IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO.

8, OCTOBER 2012 3365

Torque Distribution Strategy for a Front- and

Rear-Wheel-Driven Electric Vehicle
Xibo Yuan, Member, IEEE, and Jiabin Wang, Senior Member, IEEE

Abstract—Electric vehicles (EVs) with a distributed drive train

configuration offer great potential and flexibility for improving
system efficiency, performance, reliability, and safety. This pa-
per investigates a torque distribution scheme for a front- and
rear-wheel-driven microsized EV to improve drive train efficiency
over a wide torque and speed range. The loss model of the
traction permanent-magnet (PM) motor is characterized in both
the constant-torque and flux-weakening regions. The relationship
between motor efficiency and torque at a given speed is then
derived. It has been shown that maximum efficiency is achieved if
the total torque required by the vehicle is equally shared between
the two identical motors. In addition, the distribution of the energy
consumption over a New European Driving Cycle (NEDC) is ana-
lyzed, and the regions of high speed and low torque are identified
to have a high level of energy consumption; in these regions, Fig. 1. Four possible drive train architectures. (a) Front wheel driven. (b) rear
motor efficiency improvement is the most important. Therefore, wheel driven. (c) Both front wheel and rear wheel driven. (d) Four-wheel driven.
this paper further proposes to operate just one motor to provide
the total required torque in the low-torque region. A clutch may and series–parallel formats with or without plug-in facilities
be employed between one motor and gearbox (differential), thus [6]–[9] and engine downsizing [10]. Due to the fact that elec-
“switching off” its idle loss (no-load loss and flux-weakening loss) tricity can be generated from many alternative energy sources
and improving drive train efficiency. An online optimized torque
distribution algorithm has been devised based on the motor effi-
or renewable sources, electric vehicles (EV) have recently
ciency map to determine whether the second motor should be dis- been widely recognized and adopted in many countries as an
engaged by the clutch in the low-torque region. With the proposed effective means to reduce pollution, CO2 emission, and the
optimization scheme, drive train efficiency can be improved by 4% use of fossil fuels. Moreover, EVs may generally be recharged
over the NEDC. Experimental test results validate the proposed when power utilities have excess energy available; hence, by
torque distribution strategy.
storing energy in their batteries, they have the potential to
Index Terms—Drive train, electric vehicle (EV), front and rear support grid operation if bidirectional vehicle-to-grid power
wheel driven, motor efficiency, torque distribution. transfer functions are incorporated [11]. The use of electric
power also facilitates drive train design to have various possible
I. I NTRODUCTION configurations, thus enhancing the driving performance and
improving integration and safety. Fig. 1 shows four possible
T HE potential shortage of gasoline and the continuous
rise in prices, along with increased concern about pollu-
tion produced by fossil fuel engines, are forcing the current
drive train configurations with different motor positioning:
front wheel driven, rear wheel driven, both front and real
vehicle market to find new alternatives to reduce fossil fuel wheel driven, or four-wheel driven, where each topology has
usage [1], [2]. This has led to significant development of its advantages and disadvantages with respect to performance,
hybridization of vehicle power trains [3]–[5] via series, parallel, safety, reliability, and cost [12]–[14]. The associated power
converter (inverter) and battery can use a centralized structure
or can be integrated with the motor in a modular structure.
Manuscript received November 26, 2011; revised March 19, 2012 and July 1, Considering safety, multiple-motor configuration may provide
2012; accepted July 25, 2012. Date of publication August 15, 2012; date of redundancy to improve reliability and fail-safe operation. When
current version October 12, 2012. This work was supported by the European
Commission Integrated Enabling Technologies for Efficient Electrical Personal
one motor fails, the health motor/motors may be able to take
Mobility Project under Grant 260087. The review of this paper was coordinated over control of the vehicle. Meanwhile, multiple-motor solution
by Prof. M. Krishnamurthy. enables power sharing between different motors, thus reducing
X. Yuan was with the Electrical Machines and Drives Research Group,
Department of Electronic and Electrical Engineering, University of Sheffield, the power rating of each motor and associated converter, which
Sheffield S1 3JD, U.K. He is currently with the Electrical Energy Management would be favored in terms of integration and modularity.
Group, Department of Electrical and Electronic Engineering, University of Specifically, this paper will focus on the investigation of the
Bristol, Bristol BS8 1UB, U.K. (e-mail: yuanxibo@ieee.org).
J. Wang is with the Electrical Machines and Drives Research Group, De- torque distribution (split) of the front- and rear-wheel-driven
partment of Electronic and Electrical Engineering, University of Sheffield, EV, as shown in Fig. 1(c), where two permanent-magnet (PM)
Sheffield S1 3JD, U.K. (e-mail: j.b.wang@sheffield.ac.uk). motors are coupled to the front and rear axles, respectively, via
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org. a differential. The use of two independently controlled motors
Digital Object Identifier 10.1109/TVT.2012.2213282 provides not only a degree of fault tolerance but freedom in
0018-9545/$31.00 © 2012 IEEE
3366 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

