The research article explores a low-carbon economic operation method for Integrated Energy Systems (IES) to align with energy-saving and emission reduction goals. It introduces a two-stage operational framework of Power-to-Gas (P2G) technology, focusing on hydrogen energy benefits through electrolyzers, methane reactors, and hydrogen fuel cells (HFCs). A cogeneration and HFC operational strategy with adjustable heat-to-electricity ratio aims to improve the overall performance of IES in terms of low-carbon operations and economic efficiency. Additionally, a carbon trading mechanism is proposed to guide the IES towards effective carbon emission control. The study emphasizes the importance of energy efficiency, optimal scheduling, and carbon emissions reduction in sustainable energy systems, with a positive sentiment towards the integration of hydrogen technology for achieving these objectives.