## 5 Results and Discussions
### System Performance Optimization and Comparison  
Finally, parameter optimizations are carried out in this section to provide references for the practical design and operation. The overall performances of a single sCO2 system, sCO2/DH system, sCO2/ammonia-water AHP system and sCO2/LiBr-H2O AHP system are optimized by using the particle swarm optimization (PSO) algorithm, which was proposed by [PERSON] and [PERSON] (2016). The PSO algorithm shows higher accuracy and converges faster compared to other optimization algorithms,  
Figure 8: Variation trends of system performance indicators with \(T_{\rm A1}\) for different thermal systems: (**a**) \(\eta_{ex}\) and \(c_{total}\); (**b**) \(COHP\). and has been successfully applied to optimize performances for thermal systems [55; 56]. A swarm of particles is included in the PSO algorithm to represent the candidate solutions. Each candidate solution has a velocity vector \(\overrightarrow{v}\) and a position vector \(\overrightarrow{u}\). In addition, a best global position \(\overrightarrow{g}(t)\) and a best personal position \(\overrightarrow{p}(t)\) are stored for each particle. For each time step \(t\), the particles move to a better position in the space so that the velocity vector \(\overrightarrow{v}\) and the position vector \(\overrightarrow{u}\) update correspondingly, as shown in Equations (46) and (47):  
\[\overrightarrow{u}(t+1)=\overrightarrow{u}(t)+\overrightarrow{v}(t+1) \tag{46}\]  
\[\overrightarrow{v}(t+1)=\omega\overrightarrow{v}(t)+U(0,\varphi_{1})\Big{(} \overrightarrow{p}(t)-\overrightarrow{u}(t)\Big{)}+U(0,\varphi_{2})\Big{(} \overrightarrow{g}(t)-\overrightarrow{u}(t)\Big{)} \tag{47}\]  
where \(\phi_{1}\) and \(\phi_{2}\) denote the importance of \(\overrightarrow{p}(t)\) and \(\overrightarrow{g}(t)\), respectively. \(\omega\) is the inertia weight that controls the velocity \(\overrightarrow{v}(t)\). In this study, the key parameters studied include the compressor pressure ratio \(PRc\), the turbine inlet temperature \(T_{5}\), the generator outlet temperature \(T_{\text{AS}}\), and the evaporator temperature \(T_{\text{A1}}\). The constraints of key parameters for the PSO algorithm are displayed in Table 13. The exergy efficiency \(\eta_{cx}\) and the total product unit cost \(c_{total}\) are chosen as the objective functions. The optimization is achieved by maximizing \(\eta_{cx}\) or minimizing \(c_{total}\). So two optimal design cases are considered, namely, the exergy efficiency optimal design (EOD) case and the cost optimal design (COD) case. The inertia weight \(\omega\) and the swarm size for the PSO algorithm are chosen as 0.6 and 25, respectively. Both \(\phi_{1}\) and \(\phi_{2}\) are chosen as 1.8. In addition, a maximal velocity \(v_{max}\) of 15% is adopted to constrain the velocity at each time step [57]. The following Table 13 shows the boundary conditions of decision variables for the PSO algorithm. Tables 14 and 15 show the optimized results of these four thermal systems for the EOD case and the COD case, respectively. Obviously, due to the different optimization targets, the exergy efficiencies \(\eta_{cx}\) for the EOD case are much higher than those for the COD case, while the total product unit costs \(c_{total}\) for the COD case are lower than those for the EOD case. The optimum \(PRc\) for the COD case is smaller than that for the EOD case, meaning that the capital investment, operation, and maintenance costs for the turbine, compressors and pressure vessels are lower, which leads to a lower \(c_{total}\) in the COD case. The total product unit costs \(c_{total}\) of a sCO\({}_{2}\) system, sCO\({}_{2}\)/DH system, sCO\({}_{2}\)/ammonia-water AHP system, and sCO\({}_{2}\)/LiBr-H\({}_{2}\)O AHP system for the COD case are about 4.00%, 4.39%, 4.39%, and 3.87% lower than those for the EOD case.