How close is German wind energy use to its limit? A quick check using climate data shows that it currently represents a few percent of the maximum, but may get quite close to its limits by 2050.

From time to time I get e-mails asking me about what our work on wind energy limits implies for the German transition to sustainable energy. With the substantial expansion of wind power in Germany over the last decade, are we getting close to the limits of wind energy that the atmosphere can provide? I looked at the latest ERA-5 weather data product to get answers, and instead of just e-mailing answers, I wrote this blogpost as well to share the insights.

Estimating wind energy potentials needs to include the atmospheric response. As a quick background: The typical way to estimate wind energy resource potentials is to use fixed wind speeds and turbine technology, and then to scale these up to larger regions, with certain assumptions of turbine spacings. However, this ignores the effects that wind turbines have. After all, they are made to remove kinetic energy from the atmosphere to convert it into renewable energy. The typical way to derive wind energy resource potential basically assumes an infinite reservoir of wind energy that is available to get harvested, so that the turbines have a negligible effect on the atmosphere. What we do in my group is to take a different approach. Rather than using fixed wind speeds, we base our approach on atmospheric energetics, focusing on the ability of the atmosphere to generate and distribute the energy associated with its motion.  The atmosphere generates winds at the global scale at a rate of about 2 W m^-2, which reflects a strong thermodynamic limitation on the power to generate this energy. The atmosphere literally works as hard as it possibly can to generate motion. This low rate then results in wind resource potentials that are typically quite a bit lower. Which may not sound as thrilling as some highly optimistic estimates, but at least they are physically sound. So our low estimates do not reflect an aversion against wind energy, but rather conveys our belief that it is really important to be physically sound when deriving estimates of renewable energy resources. For wind, this means to take the effects that turbines have on the atmosphere into account. And yes, this implies that quite a few, high-profile wind energy resource estimates are quite likely not physically sound.

Limits to wind energy use in Germany. How close are we actually to this limit? To get the answer, I used the boundary layer dissipation output from the ERA-5 reanalysis product from the European Centre for Medium-Range Weather Forecasts (ECMWF) as a start. This output describes how much kinetic energy the atmosphere dissipates in the lower atmosphere (the so-called boundary layer, typically the lower 1-2 km) due to surface friction. In the global mean, it yields a value of about 2 W m^-2, thus matching the generation rate described above. Wind turbines based at the surface divert some of this energy from the lower atmosphere, so rather than ending up in heat, some of it is converted into electricity. Hence, this frictional dissipation sets the starting point for the limit how much wind energy can be used at larger scales.

When taking the average of this field over Germany (see figure), we get an average of about 3.9 W m^-2, which is about twice the global mean. But then, Germany is windier than the average, so this makes perfect sense. Multiplied by the surface area of Germany (357 000 km²), this yields a number of about 1.4 TW of kinetic energy (1 TW = 10¹² W) that the global atmosphere dissipates into heat over Germany. Converted to an energy amount per year, which is the typical way energy consumption is reported, this corresponds to 44 000 PJ per year. To set this into context, German primary energy consumption is 13 000 PJ per year (AG Energiebilanzen). So compared to how much energy Germans consume, this number is no longer that large! The atmosphere does not bring that much wind energy to Germany, despite it being a windier place than the world’s average. Or, put into other words, Germans consume a lot of energy!

Not all wind energy can be converted. However, not all of the 1.4 TW of kinetic energy that the atmosphere dissipates over Germany can be converted into renewable energy. As the atmosphere transports momentum from higher layers down to the surface, some of the kinetic energy is inevitably lost. The mixing necessary to replenish the wakes that the turbines leave in the atmosphere also dissipates some kinetic energy, about half of what the turbines generate in electricity. Physical considerations (Miller et al. 2011, Miller et al. 2015) show that only a fraction of 26% can at best be used, and this would go hand-in-hand with a substantial decline in wind speeds by 42% (Miller et al. 2016). It is this unavoidable reduction in wind speeds that leads to lower, large-scale potentials.

To get back to Germany, we can apply this fraction of 26% to the atmospheric dissipation field, average over the different states, and compare this limit to how much electricity wind turbines produced there (more on the methods and a table with the numbers is provided at the end).

