International Journal of Automotive Technology, Vol. 14, No. 5, pp. 763−772 (2013) DOI 10.1007/s12239−013−0084−1
Copyright © 2013 KSAE/ 073−12 pISSN 1229−9138/ eISSN 1976−3832
ENERGY EFFICIENCY OPTIMIZATION OF ELECTRIC VEHICLE DRIVEN BY IN-WHEEL MOTORS J. GU, M. OUYANG*, D. LU, J. LI and L. LU State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China (Received 9 January 2012; Revised 10 December 2012; Accepted 23 January 2013) 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. KEY WORDS : Electric vehicle, Energy efficiency optimization, In-wheel motor, Permanent magnet synchronous motor, Motor efficiency model
Pout Pin Ploss Ploss,t Ploss,f Ploss,r Pl PCu PFe Pm Ps Pinv PC PC,MOS PC,D PSW Ra Rc Rds Rak Rhi Rgate
NOMENCLATURE adr, bdr, cdr : coefficient for the equation of motor power loss in driving condition arb, brb, crb : coefficient for the equation of motor power loss in braking condition : MOSFET input capacitance (F) Ciss : MOSFET reverse-transfer capacitance (F) Crss eSW : energy loss during one switching (J) : d-axis armature current (A) id : q-axis armature current (A) iq : d-axis copper loss current (A) iod : q-axis copper loss current (A) ioq : d-axis iron loss current (A) icd : q-axis iron loss current (A) icq : phase current amplitude (A) im : average gate current during the second phase of ig2 MOSFET switching on (A) : average gate current during the third phase of ig3 MOSFET switching on (A) J : cost function of energy efficiency optimization k1, k2 : coefficient for the expression of inverter loss L : motor inductance (H) : d-axis inductance (H) Ld : q-axis inductance (H) Lq : rotating speed of the ith motor (rpm) ni : number of pole pairs np
Rgi t2 t3 tc
*Corresponding author. e-mail:
[email protected] 763
: output power (W) : input power (W) : loss power (W) : total loss power of four motors (W) : loss power of the front motor (W) : loss power of the rear motor (W) : power loss without copper loss (W) : copper loss (W) : iron loss (W) : friction loss (W) : stray loss (W) : inverter loss (W) : inverter conduction loss (W) : MOSFET conduction loss (W) : diode conduction loss (W) : inverter switching loss (W) : armature resistance (Ω) : iron loss equivalent resistance (Ω) : MOSFET resistance during conduction (Ω) : diode resistance during conduction (Ω) : MOSFET driver resistance (Ω) : resistance between MOSFET driver and MOSFET gate (Ω) : MOSFET gate resistance (Ω) : time duration of the second phase of MOSFET switching (s) : time duration of the third phase of MOSFET switching (s) : PWM cycle time (s)
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td T Te Ti Treq Tf Tr Tm Tmin Tmax Ti0 Tdrag ud uq uth ugs,mil udrv ubat uds,off uds uak uf η ηi ηf ηr ηdr ηrb ω ωc Ψd Ψq Ψf
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: dead time (s) : motor output torque (Nm) : motor electromagnetic torque (Nm) : output torque of the ith motor (Nm) : total torque requirement (Nm) : output torque of the front motor (Nm) : output torque of the rear motor (Nm) : friction torque (Nm) : minimum torque output (Nm) : maximum torque output (Nm) : no-load iron loss torque (Nm) : dynamometer dragging torque (Nm) : d-axis terminal voltage (V) : q-axis terminal voltage (V) : gate threshold voltage (V) : gate miller plateau voltage (V) : MOSFET driving circuit voltage (V) : battery voltage (V) : voltage across the drain and source when MOSFET is off (V) : MOSFET voltage drop during conduction (V) : diode voltage drop during conduction (V) : diode voltage drop at zero current (V) : energy efficiency of the motor (%) : energy efficiency of the ith motor (%) : energy efficiency of the front motor (%) : energy efficiency of the rear motor (%) : motor energy efficiency in driving condition (%) : motor energy efficiency in braking condition (%) : motor electrical angular velocity (rad/s) : motor mechanical rotating speed (rad/s) : d-axis flux-linkage (Wb) : q-axis flux-linkage (Wb) : permanent magnet flux-linkage (Wb)
