Since the invention of phasor measurement unit (PMU), there has been growing interest in developing methodologies for finding the minimum number of units for complete system observability. The methods for the PMU placement must consider the fact that the network topology may change when the power system is affected by a contingency event (transmission lines and transformers). In order to design a robust wide area measurement (monitoring) systems (WAMS) which can ensure complete system observability under the failure of any transmission line or even a PMU, some works have considered power system contingencies and loss of measurements (failure of a PMU or its communication links).