## 4 Comparative Analysis
### Clustering Performance Evaluation  
After determining appropriate cell clusters using SVC, K-means, or GMMs, it is essential to verify that these groupings also perform well under practical operating conditions. A purely data-driven clustering approach can overlook system-level constraints such as voltage, current, and thermal behavior during charge-discharge cycles. Therefore, a MATLAB/Simulink-based simulation block diagram, shown in Figure 8, is a valuable bridge between theoretical clustering outcomes and actual battery pack performance. By modeling the battery modules in software, we can accurately estimate how each cluster will behave as part of a 48 V battery pack. Residential ESS solutions commonly use a nominal 48 V battery pack design for reasons of safety, modularity, and compatibility. To achieve this nominal voltage using Li-ion cells (with each cell having a nominal voltage of 3.3 V), the typical solution is to connect around 15 cells in a series. In our case, a 15S chain ensures the battery pack can reach the required voltage range under normal conditions. While 15 cells in series fix the pack voltage, adding parallel branches increases the total capacity and extends the usable energy for the module. Depending on the energy needs, the number of parallel branches can be scaled up, allowing for a flexible approach to capacity sizing without changing the nominal voltage. Figure 9 shows the voltage, current, and state of the charge waveforms of the 15S2P (30 cells) simulation for one of the clustering groups. The effectiveness of each clustering method was evaluated by simulating battery modules using the actual parameters of the clustered cells from the dataset, including  
Figure 8: Simulation block diagram. Figure 9: Voltage, current, and SOC waveforms of 15s2p simulation for CCCV of regrouped cells. internal resistance, actual capacity, SOC-OCV values, etc. Each module was constructed using 15 representative cells per cluster and configured as a 1552P system. The modules were subjected to constant current (CC) charging until the voltage limit was reached, followed by constant voltage (CV) charging, and then constant current discharging. The key performance indicators used for comparison were as follows:  
* The standard deviation of the final charging voltages measured across all 15 cells within the battery module, which indicates the degree of voltage imbalance among the cells at the end of the charging process. * The average charge throughput of the 15 cells during the charging process, representing the total amount of charge each cell accepted on average, used as a measure of the overall charging performance and uniformity within the module. * The difference between the maximum and minimum cell capacities within each cluster reflects the internal consistency of the clustering method in grouping cells with similar energy storage capabilities. * The Coulombic efficiency of the battery module, calculated as the ratio of discharge capacity to charge capacity, used to evaluate how effectively the input electrical energy is converted into usable output energy. These indicators compare the performance across modules formed via SVC-, K-means-, and GMM-based clustering. Each parameter was extracted from the simulation models to evaluate if the inconsistency of the LIBs group is reduced, and if the performance of the groups has been improved. In this simulation, a 1552P battery pack underwent a 1.5 A constant-current-constant-voltage (CCCV) charge. The final cell voltages within a group were then monitored, and the standard deviation of these final charge voltages were calculated to gauge the voltage spread across the cells in one group. As shown in Figure 10, comparing the random grouping, SVC, K-Means, and GMMs methods, it is clear that the GMM-based module exhibits the lowest voltage spread. Specifically, clusters B and D achieve standard deviations of 0.01320 and 0.01133, respectively.