LINEARIZED MODEL FOR WIND TURBINES IN YAW (HORIZONTAL AXIS, STATIC STABILITY)

The analysis of rigid hub, three-bladed horizontal-axis, axisymmetric wind turbines in yaw is made using a linearized, four-degree-of-freedom model. The linearized equations of motion of rotor and nacelle are developed using quasi-steady blade element theory and Lagrange's equations.;The yaw behavior of the system is studied from coefficients of the equations of motion. Analytical results for two wind turbines are presented and studied. The study shows that yaw tracking error is primarily caused by tower shadow. The contribution of the nacelle to the yaw stability is proved to be a destabilizing one. The yaw stability of a wind turbine in a reverse position is investigated and used for verification of the analysis.;The characteristics of yaw static stability are primarily determined by the characteristics of the in-plane force coefficient and the location of the yaw axis relative to the rotor plane. A sensitivity study of the terms in the yaw stiffness coefficient is made. The yaw static stability is strongly affected by a change in the coning angle.;Two Fortran computer programs are developed to compute the numerical values of coefficients of the equations of motion. Program listings and sample outputs are included.