5.3.1. Time Domain Analysis

For brevity of this paper, only the time histories of responses under cases 3 and 4 are provided as representatives, as shown in Figures 15 and 16. TwrBsMy and RootMy denote the tower-base fore-aft bending moment and the blade-root out-of-plane bending moment, respectively. Additionally, the time histories of wave elevation and horizontal wind speed are also plotted in the figures.

From the figures, it is found that the cage motions obviously oscillate in time due to the action of turbulent wind and irregular waves, especially the surge motion with a non-zero mean value. In particular, under the extreme load case, with the wind turbine parked and the blade pitched to the feather, the cage motion oscillation is much different from the operating case, because there is no damping from the controller and the oscillation is wave-dominated. Additionally, in the extreme condition, the maximum surge offset reaches up approximately 13 m, which is almost 65% of the allowable offset (20 m). It means that the stiffness of the mooring lines is just enough for the fishing cage.

The high oscillation In the curves of the blade pitch angle under condition 3 Is observed to maintain the rated generator power output of 5 MW. This indicates that the blade pitch controller is operating properly, in this case. However, there are still some places on the power curve below the rated value 5 MW, indicating that the wind speed on the rotor is dropped below the rated wind speed (11.4 m/s). Under the action of nonlinear aerodynamics, the tower-base fore-aft bending moment and blade-root out-of-plane bending moment oscillate significantly.

**Figure 15.** Time histories of responses of the cage and wind turbine under condition 3. (**a**) Cage responses. (**b**) Wind turbine responses.

**Figure 16.** Time histories of responses of the cage and wind turbine under condition 4. (**a**) Cage responses. (**b**) Wind turbine responses.

Several statistical properties, including mean, absolute maximum (Abs Max) and standard deviation of the fishing cage responses (surge, heave and pitch motions) and wind turbine responses (blade pitch angle, generator power, tower-base fore-aft bending moment and blade–root out-of-plane bending moment) are calculated as evaluation indices, as shown in Figure 17. Standard deviations of responses are plotted as error bars on top of mean values.

**Figure 17.** Statistical properties of the cage and wind turbine responses. (**a**) Cage responses. (**b**) Wind turbine responses.

For the statistical results of cage responses, it is seen that the heave and pitch motions exhibit similar patterns with almost zero mean values, while the surge motion dominates the cage response. The peak value of mean surge motions occurs at the rated wind speed condition. In addition, it is observed that the maximums and standard deviations of the surge, pitch and heave motions all occur in the extreme wind condition. For the statistical results of wind turbine responses, with the increase in wind speed, the generator power output increases, and no power is output at the parked condition. The standard deviation of generator power reaches the largest at the rated wind speed condition. This is expected because the wind speed fluctuates frequently around the rated value. The mean and maximum values of the blade-root out-of-plane bending moment show a similar pattern. Specifically, the peaks of the mean and maximum blade-root bending moments occur at the rated wind speed condition, while the lowest values appear at the extreme condition. Moreover, the mean and maximum tower-base fore-aft bending moments have peak values at the rated wind speed condition, while the largest standard deviation occurs in the extreme condition.

### 5.3.2. Frequency Domain Analysis

In order to further investigate the effect of turbulent wind, a spectral analysis is performed for the cage and wind turbine responses. The smoothed spectra are shown in Figure 18. The spectra of wave elevation and horizontal wind speed are also plotted so that they can be used to compare each response spectrum and help to identify the source of the most energetic response.

**Figure 18.** Smoothed spectra of the cage and wind turbine responses under condition 3. (**a**) Cage responses. (**b**) Wind turbine responses.

From Figure 18a, it is observed that the surge motion is dominated by the lowfrequency responses due to the turbulent wind and surge resonant responses. A peak occurs at the surge resonant frequency, while the pitch motion and wave excitation also influence the surge motion. For the heave spectrum, two peaks occur at approximately 0.05 Hz and 0.1 Hz, which correspond to the heave natural frequency and wave natural

frequency component, respectively. The surge and pitch motions have no influence on the heave motion. For the pitch response, in addition to the low-frequency component of the turbulent wind, there are also obvious pitch resonance frequency and wave frequency components. Overall, the turbulent wind has some influence on the surge and pitch motions, but with no influence on the heave motion. The possible reason is that wind inclination is not considered in simulations, which means that the wind direction is always horizontal. Moreover, the wave frequency response generates some influence in all three DOFs.

From Figure 18b, it is observed that the tower–base fore-aft bending moment (TwrBsMy) is mostly affected by turbulent wind, in addition to the cage pitch motion, irregular waves and 2P-effect. Moreover, there is a small peak at approximately 0.6 Hz, which is possible due to the 3P-effect of the blades. For the blade–root out-of-plane bending moment (RootMy), it is obvious that the turbulent wind and 1P-effect have important effect on the blade response. Moreover, the 2P-effect and 3P-effect also contribute to the blade–root out-of-plane response.
