Part 1: Multifractal analysis of wind turbine power and the associated biases

Abstract. The inherent variability in atmospheric fields, which extends over a wide range of temporal and spatial scales, also gets transferred to energy fields extracted off them. In the specific case of wind power generation, this can be seen in the theoretical power available for extraction in the atmosphere as well as the empirical power produced by turbines. Further the power produced by turbines are affected by atmospheric turbulence as well as other fields it interact with. For modelling as well as analyzing them, quantification of their variability, intermittency and correlations with other interacting fields is important. To understand the uncertainties involved in power production, power outputs from four 2MW turbines are analyzed from an operational wind farm at Pay d’Othe, 110 km southeast of Paris, France. Using simultaneously measured wind velocity from the same location, the variability in power available at the wind farm, and power produced by wind turbines were analyzed.

To account for the intermittency and variability in said fields, the framework of Universal Multifractals (UM) is used. UM is a widely used, physically based, scale invariant framework for characterizing and simulating geophysical fields over a wide range of scales. While statistically analysing the power produced by the turbine, rated power acts like an upper threshold resulting in biased estimators. This is identified and quantified here using the theoretical framework of UM along with the actual sampling resolution of instruments under study. The validity of this bias in framework is further tested and illustrated using numerical simulations of fields with the same multifractal properties. Understanding instrumental thresholds and their effect in analysis is important in retrieving actual fields and modelling them, more so, in the case of power production where the uncertainties due to turbulence are already a leading challenge. This is further expanded in the second part where the influence of rainfall in power production is studied using scale invariant tools of UM and joint multifractals.