A Stochastic Model for Wind Turbine Power Quality using a Levy Index Analysis of Wind Velocity Data

Abstract

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. After a brief review of the statistics of typical wind speed data, a nonGaussian model for the wind velocity is introduced that is based on a Levy 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 Levy index. A Levy index numerical analysis is then performed on wind velocity data for both rural and urban areas where, in the latter case, the index has a larger value. Finally, an empirical relationship is derived for the power output from a wind turbine in terms of the Levy index using Betz law.