###### Abstract  
The integrated power and natural gas energy system (IPGES) is of great significance to promote the coordination and complementarity of multi-energy flow, and it is an important carrier to increase the proportion of wind power accommodation and achieve the goal of carbon emission reduction. In this paper, firstly, the reward and punishment ladder-type carbon trading model is constructed, and the impact of the carbon trading mechanisms on the carbon emission sources in the power system is comparatively analyzed. Secondly, in order to achieve a reasonable allocation of carbon resources in IPGES, a bi-level optimization model is established while taking into account the economics of dispatching and the requirements of carbon emission reduction. Among them, the outer layer is the optimal carbon price solution model considering carbon trading; in the inner layer, considering the power system constraints, natural gas system constraints, and coupling element operation constraints, a stochastic optimal dispatching model of IPGES based on scenario analysis is established. Scenario generation and reduction methods are used to deal with the uncertainty of wind power, and the inner model is processed as a mixed integer linear programming problem. In the MATLAB environment, program the dichotomy and call the Gurobi optimization solver to complete the interactive solution of the inner and outer models. Finally, case studies that use an integrated IEEE 39-bus power system and Belgian 20-node gas system demonstrate the effectiveness and scalability of the proposed model and optimization method. integrated power and natural gas energy system; carbon trading; reward and punishment ladder-type; optimal carbon price; stochastic optimal; bi-level model +
Footnote †: journal: Applied Sciences  
capacity of coal-fired power plants accounted for about 58% of total generation capacity in China [3]. The total CO2 emission produced by coal-fired power plants (CFPPs) in China occupies 37% of the carbon emission caused by fossil fuels combustion [4]. Hence, it is necessary to develop low-carbon power generation technology to handle this challenge. There are many low-carbon technologies for the decarbonization of the power industry in China. For example, developing renewable generation and gas-fired generation to replace coal-fired power generation. By the end of November 2020, the installed capacity of the gas-fired power plants (GFPP), wind and solar power accounted for about 4.6%, 10.8% and 11.3% in China [3], respectively. The electricity system is transitioning towards a renewable-based system, mainly due to worldwide environmental concerns, and natural gas is expected to play an important role in the future development of the electricity system [5]. This is due to the fact that GFPP are one of the least polluting conventional technologies, as well as efficient and flexible. The co-existence of these two types of power production technologies serves as a promising combination for a smooth transition to a sustainable energy system that is flexible enough to accommodate high shares of renewables [6]. As a consequence, the interactions between the electricity and natural gas systems will be strengthened, while the uncertainty and variability of renewables will eventually affect the operation of both systems. Wind power is one of the most important renewable generations in power systems, albeit volatile with significant uncertainties [1]. Due to the uncertainties and power network operating constraints, wind power curtailment occurs [7]; storing the excess power can facilitate the integration of wind power. For that reason, power-to-gas (P2G) technology has been attracting a lot of interest [8; 9]. P2G technology produces synthetic natural gas consuming electric energy, which can enhance the flexibility of IPGES. At present, the cost of P2G technology is relatively high, but it is widely considered to be the most suitable scenario for P2G to absorb the excess wind power.