## 6 Conclusions  
To enhance the renewable energy accommodation rate and operational reliability of the DN while reducing operational costs, a multi-time scale hierarchical coordinated optimization strategy for DNs considering the aggregation of DES resources is proposed in this paper. A DES aggregation method based on the inner approximation of the Minkowski Sum is proposed. A power allocation method for DES clusters based on the WFA is proposed. Based on the case study analysis, the following conclusions are drawn:  
* Considering the participation of DES resource clusters in the optimal operation of DNs can reduce operational costs, improve the operational reliability of the DN, and enhance the renewable energy accommodation rate.
* The proposed multi-time scale optimization operation method effectively utilizes the fast regulation capabilities of ESS and DES resources, thereby improving the accuracy of the system's response to forecast data.
* The application of the WFA for decomposing control commands of the DES clusters effectively balances the loads of individual DES units, optimizes resource allocation, and provides a feasible solution for large-scale distributed DES deployment.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenarios** & **Carbon Emission Allowance** & **Carbon Emissions** & **Carbon Emission Cost** \\ \hline Before DES Integration & 2407.9 T & 1633.2 T & \(-\)38,736 CNY \\ After DES Integration & 2399.4 T & 1607.4 T & \(-\)39,605 CNY \\ \hline \hline \end{tabular}
\end{table}
Table 6: Economic and Environmental Effects Before and After DES Integration.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Scenarios** & **Accommodation Rate Before** & **Accommodation Rate After** \\  & **DES Integration** & **DES Integration** \\ \hline
1 & 95.90\% & 100\% \\
2 & 96.67\% & 100\% \\
3 & 97.36\% & 100\% \\
4 & 96.20\% & 99.14\% \\
5 & 96.58\% & 98.95\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Renewable Energy Accommodation Effect in Each Scenario Before and After DES Integration.  
In future work, further improvements in the approximation accuracy of the aggregation method will be required, and research on the optimal aggregation scope of DES will be conducted.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15042075/s1](https://www.mdpi.com/article/10.3390/app15042075/s1)]([https://www.mdpi.com/article/10.3390/app15042075/s1](https://www.mdpi.com/article/10.3390/app15042075/s1)), Table S1: Branch-node matrix; Table S2: Structure matrix; Table S3: Branch impedance matrix.  
Conceptualization, J.L., C.N. and Z.L.; data curation, S.Y. and S.Q.; formal analysis, Y.Z., A.X. and R.L.; funding acquisition, J.L., Y.Z., A.X. and R.L.; investigation, J.L. and C.N.; methodology, J.L., C.N. and Y.Z.; project administration, J.L. and Z.L.; resources, Y.Z. and Z.L.; software, C.N., A.X. and S.Y.; supervision, Z.L.; validation, C.N., S.Y. and Z.L.; visualization, S.Y. and S.Q.; writing--original draft, J.L., S.Y. and Y.Z.; writing--review and editing, C.N., S.Y. and Z.L. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the Science and Technology Project of State Grid Henan Economic Research Institute. (No. 5217L024000Y).  
Not applicable.  
The original contributions presented in the study are included in the article/Supplementary Materials, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.