Limits of electricity generation from wind: characterizing transitional scales in wind farm power density

In 2018, the share of electricity generated from wind amounted to 6.6% in the United States and 3.7% worldwide. Such figures are expected to significantly grow as more renewable energy sources will be used in the effort to limit carbon dioxide emissions and the increase of the global average temperature to below 1.5 °C above pre-industrial levels. In such a scenario, the size of future wind farms is likely to extend far beyond that of current installations. When wind turbines are arranged in clusters, their performance is mutually affected, and the energy generation is reduced with respect to undisturbed conditions. Studies have shown that there exists an upper limit in power density for large-scale wind farms that is of the order of 1 W/m², whereas much higher values can be obtained for smaller installations. In this study, we aim to characterize the transitional scales at which this change occurs. We run a set of idealized atmospheric simulations using the Weather Research and Forecasting (WRF) model where the wind turbines are parametrized as momentum sinks. In these simulations, we vary the farm size and arrangement, the wind conditions, the terrain roughness, and the Coriolis force. The results in terms of wind farm power density are compared with previous studies and observations and provide a deeper understanding of how power density scales with wind farm size.