## 4 Results and Discussion
### Results in Power-Split Operations  
The mesh grid used in input to the script was obtained by the arrays \(\omega_{in}=1000:10:6000\) rpm and \(T_{in}=10:1:140\) Nm. The procedure described in Section 3.1 was carried out for each vehicle speed, whereby the respective optimal operating point was selected after excluding those outside the boundaries of Figures 4 and 5, Table 5, Equation (11), and Table 6. The results of Figures 6-11 show the optimal operating points resulting from the optimization procedure aimed at minimizing the powertrain power losses. Figure 6: (**a**) Best global efficiency in power-split operation; (**b**) battery power in the optimal power-split operating points. Figure 8: MG I optimal functioning points in power-split operation. Figure 7: ICE optimal power-split operation: (a) ICE functioning points; (b) ICE power. Figure 10: Electric machines optimal power in power-split operation: (a) MG I power; (b) MG O power. Figure 9: MG O optimal functioning points in power-split operation. Figure 6a shows that the best results are achieved for SOC = FREE since the availability of the battery both as a power source and power storage would enable the achievement of the most efficient power flows (Figure 10). Nevertheless, the maximum global efficiency is lower than 0.33 up to 50 km/h, therefore it would be more advisable to turn off the engine and drive in FEV operation (see Section 4.2). The only reason to let the ICE work at lower speeds is to recharge the battery if possible (SOC = FREE or SOC = 0). In this case, the ICE should operate in the maximum efficiency region, otherwise, it should be turned off also for higher speeds if the battery can supply power for propulsion (SOC = FREE or SOC = 1) (Figure 7). In this way, the global efficiency would be significantly enhanced (Figure 6a), since the demanded output power would be provided by the electric unit (Figure 6b), which is more efficient than the ICE. Nevertheless, a more robust control strategy should regulate the battery power according to the instantaneous SOC, so as to ensure sufficient range. Indeed, for speeds higher than 100 km/h, the optimal powertrain operation would be achieved at the expense of the driving range. Therefore, over 100 km/h would be even more advisable to limit the power supplied by the battery and increase that provided by the ICE, even though this would reduce the global efficiency. On the other hand, if the battery is completely discharged (SOC = 0) or a maintaining-charge driving is desired (SOC = CONSTANT), the demanded output power should be provided mainly by the engine (Figure 7b). In this case, the battery charging would be recommended between 50 and 145 km/h, while over 145 km/h keeping the SOC constant would result in greater efficiency. Nonetheless, since the ICE maximum power is 75 kW [37], the vehicle speed cannot exceed 190 km/h with SOC = 0 or SOC = CONSTANT. Figures 8-10 show the optimal exploitation of the electric machines in power-split operation. They suggest using both MG I and MG O as generators for battery recharging up to 50 km/h. It should be the same from 50 to 130 km/h if SOC = 0, while MG I should be used as a motor and MG O as a generator if the battery can provide power (SOC = FREE or SOC = 1). In the latter case, the mechanical energy converted to electric energy by MG O is reconverted to the mechanical form by MG I. Over 155 km/h, both MG I and MG O should be used as motors for SOC = FREE or SOC = 1. To assess the optimal mode selection, it is sufficient to analyze the optimal overall transmission ratio of Figure 11.  
Figure 11: Optimal overall transmission ratio and mode selection in power-split operation. Figure 11 shows that for lower speeds the input-split mode should be preferred, while the compound-split mode is advisable at higher speeds.