Spatial constraints in large-scale expansion of wind power plants

When wind turbines are arranged in clusters, their performance is mutually affected, and their energy generation is reduced relative to what it would be if they were widely separated. Land-area power densities of small wind farms can exceed 10 W/m2, and wakes are several rotor diameters in length. In contrast, large-scale wind farms have an upper-limit power density in the order of 1 W/m2 and wakes that can extend several tens of kilometers. Here, we address two important questions: 1) How large can a wind farm be before its generation reaches energy replenishment limits and 2) How far apart must large wind farms be spaced to avoid inter-wind-farm interference? We characterize controls on these spatial and temporal scales by running a set of idealized atmospheric simulations using the Weather and Research Forecasting model. Power generation and wind speed within and over the wind farm show that a timescale inversely proportional to the Coriolis parameter governs such transition, and the corresponding length scale is obtained by multiplying the timescale by the geostrophic wind speed. A geostrophic wind of 8 m/s and a Coriolis parameter of 1.05 x 10-4 rad/s (latitude of similar to 46 degrees) would give a transitional scale of about 30 km. Wind farms smaller than this result in greater power densities and shorter wakes. Larger wind farms result instead in power densities that asymptotically reach their minimum and wakes that reach their maximum extent.