Optimization Study on Integrated Energy Mutual Aid–Response Considering Multi-Energy Flow Carbon Responsibility Allocation

Improving the sustainability of regional integrated energy systems requires carbon signals that reflect the coupled use of electricity, cooling, and heating. In this paper, we propose a multi-energy flow responsibility factor construction method that accounts for carbon responsibility allocation on both the source and demand sides, and employ it as a low-carbon signal within a multi-regional collaborative optimization framework for mutual aid and response. First, a dynamic weighting mechanism based on real-time electricity–heat (cooling) supply–demand matching is established to enable fine-grained allocation of carbon responsibility among the three energy flows. Subsequently, a joint capacity configuration and operational optimization model is developed by integrating low-carbon demand response (LCDR) with carbon trading. The proposed approach is then validated using measured data from the Higashida area of Kitakyushu, Japan, to investigate the low-carbon response benefits under two operating scenarios: independent operation and mutual aid operation across multiple systems. The results demonstrate that the proposed method effectively shifts loads toward low-carbon periods and enhances local photovoltaic utilization. Specifically, compared with interconnected operation without LCDR (Case 1), the proposed LCDR method reduces carbon emissions by 1.4%. Furthermore, compared with independent operation with LCDR (Case 3), the proposed multi-regional interconnection strategy reduces external power purchases by 18.2% and lowers total operational costs by 4.1%. Although this interconnected strategy leads to a moderate 5.5% increase in local carbon emissions due to higher local natural gas consumption, it represents a rational trade-off that significantly enhances system economic viability and energy autonomy, achieving the greatest overall benefit.