Coleman-free aero-elastic stability methods for three- and two-bladed floating wind turbines

Abstract. An accurate prediction of aerodynamic damping is important for floating wind turbines, which can enter into resonant low-frequency motion. The Coleman transform is not directly valid for the stability analysis of two-bladed floating wind turbines without applying an additional method to eliminate the system matrix time dependence. Therefore, here we pursue methods that do not rely on it. We derive a time domain model that takes into account the dynamic stall phenomenon and is used for developing Coleman-free aero-elastic stability analysis methods which can quantify the damping without actual simulation. It contains four structural degrees of freedom, namely the floater's pitch angle and the three blade deflection amplitudes, as well as three dynamic stall aerodynamic degrees of freedom, one for each blade. The time domain model is linearized by considering part of the aerodynamic forcing as an added damping contribution. The linearized model is then made time-independent through the application of Hill's or Floquet's method. This enables the possibility of carrying out a stability analysis where the eigenvalue results obtained with both methods are compared. A first modal analysis serves to demonstrate the influence of aerodynamic damping through the variation of the dynamic stall time constant. Thereafter, a second modal analysis is reported as a Campbell diagram also for cross-comparison of the Hill- and Floquet-based results. Moreover, the blade degrees of freedom are converted from the rotational basis to the non-rotational one using the Coleman transform so that results in both frames can be further cross-validated. Finally, we apply the validated stability methods to a two-bladed floating wind turbine and demonstrate their functionality. The stability analysis for the two-bladed wind turbine yields new insight into the blade modal damping and is discussed with comparison to the three-bladed analysis.