1. INTRODUCTION With the challenges of energy and environment crisis, newenergy vehicles have been the focus of the automotive industry. Battery electric vehicles have been developed intensively due to the advantages of high efficiency and zero emission. However, they are still not competitive enough compared with conventional vehicles limited by the low energy density and the high cost of power batteries. Generally, the required battery capacity is proportional to the vehicle mass in order to maintain the same driving range. So micro electric vehicle require less batteries because of their smaller weight and the cost increase is more acceptable compared to larger vehicles. As a result, micro electric vehicles should be given priority in research and development as the first step into the electric driving era. Electric vehicles could be driven by one central motor or distributed motors in wheels. Compared to the conventional central motor driving, transmission, differential and driving axle could be eliminated and the mechanical loss could be reduced a lot for in-wheel motor driving. Vehicle stability
Figure 1. “Micro-Harry” EV developed by Tsinghua University. Table 1. Specifications of “Micro-Harry” EV. Parameter name
Value
Curb weight (kg)
620
Max. speed (km/h)
50
Wheel radius (m)
0.25
Motor continuous/peak power (W)
1000 / 2000
Max. motor speed (rpm)
600
Motor pole pairs
23
Battery voltage (V)
48
Battery capacity (Ah)
150
Range per charge (km)
80
could be enhanced thanks to the rapid and precise independent control of the output torque of each wheel (Hori, 2004; Sakai et al., 1999). Besides, it also brings much flexibility to the vehicle design. So it’s considered to be the future for vehicle driving. On the other hand, additional costs due to more motors and power electronics, increased unsprung mass and complexity of control strategy are still the drawbacks of in-wheel motor driving. “Micro-Harry” is an experimental EV developed by Tsinghua University, as shown in Figure 1. The EV is driven by four in-wheel motors. Permanent magnetic synchronous motor (PMSM) is selected to be the driving motor because of its high efficiency and high power density. The specifications are listed in Table 1. Energy efficiency is of high importance especially for battery electric vehicles because of the limited energy onboard. Much research could be referenced in literature to improve the efficiency from aspects of motor design (Fang et al., 2008; Cvetkovski and Petkovska, 2008), motor control algorithm (Morimoto et al., 1994; Cavallaro et al., 2005) and power electronics (Wai et al., 2005; Lai et al., 1995). As we know, the efficiency of PMSM is low at the low-torque and low-speed range. For electric vehicles driven by four in-wheel motors, additional control flexibility seems to be a chance for further efficiency improvement by allocating different torques among four motors (Wang et al., 2011; Yu et al., 2005; Wang et al., 2010). This efficiency optimization problem could be
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formulated as in Equation (1): ⎧ i T i⎞ ⎪ min ⎛⎝ ∑ n-------⎠ η i ⎪ i = 1∼4 J=⎨ ⎞ ⎪ max ⎛ ⎝ ∑ niTi ηi⎠ ⎪ i = 1∼4 ⎩
in driving mode
(1) in braking mode
Figure 2. PMSM model with iron loss.
