PMU Placement Optimization for Efficient State Estimation in Smart Grid

This paper investigates phasor measurement unit (PMU) placement for informative state estimation in smart grid by incorporating various constraints for observability. Observability constitutes an important property for PMU placement to characterize the depth of the buses' reachability by the placed PMUs, but addressing it solely by binary linear programming as in many works still does not guarantee a good estimate for the grid state. Some existing works have considered optimization of some estimation indices by ignoring the observability requirements for computational ease and thus potentially lead to trivial results such as acceptance of the estimate for an unobserved state component as its unconditional mean. In this work, the PMU placement optimization problem is considered by minimizing the mean squared error or maximizing the mutual information between the measurement output and grid state subject to observability constraints, which incorporate operating conditions such as presence of zero injection buses, contingency of measurement loss, and limitation of communication channels per PMU. The proposed design is thus free from the fundamental shortcomings in the existing PMU placement designs. The problems are posed as large scale binary nonlinear optimization problems involving thousands of binary variables, for which this paper develops efficient algorithms for computational solutions. Their performance is analyzed in detail through numerical examples on large scale IEEE power networks. The solution method is also shown to be extendable to AC power flow models, which are formulated by nonlinear equations.