**6. Results and discussion**

To investigate the effectiveness of the proposed framework, simulation and optimization over NEDC driving cycle are performed and the results are provided in this section. The comparisons are considered for an initial non-optimized case (before integrated design) versus optimized cases (after integrated design). The main objective of the integrated design is to minimize component sizes and as a result the cost of powertrain besides achieving optimized fuel consumption while satisfying the constraints through the developed nested iterative framework. For achieving close enough values of the initial and final SoC, *ε*<sup>0</sup> ¼ 0*:*3%, and for providing slight degree of freedom on allowable SoCmin and SoCmax, small *ε* allowable sliding value as 4%, were all considered in the formulations of the optimization constraints. **Figure 10** presents the power sharing between the battery and the ICE satisfying driving power. In addition, evolution of the battery SoC and C-Rate for the studied driving cycle after the integrated design are plotted in the same figure. As can be seen, the regulated EMS could successfully recover the SoC to achieve close values for initial and final SoC over the full cycle (*SoCf* ≃*SoCf* ) having the ICE charging the battery when needed while considering the defined *C*\_*Rate t*ð Þ violation limit at the meantime. In addition, the SoC allowable minimum and maximum boundary is satisfied through the desired window range for the whole cycle. Consequently, **Table 4** provides detailed evaluations in terms of control constraints satisfaction related to triggered EMS goals.

Correspondingly, **Table 5** summarizes the design parameters before and after optimal integrated design while fuel consumption besides powertrain cost

**Figure 10.** *Power distribution (kW), SoC (%) recovery, and C-rate results.*


**Table 4.** *Control goals satisfaction.*

