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

TL;DR

This paper extends the two-scale momentum theory to better predict wind farm power output by incorporating farm-induced pressure effects, validated through high-fidelity simulations, enabling improved regional wind farm optimization.

Contribution

The paper generalizes the two-scale momentum theory to include pressure differences caused by wind farms, making it applicable to real-world, finite-sized farms.

Findings

The generalized model accurately predicts power output across various conditions.

Simulations validate the model's effectiveness for large but finite wind farms.

Potential integration with regional atmospheric models for optimization.

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.