## 4 Discussion  
Once the gap in the results related to a comparison with an RB EMS commonly used in commercial PHEVs was filled, the resulting dataset was studied. To facilitate comparison, the results related to the fuel consumption (depending on the work, different variables were considered for this: fuel consumption, equivalent energy consumption, fuel economy, etc.) were normalized, rescaling data to have values between 0 and 1. In this scale, 1 corresponds to the optimum result, which in the vast majority of the works corresponds to DP, and 0 corresponds to the result of a common RB EMS. Thus,  
Figure 6: FASTsim simulation results for the HEV of [49] for NEDC cycle. (**a**) Battery SOC; (**b**) powers of the battery and the ICE; (**c**) cumulative equivalent gasoline consumption in gallons. the proposed EMS would achieve a rating between these values that gives information about how far it is with regard to the benchmarks. Figure 7 show boxplots for fuel consumption results for all the proposed EMSs (Figure 7a) and for the EMSs classified according to the categories presented previously. Figure 7a shows a median value of 0.7503 with broad interquartile and maximum-minimum ranges that indicate great differences among the performance of the EMSs studied. The upper skewness of this boxplot indicates that most of the EMSs are nearer to the optimum than to common RB EMSs. Figure 7b shows a comparison among the different categories of EMSs. RB, ECMS and OB show better medians (between 0.7 and 0.9) than MPC and LB (around 0.6). Apart from this, the difference between the spreads of ECMS with respect to the rest of the groups indicates that ECMS offer, in general, less variation between the performances of the different approaches. In addition, the lower spreads of RB and ECMS may be produced because these EMSs are more closed and allow less tuning: in the case of the ECMS, the equivalence factors used in the problem formulation and, in the case of RB EMSs, the rules edition, usually modify the thresholds. The rest of the groups (MPC, OB and LB) show more variation since these methodologies allow more approaches (e.g., for optimization-based methods, evolutionary algorithms, genetic algorithms and particle swarm optimization, among many other heuristics, can be found) that result in more variation in their performances. In general, it can be seen that the EMSs analyzed are closer to the optimum performance than to a common RB EMS. However, it would be interesting to quantify this improvement with regard to RB EMSs. Figure 8 shows the percentage of improvement of the proposed EMSs with regard to the commercial RB EMSs of the normalized rescaled results. It can be seen that the medians for the different groups are around the range of 5% and 10%. It could be considered that the best results correspond to MPC EMSs with a higher median value and whose upper interquartile show results over 18%. ECMS and OB EMSs show similar results with regard to medians and similar spreads and could be considered as the following in the performance ranking. These results, according to the authors, make sense since these EMSs have a long trajectory of development. The worse results of LB EMSs may be due to their focus  
Figure 7: Normalized fuel consumption results for the EMSs of the works reviewed. (**a**) Boxplot for all the EMSs; (**b**) boxplot for the different categories of EMSs. on the real-time implantation that forces them to be more adaptable to disturbances and, consequently, more suitable for being applied to commercial vehicles. This differs from ECMS EMSs, which are less adaptable and whose good results, as stated in the analyzed works, can be worsened when there are unexpected disturbances. Apart from this, the different rankings resulting from Figures 7 and 8 may be derived from the fact that each work estimated the optimum result from their own DP approach. It is possible that the approach used in some of them was better than those used in others and it affected to how close they were to the optimum.