Under the background of ”dual carbon”, we must develop clean energy, build integrated energy systems (IES), and optimize their operation to achieve carbon neutrality. This study presents a strategy for the IES, whose goal is to reduce the carbon content of the power system, which aims to constrain the carbon emission of IES further, improve energy conversion efficiency, and reduce the carbon content of IES. First of all, we focus on the current situation and the improvement of the economic efficiency of the carbon trading market and introduce a tiered and hierarchical electricity carbon trading mechanism to promote IES to control carbon emissions more effectively. Then, we refine the two-stage operation process of power to gas (P2G) and propose a P2G process. This novel approach can significantly enhance the efficiency of hydrogen energy utilization and save operational expenses. In addition, this paper proposes a flexible supply and demand dual response mechanism. On the supply side, energy efficiency is improved through cogeneration with adjustable heat and power ratio. On the demand side, the efficiency of the cogeneration system in terms of energy should be improved through a flexible supply and demand side dual response mechanism. With this mechanism, the environmental protection and economic viability of IES can be further enhanced.