What question did this study set out to answer?

The research aims to optimize the placement of phasor measurement units while addressing the challenges posed by zero-injection buses and practical constraints.

February 26, 2026Open Access

A novel MILP formulation for optimal placement of phasor measurement units with comprehensive modeling of zero-injection buses and practical constraints

Key Points

The research aims to optimize the placement of phasor measurement units while addressing the challenges posed by zero-injection buses and practical constraints.
Developed a novel MILP formulation for PMU placement.
Incorporated zero-injection bus effects in observability analysis.
Extended the model to include practical constraints like budget and outage contingencies.
Applied methods to various standard test networks, including IEEE and Polish networks.
Achieved a 10% reduction in the number of required PMUs under normal conditions.
Demonstrated over a 24% reduction in required PMUs during single outages.
Validated the models with numerical results across medium- and large-scale networks.

Abstract

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.

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