The stability of Power system installed Hi-Tc Superconducting Fault Current Limiter(SFCL) is analyzed as a process of developing SFCL. For investigation, a simple mimic system(only one generator) is assumed and then the circuit with SFCL in that system is solved for transient performance. In case the SFCL is installed in the power system, it protected synchronization more effectively both in symmetrical 3-phase fault and single phase line to ground fault in that the machine remains in synchronism for the more time than of without superconducting fault current limiter. It shows that the superconducting fault current limiter not only limits fault current but also protest synchronism. So for design of this SFCL, its synchronism protection property must be considered.