## 1 Introduction  
The environmental problems caused by carbon emissions in today's world are becoming increasingly serious. In 2020, China proposed a \"dual carbon\" goal, aiming to reach a carbon peak by 2030 and carbon neutrality by 2060 [1]. According to statistics, carbon emissions from China's major power industry account for about 40% of the total carbon emissions from the energy industry; the power system is facing severe pressure regarding carbon emission reduction [2]. Under this trend, the concept of carbon has been gradually integrated into all aspects of power market construction. In particular, with the continuous development of the smart grid, the information interaction between source and load has been strengthened [3; 4; 5; 6]. Based on this, designing a flexible and efficient market mechanism to both optimize the allocation of source and load resources and promote carbon mitigation has become one of the important ways to achieve the goal of carbon neutrality. Therefore, it is crucial to address the urgent problem of implementing low-carbon power market dispatch at multiple levels, including source and load coordination [7], carbon responsibility allocation [8], and market mechanism design [9], all from the perspective of carbon [10]. At present, the coordination of source and load has become an important way to realize the optimal scheduling of a power system: to coordinate the generation side and user side dispatchable resources to realize their combined participation and optimize the system operation so as to obtain the best economic and environmental benefits [11]. Typically, source-load coordination is achieved through a demand response. It was found that the demand side response can improve the consumption rate of new energy through load regulation to maximize the benefits of participants in the market [12]. However, before carbon trading was paid great attention to in the market, the most optimal scheduling was from the perspective of a penalty incentive which reduces the output of thermal power units by imposing the cost of wind and light abandonment; there is a lack of research on carbon incentives for the market players to actively reduce their own carbon responsibility in response to emission reduction. The carbon emission flow theory (CEF) of power systems is often used in the calculation of carbon responsibility allocation of load nodes. In this theory, carbon emissions will not be considered as a type of greenhouse gas but as a type of network flow which represents the flow of carbon from one node to another along network branches or paths in an energy network with visible structures and facilities. Based on this concept, the carbon emission flow theory tracks carbon emission from the generation side to the user side and closely links source-load with carbon emission flow as a bond so as to realize the allocation of carbon responsibility [13; 14]. In [15], the theory of carbon emission flow and the power flow information of the electric energy transmission network were used to determine the transfer amount of carbon emissions on the power generation side at each node of the system, thus accurately tracking the carbon emission trajectory and clarifying the carbon responsibility of user nodes which laid the foundation for subsequent research. From the \"carbon perspective\", the low-carbon demand response mechanism was investigated in [16; 17; 18]; based on the carbon emission flow theory, dynamic carbon emission factors were used as guidance signals for users to actively change their electricity consumption behaviors which shows that under carbon incentive users had a more obvious tendency to actively choose green generators through the demand response.