Engineering Engineers, Part D: Journal of Automobile

Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering http://pid.sagepub.com/

Instantaneous optimal regenerative braking control for a permanent-magnet synchronous motor in a four-wheel-drive electric vehicle Dongbin Lu, Minggao Ouyang, Jing Gu and Jianqiu Li Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering published online 21 February 2014 DOI: 10.1177/0954407014521173 The online version of this article can be found at: http://pid.sagepub.com/content/early/2014/02/20/0954407014521173 A more recent version of this article was published on - Jul 22, 2014

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Original Article

Instantaneous optimal regenerative braking control for a permanentmagnet synchronous motor in a four-wheel-drive electric vehicle

Proc IMechE Part D: J Automobile Engineering 1–15 Ó IMechE 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954407014521173 pid.sagepub.com

Dongbin Lu, Minggao Ouyang, Jing Gu and Jianqiu Li

Abstract Recovering the kinetic energy of a vehicle is one inherent advantage of an electric vehicle. A permanent-magnet synchronous motor is widely adopted for the traction motor in an electric vehicle with the advantage of a high efficiency and a high torque density. The principle for electric braking control of the permanent-magnet synchronous motor under fieldoriented control is studied. The efficiency model of the electric drive system, which is different from that of the internalcombustion engine drive system, can be exactly described by analytical equations. On this basis, the battery power can be expressed as a function of the angular velocity and the electromagnetic torque of the motor. By solving the partial differential equation for the battery power, the instantaneous optimal regenerative braking torque of the permanentmagnet synchronous motor is simply calculated according to the vehicle braking torque demand and the motor speed. Compared with the existing efficiency map method, the analytical technology is easily implemented. Then a four-wheeldrive electric vehicle is investigated to achieve optimal regenerative braking control. The dynamic behaviour of braking in the four-wheel-drive electric vehicle is also considered. The parallel braking pattern and the series braking pattern are investigated in order to evaluate the availability of braking energy recovery. The instantaneous optimal regeneration energy can be recovered for the series braking system, and a significant amount of energy can be recovered for the parallel braking system by adjusting the free travel of the brake pedal.

Keywords Permanent-magnet synchronous motor, field-oriented control, efficiency model, electric vehicle, optimal regenerative braking, series braking

Date received: 31 January 2013; accepted: 9 December 2013

Introduction Studies show that, in urban driving, about one third to one half of the total energy is dissipated in the brakes.1,2 The regenerative braking system provides the electric vehicle (EV) with the capability to recover a significant amount of energy during braking.1 Therefore, recovering the braking energy is an effective approach for improving the driving range of an EV. Regenerative braking patterns for an EV and a hybrid electric vehicle (HEV) can be divided into parallel types and series types. The parallel braking system is relatively simple, exerting the braking torque of the electric motor via transmission on the wheels without modulating the frictional braking torque apart from the control of the driver. In the series braking system, a regenerative braking torque is exerted and the frictional braking torque modulated, targeting the need to give a

certain overall braking torque according to the stroke of the braking pedal. It is obvious that, under the series braking strategy, more braking energy can be recovered.3 With the parallel braking approach, which has a very simple structure and is technically available, a significant amount of energy can be recovered.1 The regenerative braking strategies and the effectiveness of regenerative braking for an EV and an HEV have been investigated by Gao et al.1 andWyczalk and Wang.4 A regenerative braking model for a parallel

State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, People’s Republic of China Corresponding author: Minggao Ouyang, Room 213, Automotive Research Institute, Tsinghua University, Haidian District, Beijing 100084, People’s Republic of China. Email: [email protected]


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Proc IMechE Part D: J Automobile Engineering

