## 5 Case Simulation
### Discussion of Reactive Power Output Ratio by PV Inverter
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Mode** & **Voltage Deviation (Ranking)** & **Network Loss (Ranking)** \\ \hline Mode 1 & 0.8355 (5) & 0.0945 (3) \\ Mode 2 & 0.7976 (4) & 0.0933 (2) \\ Mode 3 & 0.7883 (3) & 0.0927 (1) \\ Mode 4 & 0.7253 (2) & 0.0970 (5) \\ Mode 5 & 0.7138 (1) & 0.0963 (4) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation results of five reactive power output modes. Figure 7: Optimization results under five modes and with different FID port numbers. Simulations are carried out for case 4 (before optimization) and case 3 (after optimization). As seen from Figure 8a, the voltage reduces to 0.9130 pu at some nodes and some moments. Due to the injection and fluctuation of PVs, voltage is occasionally out-of-limit. The power quality turns bad, which further impedes the consumption of the PV. When the synergetic optimization of the PV and FID is utilized, the voltage amplitude is stabilized. The minimum voltage is 0.9615 pu. The voltage deviation is 0.2004 pu and the network loss is 0.0289 MW. It indicates that the power quality is improved. The optimization results of PVs are shown in Figure 9. The active power output approximately equals the value of MPPT for all the PVs, as shown by the black line in Figure 9. Owing to the setting of the PV abandonment ratio as an objective function, the active power output of the PV is optimized to minimize the PV abandonment ratio. The PV abandonment ratio does not exceed 3%. The reactive power output is displayed with a red line in Figure 9. During the daytime, the reactive power output is mainly limited by capacity constraints. Due to the injection of the PV active power, reactive power compensation is required to stabilize the voltage. During the night, the active power of the PV is 0. The reactive power output of the PV is used to compensate the reactive power of the devices. The reactive power output is related to the position of the PV, the position of the FID, and the distribution of the load. The optimization result of the FID is also analyzed. The active power flow is shown in Figure 10a. Owing to the four ports of the FID, the active power flows more flexibly. The active power flows among the four ports according to the PV access position, output, and the load. Port 1 and port 2 connect to the terminal nodes of two feeders. Thus, during the night, active power is transformed from port 3/port 4 to port 1/port 2, ensuring the effective utilization of active power. During the daytime, the PVs output active power. The access position of PV\({}_{3}\) and PV\({}_{4}\) is close to port 2 and port 3. Active power flows from port 2/port 3 to port 1/port 4 for active power balance. The reactive power flow is shown in Figure 10b. During most time periods, the FIDs output reactive power. The reactive power output is limited by the port capacity. It is also influenced by the output of the PVs and the distribution of the load. Due to the close connection of the PVs to port 2 and port 3, the reactive power output of port 2/port 3 is lower than that of port 1/port 4. With the development of the PV and the requirement of environmental friendliness, more PVs are connected to the distribution network. PV permeability grows quickly. To  
Figure 10: Optimal scheme of FID. In (**a**), positive value means active power flow from port; negative value means active power flow into port. (**a**) Active power flows among ports. (**b**) Reactive power output of ports. testify the applicability of the proposed method, the optimization under the conditions of different PV permeabilities is simulated. Simulations of cases 3, 5, 6, and 7 are compared. The results are listed in Table 4.  
With the increase in PV permeability, the voltage deviation and the network loss are both reduced. When the PV permeability reaches 86.1%, the reduction ratio of voltage deviation and network loss is 87.4% and 84.2%, respectively. The power quality is obviously improved. When the PV permeability increases, the ratio of PV abandonment increases slightly.