In this research thesis, according to the input properties of the graph neural network model, the structural characteristics and node attribute natures of the distribution network are selected as the input features which are used in the distribution network graph data. Through the comparison of the zero-sequence current wave shapes at the two ends of one section, the earth-fault section can be gotten out.Utilizing the measurement data which come from two sides of the faulted section, a quantum variation autoencoder ranging model which has been studied by us is established. This model makes the broken voltage and current phase wave forms connect with the fault distance. After that, an end-to-end strategy for fault position finding has been devised by us.The distribution network model is constructed and simulation experiments of ground fault detection are carried out. The initial 15 features are downscaled by Pearson’s correlation coefficient, and 12 key features are retained after removing redundancy. Based on the experiments which were carried out on 20 test samples, the discrimination error of the method put forward in this paper is obviously better than that of the full connection neural network. When it is put under the simulated load casting and noise interference situations which appear in the process of real working, the average distinguishing error of the method which is written here rises to 0.033. Notwithstanding this point, it yet maintains a relatively elevated degree of stability. The research that this paper has done puts forward a brand new method for the intelligent breakdown judgement of distribution power networks. This method possesses high exactness, strong anti-disturbance abilities, and cheap calculation costs. This possesses very important practical meaning for promoting the safety of power grid movement.