Aerodynamic Roll-Yaw Instabilities of Floating Offshore Wind Turbines

This paper presents an investigation of a newly discovered motion instability phenomenon for floating wind turbines. The instability is due to anti-symmetric coupling terms in roll and yaw caused by the turbine thrust force. For floaters with small separation between the uncoupled roll and yaw natural periods these coupling forces may result in rigid body roll and yaw oscillations. The paper explains the theory and the physics of the instability phenomenon, and analytical expressions for these stiffness coupling terms (K₄₆ and K₆₄) are derived.

The instability phenomenon is demonstrated using several points of attack, by using time domain simulations, conservation of energy flow and eigenvalue stability analysis. The problem is stripped down to a simplified two degree of freedom roll-yaw model where analytical stability criteria are developed. The instability is also demonstrated in tailor made six degree of freedom time domain simulations, and in simulations using a fully coupled aero-hydro-servo elastic simulation tool including a BEM model.

An important finding is that damping forces are needed to fully understand the observed instability. It is demonstrated, quite counter-intuitively, that damping reduces the stability margin. This is explained by considering the effect damping forces has on roll-yaw phasing, for the typical damping values relevant for a floating offshore wind turbine.