Regulatory-driven optimization of integrated energy systems: A legal and policy-compliant framework for flexibility and carbon management

This paper develops a technically rigorous optimization framework for regulatory-compliant dispatch in integrated power systems operating under complex carbon market structures, with specific emphasis on California's cap-and-trade regime and demand-side policy instruments. A hierarchical bilevel optimization model is constructed, wherein the upper level represents the policy authority setting dynamic emissions caps and DR incentive structures, while the lower level captures the optimal operation of multi-energy power systems — including electricity, thermal, and gas subsystems — subject to intertemporal unit commitment, network constraints, and compliance penalties. To address deep uncertainty in carbon pricing and market responses, the lower-level model embeds a Wasserstein-metric-based Distributionally Robust Optimization (DRO) formulation, ensuring operational resilience under ambiguous regulatory signals. Furthermore, a Non-dominated Sorting Genetic Algorithm III (NSGA-III) is employed to identify Pareto-efficient strategies balancing cost minimization, flexibility enhancement, and legal adherence. Numerical experiments on a testbed modeled after Kern County, California — comprising high-penetration renewables, battery storage, and flexible loads — demonstrate that the proposed framework can enhance nodal flexibility by 27%, reduce emissions penalties by 19%, and dynamically adjust dispatch strategies in response to fluctuating regulatory parameters. The results underscore the critical need for power systems to embed policy-awareness into optimization routines to achieve resilient and regulation-compliant operations under evolving carbon-constrained environments.