Mathematical Modeling the Performance of an Electric Vehicle Considering Various Driving Cycles
Abstract
:1. Introduction
- to develop a complex mathematical model of the system of traction electrical equipment, for a qualitative and quantitative assessment of the charge–discharge modes of the battery;
- to analyze the operating modes of the battery using mathematical and simulation modeling, as part of the traction electrical equipment system of an electric vehicle; determine the thermal conditions of the battery, using simulation modeling of charge–discharge modes, with intensive movement of the electric vehicle;
- to develop methods for determining resource characteristics based on the operating cycles of electric vehicles.
- parallel—they combine the operation of electric and gasoline engines and allow the battery to be charged from the network;
- series-parallel—capable of operating as both serial and parallel hybrid vehicles with an electric motor as the main drive;
- sequential (REEV/REX)—electric vehicles with an increased range. In this type of hybrid, the car is always powered by an electric motor that is powered directly from the battery, but the battery itself is charged while driving by the built-in fuel generator;
- fully electric vehicles (EV/BEV) and fuel cell vehicles (FCV), which include an electrochemical generator to convert hydrogen into electrical energy.
1.1. Cycles of Movement of an Electric Vehicle for Mathematical Modeling of Energy Characteristics
1.2. Model Range of Electric Vehicles and Parameters of Mathematical Modeling
1.3. Features of the Choice of Driving Cycles for Mathematical Modeling of Battery Operating Parameters
2. Materials and Methods
- Development of a mathematical model for studying the range of an electric vehicle, taking into account four driving cycles, in which the lengths of cycles and the forces acting on the electric vehicle are determined.
- Creation of a mathematical model for calculating the forces of resistance to movement was carried out taking into account the efficiency of the electric motor. Then, on its basis, the determination of the energy consumption of an electric vehicle.
- Conduct of a simulation of the study of cycles of movement of an electric vehicle on the presented model and performance of a mathematical assessment of the battery life based on the simulation results.
- Formulation of recommendations for developers of mathematical software for the microcontroller for controlling the electric vehicle charging battery, which would allow the control of the electric vehicle to be adjusted in Eco mode, taking into account the efficient energy consumption of the electric vehicle and saving battery life.
2.1. Canned Cycles for Power Reserve Research
2.2. Calculation of the Characteristics of an Electric Vehicle
2.3. Model Structure
- Specific energy consumption per cycle, Wh/km;
- Range of the electric vehicle, determined by Expression (17), km;
- Energy consumption per cycle, MJ;
- Remaining battery charge, MJ;
- SoC batteries, %.
3. Results and Discussion
3.1. Simulation Results
- V(t), m/s—the investigated cycle of movement;
- a(t), m/s2—changes in the acceleration of the electric vehicle during the cycle;
- P(t), W—consumed mechanical power from cycle time;
- E(t), MJ—current energy supply;
- SoC, %—the degree of battery charge.
3.2. Battery Life Estimation Based on Simulation Results
3.3. Verification and Limitations of the Mathematical Model of the Traction Electrical Equipment System
- Low performance of electric vehicles in general, including the life of traction batteries, significant limited autonomous driving compared to vehicles based on internal combustion engines, the continued high cost of batteries, limited introduction of a charging infrastructure, and deterioration in efficient operation at low ambient temperatures environment.
- The braking control system increases the moment of resistance on the motor shaft if the vehicle speed is higher than the speed in a given driving cycle. The model is necessary when comparing the results according to the test protocol. In addition to the standard braking system, the electric vehicle uses regenerative braking. The energy obtained from generating the braking torque of the electric motor is used to charge the battery. However, in the case when the battery is fully charged and cannot receive energy, the regenerative torque must be limited using the standard braking system. The efficiency and consumption of electrical energy, as well as the efficiency of recuperation, depend on the ratio of the mechanical brake system and the electric one.
4. Conclusions
- The US06 maximum speed cycle provides the smallest EV range. High energy consumption is mainly associated with country driving at speeds above 100 km/h.
- Cycles JC08 and NEDC have similar developed speeds in urban conditions; however, in NEDC there is a phase of suburban traffic and due to the higher speed, the electric vehicle covers a greater distance in equal time compared to JC08. In this case, the NEDC cycle is the least dynamic; the acceleration values do not exceed 1 m/s2. Low dynamics allows for a longer range of an electric vehicle, however, the actual urban operation of an electric vehicle requires more dynamics, and therefore, measurements for the NEDC cycle will not be taken into account in the future in order to approximate real conditions.
- The modern WLTC measuring cycle provides sufficient range. Frequent braking, taking into account operation in city traffic, provides a significant return of electricity to the battery.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Battery Parameters | Tesla Model S | Nissan Leaf | BMW i3 |
---|---|---|---|
Battery capacity, kWh | 85 | 24 | 22 |
Power reserve to full charge, km | 426 | 175 | 160 |
Resource, years | 7 | 5 | 5 |
Full charge cycle (220 V), h | 8 | 8 | 8 |
Energy consumption, kWh/100 km | 27.7 | 21 | 12 |
Cycle Parameter | US06 | JC08 | NEDC | WLTC |
---|---|---|---|---|
Time range, s | 600 | 1200 | 1200 | 1800 |
Cycle length, km | 12.89 | 8.15 | 11.04 | 22.77 |
Specific consumption, Wh/km | 191 | 127 | 76 | 159 |
Energy consumption per cycle, MJ | 8.9 | 3.7 | 3 | 13 |
Remaining battery charge, MJ | 141.1 | 146.3 | 147 | 137 |
SoC, % | 94.1 | 97.5 | 98.0 | 91.3 |
Power reserve, km | 218 | 328 | 546 | 262 |
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Martyushev, N.V.; Malozyomov, B.V.; Sorokova, S.N.; Efremenkov, E.A.; Qi, M. Mathematical Modeling the Performance of an Electric Vehicle Considering Various Driving Cycles. Mathematics 2023, 11, 2586. https://doi.org/10.3390/math11112586
Martyushev NV, Malozyomov BV, Sorokova SN, Efremenkov EA, Qi M. Mathematical Modeling the Performance of an Electric Vehicle Considering Various Driving Cycles. Mathematics. 2023; 11(11):2586. https://doi.org/10.3390/math11112586
Chicago/Turabian StyleMartyushev, Nikita V., Boris V. Malozyomov, Svetlana N. Sorokova, Egor A. Efremenkov, and Mengxu Qi. 2023. "Mathematical Modeling the Performance of an Electric Vehicle Considering Various Driving Cycles" Mathematics 11, no. 11: 2586. https://doi.org/10.3390/math11112586
APA StyleMartyushev, N. V., Malozyomov, B. V., Sorokova, S. N., Efremenkov, E. A., & Qi, M. (2023). Mathematical Modeling the Performance of an Electric Vehicle Considering Various Driving Cycles. Mathematics, 11(11), 2586. https://doi.org/10.3390/math11112586