## 3 Construction and Solving Method for the Bi-Level Multi-Objective Optimization Model
### Construction Life Cycle Bi-Level Optimization Model for MCSs
#### 3.2.1 Upper Optimization Model
The upper optimization model and constraint conditions can be expressed as [14]:  
\[\min F_{up}=\left(F_{up.1}(x),F_{up.2}(x),-F_{up.3}(x)\right)^{T} \tag{5}\]  
\[F_{up.1}=1.3\psi\cdot\sum_{i=1}^{N_{tp}}\lambda_{i}W_{i}+\sum_{t=1}^{N_{t}}[ \lambda_{e}(t)P_{e}(t)+P_{GB.in}^{\delta}(t)\lambda_{g}(t)+\xi_{i.m}\sum_{i}^ {N_{i}}C_{up.i}]+C_{EH}W_{EH}-\delta\sum_{i}^{N_{i}}C_{up.i} \tag{6}\]  
\[\psi=\frac{\zeta(1+\zeta)^{y}}{(1+\zeta)^{y}-1} \tag{7}\]  
\[F_{up.2}=\sum_{t=1}^{N_{t}}P_{GB.in}^{\delta}(t)\cdot F_{CO_{2},g}+P_{e}(t) \cdot F_{CO_{2},e}+P_{EH}^{in}(t)\cdot\tau \tag{8}\]  
\[F_{up.3}=\sum_{t=1}^{N_{t}}\frac{P_{eb}(t)+P_{ac}(t)+P_{ah}(t)+P_{uh}(t)}{\mu _{e}P_{e}(t)+\mu_{g}P_{GB.in}^{\delta}(t)/L} \tag{9}\]  
\[W_{i.\min}\leq W_{i}\leq W_{i.\max} \tag{10}\]  
\[\beta_{i.\min}W_{i}\leq P_{i.out}(t)\leq\beta_{i.\max}W_{i} \tag{11}\]  
\[-R_{d}\leq P_{e}(t+1)-P_{e}(t)\leq R_{u} \tag{12}\]  
\[0\leq P_{EH}^{in}(t)\leq v_{in}W_{EH} \tag{13}\]  
\[0\leq P_{EH}^{out}(t)\leq v_{out}W_{EH} \tag{14}\]  
\[F_{up.1}=1.3\psi\cdot\sum_{i=1}^{N_{tp}}\lambda_{i}W_{i}+\sum_{t=1}^{N_{t}}[ \lambda_{e}(t)P_{e}(t)+P_{GB.in}^{\delta}(t)\lambda_{g}(t)+\xi_{i.m}\sum_{i}^ {N_{i}}C_{up.i}]+C_{EH}W_{EH}-\delta\sum_{i}^{N_{i}}C_{up.i} \tag{6}\]0  
\[F_{up.1}=1.3\psi\cdot\sum_{i=1}^{N_{tp}}\lambda_{i}W_{i}+\sum_{t=1}^{N_{t}}[ \lambda_{e}(t)P_{e}(t)+P_{GB.in}^{\delta}(t)\lambda_{g}(t)+\xi_{i.m}\sum_{i}^ {N_{i}}C_{up.i}]+C_{EH}W_{EH}-\delta\sum_{i}^{N_{i}}C_{up.i} \tag{6}\]1  
\[F_{up.1}=1.3\psi\cdot\sum_{i=1}^{N_{tp}}\lambda_{i}W_{i}+\sum_{t=1}^{N_{t}}[ \lambda_{e}(t)P_{e}(t)+P_{GB.in}^{\delta}(t)\lambda_{g}(t)+\xi_{i.m}\sum_{i}^ {N_{i}}C_{up.i}]+C_{EH}W_{EH}-\delta\sum_{i}^{N_{i}}C_{up.i} \tag{6}\]2  
\[F_{up.1}=1.3\psi\cdot\sum_{i=1}^{N_{tp}}\lambda_{i}W_{i}+\sum_{t=1}^{N_{t}}[ \lambda_{e}(t)P_{e}(t)+P_{GB.in}^{\delta}(t)\lambda_{g}(t)+\xi_{i.m}\sum_{i}^ {N_{i}}C_{up.i}]+C_{EH}W_{EH}-\delta\sum_{i}^{N_{i}}C_{up.i} \tag{6}\]3  
\[F_{up.1}=1.3\psi\cdot\sum_{i=1}^{N_{tp}}\lambda_{i}W_{i}+\sum_{t=1}^{N_{t}}[ \lambda_{e}(t)P_{e}(t)+P_{GB.in}^{\delta}(t)\lambda_{g}(t)+\xi_{i.m}\sum_{i}^ {N_{i}}C_{up.i}]+C_{EH}W_{EH}-\delta\sum_{i}^{N_{i}}C_{up.i} \tag{6}\]4  
where \(x\) is the optimal decision variable set of the design capacity of MCS energy supply and conversion equipment (kW); \(\psi\) is the conversion coefficient of the purchase cost converted into the equivalent annual fee according to its life years (namely, the capital recovery coefficient); \(N_{tp}\) represents the total amount of equipment in the MCS system; \(N_{t}\) represents the system planning period, taken as 20 years; \(\lambda_{i}\) is the unit capacity