A three-dimensional wake model for wind turbines based on a polynomial distribution of wake velocity

Abstract

Accurate and fast prediction of wake is essential for power generation prediction of wind farms. This paper proposes a three-dimensional wake model that considers the effect of wind shear and the mass loss caused by such shear. The model simplifies the wake velocity distribution by assuming a straightforward polynomial shape rather than a complex Gaussian distribution, which makes the model simpler and more intuitive. To be close to reality, it incorporates the anisotropic expansion of the wake boundary and provides expressions for crossflow and vertical wake expansion rates. By solely possessing information regarding the incoming wind conditions and wind turbine parameters, wake velocity at any position can be calculated in a fast way. This model's prediction accuracy is demonstrated by four cases including three experimental as well as large eddy simulation (LES) data. Compared to conventional Gaussian models, it can maintain a higher level of accuracy in all cases. The model is quite simple and offers high accuracy and low cost. It can be used in wind farm layout optimization and wake control.