Subject to ⎧ ⎪ ∑ Ti = Treq ⎨i = 1 ∼ 4 ⎪T ≤ T ≤ T ⎩ min i max
2. MOTOR EFFICIENCY MODEL (2)
Only the longitudinal vehicle dynamics is considered, so there is no speed difference between the left and the right wheels. The motor speeds are determined by the vehicle speed, and all the motor speeds are the same during normal driving when wheel slips are small. Therefore, the formulation of the control problem could be further simplified as Equation (3): ⎧ Tr⎞ Tf ---⎪ min ⎛ ---in driving mode ⎝ ηf + ηr⎠ J=⎨ ⎪ max ( T η + T η ) in braking mode f f r r ⎩
(3)
Subject to ⎧ Tf + Tr = Treq ⁄ 2 ⎨ Tmin ≤ Tf ≤ Tmax ⎩ Tmin ≤ Tr ≤ Tmax
(4)
The energy optimization algorithm in literature is basically developed by looking up the motor efficiency map. And the motor efficiency map shows that the efficiency is low at the low torque region, so most or all of the torque requirement is allocated to the front (or rear) two wheels when the total torque requirement is low (Wang et al., 2011; Yu et al., 2005; Wang et al., 2010) in order to improve the overall energy efficiency. When the total torque is allocated to the front (or rear) wheels, the vehicle is actually working in two-wheel-driving (2WD) mode. However, to the best knowledge of the authors, all these studies have only been verified in simulation and no experiment results have been presented. When we tried to implement this efficiency optimization algorithm to “Micro-Harry”, although the simulation gave a positive result, no efficiency improvement could be observed in road vehicle tests. It seems that the motor efficiency map is misleading. So this paper tries to find an explanation based on the efficiency model of PMSM and its inverter. This paper is organized as follows. Firstly, a comprehensive efficiency model of the motor including the motor inverter is explained in details, based on which the problem of the energy efficiency optimization is analyzed. The road test results are presented and the conclusion is drawn finally.
The efficiency is defined as the ratio of the output power to the input power and the difference between the input power and the output power is the power loss, which consists of copper loss, iron loss, inverter loss, friction loss and stray loss. Normally, stray loss could be neglected. Pout- P in −P loss = -----------------η = ------Pin Pin
(5)
Ploss = PCu + PFe + Pinv + Pm + Ps
(6)
2.1. Copper Loss and Iron Loss An equivalent circuit model is used to calculate the copper loss and iron loss (Morimoto et al., 1994; Xu, 2003), as shown in Figure 2. The selected motor is an outer-rotor type surface mounted permanent magnet synchronous motor (SPMSM). Because of the non-saliency characteristics of the motor, Ld=Lq=L, and this equivalent circuit model could be described with the Equations (7) to (10). ⎧ R-a⎞ ⎪ ud = Raiod− ⎛ 1 + ---⎝ Rc⎠ ωLioq ⎪ ⎨ ⎪u = R i + ⎛1 + R -----a⎞ a oq ⎪ q ⎝ Rc⎠ ( ωψf + ωLioq) ⎩
(7)
⎧ id = iod + icd ⎨ ⎩ iq = ioq + icq
(8)
⎧ i = −ωLi ---------------oq⎪ cd Rc ⎨ ω ( ψ + Lioq-) f ⎪ icq = -------------------------⎩ Rc
(9)
Te = npψf ioq
(10)
The relationship between id, iq and iod, ioq is expressed in Equation (11): ⎧ ψ ωL- ⎛ ---1 - ⎛ -----i + -f⎞⎞ ⎪ ioq = -----------------2 2 ⎝ iq − Rc ⎝ d L ⎠ ⎠ ω L ⎪ 1 + ---------⎪ R2c ⎨ ωψ-f⎞ ⎞ 1 - ⎛ ωL ⎪ i = ------------------------ ⎛ iq− -------2 2 ⎝ iq + ⎪ od Rc ⎝ Rc ⎠ ⎠ ω L ⎪ 1 + ---------2 Rc ⎩
(11)
Normally, Rc>>ωL (Urasaki et al., 2000), so Equation (11) could be simplified as Equation (12):
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⎧ ψ ωL- ⎛ ---⎪ ioq = iq− -----i + -f⎞ Rc ⎝ d L ⎠ ⎪ ⎨ ωψ-f⎞ ⎪ i = i + ωL - ⎛ i − -------⎪ od d -----Rc ⎝ q Rc ⎠ ⎩
Figure 3. (12)
The control strategy of “maximum torque per ampere” is implemented with id set to be zero, so (13)
