## 6 Simulation Results
### Case Studies  
Case 1: The wind speed is 9 m/s, and the system suddenly increases the load by 0.2 MW at 5 s. Virtual damping coefficients are set as 2 pu, 4 pu, and 5.53 pu, respectively, where 5.53 pu is the result according to the design method in this paper. The simulation results are shown in Figure 9.  
According to Figure 9a, in the initial phase of the disturbance, the load on the power system increases and the frequency decreases. When the virtual damping coefficients are 2 pu, 4 pu, and 5.53 pu, respectively, the lowest points of frequency are 49.792 Hz,  
Figure 9: The simulation results of Case 1. (**a**) Frequency. (**b**) Rotor speed. (**c**) Output active power of WTG. 49.808 Hz, and 49.822 Hz, respectively. When \(D_{\rm vsg}\) is 2 pu, the frequency response reaches its lowest point after 2.52 s. When the \(D_{\rm vsg}\) is 4 pu, the time to reach the lowest point is 3.21 s. When the \(D_{\rm vsg}\) is 5.53 pu, the system frequency response drops to the lowest point after 3.92 s, indicating that the frequency change rate can be reduced during the frequency decline period when the \(D_{\rm vsg}\) is 5.53 pu, as well as that the recovery rate is more stable during the frequency recovery process. The WTG based on VSG control has the ability to regulate frequency; the rotor speed of the WTG decreases in the initial stage of frequency response, and the kinetic energy of the rotor is released for frequency support. Further, the active power output of the WTG is increased to compensate for the active power shortage of the power system. Figure 9b shows that when the virtual damping coefficient is set to 5.53 pu, the minimum rotor speed is close to but not less than 0.7 pu, indicating that the proposed strategy can make full use of the rotor kinetic energy of the WTG and improve the frequency stability of the system. Case 2: The wind speed is 11 m/s, and the load disturbance is 0.5 MW at 5 s. Virtual damping coefficients are set as 4 pu, 6 pu, and 8.05 pu, respectively, where 8.05 pu is the virtual damping coefficient optimized according to the method proposed in this paper. The simulation results are shown in Figure 10.  
In Figure 10a, in the initial phase of the disturbance, the unbalanced power of the system causes the frequency of the system to decrease. When the virtual damping coefficients are set as 4 pu, 6 pu, and 8.05 pu, respectively, the lowest points of frequency are 49.468 Hz, 49.476 Hz, and 49.490 Hz, respectively. In the process of PFR, when the \(D_{\rm vsg}\) is 4 pu, the frequency response reaches its lowest point after 3.01 s. When the \(D_{\rm vsg}\) is 6 pu, the time to reach the lowest point is 3.36 s. When the \(D_{\rm vsg}\) is 8.05 pu, it drops to the lowest point after 3.78 s, representing that the frequency change rate can be reduced when the \(D_{\rm vsg}\) is 8.05 pu. In the frequency recovery process, the change rate with \(D_{\rm vsg}\) (8.05 pu) is  
Figure 10: The simulation results of Case 2. (**a**) Frequency. (**b**) Rotor speed. (**c**) Output active power of WTG. more stable. The method proposed in this paper can improve the lowest frequency and the frequency change rate of the system. The WTG based on VSG control compensates for the unbalanced power of the kinetic energy of the rotor in the power system, which causes the rotor speed to decrease. In Figure 10b, when the virtual damping coefficient is set to the calculated value of the strategy proposed in this paper, the minimum rotor speed is 0.74 pu, indicating that the wind turbine unit makes full use of the available frequency regulation capacity to improve the frequency support performance of the WTG under the condition of stable wind speed. After the inertial response ends, the rotor speed of the WTG recovers, but due to the steady-state deviation of system frequency, the steady-state rotor speed of the WTG is less than the initial rotor speed.