## 3 Method and Material
### Multi-Objective Optimization Model for Polygeneration System
#### 3.2.2 Objectives  
In addition to ensuring the realization of single-dimension environmental goals, including energy conservation and pollution emission reduction, the synergistic and conflicting effects of various technologies on environmental objectives and the corresponding economic benefit are also considered in this study. Consequently, three optimization objectives are set in this study, including: (a) the maximum of energy conservation; (b) the maximum of pollutants emission reduction; and (c) the maximum of economic benefits. It should be emphasized that SO\({}_{2}\), NO\({}_{\times}\), and PM will be converted into unified pollutant emission indicators according to their pollutant emission trading prices in order to simplify the calculation. The energy benefit of polygeneration systems includes two parts: direct energy benefit and indirect benefit. The former refers to energy saved, or secondary energy generated in the way of energy utilization, while the latter refers to the energy consumption of resources. Production and processing can be reduced by reducing the resource consumption of the given sink industry under the resource utilization approach. Thus, the energy benefit of the polygeneration system can be calculated by Equation (1). \[EC=CSO\times\sum_{pro}\sum_{bp}\sum_{t}SR_{pro}\times GF_{pro,bp}\times Ratio_{ pro,bp,t}\times(\sum_{e}E_{t,e}\times Ecoe_{e}+\sum_{res}E_{t,res}\times Ecoe_{res}) \tag{1}\]  
where \(EC\) represents the energy benefit of a polygeneration system; \(CSO\) is the crude steel output; \(pro\) is the production process; \(bp\) is the by-product; \(t\) is the polygeneration technology; \(e\) is the type of fuel; \(res\) is the type of resource; \(SR_{pro}\) is the process product coefficient of \(pro\); \(GF_{pro,bp}\) is the production coefficient of by-product \(bp\) from the production process \(pro\); \(Ratio_{pro,bp,t}\) is the utilization ratio of by-products \(bp\) from the production process \(pro\) when applying technology \(t\); \(E_{t,e}\) is the conservation amount of fuel \(e\) contributed by technology \(t\); \(E_{ceo}\) is the conversion coefficient of fuel \(e\) to standard coal; \(E_{t,res}\) is the conservation amount of resource \(res\) contributed by technology \(t\); and \(Ecoe_{res}\) is the energy consumption coefficient of resource \(res\) in the production process. The environmental benefits of polygeneration systems are mainly reflected in the reduction in three types of air pollutants in this study, which are SO\({}_{2}\), NO\({}_{\times}\), and PM, respectively. Similar to energy benefit, environmental benefit can also be divided into direct and indirect benefit, where direct benefit refers to the pollutants emissions reduction from the polygeneration system with polygeneration technologies application, and indirect benefit refers to the pollutants emissions avoided by saving energy and resources with polygeneration technologies application. Therefore, the environmental benefit of polygeneration systems can be calculated by Equation (2). \[ER_{p}=CSO\times\sum_{pro}\sum_{bp}\sum_{t}SR_{pro}\times GF_{pro,bp}\times Ratio _{pro,bp,t}\times(DER_{t,p}+\sum_{e}E_{t,e}\times EF_{e,p}+\sum_{res}E_{t,res} \times EF_{res,p}) \tag{2}\]where \(ER\) is the emission reduction amount of pollutant \(p\); \(DER_{t,p}\) is the direct emission reduction effect of technology \(t\) on pollutant \(p\); \(EE_{e,p}\) is the pollutant \(p\) mission factor of fuel \(e\) during the production or combustion process; and \(EF_{res,p}\) is the pollutant \(p\) mission factor of resource _res_ during the production process. The economic benefits of polygeneration systems are mainly determined by investment in fixed assets, operation and maintenance expenses, and the economic benefits of by-products. The investment in fixed assets refers to the equipment investment required by various polygeneration technology applications.