With the continuous expansion and increasing complexity of electrical systems, traditional state estimation and fault location methods no longer meet the accuracy requirements of modern electrical systems. Graph Neural Networks (GNNs) and Variational Autoencoders (VAEs), as emerging machine learning technologies, have shown great potential in handling complex network structures and potential data representations. This article proposed a state estimation and fault localization method for a multi-machine power system that combines neural graphs and variational autoencoders. Firstly, neural graph networks were used to capture the topology and relationships between nodes in the energy system. Secondly, learning the latent representation of the system state through variational autoencoder can improve the accuracy of state estimation. Finally, combining the advantages of both, the fault can be quickly located. The experimental results indicate that the current system load is within the normal range of 110 nm to 140 nm. By monitoring the voltage level track, potential fault risks can be detected in a timely manner.