## 1 Introduction
### Literature Review  
Currently, there are mainly two approaches for the optimal dispatch of multi-energy integrated systems: centralized methods and decentralized methods [7; 8]. The centralized fashion facilitates the coordinated control of the entire system, but faces challenges such as high communication requirements, heavy computational load for the central controller, information security sharing, and topology construction lacking flexibility. On the other hand, the decentralized optimization methods only require essential information from each participant agent and could solve complicated, large-scale problems via autonomous action from the agents, effectively compensating for the centralized approach's deficits [9].  
Many studies have implemented decentralized methods to tackle centralized economic dispatch issues. Among a variety of decentralized approaches, the Alternating Direction Method of Multipliers (ADMM) exhibits advantageous properties such as simplicity, superior convergence, and flexible reformulation for solving large-scale problems. It also ensures the information security of the participants. Consequently, it has been widely employed in recent years. References [10; 11] utilize the ADMM algorithm to address the joint dispatch issue of microgrid clusters, mitigating communication loads and safeguarding user security simultaneously. References [12; 13] leverage the ADMM algorithm to solve the carbon emission economic dispatch issue for various energy hubs. References [14; 15; 16] instantiate the ADMM framework, allowing upper and lower-level entities to interact via energy trading strategies, culminating in cooperative operation. Moreover, in the actual resolution of ADMM, while the iterative step sizes affect the convergence speed and not the convergence precision, a paucity of literature considers dynamically adjusting step sizes to enhance convergence speed.  
In addition, as a low-carbon technology, carbon capture and storage (CCS) plays a pivotal role in transforming high-carbon emission devices for low-carbon operation, significantly contributing to the greening of energy systems. Studies [17; 18] integrated power-to-gas (P2G) and CCS technologies, establishing a coupling of CO\({}_{2}\) capture and utilization processes. The authors of [19] created a novel approach for virtual power plant dispatch strategy by coupling CCS, P2G, and electric vehicles. Another study [20] proposed a coal-fired unit's low-carbon and economic operation using an amalgamation of CCS and the organic Rankine cycle; and lastly, [21] demonstrated energy cascade utility through the compound power generation system, CCS, and the use of liquefied natural gas (LNG) cold energy. However, such literature related to the application of CCS technology is predominantly focused on coupling with other devices, without considering the perspective of multi-energy integrated systems.  
In conclusion, this paper presents a tiered low-carbon optimization dispatch strategy for multi-park IEMGs incorporating P2G and CCS, grounded on the synchronized ADMM algorithm. Through the application of the revised synchronized ADMM and by taking into account the impact factors for carbon emissions, it successfully addresses the challenge of economic and low-carbon cooperative optimization. Significantly, it expedited convergence speed by dynamically adjusting iterative step sizes.