hybrid electric vehicle (PHEV) has been developed by Panagiotidis et al.5 A new and improved parallel regenerative braking system for a PHEV which maximizes the regenerative braking force based on various vehicle attributes has been discussed by Cikanek and Bailey.6 Braking force distribution strategies for a mild HEV to recover the vehicle’s kinetic energy maximally were presented according to the actual regenerative braking force of the integrated starter–generator by Ye et al.7 The effects of different regenerative braking strategies on the braking performance and the fuel economy in a hybrid electric bus were simulated using CRUISE by Sandtarash et al.8 All the above references revealed little consideration of the electric motor generation principle and the charging efficiency of the electric drive system during braking. Because of this, the conclusion that regenerative braking should be used first in order to recover as much braking energy as possible reached by Gao et al.1, 3 and Sandtarash et al.8 is not correct. The brake system of the Toyota Prius, which improves the stability performance and makes maximum use of regenerative braking, was presented by Nakamura et al.9 and Kim et al.10 Mechanical braking is utilized only when the electrical braking torque is not sufficient, or if the vehicle speed is low. Electrical braking is not preferred at a low speed, since the electrical system is not only inefficient at a low speed but also less stable than the mechanical braking system. However, the derivation of the optimal regenerative braking torque at a low speed is not presented. A permanent-magnet synchronous motor (PMSM) is widely adopted as the traction motor in an EV with the advantage of a high efficiency and a high torque density. The objective of this study is to obtain the optimal regenerative braking torque of the PMSM in the braking process. First the efficiency model of the electric drive system (including the PMSM, the inverter and the battery) and the principle for electric braking control of the PMSM under field-oriented control (FOC) are studied. Then the maximum braking torque in the regeneration mode and the braking torque for the maximum regeneration power respectively can be deduced. On this basis, the instantaneous optimal regenerative braking control strategy for the EV is obtained with the model of the electric drive system. Then the braking control strategies in three different braking systems are presented to recover their maximum kinetic energies respectively. A four-wheel-drive EV is investigated to validate the instantaneous optimal regenerative braking control strategy. The paper is organized as follows. The second section presents the vehicle and electric drive system model. The braking principle for the PMSM under FOC is described in the third section. Then the dynamic behaviour of braking in the four-wheel-drive EV is described in the fourth section, and three regenerative braking control systems for the EV are compared in the fifth section. Simulation results and validation analysis are discussed in the sixth section. The seventh section contains the conclusions.

Dynamics modelling Equation for the vehicle resistance The force needed when driving on a slope road in an EV can be expressed as11 Ttq ig i0 hT 1 dv = mgf cos a + CD rAv2 + mg sin a + dm r 2 dt Ttq = Te Tmec

ð1Þ

where Ttq, Te and Tmec are the motor output torque, the electromagnetic torque and the mechanical torque respectively, ig is the transmission ratio, i0 is the reducer ratio, hT is the efficiency of the transmission system, r is the radius of the wheels, m is the mass of the vehicle and the payload, f is the rolling resistance coefficient, a is the angle of the slope, CD is a dimensionless coefficient, A is the cross-sectional area exposed to flow, v is the vehicle velocity, d is the rotating mass conversion factor of the vehicle, dv/dt is the vehicle acceleration and r is the air density.

Efficiency model of the PMSM Considering the iron loss, the d- and q-axis equivalent circuit model (ECM) of the PMSM12, 13 can be shown to be as in Figure 1 (where d indicates direct and q indicates quadrature). The d-axis stator current id and the q-axis stator current iq are divided into the iron loss currents idi and iqi and the torque currents idt and iqt. In the steady-state case, the voltage balance equations can be expressed as ud = Ra id vcq uq = Ra iq + vcd

Figure 1. The efficiency model of the PMSM. (a) d-axis equivalent circuit; (b) q-axis equivalent circuit.


ð2Þ

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The flux equations can be expressed as cd = Ld idt + cf

ð3Þ

cq = Lq iqt

The electromagnetic torque equation is Te = p(cd iqt cq idt ) = p cf iqt + (Ld Lq )idt iqt

ð4Þ

where ud and uq are the d-axis terminal voltage and the q-axis terminal voltage respectively, id and iq are the daxis armature current and the q-axis armature current respectively, idi and iqi are the equivalent d-axis iron loss current and the equivalent q-axis iron loss current respectively, idt and iqt are the equivalent d-axis torque current and the equivalent q-axis torque current respectively, cd and cq are the d-axis stator flux linkage and the q-axis stator flux linkage respectively, cf is the magnet flux linkage, Ld and Lq are the d-axis inductance and the q-axis inductance respectively, v is the electrical angular velocity, Ra is the armature resistance and p is the number of pole pairs. The surface-mounted permanent-magnet synchronous motor (SPMSM) will be used for the study in this paper, and the method can also be adapted to study the interior PMSM and the induction motor. In the SPMSM, the d-axis inductance is approximately equal to the q-axis inductance. Assuming that Ld = Lq = L, the torque equation can be simplified to Te = p(cd iqt cq idt )

ð5Þ

= pcf iqt

The torque generated by the SPMSM is proportional to the q-axis current and has no relationship with the daxis current. Figure 2 is the power flow diagram of the PMSM in the driving mode. The input power of the PMSM can be deduced from equation (2), equation (3) and the efficiency model in Figure 1 and is expressed as Pin = ud id + uq iq = Ra id vcq id + Ra iq + vcd iq v2 c2d + c2q = Ra i2d + i2q + + vcf iqt Ri

