Bilevel Stochastic Low-Carbon Operation Optimization of Integrated Energy Systems Based on Dynamic Mean–Conditional Value at Risk (CVaR) and Stepwise Carbon Trading Mechanism

To enhance the low-carbon operational performance of integrated energy systems (IESs) under multi-source uncertainties, this study proposes a bilevel stochastic optimization framework incorporating a dynamic mean–CVaR risk model and a tiered carbon pricing mechanism. The upper level adopts an improved NSGA-II to jointly optimize economic cost, carbon emissions, and system flexibility through capacity planning decisions. The lower level performs scenario-based operation evaluation with a time-varying risk aversion coefficient, enabling differentiated risk responses across operating periods. A stepwise carbon price function and a capped carbon revenue mechanism are introduced to represent real carbon market regulations and avoid excessive emission reduction benefits. Multidimensional uncertainty scenarios—covering renewable variability, load fluctuations, and market price disturbances—are generated for risk-aware evaluation. Simulation results show that the proposed approach effectively reduces cost and emission volatility and achieves a more balanced trade-off between economy and low-carbon performance compared with conventional static-risk models. Sensitivity analyses further reveal that increased risk aversion shifts system operation strategies from economy-oriented to robustness-oriented modes, highlighting the importance of dynamic risk modeling and carbon policy design for future low-carbon multi-energy systems.