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Prony’S Method Used for Testing Harmonics and Interharmonics in Electrical Power Systems

Janusz Mroczka Jarosław Zygarlicki
Metrology and Measurement Systems | 2012 | No 4 | 659-672 | DOI: 10.2478/v10178-012-0058-z
Keywords measurements Prony’s method signal processing harmonics
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Abstract

The article presents an application of Prony’s method with some known components in the analysis of electric power quality. Modifications of the Prony algorithm broaden the scope of method application. Modification of the filter of known components enables more accurate analysis of the parameters of unknown components and components with known or assumed frequencies. This article presents a comparison of the results of analyses conducted with the proposed algorithm for simulated and real signals and the results obtained by means of a commercial electric power quality testing device, operating in class A and using the Fourier transform. The proposed method enables to estimate the levels of the harmonic components, the frequency of the fundamental signal and real parameters of the interharmonic components, which are grouped and averaged in the contemporary monitoring equipment. Knowledge of the individual parameters of the interharmonics has considerable diagnostic importance while removing causes of incorrect operation affecting sensitive equipment in some electric power systems. Additionally, the algorithm is capable of analyzing exponentially damped components and finds its application in analysis of disturbances, for example, transient oscillations.

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Authors and Affiliations

Janusz Mroczka
Jarosław Zygarlicki

Fast Second Order Original Prony’s Method for Embedded Measuring Systems

Jarosław Zygarlicki
Metrology and Measurement Systems | 2017 | vol. 24 | No 4 | 721–728 | DOI: 10.1515/mms-2017-0058
Keywords Prony’s method signal processing harmonics measurements
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Abstract

The paper presents a method of adaptation of the original second order Prony’s method for applications in lowcost digital measurement systems with low computing performance. The presented method can be used in measuring systems where it is important to obtain in real time the values of amplitude, frequency, initial phase and damping coefficient of a single sinusoidal component of an analysed signal. The paper presents optimized, in terms of the number of mathematical operations, implementation of the method in selected embedded devices as well as the calculation times of the method for each platform.

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Authors and Affiliations

Jarosław Zygarlicki

Short Time Algorithm of Power Waveforms Fundamental Harmonic Estimation With Use of Prony's Methods

Janusz Mroczka Jarosław Zygarlicki
Metrology and Measurement Systems | 2011 | No 3 | 371-378 | DOI: 10.2478/v10178-011-0004-z
Keywords power quality Prony's method harmonics measurements
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Abstract

This paper presents an example of practical use of Prony's method for monitoring of power waveform fundamental harmonic fluctuations, which is required for the analysis of window synchronizations in frequency analyses in power monitoring systems. The example presented offers verification of the authors' theoretical considerations published earlier in articles about Prony's method and its opportunities for practical use for real life signals. The investigations shown are based on the least squares Prony's method, which, in connection with digital filtrations, enables estimations of fundamental frequency at the rate of even tens of times per one fundamental harmonic period.

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Authors and Affiliations

Janusz Mroczka
Jarosław Zygarlicki

Fast one-cycle frequency estimation of a single sinusoid in noise using downsampled linear prediction model

Krzysztof Duda Tomasz P. Zieliński
Metrology and Measurement Systems | 2021 | vol. 28 | No 4 | 661-672 | DOI: 10.24425/mms.2021.137701
Keywords frequency estimation linear prediction Prony method smart DFT
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Abstract

A new solution to the problem of frequency estimation of a single sinusoid embedded in the white Gaussian noise is presented. It exploits, approximately, only one signal cycle, and is based on the well-known 2nd order autoregressive difference equation into which a downsampling is introduced. The proposed method is a generalization of the linear prediction based Prony method for the case of a single undamped sinusoid. It is shown that, thanks to the proposed downsampling in the linear prediction signal model, the overall variance of the least squares solution of frequency estimation is decreased, when compared to the Prony method, and locally it is even close to the Cramér–Rao Lower Bound, which is a significant improvement. The frequency estimation variance of the proposed solution is comparable with, computationally more complex, the Matrix Pencil and the Steiglitz–McBride methods. It is shown that application of the proposed downsampling to the popular smart DFT frequency estimation method also significantly reduces the method variance and makes it even better than the least squares smart DFT. The noise immunity of the proposed solution is achieved simultaneously with the reduction of computational complexity at the cost of narrowing the range of measured frequencies, i.e. a sinusoidal signal must be sufficiently oversampled to apply the proposed downsampling in the autoregressive model. The case of 64 samples per period with downsampling up to 16, i.e. 1/4th of the cycle, is presented in detail, but other sampling scenarios, from 16 to 512 samples per period, are considered as well.
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Bibliography

