When a fault occurs on a distribution line, transient fault signals fade quickly, leaving only a short period of time for measurement and sampling. In addition, timing discrepancies between multiple measuring devices affect the accuracy of fault localization. This study proposes a method for fault detection in distribution lines based on an auxiliary inductance approach, where auxiliary inductors are introduced after the trip to provide steady-state fault data for localization. For asymmetrical short-circuit faults, the fault voltage is calculated from current and voltage measurements at both ends of the line, and the ratio of positive to negative sequence voltages is used to compensate for the phase angle and generate fault location functions. For symmetrical short-circuit faults, the voltage ratio between two faulted phases eliminates asynchronous angles, facilitating the derivation of fault location functions. Simulation results show that this method achieves high accuracy and is robust to differences in fault location, transition resistance, fault types, and synchronous angles.