A Novel Vector Control Hysteresis Current Controller for Induction Motor Drives

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IEEE Transactions on Energy Conversion, Vol. 9, No . 2, June 1994 297

A NOVEL VECTOR CONTROL HYSTERESIS CURRENT CONTROLLERFOR INDUCTION MOTOR DRIVES

Ting-Yu C hang, Kuie-Lin Lo, and Ching-Tsai Pan, Menber, IEEE

DEPARTMENT OF ELECTRICAL ENGINEERING

NATIONAL TSING HUA U NIVERSITYHSINCHU, 300, TAIWAN, R.0.Cw-n this paper, a novel vector con trol hysteresis cur-rent controller for induction motor drives is proposed. Coor-dination of three phase switches is made in the d-q phaseplane. In addition to the current error, information of thecurrent erro r derivative is further employed so that one can

take full advantages of adding the zero voltage vector forreducing the switching frequency. A simple hardware imple-

mentation is also proposed such that merits of the conven-tional hysteresis current controller can still be kept.

Theoretical basis and some simulation and experimentalresults are also covered in this context.

Ke-wo rds; vector control, hysteresis current controller,induction motor drive

Due to the advances of power electronics and the vector

control technology induction motor drives have becomemore and m ore popular and gradually take the place of the

dc motor drives [1-31. Basically, to achieve quick response, acurrent controller is usually preferred to follow the current

command of the drive for generating the desired electromag-netic torque directly. Although, various current controllers

have been proposed [4-131, however, considering easy

implementation, quick response, maximum current limit andinsensitive to load parameter variations, the three-

independent hysteresis current controller [5 ] is a rather pop-ular one. Nevertheless, due to lack of coordination among

individual hysteresis controllers of three phases, very highswitching frequency at low er modulation index may happen.

This will of course increase the switching loss. In addition,the current e rror is not strictly limited. Double current errormagnitude permitted by one hysteresis controller may occur[4]. Recently Kazmierkowski et al. [13] have proposed a

93 SM 5 53-8 EC A paper recommended and approvedby the IEEE Electric Machinery Committee o f theIEEE Power Engineering Society for presentation

at the IEEE/PES 1993 Summer Meeting, Vancouver,B.C., Canada, July 18-22, 1993. Manuscript

submitted December 23, 1993; made available for

printing May 3, 1993.

three-level hysteresis strategy to apply the zero vo ltage vec-tor for reducing the switching frequency. By transforminginto the d-q domain, coordination of the three phaseswitches can be considered. Only two hysteresis controllers

are required for three phases. In addition, a zero voltage vec-

tor can be applied while encountering a zero current error toreduce the switching frequency. However, up to now , there

is not any hysteresis controller which has used the informa-tion of the derivative of the current error [4-131. Since the

command signal and the motor back emf may greatlyinfluence the current control under some conditions, if some

information of the derivative of the current error is also

available, then one would know the changing tendency ofthe current error. Therefore, one can take full advantage ofthe zero voltage vector to reduce the switching frequency

greatly. In this paper, a no vel hysteresis current contro ller isproposed by further employing the derivative sign of the

current error such that full advantage of the zero voltagevector canbe taken for reducing the sw itching loss. A simplehardware implementation is also proposed w ithout requiringadditional calculations such that advantages of the original

hysteresis controller can still be kept. Theoretic basis andsome experimental results of the proposed method aredetailed in the following context.

BASIC PRINCIPLE

Consider the basic voltage source inverter circuit as

shown in Fig. 1where each phase of the induction motor hasbeen represented as a series RL impedance together with its

back emf. The neutral point o f the indu ction motor circuit isassumed isolated. The induction motor stator voltage can be

controlled by casting the in verter switches to the positive o rthe negative dc voltage source terminals. Mathematically,the terminal voltage of the inverter can be written as

V , = S , * V d C

I/, = S b * V d C

I/, = S c* V , ,

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298

Iv0

I I I I

Ivc EcmJ

Due to the balance condition, the third equation o f phase 'I bI' can be obtained from equations (7)nd (8) as

Fig-1 A current for induction For convenien t analysis, define the fo llowing space vectors:motor drives.

