COMPARISON OF PRONY AND ADALINE METHOD IN INTER-HARMONIC ESTIMATION

Yıl 2020, , 405 - 418, 30.04.2020

Nedim Aktan Yalçın , Fahri Vatansever

https://doi.org/10.17482/uumfd.592988

Cited By: 3

Öz

Especially in energy and power systems, harmonic estimation has crucial role. Many techniques developed in the subject of harmonic and inter-harmonic estimation. These techniques and methods include mathematical transformation (Fourier, Hartley, Hilbert-Huang, etc.) filters (adaptive, Kalman, etc.) and parametric methods (Prony, ADALINE, MUSIC, etc.) In realized study, performance of ADALINE and Prony methods are investigated in terms of harmonic and inter-harmonic prediction capability. Required data for simulations are produced from P&O MPPT algorithm for photovoltaic systems. Therefore, this model gives opportunity to try compared methods according to different harmonic intensity (closeness of harmonics to each other). At the result of different simulations, it is observed that Prony method is more preferable for low number of data and ADALINE produces more successful results than Prony method if there is high number of data and selection of high neuron size relatively.

Anahtar Kelimeler

Inter-harmonic, Prony method, ADALINE

Ara Harmonik Kestiriminde Prony ve ADALINE Yöntemlerinin Karşılaştırılması

Öz

Özellikle enerji ve güç sistemlerinde harmonik kestirimi, önemli rol oynamaktadır. Harmonik ve ara harmoniklerin kestirimi konusunda birçok yöntem ve teknik geliştirilmiştir. Bunlar arasında matematiksel dönüşümler (Fourier, Hartley, Hilbert-Huang vb.), filtrelemeler (adaptif, Kalman vb.) ve parametrik yöntemler (Prony, ADALINE, MUSIC vb.) yer almaktadırlar. Gerçekleştirilen çalışmada; Prony ve ADALINE yöntemlerinin ara harmonik kestirimindeki performansları incelenmiştir. Benzetimler için gerekli veriler, fotovoltaik sistemler için uygulanan P&O MPPT algoritmasından üretilmektedir. Böylece bu model; karşılaştırılan yöntemleri farklı harmonik içerik yoğunlukları (harmoniklerin birbirine yakınlıkları) açısından deneme olanağı vermektedir. Farklı benzetimlerle yapılan karşılaştırmalar sonucunda, veri sayısının düşük olduğu durumlarda Prony yönteminin daha tercih edilebilir olduğu; yüksek olduğu ve görece olarak çok sayıda nöronun kullanıldığı durumlarda da ADALINE yönteminin Prony yönteminden daha başarılı sonuçlar verdiği görülmüştür.

