## 7 Experimental Verification  
To further validate the effectiveness of the proposed control strategy, experimental verification was carried out on a hardware-in-the-loop (HIL) system development platform, as depicted in Figure 17. The experimental procedure involved splitting the real-time model of the system. The system's main circuit topology was uploaded to the HIL real-time simulator's field-programmable gate array (FPGA), while the control program was loaded onto the central processing unit (CPU). A mapping relationship between the main circuit and the control program was established through the host computer interface. This configuration enabled the execution of the hardware-in-the-loop (HIL) semi-physical experiment. The control parameters used in the hardware experiments were aligned with those employed in the simulations. Test Condition 1 involved stepping the active power command \(P_{\text{ref}}\) from 0 kW to 15 kW, whereas Test Condition 2 maintained \(P_{\text{ref}}\) at 15 kW while increasing the grid frequency from 50 Hz to 50.1 Hz. The detailed experimental results are illustrated in Figure 18.  
As shown in Figure 18a, when \(D_{\omega}\) = 0, the TVSG exhibits significant transient oscillations under active power disturbances, with a power overshoot of 5.5 kW and a frequency deviation of 0.34 Hz. When \(D_{\omega}\) = 20, the transient oscillations and power overshoot are effectively mitigated, reducing the system's frequency deviation to 0.18 Hz. The inclusion of transient damping in the TDP-VSG control successfully suppresses transient oscillations during active power disturbances, resulting in a smaller power overshoot and a frequency deviation of 0.16 Hz. Notably, the proposed APFBC-VSG control almost completely eliminates transient oscillations and power overshoot during active power  
Figure 17: HIL hardware experiment platform.  
disturbances, achieving a frequency deviation of 0.26 Hz and enabling a smooth transition in VSG output power.  
As shown in Figure 18b, when \(D_{\omega}=0\), the TVSG experiences significant transient oscillations when the grid frequency drops by 0.1 Hz, with a power overshoot of 4.7 kW and a frequency deviation of 0.138 Hz. When \(D_{\omega}=20\), the transient oscillations and power overshoot are effectively mitigated, but a substantial steady-state power deviation of 7.2 kW remains. The TDP-VSG control, incorporating transient damping, successfully suppresses transient oscillations during grid frequency drops, although it still exhibits a power overshoot of 7.2 kW, with a frequency deviation of 0.134 Hz. The proposed APFBC-VSG control effectively suppresses both transient oscillations and power overshoot during grid frequency drops and demonstrates a faster regulation rate compared to other control strategies.  
In summary, TVSG control with fixed damping efficiently mitigates transient oscillations under both given power disturbances and grid frequency disturbances, but it results in substantial steady-state active power deviations. The TDP-VSG control, utilizing transient damping, resolves the steady-state deviations caused by damping characteristics under grid frequency disturbances. However, it experiences severe power overshoot issues, which may result in transient currents exceeding limits and activating overcurrent protection. In contrast, the proposed APFBC-VSG control strategy demonstrates superior performance in suppressing transient oscillations and enhancing transient response compared to other control strategies. It maintains stable output power without overshoot under both given power and grid frequency disturbances, thereby offering robust support for integrating renewable energy sources into the grid.