**4. Hybrid Powertrain's Control Strategy**

This section gives a brief overview of the control strategy developed for the hybrid powertrain model, highlighting its essential structure and operating principles.

If the modeled HEV is equipped with the start–stop feature, the control algorithm of the latter is quite simple: when the vehicle stops, the engine shuts down; the engine starts again when the vehicle resumes moving (i.e., velocity crosses the minimum threshold). When the ICE is on, the powertrain can operate in one of the two basic modes, namely the electric mode or the hybrid mode, which is illustrated in Figure 9. The former implies for the ICE to be in the idling state having the corresponding torque *Te*,*idle*, while the electric machine drives and decelerates the vehicle; the EM torque is a function of the accelerator (acc.) and brake pedal signals. In the hybrid mode, both the ICE torque and the electric machine torque are functions of the accelerator and brake signals, as well as the supercapacitor current *iSC* and voltage *uSC*.

In Figure 9, several conditions (C1–C6) are assigned to the transition arrows, as well as the logical relations between these conditions (i.e., "and" and "or" operators). The conditions are detailed in Table 5.

**Figure 9.** A simplified diagram of the hybrid powertrain operating modes.

**Table 5.** Basic conditions for the transitions between the hybrid powertrain modes.


The parameters *vup*, *vlow*, acc. *up*, and acc. *low* specify the upper and lower thresholds for the vehicle velocity and accelerator signals. The default values of *vup* and *vlow* are 25 km/h and 15 km/h, respectively. The default values of acc. *up* and acc. *low* correspond to 50% and 10% of the maximum ICE torque. These values are used when the ESS voltage stays near its maximum (650 V). When the voltage lowers, the thresholds decrease to engage the ICE earlier and to reduce the electric machine traction torque, preventing an excessive consumption of the supercapacitor energy.

Besides the electric mode, the engine becomes disconnected from the transmission upon gear shifting. During a shift, the electric machine provides gear synchronization.

The hybrid mode implies the torques of the ICE and the electric machine should be combined. When the SC voltage drops below the lower threshold (the default value is in the range of 500–550 V), the ICE begins delivering an excessive power consumed by the electric machine whose torque becomes a function of the SC voltage drop (the deeper the discharge, the higher the torque). When the driver's torque request exceeds the maximum ICE torque, the electric machine provides the "torque boost" in accordance with the map shown in Figure 10 using the example of the diesel-based powertrain (the resulting curve of the hybrid unit's maximum torque is denoted "Hybrid max. trq"). Like the thresholds of the velocity and accelerator signals, the boosting torque constitutes a function of the ESS voltage.

**Figure 10.** Superimposed torque characteristics of the hybrid unit and its components.

### **5. Driving Cycles**

Several driving cycles intended for heavy-duty vehicles were employed in the simulations to represent the variety of possible driving conditions. These included urban and suburban cycles, which constitute the major interest of the study, as well as highway cycles.

The driving cycles employed in the simulations are shown in Figure 11. The GOST cycles are road-performed (rather than using a chassis-dynamometer) schedules provided by a national standard named the GOST. All the driving cycles, except for the WHVC, imply level roads.

**Figure 11.** Driving cycles employed in the simulations. (**a**,**b**) velocity and road slope of the World Harmonized Vehicle Cycle (WHVC), (**c**) the West Virginia University city cycle (WVUCITY), (**d**) the West Virginia University suburban cycle (WVUSUB), (**e**) the GOST city cycle (GOST city), (**f**) the GOST highway cycle (GOST highway).
