The Burr XII Model and its Bayes Estimation for Wind Power Production Assessment

The probabilistic Burr XII model for the characterization and estimation of the wind-speed distribution is analyzed in the paper, in view of wind power production evaluation. Most of the existing methods for such evaluation are based upon the popular Weibull distribution for wind speed statistics. However, recent studies have pointed out some inadequacies in the Weibull distribution. The analysis of many field data show indeed significant “heavy tails” in the probability distribution of wind speed for large values of speed. This constitutes a critical aspect when the Weibull model is adopted, not only for its consequences on wind speed estimation, but especially on wind power estimation. The Burr model is here justified on theoretical grounds, being based on a proper "mixture" of Weibull probability distributions. After illustrating such derivation, a suitable Bayes approach for the estimation of the Burr model is proposed. The method is based upon the Negative Log-Gamma distribution for the assessment of prior information in a novel way which should be easily feasible for the system engineer. The method appears indeed to be very practical, since it only requires some prior information on the probability distribution of the wind speed. The results of a large set of numerical simulation are reported to illustrate the simplicity and efficiency of the proposed method.