Power system observability relies on accurate information about the system’s operational state, obtained through phasor measurement units (PMUs). However, the high cost of PMUs has led to extensive research on optimal PMU placement (OPP) to determine the minimum required number of PMUs for complete observability. Since modeling the effect of zero-injection (ZI) buses has been proven challenging in this context, we comprehensively study the effect of multiple-connected ZI buses in the OPP problem and introduce new observability analysis rules. Based on these rules, we propose a novel mixed-integer linear programming (MILP) formulation to overcome the limitations of measurement redundancy and to guarantee the global optimum. Moreover, we extend our study by proposing a generalized MILP model for the OPP problem that incorporates important practical constraints arising in real-world scenarios, such as limited budget and outage contingencies. We applied the proposed approaches to the IEEE 14-Bus, 30-Bus, 57-Bus, and the New-England 39-Bus standard test networks as well as the large-scale Polish 2383-Bus network. Numerical results demonstrate that, on average across different medium- and large-scale test networks, our proposed MILP models result in 10% less required PMUs under normal operating conditions and over 24% reduction under single outage contingencies compared to the existing studies.
Dolatabadi et al. (2026) studied this question.