More wind turbines should lead to less wind and less efficient wind turbines, but how to account for this? We showed that our simple spreadsheet KEBA model is about as good as complex WRF simulations to describe this effect.

Wind energy has seen a tremendous increase over the last decades, a trend that is likely to continue into the future with the transition towards a sustainable energy system. Yet, each wind turbine removes energy from the atmosphere, so the more wind turbines there are within a region, the more wind speeds should decline, making each turbine less efficient. This effect has clearly been shown by atmospheric simulation models (e.g., in our previous work), but this effect has typically not been accounted for in regional to continental wind energy resource estimates and energy scenarios for the future. The effect sounds complicated, so what should be done?

We just published a paper that shows that this wind removal effect of many wind turbines can be accounted for in a rather simple way. The key concept is to account for the fluxes of kinetic energy in the lower atmosphere (the so-called boundary layer), the ones that sustain wind speeds near the surface and drive renewable energy generation. We call our approach the Kinetic Energy Budget of the Atmosphere, or KEBA model (see Figure 1). It accounts for the influxes of kinetic energy from upwind regions (dark blue arrow) and downwards mixing from the atmosphere above (light blue arrow), and the loss terms by surface friction (red arrow), the turbines (yellow arrow) and the losses in their wakes (orange arrow), as well as the downwind export of kinetic energy by the flow (purple arrow).

Figure 1: The KEBA model accounts for the different fluxes of kinetic energy of the lower atmosphere that sustain winds and wind energy generation within a region. (This is Figure 1 from Kleidon and Miller, 2020).

As it turns out, the description of these fluxes depends only on a few parameters, such as the dimensions of the box, the number of turbines, and a meteorological parameter, and, of course, the prevailing wind speed of the region, observed in the natural setting without wind turbines being present. KEBA then simultaneously predicts wind speed reductions as well as the total yield of the turbines. The equations of the model are easy to solve, and were implemented in a spreadsheet. Given the histograms of wind speeds of three contrasting regions, we then compared KEBA to a set of sensitivity simulations done with the WRF regional atmospheric model, published by Volker et al in 2017. The relative yield reductions due to reduced wind speeds is captured surprisingly well, as shown in Figure 2.

Figure 2: Implemented as a spreadsheet, KEBA (y-axis) can reproduce the simulated yield reductions of many turbines within a region, calculated with a much more complex atmospheric model (x-axis), remarkably well. (This is Figure 3 from Kleidon and Miller, 2020).

What our results imply is that at the regional scale, it is the transport of kinetic energy into the region that is the limiting factor, rather than technology. The greater the area becomes that is covered by wind turbines, the relative contribution by the horizontal influx of kinetic energy decreases, while the contribution of the vertical downward mixing from the so-called free atmosphere increases. This latter flux is, however, much smaller, so that as the downwind dimension of wind energy use increases, the average yield per turbine must decrease. As it turns out, KEBA provides an expression for the scale at which this decline takes place, yielding about 50 – 100 km as a length scale, as shown in Figure 3. So a single turbine, representing a downwind length of zero, can have high yields. But once wind turbines populate larger and larger regions, their average yield must decline to much lower yields, as shown by climate models (as, e.g., by Miller and Kleidon, 2016). The spatial arrangement does not matter much in this, because the major effect that describes this decline is simply that each turbine does what it is supposed to do: remove kinetic energy from the wind to turn it into renewable energy.

Figure 3: As wind farms cover greater downwind lengths, the relative contribution by the horizontal flux (dark blue) of kinetic energy declines compared to the downward mixing from above (light blue). Consequently, mean yields per surface area (black lines, showing three different densities of wind turbines) need to decline with greater scales. (This is Figure 6c from Kleidon and Miller, 2020).

This decline in turbine yields is not just an academic exercise. As was shown in a recent policy study with Agora Energiewende, to which we contributed with KEBA, it notably lowers the expectations for how much electricity can be generated in offshore wind energy scenarios for Germany in the decades to come (see also previous blogpost here). So hopefully, KEBA can help to provide more realistic expectations regarding regional-scale wind resource potentials.

References:

Axel Kleidon and Lee M Miller (2020) The Kinetic Energy Budget of the Atmosphere (KEBA) model 1.0: a simple yet physical approach for estimating regional wind energy resource potentials that includes the kinetic energy removal effect by wind turbines. Geosci. Model Dev., 13, 4993–5005.

Presentation on the KEBA model at the EGU 2020 conference.

KEBA spreadsheet

Application to German offshore scenarios (see also report by Agora Energiewende, and this blogpost)

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