Multi-objective optimization for the operation of district heating systems considering flexibility and economy

Facing the transition of energy systems, a critical challenge for the operation and scheduling of the nextgeneration district heating system (DHS) is achieving flexible dynamic matching of thermal energy supply and demand whilst reducing operational costs. This study introduces the Gram-Charlier A expansion method to establish a source-load uncertainty quantification model and thus formulates a method to quantify the operation flexibility considering source-load fluctuations. Furthermore, this study establishes a multi-objective optimization model that considers operation cost and flexibility as optimization objectives, analyzing the optimal dispatch strategy for multi-energy coupled DHS. Utilizing a compromise programming approach, a trade-off curve was obtained, and the impact of total heat supply and heat source configuration on the optimization results was analyzed. A case study of an integrated "thermal-electrical-photovoltaic-storage" DHS in a northern Chinese city demonstrates the effectiveness of the proposed method. The case study indicates that operation cost and flexibility are inversely related; enhancing operation flexibility requires higher operational costs. The results also reveal a threshold effect between the rated power of the heating units and the operation flexibility, where an increase in rated power to a critical value no longer provides gains in flexibility. The study concludes that the proposed multi-objective optimization dispatch method achieves a balance between operational cost and flexibility, effectively reducing system operating costs and enhancing the DHS's adaptability to the dynamic characteristics of multi-energy systems. This research offers valuable insights into the rational configuration of heating units and the integration of renewable energy sources into comprehensive energy systems.