High impedance faults constitute one of the biggest challenges in electrical power systems. In overhead distribution systems, faults are caused by tree branches that touch the electrical grid or by the rupture of energized conductors on low conductivity soils. They are also known as low-current faults, which are not detected by conventional protection systems, compromising the quality of the power supply and causing hazardous risks to the electrical system. This paper aims to address the problem of high impedance faults detection using Artificial Neural Networks: two Multi Layer Perceptron networks, being one Neural Pattern Recognition and another Neural Fitting, and a Convolutional Neural Network. The neural networks are trained and analyzed in scenarios based on a medium-voltage distribution grid model, located in the Basque Country, Spain. The network topologies are implemented, repeatedly trained considering multiple architectures, and validated in other scenarios with different location, time, and duration of the fault using the Matlab software. After, the criteria of accuracy, reliability, security, safety and sensitivity are evaluated. At last, a comparative analysis between them is carried out, and from the results obtained, a superior performance of the Convolutional Neural Network in compared to the Multi Layer Perceptron networks is observed.