*4.4. Spectrum Analysis*

In this section, the power spectral density (PSD) of platform motion response, mooring line force, damping force, and produced wave power were presented and compared for F2A simulation and AQWA simulation.

#### 4.4.1. Motion Spectrum

Figure 13a,d,g display the PSD of the platform surge under the three load cases. The energy was mainly concentrated in the natural frequency of the surge and the wave frequency. For the mild sea state (LC2) in Figure 13a, there is a reduction for surge motion at the surge resonance peak in F2A simulation compared with AQWA simulation due to the aerodynamic damping effect. However, this reduction is not significant for worse sea state (LC3 and LC4) for surge motion in Figure 13d,g. For the relative heave motion, the

responses are dominated by the frequency from 0.3 to 0.9 rad/s which is related to the wave peak frequency. Therefore, both F2A simulation and AQWA simulation are very similar to each other (Figure 13b,e,h). Figure 13c,f,i are the PSD of the platform pitch motion. Observing the PSD curves of surge and pitch, the reason for the difference in the low frequency area around pitch resonance peak was the influence of aerodynamic damping considered in F2A simulation. It was obvious that when the wind velocity was small, aerodynamic damping obviously reduced the resonance response in the lowfrequency region but had little effect on the wave frequency range. This phenomenon conforms well to the known characteristics of the general damping effect. However, when the wind velocity gradually increased (LC2–LC4), the influence of air damping gradually decreased. This was because the aerodynamic thrust acting on the rotor increases rapidly with increasing wind velocity, offsetting the increase in the aerodynamic damping effect caused by surge. Among these effects, aerodynamic damping and wind velocity had a firstorder relationship, and aerodynamic thrust and wind velocity had a quadratic relationship. Therefore, at low wind velocities, aerodynamic damping had a greater influence, and at high wind velocities, aerodynamic thrust had a more obvious influence. It can be found that aerodynamic damping had a greater impact on pitch than surge and a stronger reduction in pitch motion.

**Figure 13.** *Cont*.

**Figure 13.** Comparisons of the PSD of the motion for LC2, LC3, and LC4: (**a**) Surge Motion of LC2; (**b**) Relative Heave Motion of LC2; (**c**) Pitch Motion of LC2; (**d**) Surge Motion of LC3; (**e**) Relative Heave Motion of LC3; (**f**) Pitch of LC3; (**g**) Surge Motion of LC4; (**h**) Relative Heave Motion of LC4; (**i**) Pitch Motion of LC4.

4.4.2. Mooring Tension Spectrum

The mooring line responses in the frequency domain in the head sea under different load cases from F2A simulation and AQWA simulation are shown in Figure 14. For all the load cases, the most significant contribution to the ML 1 and ML2 tension comes from the low-frequency region (surge mode response). The contributions from pitch mode response are also identified. For worse sea state (LC4), the contributions to the ML1 and ML2 tension from the wave frequency range from 0.3 rad/s to 0.9 rad/s are comparable to the contribution from surge mode response. Similar to the PSD of the motion response, in the F2A simulation, aerodynamic damping had a weakening effect on the response

at surge and pitch natural frequencies. With the wind velocity increases (LC2–LC4), the aerodynamic damping effect gradually decreased.

**Figure 14.** Comparisons of the PSD of the mooring line force of: (**a**) ML1 of LC2; (**b**) ML2 of LC2; (**c**) ML1 of LC3; (**d**) ML2 of LC3; (**e**) ML1 of LC4; (**f**) ML2 of LC4.

4.4.3. Damping Force and Produced Wave Power Spectrum

Figure 15 shows the damping force in the vertical direction and the produced wave energy power. The simulation results of the two simulation tools are slightly different. The energy was mainly concentrated in the wave frequency. Figure 15b,d,f are the PSDs of the produced power. The produced wave power frequencies are located in the dou-

ble wave frequency and low frequency regions. There was no significant effect from aerodynamic damping.

**Figure 15.** Comparisons of the PSD of: (**a**) Damping Force of LC2; (**b**) Produced Power of LC2; (**c**) Damping Force of LC3; (**d**) Produced Power of LC3; (**e**) Damping Force of LC4; (**f**) Produced Power of LC4.

### *4.5. Dynamic Responses in Extreme Conditions*

Under extreme condition (LC5), the WEC and the semisubmersible platform were locked to each other, and there was no relative motion. The PTO system and the wind turbine were parked. As shown in Figure 16a, the WEC and the semisubmersible platform had the same heave motion and were in a locked state. Figure 16b,c show the PSDs of the platform surge and heave. The PSD of the platform surge was mainly dominated by the wave frequency and the natural frequency of the surge. The PSD of the platform heave was mainly dominated by the wave frequency. From the PSD of the pitch (Figure 16e), it can be seen that the energy was mainly concentrated on the wave frequency and the natural frequency of the pitch, but the resonance effect on the pitch simulated by AQWA was much smaller than the result of the F2A simulation. When using F2A simulation, the upper wind turbine was parked, and the pitch angle was set to 90◦. Figure 16e,f show the mooring forces of ML1 and ML2. The energy was mainly dominated in the wave frequency range.

**Figure 16.** Motion and mooring force response of the platform under LC5: (**a**) Heave motion time series; (**b**) PSD of platform surge; (**c**) PSD of platform heave; (**d**) PSD of platform pitch; (**e**) PSD of ML1; (**f**) PSD of ML2.
