Square-root-extended complex Kalman filter for estimation of symmetrical components in power system

Abstract

The paper presents a square-root-extended complex Kalman filter (SRECKF) by decomposing covariance matrix with its square-root forms to improve stability of the filter for estimating complex number. αβ transformation is used to map three-phase instantaneous voltages in the abc phases into instantaneous voltages on the αβ axes, and a non-linear state equation and observation equation of the three-phase voltages are built by introducing a complex vector and defining state variables. Positive symmetrical component, negative symmetrical components, and frequency of the three-phase voltages are estimated using traditional extended complex Kalman filter (ECKF), the estimation results show that the method proposed here are superior to traditional extended complex Kalman filter on estimation accuracy and convergence rate.

Keywords

• covariance matrices
• Kalman filters
• power system state estimation
• matrix decomposition
• nonlinear equations
• vectors
• square-root-extended complex Kalman filter
• complex number
• observation equation
• three-phase voltages
• complex vector
• positive symmetrical component
• negative symmetrical components
• traditional extended complex Kalman filter
• state variables
• three-phase instantaneous voltages
• covariance matrix decomposition
• filter stability
• αβ transformation
• abc phases
• αβ axes
• nonlinear state equation
• ECKF
• convergence rate