## 4 Numerical Simulation
### Analysis and Comparison of Tensioned and Catenary Mooring Systems  
In order to select a mooring system with better performance in small water depth, two mooring methods are used to simulate the floating wind turbine under the same working conditions. The irregular wave is simulated by JONSWAP wave spectrum. The significant wave height is 6.42 m and the peak period is 11.58 s, the wind speed of steady wind is 21 m/s. The time-domain coupling results of floating wind turbine using two different mooring systems are compared and analyzed. The total time of SIMA simulation response process is 10,800 s, and the three degrees of freedom that are greatly affected by wind, wave and current conditions in the time-domain coupling results are mainly compared and analyzed. Response and tension, the three degrees of freedom are surge, heave and pitch [28].  
Under the same working conditions, the motion response and tension comparison of the tensioned and catenary floating wind turbines are shown in Figure 5. Comparing and analyzing the motion response, tension time history curve and statistical results obtained by the two mooring methods of the floating wind turbine. We can see that: The mean value of the surge of the tensioned mooring is smaller than the mean value of the catenary, but the standard deviation of the tensioned mooring is larger than that of the catenary mooring. It shows that the dispersion degree of the motion response amplitude of the tensioned mooring is larger than that of the catenary mooring; The maximum value, mean and standard deviation of the heave and pitch of the catenary mooring are smaller than those of the tensioned mooring, indicating that the catenary mooring is better than the tensioned mooring in the response of heave and pitch; The No. 2 mooring line is the windward line of the floating wind turbine, so the tension of the No. 2 mooring line is mainly analyzed. From Table 5, it is not difficult to see that the maximum value of the catenary mooring tension is smaller than that of the tensioned mooring, while the average and the standard deviation is much smaller than that of the tensioned mooring. Although the maximum tension of the two mooring methods is smaller than the breaking tension, the maximum tension of the tensioned mooring is obviously larger.  
In general, although the mean value of the catenary mooring system's surge is greater than that of the tensioned mooring, considering that the suspension section of the catenary mooring is shorter in small water depth, the positioning ability of the floating wind turbine in the windward direction is better, and the discrete degree of the catenary mooring's pitch motion response is smaller than that of the tensioned mooring. Comparing the heave and pitch motion responses, it can be seen that the catenary mooring system is more effective in motion control. Considering the size of the tension, the catenary mooring system has better safe operation ability, so considering the advantages and disadvantages of both, it is more reasonable for the floating wind turbine to choose the catenary mooring system.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Mooring Mode** & **Response Type** & **Max** & **Min** & **Mean** & **STD** \\ \hline Tensioned & Surge/m & 4.758 & \(-3.557\) & 0.7757 & 1.124 \\ Catenary & & 8.988 & \(-4.386\) & 4.337 & 0.9878 \\ Tensioned & & 2.869 & \(-3.124\) & \(-0.2909\) & 0.8235 \\ Catenary & Heave/m & 2.353 & \(-2.394\) & \(-0.1490\) & 0.6337 \\ Tensioned & & 8.974 & \(-2.289\) & 3.131 & 0.6784 \\ Catenary & Pitch/\({}^{\circ}\) & 8.499 & \(-3.386\) & 2.582 & 0.6465 \\ Tensioned & & 6978 & \(-\) & 1167 & 1216 \\ Catenary & Mooring 2 tension/KN & 5846 & \(-\) & 741 & 277.2 \\ \hline \end{tabular}
\end{table}
Table 5: Motion response and tension statistics of floating wind turbine.