# Battery Sizing for Mild P2 HEVs Considering the Battery Pack Thermal Limitations
## 4 Results and Experimental Validation of the Developed Model
### Simulation Results for P2 HEV  
Once the simulation model was validated experimentally, the simulation was performed with the P2 HEV (with 1486p battery pack) complete simulation model on different driving cycles (UDDS, NEDC and WLTC). As an example, the results for UDDS driving cycle with three levels of limitations are presented in Figures 17-19. The figures represent (a) ICE torque, (b) EM torque, (c) the battery SOC, (d) fuel consumption rate and (e) the speed profile on UDDS driving cycle. Note that here, results are shown for when the C0 clutch was engaged during the declaration phase, which means that regenerative braking will be affected by the resistive torque of the engine. In all the cases, the SOC was maintained at the beginning and at the end of driving cycle. For this reason, the initial SOC was varied in different cases to ensure the electrical energy equilibrium. The overall fuel efficiency was improved by 8.6% compared to conventional vehicle simulation results (699.9 g) in the case where no thermal limitations are applied (Figure 17). However, the temperature of the battery reached about 160 \({}^{\circ}\)C (see Figure 19a solid blue line) under UDDS cycle. Figure 17: Simulation results with no limitation on the temperature on UDDS driving cycle: (**a**) ICE torque, (**b**) EM torque, (**c**) Battery SOC, (**d**) Fuel consumption rate and (**e**) Vehicle speed. Figure 18: Simulation results with the on/off penalty on the temperature on UDDS driving cycle: (**a**) ICE torque, (**b**) EM torque, (**c**) Battery SOC, (**d**) Fuel consumption rate and (**e**) Vehicle speed. In Figure 18, results are described for ECMS with thermal limitation implemented by means of an on/off penalty factor (discussed in Equation (22)). In this case, the overall fuel consumption was reduced by only 3.8% compared to the conventional vehicle model (699.9 gr). Since, traction power contribution by EM is possible only if battery temperature is below 55 \({}^{\circ}\)C (see Figure 19a). With the penalty factors on both the temperature \(PF_{\theta}\) and the temperature change rate \(PF_{\theta}\) (discussed in Equations (24)-(27)), the battery temperature was kept below 55 \({}^{\circ}\)C (see Figure 20a), and overall fuel usage was improved by 4.8% with respect to conventional vehicle model as in Figure 19.  
The temperature profile of the battery for UDDS, NEDC and WLTC driving cycles are given in Figure 20. For the case with no thermal limitations (blue, solid lines), the more aggressive cycles such as UDDS and WLTC have higher power demand, therefore, the temperature of the battery went up to 160 \({}^{\circ}\)C and 180 \({}^{\circ}\)C (Figure 20a,c), respectively. The temperature for the low power demanding NEDC cycle stayed within 85 \({}^{\circ}\)C (Figure 20b). Figure 19: Simulation results with the penalty on the temperature and the temperature change rate on UDDS driving cycle: (**a**) ICE torque, (**b**) EM torque, (**c**) Battery SOC, (**d**) Fuel consumption rate and (**e**) Vehicle speed. Figure 20: The battery temperature for different temperature limitation strategies and driving cycles: (**a**) UDDS; (**b**) NEDC; and (**c**) WLTC. Blue, solid line—No thermal limitation; Orange, dashed line—on/off temperature control; Yellow, dotted line—Temperature and temperature change rate limitation. The case with limitation on both temperature and temperature change rate (yellow, dotted line) showed more stable the battery temperature profile compared to the on/off temperature limitation (orange, dashed line) strategy. The reason is that introducing penalty factor due to the temperature changing rate \(PF_{\theta}\), which limits the rapid changes in the battery temperature. Moreover, in three driving cycles (UDDS, NEDC, and WLTC) this limitation led to fuel consumption improvement of 1%, 0.3% and 0.7%, respectively, compared to the on/off strategy. As can be seen, the introduction of the thermal limitation positively affects the thermal behaviour that helps to avoid the thermal runaway.