The superconducting magnet power supply for the Comprehensive Research Facility for Fusion Technology (CRAFT) has the abilities of large current steady-state operation, high power pulse operation and transient fault suppression, which is closely related to the short circuit impedance of converter transformer. On the basis of parameters of AC system and equivalent circuit model of converter transformer, the relationship between the performance of superconducting magnet power supply and the short circuit impedance of converter transformer is studied. The research shows that the small short circuit impedance is beneficial to the output voltage and the reactive power loss of superconducting magnet power supply, but the short-circuit fault current and harmonic current increase accordingly. For short-circuit impedance design for converter transformer purposes, firstly, short-circuit impedance must satisfy the transient fault suppression capability and the rated output voltage, and secondly, it is easy to suppress the high characteristic harmonic current brought by thyristor multi-phase converter for CRAFT, hence small short-circuit impedance should be chosen.