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1
Content available Interpolated-DFT-Based Fast and Accurate Amplitude and Phase Estimation for the Control of Power
Borkowski J., Kania D.
Metrology and Measurement Systems
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2016
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Vol. 23, nr 1
13--26
EN
Quality of energy produced in renewable energy systems has to be at the high level specified by respective standards and directives. One of the most important factors affecting quality is the estimation accuracy of grid signal parameters. This paper presents a method of a very fast and accurate amplitude and phase grid signal estimation using the Fast Fourier Transform procedure and maximum decay side-lobes windows. The most important features of the method are elimination of the impact associated with the conjugate’s component on the results and its straightforward implementation. Moreover, the measurement time is very short ‒ even far less than one period of the grid signal. The influence of harmonics on the results is reduced by using a bandpass pre-filter. Even using a 40 dB FIR pre-filter for the grid signal with THD ≈ 38%, SNR ≈ 53 dB and a 20‒30% slow decay exponential drift the maximum estimation errors in a real-time DSP system for 512 samples are approximately 1% for the amplitude and approximately 8.5・10‒2 rad for the phase, respectively. The errors are smaller by several orders of magnitude with using more accurate pre-filters.
2
Content available Investigation of continuous change of α parameter in the interpolated DFT algorithm for cosα(X) windows
Barczentewicz S.
Measurement Automation Monitoring
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2015
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Vol. 61, No. 4
90--91
EN
Currently known IpDFT algorithms use the cosα(X) windows with the step change of the window’s order. This work presents IpDFT method designed for the signal analyzed with cosα(X) window, which allows continuous change of the window’s parameter α, so that a full regulation of the sidelobes position becomes possible. Proposed algorithm is a generalization of known IpDFT solutions for cosα(X) windows.
3
Content available Systematic errors of the LIDFT method: analytical form and verification by a Monte Carlo method
Borkowski J.
Metrology and Measurement Systems
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2012
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Vol. 19, nr 4
673-684
EN
This paper derives analytical formulas for the systematic errors of the linear interpolated DFT (LIDFT) method when used to estimating multifrequency signal parameters and verifies this analysis using Monte-Carlo simulations. The analysis is performed on the version of the LIDFT method based on optimal approximation of the unit circle by a polygon using a pair of windows. The analytical formulas derived here take the systematic errors in the estimation of amplitude and frequency of component oscillations in the multifrequency signal as the sum of basic errors and the errors caused by each of the component oscillations. Additional formulas are also included to analyze particular quantities such as a signal consisting of two complex oscillations, and the analyses are verified using Monte-Carlo simulations.
4
Content available remote An induction motor speed measurement method based on supplying current analysis
Bień A., Duda K.
Przegląd Elektrotechniczny
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2011
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R. 87, nr 3
201-203
EN
We present a new technique for estimating speed and slip of the induction motor. The method is based on the time-frequency analysis of the current suppling the motor. Interpolated OFT, computed in the sliding time window, is used for obtaining current spectrograms with high frequency resolution. The speed and the slip are estimated from the fluctuation of amplitude of the main current harmonic. The proposed method is validated by Iaboratory experiment.
PL
Przedstawiony tekst opisuje nową technikę pomiaru prędkości obrotowej - poślizgu silnika indukcyjnego. Prezentowana metoda opiera się o analizę czasowo-częstotliwościową prądu zasilania silnika w jednej fazie. Wyznaczana jest interpolowana OFT w analizowanych oknach czasowych, tak by uzyskać konieczną rozdzielczość częstotliwościową spektrogramów prądu. Poślizg i prędkość obrotowa wyznaczana jest na podstawie fluktuacji amplitudy podstawowej harmonicznej. Opisano wyniki badań laboratoryjnych metody.
5
Content available Minimization of maximum errors in universal approximation of the unit circle by a polygon
Borkowski J.
Metrology and Measurement Systems
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2011
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Vol. 18, nr 3
391-402
EN
This paper presents a universal approximation of the unit circle by a polygon that can be used in signal processing algorithms. Optimal choice of the values of three parameters of this approximation allows one to obtain a high accuracy of approximation. The approximation described in the paper has a universal character and can be used in many signal processing algorithms, such as DFT, that use the mathematical form of the unit circle. One of the applications of the described approximation is the DFT linear interpolation method (LIDFT). Applying the results of the presented paper to improve the LIDFT method allows one to significantly decrease the errors in estimating the amplitudes and frequencies of multifrequency signal components. The paper presents the derived formulas, an analysis of the approximation accuracy and the region of best values for the approximation parameters.
6
Content available Frequency and Damping Estimation Methods - An Overview
Zieliński T. P., Duda K.
Metrology and Measurement Systems
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2011
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Vol. 18, nr 4
505-528
EN
This overview paper presents and compares different methods traditionally used for estimating damped sinusoid parameters. Firstly, direct nonlinear least squares fitting the signal model in the time and frequency domains are described. Next, possible applications of the Hilbert transform for signal demodulation are presented. Then, a wide range of autoregressive modelling methods, valid for damped sinusoids, are discussed, in which frequency and damping are estimated from calculated signal linear self-prediction coefficients. These methods aim at solving, directly or using least squares, a matrix linear equation in which signal or its autocorrelation function samples are used. The Prony, Steiglitz-McBride, Kumaresan-Tufts, Total Least Squares, Matrix Pencil, Yule-Walker and Pisarenko methods are taken into account. Finally, the interpolated discrete Fourier transform is presented with examples of Bertocco, Yoshida, and Agrež algorithms. The Matlab codes of all the discussed methods are given. The second part of the paper presents simulation results, compared with the Cramér-Rao lower bound and commented. All tested methods are compared with respect to their accuracy (systematic errors), noise robustness, required signal length, and computational complexity.
7
Content available Estimation of the amplitude square using the interpolated Discrete Fourier Transform
Lušin T., Agrež D.
Metrology and Measurement Systems
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2011
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Vol. 18, nr 4
583-596
EN
To improve the estimation of active power, the possibility of estimating the amplitude square of a signal component using the interpolation of the squared amplitude discrete Fourier transform (DFT) coefficients is presented. As with an energy-based approach, the amplitude square can be estimated with the squared amplitude DFT coefficients around the component peak and a suitable interpolation algorithm. The use of the Hann window, for which the frequency spectrum is well known, and the three largest local amplitude DFT coefficients gives lower systematic errors in squared interpolated approach or in better interpolated squared approach than the energy-based approach, although the frequency has to be estimated in the first step. All investigated algorithms have almost the same noise propagation and the standard deviations are about two times larger than the Cramér-Rao lower bound.
8
Content available Continuous and discontinuous linear approximation of the window spectrum by least squares method
Borkowski J.
Metrology and Measurement Systems
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2011
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Vol. 18, nr 3
379-390
EN
This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.
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