Dual-inverter control strategy for high-speed operation of EV induction motors

312 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 51, NO. 2, APRIL 2004

Dual-Inverter Control Strategy for High-SpeedOperation of EV Induction Motors

Junha Kim, Student Member, IEEE, Jinhwan Jung, Associate Member, IEEE, and Kwanghee Nam, Member, IEEE

Abstract—An integrated starter/alternator (ISA) is normallydesigned to have high pole structure (10–14 poles) for highstarting torque. However, its back electromotive force (EMF) atthe peak revolutions per minute should be less than its batteryvoltage for the power flow control. For example, the back-EMFof a 12-pole ISA should be 42 V at 6000 r/min. These types ofconflicting requirements lead to a nonclassical motor design thathas extremely large field-weakening range (8:1 10:1). In thispaper, we are considering the use of an induction machine insteadof a permanent synchronous machine. As an idea for solving thevoltage limit problem, two inverters are utilized with an objectiveof sharing the required voltage. The secondary inverter only takescare of the reactive voltage component that grows very fast inhigh-speed operation. Therefore, an extra voltage source is notrequired for the secondary inverter. Only a capacitor bank sufficesfor the secondary inverter.

Index Terms—Dual inverter, field-weakening operation, hybridelectric vehicle (HEV), induction motor, integrated starter/alter-nator (ISA), redundancy provision.

NOMENCLATURE

Stator voltage (current) vector.Rotor flux vector.Angle of .Angular frequency of .Slip angular frequency.Rotor speed.

-axis rotor flux in the rotor flux reference frame(RFRF) [15].

-axis voltage in the RFRF.-axis stator current in the RFRF.

Stator (rotor) resistance.Stator (rotor, mutual) inductance.Total leakage coefficient .Rotor time constant .Generated torque.Number of poles.

Manuscript received January 21, 2003; revised October 13, 2003. Abstractpublished on the Internet January 13, 2004.

J. Kim was with the Department of Electrical Engineering, Pohang Universityof Science and Technology, Pohang 790-784, Korea. He is now with Seoho Elec-tric Company, Ltd., Anayang 430-817, Korea (e-mail: [email protected]).

J. Jung was with the Department of Electrical Engineering, Pohang Universityof Science and Technology, Pohang 790-784, Korea. He is now with the Elec-tric Power Train Development Team, Advanced R&D Center, Hyundai MotorCompany, KyungKi-Do, Korea (e-mail: [email protected]).

K. Nam is with the Department of Electrical Engineering, PohangUniversity of Science and Technology, Pohang 790-784, Korea (e-mail:[email protected]).

Digital Object Identifier 10.1109/TIE.2004.825232

I. INTRODUCTION

THE power demand in a car grows steadily due to the in-crease in the electrical equipment and accessories. Today,

the electrical power demand ranges between 750 W–1 kW.However, in luxury cars in 2005–2010, the auxiliary electricpower requirement is expected to increase up to 6 kW [1]. Thisturns out to be one motivation to adopt a 42-V system.

An integrated starter/alternator (ISA) is a multifunctional in-tegrated device that functions as starting motor, generator, ortorque assistor to the combustion engine. The interior perma-nent-magnet (IPM) machine is used for an ISA due to its wideconstant power operating range, high efficiency, high torque tocurrent ratio, etc. [2]–[6]. However, the IPM machine for an ISAis specially designed for a very large range of field-weakeningoperation. Specifically, the rotor is designed so that it has a verylarge saliency ratio, i.e., the reluctance along the -axis flux pathis about 8–10 higher than that along the -axis flux path [5],[6]. This high saliency requirement often leads to unusual ma-chine work and an increase in cost.

