## 5 Simulation Study
### Determination of the Control Parameters  
In order to select the appropriate control parameters, the numerical statistical curves with different control parameters are drawn, as shown in Figure 10. In the simulation, the wind speed at the hub center is constant at 14 m/s, the regular wave height is 2.4 m, the wave period is 6 s, and the wind and  
Figure 8: Time domain and frequency domain results of the blade root flap-wise load without and with random wave: (**a**) The blade root flap-wise load; (**b**) Frequency spectrum density of the blade root flap-wise load. Figure 7: Time domain and frequency domain results of the fore-aft load on tower at the MWL without and with random wave: (**a**) The fore-aft load on tower at the MWL; (**b**) Frequency spectrum density of the fore-aft load on tower at the MWL. Figure 9: Time domain and frequency domain results of the aerodynamic torque without and with random wave: (**a**) The aerodynamic torque; (**b**) Frequency spectrum density of the aerodynamic torque. wave are in a consistent direction. To select the appropriate control parameters, the standard deviations of aerodynamic torque, blade root flap-wise load and wind wheel speed are tracked since the standard deviation of dynamic responses is a better representation for the fluctuation level of vibration. Figure 10a shows that the standard deviation of aerodynamic torque decreases first and then increases with the increase of \(G^{\prime}\). According to Equation (18), when \(-(\hat{T}_{aero})^{\prime}_{\beta}G^{\prime}>(\hat{T}_{aero})^{\prime}_{\
u}\), the additional torque will add a new fluctuation component after offsetting the fluctuating component of hydrodynamic frequency in aerodynamic torque. So, when \(G^{\prime}>0.04\), the standard deviation of aerodynamic torque increases with the increase of \(G^{\prime}\). From Figure 10b,c, it can be seen that the standard deviation of wind wheel speed increases with the increase of \(K_{p}\) and \(K_{i}\), and within a certain range, the standard deviation of the blade root flap-wise load decreases with the increase of \(K_{p}\) and \(K_{i}\), but when \(K_{p}\) and \(K_{i}\) are large at the same time, the vibration of the blade root will be aggravated. Considering the stability of the wind wheel speed, that is, the stability of output active power, and further considering the stability of the blade root flap-wise load, the \(K_{p}\) value in this paper should be less than 0.6, and the \(K_{i}\) value should be less than 0.004. For comparison, here we use turbulent wind and random waves instead of constant wind speed and regular waves. Suppose the turbulent wind intensity is 0.08, the average wind speed at the hub is 14 m/s, the significant wave height of the random wave is 2.5 m, the spectrum peak period is 9.5 s, and the wind and waves are in a consistent direction. The response of aerodynamic torque, blade root  
Figure 10: Control performance with different pitch control parameters: (**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 \(K_{p}\), \(K_{i}\). load and wind wheel speed of the wind turbine with different pitch control parameters after changing working conditions is shown in Figure 11.  
From Figure 11, it can be seen that the response of aerodynamic torque, blade root load and wind wheel speed of the wind turbine with different pitch control parameters under random wind-wave conditions is similar to that under regular wind-wave conditions. The suitable ranges of \(K_{p}\) and \(K_{i}\) remain unchanged, but the suitable range of \(G^{\prime}\) is reduced.