TABLE I Previous papers [17]–[19] have compared the suitability of

EV CHARACTERISTICS (MICROSIZED CAR)
different types of motors for EV application, e.g., dc motor,
induction motor (IM), PM synchronous motor (PMSM), and
switched reluctance motor. It has been identified that the PMSM
has the highest power density and efficiency, albeit the contin-
uous increase in price of rare-earth magnet material being of
great concern. Drive train modeling and design for a single-
motor-driven EV has been presented in [20], and motor control
and loss minimization have been dealt with in [21]. However,
there is a lack of literature investigating the torque distribution
scheme in the two-motor distributed EV drive train, where the
second motor provides the possibility for efficiency improve-
ment. This paper therefore proposed the torque distribution
scheme based on the loss models of the PM motors to optimize
motor efficiency. The relationship between the motor efficiency
and the torque split ratio at a given speed is derived. Further-
more, the distribution of energy consumption over an NEDC is
analyzed. It is shown that a high level of energy consumption
occurs in low-torque and high-speed regions where the motor
efficiency is relatively low. Thus, an optimization algorithm is
proposed to minimize motor losses in the low-torque regions.
It has also been shown that, if a mechanical clutch is employed
to eliminate the no-load loss of one of the PM motors in the
power train, then the total energy efficiency can be improved by
4% over the NEDC. Alternatively, motor drive technology, such
as IM or synchronous reluctance motor, which does not incur
much no-load loss when it is not being excited, may be used to
replace one of the PM motors to improve the efficiency and cost
effectiveness of the drive train. Experimental results validate
the theoretical analysis and the proposed torque distribution
scheme.
This paper is organized as follows: Section II describes
the objective of motor efficiency optimization based on the
motor loss model and torque requirement. The optimized torque
split ratio for two identical PM motors is derived. Section III
investigates the distribution of the energy consumption of the
Fig. 2. (a) System components used in test: the battery, inverters, PM motors, motors over the NEDC, and the low-torque region is identi-
and car chassis. (b) Distribution of motor loss, inverter loss, and battery loss fied to be of a high level of energy consumption. Section IV
over the NEDC.
addresses the torque optimization issues in the low-torque
torque apportioning for improving drive train efficiency under region, and an online optimization strategy is proposed.
various operating conditions as well, which is important since Section V presents an experimental comparison regarding the
the EV driving range today is still limited by the battery capac- motor losses and efficiency with and without application of
ity [15], [16]. The EV under study is a microsized two-seat car the proposed torque distribution strategy. Section VI concludes
of ∼600-kg curb weight, with a top speed of 120 km/h as part of this paper.
the European-Union-funded Integrated Enabling Technologies
for Efficient Electrical Personal Mobility (P-MOB) project.
The detailed car parameters are given in Table I. Appendix A
II. M OTOR L OSS M ODEL AND E FFICIENCY
provides the model of the vehicle.
The schematic of the drive train, including battery, inverter, The motors used in the study and the tests are two
and motor, is shown in Fig. 2(a). By improving drive train surface-mounted PM motors, with fractional slot per pole
efficiency, particularly motor-operating efficiency, the driving and concentrated stator winding. This motor topology features
range can be extended, or the weight and size of the battery short-end winding and relatively large inductance, which are
can be reduced. Fig. 2(b) shows the drive train loss variation conducive for high power density, high efficiency, and good
over the New European Driving Cycle (NEDC), where it can flux-weakening capability for EV applications [22]. The de-
be seen that the motor loss accounts for the largest portion tailed motor parameters are summarized in Table II. It should
of the total losses. It is therefore important to minimize the be noted that, although the analysis and the proposed technique
motor losses (e.g., through optimized torque distribution) under given in this paper are based on the surfaced-mounted PM
various driving conditions subject to any safety requirement. motors, they can also be applied to other types of PM motors.
YUAN AND WANG: TORQUE DISTRIBUTION STRATEGY FOR FRONT- AND REAR-WHEEL-DRIVEN EV 3367

