This research paper deals with failures and faults in power smart grids. We propose an original multi-agent approach for power system recovery based on fault classification. For that, we propose the classification of faults as dominant or equivalent ones. This classification has the advantage of optimizing the task of power system recovery. To test and validate our approach, we develop a simulator, named FDIRSY (Fault Detection, Isolation and Recovery SYstem). The experimental study showed that our approach ensures the search for the best solution from the existing ones thanks to the use of mobile agents. These agents have the advantage of evaluating all the existing alternatives while reducing the communication cost (in terms of exchanged messages). We demonstrate that our approach is gainful in terms of required times, actions to be performed as well as the faults to be resolved thanks to the proposed fault classification.