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Spatial constraints in large-scale expansion of wind power plants

Enrico G. A. Antonini and Ken Caldeira · Proceedings of the National Academy of Sciences 118 · 2021

Key finding. As the spatial scale of a wind farm increases, mean generation per unit of land decreases and the extension of its wake shadow on neighbouring plants increases — which together bound both how large a single wind farm can usefully be and how widely large farms must be spaced.

Six contour panels of normalised wind speed in a vertical slice through the atmosphere, extending 1000 km downstream and 2 km up. Each panel shows a wind farm as a row of markers along the surface, with a pale slowed-air region above and behind it. Panels vary the Coriolis parameter across two columns and the geostrophic wind speed across three rows, and each is annotated with the transition and recovery lengths, which range from about 30 to 290 km.
A large wind farm slows the air above and well downstream of itself. The recovery length — the distance needed before the wind returns to its undisturbed speed — reaches several hundred kilometres, which is what sets the minimum spacing between farms. Figure 2 from Antonini and Caldeira (2021), Proceedings of the National Academy of Sciences 118, e2103875118. Reproduced under author reuse rights. Extracted from the published PDF and resized for web display.

What question did this research address?

Wind supplied 6.1 per cent of worldwide electricity generation in 2020. If that share is to grow enough to decarbonize electricity systems, future wind farms will be far larger than anything built so far.

Scale changes the physics. This paper asked two specific questions — how large a wind farm can become before its generation runs into energy replenishment limits, and how far apart large farms must be placed to avoid interfering with one another.

What did we find?

Two distinct penalties grow with scale. Within a farm, mean generation per unit of land declines as the area expands, because the atmosphere cannot replenish kinetic energy fast enough across a large footprint.

Outside the farm, the wake it casts extends further as the farm grows, reducing the wind available to downstream installations.

The first penalty limits how large it is worth building any individual farm — beyond a certain size, additional area yields sharply diminishing generation.

The second sets a minimum spacing between farms, since installations placed too close together compete for the same replenished energy rather than each drawing on its own.

Why does it matter?

Together these constraints mean wind capacity does not scale linearly with land. Estimates of national or global wind potential built by multiplying an area by a power density will overstate what is achievable once farms reach the sizes decarbonization would require.

The spacing requirement also makes wind development a coordination problem. One developer's farm reduces the resource available to a neighbour's, which is a form of interference that siting policy has to address explicitly.

Citation

Enrico G. A. Antonini and Ken Caldeira (2021). Spatial constraints in large-scale expansion of wind power plants. Proceedings of the National Academy of Sciences 118.

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