Bilevel Carbon-Aware Dispatch and Market Coordination in Power Networks Under Distributional Uncertainty

The accelerating transition toward carbon neutrality necessitates the synergistic integration of power and hydrogen systems to mitigate renewable intermittency; however, coordinating regulatory policies with the operational flexibility of these coupled systems remains a critical challenge under deep uncertainty. Motivated by this gap, this study develops a bilevel carbon price-coupled optimization framework for integrated power–hydrogen systems, aiming to coordinate environmental policy design with operational scheduling under deep uncertainty. The upper-level model represents the decision-making of a market regulator that determines the optimal carbon price and emission allowances to maximize overall social welfare, while the lower-level model captures the coordinated operation of electricity and hydrogen subsystems that minimize total dispatch cost, including renewable utilization, electrolyzer conversion, and fuel-cell recovery.To address stochastic variations in renewable generation and load demand, a Distributionally Robust Optimization (DRO) formulation is introduced using Wasserstein ambiguity sets, ensuring decision feasibility against worst-case probability distributions. The bilevel structure is efficiently solved via a Benders–Column-and-Constraint Generation (CCG) algorithm, which decomposes policy and operation layers into tractable subproblems with provable convergence. Case studies on a 33-bus integrated power–hydrogen network demonstrate that the proposed framework effectively balances economic efficiency and carbon reduction. Results show that the optimal carbon price of approximately 45 $/tCO2 achieves a 27% emission reduction with only a 9% cost increase, revealing a near-optimal social welfare equilibrium. Hydrogen subsystems operate flexibly, with electrolyzer utilization increasing by 30% and storage cycling deepening by 15%, enabling enhanced renewable absorption. Sensitivity analyses confirm that the DRO layer reduces operational risk by 4% compared with stochastic optimization, validating robustness against distributional shifts. The study provides a rigorous and computationally efficient paradigm for policy-coordinated decarbonization, highlighting the synergistic role of carbon pricing and cross-energy scheduling in the next generation of resilient low-carbon energy systems.