In the context of the "double carbon" initiative, the exploration of strategies for energy conservation and emission reduction through both policy and technological approaches has emerged as a significant area of contemporary research. Based on this, a low-carbon economic dispatch model of the integrated energy system (IES) including oxygen-enriched combustion power plant (OCPP), two-stage power-to-gas (P2G), and combined heat and power (CHP) units is constructed. The objective of the model is to optimize total operational expenditures while simultaneously improving carbon resource recovery and mitigating emissions. Notable advancements encompass the transformation of traditional thermal power units into OCPP, the formulation of mathematical models for OCPP, the implementation of two-stage P2G systems, and CHP systems, as well as the incorporation of a demand response (DR) mechanism. The findings from the simulation demonstrate that the OCPP-P2G-CHP integrated system exhibits a marked enhancement in carbon capture efficiency when juxtaposed with conventional systems. Additionally, it results in a 7.8% reduction in overall costs and a 30.2% decrease in carbon emissions. This research substantiates the viability and innovative nature of the proposed model, underscoring its potential for scalable application within industrial and urban energy networks.