Modeling Correlated Wind Speeds by Trigonometric Archimedean Copulas

  • Qing Xiao
  • Shao-Wu ZhouEmail author
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 582)


In this paper, the statistical features of correlated wind speeds at multiple sites are characterized by marginal distributions and Archimedean copulas. Firstly, the generalized lambda distribution (GLD), kappa distribution and Weibull distribution are employed to recover the quantile function of wind speed at each site. Then, three new Archimedean copula models are constructed to characterize the dependence structure of historical wind speed data. Based on Rosenblatt transformation, a generic algorithm is presented to produce sample realizations of correlated wind speeds, which would have the same statistical features as historical wind speed data. Finally, numerical examples are given to illustrate the proposed methods.


Correlated wind speeds Generalized lambda distribution Kappa distribution Weibull distribution Archimedean copula Rosenblatt transformation 



This research is partially supported by National Natural Science Foundation of China (Grant No. 51577057).


  1. 1.
    Akgül, F.G., Şenoğlu, B., Arslan, T.: An alternative distribution to Weibull for modeling the wind speed data: inverse Weibull distribution. Energ. Convers. Manage. 114, 234–240 (2016)CrossRefGoogle Scholar
  2. 2.
    Asiabanpour, B., Almusaied, Z., Rainosek, K., Davidson, K.: A comparison between simulation and empirical methods to determine fixed versus sun-tracking photovoltaic panel performance. Int. J. Comput. Appl. Technol. 60(1), 37–50 (2019)CrossRefGoogle Scholar
  3. 3.
    Hagspiel, S., Papaemannouil, A., Schmid, M., Andersson, G.: Copula-based modeling of stochastic wind power in Europe and implications for the Swiss power grid. Appl. Energy 96, 33–44 (2012)CrossRefGoogle Scholar
  4. 4.
    Hofert, M.: Sampling Archimedean copulas. Comput. Stat. Data. Anal. 52(12), 5163–5174 (2008)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hofert, M.: Efficiently sampling nested Archimedean copulas. Comput. Stat. Data. An. 55(1), 57–70 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Khooban, M.-H., Dehghani, M., Dragičević, T.: Hardware-in-the-loop simulation for the testing of smart control in grid-connected solar power generation systems. Int. J. Comput. Appl. Trans. 58(2), 116–128 (2018)CrossRefGoogle Scholar
  7. 7.
    Lebrun, R., Dutfoy, A.: Do Rosenblatt and Nataf isoprobabilistic transformations really differ? Probabilist. Eng. Mech. 24(4), 577–584 (2009)CrossRefGoogle Scholar
  8. 8.
    Lojowska, A., Kurowicka, D., Papaefthymiou, G., van der Sluis, L.: Stochastic modeling of power demand due to EVs using copula. IEEE Trans. Power Syst. 27(4), 1960–1968 (2012)CrossRefGoogle Scholar
  9. 9.
    Louie, H.: Evaluation of bivariate Archimedean and elliptical copulas to model wind power dependency structures. Wind Energy 17(2), 225–240 (2014)CrossRefGoogle Scholar
  10. 10.
    McNeil, A.J.: Sampling nested Archimedean copulas. J Stat. Comput. Sim. 78(6), 567–581 (2008)MathSciNetCrossRefGoogle Scholar
  11. 11.
    McNeil, A.J., Neslehova, J.: Multivariate Archimedean copulas, \(d\)-monotone functions and \(\ell _1\)-norm symmetric distributions. Ann. Stat. 37(5B), 3059–3097 (2009)CrossRefGoogle Scholar
  12. 12.
    Ozay, C., Celiktas, M.S.: Statistical analysis of wind speed using two-parameter Weibull distribution in alaçatı region. Energ. Convers. Manage. 121, 49–54 (2016)CrossRefGoogle Scholar
  13. 13.
    Papaefthymiou, G., Kurowicka, D.: Using copulas for modeling stochastic dependence in power system uncertainty analysis. IEEE Trans. Power. Syst. 24(1), 40–49 (2009)CrossRefGoogle Scholar
  14. 14.
    Pirmoradian, A.: A New One Parameter Family of Archimedean Copula and Its Extensions. Ph.D. thesis, University of Malaya (2013)Google Scholar
  15. 15.
    Samal, R.K., Tripathy, M.: Estimating wind speed probability distribution based on measured data at Burla in Odisha, India. Energ. Sour. Part. A 41(8), 918–930 (2019)CrossRefGoogle Scholar
  16. 16.
    Stephen, B., Galloway, S.J., McMillan, D., Hill, D.C., Infield, D.G.: A copula model of wind turbine performance. IEEE Trans. Power. Syst. 26(2), 965–966 (2011)CrossRefGoogle Scholar
  17. 17.
    Wang, Y., Ming, Y., Tang, X.: Study on licence plate location algorithm in complex weather. Int. J. Comput. Appl. Trans. 57(2), 85–93 (2018)CrossRefGoogle Scholar
  18. 18.
    Xiao, Q.: Modeling uncertainties in power system by generalized lambda distribution. Int. J. Electr. Pow. Syst. 15(3), 195–203 (2014)Google Scholar
  19. 19.
    Xiao, Q., Zhou, S.: Probabilistic power flow computation considering correlated wind speeds. Appl. Energy 231, 677–685 (2018)CrossRefGoogle Scholar
  20. 20.
    Xie, K., Li, Y., Li, W.: Modelling wind speed dependence in system reliability assessment using copulas. IET Renew. Power. Gen. 6(6), 392–399 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.School of Information and Electrical EngineeringHunan University of Science and TechnologyXiangtanChina
  2. 2.College of Mechanical and Electrical EngineeringHunan University of Science and TechnologyXiangtanChina

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