skip to main content

Estimating mixture hybrid Weibull distribution parameters for wind energy application using Bayesian approach

1Centre d'Excellence Régional pour la Maîtrise de l'Electricité (CERME), University of Lome, Lome, P.O. Box 1515, Lome , Togo

2Department of Electrical Engineering, Ecole Polytechnique de Lomé (EPL), University of Lome, P.O. Box 1515, Lome, Togo

3Laboratoire de Recherche en Sciences de l’Ingénieur (LARSI), University of Lome, P.O. Box 1515, Lome, Togo

4 Polytechnic University of bobo-Dioulasso, Burkina-Faso

View all affiliations
Received: 21 May 2023; Revised: 24 Jun 2023; Accepted: 30 Jul 2023; Available online: 20 Aug 2023; Published: 1 Sep 2023.
Editor(s): H Hadiyanto
Open Access Copyright (c) 2023 The Author(s). Published by Centre of Biomass and Renewable Energy (CBIORE)
Creative Commons License This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Citation Format:

The Weibull distribution function is essential for planning and designing wind-farm implementation projects and wind-resource assessments. However, the Weibull distribution is limited for those areas with high frequencies of calm winds. One solution is to use the hybrid Weibull distribution. In fact, when the wind speed data present heterogeneous structures, it makes sense to group them into classes that describe the different wind regimes. However, the single use of the Weibull distribution presents fitting errors that should be minimized. In this context, mixture distributions represent an appropriate alternative for modelling wind-speed data. This approach was used to combine the distributions associated with different wind-speed classes by weighting the contribution of each of them. This study proposes an approach based on mixtures of Weibull distributions for modelling wind-speed data in the West Africa region. The study focused on mixture Weibull (WW-BAY) and mixture hybrid Weibull (WWH-BAY) distributions using Bayes' theorem to characterize the wind speed distribution over twelve years of recorded data at the Abuja, Accra, Cotonou, Lome, and Tambacounda sites in West Africa. The parameters of the models were computed using the expectation-maximization (E-M) algorithm. The parameters of the models were estimated using the expectation-maximization (E-M) algorithm. The initial values were provided by the Levenberg-Marquardt algorithm. The results obtained from the proposed models were compared with those from the classical Weibull distribution whose parameters are estimated by some numerical method such as the energy pattern factor, maximum likelihood, and the empirical Justus methods based on statistical criteria. It is found that the WWH-BAY model gives the best prediction of power density at the Cotonou and Lome sites, with relative percentage error values of 0.00351 and 0.01084. The energy pattern factor method presents the lowest errors at the Abuja site with a relative percentage error value of -0.54752, Accra with -0.55774, and WW-BAY performs well for the Tambacounda site with 0.19232. It is recommended that these models are useful for wind energy applications in the West African region.

Fulltext View|Download
Keywords: Wind speed; Weibull distribution; Mixtures models; Bayesian approach; E-M algorithm; Levenberg-Marquardt Algorithm

Article Metrics:

  1. Akdağ, S. A., & Güler, Ö. (2018). Alternative Moment Method for wind energy potential and turbine energy output estimation. Renewable Energy, 120, 69–77.
  2. Akpinar, S., & Akpinar, E. K. (2009). Estimation of wind energy potential using finite mixture distribution models. Energy Conversion and Management, 50(4), 877–884.
  3. Alavi, O., Sedaghat, A., & Mostafaeipour, A. (2016). Sensitivity analysis of different wind speed distribution models with actual and truncated wind data: A case study for Kerman, Iran. Energy Conversion and Management, 120, 51–61.
  4. Albani, A., & Ibrahim, M. Z. (2013). Statistical analysis of wind power density based on the weibull and rayleigh models of selected site in Malaysia. Pakistan Journal of Statistics and Operation Research, 9(4), 393–406.
  5. Alcalá, G., Perea-Moreno, A. J., & Hernandez-Escobedo, Q. (2019). Wind Resource Assessment using Weibull Function for Different Periods of the Day in the Yucatan Peninsula. Chemical Engineering Transactions, 76, 1003–1008.
  6. Aras, N., Erisoglu, U., & Yıldızay, H. D. (2020). Pakistan Journal of Statistics and Operation Research Optimum Method for Determining Weibull Distribution Parameters Used in Wind Energy Estimation. 16(4), 635–648.
  7. Arrabal-Campos, F. M., Montoya, F. G., Alcayde, A., Baños, R., & Martínez-Lao, J. (2020). Estimation of weibull parameters in winds speed mixture using nonlinear optimization for wind energy applications. Renewable Energy and Power Quality Journal, 18(18), 351–355.
  8. Bastin, J., Haribhaskaran, A., Boopathi, K., Krishnan, B., Vinod Kumar, R., & Reddy Prasad, D. M. (2023). Wind characteristics of Tamil Nadu coast towards development of microgrid - A case study for simulation of small scale hybrid wind and solar energy system. Ocean Engineering, 277(January), 114282.
  9. Bishop, C. M., & Nasrabadi, N. M. (2006). Pattern recognition and machine learning (Vol. 4, Issue 4). Springer
  10. Carta, J. A., & Ramírez, P. (2007). Analysis of two-component mixture Weibull statistics for estimation of wind speed distributions. Renewable Energy, 32(3), 518–531.
  11. Celik, A. N. (2004). A statistical analysis of wind power density based on the Weibull and Rayleigh models at the southern region of Turkey. Renewable Energy, 29(4), 593–604.
  12. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39(1), 1–22. . Accessed: 16/08/2023
  13. Elamouri, M., & Ben Amar, F. (2008). Wind energy potential in Tunisia. Renewable Energy, 33(4), 758–768.
  14. Elmahdy, E. E. (2015). A new approach for Weibull modeling for reliability life data analysis. Applied Mathematics and Computation, 250, 708–720.
  15. Elmahdy, E. E. (2017). Modelling reliability data with finite Weibull or Lognormal mixture distributions. Applied Mathematics and Information Sciences, 11(4), 1081–1089.
  16. Elmahdy, E. E., & Aboutahoun, A. W. (2013). A new approach for parameter estimation of finite Weibull mixture distributions for reliability modeling. Applied Mathematical Modelling, 37(4), 1800–1810.
  17. García-caballero, E., Appendini, C. M., Figueroa-espinoza, B., Allende-arandía, M. E., Magar, V., & Gross, M. S. (2023). Energy for Sustainable Development Wind energy potential assessment for Mexico ’ s Yucatecan Shelf. Energy for Sustainable Development, 74(April), 415–429.
  18. Guenoukpati, A., Salami, A. A., Kodjo, M. K., & Napo, K. (2020). Estimating Weibull Parameters for Wind Energy Applications Using Seven Numerical Methods: Case studies of Three Coastal Sites in West Africa. International Journal of Renewable Energy Development, 9(2).
  19. Höök, M., & Tang, X. (2013). Depletion of fossil fuels and anthropogenic climate change—A review. Energy Policy, 52, 797–809.
  20. Jaramillo, O. A., & Borja, M. A. (2004a). Bimodal versus Weibull wind speed distributions: An analysis of wind energy potential in La Venta, Mexico. Wind Engineering, 28(2), 225–234.
  21. Jaramillo, O. A., & Borja, M. A. (2004b). Wind speed analysis in La Ventosa, Mexico: A bimodal probability distribution case. Renewable Energy, 29(10), 1613–1630.