TABLE II motor. For the surface-mounted PM machine, the q-axis current

PM MOTOR PARAMETERS (SINGLE MOTOR)
is proportional to the torque T and can be expressed in
Ti
iqi = (4)
kti
where kti is the torque constant of the ith motor. By combining
(3) and (4), it can be seen that the copper loss has a second-order
polynomial relationship with the torque, as shown in
  2 
3 Ti
Pcui = Ri · i2di + . (5)
A. Control Objective and Constraints 2 kti
For a given speed and traction torque demand under normal The d-axis current idi is determined by the flux-weakening
driving conditions, the distribution of torque between the two control strategy in the high-speed region and is therefore de-
motors should aim to maximize the motors’ efficiency, which pendent on speeds and torque. The control scheme for the
can be expressed in (1), shown below, in terms of the total maximum torque per ampere in the constant-torque region and
required torque T and motor speed ω that for the maximum torque per flux in the flux-weakening
T ·ω region [23]–[25], as well as the corresponding id and iq for a
η= (1)
T · ω + Ploss given speed and torque, are described in Appendix B.
A computationally efficient iron loss model, which was
where η is the combined efficiency of the two motors, and T is validated by finite-element (FE) analysis and experiments [26],
the total required traction torque, which should be provided and is employed to quantify the iron loss in both the constant-torque
shared by the two motors. ω is the motor angular speed, which region and flux-weakening region. The iron loss Pironi of the ith
is related to the vehicle speed by the factor of wheel radius and motor are calculated according to
gear ratio. Ploss is the total loss incurred in the two motors. To
maximize system efficiency in (1), the control objective is to ah aJ bh bJ
Pironi = Vm + 2 Vm2 + Vd + 2 Vd2 (6)
determine an optimal torque split ratio that yields the minimum λ λ λ λ
total losses of the two motors Ploss subject to the constraint that where ah and aJ are the coefficients of the hysteresis and
the sum of the two motor torques is equal to the total required Joule eddy current loss associated with the main flux link-
traction torque. Hence, the control objective and constraint are age of the motor, respectively, and bh and bJ are the cor-
given in responding loss coefficients associated with the leakage flux


min Ploss = Pcu + Piron + Pf through the machine-tooth and tooth-tip regions, respectively.
(2) These coefficients can be obtained by performing FE analy-
const. T = T1 + T2
sis and computing iron losses under open-circuit and short-
where Pcu is the total copper loss of the two motors, and Piron circuit conditions [26]. For the motor in this study, they are
is the total iron loss, including eddy current loss and hysteresis given as follows: ah = 111.6072e-3, aJ = 0.5342e-3, bh =
loss. Pf is the friction (bearing) loss. T1 and T2 are the torque 60.3234e-3, and bJ = 0.1172e-3. λ is the motor back-emf
values provided by motor 1 and motor 2, respectively. It will be constant expressed as rms voltage Vrms per stator frequency f
shown in the subsequent section that, at a given speed, both the given in
copper loss Pcu and iron loss Piron are a function of the motor
torque. Therefore, the torque split ratio between the two motors Vrms
λ= . (7)
will affect the combined copper and iron losses. It is assumed f
that the friction loss Pf is independent of the torque and will
Vm are the rms voltages due to the back emf and the q-axis
not be affected by the torque distribution.
current. Vd is the rms voltage due to the d-axis current, and Vm
and Vd are given by
B. Relationship Between Motor Losses and Torque  2  2
id iq
To find the optimal torque distribution for loss minimization, Vm = λf 1− + (8)
the relationship between the main motor loss components viz. ISC ISC
iron loss and copper loss, and the motor torque at a given speed id
should be derived. The copper loss Pcui of the ith PM motor Vd = λf (9)
ISC
can be calculated by
  where ISC is the short-circuit current of the motor. For the
3
Pcui = Ri · i2di + i2qi , i = 1, 2 (3) surface-mounted PM motor, id becomes nonzero only in the
2 flux-weakening region and is dependent on speed and torque.
where idi and iqi are the d-axis and q-axis stator currents, Hence, it can be seen from (4), (6), (8), and (9) that the motor
respectively, of the ith motor in the d − q rotational frame under torque and corresponding q-axis current (iq ) will affect the iron
rotor-flux oriented control. Ri is the stator resistance of the ith loss, mainly through the change in flux due to the armature
3368 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

same as well as the characteristics of the two motors, an1 and

an2 are identical. Equation (11) can be simplified to
N
Ploss = an1 (T1n + (T − T1 )n ) . (12)
n=0

