  In this paper, we compare four measures of the empirical observability
gramian, including the determinant, the trace, the minimum eigenvalue, and the
condition number, which can be used to quantify the observability of system
states and to obtain the optimal PMU placement for power system dynamic state
estimation. An adaptive optimal PMU placement method is proposed by
automatically choosing proper measures as the objective function. It is shown
that when the number of PMUs is small and thus the observability is very weak,
the minimum eigenvalue and the condition number are better measures of the
observability and are preferred to be chosen as the objective function. The
effectiveness of the proposed method is validated by performing dynamic state
estimation on an Northeast Power Coordinating Council (NPCC) 48-machine 140-bus
system with the square-root unscented Kalman filter.
