Multifractal analysis of wind turbine power and rainfall from an operational wind farm - Part 1: Wind turbine power and the associated biases

The inherent variability in atmospheric fields, which extends over a wide range of temporal and spatial scales, is also transferred to energy fields extracted from them. In the specific case of wind power generation, this can be seen in the theoretical power available for extraction and the empirical power produced by turbines. To model and analyse them, it is important to quantify their variability, intermittency, and correlations with other interacting fields across scales. To understand the uncertainties involved in power production, power outputs from four 2 MW turbines are analysed (from an operational wind farm at Pay d'Othe, 110 km south-east of Paris, France) using the scale-invariant framework of universal multifractals (UM). Their scaling properties were compared with power available at the same location from simultaneously measured wind velocity. While statistically analysing the turbine output, the rated power acts like an upper threshold that results in biased estimators. This is identified and quantified here using the theoretical framework of UM and validated using numerical simulations. Understanding the effect of instrumental thresholds in statistical analysis is important in retrieving actual fields and modelling them, more so in wind power production, where the uncertainties due to turbulence are already a leading challenge. This is expanded in Part 2, where the influence of rainfall on power production is studied across scales using UM and joint multifractals.