Communications - Scientific Letters of the University of Zilina 2017, 19(11):79-86 | DOI: 10.26552/com.C.2017.2A.79-86

Monte Carlo Comparison of the Methods for Estimating the Weibull Distribution Parameters - Wind Speed Application

Ivana Pobocikova1, Zuzana Sedliackova1, Maria Michalkova1, Florence George2
1 Department of Applied Mathematics, Faculty of Mechanical Engineering, University of Zilina, Slovakia
2 Department of Mathematics & Statistics, Florida International University, Miami, USA

Wind energy is considered one of the most significant alternative energy sources for electrical energy production. The most important factor for modelling wind energy is the wind speed. The two-parameter Weibull distribution is commonly used for modelling wind speed. Its parameters play an important role in the wind energy applications and so it is important to choose the best method for the estimation of these parameters. In this paper we investigate and compare six different methods for estimating the Weibull distribution parameters. The methods we considered are the maximum likelihood method, the method of moments, the empirical method, the power density method, the least squares method and the weighted least squares method. The performance of these methods is compared and discussed through the Monte Carlo simulation.

Keywords: wind speed; Weibull distribution; parameter estimation; Monte Carlo simulation

Published: April 30, 2017  Show citation

ACS AIP APA ASA Harvard Chicago Chicago Notes IEEE ISO690 MLA NLM Turabian Vancouver
Pobocikova, I., Sedliackova, Z., Michalkova, M., & George, F. (2017). Monte Carlo Comparison of the Methods for Estimating the Weibull Distribution Parameters - Wind Speed Application. Communications - Scientific Letters of the University of Zilina, 19(2A), 79-86. doi: 10.26552/com.C.2017.2A.79-86
Share...
Download citation
  • BibTeX (.bib)
  • Bookends (.ris)
  • EasyBib (.ris)
  • EndNote (.enw)
  • EndNote 8 (.xml)
  • ISI WoS (.isi)
  • Medlars (.medlars)
  • Mendeley (.ris)
  • MODS (.xml)
  • Papers (.ris)
  • RefWorks (.txt)
  • RefManager (.ris)
  • RIS (.ris)
  • MS Word (.xml)
  • Zotero (.ris)
    • Open full article

    References

    1. AKPINAR, E. K., AKPINAR, S.: Determination of the Wind Energy Potential for Maden, Energy Conversion and Management, 45, 2004, 2901-2914. Go to original source...
    2. Atlas of Renewable Energy Sources in Slovakia (in Slovak), Energetické centrum Bratislava, 2012. ISBN 978-80-969646-8.
    3. CARTA, J. A., RAMIREZ, P., VELASQUEZ, S.: A Review of Wind Speed Probability Distributions Used in Wind Energy Analysis Case Studies in The Canary Island. Renewable and Sustainable Energy Reviews, 13, 2009, 933-955. Go to original source...
    4. CELIK, A. N.: A Statistical Analysis of Wind Power Density Based on the Weibull and Rayleigh Models at the Southern Region of Turkey. Renewable Energy, 29, 2003, 593-604. Go to original source...
    5. JUSTUS, C. G., HARGRAVES, W. R., MIKHAIL, A., GRABER, D.: Methods for Estimating Wind Speed Frequency Distributions. J. of Applied Meteorology, 17, 1978, 350-353. Go to original source...
    6. MORGAN, M. C., LACKNER, M., VOGEL, R. M., BAISE, L. G.: Probability Distributions for Offshore Wind Speeds. Energy Conversion and Management, 52, 2011, 15-26. Go to original source...
    7. SEGURO, J. V., LAMBERT, T. W.: Modern Estimation of the Parameters of the Weibull Speed Distribution for Wind Energy Analysis. J. of Wind Engineering and Industrial Aerodynamics, 85, 2000, 75-84. Go to original source...
    8. LUN, I. Y. F., LAM, J. C.: A Study of Weibull Parameters Using Long-Term Wind Observation. Renewable Energy, 20, 2000, 145-153. Go to original source...
    9. STEVENS, M. J. M., SMULDERS, P. T.: The Estimation of the Parameters of the Weibull Wind Speed Distribution for Wind Energy Utilization Purposes. Wind Engineering, vol. 3, 2, 1979, 132-45.
    10. DORVLO, A. S. S.: Estimating Wind Speed Distribution. Energy Conversion and Management, 43, 2002, 2311-2318. Go to original source...
    11. WU, D., ZHOU, J., LI, Y.: Methods for Estimating Weibull Parameters for Brittle Materials. J. of Materials Science, 41, 2006, 5630-5638. Go to original source...
    12. AKDAG, S. A., DINLER, A.: A New Method to Estimate Weibull Parameters for Wind Energy Application. Energy Conversion and Management, 50, 2009, 1761-1766. Go to original source...
    13. KANTAR, Y. M., SENOGLU, B.: A Comparative Study for the Location and Scale Parameter of the Weibull Distribution with Given Shape Parameter. Computers & Geosciences, 34, 2008, 1900-1909. Go to original source...
    14. COSTA ROCHA, P. A., DE SOUSA, R. C., DE ANDRADE, C. F., DA SILVA, M. E. V.: Comparison of Seven Numerical Methods for Determining Weibull Parameters for Wind Energy Generation in the Northeast Region of Brazil. Applied Energy, 89, 2012, 395-400. Go to original source...
    15. CHANG, T. P.: Performance Comparison of Six Numerical Methods in Estimating Weibull Parameters for Wind Energy Application. Applied Energy, 88, 2011, 272-282. Go to original source...
    16. KANTAR, Y. M., KURBAN, M., HOCAOGLU, F. O.: Comparison of Six Different Parameter Estimation Methods in Wind Power Applications. Scientific Research and Essays, vol. 6, 32, 2011, 6594-6604. Go to original source...
    17. GEORGE, F.: A Comparison of Shape and Scale Estimators of the Two-Parameter Weibull Distribution. J. of Modern Applied Statistical Methods, vol. 13, 1, 23-35.
    18. LYSEN, E.H.: Introduction to Wind Energy, The Netherlands: SWD Publication SWD 82-1, 1983.
    19. POBOCIKOVA, I., SEDLIACKOVA, Z.: The Least Square and the Weighted Least Square Methods for Estimating the Weibull Distribution Parameters-A Comparative Study. Communications - Scientific Letters of the University of Zilina, vol. 14, No. 4, 2012, 88-93. Go to original source...
    20. BERGMAN, B.: Estimation of Weibull Parameters Using a Weight Function. J. of Materials Science Letters, 5, 1986, 611-614. Go to original source...

    This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.


    Return to the content