scholarly journals A Frequency Estimation Method Based on a Revised 3-Level Discrete Fourier Transform with an Estimation Delay Reduction Technique

Energies ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2256
Author(s):  
Sang-Hee Kang ◽  
Woo-Seok Seo ◽  
Soon-Ryul Nam
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Frequency Estimation ◽  
Estimation Error ◽  
Estimation Method ◽  
Reduction Technique ◽  
Delay Reduction ◽  
Zero Crossing ◽  
Orthogonal Components ◽  
Frequency Changes

In this paper, a frequency estimation method based on a revised three-level discrete Fourier transform (DFT) with an estimation delay reduction technique is proposed. First, the input signal passes through a sine filter twice to improve the ability to decrease the level of harmonics and inter-harmonics. Secondly, the second sine-filtered signal is decomposed into two orthogonal components by DFT with a hamming window to enhance the ability to suppress inter-harmonics. The frequency of the signal is derived using orthogonal components without a zero-crossing problem, which can cause numerical estimation error. This process causes the estimation delay of three cycles and three samples in total. Therefore, the estimation delay reduction technique compensating for the phase delay of the phasor is proposed. To evaluate the performance of the proposed method, several frequency changes were considered when the test signals were generated according to the IEEE PMU Standards C37.118.1a-2014. The performance of the proposed method was also evaluated under dynamic and fault conditions in a five-bus transmission system modeled with PSCAD/EMTDC. The simulation results show that the proposed method accurately estimated the frequency of the signal.

Frequency estimation using warped discrete Fourier transform

2003 ◽  
Vol 83 (8) ◽  
pp. 1661-1671 ◽  
Author(s):  
Stefan Franz ◽  
Sanjit K. Mitra ◽  
Gerhard Doblinger
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Frequency Estimation

scholarly journals Reducing the Impact of the Frequency Change on the Formation of Orthogonal Components of the Relay Protection Input Signals

2020 ◽  
Vol 63 (1) ◽  
pp. 42-54 ◽  
Author(s):  
E. A. Romaniuk ◽  
V. Yu. Rumiantsev ◽  
Yu. V. Rumiantsev ◽  
A. A. Dziaruhina
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Digital Filter ◽  
Input Signal ◽  
Digital Filters ◽  
Signal Frequency ◽  
Filter Model ◽  
Input Signal Frequency ◽  
Orthogonal Components ◽  
The Impact

Digital filters made with the use of discrete Fourier Transform are applied in most microprocessor protections produced both in the home country and abroad. When the input signal frequency deviates from the value to which these filters are configured, a signal is generated at their output with oscillation amplitude that is proportional to the deviation of the signal frequency from the specified one. The article proposes an algorithm for compensating the oscillations of orthogonal components of the output signals of digital filters implemented on the basis of a discrete Fourier transform, when the input signal frequency deviates from the nominal one. A mathematical model of the proposed digital filter with an algorithm for compensating the oscillations of its orthogonal components, as well as a signal model for reproducing input effects, is implemented in the MatLab-Simulink dynamic modeling environment. The digital filter model is provided with two channels, viz. a current channel and a voltage channel, which makes it possible to simulate their operation in relation to protections that use one or two input values, for example, for current and remote protection. Verification of the functioning of the digital filter model with compensation for fluctuations in its output signal was carried out with the use of two types of test effects, viz. a sinusoidal signal with a frequency of 48–51 Hz (idealized effect), and the effects that are close to the real secondary signals of measuring current transformers and voltage transformers in case of short circuits accompanied by a decrease in frequency. The conducted computational experiments with deviation of frequency from the nominal one, revealed the presence of undamped oscillations at the output of standard digital Fourier filters and their almost complete absence in the proposed digital filters. This makes us possible to recommend digital filters based on a discrete Fourier transform supplemented by an algorithm for compensation of fluctuations in the amplitudes of the output signals for the use in microprocessor protection.

scholarly journals Multi-Tone Frequency Estimation Based on the All-Phase Discrete Fourier Transform and Chinese Remainder Theorem

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5066
Author(s):  
Xiangdong Huang ◽  
Lu Cao ◽  
Wei Lu
Keyword(s):  
Fourier Transform ◽  
Closed Form ◽  
Discrete Fourier Transform ◽  
High Efficiency ◽  
Chinese Remainder Theorem ◽  
Frequency Estimation ◽  
High Accuracy ◽  
Single Frequency ◽  
Tone Frequency ◽  
Spectrum Correction

The closed-form robust Chinese Remainder Theorem (CRT) is a powerful approach to achieve single-frequency estimation from noisy undersampled waveforms. However, the difficulty of CRT-based methods’ extension into the multi-tone case lies in the fact it is complicated to explore the mapping relationship between an individual tone and its corresponding remainders. This work deals with this intractable issue by means of decomposing the desired multi-tone estimator into several single-tone estimators. Firstly, high-accuracy harmonic remainders are calculated by applying all-phase Discrete Fourier Transform (apDFT) and spectrum correction operations on the undersampled waveforms. Secondly, the aforementioned mapping relationship is built up by a novel frequency classifier which fully captures the amplitude and phase features of remainders. Finally, the frequencies are estimated one by one through directly applying the closed-form robust CRT into these remainder groups. Due to all the components (including closed-form CRT, the apDFT, the spectrum corrector and the remainder classifier) only involving slight computation complexity, the proposed scheme is of high efficiency and consumes low hardware cost. Moreover, numeral results also show that the proposed method possesses high accuracy.

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