Thus, the objective becomes to find an optimal T1 to mini-

mize the total motor power losses Ploss . Since, at a given speed,
all the coefficients an1 are constant, the optimal value occurs
when the derivative of Ploss with respect to T1 is zero:
N 
d an1 (T1n + (T − T1 )n )
dPloss n=0
= =0
dT1 dT1
T
when T1 = . (13)
2
As can be seen, the total losses of the two motors are at
Fig. 3. Variation of motor losses with motor torque at speeds of 1000 and
minimum when the two motors equally share the torque under
2000 rev/min (single motor). the assumption that the two motors are identical. If the power
rating and characteristics of the two motors are different, the
optimal torque split ratio may change, depending on their
reaction field. By expressing (8) as a Taylor series with respect
specific power rating and associated motor loss model.
to iq , it can be shown that the iron loss at a given speed can
Fig. 4 shows the variations of the combined efficiency of the
be formulated as a polynomial function of torque. The param-
two motors, as defined in (1), with torque split ratio at 1000 and
eters in (6)–(9) can be found by FE analysis or experimental
4000 rev/min for different values of the total traction torque T .
tests.
It can be seen that, regardless of the values of the total torque
The motor friction loss consists of windage loss and viscous
T and motor speed, the maximum efficiency (minimum loss)
and Coulomb frictional loss of the bearings. For the motor
always occurs when the torque is equally shared by the two
under study, the windage loss and viscous damping loss are
motors (i.e., with the split ratio of 0.5).
negligible. The friction loss can, therefore, be expressed in
It can also be noted that the maximum efficiency that can
be achieved varies with torque and speed. At 1000 rev/min,
P f i = Kf i · ω m (10) for example, the maximum efficiency that results with the
total torque of 5, 25, 45, 65, and 85 N · m is 88.5%, 95.5%,
where Kf i is the friction loss coefficient of the ith motor 94.7%, 93%, and 91.2%, respectively. The efficiency is low
(0.1167 W/rad/s in the study), and ωm is the motor mechanical under both light- and heavy-load torque conditions. A similar
angular speed. trend is found at other speeds. This result is expected from the
Therefore, the total motor loss can be calculated by the sum efficiency map of a single motor shown in Fig. 5. It is evident
of the copper loss, iron loss, and friction loss. From these losses, that, at a given speed, the motor efficiency is relatively low
the motor efficiency can be obtained at any given torque and when the load torque is either high or low.
speed within the operating range. Fig. 3 shows the variation of Therefore, if the total required traction torque is high (or in
the total losses of a single motor at 1000 and 2000 rev/min with the high-torque region shown in Fig. 5), it is always desirable to
motor torque. As indicated in (5) and (6), for a given speed, the share the torque between the two motors with 50% split ratio,
motor loss increases with torque in a form of the polynomial because the efficiency will be improved by lowering the torque.
function. This also agrees with the fact that the peak torque required by
It follows that the combined loss of motor 1 and motor 2 can the EV should be shared and provided by the two motors to
be expressed by avoid overheating of a single motor. When the traction torque
is low (i.e., in the low-torque region), although it is possible that
N N
the torque is provided by one motor that operates in relatively
Ploss = an1 T1n + an2 T2n high efficiency region, the presence of the no-load loss, i.e., the
n=0 n=0
iron loss and friction loss, as well as the copper loss due to the
N N need for flux weakening in the high-speed region of the second
= an1 T1n + an2 (T − T1 )n (11) motor, offsets any gain, and consequently, the combined motor
n=0 n=0 efficiency is lower than that of equal torque sharing.
where an1 and an2 are the coefficients associated with the nth-
III. E NERGY D ISTRIBUTION OVER THE
order term of the polynomials of motor 1 and motor 2 losses,
N EW E UROPEAN D RIVING C YCLE
respectively. They are functions of speeds. N is the number of
polynomial terms used to represent the loss model in a Taylor Since the efficiency of the motor varies with torque
series. If the gear ratios of the front and rear differentials are the and speed, it is important to understand how the energy
YUAN AND WANG: TORQUE DISTRIBUTION STRATEGY FOR FRONT- AND REAR-WHEEL-DRIVEN EV 3369

Fig. 5. Motor efficiency as a function of torque and speed (single motor).

Fig. 6. Speed, torque, and power over the NEDC.

Fig. 4. Variation of motor efficiency with torque split ratio. (a) 1000 rev/min.
(b) 4000 rev/min.

consumption of a driving cycle is distributed within the

torque–speed region of the traction motors. Without loss of
generality, this paper investigates the energy consumption of
the vehicle over the NEDC by using the vehicle model given
in Appendix A. Fig. 6 shows the speed and resulting torque
and power in absolute values of the vehicle contributed by
one motor over an NEDC, assuming that the required traction
torque and power is equally shared between the front and rear
motors.
For a given time instant, t = ti , the corresponding speed,
torque, power, and energy consumption are ωm (ti ), Tm (ti ),
Pm (ti ), and ∆ti Pm (ti ), respectively, where ∆ti is the time
interval over which ωm (ti ) and Tm (ti ) are assumed to be
constant. Thus, the energy consumption can be calculated at any Fig. 7. Energy consumption distribution over the NEDC.
time instant over the NEDC and can also be plotted as a function
of speed and torque, as shown in Fig. 7. It can be seen that the Fig. 6. The motor efficiency over these points is therefore of
energy is distributed over the torque and speed range. However, great importance. The distribution of the energy consumption
there are six points at which the energy consumption is much is summarized in Table III. It can be seen that the six significant
higher than others. These points correspond to the constant- points, together with other points with torque below 15 N · m
speed operations of the cycle, in which the time duration is (the low-torque region), account for 89.55% of the total energy
much longer while the torque is relatively low, as shown in consumption.
3370 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

TABLE III
DISTRIBUTION OF ENERGY CONSUMPTION OVER THE NEDC CYCLE

It can be seen from the foregoing analysis that the efficiency

in the low-torque region is very important because a large
portion of the energy consumed over the NEDC is in the
low-torque region. Therefore, a control scheme that improves
efficiency in the low-torque region is of great importance.

