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Non-effective neutral grounding is a common practice in the power distribution systems of some European and Asian countries. This configuration is also used in some industrial plants in North America. When single-phase-to-ground faults occur, the system can continue to operate without tripping immediately. This significantly improves the service reliability of the system. However, the faulted line must be identified within a required time frame (typically 30 minutes to 2 hours). It turns out that identifying the faulted line is a significant challenge. This challenge has attracted a lot of research work since 1980's. Although many methods have been proposed or developed, there is still no satisfactory solution to the problem. This paper proposes a new method to solve the problem basing on the system identification theory. The idea is to use the disturbance produced by the fault to determine the impedance of the unfaulted side of the system. The sign of the impedance can reveal which line is experiencing a single-phase to ground fault. In other words, the proposed method is an improved version of the directional relay concept for application of the faulted line identification. This paper presents detailed research results on the proposed method. The method is evaluated using computer simulations and lab experiments. Several improvements of the method are made based on the results. The results show that the proposed method can work effectively under various system situations and it is a viable competitor to the existent methods.