Model for power spectra of the blade of a wind turbine measured from the moving frame of reference

While the static aerodynamic loads on wind turbine blades seem to a large extent predictable, little work has been done to clarify the dynamic loads due to atmospheric turbulence. A simple kinematical model is here derived in order to predict the power spectrum of the turbulence component of the wind along the mean wind direction, observed from a frame of reference that is moving with constant angular velocity along the circumference of a circle perpendicular to the direction of the mean wind velocity. The results deviate significantly from those obtained when disregarding the rotation. The model is based on the assumption that the turbulence is stationary, homogeneous, and isotropic. Predictions of power spectra seem to be in good agreement with experiments. In particular, comparison with a spectrum of structural response for the Gedser wind turbine is interesting, because it demonstrate the applicability of the overall concept of the model. A technique is outlined to obtain cross-spectra between turbulence wind components measured at different points in the moving frame of reference.