A modified optimal PMU placement problem formulation considering channel limits under various contingencies

Phasor measurement units (PMU) are populating the electricity grids throughout the world rapidly due to their wide range of benefits and applications. The traditional optimal PMU placement (OPP) formulations ensure complete network observability with a minimum number of PMU installation. Most of them disregard the PMU channel limitations, the existence of passive measurements/zero injection buses (ZIB), and enhancement of measurement redundancy. This paper presents a modified and effective OPP formulation considering various contingencies and constraints aiming at minimizing the required number of PMU installation and achieving the maximum number of measurement redundancy subjected to complete network observability. The availability of channels per PMU and the presence of ZIB are also taken into account. Besides, the vulnerability of the PMU along with the possibility of line outages is also considered. The formulated OPP problem is tested on five IEEE test networks employing constriction factor particle swarm optimization (CF-PSO). The proposed formulation effectively ensures complete network observability with the installation of a minimal number of PMU. Furthermore, the obtained results prove the efficacy and superiority of the CF-PSO approach over the mixed integer linear programming (MILP) approach and the reported methodologies in literature in terms of achieved measurement redundancies through the installation of less or same number of PMU. Finally, this research applies the proposed OPP formulation on a large-scale electric network of three different scenarios to justify its’ applicability, scalability, and robustness.