## 3 Construction and Solving Method for the Bi-Level Multi-Objective Optimization Model
### Construction Life Cycle Bi-Level Optimization Model for MCSs
#### 3.2.2 Lower Level Optimization Model  
Due to different energy attributes, each energy system should adopt a self-organizing collaborative operation scheduling mode in the process of system operation. Carbon emissions in the process could be reduced via the internal optimization of each energy source in order to achieve the global low-carbon operation of the system. Different types of energy have coupling effects in the operational process, and these coupling characteristics are mainly reflected in the energy interaction. In the comprehensive evaluation of MCSs, such coupling is the key link while the coupling correlation models between different energy flow characteristics and energy sources are constructed. The primary problem to be considered is to meet the requirements of large-scale utilization of renewable energy with high permeability [25]. The essence of optimizing electricity and natural gas is to improve the utilization rate of renewable energy or new energy. Therefore, the development of a safe and stable multi-energy complementary system with high renewable energy penetration is an important part of energy system reform, based on considering the policy and demand of renewable energy applications in the framework of the current social goal of \"carbon neutrality\" [26]. To fully tap into the advantages of MCSs in terms of high environmental protection and energy efficiency, renewable energy penetration and carbon transaction cost are identified as the key factors for system operational optimization. The carbon transaction cost is included in the objective function of the optimization model. The high penetration of renewable energy is used as the constraint condition of operational optimization in order to achieve the comprehensive collaborative optimization of MCSs under the high penetration of renewable energy. The lower level optimization is based on system operational optimization. The objective is to minimize the total operational cost. The optimization model expression can be written as:  
\[\text{min}F_{d}=F_{d}(y) \tag{20}\]\[F_{d}=\sum_{t=1}^{N_{t}}\left[\lambda_{e}(t)P_{e}(t)+P_{GB,in}^{g}(t) \lambda_{g}(t)+C_{CO_{2}}(t)\right]+\xi_{i.m}\sum_{i}^{N_{i}}C_{\alpha,i.j}+\sum _{i=1}^{N_{i}}C_{\epsilon,q,i}\frac{(1-\delta)}{y_{i}} \tag{21}\] \[C_{CO_{2}}(t)=\lambda_{c}(t)\cdot[P_{GB,in}^{g}(t)\cdot F_{CO_{2 },g}+P_{e}(t)\cdot F_{CO_{2},e}+P_{EH}^{in}(t)\cdot\tau-\varepsilon_{e}P_{eb}( t)+\varepsilon_{h}P_{wh}(t)] \tag{22}\]  
where \(y\) represents the decision variables of the lower optimization model (namely, MCS energy supply and conversion equipment efficiency); \(y_{i}\) is the service life of equipment i (years); \(C_{CO_{2}}(t)\) is the system's carbon transaction cost at time t (CNY); \(\varepsilon_{e}\) is the emission quota coefficient of unit electricity, which is taken as 0.7567 kg/kWh; and \(\varepsilon_{h}\) is the unit thermal emission quota coefficient, which can be calculated by the total amount of thermal production and the total amount of fuel consumed in each region, taken as 0.385 kg/kWh.