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Localized Spectral Analysis of Fluctuating Power Generation from Solar Energy Systems

Abstract

Fluctuations in solar irradiance are a serious obstacle for the future large-scale application of photovoltaics. Occurring regularly with the passage of clouds, they can cause unexpected power variations and introduce voltage dips to the power distribution system. This paper proposes the treatment of such fluctuating time series as realizations of a stochastic, locally stationary, wavelet process. Its local spectral density can be estimated from empirical data by means of wavelet periodograms. The wavelet approach allows the analysis of the amplitude of fluctuations per characteristic scale, hence, persistence of the fluctuation. Furthermore, conclusions can be drawn on the frequency of occurrence of fluctuations of different scale. This localized spectral analysis was applied to empirical data of two successive years. The approach is especially useful for network planning and load management of power distribution systems containing a high density of photovoltaic generation units.

References

  1. Misiti M, Misiti Y, Oppenheim G, Poggi J-M: Décomposition par ondelettes et méthodes comparatives: étude d'une courbe de charge électrique. Revue de Statistique Appliquée 1994,42(2):57-77.

    Google Scholar 

  2. Degaudenzi ME, Arizmendi CM: Wavelet-based fractal analysis of electrical power demand. Fractals 2000,8(3):239-245. 10.1142/S0218348X0000024X

    Article  Google Scholar 

  3. Santoso S, Powers EJ, Grady WM: Power quality disturbance data compression using wavelet transform methods. IEEE Transactions on Power Delivery 1997,12(3):1250-1256. 10.1109/61.637001

    Article  Google Scholar 

  4. Santoso S, Grady WM, Powers EJ, Lamoree J, Bhatt SC: Characterization of distribution power quality events with Fourier and wavelet transforms. IEEE Transactions on Power Delivery 2000,15(1):247-254. 10.1109/61.847259

    Article  Google Scholar 

  5. Pierz P, Rosołowski E: Analysis and reconstruction of the shape of the voltage sag using wavelet transform. Fachtagung Elektrische Energiewandlungssysteme, March 2002, Magdeburg, Germany 74–77.

    Google Scholar 

  6. Croes T, Gherasim C, Van Den Keybus J, Ghijselen J, Driesen J, Belmans R: Power measurement using the wavelet transform of analytic signals. Proceedings of the 11th International Conference on Harmonics and Quality of Power, September 2004, Lake Placid, NY, USA 338–341. CD-ROM

    Google Scholar 

  7. Lee C-H, Wang Y-J, Huang W-L: A literature survey of wavelets in power engineering applications. Proceedings of the National Science Council, Republic of China, Part A 2000,24(4):249-258.

    Google Scholar 

  8. Woyte A, Thong VV, Belmans R, Nijs J: Voltage fluctuations on distribution level introduced by photovoltaic systems. IEEE Transactions on Energy Conversion 2006,21(1):202-209. 10.1109/TEC.2005.845454

    Article  Google Scholar 

  9. Woyte A, Bodach M, Belmans R, Nijs J: Power fluctuations in micro-grids introduced by photovoltaics: analysis and solutions. Proceedings of the 2nd European PV-Hybrid and Mini-Grid Conference, September 2003, Kassel, Germany 449–454.

    Google Scholar 

  10. Woyte A, Belmans R, Nijs J: Fluctuations in instantaneous clearness index: Analysis and statistics. Solar Energy 2007,81(2):195-206. 10.1016/j.solener.2006.03.001

    Article  MATH  Google Scholar 

  11. Nason GP, Silverman BW: The stationary wavelet transform and some statistical applications. In Wavelets and Statistics, Lecture Notes in Statistics. Volume 103. Edited by: Antoniadis A, Oppenheim G. Springer, New York, NY, USA; 1995:281-299. 10.1007/978-1-4612-2544-7_17

    Google Scholar 

  12. Nason GP, von Sachs R, Kroisandt G: Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. Journal of the Royal Statistical Society. Series B 2000,62(2):271-292. 10.1111/1467-9868.00231

    Article  MathSciNet  Google Scholar 

  13. Van Bellegem S, von Sachs R: Locally adaptive estimation of sparse evolutionary wavelet spectra. In Discussion Paper 310. Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium; 2003. https://doi.org/www.stat.ucl.ac.be/ISpersonnel/vanbelle/res.html

    Google Scholar 

  14. Kern EC Jr., Gulachenski EM, Kern GA: Cloud effects on distributed photovoltaic generation: slow transients at the Gardner, Massachusetts photovoltaic experiment. IEEE Transactions on Energy Conversion 1989,4(2):184-190. 10.1109/60.17910

    Article  Google Scholar 

  15. Jewell W, Ramakumar R: The effects of moving clouds on electric utilities with dispersed photovoltaic generation. IEEE Transactions on Energy Conversion 1987,2(4):570-576.

