Advertisement

KSCE Journal of Civil Engineering

, Volume 23, Issue 8, pp 3476–3492 | Cite as

Weibull and Generalized Extreme Value Distributions for Wind Speed Data Analysis of Some Locations in India

  • Arnab SarkarEmail author
  • Sneh Deep
  • D. Datta
  • Amit Vijaywargiya
  • R. Roy
  • V. S. Phanikanth
Structural Engineering
  • 31 Downloads

Abstract

Wind velocity data modeling plays a crucial role for the estimation of wind load and wind energy. Apart from these, the same modeling must also be used in the load cycle analysis of fatigue failure in slender structures to address periodic vortex shedding. Most authors fitted the entire available range of wind velocities of various locations using Weibull models. However, they did not check the validity of the model in describing the range of extreme wind velocity. In this work, the validity of Weibull models for describing parent as well as extreme hourly mean wind velocity data for four places on the east coast of India has been checked. While it predicts lower wind speeds accurately, the Weibull model has been found to become inappropriate for describing wind velocity in the range of extremes, i.e., above a certain threshold value. Therefore, this article focuses on the techniques of determining a limiting wind velocity beyond which the Weibull distribution is rendered unsuitable. In the range where the Weibull distribution fails, various extreme value distributions, such as Gumbel, Fréchet and reverse Weibull distributions have been compared, thereby determining the best estimator for each location.

Keywords

weibull distribution wind velocities non-exceedance probability gumbel distribution chauvenet’s criterion probability factor 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgments

The authors are grateful to the Indian Meteorological Department, Pune, for supplying wind velocity data. The corresponding author would like to thank professor Michael Kasperski for encouraging him to conduct research in wind climatology during his DAADsupported stay in Germany. The authors would like to thank BRNS, Department of Atomic Energy, Govt. of India for providing financial support for this research via Grant No. 2012/36/65-BRNS. The authors would also like to acknowledge Ms. Debanshee Datta, SRF and Mr. Ahin Banerjee, JRF for providing necessary help and logistic support. They are also obliged to Dr. Arabin Kumar Dey, Associate Professor, Department of Mathematics, IIT, Guwahati for helping them to reply reviewers’ comments.