ð6Þ

where Pin is the input power and Ri is the equivalent iron consumption resistance, which can be obtained by experiment.13 On the right-hand side of the equation, the first part is the copper loss PCu, the second part is the iron loss PFe and the third part is the electromagnetic power Pe. The electromagnetic power, which is the sum of the mechanical loss Pm, the stray loss Ps and the output power Pout, can be expressed as ð7Þ

vcf iqt = Pmec + Ps + Pout

Maximum torque–current control can be realized by controlling the d-axis current id = 0 for the SPMSM, which is applied to the traction motor of this paper. According to the equivalent circuit and equations (2) to (6), the relations between the power losses, the electromagnetic torque and the electric angular velocity can be expressed as

2 v2 L2 Te vcf + 1 + pcf Ri R2 n i o 2 2 2 v vL Ri ðTe =pcf Þ + cf + ½LðTe =pcf Þ2

PCu = Ra

PFe =

Ri

ð8Þ

The input power can be deduced from

2 2 2 v v L Te vcf Pin = Te + Ra +1 + p pcf Ri Ri 2 n o 2 v2 vL2 Ri ðTe =pcf Þ + cf + ½LðTe =pcf Þ2 + Ri ð9Þ

Efficiency model of the inverter In order to evaluate the inverter efficiency accurately, we must have well-developed component models and an inverter switching algorithm. Otherwise, an accurate evaluation can only be obtained by actual tests. However, by making some assumptions and simplifying device models, the analytical model can be applied to inverter efficiency evaluation.14–16 For conduction loss evaluation, a simplified device model is employed: a pure resistor for power metal–oxide–semiconductor field effect transistors (MOSFETs), and a voltage source in series with a resistor for insulated gate bipolar transistors and diodes. In this paper, the loss of a three-phase MOSFET-based full-bridge inverter is discussed, and space vector pulse width modulation (SVPWM) is adopted by this inverter. Conduction loss. The simplified models for the power MOSFET and diode are expressed as Vds = IRds Vak = Vf + IRak

Figure 2. Power flow diagram of the PMSM.

ð10Þ

where Vds and Vak are the on-state voltage drop of the MOSFET and the on-state voltage drop of the diode


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respectively, Vf is the diode voltage drop in the zerocurrent condition, Rds and Rak are the resistive element of the MOSFET and the resistive element of the diode respectively and I is the device current. The conduction loss of the MOSFET and the conduction loss of the anti-parallel diode are given by 1 mi 2 + cos u ð11aÞ Pc-MOSFET = Im Rds 8 3p

Pinv = Pc + Psw 12td Vf 3kon fs 3koff fs + = + Im ptc p p

3Rak td 3 2td + + Rds 1 I2m 2 tc tc

ð16Þ

where the relationships between Im and iq and between Im and Te are rffiffiffi 2 and Im = iq 3 ffiffi ffi r ð17Þ 1 mi 1 m 1

i cos u + I2m Rak cos u Pc-D = Im Vf 2 v2 L2 Te vcf 2 p 4 8 3p = +1 + 3 pcf Ri Ri 2 ð11bÞ The loss of the inverter can be expressed by the electrorespectively, where mi is the per unit fundamental stamagnetic torque and electrical angular velocity of the tor voltage, u is the load power factor angle and Im is PMSM as the peak value of the sinusoidal wave. rffiffiffi 2 2 In this paper, the conduction loss of the inverter con2 12td Vf 3kon fs 3koff fs v L Te vcf + Pinv = + +1 + tains the conduction loss of the MOSFETs and the con2 3 ptc p p pcf Ri Ri

2 2 2 duction loss of the anti-parallel diodes. As the SVPWM 2Rak td 2td v L Te vcf + + Rds 1 +1 + is adopted and the MOSFETs conduct current bidirectc tc pcf Ri Ri 2 tionally, the diodes conduct only in the dead time. ð18Þ Considering the dead time effect, the conduction loss of the MOSFETs and the conduction loss of the antiparallel diodes in the three-phase inverter can be simpliBattery model fied to The electric model of the battery, which is described by 3 2td Pc-MOSFETs = I2m Rds 1 ð12aÞ a circuit consisting of basic elements, such as a resistor 2 tc and a capacitor, is called an ECM and is widely used to analyse the dynamic properties of the battery voltage and and current.17–19 The error in analysing the battery 6 3 2td Vf Im + I2m Rak Pc-Ds = ð12bÞ charge 19and discharge properties does not extend p 2 tc beyond 5%, which can satisfy the engineering requirements. Typically, the architecture of the circuit is comwhere td is the dead time and tc is the period time of the posed of a fundamental ohmic resistor and one or more SVPWM. RC networks connected in series to simulate both the The conduction loss of the inverter is transient response and the steady-state response of the Pc = Pc-MOSFETs + Pc-Ds ð13Þ battery. One of the ECMs used to simulate the cell performance is illustrated in Figure 3, where an ohmic resistor with a resistance Rs, an RC network (Rt//Ct) Switching loss. According to Dong et al.,16 the switching and a d.c. source with an open-circuit voltage voc, loss of the hard switch circuit is which is a function of the state of charge (SOC) of the battery, are connected in series. vb is defined as the terkon Im fs minal voltage of the battery and ib is the outflow Psw-on = p ð14Þ current. koff Im fs Psw-off = p where Psw-on and Psw-off are the turn-on loss and the turn-off loss respectively, fs is the switching frequency and kon and koff can be obtained from the device data sheet or test data. The switching loss of the three-phase inverter is Psw = 3ðPsw-on + Psw-off Þ

