Generalisation of the two-scale momentum theory for coupled wind turbine/farm optimisation

Abstract

An extended theoretical approach is proposed to predict the average power of wind turbines in a large finite-size wind farm. The approach is based on the two-scale momentum theory proposed recently for the modelling of ideal very large wind farms, but the theory is now generalised by introducing the effect of additional pressure difference induced by the farm between the upstream and downstream sides of the farm, making the approach applicable to real wind farms that are large but not as large as the size of the relevant atmospheric system driving the flow over the farm. To validate the generalised theoretical model, 3D Reynolds-averaged Navier-Stokes simulations of boundary layer flow over a large array (25 x 25) of actuator (drag) discs are conducted at eight different conditions. The results suggest that the generalised model could be embedded in a regional-scale atmospheric model to predict the average power of a given wind farm effectively. This approach may also be combined with the blade element momentum (BEM) theory for coupled wind turbine/farm optimisation.