Optimal Allocation of Phasor Measurement Units Considering Various Contingencies and Measurement Redundancy

This article presents an efficient and comprehensive method to find out the minimum number of and the corresponding locations of phasor measurement units (PMUs) guaranteeing full numerical observability of a power system as well as maximize the measurement redundancy in conjunction with preexisting conventional measurements. Furthermore, the effect of number of available channels of PMUs on their optimal placement can be taken into account. The proposed optimal PMU placement (OPP) formulation is extended to consider the case of two types of contingencies, single PMU loss and single branch outage. The objective of the OPP method is the numerical observability, unlike the majority of earlier works which are based on topological observability and do not always ensure numerical observability required for the successful execution of state estimation (SE). The problem is formulated as a binary semidefinite programming (BSDP) model with binary decision variables, minimizing a linear objective function subject to linear matrix inequality (LMI) observability constraints. The BSDP problem is solved using an outer approximation scheme based on binary integer linear programming. The effectiveness of the proposed method is verified on different IEEE test systems.