[1] Kay, S. M. (1993). Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall
[2] Kay, S. M., & Marple, S. L. (1981). Spectrum analysis – A modern perspective. Proc. IEEE, 69, 1380–1419. https://doi.org/10.1109/PROC.1981.12184
[3] Kay, S. M. (1987). Modern Spectrum Analysis. Prentice-Hall.
[4] Zielinski, T. P., & Duda, K. (2011). Frequency and damping estimation methods - an overview. Metrology and Measurement Systems, 18(3), 505–528. https://doi.org/10.2478/v10178-011-0051-y
[5] Duda, K., & Zielinski, T. P. (2013). Efficacy of the frequency and damping estimation of a real-value sinusoid. IEEE Instrumentation & Measurement Magazine, 16(1), 48–58. https://doi.org/10.1109/ MIM.2013.6495682
[6] Borkowski, J., Kania, D., & Mroczka, J. (2018). Comparison of sine-wave frequency estimation methods in respect of speed and accuracy for a few observed cycles distorted by noise and harmonics. Metrology and Measurement Systems, 25(1), 283–302. https://doi.org/10.24425/119567
[7] Harris, F. J. (1978). On the use of windows for harmonic analysis with the discrete Fourier transform. Proceedings of the IEEE, 66(1), 51–83. https://doi.org/10.1109/PROC.1978.10837
[8] Zygarlicki, J., Zygarlicka, M., Mroczka, J., & Latawiec, K. J. (2010). A reduced Prony’s method in power-quality analysis – parameters selection. IEEE Transactions on Power Delivery, 25(1), 979–986. https://doi.org/10.1109/TPWRD.2009.2034745
[9] Zygarlicki, J., & Mroczka, J. (2014). Prony’s method with reduced sampling – numerical aspects. Metrology and Measurement Systems, 21(2), 521–534. https://doi.org/10.2478/mms-2014-0044
[10] Zygarlicki, J. (2017). Fast second order original Prony’s method for embedded measuring systems. Metrology and Measurement Systems, 24(3), 721–728. https://doi.org/10.1515/mms-2017-0058
[11] Hua, Y., & Sarkar, T. K., (1990). Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoid in noise. IEEE Transactions on Acoustics, Speech, and Signal Processing, 38(4), 814–824. https://doi.org/10.1109/29.56027
[12] Steiglitz, K.,&McBride, L. (1965). A technique for identification of linear systems. IEEE Transactions on Automatic Control, 10(3), 461–464. https://doi.org/10.1109/TAC.1965.1098181
[13] McClellan, J. H., & Lee, D. (1991). Exact equivalence of the Steiglitz–McBride iteration and IQML. IEEE Transactions on Signal Processing, 39(1), 509–512. https://doi.org/10.1109/78.80841
[14] Wu, R. C., & Chiang, C. T. (2010). Analysis of the exponential signal by the interpolated DFT algorithm. IEEE Transactions on Instrumentation and Measurement, 59(12), 3306–3317. https://doi.org/10.1109/TIM.2010.2047301
[15] Derviškadic, A., Romano, & P., Paolone, M. (2018). Iterative-Interpolated DFT for Synchrophasor Estimation: A Single Algorithm for P- and M-Class Compliant PMUs. IEEE Transactions on Instrumentation and Measurement, 67(2), 547–558. https://doi.org/10.1109/TIM.2017.2779378
[16] Jacobsen, E., & Kootsookos, P. (2007). Fast, accurate frequency estimators. IEEE Signal Processing Magazine, 24(2), 123–125. https://doi.org/10.1109/MSP.2007.361611
[17] Duda, K., & Barczentewicz, S. (2014). Interpolated DFT for sin α (x) windows. IEEE Transactions on Instrumentation and Measurement, 63(3), 754–760. https://doi.org/10.1109/TIM.2013.2285795
[18] Yang, J. Z., & Liu, C. W. (2000). A precise calculation of power system frequency and phasor. IEEE Transactions on Power Delivery, 15(1), 494–499. https://doi.org/10.1109/61.852974
[19] Yang, J. Z., & Liu, C. W. (2001). A precise calculation of power system frequency. IEEE Transactions on Power Delivery, 16(2), 361–366. https://doi.org/10.1109/61.924811
[20] Xia, Y., He, Y., Wang, K., Pei, W., Blazic, Z., & Mandic, D. P. (2017). A complex least squares enhanced smart DFT technique for power system frequency estimation. IEEE Transactions on Power Delivery, 32(2), 1270–1278. https://doi.org/10.1109/TPWRD.2015.2418778
[21] Li, Z. (2021). A total least squares enhanced smart DFT technique for frequency estimation of unbalanced three-phase power systems. International Journal of Electrical Power & Energy Systems, 128, 106722. https://doi.org/10.1016/j.ijepes.2020.106722
[22] Xu, S., Liu, H., & Bi, T. (2020). A novel frequency estimation method based on complex Bandpass filters for P-class PMUs with short reporting latency. IEEE Transactions on Power Delivery. https://doi.org/10.1109/TPWRD.2020.3038703
[23] Duda, K., & Zielinski, T. P. (2021). P Class and M Class Compliant PMU Based on Discrete- Time Frequency-Gain Transducer. IEEE Transactions on Power Delivery. https://doi.org/10.1109/TPWRD.2021.3076831
[24] IEC, IEEE. (2018). Measuring relays and protection equipment – Part 118–1: Synchrophasor for power systems – Measurements (IEC/IEEE Standard No. 60255-118-1).
[25] Moon, T. K., & Stirling W. C. (1999). Mathematical Methods and Algorithms for Signal Processing. Prentice Hall.

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Authors and Affiliations

Krzysztof Duda
1
Tomasz P. Zieliński
2
  1. AGH University of Science and Technology, Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering, Department of Measurement and Electronics, al. Mickiewicza 30, 30-059 Kraków, Poland
  2. AGH University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Institute of Telecommunications, al. Mickiewicza 30, 30-059 Kraków, Poland

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