Parameter estimation of mixed Weibull probability distributions for wind speed related to power statistics

Estimation of wind-speed statistics is essential for an efficient assessment of wind power generation, and thus for any rational decision upon the installation and operation of a wind farm. Most existing methods for the above estimation are based upon the popular Weibull distribution. However, a few recent papers have pointed out, based upon field data analysis, some drawback of the above model. Such data show indeed significant “heavy tails” in wind-speed probabilistic distribution for large wind speed values, constituting a crucial aspect for wind power estimation. Alternative models for such distribution, such as the Log-logistic (as discussed in a previous paper) or the Burr model, appear to be natural candidates for the wind statistics modeling, also on theoretical grounds. In particular, the Burr model is analyzed in the paper, based on a proper “mixture” of Weibull probability distributions. After illustrating such derivation, a suitable Bayes approach for the estimation of the Burr model (also including the Log-logistic model as a particular case) is proposed. The method, whose simplicity and efficiency is shown by means of a numerical application, is based upon the transformation of a Gamma distribution for converting prior information in a novel way which should be very practical for the system engineer.