*4.1. Vehicle Parameters*

The model for this research was implemented with Matlab/Simulink. The parameters of the vehicle are shown in Table 1. A V6 3.6 L engine was applied in this research. This engine had a manufacturer configuration for a midsize power-split HEV, and it was compatible with the power of M/Gs applied in this vehicle. The power-split HEV was designed with this engine in order to maintain the performance as the original ICE version. The additional M/Gs provided the HEV with better acceleration and gradeability.


**Table 1.** Vehicle parameters.

## *4.2. Charge and Discharge*

In this research, the working range of the battery's SOC was set between 0.4 and 0.6, which could effectively extend the battery's service life. At the same time, the battery's internal resistance was low in this working range, regardless of the state of charge or discharge, as shown in Figures 8 and 9.

**Figure 8.** Relation between battery state of charge (SOC) and internal resistance during battery discharge.

**Figure 9.** Relation between battery SOC and internal resistance during battery charge.

### *4.3. Simulation Results*

EPA FTP-75 driving cycles were applied in the simulation. The urban and highway driving curves are shown in Figures 2 and 3, respectively. Rule-based simulation results are shown in Table 2. The fuel economy (FE) of urban and highway simulations were 46.28 mpg and 39.11 mpg, respectively, and the composite FE was 42.74 mpg. The formula for composite FE is shown in Equation (22) As

shown in Table 2, the difference between the composite FE of the rule-based simulation and that of the manufacturer data was 0.9%, which was within the allowable range. Therefore, the rule-based control model was applied as a base model to evaluate the optimization simulation of the PSO algorithm.

$$Composite\ FE = \frac{1}{\frac{0.55}{\text{Clty FE}} + \frac{0.45}{H \text{lightway FE}}}\tag{22}$$



Rule-based control and PSO simulation results are presented in Table 3. In the urban driving cycle, the FE of the rule-based simulation was 46.28 mpg, and the FE of the PSO simulation was 51.79 mpg. PSO showed a 12% improvement over rule-based control. In the highway driving cycle, the FE of the rule-based simulation was 39.11 mpg, and the FE of the PSO simulation was 41.85 mpg. PSO showed a 7% improvement over rule-based control. For composite FE, rule-based control was 42.74 mpg and PSO was 46.78 mpg. PSO showed an improvement of 9.4% compared to rule-based control.

**Table 3.** Comparison of fuel economy.


To understand the reasons for the improvements with the PSO algorithm, the instantaneous fuel consumption of the rule-based control and PSO models were compared, as shown in Figures 10 and 11. Figure 10 shows the urban simulation results; the instantaneous fuel consumption of the PSO was generally smaller than that of the rule-based controller. The switching timing for the engine to turn on/off depended on the required engine torque and battery SOC. In rule-based control, the results were obtained from the pre-set rules/tables. In PSO, the algorithm searched for better fuel consumption under the desired engine torque. Therefore, the fuel rate of PSO was smaller and engine-switch timing was different from rule-based control. Figure 11 shows the instantaneous fuel consumption for the highway driving cycle. It can be seen that the maximum instantaneous fuel consumption was 2.6 g/s for rule-based control and 2.3 g/s for PSO. PSO would affect the engine switch timing and engine operating points. The fuel consumption of PSO was better than that of the rule-based control.

**Figure 10.** Comparison of instantaneous fuel consumption in the urban driving cycle.

**Figure 11.** Comparison of instantaneous fuel consumption in the highway driving cycle.

Figures 12 and 13 are comparisons of engine speeds on urban and highway driving cycles, respectively. The engine speeds of PSO and rule-based control were mainly determined by driving resistance and SOC. According to the simulation results of the two methods, most of the engine speeds in urban areas were around 1400 to 2000 rpm. The improvement in fuel consumption was affected by engine torque.

**Figure 12.** Comparison of engine speed in the urban driving cycle.

**Figure 13.** Comparison of engine speed in the highway driving cycle.

Figures 14 and 15 are comparisons of engine torque in urban and highway driving cycles, respectively. It can be seen that the engine torque in PSO was less than that in rule-based control. The peak torque values in urban driving cycles decreased from 250 Nm in rule-based control to 160 Nm in PSO. The reason that PSO algorithm provided a better fuel consumption is mainly due to the engine torque being reduced. In the highway driving cycle, the improvement of fuel consumption was because of different engine operating points and engine running time.