ð15Þ

The total loss of the three-phase inverter, which is the sum of the conduction loss and the switching loss, can be expressed as

Figure 3. A generalized ECM for lithium batteries.


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Figure 4. Diagram of FOC with feedforward control for PMSM. PI: proportional-integral controller; SVPWM: space vector pulse width modulation; PMSM: permanent-magnet synchronous motor.

Using Kirchhoff’s law, the dynamics of the ECM shown in Figure 3 can be expressed as 1 1 vc + ib Ct Rt Ct vb = voc Rs ib vc

v_c =

ð19Þ ð20Þ

where vc is defined as the voltage across the RC network, as seen in Figure 3. In the steady-state case, the power consumption in the battery can be expressed as PbR = ðRs + Rt Þi2b

ð21Þ

The energy consumption in the battery can be also expressed by the electromagnetic torque and the electrical angular velocity of the PMSM as PbR =

voc

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 v2oc 4ðRs + Rt ÞðPin + Pinv Þ 4ðRs + Rt Þ

ð22Þ

where Pin and Pinv are a function of the electromagnetic torque and a function of the electrical angular velocity respectively of the PMSM, as shown in equation (9) and equation (18) respectively.

Braking principle of the PMSM The scheme of FOC for the PMSM is shown in Figure 4. Feedforward control is applied to improve the dynamic performance. In FOC, the stator phase currents are measured and converted into a corresponding complex vector. This current vector is then transformed to a coordinate system rotating with the rotor of the machine. Now the real x-axis component of the stator current vector id in this rotor flux-oriented coordinate system can be used to control the rotor flux linkage and the imaginary y-axis component iq can be used to

control the motor torque, as shown in Figure 5(a). For the SPMSM, maximum torque–current control can be achieved by controlling the d-axis current id = 0. Electric braking control based on FOC is realized by requesting a negative q-axis current according to the braking torque demanded. Electric braking has two modes: regenerative braking and power consumption braking. For a given motor speed, if the back electromotive force can provide the necessary braking current, the PMSM is running in the regenerative braking mode, as shown in Figure 5(b). Otherwise, the PMSM is running in the power consumption braking mode, as shown in Figure 5(c). Taking into account that there is no weakening control in the SPMSM, the d-axis current reference equals zero. The input power and the electromagnetic power can be expressed as v2 Ld Lq iqt + R a iq iq Pin = vcf + Ri ð23Þ Pe = vcf iqt Generally iqiiq, and so iqt ’ iq. Replacing iqt by iq, equation (23) can be simplified to Pin = vcf + Rl iq iq ð24Þ Pe = vcf iq where Rl =

v2 Ld Lq + Ra R1

Obviously, at a given motor speed, the braking power is proportional to the braking torque, while the regeneration power is a quadratic function of the braking torque, as shown in Figure 6. If –vcf/Rl \ iq \ 0, the


6


Figure 5. Phasor diagram of PMSM in FOC. (a) Driving; (b) Regenerative braking; (c) Power consumption braking.

Figure 6. Relationship between motor input power and q-axis current in a certain v.

input power is negative and the motor regenerates energy to the battery. The input power is the negative maximum, and the maximum regeneration power is achieved at iq = –vcf/2Rl. If iq = –vcf/Rl, no electric energy is recovered, and all the kinetic energy is transformed into heat in the motor stator winding. If iq \ –vcf/Rl, the input power is positive, and the motor consumes the battery and kinetic energy in the motor stator winding. According to equation (24), the q-axis currents for the maximum brake torque in the regenerative mode and the maximum regenerative power are shown in Figure 7 respectively. Based on the above analysis, the available maximum electromagnetic torque in the regenerative braking mode must satisfy the conditions vc2f p Rl Tebrk = Temax , Pen p, Tebrk = v Tebrk =

if Tebrk 4 Temax if Pe \ Pen

ð25Þ

Figure 7. The q-axis current in different braking modes. rpm: r/min; max; maximum.