IV. C ONTROL S TRATEGY IN THE L OW-T ORQUE R EGION

As has been previously illustrated, in the high-torque region,
the torque should be equally shared between the two motors to
achieve the maximum efficiency (or minimum losses). How-
ever, in the low-torque region, it is possible that the torque
required by the vehicle can be solely provided by one motor
that operates in its middle-torque range and hence exhibits high
efficiency. The combined motor efficiency will be improved if
the loss of the second motor is very low or can be eliminated.
In the case of PM motors, the presence of the PM field not
only causes significant iron loss but requires a flux-weakening
current as well, i.e., a negative d-axis current, at high speed
to prevent overvoltage and uncontrollable rectifying operation. Fig. 8. Torque distribution strategy with and without a clutch. (a) Idling loss
This current will incur additional copper loss, even if the motor cannot be switched off. (Point B is preferred.) (b) Idling loss can be switched
off by a clutch in the high-torque region. (Point B is preferred.) (c) Idling loss
output torque is zero. Thus, the relatively high idling loss of the can be switched off by a clutch in the low-torque region. (Point A is preferred.)
PM motor makes it impossible to improve the efficiency in the
low-torque region by electrical means only. with no mechanical clutch. In this case, the optimal torque split
There are two possible solutions to the aforementioned prob- is at point B, with the total torque being equally shared (T/2).
lem: One is to add a clutch between one of the motors and In the second scenario, as shown in Fig. 8(b), it is assumed that
the differential/gear so that the motor can be detached from the required traction torque is within the peak torque capability
the wheels in the low-torque region. This way, one motor of one motor and the idling losses of motor 2 can be eliminated
can operate with higher efficiency, whereas the other motor is by using a clutch. If the total torque T is relatively high, the loss
mechanically detached, without generating any loss. The other associated with one-motor operation to provide the full torque,
possibility is to use one induction or synchronous reluctance as illustrated by point A in Fig. 8(b), is still higher than that
motor to replace one of the PM motors. The idling loss of the of the two motors equally sharing the torque at point B. Conse-
second motor will be much lower due to the absence of the PM quently, point B should still be preferred. It should also be noted
field when it is not excited. With this motor combination, only that the loss at point A increases with torque. Thus, point B
the PM motor is operational in the low-torque region to improve is preferred at high-torque load. On the other hand, when the
efficiency. total required traction torque is low, as shown in Fig. 8(c), the
Fig. 8 shows how to distribute the torque according to the losses associated with one-motor operation at point A becomes
torque demand and whether the idling loss of one motor can less than that at point B. One-motor operation will result in less
be switched off or not. In the following analysis, the “idling loss and, hence, better efficiency.
loss” refers to the combined losses of the no-load iron loss, From the aforementioned analysis, the combined motor effi-
the copper loss due to flux weakening when iq = 0, and the ciency in the low-torque region can be improved by employing
friction loss of the PM motor. In the first scenario, as shown in a clutch. To implement the torque distribution strategies, it is
Fig. 8(a), the idling loss of the second motor cannot be switched necessary to determine the torque boundary between two-motor
off, which implies that two identical PM motors are employed operation with torque equal sharing and one-motor operation
YUAN AND WANG: TORQUE DISTRIBUTION STRATEGY FOR FRONT- AND REAR-WHEEL-DRIVEN EV 3371

Fig. 9. Flowchart of optimal torque distribution.

Fig. 11. Test setup. (a) Motor test rig. (b) Motor stator. (c) Inverter.

Fig. 10. Experimental setup.

with the second motor being clutched off. This boundary can
be determined offline based on the motor efficiency map or Fig. 12. Functional block diagram for quantifying motor losses and efficiency
calculated online. The efficiency map in Fig. 5 provides an over the NEDC.
initial torque boundary Tth of 15 N · m between the low-torque
and high-torque regions. When the total required traction torque and the inverter. A Lithium-ion battery is used to supply the
is larger than 2 × Tth , it should be equally shared by the two energy to the inverter, which drives the PM motor in speed
motors to minimize the losses. When the total torque is below control mode, whereas the dynamometer operates in torque
this threshold torque, then the online loss calculation is carried control mode. A power analyzer is used to measure the input
out according to (5)–(9) to compare losses at point A for power to the motor, and the motor output power is obtained
one-motor operation and at point B for two-motor operation. from the speed and torque signals of the torque transducer.
The operation with lower loss will be selected. Fig. 9 shows Thus, the motor losses or the motor efficiency at a given torque
the flowchart of the online optimization scheme for torque and speed can be directly measured. The test was carried out
distribution. in a speed range of 10–4500 rev/min, and for each speed, the
It should be noted that the preceding strategy does not require torque was varied from 0 to the maximum in a 5-N · m step.
an efficiency map being stored in the controller and results in This way, a measured efficiency map similar to that shown in
the torque contributed by one motor being only less than or Fig. 5 can be obtained.
equal to 30 N · m, which is below the continuous torque rating A MATLAB program has been written and used to quantify
of the motor of 35 N · m. The application of the proposed torque the overall motor losses and efficiency over the NEDC based
distribution strategy will not give rise to any risk of overheating. on the vehicle data and the experimental measurements. Fig. 12
shows the functional block diagram of the program. The re-
quired traction torque and motor speed at a given time instant
V. E XPERIMENTAL T EST AND R ESULTS
is determined according to the NEDC and vehicle data. This
An experimental test is carried out to validate the proposed torque is then used as the input of the torque distribution strat-
torque distribution strategy for motor loss minimization over egy. Then, the proposed optimal torque distribution strategy
the NEDC. Fig. 10 shows the schematic of the experimental determines the split of the total torque among the two motors
setup, and Fig. 11(a) shows the test rig, including the PM motor based on the motor speed and the measured efficiency map (the
and the dynamometer. Fig. 11(b) and (c) shows the motor stator corresponding losses).
3372 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

