## 3 Equipment Efficiency and Economical Models
### PV Power Generation System  
The output model of the PV system is [25]:  
\[P_{\text{PV}}(t)=f_{\text{PV}}P_{\text{PV,rated}}\frac{A(t)}{A_{S}}\big{[}1+ \alpha_{\text{P}}(TEM(t)-TEM_{\text{STC}})\big{]} \tag{8}\]  
where \(f_{\text{PV}}\) is the power reduction factor of PV, which is set as 0.9; \(P_{\text{PV,rated}}\) is the rated power of PV; \(A(t)\) is the actual irradiance on the PV current tilt plane; \(A_{S}\) is the irradiance under standard test conditions, which is set as 1 kW/m\({}^{2}\); \(\alpha_{\text{P}}\) is the power temperature coefficient, which is set as \(-0.47\%/^{\circ}\)C; \(TEM(t)\) is the surface temperature of PV; and \(TEM_{\text{STC}}\) is the temperature of PV under standard test conditions, which is set as 25 \({}^{\circ}\)C in this study. Unlike other components in the multi-energy microgrid, the PV system does not need primary energy. Thus, no fuel cost is needed. It is much less expensive to operate PV than it is to run other equipment. By fully considering the PV construction cost, maintenance cost, labor cost, price increase indices, government subsidies, the actual service life of the PV system, the net PV residual value, and the unit conversion cost of PV, power generation is calculated to simplify the following economical calculations. The conversion cost is as follows:  
\[C_{\text{output}}^{\text{PV}}=\frac{N_{\text{PV}}P_{\text{PV,rated}}c_{\text{ PV0}}(1-\rho)+\sum\limits_{Y_{PV}=1}^{N_{\text{PV}}}f(Y)}{N_{\text{Y,PV}}N_{\text{PV}}T_{ \text{PV,max}}M_{\text{PV}}}-B_{\text{subsidy}} \tag{9}\]  
where \(N_{\text{PV}}\) is the number of PVs; \(c_{\text{PV0}}\) is the unit capacity investment in PV construction; \(\rho\) is the net residual rate, which is set as \(3\%\); \(f(Y)\) is the net residual value of PV; \(M_{\text{PV}}\) is the installation capacity of PV; and \(B_{\text{subsidy}}\) is the national subsidy for energy-saving and emission reduction, which is set as 0.1 \(\text{\text{\  
where \(SOC(t)\) is the electric quantity of ES at time interval \(t\); \(\delta\) is the ES self-discharge rate, which is set as 0.5%/h; \(P_{\rm C}^{\rm ES}(t)\) and \(P_{\rm D}^{\rm ES}(t)\) are the charging and discharging power of ES at time interval \(t\), respectively; \(\eta_{\rm C}^{\rm ES}\) and \(\eta_{\rm D}^{\rm ES}\) are the charging or discharging efficiency of ES, which are set as 90% and 90%, respectively; and \(E_{\rm SOC}\) is the rated capacity of ES. LB has a low self-discharge rate, so self-discharge loss is ignored. The cost lost in ES during operation mainly includes the costs of life loss \(C_{\rm life}^{\rm ES}\) and power transmission loss \(C_{\rm trans}^{\rm ES}\). The cost of life loss in the power storage device can be calculated as follows:  
\[C_{\rm life}^{\rm ES}=\frac{\mu^{\rm ES}C_{\rm invest}^{\rm ES}}{N(|ES(t-1)-ES(t )|)} \tag{12}\]  
where \(\mu^{\rm ES}\) is the regulating coefficient of ES, which is set as 1; \(C_{\rm invest}^{\rm ES}\) is the one-time ES purchase cost; \(N(\cdot)\) is the discharge depth function, which is typically a four-order function that denotes the relationship between cycle life and discharge depth [23]; ES(\(t\)) is the power energy proportion of the current LB, which can be calculated as follows:  
\[ES(t)=\frac{SOC(t)}{E_{SOC}} \tag{13}\]  
The power transmission loss \(C_{\rm trans}^{\rm ES}\) of ES devices results from incomplete transmission. It can be expressed as follows:  
\[C_{\rm trans}^{\rm ES}(t)=c_{\rm trans}^{\rm ES}[(1-\eta_{\rm C}^{\rm ES})P_{ \rm C}^{\rm ES}(t)+(1/\eta_{\rm D}^{\rm ES}-1)P_{\rm D}^{\rm ES}(t)] \tag{14}\]  
When the multi-energy microgrid system runs in grid-connected mode, ES devices serve to stabilize the fluctuation of renewable energy and improve the economical performance of the system. The charging and discharging states of ES devices are associated with the output of the relevant unit and the electricity pricing mechanism. When the microgrid system runs in electric-isolated mode, the ES devices provide a significant backup energy supply.