Fault-tolerant PMU placement using algebraic connectivity of graphs

Abstract

We consider fault-tolerant Phasor Measurement Unit (PMU) placement aiming to minimize the number of PMUs while maintaining system observability under various contingencies. Conventionally, the optimal number of PMUs in a system is determined based on the system's connectivity matrix under no contingency. This paper considers fault-tolerant PMU placement under single branch failure, using integer programming based methodology. Algebraic connectivity, or Fiedler value, is utilized to identify the worst-case single branch failure in terms of connectivity degradation. The proposed PMU placement accounts for this worst-case and covers a large percentage of other single-branch failures. The resulting placement is compared with that obtained without considering connectivity degradation in terms of the percentages of observable systems during any single branch failure. The proposed PMU placement has increased percentages of fully observable systems in the event of any single branch failure compared to non-contingency based placement, with a reasonable increase in number of PMUs.