Uncertainty‐Aware Coordinated Transmission‐Distribution Dispatch via GNN‐Augmented Distributionally Robust Optimal Power Flow

This paper proposes a Learning‐Augmented Distributionally Robust OPF (LA‐DROPF) framework for coordinated transmission‐distribution dispatch under deep uncertainty. The framework embeds GNN‐derived power flow sensitivities within Wasserstein‐metric DRO, where surrogate errors are absorbed by an inflated ambiguity radius. A hybrid Benders‐ADMM decomposition maintains inter‐operator privacy with convergence guarantees, and a CVaR layer controls tail voltage‐security risk. Finite‐sample guarantees ensure exponential decay of out‐of‐sample constraint violations, and an online mirror‐descent mechanism adapts the ambiguity set in real time. Experiments on 217‐bus and 630‐bus coupled systems—including tests with heterogeneous distribution feeder topologies—show that LA‐DROPF reduces DS‐level worst‐case cost by 33% relative to stochastic OPF and eliminates voltage violations that afflict deterministic and GNN‐only methods. A controlled ablation isolating the CVaR and radius‐inflation effects—including a fair comparison against exact‐sensitivity DRO augmented with the same CVaR layer and equivalent total radius—confirms that the combined mechanism yields up to 7% worst‐case cost reduction under heavy‐tailed uncertainty beyond what the Wasserstein radius alone provides. Benders‐ADMM convergence to within 1% optimality gap and AC power flow feasibility are verified explicitly across all test systems.