Phasor measurement units (PMUs) can make state estimation more accurate by providing synchronized voltage phasor and current phasor measurements. Optimal PMU placement (OPP) minimizes the number of PMUs required for the system to be completely observable. This paper presents a DC state estimation model using mixed integer semidefinite programming (MISDP) approach for the OPP problem. A comparison between MISDP and mixed integer linear programming (MILP) is conducted. Power flow measurements, injection measurements, limited communication facility, and single PMU failure are studied for each approach. A formulation for MISDP-based PMU placement considering a single PMU failure is proposed. The advantages and disadvantages of each formulation are discussed.