Optimal Zero Injection Considerations in PMU Placement: An ILP Approach

This paper addresses various aspects of opti- mal Phasor Measurement Unit (PMU) placement problem. Zero injection busses, which are analogous to transshipment nodes have the potential to reduce the number of PMUs to obtain the complete system observability. Hitherto, model- ing of zero injection constraints had been a challenge due to intrinsic nonlinearities, which increases the complexity of the discrete optimization problem. We show that zero in- jection constraints can also be modeled as linear constraints in an Integer Linear Programming (ILP) framework. Fur- ther, we observe that the minimum PMU placement prob- lem has multiple solutions with the same cost. We propose two indices, viz.: the Bus Observability Index (BOI) and the System Observability Redundancy Index (SORI), to further rank these multiple solutions. BOI gives a measure of the number of PMUs observing a given bus and the SORI is sum of all BOI for a system. Results on the IEEE 118 bus system are presented. The results indicate that: (1) the proposed method of modeling zero injection constraints improves com- putational performance, and, (2) BOI and SORI help in im- proving the quality of PMU placement. We show that the solution with maximum SORI outscores other optimal solu- tions. Subsequently, we also develop a simple and elegant method to handle single PMU outage as well as different sys- tem topologies arising due to single line outage in the system.