iod + icd = 0
Copper loss and iron loss could be derived as Equations (14) and (15): ωψ PCu = Ra( i2d + i2q) = Ra⎛⎝ ioq + ---------f⎞⎠ Rc 2 2 2ψf ω ψ2 ω L 2 2 2 PFe = Rc ( id + iq ) = ----------- ⎛⎝ ioq + -----------ioq + -----2f ⎞⎠ Rc Rc L 2
(14) (15)
The armature resistance Ra and inductance L are measured using a high-precision AC impedance meter. According to the PMSM model, the motor electromagnetic torque Te is linear with iq and the coefficient is npψf, so ψf could be derived using curve fitting method. The measurement method for iron loss equivalent resistance Rc is proposed by Dubhashi and Pelly (1989) as expressed in Equation (16): 1 P1 = ----- ω 2( ψ2d + ψ2q ) + Pm + Ps Rc
(16)
When the motor is running at a constant motor torque and speed, Pm and Ps are also constant and Pl is linear with ω 2( ψ2d + ψ2q ) . So Rc could be measured as follows: Set the motor to run at a fixed torque and a fixed speed by giving a constant target iq, then change id and measure the motor loss power. Pl is calculated by subtracting the motor loss power by the copper loss. Then Rc could be derived using curving fitting method. Rc is constant with the motor torque, but increases with the motor speed (Urasaki et al., 2000). The relationship between Rc and the motor speed n is shown in
2.2. Inverter Loss MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) is selected to be the power device for the motor inverter due to the fact that MOSFET is more favorable for low voltage and low power applications (Dubhashi and Pelly, 1989). The inverter loss consists of switching loss and conduction loss. In FOC (Field Oriented Control), SVPWM (Space Vector Pulse Width Modulation) is employed to generate the rotating voltage vector. High-side and low-side MOSFETs conduct complementarily. A dead time is inserted between the switching transitions of high-side and low-side MOSFETs to avoid shoot-through. 2.2.1. Conduction loss According to Lai et al. (1995), the conduction characteristics of the MOSFET and the free-wheeling diode could be expressed as Equations (17) and (18): uds = iRds
(17)
uak = uf + iRak
(18)
The inverter conduction loss consists of MOSFET conduction loss and free-wheeling diode conduction loss. Due to the bi-directional current conducting capability of MOSFET, the current only flows through the free-wheeling diode during the dead time. The conduction losses of MOSFET and the free-wheeling diode could be expressed as Equations (19) and (20): 2t 3 PC, MOS = --- i2m Rds ⎛⎝ 1− ------d⎞⎠ 2 tc
(19)
2t 6 3 PC, D = ⎛⎝ --- uf im + --- i2m Rak⎞⎠ ------d tc π 2
(20)
So the total conduction loss of the inverter could be derived as Equation (21): PC = PC, MOS + PC, D 2t 2t 12t 3 = ---------d uf im + --- ⎛⎝ Rds ⎛⎝ 1− ------d⎞⎠ + Rak ------d⎞⎠ i2m 2 πtc tc tc
(21)
Equation (21) could also be rewritten as Equation (22): 4 6t 2t 2t PC = -------------d uf iq + ⎛⎝ Rds ⎛⎝ 1− ------d⎞⎠ + Rak ------d⎞⎠ i2q πtc tc tc
Figure 3. Iron loss equivalent resistance changes with motor speed.
(22)
2.2.2. Switching loss The MOSFET switching model could be found in Balogh (2001). As shown in Figure 4, the switching process could be divided into four phases. Switching loss is generated during the second and the third phases. The calculation of switching ON loss is illustrated in Equations (23) to (27). And the calculation of switching OFF loss is just similar as
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Figure 5. Motor efficiency experiment setup. Where (31)
2t 2t k2 = Rds ⎛⎝1− ------d⎞⎠ + Rak ------d tc tc
(32)
2.3. Friction Loss The setup of experiment for motor efficiency testing is shown in Figure 5. Friction torque exists in the bearings in the motor and the dynamometer. The friction loss is expressed as Equation (33).
