Sensor Placement Algorithms

The objective of this paper is to find numerical bounds on the performances of algorithms for the placements of phasor measurement units (PMUs) in the power grid. Given noisy measurements and knowledge of the state correlation matrix, we use a linear minimum mean squared error estimator as the state estimator to formulate the PMU placement problem as an integer programming problem. Finding the optimal placements of a fixed number of PMUs in a large network is prohibitively complex, forcing us to look for suboptimal algorithms and bounds on the optimal performance. In this paper, we present a sequence of nested bounds using matrix pencils and generalized eigenvalues, that upper bound the optimal performance. Finally, we numerically compare the performances of the suboptimal solutions with the upper bounds using the IEEE 30and 57-bus test systems, showing that the proposed bounds provide a valid basis for determining the quality of different suboptimal solutions. Keywords–phasor measurement units; matrix pencils; generalized eigenvalues.