Adaptive adjustment of noise covariance in Kalman filter for dynamic state estimation

Accurate estimation of the dynamic states of a synchronous machine (e.g., rotor's angle and speed) is essential in monitoring and controlling transient stability of a power system. It is well known that the covariance matrixes of process noise (Q) and measurement noise (R) have a significant impact on the Kalman filter's performance in estimating dynamic states. The conventional ad-hoc approaches for estimating the covariance matrixes are not adequate in achieving the best filtering performance. To address this problem, this paper proposes an adaptive filtering approach to adaptively estimate Q and R based on innovation and residual to improve the dynamic state estimation accuracy of the extended Kalman filter (EKF). It is shown through the simulation on the two-area model that the proposed estimation method is more robust against the initial errors in Q and R than the conventional method in estimating the dynamic states of a synchronous machine.

I. Introduction

Timely and accurately estimating the dynamic states of a synchronous machine (e.g., rotor angle and rotor speed) is important for monitoring and controlling the transient stability of a power system over wide areas [1]. With the worldwide deployment of phasor measurement units (PMUs), many research efforts have been made to estimate the dynamic states and improve the estimation accuracy using PMU data [2]–[11], among which the Kalman filtering (KF) techniques play an essential role. For instance, Huang et al. [2] proposed an extended Kalman filtering (EKF) approach to estimate the dynamic states using PMU data. Ghahremani and Innocent [3] proposed the EKF with unknown inputs to simultaneously estimate dynamic states of a synchronous machine and unknown inputs. [4]–[7] proposed the unscented Kalman filtering to estimate power system dynamic states. Zhou et al. [8] proposed an ensemble Kalman filter approach to simultaneously estimate the dynamic states and parameters. Akhlaghi, Zhou and Huang [9]–[10] proposed an adaptive interpolation approach to mitigate the impact of non-linearity in dynamic state estimation (DSE). These studies have laid a solid ground for estimating the dynamic states of a power system and also revealed some needs for further studies.