## 6 Simulation Results
### Case Studies
Case 3: The wind speed is 13 m/s, and the system suddenly increases the load by 0.5 MW at 5 s. The virtual damping coefficients \(D_{\text{vgg}}\) are 6 pu, 7.9 pu, and 9.87 pu, respectively, of which 9.87 pu is the virtual damping coefficient designed according to the strategy proposed in this paper. The simulation results are shown in Figure 11.  
As can be seen from Figure 11a, the increased load causes the system frequency to drop at 5 s. When the virtual damping coefficients are set as 6 pu, 7.9 pu, and 9.87 pu, respectively, the lowest points of frequency are 49.730 Hz, 49.752 Hz, and 49.773 Hz, respectively. At the same time, as the frequency drop rate is observed, it can be seen that the time to reach the lowest point is almost the same. However, when the \(D_{\text{vgg}}\) is 9.87 pu, the lowest point is higher than the other two values, which indicates that the frequency change rate can be reduced during the frequency drop period and the frequency recovery process is more moderate. Because the WTG is at a high wind speed, the rotor speed of the WTG does not change much. The WTG with frequency regulation ability increases the active power output and reduces the unbalanced power of the power system for frequency support. According to Figure 11c, when the virtual damping coefficient is set to 9.87 pu, the maximum active power output of the WTG is close to 1.2 pu, indicating that the proposed control strategy  
Figure 11: The results of Case 3. (**a**) Frequency. (**b**) Rotor speed. (**c**) Output active power of WTG. can make full use of the rotor kinetic energy of the WTG and satisfy the converter capacity within its limit. As a result, the frequency support capability of the WTG is improved. By analyzing the simulation results of Case 1, Case 2, and Case 3, it can be seen that under different wind speed conditions, the optimization method of the virtual synchronous control parameter proposed in this paper can effectively use the rotor kinetic energy of the WTG for PFR. At the same time, the physical constraint boundary of the PFR is guaranteed, and the frequency stability of the system is improved. Further, under the three cases of low wind speed, medium wind speed, and high wind speed, the proposed method is compared with the WTG without frequency regulation capability and the WTG with comprehensive inertia control [27]. Case 4: The wind speed is 9 m/s, and the system suddenly increases the load by 0.2 MW at 5 s. The strategy proposed in this paper is compared and analyzed with the WTG without frequency regulation control and the WTG with comprehensive inertia control. The simulation results are shown in Figure 12.  
As can be seen from the simulation results in Figure 12, compared with the comprehensive inertia control and the control without frequency regulation capability, the proposed strategy reduces the frequency deviation of the power system and slows down the frequency drop rate. It also improves the frequency stability of the system and fully releases the frequency regulation ability of the WTG. Compared with comprehensive inertia control, the proposed strategy in this paper increases the active power of the system at the initial stage of the frequency drop, which fully releases the kinetic energy of the rotor for WTG. By comparing different strategies, it can be seen that the frequency deviation of the strategy proposed in this paper is the smallest, and the lowest frequency is 49.822 Hz. Simulation results show that the proposed method can reduce the frequency deviation of the power system by 19.1% compared with comprehensive inertia control. When the WTG does not have the ability to adjust the frequency, the frequency deviation is the largest,  
Figure 12: Comparison results for Case 4. (**a**) Frequency. (**b**) Rotor speed. (**c**) Output active power of WTG. and the lowest frequency is 49.715 Hz.