The fault line segment location is a difficult problem of the feeders of low-voltage distribution network due to the short line segment length, a large number of line branches and complex field conditions. Moreover, the scheme that deploying a fault monitoring device at each node is impractical due to limited equipment investment. It is of practical significance to study the method of optimal configuration of fault location devices in low-voltage active distribution networks. In this paper, fault monitoring devices installed at the line section switches or tie switches are employed to monitor fault current information, the edge computing technology is applied to the fault location system. And the number of the head end of each feeder line involved in a fault occurring in each feeder section is counted to calculate the node participation degree. The objective function of the optimal monitoring device configuration is built by comprehensively considering the overall participation and the uniformity of the monitoring units, and the economic constraint is considered. The correctness and effectiveness of the proposed method are verified by multiple simulations. The proposed method can effectively ensure the accuracy of fault location in low-voltage active distribution network, and improve the reliability and economy of low-voltage distribution network operation.