  In this paper, we study the placement of Phasor Measurement Units (PMU) for
enhancing hybrid state estimation via the traditional Gauss-Newton method,
which uses measurements from both PMU devices and Supervisory Control and Data
Acquisition (SCADA) systems. To compare the impact of PMU placements, we
introduce a useful metric which accounts for three important requirements in
power system state estimation: {\it convergence}, {\it observability} and {\it
performance} (COP). Our COP metric can be used to evaluate the estimation
performance and numerical stability of the state estimator, which is later used
to optimize the PMU locations. In particular, we cast the optimal placement
problem in a unified formulation as a semi-definite program (SDP) with integer
variables and constraints that guarantee observability in case of measurements
loss. Last but not least, we propose a relaxation scheme of the original
integer-constrained SDP with randomization techniques, which closely
approximates the optimum deployment. Simulations of the IEEE-30 and 118 systems
corroborate our analysis, showing that the proposed scheme improves the
convergence of the state estimator, while maintaining optimal asymptotic
performance.
