Short-circuit fault current suppression is a very important issue in modern large-interconnected power networks. Conventional short-circuit current limiters, such as superconducting fault current limiters, have to increase additional equipment investments. Fast power electronics controlled flexible AC transmission system (FACTS) devices have opened a new way for suppressing the fault current levels, while maintaining their normal functionalities for steady-state and transient power system operation and control. Thyristor controlled phase shifting transformer (TCPST) is a beneficial FACTS device in modern power systems, which is capable of regulating regional power flow. The mathematical model for TCPST under different operation modes is firstly investigated in this study. Intuitively, the phase shifting angle control can adjust the equivalent impedance of TCPST, but the effect has been demonstrated to be weak. Therefore, a novel transformer excitation impedance switching (EIS) control method, is proposed for fault current suppressing, according to the impedance characteristics of TCPST. Simulation results on IEEE 14-bus system have shown considerable current limiting characteristic of the EIS control under various fault types. Also, analysis of the timing requirement during fault interruption, overvoltage phenomenon, and ancillary mechanical support issues during EIS control is discussed, so as to implement the proposed EIS control properly for fast fault current suppression.