## 3 Operation Modes of the Electricity-Gas-Heat IES  
The EGH-IES studied in this paper includes three subnetworks (i.e., electricity network, natural gas network and district heating network) and four kinds of coupling equipment (i.e., CHP unit, P2G, P2H and electricity-driven compressor), as shown in Figure 1.  
According to the energy conversion relationships of the various pieces of coupling equipment and the power balances of each subnetwork, four typical operation modes of the EGH-IES (i.e., \"electricity following heat\" mode, \"electricity/gas following heat\" mode, \"gas/heat following electricity\" mode and \"electricity following gas\" mode) are suggested in this paper and depicted in Figure 2.  
* **Mode 1: \"Electricity following heat\" mode** As shown in Figure 2, when the EGH-IES works in mode 1, the heat node (i.e., the node in the heating network) connected to the P2H is set as the heat slack node and the P2H will maintain the overall heat power balance of the heating network. Therefore, variations in the heating network caused by such as variations in heat loads will change the heat power supplied by the P2H and then be transmitted to the electricity network via the P2H coupling. That is to say, the operation state of the electricity network in this mode will vary according to that of the heating network, or, in other words, variations in the heating network are followed by those of the electricity network. Note that, in this mode, the variation transmission between the electricity and heating network is single-directional and there is no reverse variation transmission from the electricity network to the heating network. Moreover, when the EGH-IES works in mode 1, both the CHP and P2G are working with constant inputs/outputs and variations in one subnetwork will not be transmitted to the other via CHP or P2G. That is to say, there is no variation transmission between the gas and heating networks or between the electricity and gas networks provided that all compressors are gas-driven. It should be noted that if there is even one electricity-driven compressor in the EGH-IES, there will be a variation transmission from the gas network to the electricity network. This is because the electrical power consumed by an electricity-driven compressor is determined by its pressure ratio and gas flow (see Equations (4) and (5)). This variation transmission is also single-directional (i.e., from the gas network to the electricity network) and can be found in all the four typical operation modes presented in this paper. Description of variation transmission from the gas network to the electricity network caused by electricity-driven compressor will not be repeated for the following three operation modes. Figure 1: Schematic diagrams of the EGH-IES. Figure 2: Schematic diagrams of the four typical operation modes. * **Mode 2: \"Electricity/gas following heat\" mode**  
As also shown in Figure 2, when the EGH-IES works in mode 2, the heat node connected to the CHP is set as the heat slack node and the CHP will maintain the overall heat power balance of the heating network. Both the electrical power generated and gas consumed by the CHP in mode 2 are determined by its heat demands, which indicates that heat service has a priority over electricity service, and variations in the heating network will be transmitted to both the electricity and gas networks. This will finally lead to a three-sided variation transmission; that is, the variation transmission from the heating network to the electricity network and the variation transmission from the heating network to the gas network. In mode 2, both P2H and P2G are working with constant inputs/outputs, and there is no variation transmission between the electricity and heating networks via P2H coupling or between the electricity and gas networks via P2G coupling.