~ ~ ~ ( i n + a i ~ + a 2 i c ) - ~ d + ~ ~ q10)

~ = & v n + a v , + a 2 v c ) - v d +v, ( 1 1 )

where S ,

sponding to each phase, and

S, an d S , re the switching functions corre-

S , S , S = 1 when connected to+ I/ terminal (4) ~ = 1 / ~ ( E n , + U E b m + a 2 E c m ) w E d m +j E , ,

0 when connected to - I/ ,terminal

(12)

From Fig. 1, it is straightforward to use he K.V.L to obtainthe following equations

where

-1 2 1 1-a = e

di di

dt dt2 L " + L I = - 2Rtn Ri, ( V , - V , ) - ( E n m E b m )

(')From equations (1)-(3) and (l l) , for various switching pat-

terns the inverter output voltage spa ce vector can begiven as

follows:d i n d i

d t d tL - + 2L2 = - R i , - 2 R i , + (V , V , ) - ( E , , - E , , )

( 6 ) v ; ( k ) =V , ( k ) + j V q ( k ) $ V d c ~ - " k - 1 , 2 , . . .6

where the three phase circuit is assumed to be balanced and0 k = 0 , 7

(13)

R

L

E - , E b m . E - :motor back em fs of the three phases

: he equivalen t stator resistance of the mo tor

: he equivalent stator inductan ce of the motorThe above six nonzero space voltage vectors and two zerospace voltage vectors are quite well known in space vector

based inverter control. For practical implementation, theabove space vector can be represented by the real (d-axis)

Table 1 shows the switching states and the correspondingspace vectors. From equations (7)-(9), and equations(10)-(13), one can obtain the following equations

From equations (5 ) and (6) One can Obtain the and imaginary (q-axis) parts, separately. For reference,form

d i n R 1

d t L 3 LI - - L a + - { z ( v a - ( v b - E b m ) - ( V c - E c m ) }

(7)

d i , 1- - R i , +- z ( V , E~, , , )- ( v b E bm ) - (I/, - E,,) }d t L 3 L d i , R 1

- = - - i q + - ( V q ( k ) - E q m ) (15)dt L L




299

concept is of the main concem if the merits of a hysteresisable 1. The inverter switching states and the corre spn d-ing voltage space vectors.

Now consider the current errors of both axes:

E , = i i - i d

E q = i i - i q

where i , i an d e d , q are the real and imaginary current

comm ands and errors, respectively. Thus it is simple to con-sider the coordination of three phase switches and only twohysteresis controllers are required. From equations (14)-(17),one can obtain the derivatives of the current errors as fol-lows:

controller are to be maintained.Qualitatively, one can see from equations (18) and (19)

that as long as a nonzero inverter voltage is applied to themotor, the current error de rivatives will be dominated by thenonzero space vector voltage, such that the motor currentcan track the command signal. On the other hand, if a zerovoltage vector is applied, equations (18) and (19) become

Hence, the current e m r derivatives will be mainlyinfluenced by the current comm and and the mo tor back emf.Under very low speed, the command signal may take themain decision role of the derivative sign while at high motorspeed, the motor back emf will take the major role. There-fore, one can see from equations (20) and (21) that during

the small time interval allowed by the original assignedhysteresis loop band, by adding a zero voltage vector, onecan observe the total effect of the command signal and theback emf. Depending on the signs of the error and the errorderivatives, the current error m agnitude may either increaseor decrease. Therefor, to reduce the switching frequency,one can consider adding a zero voltage vector whenever a

( 6 ,

(

From equations (18) and (19), one can see that the d and qaxes stator current errors of the indu ction motor have a time

constant of: and are influenced hy the current commands,

derivatives of the current commands, the motor back emfand the inverter voltage vector. Since computation of thederivatives are susceptible to noise and also very time-consuming, direct numerical calculation of the error deriv-atives is difficult and m ay no t be feasible for low speed, low

accuracy processors. Therefore, implementation of the above

hysteresis band is hit. If the zero voltage vector is added atthe correct state, e.g., with p ositive error and negative errorderivative, the current error w ill decrease and rem ains insidethe band. If a zero voltage vector is not added at the correct

state, then the error m agnitude will continue increasing andthus will be outside the hysteresis bound. Hence, in thispaper, another hysteresis loop controller using a little largerhysteresis band than that of the original is employed to

detect the total influence of the command signal and themotor back emf. Basically, it is equivalent to detecting thesigns of the current error derivatives.

