Graph-Guided Genetic Algorithm for Optimal PMU Placement Ensuring Topological and Numerical Observability

Abstract

This paper presents a novel hybrid algorithm for determining the optimal Phasor Measurement Units (PMU) configuration in power networks to ensure full topological and numerical observability through a multi-phase process. In the first phase, a graph-theoretic Heuristic Node Selector (HNS) is developed to rapidly establish topological observability via Core-Tree construction and node dominance evaluation. Unlike most existing studies that implicitly assume topological observability implies numerical observability, the second phase applies a Genetic Algorithm to refine and extend the initial solution from HNS, ensuring complete numerical observability while minimizing number of PMUs. This hybrid method significantly reduces the search space and improves convergence. The HNS procedure is further extended in this work to explicitly handle Zero Injection Buses (ZIB) through rule-based topological modifications, enabling a modified version of the algorithm applicable to real networks with complex structures. Real-world implementation practices from European Transmission System Operators are considered through the adoption of a “one PMU per feeder” configuration. The proposed method is validated on standard IEEE test systems and Serbian transmission networks. Results demonstrate high scalability, adaptability to various network topologies (with and without ZIB nodes), and efficient PMU allocation. Notably, the method consistently achieves high values of the System Observability Redundancy Index, indicating strong robustness and redundancy in measurement placement. © 2026 by the authors.