Wind energy use is currently less than 10%. What comes out of this analysis is that the wind turbines in some states already use up to 8% of what could at best be used. While the state of Bremen is rather small so that this may not matter much, the northernmost state of Schleswig-Holstein has a considerable installed capacity of 7 GW in wind turbines that appears to also use close to 8%. Three other, comparatively large states (Brandenburg, Sachsen-Anhalt, and Niedersachsen) use more than 4%. The impacts that this leaves on the wind is likely to be rather small. After all, frictional dissipation increases with the wind speed cubed (v³), so that the reductions in wind speed due to the wind turbines should be much less percentagewise than the impacts these have on the dissipation. (If you want a more quantitative estimate: Dissipation is reduced by 8% because of what the turbines extracted, and further reduced by wake dissipation, about half of the 8%. So in total, dissipation is reduced by 12% in the presence of the wind turbines. Since dissipation is proportional to v³, this would roughly translate in a wind speed reduction of (0.88)^1/3 – 1 ≈ -4%)

Greater, detrimental effects should be expected in the future. It is, of course, a matter of personal judgement whether 4-8% is a lot, or rather little. But we may very well need to consider these effects in the planning for the future. Some of the scenarios for a climate-neutral Germany in 2050 consider an expansion of windpower on land by a factor of 3 (for instance, the scenario of the WWF). Imagine that three times as many wind turbines (or bigger ones with a greater capacity) are placed in Schleswig-Holstein. Most scenarios furthermore assume increased wind turbine efficiencies due to technological developments (the WWF study, for instance, assumes an increase from 20.4% in 2020 to 24.9% in 2050). So they do not just take out more energy because of more installed capacity, but also because of greater efficiency (in relative terms, the turbines are assumed to become 22% more efficient in the mentioned scenario). This results in wind turbines aiming to take out almost 30% of the maximum that is possible ( 8% * 3 + 22% = 28.8%). At such a rate, this would quite likely slow down wind speeds (following the same calculation as above gives a reduction by 18%). The effect would be a lowering of the efficiency of the wind turbines, not because of technology, but because of the depletion of the atmospheric resource. And this finding is quite consistent with what we found for offshore wind energy (in a study from Agora Energiewende to which we contributed, see here).

So what? In summary, these estimates suggest that there is still a lot of room until the limits of wind energy use in Germany are going to be felt. So wind energy certainly contributes a lot of energy to the German electricity system, and the losses induced by its effects on the atmosphere are likely still small. But in some of the scenarios for the future, these effects should better be anticipated, because these effects increase in their importance the more wind energy is to be generated. And the importance of this effect is that it makes renewable energy generation by wind turbines less efficient, and hence more costly. This is particularly the case for those areas in Germany where wind energy is already used quite intensely. May be this means that the expansion of wind energy in Germany should focus more on the less windy places? That would be something interesting to look closer at.

---

More on the methods. The installed capacity of wind turbines in different states was taken from here. For the estimation of the generated electricity, I used a mean capacity factor of 20%, which is typical for Germany. The resulting yield summed up over Germany is 95 TWh per year, which is similar to the 100 TWh per year reported by the BDEW.

State	km2	Installed (MW)	Yield (TWh/a)	Dissipation (W m-2)	Max. Yield (TWh/a)	Ratio
Baden-Württemberg	35 751	1560	2,73	3,29	267,5	1,0 %
Bayern	70 550	2554	4,47	3,32	534,1	0,8 %
Berlin	892	12	0,02	3,57	7,2	0,3 %
Brandenburg	29 654	7383	12,94	3,72	250,9	5,2 %
Bremen	419	198	0,35	4,29	4,1	8,5 %
Hamburg	755	128	0,22	4,34	7,5	3,0 %
Hessen	21 115	2271	3,98	3,95	190,0	2,1 %
Mecklenburg-Vorpommern	23 213	3525	6,18	3,96	209,3	3,0 %
Niedersachsen	47 615	11386	19,95	4,41	478,4	4,2 %
Nordrhein-Westfalen	34 110	6025	10,56	4,27	331,5	3,2 %
Rheinland-Pfalz	19 854	3735	6,54	4,11	185,9	3,5 %
Saarland	2 570	492	0,86	3,90	22,8	3,8 %
Sachsen	18 420	1272	2,23	3,97	166,6	1,3 %
Sachsen-Anhalt	20 452	5240	9,18	3,97	184,8	5,0 %
Schleswig-Holstein	15 803	7006	12,27	4,38	157,6	7,8 %
Thüringen	16 202	1631	2,86	4,26	157,4	1,8 %
Germany Total	357 376	54418	95,34	3,89	3165,4	3,0 %

Acknowledgements. I thank for the easy accessibility of the ERA-5 output through the Copernicus data portal.