Abstract: To address the problems of insufficient reactive voltage support and poor characteristics faced by virtual synchronous generator (VSG) under low/over-voltage faults, this paper proposes an equivalent circuit model of virtual synchronous machines considering the current limitation, and the geometric characterization method regarding several reactive power and voltage controls on the phase diagram of the equivalent circuit is given based on the topological homotopy method. By leveraging the proposed method, the current-constrained transient voltage supporting mechanism of the VSG under several common Q/U controls is revealed, and an improved fault ride-through (FRT) control method is proposed, which effectively improves the transient voltage supporting performance of the VSG under low/over-voltage faults of the grid as well as the power angle stability during the fault ride-through process. The mechanism revealed in this paper and the proposed FRT control method are verified via PSCAD/EMTDC simulation. Finally, the performance of the proposed FRT control method is also verified in a three-machine-nine-bus system subjected to short circuit faults occurring in both near and far zones.