    Article  Google Scholar 

  16. Beyer H, Hammer A, Luther J, Poplawska J, Stolzenburg K, Wieting P: Analysis and synthesis of cloud pattern for radiation field studies. Solar Energy 1994,52(5):379-390. 10.1016/0038-092X(94)90115-I

    Article  Google Scholar 

  17. Otani K, Minowa J, Kurokawa K: Study on areal solar irradiance for analyzing areally-totalized PV systems. Solar Energy Materials and Solar Cells 1997,47(1–4):281-288.

    Article  Google Scholar 

  18. Iqbal M: An Introduction to Solar Radiation. Academic Press, Don Mills, Ontario, Canada; 1983.

    Google Scholar 

  19. Skartveit A, Olseth JA: The probability density and autocorrelation of short-term global and beam irradiance. Solar Energy 1992,49(6):477-487. 10.1016/0038-092X(92)90155-4

    Article  Google Scholar 

  20. Suehrcke H, McCormick PG: The frequency distribution of instantaneous insolation values. Solar Energy 1988,40(5):413-422. 10.1016/0038-092X(88)90096-5

    Article  Google Scholar 

  21. Bendt P, Collares-Pereira M, Rabl A: The frequency distribution of daily insolation values. Solar Energy 1981,27(1):1-5. 10.1016/0038-092X(81)90013-X

    Article  Google Scholar 

  22. Gordon JM, Reddy TA: Time series analysis of hourly global horizontal solar radiation. Solar Energy 1988,41(5):423-429. 10.1016/0038-092X(88)90016-3

    Article  Google Scholar 

  23. Hollands KGT, Huget RG: A probability density function for the clearness index, with applications. Solar Energy 1983,30(3):195-209. 10.1016/0038-092X(83)90149-4

    Article  Google Scholar 

  24. Liu BHY, Jordan RC: The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 1960,4(3):1-19. 10.1016/0038-092X(60)90062-1

    Article  Google Scholar 

  25. Coifman RR, Dohono DL: Translation-invariant de-noising. In Wavelets and Statistics, Lecture Notes in Statistics. Volume 103. Edited by: Antoniadis A, Oppenheim G. Springer, New York, NY, USA; 1995:125-150. 10.1007/978-1-4612-2544-7_9

    Google Scholar 

  26. Mallat S: A Wavelet Tour of Signal Processing. Academic Press, San Diego, Calif, USA; 1999.

    MATH  Google Scholar 

  27. Pesquet J-C, Krim H, Carfantan H: Time-invariant orthonormal wavelet representations. IEEE Transactions on Signal Processing 1996,44(8):1964-1970. 10.1109/78.533717

    Article  Google Scholar 

  28. Daubechies I: Ten Lectures on Wavelets. SIAM, Philadelphia, Pa, USA; 1992.

    Book  MATH  Google Scholar 

  29. Oppenheim AV, Schafer RW: Discrete-Time Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, USA; 1989.

    MATH  Google Scholar 

  30. Bodach M: Short term power backup in PV systems with ultra capacitors. Proceedings of the 17th European Photovoltaic Solar Energy Conference and Exhibition (EUPVSEC '01), October 2001, Munich, Germany 518–519.

    Google Scholar 

  31. Rahman MH, Nakayama J, Nakamura K, Yamashiro S: An intelligent grid-connected PV-ECS system with load leveling function. Proceedings of the 3rd IASTED International Conference on Power and Energy Systems (EUROPES '03), September 2003, Marbella, Spain 75–80.

    Google Scholar 

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Correspondence to Achim Woyte.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Woyte, A., Belmans, R. & Nijs, J. Localized Spectral Analysis of Fluctuating Power Generation from Solar Energy Systems. EURASIP J. Adv. Signal Process. 2007, 080919 (2007). https://doi.org/10.1155/2007/80919

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