## 1 Introduction  
With the further advancement of the industrialization reform of the energy industry, the energy internet has received increasing attention and research. Integrated energy systems (IES) that include gas units, gas to power (P2G) equipment, and combined heat and power (CHP) equipment break the barriers to exchange between different forms of energy. Therefore, the integrated energy system can fully tap the potential of each energy to complement each other efficiently, and meet various requirements of economic and environmental protection [1; 2; 3; 4]. In addition, in the open electricity market environment, the electricity supplier, gas supplier, and heating supplier in the electric heat interconnection system generally belong to different suppliers, it is important to ensure the privacy of the information in the co-ordinated operation, so data needs to be protected [5; 6].  
Many research works are reported, focusing on optimization technologies of IES which combine two types of energy flow. Some researchers established an electricity-gas system considering the influence of temperature, and convexified the power grid [7]. Finally, the optimal power flow was studied on this model. A robust co-optimization scheduling model was proposed to study the co-ordinated optimal operation of electricity-gas systems, and the optimization problem of the model was solved by the alternating direction method of multipliers [8]. The research proposed the piecewise linear approximation methods to solve the non-convex and non-linear Weymouth equation in gas networks [9]. However, the above studies are mostly based on a single electricity-gas system or electricity-heating system. There are few studies that concentrate on the electricity-gas-heating system and most are lacking consideration of network dynamic characteristics. Based on this, this paper builds a day-ahead scheduling optimization model of the electricity-gas-heating system (EGHS), considering the dynamic characteristics of the network in order to tap the potential of complementary advantages between different energy flows.  
On the other hand, in the existing research, the optimization methods of the IES system mostly adopt the centralized optimization method. A convex relaxation approach was proposed to achieve the co-ordinated operation of electricity and natural gas systems [10]. Some researchers used a genetic algorithm to achieve the co-ordinated optimization of the district electricity and heating system [11]. However, the centralized solution used in the above research requires an upper-level co-ordination center to collect the operating information of each subsystem to solve the optimal strategy, which ignores the actual needs of each subsystem to protect its privacy. Distributed computing methods can solve this problem. The distributed algorithm mainly includes the alternating direction multiplier method [12; 13; 14] and the Benders decomposition algorithm [15; 16; 17]. This kind of distributed algorithm is only for the 2-Block problem, meaning it is only used to solve the electricity-gas system or the electricity-heating system. The EGHS contains three subsystems, so it belongs to the 3-Block problem in distributed optimization. Therefore, conventional distributed algorithms cannot ensure the convergence of calculation results [18].  
Aiming at the above problems, this paper builds a day-ahead scheduling model of the EGHS considering the dynamic characteristics of the network, then uses inner and outer algorithms to solve the model. The outer penalty convex-concave procedure (PCCP) is responsible for the model convexification and the inner alternating direction method of multipliers (ADMM)-FE (forced equality) gets a convergent solution.  
The rest of the paper is structured as follows: Section 2 establishes a day-ahead scheduling model of the EGHS. Section 3 introduces the PCCP-ADMM-FE algorithm for the day-ahead scheduling. Numerical testing results are provided in Section 4. Finally, conclusions are summarized in Section 5.