Existing fault location algorithms only adapt to small samples and heavily depend on data. If abnormal data exists, it will cause larger positioning errors, and the fault area and fault location need to be solved separately. In this paper, the manifold learning method is used to extract global information in a smart grid. This makes full use of the fault information contained in the high-dimensional data. A unified model of fault area and fault location is constructed, which can get rid of the dependence on data through L1 + L2 constraints. The parameters in the algorithm are uniformly learned by the Adagard method, which can automatically adjust the learning efficiency and improve the accuracy and speed of parameter learning. The IEEE39 bus system built in PSCAD proves the algorithm's robustness and high precision in different scenarios. This work is supported by National Natural Science Foundation of China (No. 51520105011).