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illustrates the situation that the front wheels are locked andthe rear are not. 1.5,------------.-----------.------.-----------,

- ideal ditribution curve-ECE regulation curve- f ron t wheel locked curve

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0Braking force on front axle (kN)

2010 15Vehicle speed (m/s)(a) Weight factor of the vehicle speed

1 .5 , - - - - - - - - - - - . - - - - - - . - - - - - - - - - - - . - - - - - . - - - - - - - - - - - - ,

4.5. . . . -------. -----. -----. -----. -----, ------, ------, ------, ------_4.0z-;3.5xco 3.0m

2.5c:o 2.0~ 1 . 5c: 1.0m0.50 0

Fig. 1. Permitted area of force distribution

(1)

B. Motor Available Braking TorqueThe motor maximum torque is determined from the motor

characteristic curve. This is described by

{TN - - - - - OJm ~ OJbT -mmax P / OJ - - - OJ > OJN m m b

where Tmmax is the motor maximum braking torque, TN isthe motor rated torque, OJb is the motor base angular speed,OJm is the motor angular speed, PN is the motor rated power.However, it is difficult for a motor to generate electricity

and deliver to the on-board energy storage, because of thevery low electric motive force (voltage) generated at lowmotor rotational speed, which is proportional to the vehiclespeed. Thus, a weight factor K v is used. Similarly, when thebattery state of charge (SOC) is considered, a weight factorK soc is introduced to protect the battery from overchargingthat may affect the battery life. The weight factors K v andK soc are shown in Fig.2.Therefore, the available regenerative braking torque given

by the motor is obtained asTmavail =TmmaxKvKSOc (2)

C. Mathematical Model ofBrake Energy RegeneratingEVsIn this paper, a front wheel-drive configuration is

considered.When a deceleration is required, torque is transferred from

the motor and mechanical brakes to the wheels. The brakingtorque applied by the motor is converted to electric energyand transferred to the battery.

For a given deceleration, a force F,eq has to be applied atthe wheels to match it[6]. This is described by

F,eq = ~ - F, - Fw - ~ (3)

()11- - - - - - - - - - - - - - - - - - - .o't).e

1:C) 0.5

00 0.2 0.4 0.6 0.8Battery SOC(b) Weight factor of the battery SOC

Fig. 2. Weight factor

where F,eq is the braking force required, ~ is the forcerequired to give the deceleration, which has a reasonableapproximation when the angular acceleration is ignored, F,the rolling resistance force, Fw is the aerodynamic drag, ~is the hill climbing force.

The power required to slow the vehicle is calculated byP,eq =F,eqV (4)

where v is the vehicle speed.P,eq is split up between the front and rear axles according

to the distribution strategy of braking forces, and it isexpressed as

P,eq =P + P, (5)where Pj is the power provided by the front wheels, P, isthe power provided by the rear wheels.

The electric power from the motor is smaller than Pjbecause of the efficiency of the gear system and the motor.This is described by

Pmot_ele =Pj 17g 17m (6)where Pmot ele is the motor electric power, 17g is theefficiencyof the gear system, and it is assumed to be constant,17m is the efficiency of the motor, and it is modeled by the

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III. BRAKING TORQUE DISTRIBUTION STRATEGYFrom analysis above, the amount of regenerated brake

energy depends on multiple factors in EVs. To achieve highregeneration during braking without sacrificing the stabilityof the vehicle and fulfill the requirements of the factors, it isreasonable to distribute the braking torque required betweenthe front and rear axles, between regenerative braking andfriction braking by optimization algorithm. However, it willconsume large computing time and is difficult to accomplish

equationTJm=TmOJm/(TmOJm+ kcTm2 + kjOJm+ kOJOJm3 +C)

