Power fluctuation and power loss of wind turbines due to wind shear and tower shadow

The magnitude and stability of power output are two key indices of wind turbines. This study investigates the effects of wind shear and tower shadow on power output in terms of power fluctuation and power loss to estimate the capacity and quality of the power generated by a wind turbine. First, wind speed models, particularly the wind shear model and the tower shadow model, are described in detail. The widely accepted tower shadow model is modified in view of the cone-shaped towers of modern large-scale wind turbines. Power fluctuation and power loss due to wind shear and tower shadow are analyzed by performing theoretical calculations and case analysis within the framework of a modified version of blade element momentum theory. Results indicate that power fluctuation is mainly caused by tower shadow, whereas power loss is primarily induced by wind shear. Under steady wind conditions, power loss can be divided into wind farm loss and rotor loss. Wind farm loss is constant at 3α(3α–1)R2/(8H2). By contrast, rotor loss is strongly influenced by the wind turbine control strategies and wind speed. That is, when the wind speed is measured in a region where a variable-speed controller works, the rotor loss stabilizes around zero, but when the wind speed is measured in a region where the blade pitch controller works, the rotor loss increases as the wind speed intensifies. The results of this study can serve as a reference for accurate power estimation and strategy development to mitigate the fluctuations in aerodynamic loads and power output due to wind shear and tower shadow.