Mixed-integer programming embedded system dynamics model for deterministic capacity guarantee of power generation considering long-term carbon market variations

China’s energy transition emphasizes market mechanisms for price guidance, having established energy, green certificate, and carbon quota markets, with efforts to introduce a capacity market mechanism. The capacity market provides investment signals that directly influence the generation portfolio. Consequently, a systematic assessment of its design and long-term impact is critical. A key challenge lies in the capacity credit assessment of demand-side resources, such as distributed energy storage, which exhibit diminishing marginal capacity credit as their penetration increases. However, cooperation among resources may generate additional capacity credit, yet related mechanisms remain underexplored. Additionally, capacity and energy market clearing models incorporate engineering constraints, but traditional top-down macro modeling approaches struggle with solving optimization problems with such constraints. To address these issues, this paper proposes an integrated long-term simulation framework that combines system dynamics and optimization models to analyze the impact of capacity market design on generation portfolio and price signals in China. At the macro level, system dynamics is used to model multiple generation capacity and market mechanisms modules, establishing feedback relationships to analyze long-term trends. At the micro level, optimization models for energy and capacity markets are developed, incorporating engineering constraints and integrated into the system dynamics framework, overcoming traditional limitations in time scale, variable transfer, and qualitative feedback. Finally, a capacity clearing mechanism for flexible resources is designed, utilizing a linearized load duration curve-based aggregation model, which is integrated with the capacity clearing model to dynamically reflect both capacity credit decay and the additional credits generated by resource cooperation. Static parameter analysis and long-term simulations evaluate the impact of the proposed mechanism on capacity trends and market prices.