Turbine–wake and farm–atmosphere interactions influence wind farm power production. For large offshore farms, the farm–atmosphere interaction is usually the more significant effect. This study proposes an analytical model of the ‘momentum availability factor’ to predict the impact of farm–atmosphere interactions. It models the effects of net advection, pressure gradient forcing and turbulent entrainment, using steady quasi-one-dimensional flow assumptions. Turbulent entrainment is modelled by assuming self-similar vertical shear stress profiles. We used the model with the ‘two-scale momentum theory’ to predict the power of large finite-sized farms. The model compared well with existing results of large-eddy simulations of finite wind farms in conventionally neutral boundary layers. The model captured most of the effects of atmospheric boundary layer (ABL) height on farm performance by considering the undisturbed vertical shear stress profile of the ABL as an input. In particular, the model predicted the power of staggered wind farms with a typical error of 5 % or less. The developed model provides a novel way of predicting instantly the power of large wind farms, including the farm blockage effects. A further simplification of the model to predict analytically the ‘wind extractability factor’ is also presented. This study provides a novel framework for modelling farm–atmosphere interactions. Future studies can use the framework to better model large wind farms.

中文翻译：

---

预测大型风电场功率的动量可用性分析模型

涡轮机-尾流和农场-大气相互作用影响风电场的发电。对于大型海上农场，农场与大气的相互作用通常是更显着的影响。本研究提出了“动量可用性因子”的分析模型来预测农场与大气相互作用的影响。它使用稳定的准一维流假设来模拟净平流、压力梯度强迫和湍流夹带的影响。通过假设自相似的垂直剪切应力分布来模拟湍流夹带。我们使用带有“双尺度动量理论”的模型来预测大型有限规模农场的功率。该模型与传统中性边界层有限风电场大涡模拟的现有结果进行了很好的比较。该模型通过考虑大气边界层 (ABL) 的未受干扰的垂直剪切应力剖面作为输入，捕获了大气边界层 (ABL) 高度对农场绩效的大部分影响。特别是，该模型对交错风电场的功率进行了预测，典型误差为 5% 或更小。开发的模型提供了一种即时预测大型风电场功率（包括风电场堵塞效应）的新颖方法。还提出了模型的进一步简化，以分析预测“风可提取系数”。这项研究为农场与大气相互作用的建模提供了一个新颖的框架。未来的研究可以使用该框架更好地模拟大型风电场。