An induction machine is a choice for the ISA because ofreliability, ruggedness, low maintenance, low cost, and abilityto operate in hostile environments. An induction machinewas used for a starter/alternator for hybrid electric vehicles inprevious work [7]–[9]. Miller et al. [7] compared an inductionmachine with a variable reluctance machine for the starter/al-ternator. Gale et al. [8] characterized the optimum efficiencyoperating points of an 8-kW hybrid electric vehicle (HEV)starter/alternator using a fuzzy logic controller for robust,automatic mapping. McCleer et al. [9] presented a nonlinearmagnetic model of a cage rotor induction machine for a com-bined starter/alternator, and compared the calculated resultswith the measured ones. In references [7]–[9], an 8-kW 12-poleinduction machine was used for wide constant power operation,and mechanical contactors were used to give reconfigurablewinding arrangements. The winding was a series connectionfor low-speed cranking operation (corner speed at 250 r/min),while it was reconfigured to be a parallel connection (cornerspeed at 750 r/min) for generator mode. Note that constantpower range is only 2.5:1 with a normal induction motor [10],and a higher leakage inductance makes the constant powerrange narrower [11].

In this paper, an induction machine has been considered as acandidate for a combined starter/alternator machine for hybridelectric vehicles. With the objective of enlarging the constantpower region up to 10:1, a modified dual-inverter system wasconsidered as shown in Fig. 3. The other ends of phase wind-ings are connected to the secondary inverter instead of being

0278-0046/04$20.00 © 2004 IEEE

KIM et al.: DUAL-INVERTER CONTROL STRATEGY FOR HIGH-SPEED OPERATION OF EV INDUCTION MOTORS 313

Fig. 1. Equivalent circuit of an induction motor.

TABLE ILIST OF THE MACHINE PARAMETERS

shorted. The dual-inverter system was studied previously in [12]and [13]. However, the main difference of this work is that nopower source is connected in the dc-link of the secondary in-verter, i.e., it merely has a capacitor bank. The dual-invertersystem also provides a redundancy in emergency case if we addsome bypass switches.

II. MOTIVATION FOR DUAL INVERTER

We are considering the use of an induction machine for anISA. Since the ISA is mounted on the flywheel of the combus-tion engine, the speed goes up to 6000 r/min. The problem posedhere is to control the power flow between the induction machineand the 150-V battery at such a high speed. As the speed in-creases, a higher voltage source is required for current controlsince the back EMF and the reactive voltage over the leakageinductance grows with higher electric angular frequency. How-ever, since the voltage is fixed by the battery around 150 V, it isnot an easy task to control a high-pole machine at a high speed.For an induction machine, it is also difficult to obtain a largefield-weakening range.

The induction motor equivalent circuit is shown in Fig. 1. Thephasor equations of induction motors are described by

(1)

(2)

(3)

where , , , are the phasors of source voltage, statorcurrent, rotor current, and rotor flux, respectively, and ,are the projections of onto and , respectively [14].

As the electric angular speed increases, the reactive voltage, as well as the back EMF grows. In

the following, we describe in detail how far the reactive voltagegrows.

Utilizing the parameters of a four-pole induction motor listedin Table I, we obtain three phasor diagrams at the base speed

Fig. 2. Phasor diagrams showing the proportions of back EMF and couplingvoltage as speed increases: (a) ! = ! = 314 rad=s (b) ! = ! =

926 rad=s, and (c) ! = 1464 rad=s.

rad s, the speed rad swhere the voltage limit and current limit intersect, and

rad s, as shown in Fig. 2. In terms of rotor speeds,, and rad s correspond to 1385, 3927,

and 6500 r/min respectively. Here, the flux level is chosen suchthat the maximum torque [11] is obtained within the limits ofvoltage and current in the field-weakening region. Note that thevoltage is orthogonal to the stator current , makinga reactive power. The reactive component is small ascompared to the back EMF at the base speed. However, as thespeed increases, the reactive component becomes larger andlarger, and finally it exceeds the magnitude of the back EMF.

Comparing the phasors in Fig. 2(b) and (c), one can observethat the magnitude of the flux, reduces significantly, whilethe reactive voltage, and back EMF,remain constant after exceeds the boundary electrical speed,

rad s. Note also that phasors , ,and constitute an approximate right-angledisosceles triangle. Regarding it as a right-angled isosceles tri-angle, the reactive voltage term takes about 70% of the sourcevoltage after the boundary electrical speed . Therefore, if


Fig. 3. Dual-inverter system: Inverter 2 carries only capacitor banks.

