The virtual synchronous generator (VSG) control is increasingly adopted in multi-paralleled photovoltaic generation systems (MP-PGSs) due to its enhanced grid-support capability. While the transient stability of VSG-controlled photovoltaic generation systems (PGSs) under symmetrical grid faults is well-studied, instability mechanisms under asymmetrical grid faults (AGFs) remain underexplored. This paper establishes a multiple coupling analysis model for transient stability analysis of VSG-controlled MP-PGSs under AGFs. Based on this model, the impacts of coupling dynamics including sequence coupling and mutual coupling on the transient stability of VSG-controlled MP-PGSs are investigated. Furthermore, the influence laws of key parameters on the transient stability are analyzed. To improve the low voltage ride-through capability of MP-PGSs under AGFs, a multi-objective stabilization control method is proposed, which satisfies both the grid codes and current limitation requirements. Finally, simulation results validate the correctness of the theoretical analysis and the effectiveness of the proposed control method.