Optimal PMU placement for modeling power grid observability with mathematical programming methods

Phasor measurement units (PMUs) can obtain synchronized voltage and current phasors to increase the accuracy of state estimation results. Optimal PMU placement (OPP) reduces the required number of PMUs to make the system fully observable. In this paper, two mathematical programming formulations, which are mixed integer linear programming (MILP) and nonlinear programming (NLP), for power grid observability modeling to solve the OPP problem are presented. Power flow and zero injection measurement modeling along with restricted communication facilities, PMU failure, and limited channel capacity contingencies are investigated. MILP zero injection formulation is improved to overcome the observability redundancy and optimality drawbacks. A new formulation for nonlinear programming-based PMU placement for zero injection measurement is proposed. MILP and NLP methods are compared to illustrate the advantages and disadvantages of each method. The comparison and proposed formulations are examined on IEEE 14-, 57-, 118-, 300-bus test systems and a large 2383-bus Polish system to demonstrate their effectiveness.