Bayes estimation of wind speed extreme values

The rapid growth in the use of wind energy calls for a more and more careful representation of wind speed probability distribution, both for identification and estimation purpose. In particular, a key point of the above identification and estimation aspects is the one of representing the extreme values of wind speed probability distributions, which in the "static" case, as defined in the paper, may be expressed in terms of "extreme upper quantiles". This topic has indeed brought about an increasing number of studies in the last years, both for wind energy production assessment and also in risk and reliability analysis. Concerning the aspect of energy production, it is well known that a great sensitivity exists in the relationship between wind speed extreme upper quantiles and the corresponding wind energy quantiles. Concerning risk and reliability analysis, the extreme wind speed values characterization is useful for a proper understanding of the destructive wind forces which may affect mechanical tower reliability, and consequently a proper choice of the “cut off” wind speed value. The above modeling is however difficult due to uncertainty in wind speed probability distributions. For this purpose, the paper proposes a novel Bayes approach for the estimation of the probability that wind speed is lower than a prefixed extreme value. The basic feature of the method is its being not dependent on the underlying wind speed model, be it the classical Weibull distribution, or alternative models such as the recently adopted Log-logistic or Burr distributions. A large set of numerical simulations are performed in the last part of the paper, in order to illustrate the feasibility and efficiency of the above method of estimation, especially when compared to the classical Maximum Likelihood method.