Fig. 4. Basic idea showing the dual-inverter control scheme: Inverter 2 onlytakes care of the reactive voltage component.

the reactive voltage component is handled by another voltagesource, then it remains the back EMF for the battery to cover,i.e., the voltage that should be supplied by the battery reducescorrespondingly by about 30%.

In order to make the reactive voltage component handled by aseparate voltage source, we utilize a dual-inverter system shownin Fig. 3. In the dual-inverter system, two inverters are connectedat both ends of stator windings. The dual-inverter system pro-posed in this paper is different from the previous works sincethe second inverter does not have any voltage source other thanthe capacitor bank. The basic operation idea is to let the secondinverter handle only the reactive power. Note further that capac-itors suffice to handle the reactive power. If the reactive voltagepart is covered by the second inverter, its effect is equal to raisingthe dc-link voltage level of the primary inverter by about 30%.In other words, this method has the effect of increasing therequired battery voltage level without utilizing an additionalvoltage source. This is the main benefit of the proposed dual-in-verter operation strategy.

Roles of inverters are shown schematically in Fig. 4. The sec-ondary inverter (Inverter 2) produces the reactive voltage termwhich cancels out . The primary inverter (Inverter 1)can take care of the remaining components. By dividing the

roles of each inverter, we can achieve a wide speed operationrange under a given voltage limit.

III. DUAL INVERTER SYSTEM MODEL

A. Induction Motor

In the rotor-flux-oriented frame, the dynamics of the induc-tion motor are described as follows [15]:

(4)

(5)

(6)

(7)

(8)

where is a differential operator, and the superscript“ ” implies a variable in the rotor flux oriented frame.

B. Dynamic Model of Dual-Inverter System

It follows from Fig. 3 that the voltage equations for the dual-inverter system are expressed as

(9)

(10)

(11)

where , , are the flux linkages of , , windings,respectively. Note that ,

, and . Thus, adding up(9)–(11), we have

Assume that the terminal voltages of Inverters 1 and 2 are sym-metrical such that , and

. Then it follows that , anddue to the impedance symmetry of the induction motor. Thus,

we have . It follows obviously that and are virtually


Fig. 5. Equivalent circuit of dual-inverter system in the stator reference frame.

equipotential. Hence, from (9)–(11), we obtain a voltage equa-tion of the dual-inverter system such that

(12)

where

Note that , represent voltage vectors supplied by In-verter 1 and Inverter 2, respectively, and that

, since and .Thus, the voltage equation (12) is rewritten as

(13)

Based on (13), we obtain an equivalent circuit as shown in Fig. 5.We choose the axis to be aligned with the rotor flux and

denote by , , , –axes voltages of Inverters 1and 2, respectively. With definitions ,

, we obtain from (4) and (5)

(14)

(15)

IV. PROPOSED CURRENT CONTROLLERS

A. Inverter 1

Reactive voltage components over the total leakage induc-tance appear as ( , ) between , -axesdynamics, and Inverter 2 is supposed to supply exactly the samevoltage to cancel them out. Hence, the reactive voltage compo-nents do not appear for the voltage equations of Inverter 1

(16)

(17)

We choose -axis current command and –axesvoltage commands ( ) such that

(18)

(19)

(20)

where , are proportional and integral gains of the rotorflux proportional–integral (PI) regulator, respectively, andis a -axis current command, and , are proportional andintegral gains of the current controller, respectively.

B. Inverter 2

The main job of Inverter 2 is to cancel out the coupling termsby generating - voltages such that

(21)

(22)

This coupling voltage cancellation leads to the generation ofreactive power. However, without keeping a certain level ofdc-link voltage, the generation of reactive power is impossible.Hence, another scope in the role of Inverter 2 is to maintainits dc-link voltage level. However, increasing or decreasingthe dc-link voltage requires a considerable power flow. Forthe proper operation of Inverter 2, the dc-link voltage must beregulated to be sufficiently high so that Inverter 2 supplies therequired reactive voltage components. The dc-link voltage canbe regulated by a PI regulator

(23)

where is a dc-link voltage command of Inverter 2, and ,are proportional and integral gains respectively. For the reg-

ulation of the dc-link level, real power must be drawn from orrelieved to the battery through motor winding. Such a powerflow is achieved through a voltage component which is alignedto the stator current vector . In order to align the voltage com-ponent to the current vector, the – partitioning ratio must bethe same as , i.e., we need to choose the voltage componentcorresponding to real power such that

(24)

(25)

Note that is a scalar determined from (23), and ( )has the same proportionality as . The method of making thereal voltage component through paralleling to is shown inFig. 6.


