# Flexible Dispatch for Integrated Power and Gas Systems Considering Power-to-Gas and Demand Response
## 1 Introduction
In [20], each subsystem operator is allowed to pursue its own interests, and an equilibrium problem is formulated for the optimal scheduling strategy, which is the coordination of each subsystem with each other to achieve equilibrium. In addition, power to gas is an effective way to improve the consumption of wind power. In [21], a novel energy control method associated with DRL is proposed to solve the problem of economic optimization in an integrated energy system combining wind and dynamic gas technologies. In [22; 23; 24], P2G technology was introduced into the power system as a promising option to increase the wind power dispatch in the power system, considering electricity to gas as a practical solution to accommodate the variability of wind power generation output, and also providing a research-based support for the coupling and coordinated operation of the power and natural gas systems. Since the demand response has the characteristics of fast response speed, high operation economy, energy saving, and environmental protection, there are more and more researches on large-scale renewable energy integration and participation in power system reserve allocation as flexible resources. In [25], a coordinated scheduling model of gas-electric coupled system based on interval optimization is proposed by considering the dynamic characteristics of natural gas flow, wind power grid connection, and demand response management. In [26; 27; 28; 29; 30; 31; 32], demand response is used to deal with uncertainty and improve the flexibility of the power system. It is widely used in optimal dispatching to promote multi energy coordination and complementarity, and guides users to use energy reasonably and economically. However, it is important to note that the above studies are rarely considered on the basis of quantifying the dispatch flexibility of the power system. In addition, P2G and demand response were not considered simultaneously. These studies prioritize the optimization of the power system, resulting in harsh operating conditions in the natural gas system. To address these gaps, a flexible economic dispatch model for the integrated power and gas systems (IPGS) is proposed in this paper, which considers the P2G facilities and demand response under high wind power penetration level. In addition to the total operation cost of integrated power and gas systems, the flexibility margin of the power system is also considered in the objective function, where this flexibility is mainly provided by adjustable generators, P2G facilities, and demand response. Furthermore, considering the actual situation of power system and natural gas system, the whole model is solved by using a distributed coordinated optimization method. Briefly, the major contributions of this paper are summarized as follows. (1) A flexible and economic dispatch model for the electricity-gas interconnection system that incorporates P2G and demand response is proposed to improve system flexibility and economy, as well as the system's ability to cope with uncertainty. (2) The two scheduling methods of separate optimization and coordinated optimization of power and natural gas systems are compared and analyzed. To improve the overall resource utilization level of the system, it is necessary to implement coordinated optimization dispatch. (3) A two-level optimization model is developed and slack variables are introduced to solve the power system and natural gas system interactively and iteratively. The rest of this paper is organized as follows. Section 2 analyzes the flexibility of the IPGS and demand response model. The flexible economic dispatch model is formulated in Section 3. Section 4 presents the solution methodology for the proposed bi-level coordinated optimization model. A case study is presented in Section 5 to show the effectiveness of the proposed approach. Finally, the conclusions are drawn in Section 6.