  As electric power systems evolve towards decarbonization, the transition to
inverter-based resources (IBRs) presents challenges to grid stability,
necessitating innovative control solutions. Virtual synchronous generator (VSG)
emerges as a prominent solution. However, conventional VSGs are prone to
instability in strong grids, slow voltage regulation, and coupled power-voltage
response. To address these issues, this paper introduces an advanced VSG
control strategy. A novel analysis of the VSG control dynamics is presented
through a second-order closed-loop complex single-input single-output system,
employing a vectorized geometrical pole analysis technique for enhanced voltage
stability and dynamics. The proposed comprehensive controller design mitigates
issues related to control interacted subsynchronous resonance and $dq
\leftrightarrow 3\phi$ transformation-induced voltage-coupled power transients,
achieving improved system robustness and simplified control tuning. Key
contributions include a two-fold design: optimized voltage transition
characteristics through direct pole placement and transient power overshoot
correction via a compensator. Validated by simulation and experiments, the
findings offer a pragmatic solution for integrating VSG technology into
decarbonizing power systems, ensuring reliability and efficiency.
