Linear Kalman filtering algorithm applied to measurements of power system voltage magnitude and frequency: A constant-frequency model

The Kalman filtering (KF) algorithm has found widespread application in power system measurements for relaying, such as measurements of voltage and current phasors, frequency and rate of change of frequency. This paper presents the application of linear Kalman filters to optimal tracking of power system voltage phasors and frequency deviations. Frequency is assumed to be constant within the data window. Two linear state-space models are used. The first is a two-state model developed and reported earlier in the literature, while the second is newly developed by the authors and is characterized by differing numbers of state variables, depending on the number of terms taken from a Taylor series expansion. The proposed filter is tested when the measurements set is contaminated by noise. The effects of the sampling rate, data-window size and number of terms taken from the Taylor series expansion are investigated.