Formulas of the optimized yaw angles for cooperative control of wind farms with aligned turbines to maximize the power production

Cooperative yaw control of wind turbines can substantially increase the total power production of wind farms, especially for the ones with aligned turbines. However, a generalized and effective method to quickly determine the turbines' yaw angles for the wind farm control is rather limited. To this end, a systematic study was carried out on the cooperative yaw control of a single column of turbines. It is found that the optimized yaw angles are not sensitive to the turbine number. All the turbines should yaw to the identical direction for power maximization except the last turbine for which no yaw is required. The cooperative yaw control strategy can be simplified to a solution space only containing two yaw angles, i.e., the yaw angle of the first turbine and the angle for the downstream yawed turbines. Then, two algebra formulas are proposed to quickly determine the two yaw angles for the wind farm control only using three available parameters, i.e., the thrust coefficient of the rotor, the wake decay coefficient and the turbine spacing. To validate the proposed formulas, high-fidelity large-eddy simulations are performed. The results demonstrate that the proposed control strategy can increase the power production significantly for cases with strong wake effects. For one of the cases with five aligned turbines, the total power can be enhanced by 17.5%.