## 6 Simulation Verification and Analysis
### Analysis of the Dynamics of Different VSG Control Strategies  
To further confirm the feasibility of the TDC-VSG adaptive control strategy, simulation experiments on active power response were conducted for TVSG control, traditional adaptive control, and TDC-VSG adaptive control strategies under optimal control parameters, as illustrated in Figure 15. The detailed control parameters are as follows: the damping coefficients for the TVSG control strategy are configured to \(D_{\omega}=0\) and \(D_{\omega}=K_{\omega}=7.6\); the  
Figure 14: Results of the TDC-VSG control strategy with different transient damping coefficients \(D_{\rm T}\).  
Figure 13: Results of the TDC-VSG control strategy with compensation coefficient \(K_{\rm j}\).  
compensation coefficients for traditional adaptive control are set at \(K_{\text{J}}=0.2\) and \(K_{\text{d}}=10\); and the compensation coefficient for the TDC-VSG adaptive control is set at \(K_{\text{J}}=0.9\), with the steady-state damping coefficient \(D_{\text{T}}=17.32\).  
As illustrated in Figure 15, at \(D_{\omega}=0\), the TVSG has obvious transient oscillation with power overshoots reaching 4.8 kW during active power disturbances. At \(D_{\omega}=7.6\), transient oscillations under the TVSG control strategy are effectively mitigated, reducing the power overshoot during given power variations to 1.6 kW. However, the steady-state deviation increases to 3 kW under grid frequency disturbances. Applying a traditional adaptive control strategy can significantly suppress power and frequency oscillations and reduce the frequency overshoot during given power variations. Nevertheless, the steady-state deviation during grid frequency variations reaches 4.7 kW, significantly compromising the steady-state performance of the TVSG system. The proposed TDC-VSG adaptive control strategy achieves a more rapid active response rate under given power and grid frequency variations. It effectively eliminates steady-state deviations caused by damping characteristics while suppressing transient oscillations, thereby enhancing the stability of grid-connected high-penetration distributed power supplies.  
Figure 16 shows the voltage and current waveforms corresponding to various control strategies. As shown in the figure, the TVSG's output current, which lacks damping characteristics, experiences significant transient oscillations. These oscillations are particularly pronounced during given power disturbances, grid frequency fluctuations, and the grid frequency recovery phase. Introducing fixed damping can effectively mitigate the transient oscillations in the current of the TVSG; however, the peak value of the current gradually increases during grid frequency disturbances. Introducing the adaptive compensation mechanism, the traditional adaptive control strategy significantly suppresses power and frequency oscillations in the output current during given power and grid frequency variations. Meanwhile, the peak value of the steady-state output current is greater in frequency drop scenarios.  
The TDC-VSG adaptive control strategy proposed in this study effectively mitigates transient oscillations caused by active power disturbances. It is designed to restore stability rapidly during grid frequency disturbances. Importantly, this strategy does not negatively affect the steady-state outputs of the current in the TDC-VSG, thus enhancing the operational stability of distributed power supplies integrated into the grid.  
Figure 15: Results of different VSG control strategies.