## 4 TDC-VSG Control Strategy
### Transient Performance Analysis of the TDC-VSG  
Through the comparison and analysis of Equations (7) and (12), it becomes evident that the TDC-VSG introduces a zero point and a pole into the APL system; the location of the zero point is associated with \(T_{\text{T}}\). When \(T_{\text{T}}\) is small, Equation (12) approximates Equation (7), leading to less pronounced damping characteristics of the TDC-VSG; hence, \(T_{\text{T}}\) should not be excessively small. To analyze the influence of control parameters \(T_{\text{T}}\) and \(D_{\text{T}}\) on the transient stability of the TDC-VSG, the pole distribution trend of \(G_{\text{PTIDp}}(s)\) under varying \(T_{\text{T}}\) and \(D_{\text{T}}\) is constructed in Figure 6.  
Figure 5: Small-signal model of the APL in the TDC-VSG. Figure 6: The trend of pole distribution of the APL system in the TDC-VSG. Figure 6a shows that at \(T_{\rm T}\) = 0.5, the TDC-VSG's real pole \(s_{\rm T3}\) is near the imaginary axis. Similarly, poles \(s_{\rm T1}\) and \(s_{\rm T2}\) are also close to the imaginary axis, suggesting that the APL system is prone to oscillation. However, as \(D_{\rm T}\) increases, the real pole \(s_{\rm T3}\) gradually moves away from the imaginary axis while remaining as a real pole, and \(s_{\rm T1}\) and \(s_{\rm T2}\) move closer to the real axis, resulting in enhanced stability performance of the dynamics of the system. At \(D_{\rm T}\) = 17.3, the dominant poles \(s_{\rm T1}\) and \(s_{\rm T2}\) transition from conjugate poles to real-axis poles, causing the TDC-VSG system to shift from underdamped to overdamped characteristics, significantly improving oscillation suppression performance, thereby validating the effectiveness of the TDC-VSG. As shown in Figure 6b, when \(D_{\rm T}\) = 20, the new pole \(s_{\rm T3}\) of the TDC-VSG rapidly approaches the imaginary axis with increasing \(T_{\rm T}\). However, the system stability is primarily influenced by the conjugate poles \(s_{\rm T1}\) and \(s_{\rm T2}\), which are very close to the imaginary axis, preventing \(s_{\rm T3}\) from becoming the dominant pole. Furthermore, as \(T_{\rm T}\) increases, the distance between the conjugate poles and the imaginary axis exhibits only minor changes initially and gradually approaches the imaginary axis later, indicating that the overall variation is limited. This results in a small change in the system's damping ratio, suggesting that \(T_{\rm T}\) has minimal impact on the transient stability of the APL system in the TDC-VSG. Consequently, the transient stability of the APL system in the TDC-VSG is predominantly determined by the transient damping coefficient \(D_{\rm T}\). Additionally, a large \(T_{\rm T}\) extends the transient oscillation process due to hysteresis characteristics; therefore, the selection of \(T_{\rm T}\) should not be too large, so this paper takes \(T_{\rm T}\) = 0.5. To verify the impact of \(D_{\rm T}\) on system stability performance, the unit step response characteristic curve of the APL system in the TDC-VSG under given power and grid frequency variations is constructed based on Equation (12), as shown in Figure 7. It can be seen from Figure 7a that increasing \(D_{\rm T}\) enhances the power oscillation suppression characteristics of the system under active power disturbances. Figure 7b illustrates that introducing \(D_{\rm T}\) eliminates the steady-state deviation caused by the fixed damping control strategy under grid frequency variations; however, excessive transient damping \(D_{\rm T}\) prolongs the recovery time to the steady-state. Thus, the system's dynamic response performance and stability can be enhanced through a reasonable configuration of \(D_{\rm T}\). As illustrated in Figure 7c,d, when \(T_{\rm T}\) is small, the Transient Damping Compensation characteristic of the TDC-VSG is not pronounced, and the system continues to exhibit transient oscillations. When \(T_{\rm T}\) = 0.5, the system's power oscillation can be effectively suppressed.