In this research, we create a single-phase to ground synthetic fault by the simulation of a three-phase cable system and identify the location using mathematical techniques of Fourier and modal transforms. Current and voltage signals are measured and analyzed for fault location by the reflection of the waves between the measured point and the fault location. By simulating the network and line modeling using alternative transient programs (ATP) and MATLAB software, two single-phase to ground faults are generated at different points of the line at times of 0.3 and 0.305 s. First, the fault waveforms are displayed in the ATP software, and then this waveform is transmitted to MATLAB and presented along with its phasor view over time. In addition to the waveforms, the detection and fault location indicators are presented in different states of fault. Fault resistances of 1, 100, and 1,000 ohms are considered for fault creation and modeling with low arch strength. The results show that the proposed method has an average fault of less than 0.25% to determine the fault location, which is perfectly correct. It is varied due to changing the conditions of time, resistance, location, and type of error but does not exceed the above value.
