## 5 Simulation Study
### Simulation and Verification of the Pitch Angle Control Strategy  
For comparison, simulations with the collective pitch control (CPC), the individual pitch control strategy based on combined azimuth and load feedback (CALF-IPC) [7] and the improved individual pitch control strategy (IIPC) proposed in this paper, are implemented both in the time domain and frequency spectrum respectively. In this case, the constant wind and regular wave conditions are the same as that in Section 5.2, wind shear and tower shadow are considered. The simulation results are shown in Figures 12-14. Figure 11: Control performance with different pitch control parameters under random wind-wave conditions: (**a**) Standard deviation of aerodynamic torque at different \(G^{\prime}\); (**b**) Standard deviation of blade root flap-wise load at different \(K_{p}\), \(K_{i}\); (**c**) Standard deviation of wind wheel speed at different \(K_{p}\), \(K_{i}\). Figure 12: Time domain and frequency domain results of blade root flap-wise load under different control: (**a**) Curves of the blade root flap-wise load; (**b**) Frequency spectrum density of the blade root flap-wise load. Figure 13: Time domain and frequency domain results of aerodynamic torque and output power under different control: (**a**) Curves of the aerodynamic torque; (**b**) Frequency spectrum density of the aerodynamic torque; (**c**) Frequency spectrum density of the output power. From Figure 12, it can be observed that both the proposed IIPC and the CALF-IPC contribute to reducing the fluctuation amplitude of blade root flap-wise load by periodically adjusting the pitch angle of three blades. Moreover, the proposed IIPC can better reduce the fluctuation of the blade root flap-wise load. It can be seen from Figure 12b that the 1P fluctuation component in blade root flap-wise load under the proposed IIPC is reduced by about 77% and 33%, respectively, compared with that under the CPC and the CALF-IPC. Meanwhile, shown in Figure 13, the proposed IIPC has better effectiveness to suppresses the fluctuation of aerodynamic torque than CALF-IPC. As can be seen from Figure 13b, the frequency spectral density of the aerodynamic torque at the hydrodynamic frequency (0.167 Hz) and at the 3P is noticeably reduced. The results show that the hydrodynamic frequency fluctuation component and the 3P fluctuation component in the aerodynamic torque are effectively suppressed. Furthermore, decreased fluctuation components in the output power with a frequency of 0.167 Hz are also observed in Figure 13c. This is because of the direct correlation between aerodynamic torque and output power. Therefore, the proposed IIPC reduces the fluctuation of aerodynamic load and improves the stability of output power. However, from Figure 14, under the proposed IIPC, the fluctuation of the pitch angle is increased, especially at the hydrodynamic frequency, 1P and 3P frequency, with the fluctuation of the blade root flap-wise load and aerodynamic torque reduced. This might be disadvantageous for pitch actuators, as it can slightly exacerbate fatigue damage to pitch actuators. In summary, simulation results demonstrate the effectiveness of the proposed IIPC in the smoothing fluctuation of the wind turbine blade root flap-wise load and aerodynamic torque caused by wave impact, wind shear and tower shadow, which is accomplished by aggravating the fatigue damage of the pitch mechanism via frequent pitch angle adjustment. In general, the proposed IIPC can suppress the vibration of the wind turbine, and it has a certain economy. In addition, considering wind shear and tower shadow, the effectiveness of the control strategy under turbulent wind and random wave conditions is studied, and the turbulent wind and random wave conditions are the same as that in Section 5.2.