Fig. 6. Voltage vector (v ; v ) required for dc-link voltage regulation ofInverter 2 is in phase with current vector (i ; i ).

Adding reactive voltage components (21) and (22) to realones (24) and (25), respectively, we obtain voltage commandsof Inverter 2 such that

(26)

(27)

Note that during the initialization period, capacitors are chargedby the real power flow. However, once the dc-link voltageis regulated at a setting level , only reactive componentflows.

C. Control Block Diagram

Fig. 7 shows an overall control block diagram of the proposeddual-inverter control strategy. The rotor flux controller and –current controller are the same as the conventional single in-verter case with the exception of reactive voltage cancellationby Inverter 2. Thus, Inverter 1 voltage includes the output ofcurrent controller as well as back EMF. After measuring ofInverter 1 and calculating the angular frequency , the rotorflux command is synthesized according to (30) and (31).Note that the angular frequency is calculated by adding themeasured rotor speed to the calculated slip angular frequency

based on (7), i.e., . Inverter 2 voltage in-cludes the reactive voltage compensation terms (21) and (22)and dc-link voltage regulating terms (24) and (25), which areillustrated in reactive voltage compensator and dc-link voltageregulator, respectively.

V. TORQUE–POWER ENHANCEMENT IN THE

FIELD-WEAKENING REGION

The reactive voltage cancellation by Inverter 2 makes the In-verter 1 free from the reactive voltage. Thus, the whole Inverter1 output voltage is allocated to develop stator current againstback EMF. On the other hand, in the conventional case, the in-verter output voltage must cover back EMF, as well as the reac-tive voltage.

We describe how the rotor flux level is chosen in the pro-posed scheme. We denote by the maximum voltage ofInverter 1, which is limited below . Thus, the outputvoltage , of Inverter 1 satisfies

(28)

Neglecting the voltage drops on the stator resistance in thefield-weakening region, it follows from (16) and (17), and (28)that in the steady state

(29)

Solving (29) for and replacing by a rated rotorflux , we obtain equations between the base frequency

and flux reference such that

(30)

(31)

where is the frequency where the field weakening starts.Note from (6) that in the steady state. Thus, theinequality (29) is rewritten as

(32)

Note also that

(33)

where is the upper limit of the stator current. It followsfrom (8), (32) and (33) that the maximum torque and themaximum output power are obtained such that

(34)

(35)

The approximations are made with the assumptions thatand in the field weak-

ening region. Equations (34) and (35) tell us that the maximumtorque is approximately proportional to , and that themaximum power is approximately constant maintaining unitypower factor throughout a whole field-weakening region. It isthe great advantage of the proposed scheme that the maximumoutput power remains constant.


Fig. 7. Overall control block diagram with current controllers, flux regulator, reactive voltage compensator and dc-link voltage regulator of Inverter 2.

Fig. 8. Redundancy provision in case that Inverter 1 fails.

VI. PRACTICAL CONSIDERATIONS

A. Selection of Dc-Link Voltage of Inverter 2

Obviously, dc-link voltage of Inverter 2 must satisfy

(36)

where and are the maximum angular frequencyof the rotor flux and maximum rotor speed, respectively. In-equality (36) tells us that a high is required whenis large, and/or leakage inductance is large. Thus, takinginto consideration the surge voltage rating of motor and insu-

lated gate bipolar transistor (IGBT) voltage rating, mustbe selected with certain limits on and .

B. Redundancy Provision

Fig. 8 illustrates how the dual-inverter system enhances theredundancy provision in an emergency case where Inverter 1fails. Inverter 1 can be disconnected from the motor and batterysource by some bypass switches such as magnetic contactors.Then, the dc-link terminals of Inverter 2 are connected to thebattery, and the disconnected motor terminals are shorted. Next,the motor is driven by Inverter 2, and its operation is the sameas in the conventional case. A similar procedure can be takenwhen Inverter 2 fails.


