Bi-Level Collaborative Optimization of Electricity-Carbon Integrated Demand Response for Energy-Intensive Industries under Source-Load Interaction

Traditional demand response (DR) programs for energy-intensive industries (EIIs) primarily rely on electricity price signals and often overlook carbon emission factors, limiting their effectiveness in supporting low-carbon transitions. To address this challenge, this paper proposes an electricity–carbon integrated DR strategy based on a bi-level collaborative optimization framework that coordinates the interaction between the grid and EIIs. At the upper level, the grid operator minimizes generation and curtailment costs by optimizing unit commitment while determining real-time electricity prices and dynamic carbon emission factors. At the lower level, EIIs respond to these dual signals by minimizing their combined electricity and carbon trading costs, considering their participation in medium- and long-term electricity markets, day-ahead spot markets, and carbon emissions trading schemes. The model accounts for direct and indirect carbon emissions, distributed photovoltaic (PV) generation, and battery energy storage systems. This interaction is structured as a Stackelberg game, where the grid acts as the leader and EIIs as followers, enabling dynamic feedback between pricing signals and load response. Simulation studies on an improved IEEE 30-bus system, with a cement plant as a representative user form EIIs, show that the proposed strategy reduces user-side carbon emissions by 7.95% and grid-side generation cost by 4.66%, though the user’s energy cost increases by 7.80% due to carbon trading. The results confirm that the joint guidance of electricity and carbon prices effectively reshapes user load profiles, encourages peak shaving, and improves PV utilization. This coordinated approach not only achieves emission reduction and cost efficiency but also offers a theoretical and practical foundation for integrating carbon pricing into demand-side energy management in future low-carbon power systems.