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Torque control allocation based on constrained optimization with regenerative braking for electric vehicles

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Abstract

This paper proposes a constrained optimization-based torque control allocation method aimed to improve energy efficiency, and thus, driving range for electric vehicles. In the proposed method, the cost function is defined not only to achieve desired yaw moment for vehicle handling and stability, but also to minimize power losses for energy efficiency. The particular attention is paid to the power losses due to tire slips both longitudinally and laterally. The constraints are also set based on thorough investigation on various causes of power disppation such that the torque is allocated with restraint to use regenerative braking in its maximum capacity. The proposed control allocation method has been tested and verified to be effective on energy efficiency improvement through both simulation and experiment under various driving maneuvers.

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Abbreviations

C a :

aerodynamic drag coefficient

m :

vehicle mass

V x :

longitudinal velocity

R e :

effective tire radius

R x :

force due to rolling resistance

θ :

road grade angle

β :

vehicle sideslip angle

γ :

vehicle yaw rate

δ :

front wheel steering angle

C f, C r :

cornering stiffness of front and rear tires respectively

l c :

half of vehicle track

a x :

longitudinal acceleration

a y :

lateral acceleration

K r :

vehicle stability factor

E on :

insulated gate bipolar transistor turn-on losses

E on_nom :

insulated gate bipolar transistor turn-on losses nominal value

E off :

insulated gate bipolar transistor turn-off losses

E off_nom :

insulated gate bipolar transistor turn-off losses nominal value

E rec :

reverse recovery losses of freewheeling diode

E rec_nom :

reverse recovery losses of freewheeling diode nominal value

f sw :

inverter switching frequency

i d, i q :

d, q-axes current components

i cd, i cq :

d, q-axes iron losses current components

i od, i oq :

d, q-axes magnetizing current components

I a :

armature current

I s :

peak of the load current

K :

weighting coefficient of error

L d, L q :

d, q-axes inductance components

p :

number of pole pairs

P cs :

insulated gate bipolar transistor conduction loss

P cd :

freewheeling diode conduction loss

P Cu :

stator winding copper losses

P Fe :

stator iron losses

P loss_inverter :

overall losses of the inverter

P loss_motor :

motor losses

P m :

friction losses

P sw :

switching losses of three-phase inverter

P sw_ph :

switching losses of single-phase inverter

R a :

stator winding resistance

R c :

iron loss resistance

R ce, R ak :

insulated gate bipolar transistor and freewheeling diode equivalent series resistances

t :

time step

T e :

electromagnetic torque

T m :

friction torque

T out :

motor output torque

u d, u q :

d, q-axes voltage components

V d0, V s0 :

insulated gate bipolar transistor and freewheeling diode zero current conduction voltage drop

η inverter :

inverter efficiency

η motor :

motor efficiency

φ :

power factor angle

ψ a :

flux linkage due to the rotor magnets

ω s :

stator currents frequency

ω m :

rotor mechanical speed

m:

modulation index

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Authors and Affiliations

  1. State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun, 130022, China

    Yang Zhao, Weiwen Deng, Jian Wu & Rui He

Authors
  1. Yang Zhao
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  2. Weiwen Deng
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  3. Jian Wu
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  4. Rui He
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Correspondence to Jian Wu.

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Zhao, Y., Deng, W., Wu, J. et al. Torque control allocation based on constrained optimization with regenerative braking for electric vehicles. Int.J Automot. Technol. 18, 685–698 (2017). https://doi.org/10.1007/s12239-017-0068-7

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  • DOI: https://doi.org/10.1007/s12239-017-0068-7

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