price for equipment \(i\) (CNY/kW); \(W_{i}\) is the rated capacity of equipment \(i\) (kW); \(\lambda_{e}(t)\) is the price of buying electricity from the grid at time t (CNY/kWh); \(\lambda_{g}(t)\) is the price of gas at time \(t\) (CNY/m\({}^{3}\)); \(N_{i}\) is the number of device i in the planning period; \(\xi_{i.m}\) is the maintenance cost coefficient of equipment i (CNY/kWh); \(C_{\alpha_{i}.i}\) is the total investment cost of equipment \(i\) (CNY); \(C_{EH}\) is the unit replacement cost of the EH (CNY); \(W_{EH}\) is the rated capacity of the EH (kW); \(\delta\) is the net residual rate of the equipment, taken as 5%; \(y\) is the life of equipment use (namely, the investment period); \(\zeta\) is the annual benchmark yield (namely, the discount rate, taken as 6%); \(F_{CO_{2}.g}\) is the emission factor of natural gas based on the minimum calorific value, taken as 0.607 kg/kWh [22]; \(F_{CO_{2}.e}\) is the grid baseline emission factor, taken as 0.912 kg/kWh [23]; \(\tau\) is the indirect carbon emission coefficient of the energy storage equipment according to the indirect emission coefficient of electric energy storage, taken as 0.0913 kg/kWh [24]; \(\mu_{e}\) and \(\mu_{g}\) are the standard coal coefficients of electricity and natural gas, respectively, which are taken as 0.36 kg/1000 kWh and 1.33 kg/m\({}^{3}\), respectively; \(L\) is the low calorific value of natural gas, taken as 9.7 kWh/m\({}^{3}\); \(W_{i,\max}\) and \(W_{i,\min}\) are the upper and lower limits of the installation capacity of equipment i, respectively (kW); \(\beta_{i,\min}\) and \(\beta_{i,\max}\) are the minimum and maximum load rates allowed by device i, respectively, which are taken as 0.2 and 1.0, respectively; \(P_{Lout}(t)\) is the output power of device i at time \(t\) (kW); \(R_{d}\) is the downward climbing rate of electrical output power; \(R_{u}\) is the upward climbing rate of electrical output power; \(P_{EH}^{in}(t)\) and \(P_{EH}^{out}(t)\) are the charging and discharging power of energy storage at time \(t\), respectively; \(v_{in}\) and \(v_{out}\) are the charging and discharging rate of energy storage, respectively; \(T\) is the scheduling time, taken as 1 h; \(P_{e.\min}\) and \(P_{e,\max}\) are the lower and upper limits of the electric power obtained by the system from the power grid, respectively (kW); \(P_{GB,\min}^{g}\) and \(P_{GB.\max}^{g}\) are the lower and upper limits of natural gas power obtained by the gas boiler from the natural gas network, respectively (kW); \(M\) is the amount of renewable energy equipment; \(S_{s}\) is the area available for installation of equipment for on-site investigation, considering factors such as reserved clearance and space occlusion (m\({}^{2}\)); and \(S_{a}\) is the installation area for a single device (m\({}^{2}\)).