**7. Model Analysis of the Powertrain Hybridization**

Considering the main objective of the study and having analyzed the specifics of the devised hybrid powertrain design, the simulation program was formulated as the following sequence of tasks:


The simulations were conducted in identical driving conditions for all the studied powertrains. The compared variants of HEVs shared the same adjustments of the control system with slight variations due to differences in the characteristics of the engines. The gearbox shift map, which was common for both the conventional and the hybrid powertrains, was defined in a way similar to that employed within the Vecto software tool [36].

Figure 12 shows an example of simulation results obtained in the urban part of the WHVC driving cycle for the HEV equipped with the Otto-type gas engine that had the start–stop feature. ("EM" denotes the variables related to the electric machine).

**Figure 12.** Hybrid powertrain operating variables calculated in the World Harmonized Vehicle Cycle (WHVC) (fragment).

Since the considered hybrid powertrain had no external ESS charge feature, the condition of the energy balance should be pursued in the simulated driving cycles. This means that the ESS energy level at the end of the cycle has to be equal to that observed at the beginning of the cycle. This ensures that no ESS energy is spent without replenishing it and no fuel is consumed to excessively charge the ESS. Originally, since the HEV's control system was not intended to achieve the precise energy balance within a specified time interval, an ad hoc adjustment was introduced, which gradually "pulled" the ESS state of energy toward the initial value when approaching the end of the driving cycle. With the energy balance condition achieved, the fuel economy of the HEV relative to the conventional vehicle was calculated as follows:

$$FE = \frac{FC\_{\text{conv.}} - FC\_{\text{hyb.}}}{FC\_{\text{conv.}}} \times 100\% \tag{10}$$

where *FCconv*. and *FChybr*. are the fuel consumptions (*L*/100 km or m3/100 km) of the conventional and hybrid vehicles, respectively.

The average auxiliary power consumption was calculated from the simulations of all the employed driving cycles. For the conventional vehicle, it amounted 6–7 kW for the urban and suburban conditions and 2–4 kW for the highway schedules. For the hybrid vehicle, it was lower (due to the engine-independent control), with 3.5–4 kW and 1–2 kW, respectively.

Tasks 1 and 2 formulated at the beginning of the section were solved simultaneously. To do this, two sets of simulations were conducted, one of which implemented the direct connection between the ESS and the electric drive, while the other involved a DC–DC converter as the interface. Each set

included simulations with different numbers of supercapacitors, ranging from one (1.6 kWh) to four (6.4 kWh). When employing more than one SC unit, the electrical connection between the units was assumed to be parallel. When modeling the variant with a DC–DC converter, the latter maintained the electric drive input voltage at a constant 640 V. The efficiency of the converter was assumed to be 95% (the actual value would most likely be lower).

Figure 13 demonstrates the ESS voltage time histories calculated for the urban/suburban part of the WHVC driving cycle. From the plots, it is clear that using a larger ESS allows for decreasing both the depth of the discharge and the voltage amplitude. Note that this effect is the most pronounced when adding the second SC unit.

**Figure 13.** Supercapacitor voltage dynamics depending on the ESS energy content.

Table 8 summarizes the results of the simulations for the HEV equipped with the Otto-type gas engine and having the start–stop feature. The data were obtained in the WHVC urban/suburban cycle. Other powertrain variants were also estimated and showed similar results.


**Table 8.** Influence of the ESS energy content and the DC interface on the HEV fuel economy.

The results show an evident drawback of employing the DC–DC converter, which is a decrease of the fuel economy effect by 4–5%. The lowest fuel savings were obtained when using one SC unit. Although the DC–DC converter prevents the electric drive power from diminishing, therefore keeping the potential of regenerative braking at the maximum level, the SC is discharged below the threshold of the favorable efficiency. Additional losses are introduced by the DC–DC converter itself. As a result, the positive effect of the maximum electric drive power available throughout the driving cycle is not able to outweigh the adverse effect of the lowered system efficiency. However, the simulations with the higher ESS energy contents show that keeping the SC efficiency at a good level does not eliminate the

effect of the diminished fuel economy. Moreover, despite the increased ESS efficiency, the fuel economy difference between the two interface options changes negligibly. This suggests that the critical factor is the power loss within the DC–DC converter rather than in the supercapacitor.