Fig. 9. Simulation results: rotor flux (� ), current magnitude (ki k), torque(T ), and mechanical power P versus rotor speed (! ) when the speedcommand changes from 0 to 4.5 p.u. I = 31:8 A, V = 150 V, andV = 320 V.

VII. SIMULATION AND EXPERIMENTAL RESULTS

Table I shows the parameters of the induction motor used inour experiment. The parameters are obtained from either name-plate or a locked and no-load test. That induction motor is notan ISA operating under a 42-V dc source, nor a motor for hybridvehicle, but an induction motor. According to the design valueof the motor, dc-link voltage should be 245-V. However, to makethe experimental environments as close as possible to those ofhybrid vehicles, we choose 150-V for dc-link voltage of In-verter 1. Then, phase voltage is equal to 86.6 V ( V).Hence, from , the corresponding statorflux linkage for 50 Hz is given by 0.27 Wb. From

, the rotor flux level is given by 0.235 Wb.In computer simulation, C-language is used for programming

the Runge–Kutta fourth-order method and a pulsewidth-modu-lation (PWM) voltage pattern. We set the switching frequencyat 5 kHz. In both the simulation and the experiment, the cur-rent control routine, rotor flux regulation routine, and speedcontrol routine were refreshed every 200, 800, and 800 s, re-spectively. Simulation and experimental environments are thesame except that 3- s dead time is involved only in the ex-periment. An 1800- F capacitor was used in the dc-link of In-verter 2. In the experiment, a diode rectifier with a capacitorbank was used instead of a battery. In both the simulation andthe experiment, stator current limit is set A.As for the dc-link voltage of Inverter 2, we choose

V V to accommodate thereactive voltage at 6500 r/min ( rad s ) according to (36).

Fig. 9 shows the simulation results of rotor flux , currentmagnitude , torque , and mechanical power versus

rotor speed when the speed command changes from 0 to4.5 p.u. It follows from the inequality (36), V, and

A that the maximum operating angular frequencyguaranteeing the maximum output power (35) is approximatedas rad s. Note that

rad s approximately corresponds to 6970 r/mindue to the presence of slip frequency as much as 247 rad/s. Withthe conventional scheme, stator current starts to decrease at thetransition point ( p.u.) due to the voltage limit. Thetransition point is low for the low V. However, itcan be increased to p.u. with V. Notethat, with the conventional scheme, the magnitude of current iskept constant only up to p.u., and that mechanicaloutput power decreases as the power factor and the statorcurrent decreases. By contrast, with the proposed method, themechanical output power constant is kept constant up to 4.5 p.u.,as predicted by (35).

Fig. 10 shows the experimental results of rotor speed ,rotor flux , torque , electrical power , stator current,maximum inverter voltage , and magnitude of motorphase voltages , when the speed command changesstepwise from 0 to 6500 r/min. Note that the motor phase volt-ages , reach approximately to the maximum invertervoltage in both cases as soon as reaches1 p.u., i.e., , . This states that100% of dc-link voltage is utilized, i.e., there is no extra voltageto increase the speed. Hence, the voltage margin is gainedthrough weakening the field. In the plot of dc-link voltageshown in the last row of Fig. 10, a slight voltage drop wasmonitored. However, it appears that switch on-drop and internalresistance of the rectifier are the reasons. In the acceleration pe-riod, and show that the besteffort is performed in both cases, but the acceleration periodis much smaller with the proposed method. Electrical power

is shown in the fourth row of Fig. 10. If we ne-glect the iron loss and the copper loss, the electrical power isabout the same as the mechanical power .The result shows that the proposed method delivers higherpower in shorter acceleration period and that a faster speedresponse is achieved with higher electrical power. Thus, pow-ering in a high-speed range is more effective with the proposedmethod. The theoretical maximum power value based on (35)is approximately 4.0 kW, while the experimental result is about3.7 kW. As with the simulation results shown in Fig. 10, theproposed method is able to keep the electrical output powerconstant up to 6500 r/min with V, whereas with theconventional method [Fig. 10(a)] the electrical power decreasesas the speed increases.

