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

Abstract

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.

Keywords

• wind speed
• weibull distribution
• mixtures models
• bayesian approach
• e-m algorithm
• levenberg-marquardt algorithm