In this study, we have investigated the existence of a Taylor power law or temporal fluctuation scaling of power output delivered by five wind farms and a single wind turbine, with different installed capacity. The analyzed data are sampled at 1 s and five minutes, and recorded over different periods. A Taylor power law has been highlighted for all the datasets. Furthermore, a universal scaling exponent ${\lambda}_{\tau}$ close to $1/2$, is observed for time scales $1\phantom{\rule{3.33333pt}{0ex}}h<\tau <7$ days for the data sampled at 5 min, and $5\phantom{\rule{3.33333pt}{0ex}}min<\tau <6$ h for the data sampled at 1 s.

The existence of such Taylor law has been shown in multiple disciplinary fields. This universality has conducted many authors to suggest the existence of a universal mechanism for its emergence. Various approaches and theoretical investigations have been dedicated to possible explanations of the origin of Taylor law. In the framework of a complex systems whose dynamics is the result of interactions of many components belonging to a network [

6,

7], the value of

λ gives an information on the mechanism governing the fluctuations involved in the process:

$\lambda \approx 1/2$ describes processes or systems where internal factors drive dynamics and

$\lambda \approx 1$ describes processes where external factors drive the dynamics [

6,

7,

8]. This was investigated for internet traffic data and complex networks [

6,

7,

8]. This result was experimentally based and cannot be used for understanding wind energy dynamics. Recently, Fronczak and Fronczak (2010) [

24] attempted to provide an interpretation of Taylor’s relation based on the second law of thermodynamics (the maximum entropy principle) and the number of states. Kendal and Jørgensen (2011) [

25] proposed the Tweedie Convergence Theorem to give a possible explanation of the origin of Taylor law. They show that Tweedie convergence theorem, a generalization of Central Limit Theorem, provides an explanation for the genesis of Taylor laws. They also showed that Taylor law is a scaling relationship, compatible with the presence

$1/f$ scaling and multifractal properties, characteristic of a self-similar process. On the other hand, several authors have shown the presence of

$1/f$ scaling [

26] and recently multifractal properties for wind energy data [

20,

27,

28,

29]. A way to highlight multifractal properties is the use of a multi-scaling analysis including

${q}^{th}$- order central moments

versus the mean value, a natural generalization of Taylor law where

$q=2$, or multifractal analysis [

8,

27,

29]. Although the Tweedie Convergence Theorem seems offer a promising explanation, there is currently no generally accepted theory to explain the emergence of Taylor’s relation.