## 1 Introduction
RIDTMD was found to be more effective than TMD when they had the same physical mass. [PERSON] et al. [9] and [PERSON] et al. [10] applied tuned liquid column dampers in the wind turbine nacelle, which could reduce tower top and nacelle displacement. However, installing dampers in the wind turbine nacelle incurs additional construction costs; meanwhile, the wind turbine tower should be strengthened when applying dampers. Thus, applying dampers, to some extent, is not economic. Subsequently, some researchers proposed to improve the hydrodynamic performance of the floating offshore wind turbine platform, in order to reduce floating wind turbine vibration under the coupling impact of wind and wave. For spar-type wind turbine, [PERSON] et al. [11] added a heave plate on the spar-type platform. The heave plate was found to be useful in controlling platform heave movement, owing to that it could provide great added mass. [PERSON] et al. [12] also applied a heave plate on the spar-type platform, and they optimized heave plate structural parameters through a bunch of numerical simulations. The newly proposed platform had smaller wind turbine vibration and mooring tension than those of the original OC3-Hywind spar-type wind turbine platform. Innovatively, [PERSON] et al. [13] developed the original spar-type platform by attaching circular columns onto it but remaining its total volume and mass. Compared with the original spar-type platform, the developed platform could reduce wind turbine vibration in different directions simultaneously due to larger overtopping stiffness. Interestingly, [PERSON] and [PERSON] [14] combined spar-type platform and fish cage. They used FAST [15] to calculate wind turbine dynamic responses. Their numerical results indicated that fish cage could limit wind turbine vibration and the proposed platform performed better than the original one. Although the developed platforms [11; 12; 13; 14] could improve platform hydrodynamics, their construction and maintenance costs increased simultaneously. Thus, this study tries to reduce spar-type floating offshore wind turbine vibration by developing an original mooring system which has negligible effects on the wind turbine's construction and maintenance costs. When quantitatively evaluating the performance of the developed mooring systems, experiments in a real wave basin and numerical simulations in a virtual wave basin can be carried out. The experiment can only test some typical cases because the mooring system configuration can hardly be randomly changed during the experiment. Meanwhile, a real wave maker can only generate a few typical waves. Hence, the experiment is not suitable for the mooring system optimization that is needed to evaluate the various cases in this study. To this end, numerical simulation was adopted; specifically, FAST [15] was utilized to simulate the wind and wave interactions of floating offshore wind turbines. In summary, in this study, the original spar-type floating offshore wind turbine mooring system with three mooring lines and three fairleads was developed; specifically, six mooring lines were utilized to moor the wind turbine, which were divided into three groups, and two mooring lines from the same group were connected to the same fairlead (resulting in a total of three fairleads). The effects of the included angle between the two mooring lines in each group on the mooring system's performance were examined. Further, these six mooring lines were connected to six independent fairleads for comparison with the mooring system with six mooring lines and three fairleads. FAST [15] was utilized to calculate the wind turbine's dynamic response with these developed mooring systems. Wind turbine surge, pitch, and yaw movements are presented and analyzed in time- and frequency-domain to quantitatively evaluate the mooring system performance.