Abstract
An electric vehicle (EV) powertrain is comprised of a motor and reduction gear. Thus, it must be designed by considering both components to improve its dynamic and economic performances. To obtain the optimal design of powertrain components for an EV, this study employs a two-stage analysis model focusing on the motor and vehicle at each stage for accuracy and efficiency. In the first stage, a motor system model analyzes the motor characteristics, such as the maximum and minimum torque and motor losses. Using the motor design parameters, these characteristics are converted to torque curves and an efficiency map. In the second stage, a vehicle system model analyzes the target performance using converted motor data for efficient analysis of the performance. An optimization problem is formulated to minimize the maximum motor power, acceleration time, and energy consumption with dynamic constraints, including the maximum vehicle speed and ascendable gradient. To reduce the excessive computational effort when conducting the multi-objective optimization, surrogate models with respect to performance are effectively constructed by using the adaptive sampling method. From the optimization results, a Pareto front having various solutions among the objective functions is obtained.
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Abbreviations
- T em :
-
electromagnetic torque of motor, Nm
- p :
-
pole number
- φ d :
-
magnetic flux of d-axis, Wb
- φ q :
-
magnetic flux of q-axis, Wb
- φ f :
-
permanent magnet flux, Wb
- L d :
-
stator inductance of d-axis, H
- L q :
-
stator inductance of q-axis, H
- I d :
-
current of d-axis, A
- I q :
-
current of q-axis, A
- V d :
-
voltage of d-axis, V
- V q :
-
voltage of q-axis, V
- ω m :
-
rotational speed of motor, rad/s
- R w :
-
winding resistance, ohm
- R 0 :
-
winding resistance at reference temperature, ohm
- α R :
-
coefficient of winding resistance, 1/K
- T 0 :
-
reference temperature, K
- W loss :
-
total loss of motor, W
- c f :
-
coulomb friction coefficient, Nm
- v f :
-
viscous friction coefficient, Nm·s/rad
- I m :
-
magnitude of current, A
- V m :
-
magnitude of voltage, V
- η m :
-
efficiency of motor
- DC :
-
driver’s command
- v t :
-
target speed, m/s
- v :
-
vehicle speed, m/s
- K p :
-
proportional gain
- K i :
-
integral gain
- K d :
-
derivative gain
- T m :
-
mechanical torque of motor, Nm
- T b :
-
braking torque, Nm
- C b :
-
capacity of braking torque, Nm
- T reg :
-
maximum regenerative braking torque, Nm
- r g :
-
gear ratio of transmission
- J eq :
-
equivalent inertia of vehicle at wheel, kg·m2
- J w :
-
inertia of wheels, kg·m2
- J m :
-
inertia of motor, kg·m2
- M v :
-
mass of vehicle, kg
- R t :
-
radius of tire, m
- ω w :
-
rotational speed of wheel, rad/s
- η t :
-
efficiency of transmission
- μ r :
-
rolling resistance coefficient
- g :
-
gravity acceleration, m/s2
- C d :
-
air drag coefficient
- ρ a :
-
air density, kg/m3
- A f :
-
frontal area, m2
- ΔSOC :
-
amount of SOC variation, %
- C n :
-
nominal capacity of battery, kWh
- P max :
-
maximum power of motor, kW
- V max :
-
maximum voltage of motor, V
- I max :
-
maximum current of motor, A
- F t :
-
traction force, N
- ω max.rpm :
-
maximum rotational speed of motor, rev/min
- v max.kph :
-
maximum speed of vehicle, km/h
- r max :
-
maximum gear ratio
- r min :
-
minimum gear ratio
- θ max.grad :
-
maximum ascendable gradient, %
- t acc :
-
acceleration time, s
References
Buerger, S., Lohmann, B., Merz, M., Vogel-Heuser, B. and Hallmannsegger, M. (2010). Multi-objective optimization of hybrid electric vehicles considering fuel consumption and dynamic performance. 2010 IEEE Vehicle Power and Propulsion Conf., Lille, France.
Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. 1st edn. John Wiley & Sons. New York.
