2.1.1. Modeling of EV with Automated Manual Transmission
- (1)
Single-Stage Main Reducer Model Establishment
In order to build the vehicle model, the basic parameters of the vehicle should be obtained, mainly referring to the fundamental dimensional parameters, as shown in
Table 1.
- (a)
Single-stage main reducer EV powertrain architecture.
The powertrain architecture employing a single-stage primary reducer, as illustrated in
Figure 1, encompasses the power battery, inverter, motor, single-stage primary reducer, and differential. The study subsequently analyzes the energy loss and average efficiency of the components outlined by the red dashed frame.
- (b)
Motor Modeling
The motor is a crucial component of the pure electric vehicle power system. Its primary function is to convert the electrical energy from the traction battery into mechanical energy for the transmission system, providing sufficient torque to the drive wheels. During daily driving, it transforms braking energy into direct current, storing it in the battery for future use. The motor is modeled using the method based on the static efficiency MAP (Motor Axial Power) chart. The following equation can determine the relationship between motor efficiency and motor speed and torque:
where
represents the real-time efficiency of the motor,
stands for the motor torque, and
represents the motor speed; the constant 9550 is used as a factor to convert torque and rotational speed to power.
In different usage scenarios, the motor operates in different states, which can be categorized into driving mode and charging mode. When the torque is positive, the motor converts electrical energy into mechanical energy, whereas when the torque is negative, it indicates that the vehicle is braking. In this case, the motor converts mechanical energy back into chemical energy to charge the battery. The formulas for calculating motor power
in different modes are as follows:
Figure 2 illustrates the variation in torque and power of the motor at different speeds.
- (c)
Battery Modeling
As a crucial device for supplying and storing energy, the traction battery undergoes complex material, chemical, and physical changes during the charging and discharging processes. These changes are nonlinear, making it challenging to establish a theoretical model for the traction battery. Various modeling methods exist for traction batteries, including lookup table methods, first-order RC models, and second-order RC models. In this study, the first-order RC model was chosen for battery modeling, and the schematic diagram is shown in
Figure 3.
The equivalent circuit equation based on Kirchhoff’s voltage law is as follows:
where
represents the terminal voltage of the traction battery
; the open-circuit voltage of the battery
is the equivalent internal resistance of the battery; and
represents the port output current.
Power at the battery terminal is calculated using the following equations, where
represents the power of the traction battery.
In the 18,000 s simulation experiment, the battery undergoes continuous charging and discharging. In this study, discharge current and discharge voltage were extracted throughout the entire driving cycle, along with their corresponding timestamps. The following characteristics of voltage and current variation over time is shown in
Figure 4.
The design objectives of the entire vehicle in terms of performance and efficiency are shown in
Table 2.
This study created an EV model in MATLAB with a single-stage main reducer and a primary reducer speed ratio of 8.25. Critical transmission system parameters were obtained through interpolation.
- (2)
Model Validation
In order to validate the accuracy of the model, simulations were performed under the CLTC working conditions, and the simulation results are shown in
Table 3.
The simulation results indicate that the model’s accuracy meets the design requirements.
- (3)
EV with Automated Manual Transmission Establishment
The electric vehicle powertrain architecture, based on a single-stage primary reducer, incorporates an AMT, as depicted in
Figure 5. The third chapter is devoted to calculating and analyzing the energy loss and average efficiency of the parts marked by the red dashed lines.
During driving, a vehicle’s gear shifting is typically influenced by dynamic parameters. Based on the chosen criteria, gear shifting logic can be categorized into single-parameter, dual-parameter, or triple-parameter strategies [
31]. Single-parameter shifting relies primarily on the vehicle’s speed as the critical factor, reflecting driving conditions accurately and offering straightforward implementation. The critical upshift speed of this approach often corresponds to the point where the accelerator pedal is fully depressed. In contrast, dual-parameter shifting considers both speed and the real-time position of the accelerator pedal, enhancing the ability to predict shifts in driver intent during driving. Triple-parameter shifting expands on these by including acceleration and road profile inputs to identify the optimal gear at any given moment. This method focuses on keeping the vehicle in the best gear possible by utilizing dynamic rather than static data. This research employed a single-parameter shifting strategy and developed two-gear, three-gear, and four-gear vehicle models with varying transmission gear ratios and shift speeds, as detailed in
Table 4.
2.1.2. EV with Automated Manual Transmission Gear Ratio Optimization
- (1)
Multi-parameter Optimization Method
This study used the MATLAB Genetic Algorithm Toolbox to perform single-objective multi-parameter optimization, with the EV’s energy consumption per 100 km (CLTC conditions) as the optimization objective and the gear shift speeds and gear ratios as the variables.
The genetic algorithm is an optimization algorithm inspired by biological evolution theories. By simulating the processes of selection, crossover, and mutation in evolution, the genetic algorithm can find better solutions to complex optimization problems and gradually approach the optimal solution in the solution domain [
32].
The basic steps of the genetic algorithm are shown in
Figure 6:
Initialization of Population: Randomly generate a set of individuals, with each individual representing a potential solution. This set of individuals forms the initial population.
Fitness Evaluation: Compute each individual’s fitness based on a specific evaluation function for the problem. The fitness value measures the quality of the individual’s solution to the problem.
Selection Operation: Based on the fitness values, select some of the fittest individuals as parents. The selection operation is typically performed using a probabilistic selection method, where more fit individuals are more likely to be selected.
Crossover operation selects genes from the chromosomes of selected parent individuals and exchanges them to create new offspring.
Mutation operation randomly alters genes within the chromosomes.
Update Population: replace the parent individuals with the newly generated offspring to obtain an updated population.
Repeat the b–f operations until the optimal solution is obtained.
- (2)
Genetic Algorithm Parameter Settings
Firstly, selecting the Genetic Algorithm Solver in the optimization toolbox determines the corresponding fitness function, the number of variables, and the variable constraints. The number of iterations for the genetic algorithm is 50, and the output includes the best individual and fitness function values. For example, when optimizing the EV equipped with a two-gear gearbox, the number of variables is 3, representing the gear 1 ratio, gear 2 ratio, and the shift speed. In the Genetic Algorithm Toolbox, the upper and lower bounds of the gear 1 ratio are set to 1–1.25, the gear 2 ratio to 0.75–1, and the shift speed to 40–60.
Specific parameters for the AMT are shown in
Table 5.
The optimal gear ratios and shift speeds for each gear of AMT, with minimum energy consumption per 100 km as the optimization objective, are shown in
Table 6.