DFT-Based Phasor Estimation for Removal of the Effect of Multiple DC Components

A current sampled signal in a faulted transmission line can contain multiple dc components, namely a primary decaying dc component (DDC), a secondary DDC, an auxiliary DDC, and a bias DDC, and these may be due to a faulted line, current transformer, internal transformer and analog-to-digital converter in the numerical relay, respectively. The intensity of the primary DDC is much higher than those of other DDCs. The elimination of the phasor-estimation error due to the primary DDC is the main issue in numerical relays, where the presence of other DDCs can deteriorate the phasor-estimation accuracy. This paper proposes a discrete Fourier transform (DFT)-based method using a second-order finite-impulse response (FIR) notch filter to combine multiple DDCs as a certain DDC through DFT. The FIR notch filter is designed to minimize the calculation complexity of the identification. Phasor-estimation errors that are due to the multiple DDCs are corrected by identifying the combined DDC. The proposed method can be applied for both full-cycle DFT (FCDFT) and half-cycle DFT. The feasibility of the proposed FCDFT-based method is compared with those of conventional FCDFT-based methods using simulations on DDCs, harmonics, noise and a faulted transmission line.

I. Introduction

Faults on transmission lines result in decaying dc components (DDC) primarily in the power system current because of the inductance that is present in transmission lines [1]. This primary DDC time constant is determined from the characteristics of a faulted transmission line and is typically 0.5 to 5 cycles [2]. The fault current is measured using a current transformer (CT), where the primary DDC generates a secondary DDC [4]– [6]. The time constant of the secondary DDC is determined from characteristics of a CT circuit and is larger than the primary DDC time constant. An internal transformer in the numerical relay may be used to isolate, step down, and condition the current signal of the CT. The primary and secondary DDCs evoke an auxiliary DDC through the internal transformer. Finally, a sampled current signal can contain a dc bias, which mainly originates from an analog-to-digital converter at the numerical relay. The auxiliary DDC and the dc bias are generally negligible when comparing their intensity to that of the primary DDC. The intensity of the primary DDC is much higher than that of the secondary DDC. However, the secondary DDC may severely affect the phasor-estimation accuracy when the fault resistance of a transmission line is large. This is because the time constant of the primary DDC decreases, which results in its rapid fading away.