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.