Analysis of the intermittency of simultaneous wind speed and power output data of two groups of wind turbines from a wind park.

We consider wind speed and power output time series from six turbines of a wind farm located in the Guadeloupe archipelago, in the eastern Caribean Sea. Simultaneous measurements of wind speeds and power outputs were sampled at a 10-minute temporal resolution throughout the year 2024, using an anemometer mounted on the nacelle of each turbine at a height of 48 m above ground level.

We first study their power spectral behavior and scaling statistics in the framework of fully developed turbulence and Kolmogorov’s theory and also in relation with atmospheric boundary-layer effects producing an inertial range with a power-law slope different from 5/3. We obtain an inertial range between scales from 10^-7 ≤ f ≤ 10^-4 Hz (10 min ≤ T ≤ 56 days), where f is the frequency and T the time scale, for both the velocity data and the power output.

On this inertial range, the Fourier power spectra E(f) follow a scale-invariant relation of the form E(f)=Cf^-ß  , where C is a constant, f is the frequency, and  ß is the slope of the power law. We determine the values of ß_v = 1.24 ± 0.07 for the wind velocity and   ß_P= 1.18 ±0.08.  for the power output. We find a one-to-one relationship between both slopes: the steeper  ß_v , the steeper  ß_P . Furthermore, over the detected inertial range, using structure function analysis, we obtain intermittent and multifractal properties. In the framework of a lognormal model for the intermittency, we extract the different parameters to characterize this intermittency: the Hurst index H and the intermittency parameter µ. Within this intermittency and turbulent framework, our aim is to better understand the multi-scale relationship between the wind speed and the output power of the turbines.