## 5 Improved VSG Control Strategy Based on Active Transient Feedback Compensation
### The Characterisation of APFBC-VSG Power Overshoot Suppression  
To facilitate a comprehensive analysis of the power overshoot suppression efficacy of the APFBC-VSG control strategy during grid disturbances, Table 3 presents the zero points distributions for TVSG, TDP-VSG, and APFBC-VSG under both given power disturbances and grid frequency disturbances. As derived from Equation (18), the APFBC-VSG control effectively eliminates the steady-state deviation associated with damping characteristics by setting \(D_{\omega}=0\). Consequently, this leads to a distinct zero distribution under grid frequency  
Figure 9: The trend of pole distribution in APL small-signal model of APFBC-VSG: (**a**) \(T_{\mathrm{FB}}\) = 0.004, \(K_{\mathrm{FB}}\) increases from 0 to 20; (**b**) \(K_{\mathrm{FB}}\) = 2, \(T_{\mathrm{FB}}\) increases from 0 to 20.  
disturbances in comparison to the TVSG control, where zero point \(-(D_{\omega}\omega_{0}+K_{\omega})/(J_{\omega}\omega_{0})\) is approximately equivalent to zero point \(-K_{\omega}/(J_{\omega}\omega_{0})\).  
Based on the earlier theoretical analysis, the APFBC-VSG control exhibits a smaller \(T_{FB}\) than the TDP-VSG control. Under given power disturbances, the zero point \(-1/T_{\rm FB}\) of \(G_{\rm PAPFBC}(s)\) is positioned significantly far from the imaginary axis, which effectively results in the absence of an overshoot in the active power response. For grid frequency disturbances, one zero point \(-1/T_{\rm FB}\) of \(G_{\omega\rm APFBC}(s)\) is situated far from the imaginary axis, resulting in a minimal overshoot in the power response characteristics. Additionally, another zero point \(K_{\omega}\) of \(-K_{\omega}/(J_{\omega}\omega_{0})\) holds a larger value, causing \(-K_{\omega}/(J_{\omega}\omega_{0})\) to be smaller than \(-1/T_{\rm d}\), which implies that zero point \(-K_{\omega}/(J_{\omega}\omega_{0})\) is situated further from the imaginary axis compared to zero point \(-1/T_{\rm d}\). Therefore, the overshoot observed in the APFBC-VSG system response is considerably smaller than that in the TDP-VSG system.  
To validate the theoretical analysis, Figure 10 presents the unit step response curves of the APFBC-VSG control under both given power disturbances and grid frequency disturbances, derived from the closed-loop transfer function in Equation (17). As illustrated in Figure 10a,b, increasing the power compensation coefficient enhances the active oscillation suppression performance of the APFBC-VSG system, significantly reducing the power overshoot under given power disturbances and grid frequency disturbances. These results align with the previous analysis; thus, the chosen value is \(K_{\rm FB}=20\). Figure 10c,d demonstrate that varying the decay time constant \(T_{\rm FB}\) has a negligible effect on system stability, supporting the earlier analysis. Consequently, \(T_{\rm FB}=0.006\) is selected.  
Figure 10: Transient response characteristics of APFBC-VSG under different control parameters: (**a**) The response curve of \(G_{\rm PD}(s)\) (\(T_{\rm FB}=0.006\)); (**b**) The response curve of \(G_{\omega\rm D}(s)\) (\(T_{\rm FB}=0.006\)); (**c**) The response curve of \(G_{\rm PD}(s)\) (\(K_{\rm FB}=2\)); (**d**) The response curve of \(G_{\omega\rm D}(s)\) (\(K_{\rm FB}=2\)).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**The Control Method** & **Gpp(s)** & \(\mathbf{G_{\rm PD}(s)}\) \\ \hline TVSG & \(-(D_{\rm s}\omega_{0}+K_{\omega})/(J_{\omega}\omega_{0})\) \\ TDP-VSG & \(-1/T_{\rm d}\) & \(z_{1},z_{2}\) \\ APFBC-VSG & \(-1/T_{\rm FB}\) & \(-1/T_{\rm FB},-K_{\omega}/(J_{\omega}\omega_{0})\) \\ \hline \end{tabular}
\end{table}
Table 3: The zero points distribution under different VSG control strategies.