(7)where Tm is the motor braking torque, kc is the copperlosses coefficient, k1 is the iron losses coefficient k is thewwindage losses coefficient and C represents the constantlosses that apply at any speed.The power that charges the battery is the summation of

contribution of electric power from the motor and electricpower needed to run other electrical systems. This isdescribed by

where Pch is the charge power of the battery, ~ c is theaverage power of the accessories. It should be noted Phisccharge power when it is positive, otherwise it is dischargepower.When braking, a certain power is dissipated into thebattery. Here, an internal resistance battery model is adopted,

which characterizes the battery with a voltage source and aninternal resistance.Considering the situation that the current / is flowing into

the battery, charge power of the battery is obtained asPch =E/ + /2 R (9)

where E is the open circuit voltage, and it changes with thebattery SOC, / is the charge current, R is the internalresistance of the battery.The reasonable solution to (9) is

I = ( - E + ~ E 2 + 4 R ~ ) / 2 R (10)The battery SOC is represented as followsSOC =SOCo+ l ix/ /Cp (11)

where SOCo is the battery initial SOC, I i is the samplingtime, Cp is the Peukert capacity.The regenerated power of the battery is described as

Ph =Pch - /2 R (12)To evaluate the ability of regenerated brake energy for a

full driving cycle, regenerated energy efficiency is defined,and expressed by

~ h =Pmof_ele - ~ c

1] = fI;, / f ~ e q

(8)

(13)

real-time application. In following, a simple braking torquedistribution strategy is presented.A. Charge andDischarge Characteristics ofthe BatteryandMotorFig.3 shows the relation between the regenerated power

and the charge power of the battery. Maximum charge anddischarge powers of typical driving cycles are listed in TableI. In Table I, the driving cycles include ECE Driving Cycle(ECE), New European Driving Cycle (NEDC), SupplementalFederal Test Procedure (SFTP), New York City Cycle(NYCC) and Urban Dynamometer Driving Schedule(UDDS). From Fig.3 and Table I, it is found that for thetypical driving cycles, the regenerated power increases withthe increase of the charge power of the battery. That is to say,if the charge power of the battery is the maximum, theregenerated power of the battery will be the maximum.

1 2 0 . 0 , - - - , - - - - , - - - - . . , - - - - - r - - - - - - , r - - - - - r - - ~

100.080.0

3:oc.2 60.0Q) 40.0C)Q)0:: 20.0

00 20.0 40.0 60.0 80.0 100.0 120.0 140.0Charge power of battery (kW)

Fig. 3. Relation between the regenerated power andthe charge power of the battery

TABLE IMAxIMUM CHARGE AND DISCHARGE POWERS OF TYPICALDRIVING

CYCLESDriving Cycle ECE NEDC SFTP NYCC UDDSMaximum discharge 4.50 12.91 17.61 9.97 12.11power (kW)Maximum charge 16.0 38.49 49.80power (kW) 38.34 39.09

However, there exists a situation that the motor isgenerating, while the battery is discharging. The reason forthis is that the electric power generated by the motor issmaller than the average power of the accessories, whichresults in the batteries need to consume power. In this case, itis desired that the consumed power of the battery the morelittle the more good. From the relation between the consumedpower and the discharge power of the battery (Fig.4), it isfound if the discharge power of the battery is the minimum,then the consumed power of the battery is the minimum. Theminimum discharge power of the battery corresponds to themaximum electric power generated by the motor.In a word, for both situations, the electric power generated

by the motor the more big the more good.Fig.5 shows the electric power generated by the motor

during braking. It can be seen, for the same motor angular

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speed, the electric power of the motor increases with theincrease of the motor torque under the circumstance that themotor torque is below the motor maximum torque.

