## 2 Comprehensive Hydrogen-Integrated Energy System Model
### P2g-CCS Coupling Model
#### 2.1.2 P2G Model  
The P2G system uses electrical energy to convert collected CO\({}_{2}\) from CCS into natural gas. The produced natural gas is subsequently reintroduced into gas-consuming equipment, enabling the cyclical usage of carbon. In order to fully evaluate the environmental advantages of green hydrogen, the P2G process is subdivided into two distinct stages: electrolytic hydrogen production and methane generation. The equation representing the conversion model for electrolytic hydrogen production is as follows:  
\[Q_{\text{P2H}}(t)=\eta_{\text{P2H}}P_{\text{P2H}}(t) \tag{3}\]  
where \(Q_{\text{P2H}}(t)\) represents the mass of hydrogen produced by the P2G device during the time interval \(t\); \(\eta_{\text{P2H}}\) denotes the conversion efficiency of electrolysis to hydrogen at time \(t\); and \(P_{\text{P2H}}(t)\) signifies the power consumption of the P2G device at time \(t\).  
The hydrogen methanation process achieves coupling between P2G and CCS by absorbing the CO\({}_{2}\) captured from GB and GT. Simultaneously, it generates natural gas, supplying gas to GB and GT, thereby cyclically utilizing CO\({}_{2}\) and reducing the overall carbon emissions of the system. The expression for the methane generation process is as follows:  
\[\begin{split}& Q_{\text{H2G}}(t)=Q_{\text{P2H}}(t)-Q_{\text{n}}(t) \\ & G_{\text{MR}}(t)=\eta_{\text{MR}}Q_{\text{H2G}}(t)\\ & m_{\text{MR}}(t)=\frac{3600Q_{\text{H2G}}(t)}{l_{\text{CH${}_{4 }$}}}\rho_{\text{CO${}_{2}$}}\end{split} \tag{4}\]where \(Q_{\rm H2G}(t)\) and \(Q_{\rm n}(t)\) represent the hydrogen consumption through methanation and the mass supplied to the user during time interval \(t\), respectively; \(\eta_{\rm MR}\) denotes the conversion efficiency of methanation at time \(t\); \(G_{\rm MR}(t)\) signifies the gas production from methanation at time \(t\); \(l_{\rm CH_{4}}\) represents the heating value of natural gas; and \(\rho_{\rm CO_{2}}\) denotes the density of CO\({}_{2}\). This system of equations represents the process of P2G methane reforming, with the input parameter being the mass of hydrogen consumed in the methanation process. The final equation in this system indicates that the CO\({}_{2}\) feedstock for methanation is sourced from CCS, highlighting the coupling of P2G and CCS. The P2G process, through methanation, consumes a portion of CO\({}_{2}\), thereby reducing the cost associated with carbon sequestration and positively impacting the economic efficiency of the system.  
Hydrogen Storage Tank Model:  
\[\left\{\begin{array}{l}E_{\rm H_{2}}^{\rm min}\leq E_{\rm H_{2}}(t)\leq E_{ \rm H_{2}}^{\rm max}\\ E_{\rm H_{2}}(t+1)=\eta_{\rm H_{2}}^{\rm c}P_{\rm H_{2}}^{\rm d}(t)+P_{\rm H_{2 }}^{\rm d}(t)/\eta_{\rm H_{2}}^{out}\\ \lambda_{\rm H_{2}}P_{\rm H_{2}}^{\rm c,min}(t)\leq P_{\rm H_{2}}^{\rm c}(t) \leq\lambda_{\rm H_{2}}P_{\rm H_{2}}^{\rm c,max}(t)\\ (1-\lambda_{\rm H_{2}})P_{\rm H_{2}}^{\rm d,min}(t)\leq P_{\rm H_{2}}^{\rm d}(t )\leq(1-\lambda_{\rm H_{2}})P_{\rm H_{2}}^{\rm d,max}(t)\end{array}\right. \tag{5}\]  
where \(E_{\rm H_{2}}(t)\) represents the hydrogen storage capacity of the storage tank at time \(t\); \(E_{\rm H_{2}}^{\rm min}\) and \(E_{\rm H_{2}}^{\rm max}\) denote the upper and lower limits of the hydrogen storage capacity, respectively; \(\eta_{\rm H_{2}}^{\rm c}\) and \(\eta_{\rm H_{2}}^{\rm d}\) represent the efficiency of hydrogen storage and release, respectively; \(P_{\rm H_{2}}^{\rm c}(t)\) and \(P_{\rm H_{2}}^{\rm d}(t)\) represent the hydrogen storage and release power of the storage tank at time \(t\), respectively; \(P_{\rm H_{2}}^{\rm c,min}\), \(P_{\rm H_{2}}^{\rm c,max}\), \(P_{\rm H_{2}}^{\rm d,min}\) and \(P_{\rm H_{2}}^{\rm d,max}\) represent the maximum and minimum values of the storage and release power, respectively; to prevent simultaneous hydrogen storage and release, \(\lambda_{\rm H_{2}}\), a binary variable, is equal to 1 during hydrogen storage and 0 during hydrogen release.