Wind Modelling and its Possible Application to Control of Wind Farms

  • Yoshito Hirata
  • Hideyuki Suzuki
  • Kazuyuki Aihara

Because of global warming and oil depletion, the number of wind turbines is increasing. Wind turbines commonly have a horizontal axis, but some wind turbines have a vertical axis. A problem of wind turbines with horizontal axis is that we need to face them towards the wind for maximising energy production. If the geography around a wind turbine is complicated, then the wind direction keeps changing. Thus, if one can predict the wind direction to some extent, then one may generate more electricity by controlling wind turbines according to the prediction.

In this chapter, we discuss how to model the wind. First, we formulate a problem and clarify which properties of the wind we need to predict. Second, we discuss the characteristics for time series of the wind. Third, we model the wind based on the knowledge and predict it. We prepare different models for predicting wind direction and absolute wind speed. Finally, we apply the prediction and simulate control of a wind turbine. Since we integrate predictions for wind direction and absolute wind speed to obtain an optimal control, the whole scheme can be regarded as heterogeneous fusion.


Wind Direction Wind Turbine Wind Farm Surrogate Data Physical Review Letter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Garcia, S.P., Almeida, J.S.: Multivariate phase space reconstruction by nearest neighbor embedding with different time delays. Physical Review E 72(2), 027205 (2005)CrossRefGoogle Scholar
  2. 2.
    Goh, S.L., Chen, M., Popvic, H., Aihara, K., Obradovic, D., Mandic, D.P.: Complex-valued forecasting of wind profile. Renewable Energy 31(11), 1733–1750 (2006)CrossRefGoogle Scholar
  3. 3.
    Goh, S.L., Mandic, D.P.: A complex-valued RTRL algorithm for recurrent neural networks. Neural Computation 16(12), 2699–2713 (2004)MATHCrossRefGoogle Scholar
  4. 4.
    Goh, S.L., Mandic, D.P.: Nonlinear adaptive prediction of complex-valued signals by complex-valued PRNN. IEEE Transactions on Signal Processing 53(5), 1827–1836 (2005)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Hirata, Y., Horai, S., Suzuki, H., Aihara, K.: Testing serial dependence by Random-shuffle surrogates and the wayland method. Physics Letters A (2007). DOI 10. 1016/j.physleta.2007.05.061Google Scholar
  6. 6.
    Hirata, Y., Mandic, D.P., Suzuki, H., Aihara, K.: Wind direction modelling using multiple observation points. Philosophical Transacations of the Royal Society A (2007). DOI 10.1098/rsta.2007.2112Google Scholar
  7. 7.
    Hirata, Y., Suzuki, H., Aihara, K.: Predicting the wind using spatial correlation. In: Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications (NOLTA 2005) (2005)Google Scholar
  8. 8.
    Hirata, Y., Suzuki, H., Aihara, K.: Reconstructing state spaces from multivariate data using variable delays. Physical Review E 74(2), 026202 (2006)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Judd, K., Mees, A.: On selecting models for nonlinear time-series. Physica D 82(4), 426–444 (1995)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Judd, K., Mees, A.: Embedding as a modeling problem. Physica D 120(3–4), 273–286 (1998)MATHCrossRefGoogle Scholar
  11. 11.
    Judd, K., Small, M.: Towards long-term prediction. Physica D 136(1–2), 31–44 (2000)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Kantz, H., Holstein, D., Ragwitz, M., Vitanov, N.K.: Extreme events in surface wind: Predicting turbulent gusts. In: S. Bocaletti, B.J. Gluckman, J. Kurths, L.M. Pecora, R. Meucci, O. Yordanov (eds.) Proceedings of the 8th Experimental Chaos Conference, no. 742 in AIP Conference Proceedings. American Institute of Physics, New York (2004)Google Scholar
  13. 13.
    Kantz, H., Holstein, D., Ragwitz, M., Vitanov, N.K.: Markov chain model for turbulent wind speed data. Physica A 342(1–2), 315–321 (2004)CrossRefGoogle Scholar
  14. 14.
    Kantz, H., Holstein, D., Ragwitz, M., Vitanov, N.K.: Short time prediction of wind speeds from local measurements. In: J. Peinke, P. Schaumann, S. Barth (eds.) Wind Energy: Proceedings of the EUROMECH Colloquium. Springer, Berlin Heidelberg New York (2006)Google Scholar
  15. 15.
    Kennel, M.B.: Statistical test for dynamical nonstationarity in observed time-series data. Physical Review E 56(1), 316–321 (1997)CrossRefGoogle Scholar
  16. 16.
    Kennel, M.B., Brown, R., Abarbanel, H.D.I.: Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A 45(6), 3403–3411 (1992)CrossRefGoogle Scholar
  17. 17.
    McNames, J.: A nearest trajectory strategy for time series prediction. In: Proceedings of the International Workshop on Advanced Black-Box Techniques for Nonlinear Modeling (1998)Google Scholar
  18. 18.
    Ragwitz, M., Kantz, H.: Detecting non-linear structure and predicting turbulent gusts in surface wind velocities. Europhysics Letters 51(6), 595–601 (2000)CrossRefGoogle Scholar
  19. 19.
    Rissanen, J.: MDL denoising. IEEE Transactions on Information Theory 46(7), 2537–2543 (2000)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Roulston, M.S., Kaplan, D.T., Hardenberg, J., Smith, L.A.: Using medium-range weather forecasts to improve the value of wind energy production. Renewable Energy 28(4), 585–602 (2003)CrossRefGoogle Scholar
  21. 21.
    Scheinkman, J.A., LeBaron, B.: Nonlinear dynamics and stock returns. Journal of Business 62(3), 311–337 (1989)CrossRefGoogle Scholar
  22. 22.
    Schreiber, T., Schmitz, A.: Improved surrogate data for nonlinearity tests. Physical Review Letters 77(4), 635–638 (1996)CrossRefGoogle Scholar
  23. 23.
    Schreiber, T., Schmitz, A.: Surrogate time series. Physica D 142(3–4), 346–382 (2000)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Small, M., Yu, D., Harrison, R.G.: Surrogate test for pseudoperiodic time series. Physical Review Letters 87(18), 188101 (2001)CrossRefGoogle Scholar
  25. 25.
    Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., Farmer, J.D.: Testing for nonlinearity in time-series: the method of surrogate data. Physica D 58(1–4), 77–94 (1992)CrossRefGoogle Scholar
  26. 26.
    Timmer, J.: Power of surrogate data testing with respect to nonstationarity. Physical Review E 58(4), 5153–5156 (1998)CrossRefGoogle Scholar
  27. 27.
    Wayland, R., Bromley, D., Pickett, D., Passamante, A.: Recognizing determinism in a time-series. Physical Review Letters 70(5), 580–582 (1993)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Yoshito Hirata
    • 1
  • Hideyuki Suzuki
    • 1
  • Kazuyuki Aihara
    • 1
  1. 1.Institute of Industrial ScienceThe University of TokyoJapan

Personalised recommendations