Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Inverse Log-logistic distribution for Extreme Wind Speed modeling: Genesis, identification and Bayes estimation

1 Department of Industrial Engineering, University of Naples Federico II, Naples, Italy
2 Department of Engineering, University of Naples Parthenope, Naples, Italy
3 Department of Electrical Engineering and Information Technology, University of Naples Federico II, Naples, Italy

Topical Section: Wind Energy

Extreme Wind Speed modeling, i.e. the probabilistic characterization of extreme values of wind speed, is a key tool for properly understanding the destructive wind forces which may affect mechanical safety and reliability of wind power systems, but it is also extremely useful for the purpose of achieving accurate wind energy production estimations. Indeed, the need of more accurate wind estimations has been often highlighted in the literature, especially for Extreme Wind Speed, since classical adopted models, such as the Weibull distribution, behave poorly in the range of Extreme Wind Speed values. In the paper, a new model, generated by a proper mixture of the established Inverse Weibull distribution, is proposed and illustrated. The proposal is the “Inverse Log-logistic” distribution, whose adequacy in interpreting some sets of real Extreme Wind Speed data is shown after giving some hints to its identification. This study also develops a peculiar Bayesian statistical inference approach for the estimation of the above model from available data, using different prior distributions, i.e. the Lognormal, the Generalized Gamma and the Uniform distribution. Extensive numerical simulations confirm that the proposed estimation technique constitutes a very fast, efficient and robust method for the Extreme Wind Speed modeling.
  Figure/Table
  Supplementary
  Article Metrics

References

1. Kantar YM, Usta I (2008) Analysis of Wind Speed Distribution. Energ Convers Manage 49: 962–973.    

2. Feijóo A, Villanueva D (2016) Assessing wind speed simulation methods. Renew Sust Energ Rev 56: 473–483.    

3. Chiodo E, Lauria D (2009) Analytical Study of Different Probability Distributions for Wind Speed Related To Power Statistics. Int Conf Clean Electr Power 2009: 733–738.

4. Carta JA, Ramirez P, Velazquez S (2009) A review of wind speed probability distributions used in wind energy analysis: Case studies in the Canary Islands. Renew Sust Energ Rev 13: 933–955.    

5. Seguro JV, Lambert TW (2000) Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis. J Wind Eng Ind Aerod 85: 75–84.    

6. Feijóo A, Villanueva D (2014) Polynomial approximations of the Normal to Weibull Distribution transformation. AIMS Energy 2: 342–358.    

7. Mohammadi K, Alavi O, Mcgowan JG (2017) Use of Birnbaum-Saunders distribution for estimating wind speed and wind power probability distributions: A review. Energ Convers Manage 143: 109–122.    

8. Simiu E, Heckert NA (1996) Extreme wind distribution tails: A "peaks over threshold" approach. J Struct Eng 122: 305–314.

9. Simiu E, Heckert NA, Filliben JJ, et al. (2001) Extreme wind load estimates based on the Gumbel distribution of dynamic pressures: An assessment. Struct Saf 23: 221–229.    

10. Kang D, Ko K, Huh J (2015) Determination of extreme wind values using the Gumbel distribution. Energy 86: 51–58.    

11. Chiodo E, Mazzanti G, Karimian M (2015) Bayes estimation of Inverse Weibull distribution for extreme wind speed prediction. Int Conf Clean Electr Power 2015: 639–646.

12. Chiodo E, De Falco P (2016) The Inverse Burr distribution for extreme wind speed prediction: Genesis, identification and estimation. Electr Pow Syst Res 141: 549–561.    

13. Panteli ATM, Mancarella P (2015) Influence of extreme weather and climate change on the resilience of power systems: Impacts and possible mitigation strategies. Electr Pow Syst Res 127: 259–270.    

14. Gong K, Jie D, Chen X (2014) Estimation of long-term extreme response of operational and parked wind turbines: Validation and some new insights. Eng Struct 81: 135–147.    

15. Morgan EC, Lackner M, Vogel RM, et al. (2011) Probability distributions for offshore wind speeds. Energ Convers Manage 52: 15–26.    

16. Bracale A, Carpinelli G, De Falco P (2017) A new finite mixture distribution and its expectation-maximization procedure for extreme wind speed characterization. Renew Energ 113: 1366–1377.    

17. Harris RI (2005) Generalised Pareto methods for wind extremes. Useful tool or mathematical mirage? J Wind Eng Ind Aerod 93: 341–360.

18. Harris RI (2006) Errors in GEV analysis of wind epoch maxima from Weibull parents. Wind Struct An Int J 9: 179–191.    

19. Simiu E, Heckert N, Filliben J, et al. (2001) Extreme wind load estimates based on the Gumbel distribution of dynamic pressures: An assessment. Struct Saf 23: 221–229.    

20. Jung C, Schindler D (2016) Modelling monthly near-surface maximum daily gust speed distributions in Southwest Germany. Int J Climatol 36: 4058–4070.    

21. Jung C, Schindler D, Buchholz A, et al. (2017) Global Gust Climate Evaluation and Its Influence on Wind Turbines. Energies, 10.

22. Chiodo E (2013) The Burr XII Model and its Bayes Estimation for Wind Power Production Assessment. Int Rev Electr Eng 8: 737–751.

23. Chiodo E, Lauria D, Mottola F (2018) On-Line Bayes Estimation of Rotational Inertia for Power Systems with High Penetration of Renewables. Part II: Numerical Experiments. Proc of The 24th Int Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), Amalfi Coast, Italy, June 20–22, 2018.

24. Coles S (2001) An Introduction to Statistical Modeling of Extreme Values. Technometrics 44: 397.

25. Johnson NL, Kotz S, Balakrishnan N (1995) Continuous Univariate Distributions, 2nd Ed., Vol. 1 and 2. Jonh Wiley & Sons.

26. Rohatgi VK, Saleh AK (2000) An Introduction to Probability and Statistics, 2nd ed., Jonh Wiley & Sons.

27. Press SJ (2002) Subjective and Objective Bayesian Statistics: Principles, Models, and Applications, 2nd ed., Jonh Wiley & Sons.

28. Martz HF, Waller RA (1991) Bayesian Reliability Analysis. Krieger Publishing, Malabar, USA.

29. Abubakar Y, Muhammad DM (2017) Bayesian Estimation of Scale Parameter of the Log-Logistic Distribution under the Assumption of Chi-Square and Maxwell Priors. ATBU Journal of Science, Technology and Education 4: 39–46.

30. Chiodo E, Di Noia LP, Mottola F (2018) Electrical insulation components reliability assessment and practical Bayesian estimation under a Log-Logistic model, Int J Eng Technol 7: 1072–1082.

31. Modarres R, Nayak TK, Gastwirth JL (2002) Estimation of upper quantiles under model and parameter uncertainty. Comput Stat Data An 39: 529–554.    

32. Cheng E, Yeung C (2002) Generalized extreme gust wind speeds distributions. J Wind Eng Ind Aerod 90: 1657–1669.    

33. Kantar YM, Yildirim V (2014) Robust Estimation for Parameters of the Extended Burr Type III Distribution. Commun Stat-Simul C 44: 1901–1930.

© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved