Optimal Phasor Measurement Unit Placement for Numerical Observability Using A Two-Phase Branch-and-Bound Algorithm

Given an undirected graph representing the network, the optimization problem of finding the minimum number of phasor measurement units to place on the edges such that the graph is fully observed, is studied. The proposal addresses the issue of the optimization using a two-phase branch-and-bound algorithm based on combining both Depth-First Search and Breadth-First Search algorithms to attempt to find guaranteed global solutions for OPP. The problem in question is stated, outlining the underlying mathematical model in use formulated in terms of (pure) mixed-integer-linear-programming (MILP) and the branch-and-bound algorithm adopted to obtain efficient solutions in practice. A topology based on transformations considering pre-existing conventional and zero injection measurements in a power network is implemented. The (zero-one) (MILP) model is applied to IEEE systems. The numerical results indicate that the branch-and-bound ensures solution points at the optimal objective function value from a global-optimization point of view. The synchronized and conventional measurements are included in a (DC) linearized State Estimator (SE). The topological observability analysis is verified numerically based on observability criteria for achieving solvability of state estimation. Large-scale systems is also analyzed to exhibit the applicability of the proposed algorithm to practical power system cases.