While reducing the carbon emissions of traditional coal-fired units, carbon capture and storage (CCS) technology can also provide sufficient carbon raw materials for power to gas (P2G) equipment, which helps to achieve the low-carbon dispatch of an integrated energy system (IES). In this paper, an extended carbon emission flow (ECEF) model integrating CCS-P2G coordinated operation and low-carbon characteristics of an energy storage system (ESS) is proposed. On the energy supply side, the coupling relationship between CCS and P2G is established to realize the low-carbon economic operation of P2G. On the energy storage side, the concept of "state of carbon (SOCB)" is introduced to describe the carbon emission characteristics of ESS to exploit the potential of coordinated low-carbon dispatch on both sides of energy release and energy storage. On the load side, a new carbon emission reduction mechanism that guides users to actively respond and reduce carbon emissions is proposed, namely a low-carbon demand response mechanism. This mechanism uses the node carbon intensity as guiding signals, and the willingness of carbon emission reduction or the price in the carbon market as incentive signals. Furthermore, a low-carbon economic dispatch model considering multiple uncertainties such as wind power output, electricity price, and load demands is established. In order to solve the model efficiently, the parallel multi-dimensional approximate dynamic programming (PMADP) algorithm is adopted, and the solution efficiency is significantly improved compared with stochastic optimization, without losing solution accuracy under a multi-layer parallel loop nesting framework. The effectiveness of the proposed model and method is verified on an E14-H6-G6 system and an E57-H12-G12 system.