Prediction of multiple-wake velocity and wind power using a cosine-shaped wake model

It is well accepted the wakes induced by upstream turbines have an adverse impact on the power production of downstream turbines and this ubiquitous phenomenon severely affects wind farm performance. The aim of the study is to apply a new analytical wake model to prediction of multiple-wake velocity and power output inside wind farms and evaluate its performance. Unlike the classical top-hat model (Jensen model) widely embedded in industry-standard software, the newly proposed analytical wake model, which is derived based on the conservation of both mass and momentum, assumes a trigonometric distribution for the velocity deficit in the wakes of a stand-alone wind turbine and adopts a variable wake growth rate relating ambient turbulence as well as rotor-generated turbulence. Two superposition models including the SED (superposition of energy deficits) and the SVD (superposition of velocity deficits) are employed to simulate the wake-interaction flows and the performance of the new model with the superposition methods is evaluated in two cases: (1) wake interactions of two wind turbines; (2) power prediction of the Horns Rev offshore wind farm. The open-source wind-farm simulation tool FLORIS is employed to make a further comparison of different wake models. It is found that the new and the Gaussian models with the SED are in reasonably good agreement with large-eddy simulation (LES) and measurements compared with other wake models, whereas lower velocity as well as power output is predicted when using the SVD counterpart. This research proposes the SED model as an effective selection strategy for evaluating power output in wind farms when using the cosine and Gaussian models.