Traditional fixed or linear carbon prices often fail to reflect the nonlinear incentives of real carbon markets. To address this, we propose a multi-objective optimal dispatch framework for integrated energy systems (IESs) incorporating a tiered carbon trading mechanism. The system—comprising photovoltaics, wind power, a gas turbine, energy storage (ESS), power-to-gas (P2G), and grid interaction—aims to minimize operating and carbon trading costs while maximizing renewable utilization. This is solved using an improved multi-objective particle swarm optimization (IMOPSO) algorithm. Simulations across five configurations reveal that tiered pricing nonlinearly penalizes high emissions, reshaping the Pareto front toward low-carbon outcomes. Consequently, the ESS evolves from a simple economic arbitrageur into a proactive “carbon buffer”, absorbing midday photovoltaic surpluses and substituting gas turbine output during evening peaks. Compared to a grid-only baseline, the optimized multi-energy configuration (gas turbine + ESS + P2G) reduced operating costs by 13.1% and carbon emissions by 9.9%, while increasing renewable utilization by 8.5%. Ultimately, this study demonstrates that a well-designed nonlinear carbon pricing mechanism is decisive for guiding the IES to achieve coordinated economic and low-carbon operation.
Han et al. (2026) studied this question.