Against the backdrop of global climate change and energy transition, the power system is facing multiple challenges, including economic viability. To ensure the good economic benefits of the new power system and implement the low-carbon development strategy, this paper proposes an optimal scheduling method for gas power generation system under various carbon emission constraints, including carbon emission quota constraints, carbon emission intensity constraints, and the addition of carbon capture and storage technology constraints. Firstly, system economy and new energy consumption are taken as optimization objectives, and the carbon emission constraint proposed in this paper is introduced on top of the basic operational constraints. Secondly, the relevant parameters are determined, and multi-objective particle swarm optimization algorithm is used to solve the model. Finally, the optimization results are compared and analyzed under multiple constraints and scenarios. The experimental results show that this method has significant effects on reducing system costs and improving the capacity of new energy consumption, which is of great practical significance to achieve low-carbon transformation of the power system.