Multifractal correlation of rainfall and wind fields and consequences on wind power production
Authors: Gires Auguste , Jose Jerry , Garcia-Gago Angel , Tchiguirinskaia Ioulia , Schertzer Daniel 
Published: March 2024

Rainfall and wind exhibit extreme variability over wide range of space-time scales. Such features are naturally transferred to wind turbine torque and ultimately to wind energy production. Improving our understanding of wind power production requires better accounting for the impact of these small scale fluctuations. This is much needed in order to achieve UN&#8217;s (United Nations) Sustainable Development Goal 7 (affordable and clean energy for all) and in a context of increasing global transition towards renewable and carbon neutral energy. The project RW-Turb (https://hmco.enpc.fr/portfolio-archive/rw-turb/; supported by the French National Research Agency, ANR-19-CE05-0022) was developed to address this challenge and to understand better the correlation across scales between rainfall and wind fields and its impact on wind power production. A high resolution measurement campaign was set up between 12/2020 and 07/2023 with two 3D sonic anemometers (manufactured by Thies), two mini meteorological stations (manufactured by Thies), and two disdrometers (Parsivel2, manufactured by OTT) installed on a meteorological mast at 75 and 45 m respectively in the wind farm of Pays d&#8217;Othe (110 km south-east of Paris, France; operated by Boralex). The framework of Universal Multifractals (UM) is used to carry out this analysis. It is a physically based and mathematically robust framework that enables to characterize and simulate the extreme variability of geophysical fields across scales. It is furthermore parsimonious since it relies on the use of only three parameters. In a first step multifractal analysis of the available fields (wind velocity, power available at the wind farm, power produced by wind turbines, air density, and rainfall) is implemented. Event based analysis enabled to observe differences in UM parameters depending on whether it is raining or not. In general, a slightly stronger variability is found when it rains. In a second step, a joint multifractal analysis is implemented to further quantify correlation across scales between the studied fields. An increase in correlation exponent of the various fields with increase in rain rate is found. Numerical simulations are then used as a complement to data analysis. More precisely, 3D space plus time vector fields which realistically reproduce observed spatial and temporal variability of wind fields are generated with multifractal tools. Then, they are used as input into three modeling chains of increasing complexity to simulate wind turbine torque. The simplest model uses average wind field over swept area, while a more realistic one computes the torque as an integral over the blades of the turbine enabling to account for the space-time variability of wind. Finally, OpenFAST, which is widely used by researchers and practitioners is implemented. UM analysis on the simulated torque time series were performed to quantify the impact of small scale fluctuations on wind power production, as well as the ability of the various models to account for it.