## 4 Results and Discussions
### Lifespan Estimation Results  
In this section, the lifespan of the battery is estimated and plotted based on the simulation results discussed above in all two cases. The results in datasheets as described in Section 3.4 are used as the reference for LAB and LIB, respectively. The battery lifespan is predicted based on assumptions of the battery having a maximum service per day of 30 and an average surrounding temperature of \(\pm\)25\({}^{\circ}\)C. The evaluated system's temperature is assumed to be kept at \(\pm\)25 \({}^{\circ}\)C because, in the majority of ICEVs, the battery system is positioned such that constant airflow exists to cool the energy storage system. Hence, this study did not evaluate the system at different temperature values. In this study, the lifespan estimation using Equations (21)-(23) is obtained by considering the following:  
* On the battery datasheet, the curve showing the number of cycles as a function of DoD until the battery reaches _EoL_ is used;
* The curve shows the battery lifespan in days as a function of float charging voltage and temperature.  
Thus, to estimate the lifespan, the study uses the extended life cycle graph of LAB with different DoD as indicated in [37]. Figure 24 shows the estimated lifespan results of the proposed HESS for case two.  
In Figure 24, case two (a), the estimated lifespan of the hybridised batteries is 8.46 years for LAB and 8.5 years for LIB. For case two (b), the estimated lifespan for LAB is 8.39 years and 8.17 years for LIB. Figure 25 shows the estimated lifespan results for the proposed HESS for case three.  
In Figure 25, case three (a), the estimated lifespan of the hybridised batteries is 8.45 years for LAB and 8.5 years for LIB. For case one (b), the estimated lifespan for LAB is 8.48 years and 8.6 years for LIB. Case two (a) and Case three (a) have excellent performance in terms of delivered CCC, voltage, and estimated lifespan of 8.49 and 8.4 years while costing less compared with case two (b) and case three (b).  
Furthermore, the lifespan of the LAB is estimated and compared with SLAB. The proposed HESS also improves the LABs in terms of storage capacity by 10.18% and lifespan by 3.49 years for case two and by 3.3%, and lifespan by 3.5 years for case three. Additionally, the results indicate that when the LAB SoC is above 99.65%, it can significantly improve the lifespan by more than three years.  
Figure 24: The estimated lifespan of Case two (a) versus Case two (b).  
The supply of the required cold cranking current to start the vehicle, which is between 100 and 800 A for 3 s, and maintain the battery voltage above 7.2 V, while the battery DoD is between 1 to 3%. The battery's lifespan is affected by the DoD. To improve the battery lifespan, the battery SoC must be kept as high as possible. Thus, DoD will be less.  
Although LIBs as a single source for SLI applications are available in the market [5], the HESS performance is superior to these LIBs. In [52], the algorithm for LIB capability to crank the vehicle's engine is developed. Nevertheless, the algorithm shows less efficacy, and mathematical equations are heavy for computation. Table 2 shows the summary of the results for both cases.