With increasing reforms related to integrated energy systems (IESs)

each energy subsystem

as a participant based on bounded rationality

significantly influences the optimal scheduling of the entire IES through mutual learning and imitation. A reasonable multiagent joint operation strategy can help this system meet its low-carbon objectives. This paper proposes a bilayer low-carbon optimal operational strategy for an IES based on the Stackelberg master-slave game and multiagent joint operation. The studied IES includes cogeneration

power-to-gas

and carbon capture systems. Based on the Stackelberg master-slave game theory

sellers are used as leaders in the upper layer to set the prices of electricity and heat

while energy producers

energy storage providers

and load aggregators are used as followers in the lower layer to adjust the operational strategy of the system. An IES bilayer optimization model based on the Stackelberg master-slave game was developed. Finally

the Karush-Kuhn-Tucker (KKT) condition and linear relaxation technology are used to convert the bilayer game model to a single layer. CPLEX

which is a mathematical program solver

is used to solve the equilibrium problem and the carbon emission trading cost of the system when the benefits of each subject reach maximum and to analyze the impact of different carbon emission trading prices and growth rates on the operational strategy of the system. As an experimental demonstration

we simulated an IES coupled with an IEEE 39-node electrical grid system

a six-node heat network system

and a six-node gas network system. The simulation results confirm the effectiveness and feasibility of the proposed model.