Two three-dimensional super-Gaussian wake models for hilly terrain

With the increase in wind farms in hilly terrain, it is particularly important to explore the downstream wake expansion of wind turbines in hilly terrains. This study established two complex terrain-applicable super-Gaussian wake models based on the Coanda effect and the wind speed-up phenomenon. Then, by considering the wind shear effect and the law of mass conservation, two three-dimensional (3D) super-Gaussian wake models were obtained. The 3D super-Gaussian models were used to describe the shape of the wake deficit and could reflect the wake changes in the full wake region. The introduction of the Coanda effect could reflect the sinking of the wind turbine wake on the top of a hilly terrain. And considering that the wind speed-up phenomenon could better reflect the incoming velocity distribution of the actual hilly terrain. The validation results demonstrated that the prediction results of the 3D super-Gaussian wake models had negligible relative errors compared to the measured data and could better describe the vertical and horizontal expansion changes of the downstream wake. The models established in this study can assist with the development of complex terrain models and super-Gaussian models, as well as providing guidance for power prediction and wind turbine control strategies in complex terrain.