A Heuristic Solution Algorithm for a Comprehensive Optimal Phasor Measurement Unit Placement Considering Zero-Injection Buses and Practical Constraints in Power System State Observability Problem

Accurate power system observability relies on the optimal phasor measurement unit (PMU) placement to minimize costs while ensuring complete state observability. However, modeling the effect of zero-injection (ZI) buses remains a key challenge. Existing approaches use simplifying assumptions about ZI buses that compromise measurement redundancy and connectivity. We propose a novel heuristic methodology to address these shortcomings through comprehensive ZI bus modeling. This research provides a computationally-efficient heuristic optimization strategy for power systems with complex ZI bus topologies. The approach systematically analyzes ZI bus connectivity scenarios to develop enhanced observability evaluation. The proposed comprehensive observability evaluation approach is also incorporated to consider practical limitations including single outage contingencies of current measurement channels of PMUs, transmission lines, single PMUs, limited budget, lack of PMU positioning site, and incomplete observability with partial observability and depth of one unobservability for identifying optimal PMU placements that balance cost and observability. Case studies on IEEE 14, 30, 57, and New-England 39 bus test systems demonstrate the efficiency of the proposed approach in finding high-quality solutions for normal operating conditions and the capability of our proposed heuristic solution algorithm to consider different practical situations in power network observability analysis. Compared to the existing studies, our proposed solution algorithm achieves up to 21% and 29% fewer PMUs for obtaining complete state observability under normal operating conditions and for single outage contingency of PMUs, respectively.