## 4 Integrated Energy System Optimization Scheduling
### Optimal Scheduling Model without Accounting for Energy Storage Lifetime Decay  
#### 4.1.1 Objective Function  
Not taking into account the decay of energy storage life, energy storage does not generate direct freight costs when the system is operating, the system's operating costs include the initial investment cost of energy storage, power purchase cost, gas purchase cost, system operating costs, and abandoned scenery generation costs, and the objective function that the sum of all types of operating costs is the lowest.  
\[\text{min}F=F_{e}(t)+F_{g}(t)+F_{OC}(t)+F_{q}(t)+F_{R} \tag{9}\]  
where \(F_{e}(t)\) is the cost of electricity purchase; \(F_{g}(t)\) is the cost of gas purchase; \(F_{OC}(t)\) is the cost of system operation, including operation and maintenance costs and depreciation costs; \(F_{q}(t)\) is the cost of abandoned scenery penalty; and \(F_{R}\) is the initial investment cost of energy storage.  
(1) Cost of electricity purchase \(F_{e}(t)\).  
\[F_{e}(t)=\sum_{t=1}^{24}C_{grid}(t)\cdot P_{grid}(t) \tag{10}\]  
where \(C_{grid}(t)\) is the purchase price of electricity and \(P_{grid}(t)\) is the electric power purchased from the power grid.  
(2) Gas purchase cost \(F_{g}(t)\).  
\[F_{g}(t)=\sum_{t=1}^{24}C_{g}(t)\cdot q_{grid}(t) \tag{11}\]  
where \(C_{g}(t)\) is the price of purchased natural gas and \(q_{grid}(t)\) is the flow rate of gas purchased from natural gas.  
(3) Abandoned scenery penalty cost \(F_{q}(t)\).  
\[F_{q}(t)=\lambda_{PV}\sum_{t=1}^{24}\left(P_{PV}^{\text{F}}(t)-P_{PV}(t) \right)+\lambda_{WT}\sum_{t=1}^{24}\left(P_{WT}^{\text{F}}(t)-P_{WT}(t)\right) \tag{12}\]  
where \(\lambda_{PV}\) is the penalty factor for light abandonment; \(\lambda_{WT}\) is the penalty factor for wind abandonment; \(P_{PV}^{\text{F}}(t)\) is the photovoltaic power; \(P_{WT}^{\text{F}}(t)\) is the wind power; \(P_{PV}(t)\) is the photovoltaic power used to supply the electricity-gas integrated energy system; and \(P_{WT}(t)\) is the wind power used to supply the electricity-gas integrated energy system.  
(4) System operation cost \(F_{OC}(t)\).  
\[F_{OC}(t)=\sum_{i=1}^{n}f_{i}(t) \tag{13}\]  
where \(f_{i}(t)\) is the operating cost of the \(i\)-th device at the time \(t\).  
\[\left\{\begin{array}{l}f_{P2G}(t)=(K_{om}^{P2G}+C_{dp}^{P2G})\sum\limits_{t=1}^{24 }P_{P2G}(t)+\gamma_{P2G}^{H_{2}O}\sum\limits_{t=1}^{24}Q_{P2G}^{H_{2}0}(t)- \gamma_{P2G}^{O_{2}}\sum\limits_{t=1}^{24}Q_{P2G}^{O_{2}}(t)\\ f_{ES}(t)=\sum\limits_{t=1}^{24}\left[K_{om1}^{ES}\cdot C_{R}+(K_{om2}^{ES}+C_{ dp}^{ES})|P_{ES}(t)|\right]\\ \hskip 142.26378 ptf_{mt}(t)=(K_{om}^{mt}+C_{dp}^{mt})\sum\limits_{t=1}^{24}P_{ mt}(t)\\ f_{eb}(t)=(K_{om}^{eb}+C_{dp}^{eb})\sum\limits_{t=1}^{24}P_{eb}(t)\\ f_{cc}(t)=(K_{om}^{cc}+C_{dp}^{cc})\sum\limits_{t=1}^{24}P_{ec}(t)\\ f_{he}(t)=(K_{om}^{he}+C_{dp}^{he})\sum\limits_{t=1}^{24}Q_{he,in}(t)\\ f_{ac}(t)=(K_{om}^{ac}+C_{dp}^{ac})\sum\limits_{t=1}^{24}Q_{ac,in}(t)\\ f_{PV}(t)=(K_{om}^{PV}+C_{dp}^{PV})\sum\limits_{t=1}^{24}P_{PV}(t)\\ f_{WT}(t)=(K_{om}^{WT}+C_{dp}^{WT})\sum\limits_{t=1}^{24}P_{WT}(t)\\ \end{array}\right. \tag{14}\]  
In the formula, \(K_{om}^{i}\) is the operation and maintenance coefficient of the \(i\) equipment, \(C_{dp}^{i}\) is the depreciation coefficient of the \(i\) equipment, \(\gamma_{P2G}^{H_{2}O}\) is the unit price of water consumed by the P2G equipment during operation, \(\gamma_{P2G}^{O_{2}}\) is the oxygen unit price sold during the operation of the P2G equipment, \(K_{om1}^{ES}\) is the energy storage capacity maintenance cost coefficient [48], and \(K_{om2}^{ES}\) is the energy storage power maintenance cost coefficient.  
(5) Initial investment cost of energy storage \(F_{R}\).  
The initial investment cost of energy storage \(F_{R}\) is a fixed value.