References

  1. Akdağ, S. A. and Güler, Ö. (2010). “Evaluation of wind energy investment interest and electricity generation cost analysis for Turkey.” Applied Energy, Vol. 87, No. 8, pp. 2574–2580, DOI: 10.1016/J.APENERGY. 2010.03.015.CrossRefGoogle Scholar
  2. Ayodele, T. R., Jimoh, A. A., Munda, J. L., and Agee, J. T. (2012). “Wind distribution and capacity factor estimation for wind turbines in the coastal region of South Africa.” Energy Conversion and Management, Vol. 64, pp. 614–625, DOI: 10.1016/J.ENCONMAN. 2012.06.007.CrossRefGoogle Scholar
  3. Beccali, M., Cirrincione, G., Marvuglia, A., and Serporta, C. (2010). “Estimation of wind velocity over a complex terrain using the generalized mapping regressor.” Applied Energy, Vol. 87, No. 3, pp. 884–893, DOI: 10.1016/J.APENERGY.2009.05.026.CrossRefGoogle Scholar
  4. Bivona, S., Burlon, R., and Leone, C. (2003). “Hourly wind velocity analysis in Sicily.” Renewable Energy, Vol. 28, No. 9, pp. 1371–1385, DOI: 10.1016/S0960-1481(02)00230-6.CrossRefGoogle Scholar
  5. Brabson, B. B. and Palutikof, J. R (2000). “Tests of the generalized Pareto distribution for predicting extreme wind speeds.” Journal of Applied Meteorology, Vol. 39, No. 9, pp. 1627–1640.CrossRefGoogle Scholar
  6. Cabello, M. and Orza, J. A. G (2010). “Wind speed analysis in the province of Alicante, Spain: Potential for small-scale wind turbines.” Renewable and Sustainable Energy Reviews, Vol. 14, No. 9, pp. 3185–3191, DOI: 10.1016/J.RSER2010.07.002.CrossRefGoogle Scholar
  7. Calif, R. (2012). “PDF models and synthetic model for the wind velocity fluctuations based on the resolution of Langevin equation.” Applied Energy, Vol. 99, pp. 173–182, DOI: 10.1016/J.APENERGY. 2012.05.007.CrossRefGoogle Scholar
  8. Carapellucci, R. and Giordano, L. (2013). “A methodology for the synthetic generation of hourly wind velocity time series based on some known aggregate input data.” Applied Energy, Vol. 101, pp. 541–550, DOI: 10.1016/J.APENERGY2012.06.044.CrossRefGoogle Scholar
  9. Carta, J. A., Ramirez, P., and Velazquez, S. (2009). “A review of wind speed probability distributions used in wind energy analysis: Case studies in the Canary Islands.” Renewable and Sustainable Energy Reviews, Vol. 13, No. 5, pp. 933–955, DOI: 10.1016/J.RSER2008. 05.005.CrossRefGoogle Scholar
  10. Carvalho, D., Rocha, A., Santos, C. S., and Pereira, R. (2013). “Wind resource modeling in complex terrain using different mesoscale -microscale coupling techniques.” Applied Energy, Vol. 108, pp. 493–504, DOI: 10.1016/J.APENERGY2013.03.074.CrossRefGoogle Scholar
  11. Castillo, E., Hadi, A. S., Balakrishnan, N., and Sarabia, J. M. (2005). Extreme value and related models with applications in engineering and science, John Wiely & Sons, Inc., Hoboken, NJ, USA.Google Scholar
  12. Celik, A. N. (2004). “On the distributional parameters used in assessment of the suitability of wind velocity probability density functions.” Energy Conversion and Management, Vol. 45, Nos. 11–12, pp. 1735–1747, DOI: 10.1016/j.enconman.2003.09.027.CrossRefGoogle Scholar
  13. Celik, A. N. and Kolhe, M. (2013). “Generalized feed-forward based method for wind energy prediction.” Applied Energy, Vol. 101, pp. 582–588, DOI: 10.1016/J.APENERGY2012.06.040.CrossRefGoogle Scholar
  14. Chang, T. P. (2011). “Estimation of wind energy potential using different probability density functions.” Applied Energy, Vol. 88, No. 5, pp. 1848–1856, DOI: 10.1016/J.APENERGY2010.11.010.CrossRefGoogle Scholar
  15. Chen, K. and Yu, J. (2014). “Short-term wind velocity prediction using an unscented Kalman filter based state-space support vector regression approach.” Applied Energy, Vol. 113, pp. 690–705, DOI: 10.1016/J.APENERGY.2013.08.025.CrossRefGoogle Scholar
  16. Cook, N. J. (2001). “Discussion on modern estimation of the parameters of the Weibull wind velocity distribution for wind energy analysis.” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 89, No. 10, pp. 867–869, DOI: 10.1016/S0167-6105(00)00088-X.CrossRefGoogle Scholar
