Nøst Ole Anders
Oceanbox AS, Krambugata 2, Trondheim, Norway.
PLoS One. 2025 May 2;20(5):e0321528. doi: 10.1371/journal.pone.0321528. eCollection 2025.
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 [Formula: see text] 1 Wm-2, and power densities will asymptotically approach a value of 0.78 [Formula: see text] 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.
本文基于对大气中可用能量的推导以及北海现有风电场的发电数据，对风电场功率和容量密度的面积依赖性进行了分析。可用能量的量由大气边界层的机械能收支决定，并且发现它是C/A的函数，其中C是风电场的周长，A是风电场的面积。分析了31个风电场的实际发电量，其中23个最大风电场的发电量遵循与可用能量相同的函数形式，这表明这些风电场的发电量受可用能量限制。通过将现有风电场的实际功率密度与大气边界层中可用能量的表达式进行拟合，得出北海功率密度作为面积使用量的函数。面积小于10平方公里的风电场可以产生超过6瓦每平方米的功率，但功率密度会随着面积迅速下降。面积约为1000平方公里的风电场将产生[公式：见原文]1瓦每平方米的功率，并且随着风电场面积的增加，功率密度将渐近地接近0.78[公式：见原文]0.58瓦每平方米的值。由于大气能量输入是发电的限制因素，因此大气能量收支对于可靠估计海上风电潜力至关重要。
