New paper: How much wind energy is there in Germany? We estimate the efficiency losses and impacts of wind energy expansion at 200 GW in Germany using a simple, physical approach.

The expansion of wind energy plays a central role in the energy transition. But how much can actually be used, and how strongly is the atmosphere affected? I am currently receiving a number of inquiries about this, e.g., based on a video which uses earlier work (Kleidon 2019, Kleidon 2021). Conveniently, a new paper has just been published in Physik in unserer Zeit, which answers exactly these questions.

For the estimation, we use an approach we developed more than 10 years ago (Miller et al. 2011), which is now very practical because it is simple and physical. The starting point is the so-called momentum balance. Momentum is one of the physical quantities that is conserved. The wind near the surface reflects this balance. It balances the momentum – which comes from above from the so-called free atmosphere – with the friction, which depends on the wind speed. In this way, the momentum is brought from the free atmosphere into the ground. If wind turbines come into play, then the momentum balance gets another term: Wind turbines extract momentum in order to generate electricity with it, and bring it directly into the ground. This is at the expense of friction, so the wind speed must decrease. This behaviour can be formulated very simply (Miller et al. 2011, Kleidon 2021), and it reproduces very well the behaviour that we find in very complex numerical models at regional scales (Miller et al. 2015, Miller and Kleidon 2016, Kleidon 2021).

Now I have rearranged the equations so that the model can be applied very nicely to regional wind energy scenarios to estimate wind speed reductions and yield reductions. It turns out that the efficiency (or more accurately, the capacity factor, the ratio of mean, actual generation to the capacity of the generator) of wind turbines decreases linearly with the rate at which they remove energy from the atmosphere. This relationship is shown in the Figure.

**Figure:** The average capacity factor (average power generation of a turbine divided by the capacity of its generator) decreases relatively linearly the more wind energy is used in a region. We find this relationship in climate models (GCM, colored, from **Miller and Kleidon 2016**) and can explain it physically through conservation of momentum (VKE, gray). We call this approach VKE and apply it to estimate what should happen to yields as wind energy expands.

One can then perform the estimation as follows. First, one needs the capacity factor of an isolated turbine. For this I take the present capacity factor from energy statistics in Germany, it is about 20%. The linear decrease goes with the amount of energy withdrawn divided by the maximum possible energy that can be withdrawn. The latter is 38% of the dissipation rate of kinetic energy that naturally happens in the atmosphere at and below the height of the wind turbines. And the dissipation rate is obtained from the ECMWF reanalysis dataset.

Thus, for a nationwide, uniform expansion to 200 GW, one gets that the average capacity factor decreases by about 10-13%. Without this reduction effect, wind turbines would generate an average of about 200 GW x 20% capacity factor = 40 GW or 350 TWh of electricity per year. With reduction, this amount is reduced by 30-45 TWh/yr. For comparison: this is about half of the current electricity consumption in Germany, so it is still a lot of energy. If the turbines are installed on half the surface area, the reduction effect increases accordingly, as is the case with turbines that are more efficient.

The impact can also be estimated with this approach. In its natural state, the atmosphere over Germany dissipates about 4 W per square meter, i.e. converts kinetic energy back into heat. Multiplied by the area of Germany, this results in 1430 GW or 12500 TWh per year. If we now relate the yield to this friction rate, we see that wind turbines then use only 2.5% of the kinetic energy that would otherwise be naturally converted to heat. In other words, this is a really small effect for the atmosphere, and large scale effects of wind turbines are thus very unlikely to take place.

More details, for example a breakdown by state, can be found in the article (Kleidon 2023b, english translation available on arXiv). Currently, we are working on testing this approach with simulations using high-resolution weather prediction models and applying it in further studies.

References

Miller et al. (2011) Estimating maximum global land surface wind power extractability and associated climatic consequences, Earth Syst. Dynam., 2, 1–12, https://doi.org/10.5194/esd-2-1-2011.

Miller et al. (2015) Two methods for estimating limits to large-scale wind power generation, Proc. Natl. Acad. Sci USA, 112 (36), 11169-11174, https://www.pnas.org/doi/10.1073/pnas.1408251112.

Miller and Kleidon (2016) Wind speed reductions by large-scale wind turbine deployments lower turbine efficiencies and set low generation limits, Proc. Natl. Acad. Sci USA, 113 (48), 13570-13575, https://doi.org/10.1073/pnas.1602253113.

Kleidon (2021) Physical limits of wind energy within the atmosphere and its use as renewable energy: From the theoretical basis to practical implications, Met Z, 30 (3), 203 – 225, https://doi.org/10.1127/metz/2021/1062. Also described in this blogpost.

Kleidon (2023a) Windenergie in der Deutschen Bucht – Konsequenzen großskaliger Offshore-Windenergienutzung, Physik in unserer Zeit, 54 (1), 30 – 36, https://doi.org/10.1002/piuz.202201654. English version available on arXiv: https://arxiv.org/abs/2301.01043. Also described in this blogpost.

Kleidon (2023b) Windenergiepotenzial von Deutschland. Physik in unserer Zeit, 54 (3): 142-148, https://doi.org/10.1002/piuz.202301670. English version available on arXiv: https://arxiv.org/abs/2304.14159.