Fig. 11 shows the experimental results of rotor speed , cur-rent magnitude , maximum voltage of the Inverter 2 ,and output voltage magnitude of Inverter 2 when thespeed command changes stepwise from 0 to 6500 r/min. Notefrom the bottom trace of Fig. 11 that the reactive voltage magni-tude of Inverter 2 is proportional to the rotor speed timesthe the current magnitude, i.e., , while dc-linkvoltage is kept constant 320 V. Once the speed reaches 6500r/min, drops significantly. Therefore, the output voltage

of Inverter 2 also drops.


Fig. 10. Experimental results: rotor speed! , rotor flux (� ), torque (T ), electrical powerP , stator current, maximum inverter voltage (v ), and magnitudeof motor phase voltages (kv k, kv k) when the speed command changes stepwise from 0 to 6500 r/min (� 4:33 � ! ). (a) Conventional method underI = 31:8 A, V = 156 V (b) Proposed method under I = 31:8 A, V = 144 V and V = 320 V.

Fig. 11. Experimental results showing that output voltage magnitudeof Inverter 2 (kv k) is proportional to the rotor speed times the currentmagnitude, i.e., kv k / ! � ki k. The speed command changes stepwisefrom 0 to 6500 r/min (= 4:33 p.u.).

Fig. 12 shows the initial boosting stage of dc-link voltage ( )of Inverter 2. It increases to a normal value 320 V after building

Fig. 12. Experimental results showing dc-link voltage (V ) profile ofInverter 2 at the initial stage. V reaches the desired level after the rotor fluxis built up.

up the rotor flux at the start. To prevent the power surge fromthe voltage source such as the battery, the voltage command isprogrammed to change slowly from 0 to the setting value.


VIII. CONCLUSION

A new dual-inverter control strategy for high-speed operationof EV induction motors has been proposed. The reactive voltagecomponent, which becomes large in the high-speed region iscompensated by Inverter 2. Since Inverter 2 takes care of onlyreactive power, its dc-link does not need to be connected to an-other dc voltage source. Capacitors alone will suit the purpose.By sharing the voltage requirements, the proposed dual-inverterscheme enables the induction motor to have a wider constantpower operation range.

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Junha Kim (S’97) was born in Uljin, Korea, in 1970.He received the B.S., M.S., and Ph.D. degrees in elec-tronic and electrical engineering from Pohang Uni-versity of Science and Technology, Pohang, Korea,in 1997, 1999, and 2003, respectively.

He is currently with Seoho Electric Company,Ltd., Anyang, Korea. His research interests are acmotor control, electric vehicle systems, and PWMconverters.

Jinhwan Jung (S’95–A’99) was born in Seoul,Korea, in 1972. He received the B.S. degree fromPusan National University, Pusan, Korea, in 1994,and the M.S. and Ph.D. degrees from Pohang Uni-versity of Science and Technology, Pohang, Korea,in 1996 and 1999, respectively, all in electricalengineering.

He is currently a Senior Research Engineerwith the Electric Power Train Development Team,Advanced R&D Center, Hyundai Motor Company,KyungKi-Do, Korea. His main interests are ac

motor control for high-speed operation, EV and HEV motor drives, and powerconverter/inverter systems.

Dr. Jung received a Best Paper Award from the IEEE Industrial ElectronicsSociety in 2000.

Kwanghee Nam (S’83–M’86) was born in Seoul,Korea, in 1956. He received the B.S. and M.S.degrees in chemical technology and control andinstrumentation engineering from Seoul NationalUniversity, Seoul, Korea, in 1980 and 1982,respectively, and the M.A. and Ph.D. degrees inmathematics and electrical engineering from theUniversity of Texas at Austin, in 1986.

He is currently a Professor in the Department ofElectrical Engineering, Pohang University of Sci-ence and Technology (POSTECH), Pohang, Korea.

He served as Director of the POSTECH Information Research Laboratoriesand Dean of the Graduate School of Information Technology from 1998 to2000. His main interests are ac motor control, power converters, computernetworks, and nonlinear systems analysis.

Prof. Nam received a Best Paper Award from the IEEE TRANSACTIONS ON

INDUSTRIAL ELECTRONICS in 2000.

Dual-inverter control strategy for high-speed operation of EV induction motors

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