## 3 System Models
### Low-Carbon Energy Sharing Model of Multiple Gas-Electric IESs
#### 3.2.2 Constraints  
The primary constraints of the low-carbon economic model of multiple regional gas-electric IESs can be divided into two categories. The first category is the internal constraints of each gas-electric IES, mainly including unit output constraint, energy purchase constraint, electric-to-gas conversion constraint, and carbon capture constraint in the gas-electric IES. The second category of constraints includes the constraints from the interactive coupling of each gas-electric IES, mainly including constraints from electric power interaction and gas power interaction.  
Internal constraints of each gas-electric IES:  
1. Electricity balance constraint: \[P_{i,t}+P_{e,t}^{in}+P_{w,t}-P_{P2G,t}^{in}-P_{char,t}^{e}+P_{dis,t}^{e}-P_{r, t}^{CC}=L_{e}^{t}\] (17)  
where \(P_{P2G,t}^{in}\) represents the electric power consumed by the electric-to-gas converter during the period \(t\) within a day, and \(P_{char,t}^{e}\) and \(P_{dis,t}^{e}\) are, respectively, the charging and discharging power of the energy storage battery during the period \(t\).  
(2) Gas energy balance constraint:  
\[P_{g,t}^{in}+P_{P2G,t}^{in}\eta_{P2G}-P_{char,t}^{g}+P_{dis,t}^{g}={L_{g}}^{t} \tag{18}\]  
where \(L_{g,t}\) represents the original predicted value of the gas load in the period \(t\) within a day; \(\Delta L_{g,t}\) represents the change of the gas load demand response in the period \(t\) within a day; \(P_{char,t}^{g}\) and \(P_{dis,t}^{g}\) are, respectively, the charging and discharging power of the gas storage tank in the period \(t\); and \(\eta_{P2G}\) is the efficiency of the electric-to-gas conversion process.  
(3) Unit power constraint:  
\[P_{i,min}\leq P_{i,t}\leq P_{i,max} \tag{19}\]  
where \(P_{i,max}\) and \(P_{i,min}\) are the upper and lower limits of unit output from the \(i\) IES.  
(4) P2G output constraint:  
\[P_{P2G,min}\leq P_{P2G}\leq P_{P2G,max} \tag{20}\]  
where \(P_{P2G,min}\) and \(P_{P2G,max}\) are the upper and lower limits of P2G output.  
(5) Carbon capture device constraint:  
\[M_{i,t}^{CC}=\eta_{i,t}P_{r,t}^{CC} \tag{21}\]  
\[\eta_{min}\leq\eta_{i,t}\leq\eta_{max} \tag{22}\]  
where \(P_{CC,i,t}\) is the energy consumption by the carbon capture device of the coal-fired unit \(i\) in period \(t\); \(P_{r,t}^{CC}\) is the operating energy consumption by the carbon capture device; \(\eta_{i,t}\) is the corresponding carbon capture device power; and \(\eta_{max}\) and \(\eta_{min}\) are the maximum and minimum carbon capture power, generally with \(\eta_{max}\) being 90% and \(\eta_{min}\) being 0.  
(6) Constraints from power interactive coupling of each gas-electric IES:  
\[P_{i-j,e}^{\min}\leq P_{i-j,e}^{t}\leq P_{i-j,e}^{\max} \tag{23}\]  
where \(P_{i-j,e}^{t}\) is the electric power interaction between the \(i\)th gas-electric IES and the \(j\)th gas-electric IES within a day; \(P_{i-j,e}^{min}\) and \(P_{i-j,e}^{max}\) are, respectively, the lower limit and upper limit of the electric power interaction between the \(i\)th gas-electric IES and the \(j\)th gas-electric IES.  
\[P_{i-j,g}^{\min}\leq p_{i-j,g}^{t}\leq P_{i-j,g}^{\max} \tag{24}\]  
where \(p_{i-j,g}^{t}\) is the gas power interaction between the \(i\)th gas-electric IES and the \(j\)th gas-electric IES within a day; \(P_{i-j,g}^{min}\) and \(P_{i-j,g}^{max}\) are, respectively, the lower limit and upper limit of the gas power interaction between the \(i\)th gas-electric IES and the \(j\)th gas-electric IES.