Predicted power production for future wind farms.

This paper presents an analysis of the area dependency of power and capacity density of wind farms, based on derivations of the available energy in the atmosphere and data on the power production of existing wind farms in the North Sea. The amount of available energy is determined by the mechanical energy budget of the atmospheric boundary layer and is found to be a function of C/A, where C is the circumference and A is the area of the wind farm. The actual power production of 31 wind farms is analyzed, and the power production in 23 of the largest wind farms follows the same functional form as the available energy, indicating that the power production in these wind farms is limited by the available energy. The power density in the North Sea, as a function of the area usage, is found by fitting the actual power density of existing wind farms to the expression for available energy in the atmospheric boundary layer. Wind farms below 10 km2 can produce more than 6 Wm−2, but the power density rapidly decreases with area. Wind farms with an area of about 1000 km2 will produce 1 Wm−2, and power densities will asymptotically approach a value of 0.78 0.58 Wm−2 for increasing wind farm area. Since atmospheric energy input is the limiting factor for power production, an atmospheric energy budget is vital for a reliable estimate of offshore wind power potential.