## 5 Case Simulation
### Comparison of Different Algorithms  
Taking PV reactive power output mode 1 as an example, optimization results at different time periods, by different algorithms, with different reactive power optimization conditions and for different FID port numbers are compared and displayed in Figure 5. The daytime corresponds to 8:00-18:00, as shown in Figure 1, during which the PVs output active power. The night refers to 0:00-7:00 and 19:00-24:00, during which the active power output of the PVs is 0. Three algorithms of MOPSO, NSGA-II, and NSGA-III were compared. The \"Yes\" in the horizontal axis represents that the reactive power of PV is optimized. The \"No\" in the horizontal axis represents that the reactive power of the PV is not optimized. The FID of two ports, three ports, and four ports are also compared. The voltage deviation and network loss are displayed. The ratio of PV abandonment is very low for all the cases, which is not shown in Figure 5.  
By comparing the results of day and night, it can be seen that the voltage deviation and network loss are both lower during daytime than during night. It indicates that the active power and reactive power adjustment of PV improves power quality. The effect of synergetic optimization is better than that of FID optimization alone.  
During the night, the active power output of PV is 0. The reactive power output is also 0 in reactive power output mode 1. Thus, optimizing PV output does not have an impact on optimization results. The optimization results of the three algorithms are basically consistent. However, during the daytime, PVs can output both active power  
\begin{table}
\begin{tabular}{c c c} \hline
**Case** & \multicolumn{2}{c}{**Parameter Settings**} \\ \cline{2-3}
**Number** & **FID** & **PV** \\ \hline
5 & & None \\ \hline
6 & Four ports: among node 33 (port 1), node 18 (port 2), node 22 (port 3), and node 11 (port 4) & Three PVs \\
7 & & PV1: at node 8, 400 kW \\
8 & & PV2: at node 16, 500 kW \\
8 & & PV3: at node 30, 300 kW \\ \hline
7 & & Eight PVs \\
8 & & PV1–6: the same as case 1 \\
8 & & PV7: at node 25, 400 kW \\
8 & & PV8: at node 29, 300 kW \\ \hline \end{tabular}
\end{table}
Table 2: _Cont._  
Figure 5: Optimization results obtained by different algorithms for FID with different number of ports. “No” in horizontal axis means that reactive power of PVs is not optimized. “Yes” in horizontal axis means that reactive power of PVs is optimized. (**a**) FID of two ports. (**b**) FID of three ports. (**c**) FID of four ports.  
and reactive power, leading to the difference in PV optimization. If there are \(m\) PVs, the dimension of searching space increases by 2 \(m\) when the PV is optimized. The global searching ability of MOPSO is limited. The voltage deviation and network loss increase when the PV is optimized. The optimization performance of NSGA-II and NSGA-III shows the same changing trend. The power quality is better by synergetic optimization of the FID and PV than by FID optimization only. In further comparison, the searching ability of NSGA-II is better in dealing with problems of multi-port FID. The voltage deviation and network loss are lower. Thus, NSGA-II is chosen for later simulations.  
In addition, by comparing the results in Figure 5a-c, the increase in FID port number also reduce voltage deviation and network loss. Owing to the increase in FID port number, active power can be transformed among the ports flexibly. The reactive power output of the ports provides a more reactive power adjustment for the network. The distribution network is more flexible. It is beneficial to improve the power quality of the system.