Dynamics and control of spar-type floating offshore wind turbines with tuned liquid column dampers

This paper investigates the use of tuned liquid column dampers (TLCDs) for vibration control of spar-type floating offshore wind turbines (FOWTs). A 17-degree-of-freedom (17-DOF) aero-hydro-servo-elastic model for the FOWT is first established using multi-body-based formulation and the Euler-Lagrangian equation, taking into consideration the full coupling of the blade-drivetrain-tower-spar vibrations, a collective pitch controller and a generator controller. The outputs of the model are compared with FAST for model verification. Next, a reduced-order 5-DOF model is established for the TLCD-controlled FOWT in-plane vibrations including hydrodynamic added mass as well as stiffness contributions from mooring lines and buoyancy. The model enables revealing the fundamental mechanism of the coupled spar-tower-TLCD system, as well as an efficient procedure for optimal design of FOWT-mounted TLCD. It is found from modal analysis of the spar-tower system that due to the coupling to the spar roll motion, the tower side-side frequency is significantly shifted comparing with the decoupled case, which needs to be accounted for when tuning the TLCD. Based on the 5-DOF model, a frequency-domain (FD) method for TLCD optimization is proposed using random vibration theory, and robust optimization of the TLCD can be performed for given environmental conditions. The optimized damper is then incorporated into the more sophisticated 17-DOF model, and performance of the TLCD is evaluated by means of nonlinear time-domain (TD) simulations. Both FD and TD results indicate that a well-designed TLCD effectively reduces the tower side-side vibration as well as the spar roll motion.