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Phasor measurement units (PMU) have an important role for reliable operation in the power systems. Because of the high cost of PMU and also the lack of suitable communication infrastructure to transfer the measured information, the problem of optimal PMU placement (OPP) for incomplete observability has been proposed. In this paper, a new formulation was proposed to optimize the OPP problem considering the limited number of PMU in the power system. In the proposed formulation, to achieve the higher degrees of precision in state estimation, the fitness function was defined to maximize the number of observable buses and to minimize the depth of unobservability, simultaneously. Also, a comprehensive formulation of the OPP problem was introduced to have a minimum depth of unobservability and three different scenarios were designed to study the effect of considering the depth of unobservability. To simulate the results, IEEE 14, 24, 30, 39, and 57 bus test systems were used. The calculated results showed that the proposed formulation has a proper performance e.g. in IEEE 39 bus test system which had 27 observable bus in the best solution with a maximum depth of degree as 7, could reach to the 26 observable bus with a maximum depth of degree as 4 by changing the PMU placement.

Keywords: Depth of unobservability, Incomplete observability, Optimal placement, Phasor measurement unit

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