An analytical frequency‐domain model of aerodynamic mass and damping of floating wind turbines

Abstract

The fore‐aft motion of the rotor‐nacelle assembly (RNA) of a rotating floating wind turbine (FWT) can cause an oscillation in aerodynamic thrust, which may be equivalently treated as frequency‐dependent aerodynamic mass and damping effects. In this study, an explicit frequency‐domain analytical model is proposed to calculate the equivalent aerodynamic mass and damping of FWTs, with proper linearization of control system. Assuming that an FWT operates under steady wind conditions and a forced oscillation is exerted at the RNA along the wind direction, the thrust fluctuations are equivalently represented by the force and moment acting on the nacelle instead of pure aerodynamic loads. Based on the thrust oscillation expression, equivalent aerodynamic mass and damping are derived analytically. After verifying the model by numerical comparison, it is used to demonstrate equivalent aerodynamic mass and damping of three wind turbines (5–15 MW). Effects of wind turbine up‐scaling and controller dynamics are addressed. Results show that equivalent aerodynamic mass and damping present a nonlinear characteristic with oscillation frequency in the below‐rated region, while the relationship is close to linear for higher wind speeds. The effect of wind turbine up‐scaling has a visible impact on equivalent aerodynamic mass and damping, especially at near‐rated wind speed. Controller gains affect equivalent aerodynamic mass and damping and should be tuned reasonably in the controller design for FWTs. Outcomes of our study can be used to establish a frequency‐domain coupled model of FWTs and are beneficial for conceptual design and parameter optimization of the platform of FWTs.