TABLE IV
ENERGY-EFFICIENCY COMPARISON OVER THE NEDC CYCLE

TABLE V
COMPARISON OF BATTERY COST AND WEIGHT

ciency, assuming that the two motors equally share the torque.
Fig. 13(b) compares the efficiency that results in the optimal
torque distribution to that of torque equal sharing. It can be
seen that the motor efficiency in the low-torque region has been
improved, albeit in the high-torque region, the efficiencies of
the two torque distribution schemes are the same. Fig. 13(c)
shows the total motor power loss variations over the NEDC
of the two torque distribution strategies. It is evident that, by
using the proposed torque distribution scheme, the motor losses
can be reduced at the expense of an additional clutch being
required.
Table IV summaries the total energy saving by using the
optimal torque distribution. The energy is obtained by inte-
grating the power over the NEDC, assuming that the energy
during braking can fully recuperate. It can be seen that the
energy efficiency has been improved by around 4% compared
with the torque equal-sharing scheme. This gain in energy effi-
ciency is significant and illustrates the importance of improving
efficiency in the low-torque region. Consequently, the driving
range can be extended by using the proposed method with the
same battery capacity.
It is important to appreciate the significance of the 4%
energy saving and its impact on the power train cost and
size. With a conservative assumption, for 1% reduction in the
motor efficiency, there will be a total of 1.33% reduction in
the complete power train efficiency due to the losses in the
battery and inverter. To cover the 200-km range, a 14-kWh
battery is required for the vehicle when the torque is equally
shared. Table V compares the cost and weight of the two
torque distribution strategies with today’s representative price
and weight for batteries.

Fig. 13. Motor losses and efficiency over the NEDC. (a) Total required torque
and motor efficiency with the torque being equally shared between two motors. VI. C ONCLUSION
(b) Motor efficiency comparison: equal torque distribution versus optimal
torque distribution. (c) Motor power loss comparison: equal torque distribution This paper has presented an optimized torque distribution
versus optimal torque distribution. strategy for maximizing the overall motor efficiency for a front-
and rear-wheel-driven EV over the NEDC. It has been shown
Fig. 13 shows the results of the motor losses and efficiency that the total torque required by the vehicle should be equally
over the NEDC, where Fig. 13(a) shows the total required shared between the two PM motors to minimize the losses if
torque by the two motors and the corresponding motor effi- the two motors are identical. By analyzing the distribution of
YUAN AND WANG: TORQUE DISTRIBUTION STRATEGY FOR FRONT- AND REAR-WHEEL-DRIVEN EV 3373

the vehicle energy consumption over the NEDC, it has been The corresponding vehicle model parameters used in the
identified that improving efficiency in the low-torque region is study are listed in Table I.
of particular importance. Thus, if a clutch or a motor with very
low idling loss when not excited, such as IM or synchronous
reluctance motor, is employed, the efficiency in the low-torque A PPENDIX B
region can be improved by operating one PM motor with the
Here, we calculate of the d-axis and q-axis currents (id , iq )
second motor clutched off and not electrically excited. An
for a surface-mounted PM motor at a given speed ωm and
optimal torque distribution strategy to realize this has been
torque Td .
proposed and experimentally tested. It has been shown that,
The motor and drive parameters are defined as follows:
compared with the equal torque sharing, the motor losses have
been reduced by 27%, and the energy efficiency has been Ld = Lq d-axis and q-axis inductance;
improved by 4% over the NEDC. Vmax maximum voltage amplitude;
With the front- and rear-distributed drive configuration, ψm flux linkage due to PMs;
additional freedom has been provided for further efficiency Im maximum motor (inverter) current;
enhancement by optimal tuning of the efficiency map, with P number of pole pairs;
one motor having high efficiency in the low-speed range and ωe = pωm motor electrical angular speed;
the other having high efficiency in the high-speed range, for KT = (3/2)pψm torque constant.
example, so that the high-efficiency operating range can be
The d-axis and q-axis currents are determined against the
expanded with intelligent torque distribution strategies. This
electrical angular speed ωe and torque Td as follows:
will be the subject of future research.
1) Constant torque region (ωe < ωb = (Vmax /
(Ld Im )2 + ψm2 )):
A PPENDIX A
E LECTRIC V EHICLE A ERODYNAMICS AND

id = 0
E LECTROMECHANICAL M ODEL iq = KTd
. (19)
T
Three types of resistive forces are considered for the model
of the vehicle: rolling resistance, air drag, and grade resistance. 2) Flux-weakening region I:
Rolling resistance force can be expressed as
 
