A control-oriented model for floating wind turbine stability and performance analysis

A well-designed floating turbine controller should lead to small power fluctuations while keeping the system stable. Floating wind turbines can experience instability when operating above rated wind speed, due to the blade pitch controller. This phenomenon, known as negative aerodynamic damping, is the reason why a controller needs to be re-designed for floating applications. One solution is to de-tune the blade pitch controller and make it slower than the floater pitch motion. This solution, although simple, reduces the controller’s ability to react to changes in the inflow and results in large power fluctuations. A more sophisticated approach involves an additional loop feeding back the fore-aft nacelle velocity to the blade pitch or generator torque. The choice of gains, however, is not trivial. This work proposes a control-oriented model derived from first principles to investigate different controller configurations in terms of both stability and turbine performance. The linear model with seven degrees of freedom (six rigid-body motions and drivetrain) is formulated analytically and coupled with the controller. The linear formulation allows us to investigate stability via eigenvalue analysis and performance via frequency-domain response, thus bypassing the need for time-domain simulations. Parametric studies with thousands of different controller configurations can be completed in a matter of minutes.