Grid Controllability Aware Optimal Placement of PMUs With Limited Input Current Channels

This paper introduces a new method for optimally placing phasor measurement units (PMUs) aimed at enhancing smart grid controllability under perturbed conditions while maintaining system observability. To address practical concerns, the approach assumes that each PMU has a limited number of input channels when determining the optimal number of PMUs needed. To achieve this optimality objective, a minimum cost constrained quadratic objective problem over a bounded decision domain is formulated with continuous relaxation for the discrete binary constraint. An information-theoretic viewpoint is taken for characterizing the robustness of grid estimation at the phasor data concentrator. A perturbation-resistant algorithm has been developed to achieve a globally optimal PMU placement solution. The effectiveness of the proposed smart grid monitoring method is confirmed through tests on IEEE 6, 14, 30, 57, and 118-bus systems. The findings reveal that, in contrast to traditional observability-focused PMU deployment, the proposed approach ensures system controllability under general perturbation scenarios while preserving grid observability at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\approx 100\%$</tex-math></inline-formula>, achieving a minimum mean squared error of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\approx 10^{-3}$</tex-math></inline-formula>, and maintaining mutual information between estimated and measured attributes near 1 across all test cases.