New smart meters, distributed generation, renewable energy sources and the concern about the environment are redefining the way to conceive and operate electrical grids. To take full advantage of the new electrical smart grids we need to monitor and protect them. The capability of self-healing is thus important in smart grids in order to ensure a proper behavior under faults and reduce power outage times. For this purpose, this thesis proposes three different methods of fault diagnosis for low voltage (LV) distribution grids and two methods of fault isolation for grid-connected photovoltaic systems (GCPVs).In electrical power distribution systems, faults are responsible for 80% of customer interruptions. While several fault location methods for distribution grids exist in the literature, the majority of them focuses on medium voltage grids and low fault resistance values that rarely surpass the 100 Ohms. Taking into account that distribution system operators usually rely on phone calls to detect and locate faults in LV grids, the need for fault detection and location techniques that cover these cases, i.e. large fault resistances and LV distribution grids, is evident.The three fault detection and location methods proposed in this thesis are:1.A conventional fault detection method based on overcurrent monitoring in combination with a method that uses sparse voltage measurements to build the voltage profile across the faulty branch for fault location.2.Gradient boosting trees(GBT), a method that has been proven to excel in many applications the last few years.3.Deep neural networks(DNN), a method that improve the traditional neural network architecture by taking advantage of an increased number of hidden layers.Simulations on a real semi-rural LV distribution grid of Portugal are performed to validate the results. A common case study is used to compare the three methods. The influencing parameters are: a) a big variety of fault resistance values (63,772 values between 1 and 1000 Ohms), b) nine different fault locations within each sector, c) two fault types (single phase to ground and three phase faults), d) a simultaneity factor of 0.5, e) a big spectrum of PV generation and load demand scenarios with 70,334 studied combinations and f) a 2% underestimation error in measurements.Overall, DNN are the most reliable solution demonstrating a 100% accuracy in fault detection and an average of 12% of error in distance estimation. Moreover, under the minimum available measurements (on at the beginning of the feeder and one at each terminal node) case their accuracy is decreased by only 4.5%.At the same time, faults in PV generators, present an increased interest as well. A big variety of faults can occur in a PV power plant. Based on their location faults can appear: a) in the PV array, b) in the power converters, c) on the dc bus and d) in the grid side. The development of fast, efficient and reliable fault detection and isolation methods for GCPVs, capable of dealing with the different types of faults, is a recognized necessity from the scientific community and a prerequisite for their integration in the smart grids.So far, to the author’s knowledge, no research has been found to monitor the GCPV as a complete system, i.e. isolating faults in every part of the plant with a single method. For this reason, two algorithms based on a signal approach are proposed as a fault isolation strategy. They use current and voltage measurements at the output of the inverter, examining faults occurring on all four of the aforementioned possible locations. The choice of the output of the inverter, i.e. the point of common coupling, as the monitoring source of the status of the GCPV system is in accordance with the location of voltage sensors used in the previous case of fault location methods in the LV distribution grid. Finally, the proposed algorithms achieve an isolation of 15 out of the 19 studied faults cases in less than 100 ms.