## 4 Trajectory Sensitivity Analysis  
In order to further select the frequency regulation coefficient of WTG that plays a leading role in the frequency regulation process, the correlation degree between the frequency regulation parameters and the frequency response of the power system is studied in this section. The trajectory sensitivity of parameters \(J_{\text{vsg}}\), \(D_{\text{vsg}}\), \(K_{\text{vsg}}\), and \(d\) will be calculated by using the differential form parameter perturbation method. Then, in the case of a certain amount of disturbance, the intensity of the influence of each parameter on the dynamic frequency process is analyzed. On this basis, the key frequency regulation parameter will be obtained. As shown in Equation (23), trajectory sensitivity \(S_{x_{1}}^{e}\) reflects the change of the observed quantity \(e\) when the parameter \(x_{\text{i}}\) changes; additionally, the observed quantity \(e\) represents the frequency response of the power system:  
\[S_{x_{\text{i}}}^{e}=\frac{\frac{e(x_{1},\,\cdots,\,x_{\text{i}}+\Delta x_{ \text{i}},\,\cdots,\,x_{\text{m}})-e(x_{1},\,\cdots,\,x_{\text{i}},\,\cdots,\, x_{\text{m}})}{e(x_{1},\,\cdots,\,x_{\text{i}},\,\cdots,\,x_{\text{m}})}}{ \Delta x_{\text{i}}/x_{\text{i}}} \tag{23}\]  
where \(\Delta x_{\text{i}}\) is the change of the parameter of number \(I\); m represents the total number of parameters to be analyzed. The frequency regulation parameter corresponding to the larger trajectory sensitivity has a strong dynamic trajectory influence on the frequency response. In other words, when the value changes slightly, the dynamic trajectory of the frequency response will change greatly. On the contrary, the dynamic trajectory of frequency response will not change significantly if the frequency regulation parameter corresponding to the smaller trajectory sensitivity changes slightly. By calculating the trajectory sensitivity of frequency regulation parameters such as \(J_{\text{vsg}}\), \(D_{\text{vsg}}\), \(K_{\text{vsg}}\), and \(d\), the influence degree of each parameter on the dynamic trajectory in the whole frequency response process can be obtained, as shown in Figure 8.  
As can be seen from the trajectory sensitivity curve of frequency response in Figure 8, the trajectory sensitivity of the virtual damping coefficient is the largest during the whole frequency regulation response process. The result shows that the virtual damping coefficient has a strong dynamic trajectory effect on the frequency response and plays a key role in the frequency regulation process. Since the actual system is usually a discrete system, the collected observed variables are discrete, while Equation (23) is mainly used to calculate the trajectory sensitivity of continuous observed variables. By discretizing Equation (23), the average sensitivity calculation formula of discrete observed variables can be obtained, as shown in Equation (24):  
\[S_{x_{\text{i}}}=\frac{1}{L}\sum_{n=1}^{L}\frac{\frac{e(n)-e_{0}(n)}{e_{0}(n)} }{\Delta x_{\text{i}}/x_{\text{i}}} \tag{24}\]  
where \(L\) is the total length of data. The different discrete sensitivities calculated by Equation (24) are shown in Table 2, which can represent the sensitivities of different variables quantitatively. According to Table 2, \(D_{\text{vsg}}\) has the largest discrete sensitivity, which is consistent with the analysis results of the trajectory sensitivity curve. Figure 8: Trajectory sensitivity curve. Therefore, the virtual damping parameter that is most correlated with the frequency response of the system is selected for design in order to improve the dynamic performance of the frequency response more specifically. Optimization of the Virtual Damping Parameter Based on the Physical Constraint Boundary of Frequency Regulation  
It can be seen from the above analysis that the virtual damping coefficient is selected for parameter optimization design.