Froll = mc · g · froll (14) Vmax
ωb < ωe < ω2 = .
(Ld Im )2 − ψm
2
where mc is the curb weight of the vehicle, g is the gravitational
acceleration, and froll is the rolling resistance coefficient. ω2 will not exist if ψm ≥ Ld · Im , i.e.,
The air drag force is given by

1  −ψm + ( Vmax
ωe )
2
−(Ld iq )2
Fair = · cw · A · ρair · v 2 (15) id = Ld (20)
2 i = Td
q KT
where cw is the aerodynamic drag coefficient, A is the frontal 
cross-sectional area, ρair is the air density, and v is the vehicle   2 2
  2 ]
 Vωmax − [(Ld Im )2 + ψm 
velocity. 
Tmax (ωe ) = KT  2 − e

The grade resistance is formulated in Im  

.
 2Ld ψm 
Fg = mc · g · sin α (16)
(21)
where α is the slope angle.
Then, the EV electromechanical dynamics can be expressed If Td > Tmax (ωe ), then Td = Tmax (ωe ).
as 3) Flux-weakening region II ωe > ω2 :
dv 
Ft − Froll − Fair − Fg = mc (17)  −ψm + ( Vmax
ωe )
2
−(Ld iq )2
dt id = Ld (22)
where Ft is the traction force of the vehicle, and the total i = Td
.
q KT
traction torque of the two motors would be
rFt η −l If (iq > (Vmax /ωe Ld )), then iq = (Vmax /ωe Ld ).
Te =
Gr
l = sign(Ft v) (18) ACKNOWLEDGMENT
where r is the wheel radius, Gr is the gear ratio, and η is the The authors would like to thank the P-MOB project partners
transmission efficiency for permission to publish this paper.
3374 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

