# Distributed Generation Cluster Division Method Considering Frequency Regulation Response Speed
## 5 Case Study  
### Simulation System  
The IEEE 33-node system consists of 18 distributed photovoltaic nodes with a total capacity of 2770 kW; 13 distributed wind power nodes with a total capacity of 480 kW and a distributed power capacity penetration rate of 86.8%; 4 distributed energy storage nodes with a total capacity of 1480 kWh; and 4 micro gas turbine nodes with a total capacity of 2440 kW. The access to renewable energy is shown in Table 12, and the access to distributed energy storage and micro gas turbines is shown in Table 13. The improved IEEE 33-node system network topology is shown in Figure 5. An improved GA is used for cluster division calculations, with the number of populations set to 200 and the maximum number of iterations to 800, and an elite retention strategy is used to ensure convergence of the algorithm [23]. To verify the effectiveness of the metrics proposed in this paper, we used different schemes for comparative analysis. Scheme 1 uses the electrical-distance-based modularity index for division, scheme 2 uses the modularity and active balance index, and scheme 3 uses the index proposed in this paper, with the prioritized goal being the maximum participation of the cluster in the system power regulation. Figure 6 illustrates the advantages of the adaptive GA. The division results of different schemes are shown in Figure 7, where the ordinal numbers represent the numbers of small clusters. A comparison of the index results is shown in Table 1. The results of each scheme in terms of usable capacity for each response time (15 min) in the planning cycle (24 h) are shown in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline
**Index** & \(\mathbf{d}\) & \(\mathbf{\varphi_{p}}\) & \(\mathbf{\varphi_{d}}\) \\ \hline \multirow{2}{*}{Scheme 1} & \(\lambda_{1}=1\) & \(\lambda_{2}=0\) & \(\lambda_{3}=0\) \\  & 0.6593 & 0.6824 & 0.4689 \\ \hline \multirow{2}{*}{Scheme 2} & \(\lambda_{1}=0.5\) & \(\lambda_{2}=0.5\) & \(\lambda_{3}=0\) \\  & 0.6021 & 0.7685 & 0.3786 \\ \hline \multirow{2}{*}{Scheme 3} & \(\lambda_{1}=0.3\) & \(\lambda_{2}=0.3\) & \(\lambda_{3}=0.4\) \\  & 0.6075 & 0.8689 & 0.5432 \\ \hline \end{tabular}
\end{table} 
Table 1: Values of three indexes under different division schemes. Figure 5: Network topology of improved IEEE 33-node system. Figure 6 illustrates the convergence speed of different GAs with respect to the computational modularity index. The image demonstrates that the improved adaptive GA in this paper can approach the fitness optimum faster under the same hardware conditions. The results of cluster division should ensure strong coupling of nodes within clusters, while it should also satisfy the coordination and complementarity of power between nodes to achieve the purpose of a stronger active response capability. Therefore, the improved comprehensive performance index proposed in this paper was evaluated from two aspects: structural and active dynamic balance performance. Structural refers to the external characteristics, including the size of the cluster and the strength of intra-cluster and inter-cluster connections. The larger the value, the better the cluster coupling, and it usually takes a value between 0.3 and 0.7 [21]. The active balance degree and frequency regulation response speed indexes pay more attention to the balance flexibility characteristics, which will help improve the accuracy for planners in optimizing the allocation of cluster resource flexibility in future distribution network planning with a high degree of distributed generation and operation control needs. Scheme 1 only considers the modularity index, and the number of clusters after division is six. The number of clusters is higher, and the structural performance is stronger, but it neglects the matching of source and load storage in the clusters, and the usable capacity in the clusters is less, which cannot realize power autonomy and the ability to respond to the frequency adjustment of the system in the various clusters.