This study advances a hierarchical bilevel optimization paradigm to rigorously characterize the intertwined processes of strategic bidding and regulatory market participation in electricity systems increasingly dominated by renewable resources. At the upper tier, a central regulatory authority orchestrates participation rules, renewable integration mandates, and incentive mechanisms with the overarching aim of maximizing system-wide social welfare while driving decarbonization and reliability objectives. At the subordinate level, profit-maximizing generation firms—each managing heterogeneous renewable portfolios—pursue strategic bidding under deep uncertainty, conceptualized as a multi-agent game governed by imperfect and asymmetric information. The interaction between these tiers is formalized as a bilevel Stackelberg game that encapsulates price-responsive demand, intertemporal reserve adequacy, and policy-driven incentive structures. To ensure both computational tractability and robustness against strategic indeterminacy, the lower-level equilibrium is reformulated into a mathematical program with equilibrium constraints (MPEC), enabling a hybrid solution procedure that combines penalty-based regularization with exact decomposition algorithms. The framework’s efficacy is validated through a stylized multi-zone case study featuring diverse renewable assets and strategic participants, revealing how policy signals, capacity ceilings, and market power asymmetries reshape efficiency frontiers and bidding equilibria. A set of high-resolution post-processing visualizations is further employed to illustrate the dynamic evolution of marginal prices, equilibrium trajectories, and regulatory impacts under 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.