THE PROPOSED H YSTERESIS CURRENT

Based on the prev ious principle, a new hysteresis cur-

rent controller employing further information of the errorderivative is proposed and shown in Fig. 2. Two errorsensors and two error derivative sensors are required for tak-ing full advantage of adding a zero voltage vector. Amongthem two hysteresis controller, namely D and Q, are used totrack the current comm ands, >,and ii,respectively and limit

the current error within the specified bounds. The errorderivative sensors are realized by two other hysteresis con-trollers with wider bounds, namely D S and Q S , whichdetect and record the signs of the d-axis and q-axis error




300

Table 2. The switching function table of the prop osed hys-teresis current controller.

r

I

Fi g2 Schematic diagram of the proposed hysteresis cur-rent controller for induction motor drives.

ROM

for

switchingtable

sw i t ches

Fig3 The hardware circuit of the proposed hysteresiscurrent controller.

derivatives, respectively. Fig. 3 shows the simple hardwarecircuit of the pro posed hysteresis current controller. Only afew general purpose operational amplifiers (TLO74N), com -paratols (LM301) are used to construct the proposed hyster-esis current controller. Initially, the signs of the current errorderivatives are not known. One can arbitrarily se t one sign.Whenever the outer hysteresis bounds are hit due to signchanges of deriva tives, a proper nonzero space voltage vec-

tor is always triggered to red uce the error magnitude and thecorrect derivative sign is then recorded. Hence, due to

automatic updating of the sign of the error derivative of theproposed current controller, the initial signs of D S and QSare not that important.

To reduce the sw itching frequency , zero voltage vectorsare considered to be added only w hen inner bounds are hit.

How ever, only under certain conditions can the zero voltage

be added with benefit. As an example, consider the case

when E~ s positive. In this case, if its derivative is negativethen one can con sider adding a zero voltage vector. Further-

more, to consider coordination of three phases, or both d-

I

0 0.002 0.004 0.000 0.008 0.01 0.012 0.014 0.010 0.018-2.6 1

see.

Fig.4 The simulation results of the d-axis stator currentand the corresponding inner and outer bounds of thehysteresis lo o p.

-0.1 --1 -

-1.6 -

- 2 -I

-Z.6 I C I0 0.00‘2 0.004 0.000 0.000 0.01 0.019 0.014 0.010 0.0lII

sec.

Fig.5 The simulation results of the q-axis stator currentand the corresponding inner and outer bounds of thehysteresis loops.

and q-axis components equivalently, one must also considerE $nd it s derivative sign simultaneously to determine

whether to add a zero voltage vector or not. The theoreticalbasis of deciding the inverter switching pattern has beendetailed in the previous section and will not be repeated.




301

bP.

0 0.002 0.004 0.008 0.000 0.01 19 0.014 0.018 0.018sec.

0 OOOD 0004 0008 0000 00 1 0 012 0.014 0.016 0.018sec.

(a)

Nunber

Fi gd The voltage vector ( V(k) ) distribution of the pro-posed hysteresis current controller.

120 1 11 1

100 -

80 -

eo -

' I

I

0 0 008 0.004 0.008 0 OU U 0 01 0.019 0.014 0.018 E

sec.

Fig.7 The voltage vector ( V(k) ) distribution of the con-

ventional three independent hysteresis current con-troller.

