Power system restoration after a major outage requires selecting an energization sequence that ensure time efficiency and avoid operational risk. Traditional restoration strategies typically rely on predesigned backbone networks under the assumption that the backbone infrastructure itself remains intact and can be operated without issues. However, storms and other extreme events frequently induce extensive physical damage to power system components, invalidating these assumptions and highlighting the need for more adaptive restoration approaches.

This study develops a stochastic sequential optimization framework to model and enhance post-storm power system restoration under uncertainty of risk, which is explicitly represented through failure probabilities assigned to each component. These probabilities are treated as random quantities drawn from specified distributions motivated by storm-induced fragility assessments, while their exact parametric forms remain flexible within the proposed framework. The restoration task is formulated as a Markov decision process whose state captures the current restored network and feasibility conditions, including transformer energization limits, cumulative high-voltage line length thresholds, and required load pickup. To address the large state space induced by the incorporation of probabilistic risk indicators, a risk-aware Approximate Dynamic Programming (ADP) approach is developed using a post-decision state representation to construct tractable value function approximations. Monte Carlo sampling is employed to refine value estimates and guide the selection of actions that mitigate risk while accelerating backbone reconstruction and satisfying operational rules.

A case study on a regionalized 6515rte system (a large-scale French transmission network test case) demonstrates that the learned policy identifies efficient and risk-aware energization sequences under both deterministic and stochastic specifications of component failure probabilities. These results illustrate the promise of ADP as a scalable tool for risk-aware restoration planning.