Smart grids have various capabilities to meet the electricity demands of modern society in production and life, and real-time monitoring of smart grids is critical to enhance the reliability and operational efficiency of power utilities. With the development of artificial intelligence technology and cloud computing, several studies have proposed using the powerful computing ability of clouds to design fault detection systems based on deep learning. However, due to the transmission delay in the Internet backbone and the large amount of data uploaded to the system, various problems arise such as a large bandwidth load and poor real-time feedback from the cloud platform. To solve these problems, it is necessary to embed the artificial intelligence technology at the edge of a network to realize a de-centralized system. In this paper, we propose an edge computing assisted smart grid fault detection system that uses an embedded lightweight neural network device, which is placed near the edge of the monitored equipment to realize real-time monitoring. In addition, considering the limited communication resources, relatively low computation capabilities, and different monitoring accuracies of edge devices, we design an optimal allocation method for communication and computation resources, which can maximize the throughput of the system, and improve the resource utilization of the system while meeting the requirements of data transmission and delay processing. Finally, simulation experiments are carried out to show that compared with other structures of smart grid fault detection systems, our proposed system can transmit more data while meeting the requirements of the delay bound, reduce the time required for transmission, and enhance the real-time performance of smart grid fault detection systems.