DOI QR코드

DOI QR Code

The new odd-burr rayleigh distribution for wind speed characterization

  • Arik, Ibrahim (Science and Art Faculty, Bilecik Seyh Edebali University) ;
  • Kantar, Yeliz M. (Faculty of Science, Department of Statistics, Eskisehir Technical University) ;
  • Usta, Ilhan (Faculty of Science, Department of Statistics, Eskisehir Technical University)
  • Received : 2018.10.31
  • Accepted : 2019.04.18
  • Published : 2019.06.25

Abstract

Statistical distributions are very useful in describing wind speed characteristics and in predicting wind power potential of a specified region. Although the Weibull distribution is the most popular one in wind energy literature, it does not seem to be able to perfectly fit all the investigated wind speed data in nature. Thus, many studies are still being conducted to find flexible distribution for modelling wind speed data. In this study, we propose a new Odd-Burr Rayleigh distribution for wind speed characterization. The Odd-Burr Rayleigh distribution with two shape parameters is flexible enough to model different shapes of wind speed data and thus it can be an alternative wind speed distribution for the assessment of wind energy potential. Therefore, suitability of the Odd-Burr Rayleigh distribution is investigated on real wind speed data taken from different regions in the South Africa. Numerical results of the conducted analysis confirm that the new Odd-Burr Rayleigh distribution is suitable for modelling most of the considered real wind speed cases and it also can be used for predicting wind power.

