Conventional grid-forming control often destabilizes voltage source converters (VSCs) in stiff grids, and transient synchronization instability will occur in the grid fault condition. Therefore, power self-synchronization control (PSSC) is first introduced for enhancing the small-signal stability of grid-forming control in the case of a short circuit ratio ranging from 1 to infinity. Meanwhile, the transient synchronization instability for the grid-forming converter with PSSC in the grid fault condition is analyzed by the phase portrait, and a transient stability enhancement control (TSEC) scheme is combined with a PSSC-based VSC, which can efficiently eliminate the risk of losing synchronization in the arbitrary SCR. Finally, experimental results are provided to confirm the theoretical analysis.