Probabilistic Multistage PMU Placement in Electric Power Systems

This paper presents an optimization model for the calculation of the minimum number of phasor measurement units (PMUs) in electrical power networks. The problem constraint is a predefined probability of observability associated with each bus. The mixed-integer programming is used for the proposed optimization and an efficient linearization technique is proposed to convert the nonlinear function representing the probability of observability into a set of linear expressions. The PMU placement is staged in a multi-year planning horizon due to financial and physical constraints. The average probability of observability is maximized at the intermediate planning stages, subject to a limited number of PMU placements, that would satisfy the horizon year schedule. In addition, network expansion scenarios associated with intermediate stages are taken into account. Numerical studies are conducted on a nine-bus system and the IEEE 57-bus system and the results are analyzed.