Game-Theoretic Approach for Dynamic Carbon Flow Tracing in Electricity-Carbon Systems with Demand Response Consideration

The new power system faces the dual challenges of integrating a high proportion of renewable energy and real-time dynamic carbon awareness. In this background, this paper proposes an integrated power-carbon model that combines dynamic carbon flows, game and demand response. First, the dynamic carbon flows model forms the core of this paper. It primarily determines users' indirect carbon emissions through the decomposition of green power transactions based on dynamic carbon emission factors. Second, the game model focuses on analyzing total electricity traded and total profits under both cooperative and non-cooperative game scenarios. Finally, the demand response mechanism aims to stabilize power system load zones through price incentives, achieving peak shaving and valley filling. These three models are closely interrelated. Dynamic carbon flows calculate time-varying carbon costs and incorporate them into electricity prices; the game theory redistributes generation under carbon pricing, and the new generation plan in turn updates the carbon flows; demand response dynamically adjusts loads based on carbon price differentials. After peak shaving and valley filling, the load profile prompts the game theory to re-establish equilibrium. A case study based on an IEEE 14-node network demonstrates that assuming a 2000-kilowatt green power contract is signed, the carbon intensity at Node 6 would decrease by 35.7%. This indicates that the model accurately quantifies carbon emissions and enhances the traceability and fairness of responsibility allocation at the user end.