Phasor Measurement Unit (PMU), which is based on the GPS technique, is able to provide power engineers with immediate and precise measurements. By utilizing PMUs, the reliability and stability in power system are expected to be improved. Conventionally, an optimal PMU placement is considered to use the least number of units to make the entire system completely observable. In this thesis, it is recommended to not only optimize the number of PMUs but also install the majority of PMUs on the most sensitive buses in a power system. Thus a bus sensitivity analysis based on Decoupled Power Flow method is first studied. Then multiple PMU placement methods constrained by bus sensitivity analysis are proposed in this thesis. They are Integer Programming, the Genetic Algorithm method and Ant Colony Optimization. Finally results and comparisons of these proposed methods are shown and analyzed.