Department of Global Ecology, Carnegie Institution for Science, Stanford, CA 94305
Department of Global Ecology, Carnegie Institution for Science, Stanford, CA 94305.
Proc Natl Acad Sci U S A. 2021 Jul 6;118(27). doi: 10.1073/pnas.2103875118.
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/m, 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/m 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 × 10 rad/s (latitude of ∼46°) 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.
当风力涡轮机成簇排列时，它们的性能会相互影响，相对于它们之间相隔很远的情况，它们的发电能力会降低。小型风力农场的土地面积功率密度可以超过 10 W/m，而尾流的长度可达几个转子直径。相比之下，大型风力农场的上限功率密度约为 1 W/m，尾流可以延伸数十公里。在这里，我们解决了两个重要问题：1）风力农场的规模有多大才能达到能源补充的限制，2）大型风力农场之间必须间隔多远才能避免相互干扰？我们通过使用天气和研究预报模型运行一组理想化的大气模拟来描述这些时空尺度的控制。农场内和农场上方的发电和风速表明，一个与科里奥利参数成反比的时间尺度控制着这种转变，相应的长度尺度可以通过将时间尺度乘以地转风速来获得。地转风速为 8 m/s，科里奥利参数为 1.05×10 rad/s（约 46°纬度），则过渡尺度约为 30 km。小于这个尺度的风力农场会导致更高的功率密度和更短的尾流。而更大的风力农场则会导致功率密度逐渐达到最小值，尾流达到最大范围。