R EFERENCES [21] F. Mapelli, D. Tarsitano, and M. Mauri, “Plug-in hybrid electric vehicle:
Modeling, prototype realization and inverter losses reduction analysis,”
[1] C. C. Chan, “An overview of electric vehicle technology,” Proc. IEEE, IEEE Trans. Ind. Electron., vol. 57, no. 2, pp. 598–607, Feb. 2010.
vol. 81, no. 9, pp. 1202–1213, Sep. 1993. [22] J. Wang, Z. Xia, and D. Howe, “Three-phase modular permanent magnet
[2] C. C. Chan, “The state of the art of electric and hybrid vehicles,” Proc. brushless machine for torque boosting on a downsized ICE vehicle,” IEEE
IEEE, vol. 90, no. 2, pp. 247–275, Feb. 2002. Trans. Veh. Technol., vol. 54, no. 3, pp. 809–816, May 2005.
[3] A. Emadi, Y. Lee, and K. Rajashekara, “Power electronics and motor [23] D. Lu and N. C. Kar, “A review of flux-weakening control in per-
drives in electric, hybrid electric and plug-in hybrid electric vehicles,” manent magnet synchronous machines,” in Proc. IEEE VPPC Conf.,
IEEE Trans. Ind. Electron., vol. 55, no. 6, pp. 2237–2245, Jun. 2008. Sep. 2010, pp. 1–6.
[4] H. Kahlen and G. Maggetto, “Electric and hybrid vehicles,” in Proc. EPE [24] S. Morimoto, Y. Takeda, and T. Hirasa, “Expansion of operating limits
Conf., Sep. 1997, vol. 1, pp. 1030–1054. for permanent magnet motor by current vector control considering in-
[5] J. M. Miller, A. Emadi, A. V. Rajarathnam, and M. Ehsani, “Current status verter capacity,” IEEE Trans. Ind. Appl., vol. 26, no. 5, pp. 866–871,
and future trends in more electric car power systems,” in Proc. IEEE Veh. Sep./Oct. 1990.
Technol. Conf., May 1999, pp. 1380–1384. [25] M. Tursini, E. Chiricozzi, and R. Petrella, “Feed forward flux-weakening
[6] D. Wu and S. S. Williamson, “A novel design and feasibility analysis of control of surface-mounted permanent-magnet synchronous motors ac-
a fuel cell plug-in hybrid electric vehicle,” in Proc. IEEE VPPC Conf., counting for resistive voltage drop,” IEEE Trans. Ind. Electron., vol. 57,
Sep. 2008, pp. 1–5. no. 1, pp. 440–448, Jan. 2010.
[7] S. Stockar, V. Marano, M. Canova, G. Rizzoni, and L. Guzzella, “Energy- [26] P. H. Mellor, R. Wrobel, and D. Holliday, “A computationally efficient
optimal control of plug-in hybrid electric vehicles for real world driv- iron loss model for brushless AC machines that caters for rated flux
ing cycles,” IEEE Trans. Veh. Technol., vol. 60, no. 7, pp. 2949–2962, and field weakened operation,” in Proc. IEEE IEMDC Conf., May 2009,
Sep. 2011. pp. 490–494.
[8] S. Barsali, C. Miulli, and A. Possenti, “A control strategy to minimize
fuel consumption of series hybrid electric vehicles,” IEEE Trans. Energy
Convers., vol. 19, no. 1, pp. 187–195, Mar. 2004.
[9] S. M. Lukic and A. Emadi, “Effects of drivetrain hybridization on fuel Xibo Yuan (S’09–M’11) received the B.S. degree
economy and dynamic performance of parallel hybrid electric vehicles,” from China University of Mining and Technology,
IEEE Trans. Veh. Technol., vol. 53, no. 2, pp. 385–389, Mar. 2004. Xuzhou, China, and the Ph.D. degree from Tsinghua
[10] J. Wang, B. Taylor, Z. Sun, and D. Howe, “Experimental characterization University, Beijing, China, in 2005 and 2010, respec-
of a supercapacitor based electrical torque boost system for down-sized tively, both in electrical engineering.
ICE vehicles,” IEEE Trans. Veh. Technol., vol. 56, no. 6, pp. 3674–3681, From 2007 to 2008, he was a Visiting Scholar
Nov. 2007. with the Center for Power Electronics Systems,
[11] B. Kramer, S. Chakraborty, and B. Kroposki, “A review of plug-in ve- Virginia Polytechnic Institute and State University,
hicles and vehicle to grid capability,” in Proc. IEEE IECON Conf., Blacksburg. During 2010 and 2011, he was a Post-
Nov. 2008, pp. 2278–2283. doctoral Research Associate with the Electrical Ma-
[12] M. Terashima, T. Ashikaga, and T. Mizuno, “Novel motors and controllers chines and Drives Research Group, Department of
for high performance electric vehicle with four in-wheel motors,” IEEE Electronic and Electrical Engineering, University of Sheffield, Sheffield, U.K.
Trans. Ind. Electron., vol. 44, no. 1, pp. 28–38, Feb. 1997. Since 2011, he has been a Lecturer with the Electrical Energy Management
[13] N. Mutoh, Y. Takahashi, and Y. Tomita, “Failsafe drive performance Group, Department of Electrical and Electronic Engineering, University of
of FRID electric vehicles with the structure driven by the front and Bristol, Bristol, U.K. His research interests include power electronics, wind
rear wheels independently,” IEEE Trans. Ind. Electron., vol. 55, no. 6, power generation, control of high-power multilevel converters, sensorless
pp. 2306–2315, Jun. 2008. drives for induction motors and permanent-magnet motors, control of electric
[14] Y. Hori, “Future vehicle driven by electricity and control-research on vehicles, and electric aircraft technologies.
four wheel motored UOT electric March II,” IEEE Trans. Ind. Electron.,
vol. 51, no. 5, pp. 954–962, Oct. 2004.
[15] A. Khaligh and Z. Li, “Battery, ultracapacitor, fuel cell, and hybrid energy
storage systems for electric, hybrid electric, fuel cell, and plug-in hybrid Jiabin Wang (SM’03) received the B.Eng. and
electric vehicles: State of the art,” IEEE Trans. Veh. Technol., vol. 59, M.Eng. degrees from Jiangsu University of Science
no. 6, pp. 2806–2814, Jul. 2010. and Technology, Zhenjiang, China, in 1982 and
[16] J. Cao and A. Emadi, “A new battery/ultracapacitor hybrid energy storage 1986, respectively, and the Ph.D. degree from the
systems for electric, hybrid and plug-in hybrid electric vehicles,” IEEE University of East London, London, U.K., in 1996,
Trans. Power Electron., vol. 27, no. 1, pp. 122–132, Jan. 2012. all in electrical and electronic engineering.
[17] M. Felden, P. Butterling, and P. Jeck, “Electric vehicle drive trains: From He is currently a Professor of electrical engi-
the specification sheet to the drive train concept,” in Proc. EPE-PEMC neering with the Electrical Machines and Drives
Conf., Sep. 2010, pp. S11-9–S11-16. Research Group, Department of Electronic and
[18] K. T. Chau, C. C. Chan, and C. Liu, “Overview of permanent-magnet Electrical Engineering, University of Sheffield,
brushless drives for electric and hybrid electric vehicles,” IEEE Trans. Sheffield, U.K. From 1986 to 1991, he was with
Ind. Electron., vol. 55, no. 6, pp. 2246–2257, Jun. 2008. the Department of Electrical Engineering, Jiangsu University of Science and
[19] J. T. Chen, Z. Q. Zhu, S. Iwasaki, and R. Deodhar, “A novel hybrid excited Technology, where he was appointed Lecturer in 1987 and Associated Professor
switched-flux brushless AC machine for EV/HEV applications,” IEEE in 1990. He was a Postdoctoral Research Associate with the University of
Trans. Veh. Technol., vol. 60, no. 4, pp. 1365–1373, May 2011. Sheffield from 1996 to 1997 and a Senior Lecturer with the University of
[20] P. Morrison, A. Binder, and B. Funieru, “Drive train design for medium- East London from 1998 to 2001. His research interests include motion control
sized zero emission electric vehicles,” in Proc. EPE Conf., Sep. 2009, and electromechanical energy conversion to electric drives for applications in
pp. 1–10. automotive, renewable-energy, household appliances, and aerospace sectors.