A novel extended network for service restoration optimization problem under distributed generation scenarios is presented in which the main network restoration and DG island restoration problems are integrated into a unified spanning-tree problem. The proposed technique is aimed to realize synchronous optimization of both main network and island restorations

and thus ensure the algorithms that are used find the global optimization solution. A fast loop-breaking technique is also proposed in this paper. Based on the circuit-branch correlation matrix

the proposed technique can break the loops in the distribution systems through matrix operations that significantly improve calculation speeds. Simulation results verify the correctness and advantage of the proposed algorithms: the proposed integrated optimization strategy based on the extended network has better performance compared with a two-step restoration strategy; also

the proposed loop-breaking technique has faster calculation speed compared with prim algorithm and DFS based on adjacent matrix.