Table 2 shows the switching function table of the proposed

hysteresis current controller. An RO M is used for implemen-tation as shown in Fig. 3. One can see the simplicity of the

hardware implementation of the proposed controller.Moreover, merits of the conventional hysteresis controllers

are still maintaine d.

SOME SIMULATION AND EXPERIMENTALRESULTS

To verify the validity of the proposed current controller,firstly computer simulations are made and then a hardwarecircuit is constructed fo r testing.

Suppose that a sinusoidal current command of 2A isapplied to the proposed hysteresis current controller. The

inverter is fed with a dc voltage source of 80 V and the innerand outer bounds of D, Q and DS ,QS are, for clarity, set to

0.2 A an d 0.3 A, respectively. The per-phase inductionmotor model referred to the stator reference fram e is a series€U, ircuit, with R= l . l Q L=14 mH, in series with a backemf of 20 V. Figs 4 an d 5 how s the simulation results of the

' I 8sec,

@)F ig s (a)The 'la'' phase current waveform of the proposed

hysteresis current controller.@)The corresponding total switching number dur-ing the simulation period.

d- and q-axis stator currents as well as the corresponding

inner and outer hysteresis bounds. One can see clearly A, B,C an d D points where sign changes of the derivatives occur.This agrees very well with the previous theoretical basis.On e does no t need o calculate the derivative values. For be t-

ter view of the situation of adding zero voltage v ectors, Fig.

6 shows the voltage vector distributions, V(k), of the above

case.As a com parison, Fig. 7 also shows the voltage vectordistribution of a conventional three independent hysteresiscurrent controller. It is seen that the zero voltage vector is

distributed more uniformly in the proposed current control-ler. In addition, Figs. 8 an d 9 also shows the "a" phase cur-rent waveform and the corresponding switching n umbers ofboth current controllers. It is seen that, compared with thethree independent hysteresis current controller, the proposedone can achieve approximately 60 percent reduction in the

total switching number.Next consider some experimental results. A hardware

circuit as shown in Fig. 3 is constructed and a laboratory

three phase induction motor of 1.1 Hp is used. The motorparameters are J = 0.2K (I- m * , tator leakage inductance




302

' I

1 J0 0.009 0.004 0.006 0.008 0.01 0.019 0.014 0.016 0.018

80.2.

(b)F ig 9 (a)The "att phase current waveform of the conven-

tional three independent hysteresis current control-ler.@)The corresponding total switching number

during the simulation period.

I, = 14mH, mutual inductance M = 1 3 6 m H , and the sta-

tor resistance R , - 1ll . Fig. 10 shows the tracking trajec-

tory of the proposed current controller in the d-q phaseplane following a current command signal of 2 A. Th e

steady state trajectory are also shown in the same figure forreference. Fig. 11 shows the recorded "a" phase stator cur-rent as well as its spectrum. The resulting waveform inFig.11 contains only little harmonic which is very weak

compared with the fundamental component. One can see

that the output current waveform is not affected significantly

by adding the o uter hysteresis controllers.

@)Fig.10 The tracking trajectory of the proposed cu rrent con-troller for a command input from zero state. (a)starting (b) steady state.

6 . 0 0 0 4 .

C T I >

I I I I I I I

0 . 0 1 0 0 .oms

2 0 . 0

-S( T I )

.,

- 2 1 . 7

H:HZV:LOS HR6

-40.0

0 . 0 0 0 0 . 1 6 5 1 . 0 0 0KH r

@)Fig.11 (a)Wav eform of the "a" phase stator current.

@)The corresponding spectrum.




