Dynamic State Estimation for Multi-Machine Power System by Unscented Kalman Filter with Enhanced Numerical Stability

Abstract: 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.