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.

Low damping ratios of interarea modes in the power system result in peaks at their natural frequencies in the discrete Fourier transform (DFT) representation of ringdown data. This has been a motivation to develop a nonparametric DFT-based modal identification method. However, this method has difficulty estimating damping ratios. This paper proposes a parametric DFT-based method to solve such a problem in the non-parametric one. To effectively remove the decaying dc component in ringdown data, the proposed method uses a difference sequence between two sets of ringdown frequency data with oscillation against each other. This method estimates coefficients of the numerator and denominator in the Laplace transform of the frequency difference sequence by curve-fitting of DFT values around peak frequencies. Then, modal natural frequencies and damping ratios are calculated from estimated coefficients of the denominator. This method is compared to a non-parametric DFT-based method and a Prony-based method through simulations on the signal-to-noise ratio and is applied to identify real power systems from ringdown frequency data in the Frequency Monitoring Network system.

This study proposes a discrete Fourier transform (DFT)‐based parametric identification method by using a difference sequence between two sets of frequency data. An autocorrelation function of the frequency difference sequence can be represented as a linear combination of exponentially decaying sinusoidal functions, whose natural frequencies and damping ratios are equal to those of interarea modes. These modal parameters are calculated from the Laplace transform coefficients of the autocorrelation function. The coefficients are estimated by curve‐fitting the DFT values of the autocorrelation function. The proposed method is compared with the modified extended Yule Walker method through simulations on signal‐to‐noise ratio. Finally, the feasibility of the proposed method is shown by identifying real power systems from frequency data of the frequency monitoring network system.

A fault current in a power system contains both harmonics and a decaying DC component, which can produce a severe error in phasor estimation of fundamental frequency. Currently, full‐cycle discrete Fourier transform phasor estimation is widely used in numerical relays owing to harmonics immunity, which produces easy identification of the decaying DC component. It is desirable to promptly estimate the phasor for a fast protection of the power system. Such promptness is dependent on the data window length of the phasor estimation. The least error squares (LESs) method is effective to achieve this promptness as it can estimate the phasor with a data window length of less than one cycle. This study proposes a phasor estimation method using LES with the data window length less than one cycle. The time constant of the decaying DC is identified through Prony analysis, while the noise effect on the phasor estimation is investigated according to the data window length. The performances of the proposed method are investigated through simulations on time constants of the decaying DC, frequency deviations of the power system, and signal‐to‐noise ratio. The feasibility of the proposed method is verified to estimate the phasor of a fault transmission line in a MATLAB/Simulink.

The full-cycle discrete Fourier transform (FCDFT) is commonly used to estimate phasors in numerical relays because of its immunity to harmonics and accurate identification of a decaying dc component (DDC) in a fault current. For fast protection of power systems, it is necessary to speed up the phasor estimation by using a data window below one cycle. The conventional least squares (LS) methods below one cycle approximate the DDC as the first several terms of the Taylor series expansion, which degrades the phasor-estimation accuracy. This paper proposes an LS method that uses Fourier analysis for approximation of the DDC to speed up phasor estimation without accuracy degradation. The phasor-estimation accuracy of the proposed method is investigated for the data-window length in simulations using synthetic data of fault currents containing DDC, harmonics, and measurement noise. The phasor-estimation speed is also investigated with respect to the delay of the antialiasing filter in the numerical relay. The proposed method is compared with the conventional LS and FCDFT methods in simulations using synthetic fault-current data. The feasibility of the proposed method is demonstrated through the phasor estimation of simulated transmission-line faults.