**Figure 14.** Comparison of engine torque in the urban driving cycle.

**Figure 15.** Comparison of engine torque in the highway driving cycle.

Figures 16 and 17 provide the electric conversion loss from the motor/generator to charge the battery. It can be clearly seen that the conversion loss was higher with rule-based control in both driving cycles, which was one of the reasons that PSO could improve the fuel consumption.

**Figure 16.** Comparison of electric conversion loss in the urban driving cycle.

Figures 18 and 19 show the engine operating points of rule-based control and PSO in urban areas and the highway driving cycle, respectively. In the urban driving cycle, the engine torque of PSO operating points was mainly in the 50–170 Nm range. Compared to the operating points of rule-based control, the trend of overall PSO engine power decline also led to an improvement of fuel consumption. In rule-based control, some of the engine operating points were around 170–240 Nm, which is in a high-efficiency range. It did not require such a large amount of engine power to drive the vehicle, so the excess engine power would be transferred to the generator to charge the battery. That resulted in an increase of conversion loss. Furthermore, the stored energy in the battery would not stay in the

battery very long and would soon be used for driving. This resulted in a second conversion loss and would affect the fuel economy.

**Figure 17.** Comparison of electric conversion loss in the highway driving cycle.

**Figure 19.** Comparison of highway engine operating points.

On the highway driving cycle, most of the PSO engine operating points were in the range of 75–120 Nm, which is in a better efficiency range of the engine. The engine operating points of rule-based control were scattered throughout a wider range. Some points were around 200 Nm, which is in a high-efficiency region; however, the vehicle did not require such a large amount of engine power. The excess engine power would charge the battery and cause an electric conversion loss. The stored energy in the battery would be applied for driving. This resulted in a second conversion loss. It affected the fuel economy.

Figures 20 and 21 show the comparison of electric motor torque of M/G1 in urban and highway driving cycles, respectively. M/G1 was mainly driven by the engine in mode one. In the urban driving cycle, M/G1 was mostly in the charge condition. In the highway driving cycle, the powertrain mainly stayed on mode two. M/G1 worked as a driving motor and provided power to drive the vehicle.

**Figure 20.** M/G1 torque in the urban driving cycle.

**Figure 21.** M/G1 torque in the highway driving cycle.

Figures 22 and 23 were the torque of M/G2 in the urban and highway driving cycles, respectively. In the urban driving cycle, the positive torque output time of the PSO algorithm was longer than that of the rule-based control. With the optimization process of the PSO, the vehicle would have more time driven by electric motors to save fuel and improve vehicle fuel economy.

**Figure 22.** M/G2 torque in the urban driving cycle.

**Figure 23.** M/G2 torque in the highway driving cycle.

The battery SOC in urban and highway driving cycles are shown in Figures 24 and 25, respectively. Through the driving cycles, the initial SOC and the SOC at the end of the cycles remained very close. During the driving cycle the battery was charged and discharged, and the battery energy at the end of the cycle remained at the same level as at the beginning. All of the driving energy was provided by the engine.

**Figure 24.** Battery SOC in the urban driving cycle.

**Figure 25.** Battery SOC in the highway driving cycle.

### **5. Conclusions**

This research focused on the real-time control algorithm to improve the fuel economy of a two-mode, power-split hybrid electric vehicle. The vehicle model was built with Matlab/Simulink. The fuel economy simulation results of the base model with rule-based control were close to the fuel economy data provided by the original manufacturer, which confirmed the reliability of the vehicle model. Particle swarm optimization (PSO) was implemented as a real-time optimization control with the goal of reducing fuel consumption. The minimum instantaneous fuel consumption was the

objective of PSO. The engine torque was the design variable. PSO was to set up a group of sprinkled particles to search for the best solution. The particles were dispersed in a reasonable working area of the engine, and the value of the objective function was calculated for each particle position. The objective function of each particle and the instantaneous fuel consumption was compared, and the particle position was updated based on better results of the group. The above action was repeated until the particles converged, and the objective value of the particle was the current minimum instantaneous fuel consumption. The following conclusions were obtained based on the simulation results.


**Author Contributions:** Conceptualization, H.-Y.H.; investigation, H.-Y.H.; methodology, H.-Y.H.; project administration, J.-S.C.; software, J.-S.C.; validation, J.-S.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** There is no external funding for this research.

**Conflicts of Interest:** The authors declare no conflict of interest.
