Bi-Level Distribution System Parallel Restoration by Integrating Deep Reinforcement Learning with Physics-Based Optimization

Distribution system parallel restoration (DSPR) is a critical process for ensuring rapid power restoration and a resilient electricity supply following blackouts. However, the complexity of the DSPR problem, which encompasses the black start process, generator startup sequence (GSS), and sectional ization problems, poses significant challenges for rapid response due to the high computational burden from the large number of discrete decision variables involved. Thus, this paper proposes a novel bi-level DSPR method by integrating deep reinforcement learning (DRL) with physics-based optimization. Instead of solving the GSS and sectionalization problems in parallel, we design a hierarchical structure to effectively decouple the huge action space. In the upper level, DRL addresses the sectionalization problem, while the GSS problem is formulated as a mixed integer linear programming (MILP) model based on the system sectionalization results in the lower level. Once the strategies determined by the proposed method are implemented, the resulting total restoration time is used as the reward feedback. Experimental results on standard IEEE test distribution systems demonstrate the superiority of the proposed method in terms of both restoration performance and computational efficiency.