This paper introduces a new approach that effectively balances the trade-off between the strategic deployment of phasor measurement units (PMUs) with the accuracy of state estimation through a multi-objective paradigm. Utilities can achieve optimal grid visibility and reduce deployment costs by identifying the most critical PMU locations, which leads to the strategic PMU deployment (SDP) problem. The objective function includes SDP, state estimation error, and measurement redundancy. The multi-objective Brown Bear optimization is used to obtain SDP. The weighted least squares (WLS) technique is used for state estimation. The load flow analysis is performed using the Newton-Raphson method, and the state estimation error is obtained by finding the mean square difference between WLS without SDP data and WLS with SDP data. The proposed paradigm provides an improved balance between the SDP with maximum redundancy and the accuracy of state estimation. It is tested using the IEEE 30-bus and Polish 2383-bus systems. The performance metrics employed for evaluation include spread, spacing, and the hypervolume indicator. The results of the proposed paradigm derived from the application of multi-objective brown bear optimization are compared with those from other multi-objective algorithms, demonstrating that brown bear optimization produces better outcomes. The technique for order of preference by similarity to ideal solution multi-criteria decision ranking method is used to validate the performance of the proposed approach compared with other algorithms. The Wilcoxon signed-rank test is used to test the statistical superiority of MBOA compared with other algorithms.
Anand et al. (Sat,) studied this question.