References

  1. Akdag, S. and Guler, O. (2009), "Calculation of wind energy potential and economic analysis by using Weibull distribution-a case study from Turkey. Part 1: Determination of Weibull Parameters", Energy sources part B-economics planning and policy, 4, 1-8. https://doi.org/10.1080/15567240802532841. https://doi.org/10.1080/15567240802532841
  2. Akdag, S.A., Bagiorgas, H.S. and Mihalakakou, G. (2010), "Use of two-component Weibull mixtures in the analysis of wind speed in the Eastern Mediterranean", Appl. Energy, 87(8), 2566-2573. https://doi.org/10.1016/j.apenergy.2010.02.033. https://doi.org/10.1016/j.apenergy.2010.02.033
  3. Akpinar, S. and Akpinar, E.K. (2007), "Wind energy analysis based on maximum entropy principle (MEP)-type distribution function", Energ. Convers. Manage., 48(4), 1140-1149. https://doi.org/10.1016/j.enconman.2006.10.004. https://doi.org/10.1016/j.enconman.2006.10.004
  4. Ali, S., Lee, S.M. and Jang, C.M. (2018), "Statistical analysis of wind characteristics using Weibull and Rayleigh distributions in Deokjeok-do Island - Incheon, South Korea", Renew. Energ., 123, 652-663. https://doi.org/10.1016/j.renene.2018.02.087. https://doi.org/10.1016/j.renene.2018.02.087
  5. Alizadeh, M., Cordeiro, G.M., Nascimento, A.D.C., Lima, M.C.S. and Ortega, E.M.M. (2017), "Odd-Burr generalized family of distributions with some applications", J. Stat. Comput. Sim., 87(2), 367-389. https://doi.org/10.1080/00949655.2016.1209200. https://doi.org/10.1080/00949655.2016.1209200
  6. Altun, G., Alizadeh, M. Altun, E. and Ozel, G. (2017), "Odd Burr Lindley distribution with properties and applications", Hacettepe J. Math. Stat., 46(2), 255-276.
  7. Alzaatreh, A., Lee, C. and Famoye, F. (2013), "A new method for generating families of continuous distributions", Metron, 71, 63-79. https://doi.org/10.1007/s40300-013-0007-y
  8. Arik, I. (2018), "New distribution families and their statistical properties for survival analysis", Ph.D. Dissertation; Anadolu University, Eskisehir, Turkey.
  9. Arik, I. and Kantar, Y.M. (2019), "New Odd Burr-Rayleigh distribution: theory and applications", Far East J. Theor. Stat., 55(1), 53-82. https://doi.org/10.17654/TS055010053
  10. Chalamcharla, S.C.V. and Doraiswamy, I.D. (2016), "Mathematical modeling of wind power estimation using multiple parameter Weibull distribution", Wind Struct., 23(4), 351-366. https://doi.org/10.12989/was.2016.23.4.351. https://doi.org/10.12989/was.2016.23.4.351
  11. Chang T.P. (2011), "Estimation of wind energy potential using different probability density functions", Appl. Energ., 88(5), 1848-1856. https://doi.org/10.1016/j.apenergy.2010.11.010. https://doi.org/10.1016/j.apenergy.2010.11.010
  12. Hu, B., Li, Y., Yang H. and Wang H. (2017), "Wind speed model based on kernel density estimation and its application in reliability assessment of generating systems", J. Modern Power Syst. Clean Energy, 5(2), 220-227. https://doi.org/10.1007/s40565-015-0172-5
  13. Kantar, Y.M. and Usta, I. (2008), "Analysis of wind speed distributions: wind distribution function derived from minimum cross entropy principles as better alternative to Weibull function", Energ. Convers. Manage., 49(5), 962-973. https://doi.org/10.1016/j.enconman.2007.10.008. https://doi.org/10.1016/j.enconman.2007.10.008
  14. Kantar, Y.M. and Senoglu, B. (2008), "A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter", Comput. Geosci., 34(12), 1900-1909. https://doi.org/10.1016/j.cageo.2008.04.004. https://doi.org/10.1016/j.cageo.2008.04.004
  15. Kantar, Y.M. and Usta, I. (2015), "Analysis of the upper-truncated Weibull distribution for wind speed", Energ. Convers. Manage., 96, 81-88. https://doi.org/10.1016/j.enconman.2015.02.063. https://doi.org/10.1016/j.enconman.2015.02.063
  16. Kantar, Y.M., Usta, I., Arik, I. and Yenilmez, I. (2018), "Wind speed analysis using the Extended Generalized Lindley Distribution", Renew. Energ., 118, 1024-1030. https://doi.org/10.1016/j.renene.2017.09.053. https://doi.org/10.1016/j.renene.2017.09.053
  17. Mohammadi, K., Alavi, O. and McGowan, J.G. (2017), "Use of Birnbaum-Saunders distribution for estimating wind speed and wind power probability distributions: A review", Energ. Convers. Manage, 143, 109-122. https://doi.org/10.1016/j.enconman.2017.03.083. https://doi.org/10.1016/j.enconman.2017.03.083
  18. Morgan, C.E., Lackner, M., Vogel, M.R. and Baise G.L. (2011), "Probability distributions for offshore wind speeds", Energ. Convers. Manage., 52(1), 15-26. https://doi.org/10.1016/j.enconman.2010.06.015. https://doi.org/10.1016/j.enconman.2010.06.015
  19. Philippopoulos, K., Deligiorgi, D. and Karvounis, G. (2012), "Wind speed distribution modeling in the Greater Area of Chania", Greece, Int. J. Green Energy, 9(2), 174-193. https://doi.org/10.1080/15435075.2011.622020. https://doi.org/10.1080/15435075.2011.622020
  20. Safari, B. and Gasore, J. (2010), "A statistical investigation of wind characteristics and wind energy potential based on the Weibull and Rayleigh models in Rwanda", Renew Energ., 35(12), 2874-2880. https://doi.org/10.1016/j.renene.2010.04.032. https://doi.org/10.1016/j.renene.2010.04.032
  21. Sedghi, M., Hannani, S.K. and Boroushaki, M. (2015), "Estimation of weibull parameters for wind energy application in Iran's cities", Wind Struct., 21(2), 203-221. http://dx.doi.org/10.12989/was.2015.21.2.203 https://doi.org/10.12989/was.2015.21.2.203
  22. Seshaiah, C.V. and Sukkiramathi, K. (2016), "A mathematical model to estimate the wind power using three parameter Weibull distribution", Wind Struct., 22(4), 393-408. https://doi.org/10.12989/was.2016.22.4.393. https://doi.org/10.12989/was.2016.22.4.393
  23. Soholi, V., Gupta, S. and Nema, R. (2016), "A comparative analysis of wind speed probability distributions for wind power assessment of four sites", Turk. J. Elec. Eng. & Comp. Sci., 24, 4724-4735. https://doi.org/10.3906/elk-1412-207
  24. Soulouknga, M.H., Doka, S.Y., Revanna, N., Djongyang, N. and Kofane, T.C. (2018), "Analysis of wind speed data and wind energy potential in Faya-Largeau, Chad, using Weibull distribution", Renew. Energ., 121, 1-8. https://doi.org/10.1016/j.renene.2018.01.002. https://doi.org/10.1016/j.renene.2018.01.002
  25. Soukissian, T. (2013), "Use of multi-parameter distributions for offshore wind speed modeling: The Johnson SB distribution", Appl. Energ., 111, 982-1000. https://doi.org/10.1016/j.apenergy.2013.06.050. https://doi.org/10.1016/j.apenergy.2013.06.050
  26. Usta, I. and Kantar, Y.M. (2012), "Analysis of some flexible families of distributions for estimation of wind speed distributions", Appl. Energ., 89(1), 355-367. https://doi.org/10.1016/j.apenergy.2011.07.045. https://doi.org/10.1016/j.apenergy.2011.07.045
  27. Usta, I. and Kantar Y.M. (2016), "Wind power potential estimation by using different statistical distributions", DEU Muh. Fak. Fen ve Muh. Dergisi, 18(3), 362-380. https://doi.org/10.21205/deufmd.2016185407
  28. Usta, I., Arik, I., Kantar, Y.M. and Yenilmez, I. (2018), "A new estimation approach based on moments for estimating Weibull parameters in wind power applications", Energ. Convers. Manage., 164, 570-578. https://doi.org/10.1016/j.enconman.2018.03.033. https://doi.org/10.1016/j.enconman.2018.03.033
  29. WASA (2018), Wind Atlas for South Africa; Department: Energy Republic of South Africa, South Africa, http://wasadata.csir.co.za/wasa1/WASAData.
  30. Zhou, J., Erdem, E., Li G. and Shi J. (2010), "Comprehensive evaluation of wind speed distribution models: A case study for North Dakota sites", Energ. Convers. Manage., 51(7), 1449-1458. https://doi.org/10.1016/j.enconman.2010.01.020. https://doi.org/10.1016/j.enconman.2010.01.020