Why Bother on Model Complexity?—A Consistent Analytic Model for Power Output Prediction of Offshore Wind Farms

The present work concerns the further development of a simplified approach for predicting the average power output of offshore wind farms developed by Sørensen and Larsen. In this paper a correction factor, accounting for the finite size of a wind farm, was averaged over all operating wind speeds before deriving the convolution of the production of the wind farm wind turbines over the site wind speed distribution. In the present work, the wind-speed-dependent correction factor is redefined and consistently included in the wind speed Weibull distribution convolution. In addition, a simple model of the dependence of sea surface roughness on wind speed is introduced to refine the derived correction factor. Finally, a revised version of the simplified Geostrophic Drag Law has been derived to improve the dependence of the magnitude of the geostrophic wind speed on the friction Rossby number. The derived improved model is validated against a comprehensive set of quality-ensured full-scale production data from six different operating wind farms covering a diverse segment of Danish waters and further benchmarked against a series of commonly used state-of-the-art engineering simulation models. The comparison of computed results to actual monthly wind farm production data over a series of years shows mean prediction deviations and maximum standard deviations of the errors of about 4% and 8%, respectively. This is very much in accordance with predictions from the other engineering models against which the present model was benchmarked. The advantage of the present model, however, is its simplicity, the demand of only very few input data, and its low computational time, which is an order of magnitude lower than other engineering models.