Abstarct: Phasor Measurement Units (PMUs) are being considered as essential tools in modern power system studies. In this Project the instruction of Phasor Measurement Unit and their application in power electrical networks is completely introduces and general approach is proposed to place the PMUs optimally in a power system and minimize the total installation cost to make the entire system completely observable, as a basic step for linear state estimation. In this project, the placement of PMUs is performed with respect to the maximum measurement redundancy and considering single PMU loss or single branch outages. The proposed approach employs Binary Integer Linear Programming and Exhaustive search to formulate and solve the objective function. This method to using more practical assumptions, with and without consideration of zero injections buses, does not utilize the existing conventional measurement in the power network. The proposed approach is then applied to several standard IEEE test systems (14-bus, 30-bus, 39-bus, 57-bus and 118-bus) to find the optimal placement of the PMUs. The simulation results approve the capability of the proposed method in finding the optimal place of the PMUs and minimizing the installation cost.