Evaluating the physical limits to technical wind energy potential over onshore Germany in 2050

Energy scenarios envision installation of up to 230 GW of wind capacity over available areas within the German onshore by 2050. The associated technical wind energy potential is typically derived assuming that the electricity generated by the wind turbines does not affect the wind resource. Consequently, future capacity factors, the ratio of generation to installed capacity, are implicitly assumed to be independent of the extent to which the wind resource is depleted. However, capacity factors reduce as wind capacity is increased. This is because kinetic energy (KE) removal lowers wind speeds that result in lower generation from the turbines. To assess the relevance of this resource depletion effect on capacity factors, we simulated electricity generation by wind turbines with a range of hypothetical and planned deployment scenarios using the Weather Research and Forecasting (WRF) model that incorporates the effects of atmosphere - turbine interactions and compared these to estimates derived from a simple, momentum-balance approach (VKE). Despite potential biases in modelled wind speeds, we find that for a typical planned scenario of ~200 GW deployed over 13.8% of land area, mean annual wind speeds reduce by an average of 0.4 m s^-1 compared to the case where the impact of atmospheric - turbine interactions is excluded. Associated reductions in capacity factor are up to 20% in regions of high installed capacities. To isolate the key atmospheric influence, we compare the simulated range of wind speeds and capacity factors with those from the VKE model that only accounts for KE removal effects. We find that the KE removal effects play the dominant role in shaping the reductions in wind speeds and capacity factors, thus providing a simple tool to capture these effects.  We conclude that with increased deployment of wind energy in the context of the energy transition, these wind resource depletion effects need to be taken into account, but this can be done in a comparatively simple and physical way.