  22. Kececioglu, D. B., & Wang, W. (1998). Parameter estimation for mixed-Weibull distribution. Proceedings of the Annual Reliability and Maintainability Symposium, 247–252.
  23. Kiss, P., & Jánosi, I. M. (2008). Comprehensive empirical analysis of ERA-40 surface wind speed distribution over Europe. Energy Conversion and Management, 49(8), 2142–2151.
  24. Kollu, R., Rayapudi, S. R., Narasimham, S. V. L., & Pakkurthi, K. M. (2012). Mixture probability distribution functions to model wind speed distributions. International Journal of Energy and Environmental Engineering, 3(1), 27
  25. Kumar, S., & Sahay, K. B. (2018). Wind speed forecasting using different neural network algorithms. 2018 2nd International Conference on Electronics, Materials Engineering & Nano-Technology (IEMENTech), 1–4. DOI: 10.1109/IEMENTECH.2018.8465313
  26. Liu, F., Wang, X., Sun, F., & Kleidon, A. (2023). Potential impact of global stilling on wind energy production in China. Energy, 263(PB), 125727.
  27. Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics, 11(2), 431–441.
  28. Mazzeo, D., Oliveti, G., & Labonia, E. (2018). Estimation of wind speed probability density function using a mixture of two truncated normal distributions. In Renewable Energy (Vol. 115).
  29. Mohammadi, K., Shamshirband, S., Yee, P. L., Petković, D., Zamani, M., & Ch, S. (2015). Predicting the wind power density based upon extreme learning machine. Energy, 86, 232–239.
  30. Morgan, E. C., Lackner, M., Vogel, R. M., & Baise, L. G. (2009). Probability distributions for offshore wind speeds. AGU Fall Meeting Abstracts, 2009, A31F--0179.
  31. Mostafaeipour, A. (2016). Assessing different parameters estimation methods of Weibull distribution to compute wind power density. February.
  32. Nage, G. D. (2016). Analysis of Wind Speed Distribution: Comparative Study of Weibull to Rayleigh Probability Density Function; A Case of Two Sites in Ethiopia. American Journal of Modern Energy, 2(3), 10–16.
  33. Salami, Adekunlé Akim, Ajavon, A. S. A., Kodjo, M. K., Ouedraogo, S., & Bédja, K. S. (2018). The use of odd and even class wind speed time series of distribution histogram to estimate weibull parameters. International Journal of Renewable Energy Development, 7(2), 139–150.
  34. Salami, Adekunlé Akim, Ouedraogo, S., Kodjo, K. M., & Ajavon, A. S. A. (2022). Influence of the Random Data Sampling in Estimation of Wind Speed Resource: Case Study. International Journal of Renewable Energy Development, 11(1), 133–143.
  35. Salami, Akim A, Ajavon, A. S. A., Kodjo, M. K., & Bedja, K.-S. (2016). Evaluation of Wind Potential for an Optimum Choice of Wind Turbine Generator on the Sites of Lomé, Accra, and Cotonou Located in the Gulf of Guinea. International Journal of Renewable Energy Development, 5(3).
  36. Salami, Akim Adekunle, Ajavon, A. S. A., Kodjo, M. K., & Bedja, K.-S. (2013). Contribution to improving the modeling of wind and evaluation of the wind potential of the site of Lome: Problems of taking into account the frequency of calm winds. Renewable Energy, 50, 449–455.
  37. Sedzro, K. S. A., Salami, A. A., Agbessi, P. A., & Kodjo, M. K. (2022). Comparative Study of Wind Energy Potential Estimation Methods for Wind Sites in Togo and Benin (West Sub-Saharan Africa). Energies, 15(22).
  38. Speirs, J., McGlade, C., & Slade, R. (2015). Uncertainty in the availability of natural resources: Fossil fuels, critical metals and biomass. Energy Policy, 87, 654–664.
  39. Ucar, A., & Balo, F. (2009). Investigation of wind characteristics and assessment of wind-generation potentiality in Uludaǧ-Bursa, Turkey. Applied Energy, 86(3), 333–339.
  40. Zhou, K., Yang, S., Shen, C., Ding, S., & Sun, C. (2015). Energy conservation and emission reduction of China’s electric power industry. Renewable and Sustainable Energy Reviews, 45, 10–19.

Last update:

No citation recorded.

Last update: 2024-05-20 15:53:57

No citation recorded.