## 4 Comparative Analysis
### Clustering Performance Evaluation
In addition to analyzing the final voltage dispersion, we also examined the average charge throughput, which can be seen in the bar graph on Figure 11. As all cells in a series string share the same current, the throughput primarily reflects how uniformly the cells accept charge over the duration of the charging period. In our simulation, we observed that modules clustered via GMMs exhibit more consistent charge throughput, indicating fewer outlier cells that could reduce the overall capacity utilization, as group A and B have an average charge throughput higher than 1 Ah. Conversely, random grouping or other clustering approaches tend to include cells with disproportionately lower or higher acceptance rates, which ultimately lowers the group's average throughput. By aligning cells of similar condition, GMMs ensure identical charging behavior, thereby optimizing  
Figure 10: Standard deviation of final cell voltages of each module across different clustering methods. the total charge delivered to the battery pack and enhancing the reliability of second-life energy storage modules. Another key metric in analysis is the delta capacity in Figure 12, which is the difference between the highest-capacity cell and the lowest-capacity cell within each group. A smaller delta capacity indicates that the cells are more closely matched, thereby minimizing the risk of overcharging or over-discharging the weaker cells during operation. The GMM-based clusters showed notably lower delta capacity values compared to both random groupings and the two other clustering methods. Finally, we evaluated coulombic efficiency, which measures how effectively each module converts the charged energy into usable discharge energy. The 15S2P configurations derived from GMM-based clustering demonstrated a consistently higher coulombic efficiency of 98.18% relative to other methods, as shown in Figure 13, underscoring more uniform energy utilization and reduced internal losses. Cells with similar capacity and internal resistance avoid mismatch-driven inefficiencies that often occur in packs assembled through less-adaptive clustering approaches. Figure 11: Average charge throughput of each module across different clustering methods. Figure 12: Delta capacity of each module across different clustering methods. Figure 13: Coulombic efficiency of each module across different clustering methods. Overall, these findings demonstrate that the GMM-based clustering approach provides more balanced and efficient battery modules than random grouping, SVC, or K-means. The minimized voltage spread indicates tighter cell matching, while the higher average charge throughput reflects a more uniform charge acceptance across the entire module. In tandem, the reduced delta capacity confirms that the GMM consistently groups cells of similar health, mitigating the risk of over-stressing weaker cells. Finally, the notable coulombic efficiency gain underscores the method's ability to limit internal losses and capitalize on the available capacity. Taken together, these improvements validate GMMs as a robust clustering strategy for assembling second-life lithium-ion cells into reliable and long-lasting battery packs.