Wind Turbine Power Quality Estimation Using a Lévy Model for Wind Velocity Data

The power quality of a wind turbine is determined by many factors but time-dependent variation in the wind velocity are arguably the most important. In this paper a non-Gaussian model for the wind velocity is introduced that is based on a Lévy distribution. It is shown how this distribution can be used to derive a stochastic fractional diffusion equation for the wind velocity as a function of time whose solution is characterised by the Lévy index. A numerical method for computing the L´evy index from wind velocity time series is introduced and applied to example wind velocity data for both rural and urban areas where, in the latter case, the index is observed to have a larger value. Finally, an empirical relationship is derived for the power output from a wind turbine in terms of the Lévy index using Betz law.