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This paper proposes a method for optimal placement of phasor measurement units (PMUs) for complete observability of a power system for normal operating conditions, as well as for single branch outages. A binary search algorithm is used to determine the minimum number of PMUs needed to make the system observable. In case of more than one solution, a strategy is proposed to select the solution resulting in the most preferred pattern of measurement redundancy. The proposed method is used to benchmark the optimal PMU placement solutions for the IEEE 14-bus, IEEE 24-bus, IEEE 30-bus and New England 39-bus test systems. The proposed method is applied on a 298-bus system to determine the optimal placement of PMUs when conventional measurements are available.