This study optimizes the placement of μ-PMUs using the BPSO and BGWO algorithms for the IEEE 33-bus and 69-bus systems, with a focus on minimizing deployment costs while ensuring robust system observability. Three case studies are analysed: Case 1 (normal conditions), Case 2 (single μ-PMU outage), and Case 3 (Zero Injection Buses, ZIBs). In Case 1, both algorithms identified 24 μ-PMUs as the optimal placement for the IEEE 69-bus system, achieving the minimum PMUs required for full observability. For Case 2, redundancy requirements increased the μ-PMU count to 24 μ-PMUs for the IEEE 33-bus system and 51 μ-PMUs for the IEEE 69-bus system, ensuring full observability even under a single μ-PMU failure. Case 3, leveraging Zero Injection Buses (ZIBs), reduced the μ-PMU count to 20 μ-PMUs for both BPSO and BGWO, optimizing the system configuration while maintaining observability. A trade-off analysis was performed to examine the trade-off between redundancy and PMU count, showing that increasing the number of μ-PMUs improves system resilience. Voltage and current channels were measured from the optimized placements to ensure accurate voltage measurement in all case studies. Subsequently, the Weighted Least Squares algorithm was applied for voltage estimation, serving as a peripheral to the main objective of the optimal μ-PMU placement. Voltage estimation was conducted under three noise levels: 0.01 STD for basic analysis and 0.02 and 0.04 STD to observe the impact of varying measurement noise. The results highlight that higher μ-PMU placements improve voltage estimation accuracy, particularly under higher noise levels. Statistical analysis confirms that BGWO outperforms BPSO in terms of computational efficiency, stability, and convergence, especially in large-scale systems. By enhancing grid monitoring and state estimation, this research directly contributes to the development of more resilient and efficient power networks, which is a fundamental prerequisite for integrating renewable energy sources and advancing overall power system sustainability. This research emphasizes the balance between cost and reliability in μ-PMU placement and provides a comprehensive methodology for state estimation in modern power systems.
Ali et al. (Tue,) studied this question.