where Temax is the maximum electromagnetic torque and Pen is the rated electromagnetic power. When the PMSM regenerates the maximum power, the electromagnetic torque is vc2f p 2Rl Tebrk = Temax , if Tebrk 4 Temax Pen p, if Pe \ Pen Tebrk = v Tebrk =

ð26Þ

Dynamic behaviour of braking in the fourwheel-drive electric vehicle When a vehicle experiences braking, the normal loads on the front axle and the rear axle vary with the deceleration of the vehicle. In order to keep the vehicle stable while braking, the braking forces acting on the front axle and the rear axle should be limited in a reasonable


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Figure 8. Forces acting on a vehicle while braking on the level ground.

range. Figure 8 demonstrates the forces acting on the four-wheel-drive EV while braking on level ground. The normal load Ff acting on the front axle and the normal load Fr acting on the rear axle can be expressed as

1 ad r f Ff = mgLb + mghg Fw hw Lwb hg g

ð27Þ 1 ad r f mgLa mghg Fr = + Fw hw Lwb hg g where ad is the deceleration of the vehicle, Fw is the aerodynamic drag, hw is the equivalent height of the aerodynamic drag, Lwb is the wheelbase length, La is the length between the automotive centroid and the centre-line of the front axle, Lb is the length between the automotive centroid and the centre-line of the rear axle, r is the wheel radius and f is the rolling resistance coefficient. In this paper, the velocity of the four-wheeldrive EV is less than 60 km/h, and the aerodynamic drag force is relatively small. Generally, the rolling resistance of the tyres and the aerodynamic drag are much smaller than the inertial force of the vehicle. Thus they can be ignored without much influence on the accuracy of the analysis.1 Thus, equation (27) can be simplified to mg ad Ff = Lb + hg Lwb g ð28Þ mg ad Fr = La hg Lwb g The braking force Fbf acting on the front axle and the braking force Fbr acting on the rear axle are required to be proportional to their corresponding normal loads Ff and Fr respectively. These distributions of the braking forces on the front axle and the rear axle can allow the maximum braking stability of the vehicle to be obtained. Thus, the relationship between the braking force on the front axle and the braking force on the rear axle, associated with the deceleration of the vehicle, can be expressed as L b + hg ad g Fbf ð29Þ = Fbr La hg ad g

Figure 9. The ideal and average distribution of braking force on front and rear axles.

The summation of the braking force on the front axle and the braking force on the rear axle (i.e. the total braking force of the vehicle) is related to the vehicle deceleration by Fbf + Fbr = mad

ð30Þ

Substituting equation (30) into equation (29) gives the ‘ideal’ distributions of the braking force on the front axle and the braking force on the rear axle as1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi La 2hg mg Fbr L2a 4hg Lwb mg Fbr Fbf = 2hg mg ð31Þ

Figure 9 shows the ideal brake distributions on the front axle and the rear axle for the four-wheel-drive EV. This figure also shows the braking forces for various braking decelerations. The braking force on the front axle increases more quickly than that on the rear axle. This is because the normal load on the front axle increases and that on the rear axle decreases.

Instantaneous optimal regenerative braking control Instantaneous optimal regenerative braking torque calculated by the analytical model In the braking process, the braking torque target is given by the driver. As the braking torque demanded by the driver cannot be predicted, in order to recover the kinetic energy of the vehicle as much as possible, the instantaneous optimal regenerative energy can be achieved by a reasonable torque distribution between the electric brake and the mechanical brake. The battery power can be deduced as Pbat ðv, Te Þ = Preg ðv, Te Þ Pinv ðv, Te Þ PbR ðv, Te Þ

ð32Þ

where Preg(v,Te) = –Pin(v,Te). The braking torque with instantaneous optimal energy recovery can be deduced from equation (32).


8


Figure 10. Instantaneous optimal regenerative braking torque. rpm: r/min.

Area I is the power consumption braking area. Area II and area III are the regenerative braking areas. Area IV is the hybrid braking area of the electric brake and the mechanical brake. Therefore, if the braking torque demanded is in area III, the braking power is completely enveloped by the instantaneous optimal regenerative braking torque profile and can be potentially recovered by the electric brake. In area II, only the instantaneous optimal braking torque will apply, and the remaining braking torque is provided by the mechanical brake. In area I, the electric motor is running in the power consumption braking mode, which will consume battery energy in the braking process, and so all the braking force will be provided by the mechanical brake. When the commanded braking torque is greater than the available electric braking force in area IV, the electric motor will operate its instantaneous optimal braking torque, and the remaining braking force is provided by the mechanical braking system. Therefore, the optimal regenerative braking torque, and not the maximum regenerative braking torque presented by Gao et al.1,3 and Sandtarash et al.,8 should be used first. The control logic of the instantaneous optimal regenerative braking control is shown in Figure 11. The motor speed can be obtained through the vehicle velocity and the gear ratio of the transmission. Based on the motor speed, the instantaneous optimal regenerative braking torque of the motor can be obtained. If the optimal regenerative braking torque is less than the commanded braking torque, only regenerative braking is applied. Otherwise, the motor is controlled to produce its optimal braking torque, and mechanical braking produces an additional braking torque to meet the commanded braking torque.

