Optimal Placement of Phasor Measurement Units with Linear and Non-linear Models

Abstract—This article presents a non-linear programming-based model for the optimal placement of phasor measurement units. The optimal phasor measurement units placement is formulated to minimize the number of phasor measurement units required for full system observability and to maximize the measurement redundancy at all buses in a power system. A sequential quadratic programming algorithm is used for the solution of the proposed model. The existence of power flow and injection measurements, the limited phasor measurement units channel capacity, the lack of communication facilities in substations, and the single phasor measurement units loss are also incorporated into the initial proposed formulation. The non-linear programming model is applied to IEEE 14- and 118-bus test systems in MATLAB. The accuracy and the effectiveness of the proposed method is verified by comparing the simulation results to those obtained by a binary integer programming model also implemented in MATLAB. The comparative study shows that the proposed non-linear programming model yields the same number of phasor measurement units as the binary integer programming model. A remarkable advantage of the non-linear programming against binary integer linear programming is its capability to give more than one optimal solution, each one having the same minimum number of phasor measurement units (same minimum objective value), but at different locations.