Di Nicola, F., Sorniotti, A., Holdstock, T., Viotto, F. and Bertolotto, S. (2012). Optimization of a multiple-speed transmission for downsizing the motor of a fully electric vehicle. SAE Int. J. Alternative Powertrains 1, 1, 134–143.
Gao, B., Liang, Q., Xiang, Y., Guo, L. and Chen, H. (2015). Gear ratio optimization and shift control of 2-speed I-AMT in electric vehicle. Mechanical Systems and Signal Processing, 50–51, 615–631.
Kim, H., Kim, S., Kim, T., Lee, T. H., Ryu, N., Kwon, K. and Min, S. (2018). Efficient design optimization of complex system through an integrated interface using symbolic computation. Advances in Engineering Software, 126, 34–45.
Kwon, K., Seo, M. and Min, S. (2018). Optimization of gear ratio of in-wheel motor vehicle considering probabilistic driver model. Int. J. Automotive Technology 19, 6, 1081–1089.
Kwon, K., Seo, M., Kim, H., Lee, T. H., Lee, J. and Min, S. (2020a). Multi-objective optimization of hydropneumatic suspension with gas-oil emulsion for heavyduty vehicles. Vehicle System Dynamics 58, 7, 1146–1165.
Kwon, K., Seo, M. and Min, S. (2020b). Efficient multiobjective optimization of gear ratios and motor torque distribution for electric vehicles with two-motor and two-speed powertrain system. Applied Energy, 259, 114190.
Lei, Z., Qin, D., Liu, Y., Peng, Z. and Lu, L. (2017). Dynamic energy management for a novel hybrid electric system based on driving pattern recognition. Applied Mathematical Modelling, 45, 940–954.
Liu, T., Zou, Y. and Liu, D. (2016). Energy management for battery electric vehicle with automated mechanical transmission. Int. J. Vehicle Design 70, 1, 98–112.
Ramakrishnan, K., Stipetic, S., Gobbi, M. and Mastinu, G. (2018). Optimal sizing of traction motors using scalable electric machine model. IEEE Trans. Transportation Electrification 4, 1, 314–321.
Ruan, J., Walker, P. and Zhang, N. (2016). A comparative study energy consumption and costs of battery electric vehicle transmissions. Applied Energy, 165, 119–134.
Sarigiannidis, A. G., Beniakar, M. E., and Kladas, A. G. (2017). Fast adaptive evolutionary PM traction motor optimization based on electric vehicle drive cycle. IEEE Trans. Vehicular Technology 66, 7, 5762–5774.
Tan, S., Yang, J., Zhao, X., Hai, T. and Zhang, W. (2018). Gear ratio optimization of a multi-speed transmission for electric dump truck operating on the structure route. Energies 11, 6, 1324.
Urbina Coronado, P. D., Orta Castañón, P. and Ahuett-Garza, H. (2018). Optimization of gear ratio and power distribution for a multimotor powertrain of an electric vehicle. Engineering Optimization 50, 2, 293–309.
Walker, P. D., Abdul Rahman, S., Zhu, B. and Zhang, N. (2013). Modelling, simulations, and optimization of electric vehicles for analysis of transmission ratio selection. Advances in Mechanical Engineering 5, 340435.
Yang, Y. P. and Shih, G. Y. (2016). Optimal design of an axial-flux permanent-magnet motor for an electric vehicle based on driving scenarios. Energies 9, 4, 285.
Zhang, S., Xiong, R., Zhang, C. and Sun, F. (2016). An optimal structure selection and parameter design approach for a dual-motor-driven system used in an electric bus. Energy 96, 5, 437–448.
Acknowledgement
This research was supported by Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea Government (MOTIE) (N0002428, The Competency Development Program for Industry Specialist).
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Kwon, K., Seo, M. & Min, S. Multi-Objective Optimization of Powertrain Components for Electric Vehicles Using a Two-Stage Analysis Model. Int.J Automot. Technol. 21, 1495–1505 (2020). https://doi.org/10.1007/s12239-020-0141-5
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DOI: https://doi.org/10.1007/s12239-020-0141-5