## 6 Conclusions  
In this paper, a synergistic optimization operation method for a distribution network is proposed. Owing to the multi-mode output of PVs and the flexible power control capability of FIDs, PVs and FIDs are simultaneously optimized for active power and reactive power output. Taking power quality, economy, and environmental friendliness into consideration, minimizing voltage deviation, network loss, and the ratio of PV abandonment are selected as the objective functions. The constraints of power flow, voltage, and device operation are set in the optimal model. Different reactive power output modes of PVs and different port numbers of FIDs were analyzed and compared. NSGA-II, NSGA-III, and MOPSO were adopted for solving the proposed model. Simulations indicate that the proposed synergetic optimization operation method can provide satisfied results in decreasing voltage deviation and network loss. The best performance is obtained by the PV operating in reactive power output mode 5, the FID with four ports, and utilizing NSGA-II. Due to the participation of the PV in active and reactive power optimization, the proposed method shows better optimization results with the increase in PV permeability. The proposed method indicates the potential of application in the dispatching center and also provides an effective means for the integration of more renewable energy resources. It is applicable for modern and smart grids.  
Though the coordination of PVs and FIDs is simulated and verified, the intermittence and uncertainty of PVs and load are not considered. This paper focuses on the improvement of power quality and PV consumption, without considering the cost of FID investment and system operation. In subsequent research, the influence of source-load uncertainty will be discussed. The objective function will be adjusted for practical applications. More flexible resources will be integrated into the grid to enhance the flexibility and stability of the system.  
Conceptualization, Y.L., M.W. and G.N.; methodology, Y.L. and G.N.; software, J.W., Z.Z. and W.X.; validation, J.W., Z.Z. and W.X.; formal analysis, J.W., Z.Z. and W.X.; investigation, J.W., Z.Z. and W.X.; resources, J.W., Z.Z. and W.X.; data curation, J.W., Z.Z. and W.X.; writing--original draft preparation, Y.L.; writing--review and editing, Y.L. and G.N.; visualization, Y.L.; supervision,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**PV Permeability** & **Voltage Deviation** & **Network Loss** &
\begin{tabular}{c} **Ratio of PV** \\ **Abandonment** \\ \end{tabular} \\ \hline
0 & 0.9010 & 0.1071 & - \\
32.3\% & 0.3719 & 0.0475 & 0.0082 \\
67.3\% & 0.2004 & 0.0289 & 0.0250 \\
86.1\% & 0.1138 & 0.0169 & 0.0251 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Optimization result comparison of different PV permeability.  
G.N.; project administration, G.N.; funding acquisition, G.N. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Fundamental Research Funds for the Central Universities (No. 2022 YQJD13), and the Program for Outstanding Academic/Technical Leaders at Science and Technology Commission of Shanghai Municipality (China) (No. 22 XD1430400).  
The data presented in this study are available on request from the corresponding author.  
Authors [PERSON] and [PERSON] were employed by the company China Electric Power Research Institute. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.