  Under the term global blockage, the cumulative induction of wind turbines in
a wind farm has been recently suspected to be responsible for observed
overestimations of the energy yield in large-size wind farms. In this paper,
the practice of modeling this effect after linear superposition of single
turbine inductions, calculated with three of the most recent analytic models,
is compared to Large-Eddy-Simulations of wind farms. We compare the models
across two different farms, composed of 9 and 49 turbines, with two different
heights of the atmospheric boundary layer, 300 and 500 m. The results show hat
the differences between the analytical models are negligible while they
substantially differ from the LES results. The linear superposition of
induction consistently underestimates the velocity deficit in front of the farm
with an error that increases as the wind farm size grows and the ABL height
decreases. Also, when calculating the power output at the turbines of the farm,
all the analytical models considered do not agree with the LES. These
comparisons reveal that the farm interactions with the atmospheric boundary
layer may highly outclass the turbine induction in determining the extent of
the global blockage effect. Therefore, we present a first dimensional approach
to the problem based on LES, aimed at simplifying its characterization.
