A Bi-objective Optimal PMU Placement Strategy Reconciling Costs and State Estimation Uncertainty

The problem of Optimal Phasor Measurement Units (PMU) Placement (OPP) in power systems is usually driven just by cost issues, whereas less attention is paid to measurement-related aspects. In particular, most OPP strategies rely on the minimization of a single objective function including system observability constraints, with no attention to state estimation performance. In fact, the observability constraints (either with or without redundancy due to contingencies) are not enough to ensure that the uncertainty associated with system state estimation is adequate for the intended purpose. For this reason, in this paper the OPP problem is addressed by minimizing two contrasting objective functions, i.e., the classic PMU deployment costs and the maximum system state estimation uncertainty. The aforementioned bi-objective OPP formulation is solved through a Non-dominated Sorting Genetic Algorithm II (NSGA-II). The results obtained applying the proposed approach to the IEEE 14-bus and 57-bus test systems show that several trade-off solutions can be found in different scenarios both with and without considering contingencies due to line or PMU faults. Among the Pareto-optimal solutions, the most interesting ones are probably those that ensure the highest normalized System Observability Redundancy Index (SORI) per PMU and those that minimize both estimation uncertainty and cost in all scenarios.