Multi-Objective Optimization of Powertrain Components for Electric Vehicles Using a Two-Stage Analysis Model
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ght © 2020 KSAE/ 11816 pISSN 12299138/ eISSN 19763832
MULTI-OBJECTIVE OPTIMIZATION OF POWERTRAIN COMPONENTS FOR ELECTRIC VEHICLES USING A TWO-STAGE ANALYSIS MODEL Kihan Kwon1, 2), Minsik Seo1) and Seungjae Min1)* Department of Automotive Engineering, Hanyang University, Seoul 04763, Korea Department of Automotive Engineering, Honam University, Gwangju 62399, Korea
1) 2)
(Received 9 July 2019; Revised 11 October 2019; Accepted 13 March 2020) ABSTRACTAn 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. KEY WORDS : Electric vehicle, Powertrain components, Two-stage analysis model, Multi-objective optimization, Surrogate model
NOMENCLATURE Tem p d q f Ld Lq Id Iq Vd Vq m Rw R0 R T0 Wloss cf vf Im Vm m
DC vt v Kp Ki Kd Tm Tb Cb Treg rg Jeq Jw Jm Mv Rt w t r g Cd a Af SOC Cn Pmax Vmax
: electromagnetic torque of motor, Nm : pole number : magnetic flux of d-axis, Wb : magnetic flux of q-axis, Wb : permanent magnet flux, Wb : stator inductance of d-axis, H : stator inductance of q-axis, H : current of d-axis, A : current of q-axis, A : voltage of d-axis, V : voltage of q-axis, V : rotational speed of motor, rad/s : winding resistance, ohm : winding resistance at reference temperature, ohm : coefficient of winding resistance, 1/K : reference temperature, K : total loss of motor, W : coulomb friction coefficient, Nm : viscous friction coefficient, Nm·s/rad : magnitude of current, A : magnitude of voltage, V : efficiency of motor
*Corresponding author. e-mail: [email protected] 1495
: driver’s command : target speed, m/s : vehicle speed, m/s : proportional gain : integral gain : derivative gain : mechanical torque of motor, Nm : braking torque, Nm : capacity of braking torque, Nm : maximum regenerative braking torque, Nm : gear ratio of transmission : equivalent inertia of vehicle at wh
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