Optimal PMU placements under propagation depth constraints by mixed integer linear programming

Unlike the traditional optimal PMU placement problems which are assumed that PMUs have unlimited capability of monitoring remote buses via propagation rules, we formulate this problem with considering the depth of observability propagation (DOP) in this paper. Two problem formulations described by mixed integer linear programming (MILP) are proposed. Under this framework, interactions between the next placed PMUs and earlier placed PMUs can be considered to be a set of inequality constraints. Effects such as zero injection buses (ZIBs), super zero injection buses (SZIBs), power measurement injections (PMIs), and line flow measurements (FMs) can also be accommodated. Both single stage placement and multi stage placement are studied with the consideration of the DOP. Simulation results on several IEEE test systems are provided to illustrate the effectiveness of these formulations.