Analysis of the braking force distribution strategies Figure 11. Control logic of the instantaneous optimal regenerative braking control.

The partial derivative of the battery regenerative power for Te is ∂Pbat ðv, Te Þ =0 ∂Te

ð33Þ

Solving equation (33) and considering the range of Te in equation (25), the instantaneous optimal regenerative braking torque Te,opt of the PMSM in the EV can be deduced according to the efficiency model of the electric drive system, as shown in Figure 10. The battery powers and their partial derivatives for Te in the four areas can be expressed as Pbat ðv, Te Þ \ 0, Pbat ðv, Te Þ . 0, Pbat ðv, Te Þ . 0, Pbat ðv, Te Þ . 0,

∂Pbat ðv, Te Þ . 0, ∂Te ∂Pbat ðv, Te Þ . 0, ∂Te ∂Pbat ðv, Te Þ \ 0, ∂Te ∂Pbat ðv, Te Þ \ 0, ∂Te

inarea I inarea II inarea III in area IV

ð34Þ

Three different braking force distribution systems in the four-wheel-drive EV are analysed: the parallel braking system I (Figure 12(a)), the parallel braking system II (with large free travel) (Figure 12(b)) and the series braking system (Figure 12(c)). In the parallel braking system, the hydraulic pressures of the wheel cylinders have a fixed relationship with brake pedal operation. The parallel braking system I is easy to implement by adding the electric braking force to the conventional mechanical braking system. The parallel braking system II needs to modify the free travel of the brake pedal. When the brake pedal reaches the upper bound of the freedom stroke, the maximum rated electric braking force is applied. Then the electric brake maintains the maximum value, and the mechanical brake provides the remaining braking force. In the series braking system, the hydraulic pressures of the wheel cylinders are controlled freely without any influence on brake pedal operation. The electric brake can be decoupled from the mechanical brake, and instantaneous optimal regenerative braking control can be achieved. (There are different definitions for parallel


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Figure 12. Braking force distribution diagram in three different braking systems. (a) Parallel braking I; (b) Parallel braking II; (c) Series braking.

Figure 13. Braking electromagnetic torques in three different braking systems. (a) Parallel braking I (Front PMSM); (b) Parallel braking I (Rear PMSM); (c) Parallel braking II (Front PMSM); (d) Parallel braking II (Rear PMSM); (e) Series braking (Front PMSM); (f) Series braking (Rear PMSM). rpm: r/min; Req.: Required.

braking and series braking. The definitions in this paper are consistent with those employed by Gao et al.1, 3 and Kim et al.10)

The electric braking torques of the front PMSM and the rear PMSM for different commanded braking forces in three braking systems are shown in Figure 13(a) to (f)


10


Figure 14. Optimal electric braking torque interpretations in three different braking systems (a) Parallel braking I; (b) Parallel braking II; (c) Series braking. rpm: r/min.

respectively. The demand vehicle braking torques are 160 Nm, 320 Nm, 480 Nm, 640 Nm and 800 Nm respectively. The parallel braking system I has a structure such that the electric brake and the mechanical brake share the braking force with a fixed ratio (1:4). The parallel braking system II has a structure such that the electric brake provides the braking force in the required low-torque (less than 40 Nm for each PMSM) condition. If the required braking torque of the PMSM extends beyond 40 Nm, the remaining torque is supplemented by the mechanical brake. In the two parallel braking systems, the electric braking torque is decoupled from the vehicle speed. In the series braking system, according to the motor speed and the driver’s commanded torque, the traction motor provides the appropriate torque to recover the maximum instantaneous braking energy, which has been illustrated in the section on the instantaneous optimal regenerative braking torque calculated by the analytical model. At the same time, the mechanical brake must be controlled to meet the residual braking force command from the driver. The braking torque distribution between the electric brake and the mechanical brake in the series braking system is related to the vehicle speed.

According to the analysis above, the optimal electric braking torque interpretations of the brake pedal in three braking systems are shown in Figure 14. In the parallel braking systems, the electric braking torque is related only to the brake pedal value, as shown in Figure 14(a) and (b). In the series braking system, the electric braking torque is related not only to the brake pedal value but also to the vehicle speed, as shown in Figure 14(c). The premise of all the above analysis is that the battery can be charged. If the SOC value is high, the regenerative braking torque needs to be modified to adapt to the battery capacity. Further, it is also possible to add a resistance to the d.c. side of the inverter to consume the regenerative braking energy.