  17. D'Amico, G., Petroni, R., and Prattico, F. (2015). “Wind speed prediction for wind farm applications by extreme value theory and copulas.” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 145, pp. 229–236, DOI: 10.1016/J.JWEIA.2015.06.018.CrossRefGoogle Scholar
  18. Douak, F., Melgani, F., and Benoudjit, N. (2013). “Kernel ridge regression with active learning for wind velocity prediction.” Applied Energy, Vol. 103, pp. 328–340, DOI: 10.1016/J.APENERGY.2012.09.055.CrossRefGoogle Scholar
  19. El-Wakil, M. M. (2002). Power plant technology, McGraw-hill International Editions, New York, NY, USA.Google Scholar
  20. Fadare, D. A. (2010). “The application of artificial neural networks to mapping of wind velocity profile for energy application in Nigeria.” Applied Energy, Vol. 87, No. 3, pp. 934–942, DOI: 10.1016/ J.APENERGY.2009.09.005.CrossRefGoogle Scholar
  21. Garcia, A., Torres, J. L., Prieto, E., and Francisco, A. de (1998). “Fitting wind velocity distributions: a case study.” Solar Energy, Vol. 62, No. 2, pp. 139–144, DOI: 10.1016/S0038-092X(97)00116-3.CrossRefGoogle Scholar
  22. Gugliani, G. K., Sarkar, A., Ley, C., and Mandai, S. (2018). “New methods to assess wind resources in terms of wind speed, load, power and direction.” Renewable Energy, Vol. 129, pp. 168–182, DOI: 10.1016/J.RENENE.2018.05.088.CrossRefGoogle Scholar
  23. Gugliani, G. K., Sarkar, A., Bhadani, S., and Mandai, S. (2019). “A novel approach for accurate assessment of design wind speed for variable wind climate.” KSCE Journal of Civil Engineering, KSCE, Vol. 23, No. 2, pp. 608–623, DOI: 10.1007/sl2205-018-1431-6.CrossRefGoogle Scholar
  24. Gumbel, E. J. (1958). Statistics of extremes, Columbia Univ. press, New York, NY, USA.CrossRefGoogle Scholar
  25. Gunturu, U. B. and Schlosser, C. A. (2012). “Characterization of wind power resource in the United States.” Atmospheric Chemistry and Physics, Vol. 12, No. 20, pp. 9687–9702, DOI: 10.5194/ACP-12-9687-2012.CrossRefGoogle Scholar
  26. Gupta, B. K. (1986). “Weibull parameters for annual and monthly wind velocity distributions for five locations in India.” Solar Energy, Vol. 37, No. 6, pp. 469–471, DOI: 10.1016/0038-092X(86)90039-3.CrossRefGoogle Scholar
  27. Hamouda, Y. A. (2012). “Wind energy in egypt: Economic feasibility for Cairo.” Renewable and Sustainable Energy Reviews, Vol. 16, No. 5, pp. 3312–3319, DOI: 10.1016/J.RSER.2012.02.058.CrossRefGoogle Scholar
  28. Harris, R. I. and Cook, N. J. (2014). “The parent wind velocity distribution: Why Weibull?” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 131, pp. 72–87, DOI: 10.1016/JJWEIA.2014. 05.005.CrossRefGoogle Scholar
  29. Jung, S., ArdaVanli, O., and Kwon, S. (2013). “Wind energy potential assessment considering the uncertainties due to limited data.” Applied Energy, Vol. 102, pp. 1492–1503, DOI: 10.1016/IAPENERGY2012. 09.011.CrossRefGoogle Scholar
  30. IS 875 (Part III) (2015). Design loads (other than earthquake) for buildings and structures - Code of practice, IS 875 (Part III) New Delhi, India.Google Scholar
  31. Kasperski, M. (2009). “Specification of the design wind load: A critical review of code concepts.” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 97, Nos. 7–8, pp. 335–357, DOI: 10.1016/j.jweia. 2009.05.002.CrossRefGoogle Scholar
  32. Kasperski, M. (2010). “Estimation of design wind velocity.” Proc. 7th International Advanced School on Wind Engineering, New Delhi, India.Google Scholar
  33. Laib, M. and Kanevski, M. (2016). “Spatial modeling of extreme wind speed distributions in Switzerland.” Energy Procedia, Vol. 97, pp. 100–107, DOI: 10.1016/J.EGYPRO.2016.10.029.CrossRefGoogle Scholar
  34. Lujano-Rojas, J. M., Dufo-López, R., and Bernal-Agustín, J. L. (2012). “Optimal sizing of small wind/battery systems considering the DC bus voltage stability effect on energy capture, wind velocity variability, and load uncertainty.” Applied Energy, Vol. 93, pp. 404–412, DOI: 10.1016/J.APENERGY2011.12.035.CrossRefGoogle Scholar
  35. Lun, I. Y F. and Lam, J. C. (2000). “A study of Weibull parameters using long term wind observations.” Renewable Energy, Vol. 20, No. 2, pp. 145–153, DOI: 10.1016/S0960-1481(99)00103-2.CrossRefGoogle Scholar
