Modelling the Yaw Behaviour of a Small Wind Turbine

Abstract

This paper develops a mathematical model for a small wind turbine responding to changes in the wind direction. Here “small” implies that the turbine has a tail fin. Good yaw behaviour, in terms of tracking the changes in wind direction, is necessary to maximize power extraction. However large rates of change of yaw can lead to large stresses in the turbine components. The unsteady tail fin loads are more complex than implied by the “pseudo-static” assumption that the steady-state lift and drag act instantaneously. The aerodynamic model is applied first to data obtained from a 5 kW experimental turbine when it was not extracting power, because this almost removes the effect of the blades from the yaw behaviour. MATLAB's systems identification toolbox was used to optimise the fit of the model parameters to the data. The resulting values of a number of the parameters are shown to be in good agreement with earlier wind tunnel tests of the tail fin design. Some details of the comparisons, mainly in terms of the higher frequency components, suggest the need to characterise similarly the dynamics of wind vanes. When the turbine was extracting power, the flexible blades were deflected backwards by the aerodynamic loads. A blade element analysis suggests that the stabilizing moment due to this “coning” does not alter the form of the yaw response equation. The optimised fit of the model equations gave changes in the parameters broadly in agreement with the blade element analysis, but the quasi-steady analysis did not predict the measured increase in the damping associated with power extraction.