A Probabilistic Graph Reinforcement Learning for Resilient Service Restoration via Microgrid Formation

Service restoration in distribution systems after major outages is a complex and time-sensitive task under significant uncertainty and high penetration of distributed energy resources (DERs). Conventional deep reinforcement learning (DRL) methods typically rely on Markov decision processes (MDPs) and Euclidean state representations, limiting their ability to capture stochastic temporal dynamics and network topology. To address these challenges, this paper proposes a probabilistic graph reinforcement learning framework for microgrid formation. The restoration problem is formulated as a semi-Markov decision process (SMDP) to explicitly model stochastic state sojourn times. A Bayesian graph convolutional network is developed to jointly capture spatial dependencies and parameter uncertainty. Building on this, a novel Bayesian graph soft actor-critic (BGSAC) algorithm is proposed, where the entropy regularization coefficient is adaptively adjusted based on uncertainty estimates, enhancing exploration capability and robustness in uncertain environments. Experimental results on the IEEE 123-bus system demonstrate that the proposed method outperforms existing DRL approaches in convergence stability and final performance. Moreover, compared with optimization-based and heuristic baselines, it achieves comparable restoration effectiveness with substantially reduced decision time, highlighting its suitability for real-time service restoration.