  36. Morales, J. M., Minguez, R., and Conejo, A. J. (2010). “A methodology to generate statistically dependent wind velocity scenarios.” Applied Energy, Vol. 87, No. 3, pp. 843–855, DOI: 10.1016/J.APENERGY 2009.09.022.CrossRefGoogle Scholar
  37. Rocha, P. A. C., de Sousa, R. C., de Andrade, C. F., and da Silva, M. E. V (2012). “Comparison of seven numerical methods for deterrnining Weibull parameters for wind energy generation in the northeast region of Brazil.” Applied Energy, Vol. 89, No. 1, pp. 395–400, DOI: 10.1016/J.APENERGY2011.08.003.CrossRefGoogle Scholar
  38. Sarkar, A., Gugliani, G., and Deep, S. (2017). “Weibull model for wind velocity data analysis of different locations in India.” KSCE Journal of Civil Engineering, Vol. 21, No. 7, pp. 2764–2776, DOI: 10.1007/ S12205-017-0538-5.CrossRefGoogle Scholar
  39. Sarkar, A., Kumar, N., and Mitra, D. (2014). “Extreme wind climate modeling of some locations in India for the specification of the design wind velocity of structures.” KSCE Journal of Civil Engineering, Vol. 18, No. 5, pp. 1496–1504, DOI: 10.1007/sl2205-014-0428-z.CrossRefGoogle Scholar
  40. Seguro, J. V and Lambert, T. W. (2000). “Modern estimation of the parameters of the Weibull wind velocity distribution for wind energy analysis.” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 85, No. 1, pp. 75–84, DOI: 10.1016/S0167-6105(99)00122-1.CrossRefGoogle Scholar
  41. Smiiu, E., Heckert, N. A., Filliben, J. J., and Johnson, S. K. (2001). “Extreme wind load estimates based on the Gumbel distribution of dynamic pressures: An assessment.” Structural Safety, Vol. 23, No. 3, pp. 221–229, DOI: 10.1016/S0167-4730(01)00016-9.CrossRefGoogle Scholar
  42. Soukissian, T. (2013). “Use of multi-parameter distributions for offshore wind velocity modeling: The Johnson SB distribution.” Applied Energy, Vol. III, pp. 982–1000, DOI: 10.1016/J.APENERGY2013. 06.050.CrossRefGoogle Scholar
  43. Sulaiman, M. Y., Akaak, A. M., Wahab, M. A., Zakaria, A., Sulaiman, Z. A., and Suradi, J. (2002). “Wind characteristic of Oman.” Energy, Vol. 27, No. 1, pp. 35–46, DOI: 10.1016/S0360-5442(01)00055-X.CrossRefGoogle Scholar
  44. Thiaw, L., Sow, G., Fall, S. S., Kasse, M., Sylla E., and Thioye, S. (2010). “A neural network based approach for wind resource and wind generators production assessment.” Applied Energy, Vol. 87, No. 5, pp. 1744–1748, DOI: 10.1016/J.APENERGY2009.10.001.CrossRefGoogle Scholar
  45. Ulgen, K. and Hepbasli, A. (2002). “Determination of weibull parameters for wind energy analysis of Izmir, Turkey.” International Journal of Energy Research, Vol. 26, No. 6, pp. 495–506, DOI: 10.1002/ER798.CrossRefGoogle Scholar
  46. Usta, I. and Kantar, Y. M. (2012). “Analysis of some flexible families of distributions for estimation of wind velocity distributions.” Applied Energy, Vol. 89, No. 1, pp. 355–367, DOI: 10.1016/J.APENERGY. 2011.07.045.CrossRefGoogle Scholar
  47. Zaharim, A., Razali, A. M., Abidin, R. Z., and Sopian, K. (2009). “Fitting of statistical distributions to wind velocity data in Malaysia.” European Journal of Scientific Research, Vol. 26, No. 1, pp. 6–12.Google Scholar
  48. Zarate-Minano, R., Anghel, M., and Milano, F. (2013). “Continuous wind velocity models based on stochastic differential equations.” Applied Energy, Vol. 104, pp. 42–49, DOI: 10.1016/J.APENERGY. 2012.10.064.CrossRefGoogle Scholar
  49. Zhang, H., Yu, Y., and Liu, Z. (2014). “Study on the maximum entropyGoogle Scholar

Copyright information

© Korean Society of Civil Engineers 2019

Authors and Affiliations

  • Arnab Sarkar
    • 1
    Email author
  • Sneh Deep
    • 2
  • D. Datta
    • 3
  • Amit Vijaywargiya
    • 4
  • R. Roy
    • 4
  • V. S. Phanikanth
    • 5
  1. 1.Dept. of Mechanical EngineeringBanaras Hindu UniversityVaranasiIndia
  2. 2.Dept. of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia
  3. 3.Radiological Physics & Advisory DivisionBhabha Atomic Research CentreMumbaiIndia
  4. 4.Dept. of Civil EngineeringNuclear Power Corporation of India LimitedMumbaiIndia
  5. 5.Civil Engineering DivisionBhabha Atomic Research CentreMumbaiIndia

Personalised recommendations