A digital short-circuit distance relay that is used for a three-phase AC power system comprising: a direction element for receiving a voltage and a current from each phase of the three-phase AC power system, and identifying a direction of a fault based on the input voltage and input current; and a short-circuit distance relay element for identifying a fault point by calculating for each phase an impedance value from the voltage and the current, comparing the impedance with a setting impedance value of a distance element, and judging an electrical distance from a relaying point to the fault point based on a compared result, the digital short-circuit distance relay further comprising: an impedance calculation part for calculating an impedance value of at least one phase in which the direction element has identified; and a minimum phase selection part for selecting, as a fault phase, the phase that has a minimum impedance value calculated by the impedance calculation part , wherein the short circuit distance relay element includes a plurality of stage elements; and wherein an output from the minimum phase selection part regarding the fault phase selected by the minimum phase selection part , when the impedance value of the fault phase is equal to or less than the setting impedance value of the distance element of the fault phase, is configured to allow an output of the distance element of the fault phase to be valid to output the opening command to a circuit breaker. a direction element for receiving a voltage and a current from each phase of the three-phase AC power system, and identifying a direction of a fault based on the input voltage and input current; and a short-circuit distance relay element for identifying a fault point by calculating for each phase an impedance value from the voltage and the current, comparing the impedance with a setting impedance value of a distance element, and judging an electrical distance from a relaying point to the fault point based on a compared result, the digital short-circuit distance relay further comprising: an impedance calculation part for calculating an impedance value of at least one phase in which the direction element has identified; and a minimum phase selection part for selecting, as a fault phase, the phase that has a minimum impedance value calculated by the impedance calculation part , wherein the short circuit distance relay element includes a plurality of stage elements; and wherein an output from the minimum phase selection part regarding the fault phase selected by the minimum phase selection part , when the impedance value of the fault phase is equal to or less than the setting impedance value of the distance element of the fault phase, is configured to allow an output of the distance element of the fault phase to be valid to output the opening command to a circuit breaker. an impedance calculation part for calculating an impedance value of at least one phase in which the direction element has identified; and a minimum phase selection part for selecting, as a fault phase, the phase that has a minimum impedance value calculated by the impedance calculation part , wherein the short circuit distance relay element includes a plurality of stage elements; and wherein an output from the minimum phase selection part regarding the fault phase selected by the minimum phase selection part , when the impedance value of the fault phase is equal to or less than the setting impedance value of the distance element of the fault phase, is configured to allow an output of the distance element of the fault phase to be valid to output the opening command to a circuit breaker. <EOS>