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Energy efficiency optimization of electric vehicle driven by in-wheel motors

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Abstract

Electric vehicle is considered to be the solution for energy and environment crisis, but it’s still not competitive enough with conventional vehicles because of the limited energy density and high cost of the power battery. So the energy efficiency is of the most importance for the control of electric vehicles. This paper looks into the energy efficiency optimization problem of electric vehicle driven by four in-wheel motors by developing a comprehensive energy efficiency model of the permanent magnet synchronous motor including the inverter. The calculated efficiency agrees with the measured data quite well. Based on the power loss analysis, the conclusion is drawn that in all driving or braking conditions the total torque requirement should be distributed evenly to all the motors in order to maximize the energy efficiency for electric vehicles driven by permanent magnet synchronous in-wheel motors. Vehicle test results show that the energy efficiency of the evenly distributed torque control is higher than the control strategy proposed by control allocation in literature.

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Abbreviations

a dr, b dr, c dr :

coefficient for the equation of motor power loss in driving condition

a rb, b rb, c rb :

coefficient for the equation of motor power loss in braking condition

C iss :

MOSFET input capacitance (F)

C rss :

MOSFET reverse-transfer capacitance (F)

eSW:

energy loss during one switching (J)

i d :

d-axis armature current (A)

i q :

q-axis armature current (A)

i od :

d-axis copper loss current (A)

i oq :

q-axis copper loss current (A)

i cd :

d-axis iron loss current (A)

i cq :

q-axis iron loss current (A)

i m :

phase current amplitude (A)

i g2 :

average gate current during the second phase of MOSFET switching on (A)

i g3 :

average gate current during the third phase of MOSFET switching on (A)

J :

cost function of energy efficiency optimization

k 1, k 2 :

coefficient for the expression of inverter loss

L :

motor inductance (H)

L d :

d-axis inductance (H)

L q :

q-axis inductance (H)

n i :

rotating speed of the i th motor (rpm)

n p :

number of pole pairs

P out :

output power (W)

P in :

input power (W)

P loss :

loss power (W)

P loss,t :

total loss power of four motors (W)

P loss,f :

loss power of the front motor (W)

P loss,r :

loss power of the rear motor (W)

P l :

power loss without copper loss (W)

P Cu :

copper loss (W)

P Fe :

iron loss (W)

P m :

friction loss (W)

P s :

stray loss (W)

P inv :

inverter loss (W)

P C :

inverter conduction loss (W)

P C,MOS :

MOSFET conduction loss (W)

P C,D :

diode conduction loss (W)

P SW :

inverter switching loss (W)

R a :

armature resistance (Ω)

R c :

iron loss equivalent resistance (Ω)

R ds :

MOSFET resistance during conduction (Ω)

R ak :

diode resistance during conduction (Ω)

R hi :

MOSFET driver resistance (Ω)

R gate :

resistance between MOSFET driver and MOSFET gate (Ω)

R gi :

MOSFET gate resistance (Ω)

t 2 :

time duration of the second phase of MOSFET switching (s)

t 3 :

time duration of the third phase of MOSFET switching (s)

t c :

PWM cycle time (s)

t d :

dead time (s)

T :

motor output torque (Nm)

T e :

motor electromagnetic torque (Nm)

T i :

output torque of the i th motor (Nm)

T req :

total torque requirement (Nm)

T f :

output torque of the front motor (Nm)

T r :

output torque of the rear motor (Nm)

T m :

friction torque (Nm)

T min :

minimum torque output (Nm)

T max :

maximum torque output (Nm)

T i0 :

no-load iron loss torque (Nm)

T drag :

dynamometer dragging torque (Nm)

u d :

d-axis terminal voltage (V)

u q :

q-axis terminal voltage (V)

u th :

gate threshold voltage (V)

u gs,mil :

gate miller plateau voltage (V)

u drv :

MOSFET driving circuit voltage (V)

u bat :

battery voltage (V)

u ds,off :

voltage across the drain and source when MOSFET is off (V)

u ds :

MOSFET voltage drop during conduction (V)

u ak :

diode voltage drop during conduction (V)

u f :

diode voltage drop at zero current (V)

η :

energy efficiency of the motor (%)

η i :

energy efficiency of the ith motor (%)

η f :

energy efficiency of the front motor (%)

η r :

energy efficiency of the rear motor (%)

η dr :

motor energy efficiency in driving condition (%)

η rb :

motor energy efficiency in braking condition (%)

ω :

motor electrical angular velocity (rad/s)

ω c :

motor mechanical rotating speed (rad/s)

Ψ d :

d-axis flux-linkage (Wb)

Ψ q :

q-axis flux-linkage (Wb)

Ψ f :

permanent magnet flux-linkage (Wb)

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Correspondence to M. Ouyang.

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Gu, J., Ouyang, M., Lu, D. et al. Energy efficiency optimization of electric vehicle driven by in-wheel motors. Int.J Automot. Technol. 14, 763–772 (2013). https://doi.org/10.1007/s12239-013-0084-1

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  • DOI: https://doi.org/10.1007/s12239-013-0084-1

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