## 6 Simulation Verification and Analysis
### The Analysis of Transient Oscillation Suppression Mechanism with Different VSG Control Strategies  
To further illustrate the advantages of the APFBC-VSG control strategy, a comparative simulation was performed among TVSG control, TDP-VSG control, and APFBC-VSG control, each configured with optimal control parameters. Each control strategy's dynamic and static characteristics were analysed under given power disturbances and grid frequency disturbances. The simulation parameters are as follows: for TVSG control, the steady-state damping coefficients \(D_{\omega}\) are set at 0 and 20; for TDP-VSG control, the transient damping coefficient \(D_{\text{s}}\) is 30 with the decay time constant \(T_{\text{d}}=0.5\); for APFBC-VSG control, the transient compensation coefficient is \(K_{\text{FB}}=20\) with the decay time constant \(T_{\text{FB}}=0.006\). The simulation results are detailed in Figure 15, and the values of VSG response overshoot for each control strategy are summarized in Table 4.  
Based on the data presented in Figure 15 and Table 4, it is evident that when \(D_{\omega}=0\), the TVSG control exhibits substantial oscillations under both given power disturbances and  
Figure 14: Simulation results of APFBC-VSG control under different compensation coefficients. Figure 15: Simulation results under different VSG control strategies: (**a**) active power output characteristic simulation curve; (**b**) frequency output characteristic simulation curve. grid frequency disturbances, with the power overshoot of 7.6 kW and 3.5 kW, respectively, and a prolonged transient oscillation duration. When \(D_{\omega}=20\), the damping in TVSG control effectively suppresses transient oscillations but leads to considerable steady-state power deviation. The TDP-VSG control, incorporating transient damping, significantly enhances system transient stability and alleviates steady-state power deviation issues. Nonetheless, it continues to exhibit substantial power overshoot problems, with the power overshoot of 0.7 kW and 3.5 kW under given power disturbances and grid frequency disturbances, respectively. In contrast, the proposed APFBC-VSG control strategy effectively mitigates system transient oscillations and power overshoot under both given power and grid frequency disturbances, significantly reduces system regulation time, and provides superior frequency response performance. Compared to alternative control strategies, it achieves faster response rates, reduced frequency deviations, and offers exceptional frequency support capabilities, fully utilizing VSG control's damping and inertia characteristics in high renewable energy penetration scenarios. Figure 16 illustrates the simulation results comparing currents under various VSG control strategies. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**VSG Control Method**} & \multicolumn{3}{c}{\(G_{\text{PP}}\)**(s)**} & \multicolumn{3}{c}{\(G_{\text{PP}}\)**(s)**} \\ \cline{2-7}  & **Percent (\%)** & **Value** & **Adjust Time** & **Percent (\%)** & **Value** & **Power** & **Adjust Time** \\  & **Percent (\%)** & **(W)** & **(s)** & **(W)** & **Deviation (W)** & **(s)** \\ \hline TVSG (\(D_{\omega}=0\)) & 50.7 & 7610 & 1.2 & 131.3 & 1970 & 0 & 1.4 \\ TVSG (\(D_{\omega}=20\)) & 1.5 & 220 & 0.3 & 0.3 & 30 & 3950 & 0.4 \\ TDP-VSG (\(D_{\text{s}}=30\)) & 4.7 & 700 & 0.5 & 235.1 & 3527 & 0 & 1.2 \\ APFBC-VSG (\(K_{\text{FB}}=20\)) & 0.5 & 70 & 0.4 & 4.0 & 60 & 0 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The overshoot characteristics of VSG systems under different VSG control strategies. Figure 16: Simulation results of grid-connected output current under different VSG control strategies: **(a)** The simulation output three phase current of TVSG (\(D_{\omega}=0\)); **(b)** The simulation output three phase current of TVSG (\(D_{\omega}=20\)); **(c)** The simulation output three phase current of TDP-VSG (\(D_{\text{s}}=30\)); **(d)** The simulation output three phase current of APFBC-VSG (\(K_{\text{FB}}=15\)).