# Dynamic Reconfiguration of Active Distribution Network Based on Improved Equilibrium Optimizer
## 5 Case Study and Result
### Division of Load Periods  
Before presenting the clustering results, it is essential to clarify their role in driving the dynamic reconfiguration model. In the proposed framework, the improved fuzzy C-means (FCM) clustering algorithm introduced in Section 2 is not merely used to segment daily load profiles, but also directly informs the reconfiguration decisions of the distribution network. Specifically, the 24 h load data are divided into multiple representative periods, each treated as an independent reconfiguration scenario. The average load of each cluster is used as the input of the optimization model, enabling the generation of time-specific network topologies. This strategy effectively transforms the static reconfiguration problem into a dynamic, time-aware process, allowing the system to adapt to fluctuations in both load demand and DG output throughout the day.  
To support this, the enhanced FCM algorithm performs time segmentation based on both temporal characteristics and network structural similarity. The reliability and consistency of the clustering results provide a solid foundation for the subsequent optimization and performance evaluation.  
To determine the optimal number of clusters, two commonly used evaluation indicators--the elbow method and the silhouette coefficient--are employed [40; 41; 42; 43]. The elbow method assesses the reduction in the Sum of Squared Errors (SSE) by increasing, identifying the point at which adding more clusters yields diminishing returns. The silhouette coefficient, meanwhile, evaluates the cohesion and separation of clustering results, with values closer to 1 indicating better-defined clusters.  
Using these metrics, the improved fuzzy C-means clustering method achieves accurate and interpretable load period segmentation. The corresponding SSE curve is shown in Figure 5, and the clustering results are visualized in Figure 6.  
The experimental results indicate that as the number of clusters increases, the SSE value decreases progressively, but the decline significantly slows around \(k=5\), forming a typical 'elbow' shape. This suggests that \(k=5\) strikes a good balance between maintaining intra-class consistency and inter-class differentiation. Additionally, the silhouette coefficient  
Figure 5: Elbow method and Silhouette Coefficient.  
Figure 6: Clustering segmentation results.  
reaches a local maximum at \(k=4\), and although it slightly decreases at \(k=5\), it remains high, indicating that the clustering structure retains good separability.  
Considering both the time division accuracy and scheduling feasibility, \(k=5\) was ultimately chosen as the optimal number of clusters, striking a balance between the rationality of load characteristic division and the practical applicability of distribution network reconfiguration. The time period is divided into five clusters, with the periods in each cluster shown in Figure 7. Clusters 1, 2, 3, 4, and 5 correspond to the time periods 00:00-08:00, 08:00-13:00, 13:00-17:00, 17:00-21:00, and 21:00-24:00, respectively.