The performance of power distribution systems (PDS) has improved greatly in recent times ever since the distributed generation (DG) unit was incorporated in PDS. DG integration effectively cuts down the line power losses (PL) and strengthens the bus voltages (BV) provided the size and place are optimized. Accordingly, in the present work, a hybrid optimization technique is implemented for incorporating a single DG unit into radial PDS. The proposed hybrid method is formed by integrating the active power loss sensitivity (APLS) index and whale optimization meta-heuristic algorithm. The ideal place and size for DG are optimized to minimize total real power losses (TLP) and enhance bus voltages (BV). The applicability of the proposed hybrid technique is analyzed for Type I and Type III DG installation in a balanced IEEE 33-bus and 69-bus radial PDS. Optimal inclusion of type I and III DG in a 33-bus radial test system cut down TLP by 51.85% and 70.02% respectively. Likewise, optimal placement of type I and III DG reduced TLP by 65.18%, and 90.40%, respectively for 69-bus radial PDS. The impact of DG installation on the performance of radial PDS has been analyzed and a comparative study is also presented to examine the sovereignty of the proposed hybrid method. The comparative study report outlined that the proposed hybrid method can be a better choice for solving DG optimization in radial PDS.
Clustering is a fundamental data analysis task that presents challenges. Choosing proper initialization centroid techniques is critical to the success of clustering algorithms, such as k-means. The current work investigates six established methods (random, Forgy, k-means++, PCA, hierarchical clustering, and naive sharding) and three innovative swarm intelligence-based approaches—Spider Monkey Optimization (SMO), Whale Optimization Algorithm (WOA) and Grey Wolf Optimizer (GWO)—for k-means clustering (SMOKM, WOAKM, and GWOKM). The results on ten well-known datasets strongly favor swarm intelligence-based techniques, with SMOKM consistently outperforming WOAKM and GWOKM. This finding provides critical insights into selecting and evaluating centroid techniques in k-means clustering. The current work is valuable because it provides guidance for those seeking optimal solutions for clustering diverse datasets. Swarm intelligence, especially SMOKM, effectively generates distinct and well-separated clusters, which is valuable in resource-constrained settings. The research also sheds light on the performance of traditional methods such as hierarchical clustering, PCA, and k-means++, which, while promising for specific datasets, consistently underperform swarm intelligence-based alternatives. In conclusion, the current work contributes essential insights into selecting and evaluating initialization centroid techniques for k-means clustering. It highlights the superiority of swarm intelligence, particularly SMOKM, and provides actionable guidance for addressing various clustering challenges.