FREQUENCY-DOMAIN CHARACTERIZATION OF KALMAN FILTERS AS APPLIED TO POWER-SYSTEM PROTECTION

Kalman filters were first introduced in the field of digital protection as candidates for phasor estimation algorithms 10 years ago. So far, all tests on this type of recursive filter have been performed in the time domain but this paper shows that conventional signal-processing tools such as frequency response can be successfully applied for the performance analysis. The concept of frequency response as applied to Kalman filters is based on its variation with time. Consequently, it is defined with respect to a definite observation window. The paper also shows that the ratio of the initial error covariance matrix terms to the measurement noise variance, not the absolute values, is the relevant statistical quantity. The same principle applies to the ratio of the process noise covariance matrix diagonal terms to the noise measurement variance.