Search results

Filters

  • Journals
  • Authors
  • Keywords
  • Date
  • Type

Search results

Number of results: 5
items per page: 25 50 75
Sort by:
Download PDF Download RIS Download Bibtex

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.
Go to article

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.

Go to article

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
Download PDF Download RIS Download Bibtex

Abstract

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.

Go to article

Authors and Affiliations

Tomasz Zieliński
Krzysztof Duda
Download PDF Download RIS Download Bibtex

Abstract

Power quality (PQ) monitoring is important for both the utilities and also the users of electric power. The most widespread measurement instrument used for PQ monitoring is the PQM (Power Quality Monitor) or PQA (Power Quality Analyzer). In this paper we propose the usage of PMU data for PQ parameters monitoring. We present a new methodology of PQ parameters monitoring and classification based on PMU data. The proposed methodology is tested with real measurements performed in distribution system using dedicated PMU system.

Go to article

Authors and Affiliations

Szymon H. Barczentewicz
Andrzej Bień
Krzysztof Duda
Download PDF Download RIS Download Bibtex

Abstract

In this paper it is shown that M class PMU (Phasor Measurement Unit) reference model for phasor estimation recommended by the IEEE Standard C37.118.1 with the Amendment 1 is not compliant with the Standard. The reference filter preserves only the limits for TVE (total vector error), and exceeds FE (frequency error) and RFE (rate of frequency error) limits. As a remedy we propose new filters for phasor estimation for M class PMU that are fully compliant with the Standard requirements. The proposed filters are designed: 1) by the window method; 2) as flat-top windows; or as 3) optimal min-max filters. The results for all Standard compliance tests are presented, confirming good performance of the proposed filters. The proposed filters are fixed at the nominal frequency, i.e. frequency tracking and adaptive filter tuning are not required, therefore they are well suited for application in lowcost popular PMUs.
Go to article

Authors and Affiliations

Krzysztof Duda
Tomasz P. Zieliński
Download PDF Download RIS Download Bibtex

Abstract

Modern production technology requires new ways of surface examination and a special kind of surface profile parameters. Industrial quality inspection needs to be fast, reliable and inexpensive. In this paper it is shown how stochastic surface examination and its proper parameters could be a solution for many industrial problems not necessarily related with smoothing out a manufactured surface. Burnishing is a modern technology widely used in aircraft and automotive industries to the products as well as to process tools. It gives to the machined surface high smoothness, and good fatigue and wear resistance. Every burnished material behaves in a different manner. Process conditions strongly influence the final properties of any specific product. Optimum burnishing conditions should be preserved for any manufactured product. In this paper we deal with samples made of conventional tool steel – Sverker 21 (X153CrMoV12) and powder metallurgy (P/M) tool steel – Vanadis 6. Complete investigations of product properties are impossible to perform (because of constraints related to their cost, time, or lack of suitable equipment). Looking for a global, all-embracing quality indicator it was found that the correlation function and the frequency analysis of burnished surface give useful information for controlling the manufacturing process and evaluating the product quality. We propose three new indicators of burnishing surface quality. Their properties and usefulness are verified with the laboratory measurement of material samples made of the two mentioned kinds of tool steel.
Go to article

Authors and Affiliations

Daniel Toboła
Piotr Rusek
Kazimierz Czechowski
Tatiana Miller
Krzysztof Duda

This page uses 'cookies'. Learn more