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

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