  In this paper, in order to enhance the numerical stability of the unscented
Kalman filter (UKF) used for power system dynamic state estimation, a new UKF
with guaranteed positive semidifinite estimation error covariance (UKF-GPS) is
proposed and compared with five existing approaches, including UKF-schol,
UKF-$\kappa$, UKF-modified, UKF-$\Delta Q$, and the square-root unscented
Kalman filter (SR-UKF). These methods and the extended Kalman filter (EKF) are
tested by performing dynamic state estimation on WSCC 3-machine 9-bus system
and NPCC 48-machine 140-bus system. For WSCC system, all methods obtain good
estimates. However, for NPCC system, both EKF and the classic UKF fail. It is
found that UKF-schol, UKF-$\kappa$, and UKF-$\Delta Q$ do not work well in some
estimations while UKF-GPS works well in most cases. UKF-modified and SR-UKF can
always work well, indicating their better scalability mainly due to the
enhanced numerical stability.
