Small Scales Space-Time Variability of Wind Fields: Simulations with Vector Fields and Transfer to Turbine Torque Computation

Wind fields are extremely variable in space and time over a wide range of scales. This extreme variability is transferred to the wind turbine torque and ultimately to wind energy production. The Universal Multifractal (UM) framework is a powerful tool that allows to characterise and simulate the extreme variability of geophysical fields across scales with the help of only three parameters (α, C1 and H) with physical interpretation; while the 4th, the power a of a conservative flux, is absorbed by the empirical estimation of the mean singularity over a non-conservative field.

The main challenge is to simulate over 2D space plus time vector fields which realistically reproduce observed spatial and temporal variability of wind fields. The outer scale of the simulated fields should basically correspond to the size of the wind turbine in space and ten minutes in time. To achieve that, we combine two broad classes of stochastic processes: stable Levy processes and Clifford algebra. We use as input characteristic parameters obtained from the multifractal analysis of the data collected by two high-resolution 3D anemometers with approx. 33 m vertical distance on a meteorological mast. The data is collected as part of the RW-Turb measurement campaign (https://hmco.enpc.fr/portfolio-archive/rw-turb/), supported by the French National Research Agency (ANR-19-CE05-0022). The expected behaviour of the simulated field is confirmed by multifractal analysis. 

In the second step, we investigate the effect of small-scale wind variability on the wind turbine torque computation by imputing the simulated vector fields to three modelling chains with increasing complexity. The first one only considers the temporal variability, averaging the wind field and considering it at hub height. The second one is based on the angular moment definition and allows us to consider both spatial and temporal variability by computing the torque at each blade point and integrating it along the radius for each time step. Finally, the third one uses the realistic software OpenFAST developed by the US National Renewable Energy Laboratory (NREL). To analyse and physically interpret wind variability's effect, we compared the torque obtained by the three modelling chains focused on the small scales. As we expected, we found pronounced differences on small scales with stronger fluctuations exhibited in the second modelling chain, followed by OpenFAST and the first one.