Figure 14 shows the average supercapacitor efficiency and the relative fuel economy of the HEV as a function of the ESS energy content, where the plots have resulted from the driving cycle simulations. The efficiency plot denoted "Equiv. circ." was derived using Equation (8), while the second plot, "Const. eff.," was calculated using Equation (9). The difference between the plots stems from the extra-low load regimes where the efficiency of the SC may become negative (see Section 3.5). If those regimes are lumped into the bulk of the power losses, the line "Equiv. circ." lifts toward the second line, eventually coinciding with it. The effect of adding the third and fourth SC units is not so appreciable, while the cost of an ESS having that size may be rather high, outweighing the fuel savings.

**Figure 14.** Influence of the ESS energy content on the supercapacitor efficiency and relative fuel economy.

Solving tasks 1 and 2 allowed us to formulate the "optimal" solution regarding the ESS design: it should consist of two SC units having a total energy content of 3.2 kWh and interfacing with the traction electric drive via a direct DC link. This solution was used in the simulations relating to task 3. The results thereof are presented in Figure 15 in the form of histograms showing the relative fuel economy provided by the hybrid powertrains based on all the mentioned ICEs in different driving cycles.

**Figure 15.** Calculated fuel economy of the HEV relative to the conventional vehicle: (**a**) city and suburban cycles, the start–stop was disabled; (**b**) city and suburban cycles, the start–stop was enabled; and (**c**) highway cycles.

In general, the hybridization provided a similar fuel economy effect for both the diesel-based and gas-based powertrains. The average differences of the relative fuel economy between the gas-based HEVs and the diesel-based HEV are listed in Table 9.


**Table 9.** Average hybridization effect of the gas-based powertrains relative to the diesel-based powertrain.

The most pronounced effect of the hybridization is observed with the Otto gas engine. In the conventional powertrain, the Otto-cycle engine is up to 5% less effective than the two other gas engines, while the hybrid powertrain allows this engine to reach the absolute fuel economy values of its counterparts.

The fuel economy effect provided by the hybridization mainly depends on two factors: driving schedule and employing the start–stop feature. The former relates to the characteristic called the kinetic factor [10]. It expresses the share of "acceleration–deceleration" driving that directly determines the intensity of using regenerative braking, which in turn, is the major factor of a heavy-duty HEV's fuel economy. From the simulation results without the start–stop feature (i.e., when regenerative braking is the decisive factor of the fuel economy), one can conclude that among the used driving cycles, the city/suburban part of the WHVC has the highest kinetic factor.

The effect of introducing the start–stop feature is particularly pronounced for the gas-based HEVs, especially in the driving cycle containing the highest share of stops, namely the WVUCITY cycle. This is due to the ratio of the idle fuel consumption rate to the maximum fuel rate of the gas engines being approximately two-fold that of the diesel. In other words, the gas engines have a larger share of the idle consumption, which makes its elimination an effective measure to increase the fuel economy. In the absence of the start–stop feature, the same WVUCITY cycle had a 6.2–9.5% lower fuel economy effect, which emphasized the "start–stop" nature of this particular driving schedule.

In the highway cycles, the hybridization provided lower fuel savings, as expected, especially in pure highway regimes represented by the GOST cycle. The highway part of the WHVC cycle is less homogeneous regarding velocity variations, which provide more possibilities to retrieve and reuse the vehicle kinetic energy, resulting in higher fuel savings. It is also worth noting that the work in [14] shows the positive effect of regularly undulated roads with respect to the highway fuel economy due to the larger amount of regenerated energy.

The final task of the study was to estimate the influence of the vehicle's mass on the fuel economy. To do this, the vehicle mass was lowered to 35 tons (with a proportional decrease of the auxiliary power consumption). The resulting variations of the fuel economy relative to that of the initial (44 tons) vehicle are shown in Table 10. In general, the relative fuel economy changes negligibly. An unambiguous effect only shows in the case of the Otto gas-based powertrain, which, again, benefited from the hybridization more than its counterparts did.


**Table 10.** Variations of the average fuel-saving effect due to the decreased vehicle mass.
