Multiple solutions of optimal PMU placement using exponential binary PSO algorithm

In modern power systems, phasor measurement unit (PMU) is the most advanced measurement device to measure precise, fast and reliable voltage and current phasor. Due to high installation cost and other practical limitations, optimal PMU placement (OPP) is needed. An exponential binary particle swarm optimization (EBPSO) algorithm is proposed to solve the OPP problem for a completely observable network. Various practical contingencies such as zero injection, single PMU outage are considered in the proposed algorithm along with the normal operating condition. Multiple solutions for OPP problem can improve the feasibility of the placement methodology in practical environment. Even though any bus is selected as candidate location but it may not be possible to install a PMU on that bus due to the lack of necessary infrastructure. On the contrary, few buses in practical systems which require close and precise monitoring should be directly observed by PMU. Placing some extra PMUs can solve this problem but economically it is not preferable. Hence, having alternative solutions can be very effective. To ensure multiple solutions and improve the performances, an adaptive exponentially decaying inertia weight coefficient is developed. A sigmoid function is introduced to update the position of the particles in binary form. Both inter connected (IEEE 14-bus and 30-bus) and radial (IEEE 39-bus) system are tested to check the feasibility and effectiveness of the algorithm.