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Most of the transmission system has a network structure to improve the reliability and stability of a power system. Fault current is continuously expected to increase by the increase of the power demand. If fault current exceeds the cutoff capacity of a circuit breaker, the circuit breaker is broken and the damage by fault current is expanded throughout the power system. Superconducting fault current limiter (SFCL) was designed to solve this problem in a power system. In this paper, we investigated the current limiting characteristics and power burden of superconducting elements of a flux-coupling type SFCL in three-phase power system. A Flux-coupling type SFCL is one of the resistive type SFCLs. The flux-coupling type SFCL was made by using a transformer. Reactors connected in each phase shared an iron core. When the superconducting elements were quenched in fault phase, the fault current flowed into the primary and secondary coils simultaneously. Thus, the current flowed into primary and secondary coils of sound phase by the magnetic coupling flux. Meanwhile, when the current of sound phase exceeded the critical current of the SFCL, superconducting elements connected in the sound phase were quenched. The value of the fault current tended to decrease as the first reactor's ratio increased. Furthermore, the power burden of the superconducting element was reduced. The reduced power burden of the superconducting elements shortens the recovery time of the superconducting element, which is advantageous for cooperation with a reclosing system when the SFCL is applied to the system. As a result, we confirmed that the flux-coupling type SFCL operated effectively in the three-phase power system.