15o.or--------- , ------ , -------- , ------- , ----- .------------r---- , ------ ,

C100.0oC."CQ)E::J 50.0o()

0 ~ ~ 2 : : : - : : ; 0 : ' - : : . 0 = - - - - - - - - - - : 4 - = - 0 . - = - 0 - - - - : 6 ~ 0 - - - - = - . 0 - - 8 0 . l . . . - . 0 - - 1 -L0-.0--12---l.0-.0--1---.J40.0Discharge power of battery (kW)

Fig. 4. Relation between the consumed power andthe discharge power of the battery

-motor maximum torquemotor generated power

Q)::J~ 1 0 0.s

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1200000

- no recovery- parallel strategy- proposed strategy

80000 600Time(s)20012000000000 600Time(s)200

35 0.830 0.78

025g g0.76-g 20 enQ)c. Q)0 0.7415(,):cQ)> 10 0.72

0.70

Fig. 8. New European Driving Cycle Fig. 10. Comparison of the battery SOC100 r - - - - . . - - - - . . . - - - - - - - . - - - - - - . - - - - - - - - - - r - - - - - - ,

Fig. II . Comparison of regenerated energy efficiency

.parallel strategy

.proposed strategy7 . 0 ~ - - - - - r - - - - - - - - . - - - . - - - - - - - - - . - - - - - - - , - - - - . . . - - - - - - - - . - - - - - - - - - - . . . ,-+-force required6.0 -motor maximum force-e-force limit_ 5.0 -motor braking forcez~e4.0J2g>3.0:2aJ 2.01.0

01125 1130 1135 1140 1145 1150 1155 1160 1165Time(s)(a) Braking forces distribution of parallel strategy

80rQ)0IE

60E>Q)rQ)"0 40Q)1UQi

20Q)0:::

o ECE NEDC SC03 NYCC UDDSDriving cycle

7.0r-------r--------.---.---------.-------,----. . .--------.---------,-+-force required6.0 -motor maximum force-e-force limit2 5.0 -motor braking force~e4.0J2g>3.0:2aJ 2.01.0

01125 1130 1135 1140 1145 1150 1155 1160 1165Time(s)(b) Braking forces distribution of proposed strategy

V. CONCLUSIONProperties affecting braking energy regeneration are

analyzed. The mathematical model of brake energyregenerating EVs is established. By analyzing the charge anddischarge characteristics of the battery and motor, a simpleregenerative braking strategy is proposed. The strategy takesadvantage of the motor torque and can obtain maximumenergy recovery. The effectiveness of the strategy is verifiedby comparing with the parallel strategy. The proposedstrategy can improve the battery SOC and regenerated energyefficiency remarkably.

Fig. 9. Comparison of braking forces distribution

Fig. I 0 shows the comparison of the battery soc.Comparing to no recovery, both the parallel and the proposedstrategy can improve the battery soc. The effect of theproposed strategy is better.In Fig.I I, the regenerated energy efficiency is compared

on several typical driving cycles. It can be seen, comparingwith the parallel strategy, the regenerated energy efficiencyhave remarkable improvement for each driving cycle whenthe proposed strategy is adopted.Simulation results indicate, because the proposed strategy

is able to use the motor braking torque to the full extent, theproposed strategy has resulted in higher energy regenerationin all cases.

REFERENCES[I] Yimin Gao, Liang Chu and M. Ehsani, "Design and control principles

of hybrid braking system forEV, HEV and FCV." in Proc.2007 VehiclePower and Propulsion Conf., pp. 384-391.[2] S. R. Cikanek and K. E. Bailey, "Electric vehicle braking systems," inProc.1997 International Electric Vehicle Symposium.[3] N. Mutoh, Y. Hayano, H. Yahagi and K. Takita, "Electric brakingcontrol methods for electric vehicles with independently driven frontand rear wheels. " IEEE Trans. Industrial Electronics , vol.54, pp.1168-1176, Feb. 2007.[4] H. Yeo and H. Kim, "Regenerat ive braking algorithm for a hybr idelectric vehicle with CVT ratio control," Proc. IMechE, Part D: 1.Automobile Engineering, vol.220, pp. 1589-1600, Nov. 2006.[5] 1. Hellgren and E. Jonasson, "Maximisat ion of brake energyregeneration in a hybrid electric parallel car," Int. 1. Electric andHybridVehicles, vol. I, pp.95-121, Jan. 2007.[6] L. James and L. John, Electric Vehicle Technology Explained.England, UK: John Wiley & Sons, 2003, pp.183-292.

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