Most permanent magnet synchronous generator (PMSG) based wind generation systems currently employ grid-following control, relying on a phase-locked loop (PLL) for grid connection. However, it leads to a lack of inertia support in the system. To address this, the virtual inertia control (VIC) is crucial for improvement, yet it introduces potential instability due to torsional oscillation interaction with PLL and low-frequency oscillations, which is an underexplored area. This paper presents a comprehensive analysis of the grid-connected PMSG-based wind generation system. It confirms the necessity of employing a full-order model for studying stability on the quasi-electromechanical timescale (QET) by a comparison with the reduced-order model. Then, a comprehensive modal analysis is conducted to analyze the effect of VIC parameters, shaft inertia time constant, PLL parameters, and torsional oscillation damping (TOD) controller gain on the interaction of QET oscillations under two typical control strategies. The occurrence of interaction and mode conversion is observed when the oscillation frequency and root loci of the torsional, PLL, and low-frequency oscillations are close. Finally, a theoretical analysis is validated via simulation verification in Simulink. These findings offer a valuable guidance for industrial PMSG applications considering VIC.