## 4 Results and Discussions
### Case Two (12 V-70 Ah HESS Capacity)  
The proposed HESS to supplement a 12 V-70 Ah single battery is analysed for 172 s in case two (a) and for 182 s in case two (b). This case study compares the attained results to a single LAB of the same size. Figures 7 and 8 show the results of this case. Figure 8 illustrates the HESS delivering the maximum current required, which is 599.1 A for case two (a), while Figure 9 represents case two (b), where the HESS provides a maximum current  
As shown in Figures 8 and 9, the HESS supplies the required CCC. Furthermore, after three seconds, the CCC demand goes to zero, which illustrates that the engine is in running operation and no further demand is required. However, the HESS need to supply the vehicle auxiliary loads, but the study does not cover the energy needed to power up these auxiliary loads because it is beyond the scope of this research. Moreover, Figure 10 shows the LAB contribution for case two (a). In Figure 10, LAB provides 326.9 A, which represents a contribution of 53% of the required CCC. The LAB voltage response results show a minimum voltage of 11.41 V, while the SoC remains at 99.69%. Consequently, LIB supplies 290.3 A of the required CCC, which is a 37.1% contribution. LIB voltage response recorded a minimum voltage of 9.51 V, and the SoC is retained at 98.09%. Figure 11 shows the results of the HESS for case two (b). Figure 11: LAB and LIB contribution to CCC, SoC and voltage response during discharge for case two (b). Figure 10: LAB and LIB contribution to CCC, SoC and voltage response during discharge for case two (a). As shown in Figure 11, LAB supplies a portion of the required CCC, which is 378.5 A, thus accounting for 62.9% of the total CCC needed to crank the engine. The LAB minimum voltage response recorded was 11.31 V, and the SoC remained at 99.65%. Additionally, LIB provides 222.9 A of the required CCC, which accounts for 37.1%. The LIB minimum voltage response was 9.51 V, and the SoC remained at 98.09%. Moreover, the above results represent the discharging mode of the HESS. Thus, Figures 12 and 13 show the charging behaviour of the HESS. In this mode, the HESS is simulated for 179 s for case two (a) and 169 s for case two (b). In Figure 12, during HESS charging, LAB state-of-charge increases from 99.69% to 100%. Furthermore, the voltage response increases from 11.41 V to the charging reference voltage of 14.2 V and the charging reference current of \(-\)12 A. The LIB's SoC increases from 98.28% to 99.9%, whereas the voltage response increases from 10.49 V to a charging  
Figure 12: CCC contribution, SoC and voltage response of HESS during discharging and charging modes for case two (a). Figure 13: Required CCA, SoC and voltage response of HESS during charging mode for case two (b). reference voltage of 14.2 V with a charging reference current of \(-6\) A. Figure 13 shows the results of case two (b) during the charging mode. As shown in Figure 13, LAB's SoC increases from 99.65% to 100%, whereas the voltage response increases from 11.31 V to the charging reference voltage of 13.1 V and the charging reference current of \(-13\) A. The LIB's SoC increases from 98.09% to 99.9%, whereas the voltage response increases from 9.51 V to the charging reference voltage of 14.2 V and the charging reference current of \(-5\) A. The results show that when the batteries are fully charged, the charging current is 0 A, and the charging voltage reduces to the initial nominal battery voltage. Hence, compared with a single 12 V-70 Ah LAB during discharging mode for 3 s; it is clear from the results in Figure 14, which show that the proposed HESS delivers 599.1 A, whereas the minimum voltage is 11.41 V. While the SLAB delivers 538.1 A, with the minimum voltage being 10.97 V.  
Figure 15 shows that the minimum LAB's SoC after supplying CCC for 3 s is 99.69% and 99.24% for SLAB. Figure 14: The delivered HESS CCC versus SLAB and voltage response of LAB versus SLAB during discharging modes for case two.