Non-Gaussian Analysis of Wind Velocity Data for the Determination of Power Quality Control

The quality of power (i.e. the sustainable power output as a function time) of any wind dependent energy converter (including wind turbines and wave energy converters) is determined by many design and environmental factors but timedependent variations in the wind speed are arguably the most important. In this paper we consider a non-Gaussian model for analysing and then simulating wind velocity data. In particular, we consider a Lévy distribution for the statistical characteristics of wind velocity and show 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 L´evy index. A L´evy index based numerical analysis is then performed on wind velocity data for both rural and urban areas where, in the latter case, the index is shown to have a larger value. Finally, an empirical relationship is derived for the power output from a wind turbine in terms of the L´evy index using Betz law and a similar relationship obtained for a wave energy converter. In both cases, it is shown how the average power output as a function of time is (inversely) related to the Lévy index for the wind velocity. It is concluded that these relationships may have value in determining the optimal geographical locations for the construction of wind and wave farms and for monitoring their performance in terms of power quality control