An analytical model of momentum availability for predicting large wind farm power

Abstract

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.