Closed-form derivation of aerodynamic damping matrix and pitch vector of an aero-servo-elastic wind turbine system

This paper develops closed-form expressions of aerodynamic damping matrix and pitch controller of an aero-servo-elastic wind turbine (WT) system. This facilitates establishing a linearized WT model completely analytically at an arbitrary operational point, without resorting to extensive numerical linearizations or fittings. The rotor blade flexibility and pitch controller are included in the model development, thus unfolding a full understanding of the aerodynamic coupling effects. The linearized WT model is verified by good agreement with results from the original nonlinear WT model. Based on the verified linearized model, it is seen that aerodynamic coupling between tower fore-aft and side-side vibrations is solely due to the tower top rotations, and the top rotations also significantly enlarge the diagonal aerodynamic damping coefficients. Both tower top rotations and flexible blade-tower interaction play important roles in tower aerodynamic damping ratios. The developed formulas of load coefficients are also readily applicable to a FE modeling framework of the tower-foundation system.