Anahtar Kelimeler

Ara harmonik, Prony yöntemi, ADALINE

Kaynakça

• 1. Bedell, F., Mayer, E. C. (1915). Distortion of Alternating-Current Wave Caused by Cyclic Variation in Resistance, Transactions of the American Institute of Electrical Engineers, 34(1), 333–348. doi:10.1109/T-AIEE.1915.4765220
• 2. Bedell, F., Tuttle, E. B. (1906). The Effect of Iron in Distorting Alternating-Current Wave Form, Transactions of the American Institute of Electrical Engineers, 25, 671–691. doi: 10.1109/PAIEE.1906.6741940
• 3. Bettayeb, M., Qidwai, U. 2003. A hybrid least squares-GA-based algorithm for harmonic estimation, IEEE Transactions on Power Delivery, 18(2), 377–382. doi: 10.1109/TPWRD.2002.807458.
• 4. Bollen, M. H. J., Gu, I. Y.-H. (2006). Signal processing of power quality disturbances, Willey-IEEE Press, Hoes Lane Piscataway. doi: 10.1002/9780471931317.ch2
• 5. Chang, G. W., Chen, C.I. (2010). Measurement techniques for stationary and time-varying harmonics, IEEE PES General Meeting : IEEE PES General Meeting, Providence RI, USA. doi: 10.1109/PES.2010.5589611
• 6. Chang, G. W., Chen, C.I., Liang, Q.W. (2009). A Two-Stage ADALINE for Harmonics and Interharmonics Measurement, IEEE Transactions on Industrial Electronics, 56(6), 2220–2228. doi: 10.1109/TIE.2009.2017093.
• 7. Cooley, J. W., Tukey, J. W. (1965). An Algorithm for the Machine Calculation of Complex Fourier Series, Mathematics of Computation, 19(90), 297. doi: 10.1090/S0025-5718-1965-0178586-1
• 8. Dash, P. K. et al. (1999). Frequency estimation of distorted power system signals using extended complex Kalman filter, IEEE Transactions on Power Delivery, 14(3), 761–766. doi: 10.1109/61.772312.
• 9. Duhamel, P., Vetterli, M. (1990). Fast fourier transforms: A tutorial review and a state of the art, Signal Processing, 19(4), 259–299. doi: 10.1016/0165-1684(90)90158-U.
• 10. Frank, J. J. (1910). Observation of harmonics in current and in voltage wave shapes of transformers, Proceedings of the American Institute of Electrical Engineers, 29(5), 665–746. doi: 10.1109/T-AIEE.1910.4764646
• 11. Gonen, T. (1984). Bibliography of Power System Harmonics, Part I, IEEE Transactions on Power Apparatus and Systems PAS, 103(9), 2460–2469. doi: 10.1109/TPAS.1984.318400.
• 12. Grossmann, A., Morlet, J. (1984). Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape, SIAM Journal on Mathematical Analysis, 15(4), 723–736. doi: 10.1137/0515056.
• 13. Hauer, J. F. et al. (1990). Initial Results in Prony Analysis of Power System Reponse Signals, IEEE Transactions on Power Systems, 5(1), 80–89. doi: 10.1109/59.49090
• 14. Heartz, R. A., Saunders, R. M. (1954). Harmonics due to Slots in Electric Machines [includes discussion], Transactions of the American Institute of Electrical Engineers, Part III: Power Apparatus and Systems, 73(2), 946-949. doi: 10.1109/AIEEPAS.1954.4498912
• 15. Hostetter, G. (1980). Recursive discrete Fourier transformation, IEEE Transactions on Acoustics, Speech, and Signal Processing, 28(2), 184–190. doi: 10.1109/TASSP.1980.1163389
• 16. Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C.C., Liu, H. H. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 454(1971), 903–995. doi: 10.1098/rspa.1998.0193
• 17. Jain, S. K., Singh, S. N. (2011). Harmonics estimation in emerging power system: Key issues and challenges, Electric Power Systems Research, 81(9), 1754–1766. doi: 10.1016/j.epsr.2011.05.004.
• 18. Xiong, J., Wang, B., Zhang, S. (2010). Interharmonics analysis based on windowed interpolation and prony algorithm, 2nd International Asia Conference on Informatics in Control, Automation and Robotics (CAR 2010), Wuhan, China. doi: 10.1109/CAR.2010.5456806
• 19. Kalman, R. E. (1960). A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, 82, 35–45. doi: 10.1115/1.3662552
• 20. Kay, S. M., Marple, S. L. (1981). Spectrum analysis—A modern perspective, Proceedings of the IEEE, 69(11), 1380–1419. doi: 10.1109/PROC.1981.12184
• 21. Levenberg, K. (1944). A method for the solution of certain non-linear problems in least square, Quarterly of Applied Mathematics, 2(2), 164-168. doi: 10.1090/qam/10666
• 22. Mallat, S. G. (1989). A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), 674–693. doi: 10.1109/34.192463.
• 23. Marquardt, D. W. (1963). An Algorıthm For Least-Squares Estımatıon Of Nonlınear Parameters, Journal of the Society for Industrial and Applied Mathematics, 11(2), 431-441. doi: 10.1137/0111030
• 24. MATLAB, (2019). Matlab. Access Adress: http://www.mathworks.com (Accessed in: 01.06.2019).
• 25. Mishra, S. (2005). A hybrid least square-fuzzy bacterial foraging strategy for harmonic estimation, IEEE Transactions on Evolutionary Computation, 9, 61–73. doi: 10.1109/TEVC.2004.840144.
• 26. Prony, G. R. B. (1795). Essai experimantal et analytique, Journal de L’Ecole Polytechnique, 1(1), 24–76.
• 27. Rabehi R., Kouzou A., Saadi S.,Hafaifa A. (2019). Parameter selection criteria of Prony method for accurate harmonicsand inter-harmonic component identification, Electrotehnica, Electronica, Automatica (EEA), 67(1), 46-53.
• 28. Robinson, E. A. (1982). A historical perspective of spectrum estimation, Proceedings of the IEEE, 70(9), 885–907. doi: 10.1109/proc.1982.12423
• 29. Roy, R., Kailath, T. (1989). ESPRIT-estimation of signal parameters via rotational invariance techniques, IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(7), 984–995. doi: 10.1109/29.32276.
• 30. Sangwongwanich, A., Yang, Y., Sera, D., Soltani, H., Blaabjerg F. (2018). Analysis and Modeling of Interharmonics from Grid-Connected Photovoltaic Systems, IEEE Transactions on Power Electronics, 33(10), 8353-8364. doi: 10.1109/TPEL.2017.2778025.
• 31. Schmidt, R. (1986). Multiple Emitter Location and Signal Parameter Estimation, IEEE Transactions on Antennas and Propagation, 34(3), 276-280. doi: 10.1109/tap.1986.1143830
• 32. Singh, G. K. (2009). Power system harmonics research: a survey, European Transactions on Electrical Power, 19(2), 151–172. doi: 10.1002/etep.201.
• 33. Tarasiuk, T. (2004). Hybrid wavelet-Fourier spectrum analysis, IEEE Transactions on Power Delivery, 19, 957–964. doi: 10.1109/TPWRD.2004.824398.
• 34. Testa, A., Akram, M. F., Burch, R., Carpinelli, G., Chang, G., Dinavahi, V., Hatziadoniu, C., Grady, W. M., Gunther, E., Halpin, M., Lehn, P., Liu, Y., Langella, R., Lowenstein, M., Medina, A., Ortmeyer, T., Ranade, S., Ribeiro, P., Watson, N., Wikston, J., Xu, W. (2007). Interharmonics: Theory and modeling. IEEE Transactions on Power Delivery, 22(4), 2335-2348. doi: 10.1109/TPWRD.2007.905505.
• 35. Thomson, D. J. (1982). Spectrum estimation and harmonic analysis, Proceedings of the IEEE, 70(9), 1055–1096. doi: 10.1109/proc.1982.12433
• 36. Widrow, B. (1960). An adaptive “ADALINE” neuron using chemical “memistors”, Stanford University Press, San Jose.
• 37. Winograd, S. (1976). On computing the Discrete Fourier Transform, Proceedings of the National Academy of Sciences, 73(4), 1005–1006. doi: 10.1090/S0025-5718-1978-0468306-4