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Fast frequency and harmonic estimation in power systems using a new optimized adaptive filter

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Abstract

This paper presents an adaptive filter for fast estimation of frequency and harmonic components of a power system voltage or current signal corrupted by noise with low signal to noise ratio (SNR). Unlike the conventional linear combiner (Adaline) approach, the new algorithm is based on an objective function often used in independent component analysis for robust tracking under impulse noise conditions. However, the accuracy and speed of convergence of this algorithm depend on the choice of step size of the filter and its adaptation. Instead of choosing the step size η and the parameter β of the cost function by trial and error, an adaptive particle swarm optimization technique is used alternatively to obtain both η and β to reduce the error between the observed voltage or current samples and the estimated ones. Using the optimized values, the amplitude and phase of the fundamental and harmonic components are estimated. Further, the extracted fundamental component is used to estimate any frequency drift of the power system recursively using an optimized error function obtained from three consecutive voltage samples. To test the effectiveness of the algorithm, several time-varying power system signals are simulated with harmonics, interharmonics, and decaying dc components buried in noise with low signal-to-noise ratio (SNR) and are used to estimate the frequency and harmonic components. This approach will be useful in islanding detection of a distributed generating system.

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References

  1. Girgis AA, Hann FM (1998) A quantitative study of pitfalls in FFT. IEEE Trans Aerosp Electron Syst 44(1): 107–115

    Google Scholar 

  2. Wright PS (1999) Short-time Fourier transform and Wigner–Ville distributions to the calibration of power frequency harmonic analysis. IEEE Trans Instrum Meas 48(2): 475–478

    Article  Google Scholar 

  3. Zhu TX (2007) Exact harmonics/interharmonics calculation using adaptive window width. IEEE Trans Power Deliv 22(4): 2279–2288

    Article  Google Scholar 

  4. So HC (2003) A comparative study of three recursive least squares algorithms for single-tone frequency tracking. Signal Process 83(9): 2059–2062

    Article  MATH  Google Scholar 

  5. Bettayeb M, Quidiani U (2003) A hybrid least squares-GA based algorithm for harmonic estimation. IEEE Trans Power Deliv 18(2): 52–67

    Article  Google Scholar 

  6. Mishra S (2005) Hybrid least squares adaptive bacterial foraging strategy for harmonic estimation. IEEE Proc Gener Transm Distrib 152(3): 379–389

    Article  Google Scholar 

  7. Pradhan AK, Routray A, Basak A (2005) Power system frequency estimation using least mean square technique. IEEE Trans Power Deliv 20(3): 1812–1816

    Article  Google Scholar 

  8. Yang J, Xi H, Guo W (2007) Robust modified Newton algorithm for adaptive frequency estimation. IEEE Trans Signal Process Lett 14(11): 879–882

    Article  Google Scholar 

  9. Xue SY, Yang SX (2009) Power system frequency estimation using supervised Gauss–Newton algorithm. Measurement 42(1): 28–37

    Article  MathSciNet  Google Scholar 

  10. Terzija Vladimir V, Stanojevic V (2007) Two stage improved recursive Newton-type algorithm for power-quality indices estimation. IEEE Trans Power Deliv 22(3): 1351–1359

    Article  Google Scholar 

  11. Routray A, Pradhan AK, Rao KP (2002) A novel Kalman filter for frequency estimation of distorted signals in power system. IEEE Trans Instrum Meas 51(3): 469–479

    Article  Google Scholar 

  12. Costa FF, Cardoso AJM, Fernandes DA (2007) Harmonic analysis based on Kalman filtering and prony’s method. In: Proceedings of international conference on power engineering, energy electrical drives, Setúbal, pp 696–701

  13. Zivanovic R (2007) An adaptive differentiation filter for tracking instantaneous frequency in power systems. IEEE Trans Power Deliv 22(2): 765–771

    Article  Google Scholar 

  14. Barros J, Diego RI (2008) Analysis of harmonics in power systems using the wavelet packet transform. IEEE Trans Instrum Meas 57(1): 63–69

    Article  Google Scholar 

  15. Lai LL (1999) Real-time frequency and harmonic evaluation using artificial neural networks. IEEE Trans Power Deliv 14(1): 52–59

    Article  Google Scholar 

  16. Lin HC (2007) Intelligent neural network-based fast power system harmonic detection. IEEE Trans Ind Electron 54(1): 43–53

    Article  Google Scholar 

  17. Wang YN, Gu JC, Cheu CM (2003) An improved adaline algorithm for on-line tracking of harmonic components. Int J Power Energy Syst 23(2): 117–125

    MATH  Google Scholar 

  18. Joorabian M, Mortazavi SS, Khayyami AA (2009) Harmonic estimation in a power system using a novel hybrid least squares adaline algorithm. Electr Power Syst Res 79(1): 107–116

    Article  Google Scholar 

  19. Dash PK, Swain DP, Liew AC, Rahman S (1996) An adaptive linear combiner for on-line tracking of power system harmonics. IEEE Trans Power Syst 11(4): 1730–1735

    Article  Google Scholar 

  20. Marei ML, El-Saadany EF, Salama MMA (2004) A processing unit for symmetrical components and harmonic estimation based on a new adaptive linear combiner structure. IEEE Trans Power Deliv 19(3): 1245–1252

    Article  Google Scholar 

  21. Cichocki A, Amari S (2003) Adaptive blind signal and image processing. Wiley, New York

  22. Soria E, Martin JD, Camps G, Serrano AJ, Calpe J, Gomez L (2003) A low-complexity fuzzy activation function for artificial neural networks. IEEE Trans Neural Netw 14(6): 1576–1579

    Article  Google Scholar 

  23. Zhang L, Huanjun Y, Chen D, Hu S (2004) Analysis and improvement of particle swarm optimization algorithm. Inf Control 33(5): 513–517

    Google Scholar 

  24. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural network, Australia, pp 1942–1948

  25. Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: Proceedings of the IEEE international conference on evolution computation, pp 69–73

  26. La Z, Ji TY, Tang WH, Wu QH (2008) Optimal harmonic estimation using a particle swarm optimizer. IEEE Trans Power Deliv 23(2): 1166–1174

    Article  Google Scholar 

  27. Krusienski DJ, Jenkins WK (2004) A Particle swarm optimization-least mean squares algorithm for adaptive filtering. In: Proceedings of IEEE conference on signals, systems, and computers, pp 241–245

  28. So HC, Ching PC (2004) Adaptive algorithm for direct frequency estimation. IEE Proc Radar Sonar Navig 151(6): 359–364

    Article  Google Scholar 

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Correspondence to P. K. Dash.

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Patra, J.P., Dash, P.K. Fast frequency and harmonic estimation in power systems using a new optimized adaptive filter. Electr Eng 95, 171–184 (2013). https://doi.org/10.1007/s00202-012-0249-3

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  • DOI: https://doi.org/10.1007/s00202-012-0249-3

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