A reliable power system is essential to a functioning society and growing economy. Power system faults hinder system operations as well as in some cases jeopardize the public and property safety. Traditionally, the transmission level of power systems are less complicated and carefully monitored compared to interconnected distribution networks. Despite the distribution network's close interactions with consumers, it is less monitored and susceptible to life-threatening power system faults. The reliability, cost, and compatibility of sensors are the primary constraints to implement a large-scale sensing scheme at this level of networks. More so, some faults have a nonlinear pattern which demands an adaptive fault detection and locating system, which are not in practice. Magnetic sensors, particularly Magneto-Resistive (MR) sensors have the potential to utilize in the overhead line's current sensing, as they are contact-less, highly sensitive and accurate in measurements, yet cost-effective and compact. Machine Learning (ML) based algorithms are best suited to develop a non-restrained and generalized fault detection scheme. This thesis studies faults detection, classification and localizing issues in Low Voltage Distribution (LVD) networks and investigates the potential of MR sensors to provide generalized solutions to the problem. Steady-state and dynamic modeling, laboratory experimentation and computer simulation of LVD networks in New Zealand will be carried out to study and address the issue and propose generalized solutions.