## 1 Introduction
Based on this, a control strategy with flexible parameter selection to optimize the transient performance of the VSG is proposed. However, if the fault persists for an extended duration, the VSG will still encounter the challenge of desynchronization with the grid. The authors of [19] incorporate first-order differential compensation into the power swing equation of the VSG, effectively suppressing transient oscillations within the system without impacting the steady outputs of the APL system in the TVSG during grid-connected operation. However, this control strategy neglects the influence of high-frequency interference signals on system stability. The authors of [20; 21] introduce the first-order lead-lag compensator within the VSG damping feedback loop, enhancing the dynamics of the VSG while mitigating high-frequency interference effects during transient disturbances. However, this scheme does not describe the dominant pole assignment process for the APL. The authors of [22] introduce band-pass damping feedback control into the APL to construct transient damping managed by the VSG, enhancing the system's transient oscillation suppression performance. However, incorporating band-pass damping transforms the APL controlled by the VSG from a second-order system to a fourth-order system, which complicates the parameter design and may lead to power shocks. In addition, other scholars have explored controlling inertia and damping parameters in the APL by introducing fuzzy logic [23] and robust control [24]. In [25], a VSG control strategy based on fuzzy logic is provided, which effectively makes the dynamics of the APL more robust with increased adaptivity of damping and inertia. In [26], an adaptive control strategy predicated on the radial basis function (RBF) algorithm is applied. By introducing the RBF neural network into the APL system, this strategy adaptively adjusts the virtual inertia and damping coefficient, effectively enhancing the system's dynamic performance. However, the design of the fuzzy controller requires experienced personnel to verify its efficacy, and the difficulty of the design increases with the complexity of the electrical power system. Control strategies developed using neural network concepts require substantial data and time to assess their effectiveness, presenting challenges such as high sample dependency and a complex algorithmic structure. In view of the above problems, this article firstly establishes a closed-loop small-signal model of the TVSG under given power and grid frequency variations, analyzes the transient oscillation mechanism of the TVSG combined with root locus, and reveals the contradiction between the transient performance and steady-state performance of the TVSG control strategy. Secondly, a VSG control strategy incorporating Transient Damping Compensation (TDC) and virtual inertia adaptation is proposed. Utilizing the pole distribution trend and frequency response, the influence of control parameters introduced by TDC on system stability is qualitatively analyzed, and a tuning scheme for related control parameters is provided based on the dominant pole method. Subsequently, an improved virtual inertia adaptive strategy based on the ISRU approach rate is designed based on the TDC algorithm, providing the value range for adaptive changes in virtual inertia to optimize the dynamics of the TDC-VSG. Finally, the proposed strategy's effectiveness is verified through Matlab/Simulink simulations and Hardware-in-the-Loop (HIL) semi-physical experiments.