Simulation and experimental results Simulation analysis based on MATLAB/Simulink The EV used in the simulations and experiments is a four-wheel hub motor drive EV, as shown in Figure 15. The vehicle and battery parameters are shown in Table 1.


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Value

Rated phase voltage (V) Rated speed (r/min) Rated torque (Nm) Number of pole pairs Armature resistance (O) d-axis inductance (H) q-axis inductance (H) Magnet flux linkage (Wb) Iron consumption resistance (O)

21.6 500 30 23 0.031 7.6 3 1025 7.6 3 1025 0.0204 0.006v + 1.5

Figure 15. Four-wheel-drive electric vehicle.

Table 1. Parameters of the EV and battery. Vehicle parameter

Value

Kerb mass (kg) Radius (m) of the wheel Frontal area (m2) Dimensionless coefficient Rolling resistance coefficient Centroid height (m) Length between the automotive centroid and the centre-line of the front axle (m) Length between the automotive centroid and the centre-line of the rear axle (m) Voltage (V) of the battery Rated capacity (A h) of the battery

660 0.25 1.4 0.4 0.014 0.58 0.86

0.76

53 100

The parameters of the SPMSM are shown in Table 2. The EV model is built in MATLAB/Simulink to study the regenerative energy in different braking control strategies. The velocity profiles of the Economic Commission of Europe (ECE) urban driving cycle is illustrated in Figure 16. In the ECE urban driving cycle, the energy flow diagrams in the three braking control systems are shown in Figure 17(a), (b) and (c) respectively. The driving energy flows in the three braking systems are the same, while the braking energy flows are different. As the demand driving energy of the EV in the ECE urban driving cycle is constant (191.07 kJ), it is assumed to be 100%. The recovered energy capability of the three different braking systems can be compared from the recharged battery energy. In the parallel braking system I, as the ratio of the electric braking torque to the mechanical braking torque is 1:4, only 1.29% of the driving energy is recovered, and 30.84% of that is

Figure 16. ECE urban drive cycle.

consumed by the mechanical brake. In the parallel braking system II, the maximum electric braking torque (40 Nm) can provide about 0.1g deceleration, which basically meets the deceleration command in the ECE driving cycle. As a result, 22.70% of the driving energy is recovered, and only 2.83% of that is consumed by the mechanical brake. In the series braking system, the braking with optimal energy recovery can recover 23.07% of the driving energy. The mechanical brake consumes 3.42% of the driving energy, which is higher than that in the parallel braking system II. The reason is that the mechanical brake, instead of the electric brake, is used to avoid electric energy consumption in the power consumption braking area at a low speed in series braking.

Experimental results The motor and inverter efficiency model is verified first. Figure 18 shows the motor and inverter efficiency calculated using the analytical model and experimental data. It indicates that the motor and inverter efficiency calculated using analytical model can reflect the actual motor and inverter efficiency. As discussed in the third section, the motor is running in the regenerative braking mode when the braking torque demand is small. With increasing braking torque, uq keeps decreasing. If uq becomes negative, the motor is working in the power consumption braking mode. This mode transition is illustrated in Figure 19.


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Figure 17. Energy flow diagrams in the ECE urban drive cycle. (a) Parallel braking I; (b) Parallel braking II; (c) Series braking. EV: electric vehicle.

Figure 18. Motor and inverter efficiency map in braking mode. rpm: r/min.

Figure 19. Braking control of FOC at 150 r/min.

The motor is running at a speed of 150 r/min. With a steady increase in the braking torque from zero (iq decreases), the regenerative current first increases

(the battery current decreases) and then decrease back to zero. Then the braking torque keeps increasing, and the battery current becomes positive, which means that


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Figure 20. Test curves of maximum torque in regenerative braking mode and torque with maximum regenerative power.

the motor has changed from the regenerative braking mode to the power consumption braking mode. The maximum braking torque in the regeneration mode and the braking torque at the maximum regeneration power tested by experiment are in accordance with those calculated using the analytical model in the third

section in the low-torque area, as shown in Figure 20. With increasing electric braking torque, the stator resistance increases as the motor temperature increases. Therefore, there are some differences between the test results and the calculated values in the high-torque area. Figure 21 presents the q-axis current, the motor speed, the battery current and the d.c. voltage curves for each strategy during braking from 40 km/h to the stop condition. The initial SOC for the battery is about 0.6, and the battery can be charged and discharged. It can be seen that, for the series braking system, the input power and the related torque of electric motor are greater than for the other modes, leading to a higher energy saving. In Figure 21(a), the vehicle commanded braking torque in each hub motor is 40 Nm, which is the demarcation between the electric brake and the mechanical brake in the parallel braking system II. In this case, the regenerative current and the d.c. voltage in the parallel braking system II are almost the same as

Figure 21. Results in parallel and series braking systems. (a) 40Nm; (b) 80Nm; (c) 120Nm; (d) 160Nm. rpm: r/min.