Figure 4. MOSFET switching process. switching ON. uds,off-i esw = -----------( t2 + t3 ) 2
(23)
ugs, mil−utht2 = Ciss -------------------ig2
(24)
uds, offt3 = Crss ---------ig3
(25)
udrv −0.5 ( ugs,mil + uth )ig2 = --------------------------------------------Rhi + Rgate + Rgi
(26)
udrv −ugs, mil ig3 = ------------------------------Rhi + Rgate + Rgi
(27)
Pm = T m ω c = T m ω ⁄ np
uds,off is the same as battery voltage ubat. Considering the impact of the dead time, if the phase current is positive (from inverter to motor), during the switching process of the low-side MOSFETs, the phase current flows through the corresponding free-wheeling diode, so uds is almost zero, as a result, the switching loss is also almost zero. For the same reason if the phase current is negative (from motor to inverter), the switching loss of the high-side MOSFETs could also be neglected. So the inverter switching loss could be expressed as Equation (28) : 6( t2 + t3 )ubat im Psw = -----------------πtc
ubat4 6 k1 = ---------- ⎛⎝ ( t2 + t3 ) -----+t u ⎞ πtc 2 d f⎠
(33)
The friction torque Tm could be measured by dragging the motor using dynamometer when the motor is not working. However, it should be noted that even when the motor is not working the iron loss still exists as long as the motor is rotating and consequently a resistant torque is generated by the iron loss, which is called no-load iron loss torque. So the dragging torque consists of two parts: the friction torque and no-load iron loss torque. Tdrag = Tm + Ti0
(34)
According to Equation (15), this no-load iron loss torque Ti0 could be expressed as Equation (35): ω 2ψ2f ⁄ R-c Ti0 = -----------------= n2pω cψ2f ⁄ Rc ωc
(35)
(28)
Equation (28) could also be rewritten as Equation (29): 2 6( t2 + t3 )Psw = ------------------------ubat iq πtc
(29)
From the analysis above, the inverter loss is derived by adding the conduction loss and switching loss, as expressed in Equation (30): Pinv = k1 iq + k2i2q 2 ωψ ωψ = k1 ioq + ---------f + k2⎛⎝ ioq + ---------f⎞⎠ Rc Rc
(30)
Figure 6. Dynamometer drag torque changes with motor speed.
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Since Rc has already been calculated, Ti0 could be derived and Tm and Ti0 are decoupled, as shown in Figure 6. 2.4. Calculation of Motor Efficiency The motor efficiency in the driving and braking conditions respectively is calculated using the motor and inverter models. In driving condition:
(45)
The loss power in braking condition is derived as Equation (46): Ploss = arbT 2+ ( −2arbTm + brb)T + arbTm2−brbTm + crb
(46)
Where
Pout ηdr = --------------------Pout + Ploss
(36)
Pout = Tω c
(37)
Te = T + Tm
(38)
The loss power in driving condition could be derived based on the loss analysis above as Equation (39): Ploss = adrT2 + ( 2adrTm + bdr )T + adrT2m + bdrTm + cdr
Te = −(T−Tm)
(39)
Where 2 2 1 ⎛ ω L-⎞ ---------adr = ---------2 2 ⎝ Ra + k2 + R c ⎠ np ψ f
(40)
1 2ω 2L2 ωψ bdr = ---------- ⎛⎝ ⎛⎝ 2Ra + 2k2 + --------------⎞⎠ ---------f + k1⎞⎠ np ψ f Rc Rc
(41)
ω 2ψ2f ωψ cdr = ( Ra + Rc + k2 ) ----------+ k1 ---------f Rc R2c
(42)
In braking condition: Pin −Plossηrb = -----------------Pin
(43)
Pin = Tωc
(44)
arb = adr
(47)
1 2ω 2L2 ωψ brb = ---------- ⎛⎝ ⎛⎝ 2Ra + 2k2 + --------------⎞⎠ ---------f −k1⎞⎠ np ψ f Rc Rc
(48)
ω 2ψf2 ωψ crb = ( Ra + Rb + k2 ) ----------−k1 ---------f Rc R2c
(49)
2.5. Comparison of Measured Motor Efficiency and Calculation Result The comparisons of measured motor efficiency and calculation result in the driving and braking conditions are shown in Figure 7 and Figure 8 respectively. Basically, the agreement is quite good except in high load region. This could be explained by the fact that the motor efficiency is influenced greatly by the stator temperature. The heat dissipation for an outer-rotor motor without liquid cooling is not easy, so during the experiment the stator is heated especially at high load. The stator temperature rises, so copper loss increases and therefore the motor efficiency decreases. In calculation, the heating effect is not considered. So the measured motor efficiency is lower than the calculation result at high load. Motor heating is less a serious problem in real vehicle operation due to the better cooling condition. A more detailed and precise motor efficiency model needs to be developed later using a thermometer to measure the stator temperature.
