  In the power system, state estimation (SE) is important monitoring task for
the reliable operation of the system. The optimal estimate from the SE is
delivered to all EMS application such as fault analysis, automatic generation
control. Hence, it is crucial to have good estimation before taking any
critical actions. However, the SE problem is challenging problem due to
nonconvexity of power flow equations in the nonlinear AC power flow model,
which give us a usually local solution. To deal with this nonconvexity, some
recent literatures applied the convex semi-definite (SDP) relaxation technique
to relax the SE problem attaining or approximating a global solution. In this
paper, we investigate the rank of this technique, which is critical to yield a
physically meaningful solution with the five-bus test system and propose new
approach to possibly reduce the rank by complementing the traditional set of
measurement with PMU data. Numerical tests on the standard IEEE 14, 30, 57,
118-bus test system are presented for the demonstration.
