Single-phase low current grounding faults areoften seen in power distribution system of coal mines. These faults are difficult to reliably identify. We propose a new method of single-phase ground fault protection based upon a discernible matrix of the fractal dimension associated with line currents. The method builds on existing selective protection methods. Faulted feeders are distinguished using differences in the zero-sequence transient current fractal dimension. The current signals were first processed through a fast Fourier transform and then the characteristics of a faulted line were identified using a discernible matrix. The method of calculation is illustrated. The results show that the method involves simple calculations, is easy to do and is highly accurate. It is, therefore, suitable for distribution networks having different neutral grounding modes.