Wind energy production is very sensitive to instantaneous wind speed fluctuations. Thus rapid variation of wind speed due to changes in the local meteorological conditions can lead to electrical power variations of the order of the nominal power output. In small grids, as they exist for example on some islands in the French West Indies, such fluctuations can cause instabilities in case of intermediate power shortages. To palliate these difficulties, it is essential to identify and characterize the wind speed distributions. This allows to anticipate the eventuality of power shortage or power surge. Therefore, it is of interest to categorize wind speed fluctuations into distinct classes and to estimate the probability of a distribution to belong to a class. This paper presents a method for classifying wind speed histograms by estimating a finite mixture of Dirichlet distributions. The SAEM algorithm that we use provides a fine distinction between wind speed distribution classes. It's a new nonparametric method for wind speed sequences classification. However, we show that the wind speed distributions in each class correspond to specific Gram- Charlier densities.