Limits to the power density of very large wind farms

2013/09/19 by Nishino, Takafumi
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)

paper · doi:10.48550/arxiv.1309.4943

Abstract

A simple analysis is presented concerning an upper limit of the power density (power per unit land area) of a very large wind farm located at the bottom of a fully developed boundary layer. The analysis suggests that the limit of the power density is about 0.38 times τ_w0U_F0, where τ_w0 is the natural shear stress on the ground (that is observed before constructing the wind farm) and U_F0 is the natural or undisturbed wind speed averaged across the height of the farm to be constructed. Importantly, this implies that the maximum extractable power from such a very large wind farm will not be proportional to the cubic of the wind speed at the farm height, or even the farm height itself, but be proportional to U_F0.

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