Frequency domain modeling of free yaw response of wind turbines to wind turbulence

A frequency domain method has been developed in order to study the yaw dynamics and its effect on energy capture under various turbulence regimes for free yaw wind turbines. It is assumed that the primary forcing of the dynamic yaw originates from the variations from wind turbulence in the average wind direction and the horizontal gradient of the wind speed across the rotor. The horizontal components of the turbulence velocity are modeled as random processes with spectral characteristics calibrated from measurements. The corresponding statistics of the wind direction and the gradient are derived and used as input for an equivalent linear model of the system dynamics. The parameters in the simplified system model are identified from the results of a numerical test of a comprehensive yaw response and energy capture simulation model, developed at U. S. Windpower. The yaw response of the USW Model 56-100 machine to turbulence has been analyzed for a number of wind conditions and compared to test results with satisfactory agreement. The analysis shows that the effect on the yaw error from the horizontal wind gradient is twice the effect from wind direction changes.