Figure 7. Measured and simulated motor efficiency in driving condition.
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Figure 8. Measured and simulated motor efficiency in braking condition.
3. ENERGY EFFICIENCY OPTIMIZATION FROM THE POWER LOSS ANALYSIS
loss is minimized when the torques of the front motor and the rear motor are the same.
Based on the energy efficiency model, the problem of energy efficiency optimization could be formulated from the aspect of power loss minimization as in Equation (50) with the constraint expressed in Equation (4). The idea is that the maximum energy efficiency is achieved when the total power loss is minimized.
Ploss,t = min(Ploss,t), when Tf = Tr = Treq / 4
J = min(Ploss,f + Ploss,r)
(50)
Take the driving condition for example. According to Equation (39), the total power loss of four motors is derived as Equation (51): Ploss,t = 2adr( Tf2 + Tr2) + ( 4adrTm + 2bdr) ( Tf + Tr ) + 4adrTm2 + 4bdr Tm + 4cdr
(51)
Note that the coefficients in Equations (39) and (46) are only functions of the motor rotation speed and not affected by the motor torque. Considering the constraint as in Equation (4), the total power loss could be further expressed as a quadratic function of Tf as Equation (52): Ploss, t = 4adrTf2-2adrTreqTf + ( 2adrTm + bdr )Treq 2 adrTreq + 4adrTm2 + 4bdrTm + 4cdr + ------------2
(52)
Ploss,t is minimized when: dPloss,-t ⎧ ------------= 8adrTf −2adrTreq = 0 ⎪ dTf ⎨ 2 d Ploss,-t ⎪ --------------= 8adr > 0 ⎩ dT2f
(53)
This leads directly to the conclusion that the total power
(54)
And this conclusion also applies for the braking condition. That is to say, the total required torque should be distributed evenly to the four driving motors both in driving and braking conditions in order to maximize the overall energy efficiency. Besides the mathmatical derivation as illustrated above, this conclusion could be interpreted in this way: Since the power loss of each motor is not only proportional to the motor torque but also proportional to the square of motor torque, if one motor is more loaded than others, the total power loss increases and the overall energy efficiency deteriorates.
4. VEHICLE TEST RESULT According to the control allocation algorithm in the referenced literature (Wang et al., 2011; Yu et al., 2005; Wang et al., 2010), only two motors should work when the total torque requirement is low, while the conclusion derived from motor power loss analysis shows that the total torque should be distributed evenly to four motors in all conditions to maintain the best overall efficiency energy. So vehicles tests are designed to compare the energy efficiencies of these two control strategies. For the driving condition, constant-speed cruising is taken as the operating condition because it’s easily controllable and the total torque requirement is low in order to meet the condition for the control allocation algorithm in literature. For the braking condition, the energy efficiency
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is compared in constant-deceleration braking. The total braking torque is also small and no hydraulic braking is applied. During the tests, the vehicle runs on a flat road and all the necessary data are sent to CAN bus and acquired by a computer. In order to eliminate the error caused by human driver manipulation, the motor torque commands are programmed by software. Several tests are repeated at the same road in the same operating condition for several times. The measured data is highly repeatable and there is only very little difference between tests of the same operating condition. The average value for the same operating condition is taken for comparison. The driving tests are carried out at three speeds: 20 km/ h, 30 km/h and 40 km/h. Proper torque orders are given to the motors to make the vehicle firstly accelerate to the desired speed and then cruise at that speed. The power consumptions are compared in four-wheel-driving (4WD) mode and two-wheel-driving (2WD) mode. Take the driving test at 30 km/h for example, the motor speed is 330 rpm and the total torque output is set to be 26 Nm to maintain the constant speed of 30 km/h after several trials. For the 4WD mode, the torque output of each motor is 6.5 Nm. In 2WD mode, the torque output of the nonworking motor is -2Nm each as shown in Figure 6, so the working motor should each output a torque of 15Nm. By looking up the motor efficiency map, the efficiency for a motor driving at 15 Nm and 330 rpm is 73% while the efficiency for 6.5 Nm is 66%. The control allocation method neglects the negative torque output of the nonworking motor and suggests that the vehicle should run in 2WD mode in order to save energy.
