# Assessing Voltage Stability in Distribution Networks:
## 6 Conclusions  
This paper analyzed the uncertainty and correlation of distributed generators and loads within the distribution network. Addressing the shortcomings of traditional probability assessment methods to deal with the correlation between variables, the Copula function and Nataf transformation were introduced into 3 PEM, combined with the load margin index \(I_{\text{LM}}\) and a risk-preference utility function, to propose a probabilistic assessment method for SVS that accurately handled the correlations among input variables. The IEEE 33-node power distribution system was connected to distributed PV for testing, and the conclusions are as follows:  
1. Across different distribution functions, the proposed method accurately handled the correlations among input variables, demonstrating strong applicability, high computational efficiency, and precision;  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**PV Integration**} & \multicolumn{3}{c}{**Degree of Risk of Static Voltage Instability**} \\ \cline{2-4}  & \multirow{2}{*}{**MCS (5000)**} & **3 PEM** & **3 PEM** \\  & & **Considering Correlations** & **with Considering Correlations** \\ \hline Without PV Integration & 0.2372 & 0.2370 & 0.2379 \\ \hline Scenario 1 & 0.0277 & 0.0275 & 0.0287 \\ \hline Scenario 2 & 0.0135 & 0.0138 & 0.0149 \\ \hline Scenario 3 & 0.0019 & 0.0017 & 0.0035 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Degree of risk of static voltage instability.  
2. Combined with the risk-preference utility function, the degree of risk of voltage instability of the system was established, which can be a more comprehensive and quantitative assessment of the operational risks of a distribution network with distributed generators in different scenarios;
3. Distributed access not only enhances the stability of the electrical grid but also improves the performance of the grid under extreme conditions by spreading risk and enhancing system redundancy. Therefore, distributed access strategies should be prioritized in the design and planning of modern distribution networks.  
The case of the IEEE 33-node system provides validation that the method presented significantly improves computational efficiency compared to the MCS method, while maintaining high accuracy. This method is suitable for analysis and calculation tasks such as safe operation, planning, and scheduling of distribution networks under strong uncertainties on both the source and load sides. It provides more comprehensive and accurate auxiliary decision-making information for planning and scheduling personnel, thus having practical engineering application value. However, it should be noted that the proposed method does not involve the ring network structure for voltage stability analysis of the distribution network, which presents certain limitations. As part of future research, we will extend the study to distribution network systems with ring structures. By researching different network topologies and optimizing control strategies, we further enhanced the comprehensiveness and practicality of the study, providing a stronger guarantee for the safe operation and optimized dispatch of the power system.  
Conceptualization, S.L. and Y.G.; methodology, Y.G. and S.L.; software, Y.G. and X.Y.; validation, S.L. and Y.G.; formal analysis, S.L., Y.G. and X.Y.; investigation, Y.G. and X.Y.; resources, S.L. and Y.G.; data curation, Y.G.; writing--original draft preparation, Y.G., S.L. and X.Y.; writing--review and editing, Y.G. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Postgraduate Research and Practice Innovation Program of Jiangsu Province (SJCX23_1195), the Scientific Research Foundation of Nanjing Institute of Technology (ZKJ202102), and the Postgraduate Innovation Program of Nanjing Institute of Technology (TB202417075).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.