One of the most faults found in the electrical distribution network is a single line to ground fault (SLGF). It can be detected and rectified through many methods. The utilization of Peterson coil (PC), reduces the electrical arcs and make the distribution network safe from damage in contrast to the cost value. This paper focuses on the method for its detection on higher and lower values of the ground fault current (GFC). Moreover, it will identify the capacitance and earth leakage of earthling network lines as well as calculate the opposing inductance to compensate for the cause. It also presents the selfextinguishing of GFC by controlling PC through one of the novel optimization techniques called adaptive and artificial bee colony with network neural (ABCNN) to improve the algorithm's performance, like optimization efficiency, speed, solution, and iteration. As a result, the determination of the GFC equals the sound phase current. Also, the extinguishing of an electric arc results in a short time compared with classical methods. The significant advantage of this research is the increment in the system's reliability, protection of devices as well as saving in copper cost. MATLAB was used to carry out this research. For the validity, the proposed algorithm results were compared with the classical method by creating faults on separate phases also.