Bayes prediction of wind gusts for Wind Power Plants Reliability Estimation

For an efficient Wind Power Plants Reliability Estimation, the extreme gusts are the most important features of wind speed statistics, in order to quantify the destruction brought about by extreme winds. With the purpose of characterizing these destructive wind forces, which are random in nature, an appropriate stochastic model is adopted in the paper. Such model is based upon the probabilistic modeling of gusts occurrence by means of a Poisson Process, while the amplitude of extreme gust wind speeds is modeled by means of suitable extreme value distributions. This approach yields an appropriate “safety function” of the structure, which is defined as the probability that the stochastic process: “largest extreme gust amplitude” is smaller than a given threshold value, in a given time interval. Such safety function can be easily converted into a “safety horizon” (SH), i.e. a time interval in which the WGA smaller than a given threshold value z, with a given high probability value p. If z is chosen as the maximum value of the WGA that the structure can resist, then the SH is an efficient measure (i.e., an opportune quantile) of the time to failure of the structure. In the paper, attention is focused on the estimation of the above SH by means of a suitable Bayesian estimation technique, which is based upon prior (or "a priori") information which should be easily available and not difficult to implement. This may be accomplished by means of analytical or numerical techniques, as shown in the paper. Finally, the summary of a large set of numerical simulations is presented, which show the high efficiency of such Bayesian estimation methodology. In particular, its superiority with respect to the "classical" Maximum Likelihood (ML) estimation methods, traditionally adopted in power system applications, is illustrated. A remark on the robustness of the proposed procedure, with respect to the choice of prior pdf, is also outlined in the conclusions.