## 4 Simulation Verification
### EMS Results Comparison  
To verification of proposed online multi-level energy management strategy, the obtained results are compared with Opt-FLC EMS presented in [19]. The results are demonstrated in Table 4 for these strategies over 6 different driving cycles. According to Table 4, the results validate that proposed online multi-level EMS decreases the PEMFC fuel consumption, lead-acid battery power fluctuations, and \(\Delta\)ASOC. The fuel consumption in the proposed EMS is less than the Opt-FLC strategy; for instance, the proposed EMS consumes 4.37 MPG (miles per gallon) in the NEDC driving cycle, while the Opt-FLC strategy consumes 3.95 MPG. To study the proposed EMS's efficiency, the \(\Delta\)SOCs under different driving cycles are presented in Table 4. It is clear that the initial and final SOC has a minimum difference in the proposed EMS. Also, battery power fluctuations are listed in Table 4. According to Table 4, the PEMFC and battery power fluctuations have reduced in the proposed online multi-level EMS compared with the Opt-FLC strategy  
regions. Many of the reviewed studies have used only three driving cycles to classify vehicle movement identification. Moreover, these power fluctuations reduction of FC and battery can be improved in comparison to the reviewed studies.  
The proposed strategy in this paper recognizes the vehicle's dynamic movement conditions based on the VSM function's formulation. The combined efficiency of battery and UC is presented to divide SOC and VDR states based on mathematical relations. In an FC system, keeping the FC's operating point on the best output power is one of the most attractive ideas. In this study, the FC output power modes are calculated based on the HCR function to select six operating points to improve fuel consumption. Also, the battery output power modes are presented to reduce battery power fluctuations. These modes not only improve efficiency but also reduce fluctuations of the FC output power. Moreover, the battery SOC and the UC VDR are considered to determine the FC's operating point. Also, this paper identifies the vehicle's dynamic movement conditions accurately and uses them to determine the operational modes.  
The proposed EMS performance is validated through six different driving cycles. The simulation results of the online multi-level EMS indicate that the UC is charged at the optimal operation point of the PEMFC so that it can increase the total efficiency of the HESS. Not only instantaneous fluctuations of the PEMFC output power are eliminated, but also it is not required to be operated at maximum power (minimum efficiency). The battery output power has fewer fluctuations compared to the Opt-FLC method. Therefore, its lifetime is prolonged. Finally, the simulation results confirmed that the multi-level EMS could reduce fuel consumption, decrease battery power fluctuations, and optimally control the HESS.  
Although this article has well proven the performance of the proposed online EMS, a lifetime assessment of the HESS and state of health of the battery can be supposed to extend the scope of this paper. A future work of this article is to consider a model for optimizing the operational modes of HESS with machine learning methods to improve the fuel economy. Furthermore, comparing the results of the proposed VSM with results obtained from other driving condition identification methods can be an interesting subject for future studies.  
Conceptualization, H.F.G. and M.F.; Methodology, H.F.G. and M.F.; Software, H.F.G.; Validation, H.F.G. and M.F.; Formal analysis, H.F.G. and M.F.; Investigation, H.F.G. and M.F.; Data curation, H.F.G. and M.F.; Writing--original draft preparation, H.F.G.; Writing--review and editing, H.F.G. and M.F.; Visualization, H.F.G. and M.F. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.