This paper proposes a trigger type superconducting fault current limiter (SFCL), which consists of a switch, two superconducting modules, and two series connected current limiting resistances (CLRs), using twice triggering operations. The suggested trigger type SFCL has twice the triggering operations according to the amplitude of the fault current. However, these operations are thought to affect the operation of the protective relay in a power distribution system. According to the fault conditions that affect the operation of the protective relay in a power distribution system, the fault location was selected. With two representative fault locations, the fault current limiting and the bus-voltage sag suppressing characteristics in a power distribution system with the suggested SFCL were analyzed. For comparative studies, the operation of the protective relay due to the conventional trigger type SFCL using one CLR was additionally described.