Figure 9. Constant speed cruising at 30 km/h.
The test processes at 30 km/h are shown in Figure 9 and the test results for all driving conditions are summarized in Table 2, which shows that in all test driving conditions 4WD mode is more energy efficient. For the braking tests, the energy efficiency is compared in constant-deceleration braking. The vehicle is firstly accelerated to a certain speed and then constant braking torque is generated by motors to decelerate the vehicle at a constant deceleration, the total recovered energies are compared between 4WD and 2WD mode. The test processes for braking starting from 30 km/h are shown in Figure 10 and the test results for all braking conditions are summarized in Table 3. Note that, in the braking test starting from 40 km/h, limited by the length of the test ground, hydraulic braking has to be implemented to stop the vehicle at 26 second before the motor stops the vehicle completely. The test results show that in 4WD mode more energy could be recovered than in 2WD mode. In the literature which proposed to improve the energy efficiency through control allocation method, the efficiency of the non-working motor is considered to be zero, while actually the iron loss and friction loss always exist as long as the motor is rotating. So although the efficiency of the working motor in 2WD mode is higher than the motor in 4WD mode, the overall energy efficiency in 2WD mode is actually lower. As shown from the test results, the energy efficiency difference between the 2WD and 4WD mode is actually quite small because the 2WD mode is suggested by the control allocation method only when the torque requirement is small. The difference would be even smaller if the
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Figure 10. Braking from 30 km/h. other motor control algorithm remains for further research.
Table 2. Test results in driving condition. Vehicle speed Total driving Battery power Battery power (km/h) torque (Nm) in 4WD (W) in 2WD (W) 20
20.5
779.7
834.6
30
26
1366.8
1427.7
40
31
2062.2
2150.3
Table 3. Test results in braking condition. Starting vehicle speed Total braking torque (Nm) (km/h)
Recovered energy in 4WD (J)
Recovered energy in 2WD (J)
20
35.5
3.71
3.26
30
42
12.78
11.03
40
48
8.52*
7.99*
*Braking stops at 26 seconds limited by the length of the test ground
vehicle is tested in a driving cycle because the vehicle only partially works in 2WD mode in a driving cycle. Road tests in a driving cycle are not possible because there are too many uncertainties in a real road test and the errors caused by driver manipulation could easily be larger than the difference caused by the control strategies. Driving cycle tests on a dynamometer would be considered later when we have a dynamometer for 4WD vehicles. However, it should be emphasized that, this conclusion has only been verified for permanent magnet synchronous motor with field oriented control where id is set to be zero. Whether this conclusion also applies to other motor type or
5. CONCLUSION The problem of energy efficiency optimization of electric vehicle driven by four in-wheel motors has been studied. A comprehensive energy efficiency model of the permanent magnet synchronous motor including the inverter is built. The calculated efficiency agrees with the measured data quite well, especially in driving condition. Based on the power loss analysis, the conclusion is drawn that theoretically in all driving or braking condition 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 tests are carried out to compare the energy efficiency in 4WD mode and 2WD mode, and the result shows that the efficiency in 4WD mode is higher in the test conditions. The neglect of the power loss of the non-working motor in 2WD mode is the reason why the conclusion drawn by control allocation method is not correct.
REFERENCES Balogh, L. (2001). Design and application guide for high speed MOSFET gate drive circuits [online]. Texas Instruments. Available from: http://www.ti.com/lit/ml/ slup169/slup169.pdf [Accessed 20 December 2011]. Cavallaro, C., Ditommaso, A. O., Miceli, R., Raciti, A., Galluzzo, G. R. and Trapanese, M. (2005). Efficiency enhancement of permanent-magnet synchronous motor
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