Contents I. Introduction
The Discrete Fourier Transform (DFT) is the most commonly used algorithm in numerical protective relays to estimate the phasors of the voltage and current signals based on which the relays make necessary decisions. During fault, due to the combined inductive and resistive nature of the power system, a decaying-exponential transient component, known as decaying dc offset, is generated in the current signal in addition to the fundamental frequency component, harmonics, and noise. A decaying dc offset is a nonperiodic signal and has a relatively wide range frequency spectrum with larger distribution at lower frequencies. Since conventional full-cycle DFT cannot effectively attenuate the lower frequency components, unwanted errors in forms of overshoot and decaying oscillations result in the magnitude and angle of the estimated phasor. The magnitude error itself of the DFT-based phasor estimation can reach up to 15.1% as reported in [1]. The total vector error will be even larger because of the phase-angle error contribution. Since this total vector error is not tolerated in most power system protection applications, prefiltering of the current signal prior to phasor estimation is mostly employed in practice to attenuate the negative effects of the decaying dc offset of the current signal. The filter used for this purpose, known as mimic filter, is a high-pass or bandpass filter which can completely remove the decaying dc offset only when the time constant of the dc offset matches with the presumed one [1]. Use of any prefilters indeed introduces a delay in response thereby slowing down the performance of the related protection algorithms.