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Figure 22. Relationship between regenerative braking efficiency and required motor braking torque.

those in the series braking system. The difference is that the braking torque in the parallel braking system II does not change and the braking torque in the series braking system decreases when the vehicle speed is very low. Therefore, the electric motor in the parallel braking II system runs in the power consumption braking mode and consumes energy to meet the braking torque command at a low speed. In Figure 21(b), (c) and (d), the required braking torques in each hub motor of the vehicle are 80 Nm, 120 Nm and 160 Nm respectively. In these cases, the regenerative currents and d.c. voltage in the series braking system are larger than those in the parallel braking system I and the parallel braking system II. The regenerative braking efficiencies in the two parallel braking systems and the series braking system are compared in different commanded braking torques during braking from 40 km/h to the stop condition, as shown in Figure 22. When the braking torque demanded in each hub motor is less than the maximum electric braking torque (40 Nm) in the parallel braking system II, the regenerative efficiency in the parallel braking system II is almost the same as that in the series braking system. The maximum efficiency in the parallel braking system II is 61.33% and that in the series braking system is 62.71% when the braking torque demanded is 40 Nm and the corresponding deceleration is about 0.1g. With increasing commanded braking torque, the regenerative efficiency in the parallel braking system II is significantly less than that in the series braking system. The percentage of saved energy in the parallel braking system I is the lowest as the mechanical braking system dissipates such a large amount of kinetic energy. This illustrates that optimal regenerative braking is achieved in the series braking system and that good regenerative braking can be obtained by changing the free travel of the mechanical brake in the parallel braking systems.

Conclusion In urban driving, a significant amount of energy is consumed by braking. The regeneration of the braking

energy has a significant impact on the driving range of an EV. The efficiency model of the electric drive system is set up to study the instantaneous optimal regenerative braking torque in a four-wheel-drive EV. The vehicle dynamic behaviour of braking in the EV is also considered. Then the optimal regenerative braking control strategies in two parallel braking systems and a series braking system are discussed. With the parallel braking approach by adjusting the free travel of brake pedal, which has a simple structure and is technically available, a significant amount of energy can be recovered. With the series braking approach, instantaneous optimal regenerative braking control can be achieved. The regenerative efficiency in the series braking system is higher than that in the parallel braking systems, especially in the high-torque area. Declaration of conflict of interest The authors declare no potential conflict of interest with respect to the research, authorship and/or publication of this article. Funding This work was supported by the US–China Clean Energy Research Collaboration: Collaboration on Cutting-Edge Technology Development of Electric Vehicles (Program of International S&T Cooperation) (grant number 2010DFA72760). References 1. Gao Y, Chen L and Ehsani M. Investigation of the effectiveness of regenerative braking for EV and HEV. SAE paper 1999-01-2910, 1999. 2. Ehsani M, Gao Y and Butler KL. Application of electrically peaking hybrid (ELPH) propulsion system to a full size passenger car with simulated design verification. IEEE Trans Veh Technol 1999; 48(6): 1779–1881. 3. Gao Y and Ehsani M. Electronic braking system of EV and HEV-integration of regenerative braking, automatic braking force control and ABS. SAE paper 2001-012478, 2001. 4. Wyczalk F A and Wang T. Regenerative braking concepts for electric vehicle – a primer. SAE paper 920648, 1992. 5. Panagiotidis M, Delagrammatikas G and Assanis D. Development and use of a regenerative braking model for a parallel hybrid electric vehicle. SAE paper 2000-010995, 2000. 6. Cikanek SR and Bailey KE. Regenerative braking system for a hybrid electric vehicle. In: 2002 American control conference, Anchorage, Alaska, USA, 8–10 May 2002, Vol 4, pp. 3129–3134. New York: IEEE. 7. Ye M, Qin D and Liu Z. Regenerative braking control strategy in mild hybrid electric vehicle equipped with automatic manual transmission. Chin J Mech Engng 2006; 42(10): 156–160. 8. Sangtarash F, Esfahanian V, Nehzati H, et al. Effect of different regenerative braking strategies on braking performance and fuel economy in a hybrid electric bus


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Engineering Engineers, Part D: Journal of Automobile

Engineering Engineers, Part D: Journal of Automobile

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