303

Tine-Yu Chang was bom in Kaoh-

siung, Taiwan , Republic of Ch ina, inNovember 1963. He received the

Diploma of Electrical Engineeringfrom N ational Kaohsiung Institute of

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support

by the N ational Science Council of R.O.C. under contactnumber NSC 81-0404-E007-541.

tIREFERENCES

T. A. L i p , "Recent progress in the development of

solid-state ac moto r drives," IEEE Trans., Power Elec-tronics,vol. 3, No . 2, April 1988, pp . 105-117

P. C. Sen, "Electric motor drives and control-past,present, and future," IEEE Trans.. Ind. Elec., Vol. 37,

No. 6, December 1990,pp . 562-575

B. K. Bose, "Recent advances in power electronics,"IEEE Trans. Power Electronic, Vol. 7, No . 1, January

D. M. Brod, D. W. Novotny, "Current control of vsi-pwm inverters," IEEE Trans. Ind. A D U~ .,ol. 21, No.4, Maydune 1985, pp . 562-569

J. Holtz, It Pulsewidth mod ulation - a survey," IEEETrans. Ind.. Electronics, Vol. 39, No. 5, December

B.K. Bose, A n adaptive h ysteresis-band current con-troller technique of a voltage-fed pwm inverter for

machine drive system," IEEE Trans. Ind. Elec., Vol.37, No. 5, October 1990, pp . 402-408

A. B. Plunkett, "A current controlled PWM transistorinverter drive," in IEEE IAS. Ann. Mtz. Conf. Rec.,

J. Holtz and E. Bub e, "Field-orien ted asynchron ouspulse-width modulation for high-performance ac

machine drives operating at low switching frequency,"IEEE Trans.. Ind. A m i , Vol. 27, No. 3, MayIJune

A. B. Plunkett, "A current controlled PWM transistor

inverter drive," in IEEE IAS. Ann. Mte. Conf. Rec.,

1992, pp . 2-16

1992, pp . 410-420

1979, pp . 785-792

1991, pp . 574-581

1979, pp. 785-792[101 A. Nabae, S. 0. Wara, and H. Akagi, "A novel curren tscheme for current controller pwm inverters," IEEETrans. Ind. ADA, Vol. 22, No. 4, July/August 1986,

[ l l ] S. fukuda, H. Hasegawa, and Y. Iwaji, "PWM tech-nique for inverter with sinusoidal output current," inPES C Conf. Rec., 1988, pp.35-41

[12] C. T. Chang and C. T. Pan, "A field accelerationmethod for induction motor drive using a novel space

vector based current controller," IEEE Internationalsvm ms ium o n Ind. Elec., 1992, pp . 663-667

[13] M. P. Kazmierkowski and W. Sulkowski, "A novelvector control scheme for transistor pwm inverter-fed

induction motor drive," IEEE Trans.. Ind. Elec., Vol.

38, No. 1 , February 1991, pp . 41-47

pp . 697-701

Tech. and the M.S. degree from theNational Tsing Hua University,

Hsinchu, in 1985 and 1988, respec-tively, all in Electrical Engineering.

He is a Ph.D. candidate at Tsing HuaUniversity now. His research inter-

ests are in the area of pow er electron-

ics, ac motor drive and controlsystems.

Kuie-Lin Lo was born in Chung-Hua, Taiwan, R.O.C. in 1950. Hereceived the B.S. degree in E lectricalEngineering from th e NationalCheng Kung University , Tainan,Taiwan in 1972 and M.S. from SouthDakoda State U niversity, Brookings,

S.D.n 1978. Since 1979 he h as been

with Taiwan Power Com pany and iscurrently working toward his Ph.D.

degree.

I ChinP-Tsai Pan was bom in Taipei,Taiwan, Republic of china, in Octo-

ber 1948. He received the B.S.

degree in Electrical Engineeringfrom the N ational Cheng Kung Uni-versity, Tainan, Taiwan, in 1970, andthe M.S. nd Ph.D degrees from

Texas University, Lubbock, Texas,in 1974 and 1976, respectively, all in

Electrical Engineering. Since 1977,

he has been w ith the Department ofElectrical Engineering, NationalTsing Hua U niversity, Hsinchu, Tai-

wan, where he is currently Professor. From 1985 to 1986, hewas a Visiting Professor at the Department of Electrical

Engineerin g, Ecole Centrale de Lyon in France. Dr. Panserved as the D irectors of University Computer Center and

Computer Center, Ministry of E ducation from 1986 to 1989,

and from 1989 to 1992, respectively. His research interests

are in the areas of power system and power electronics. Dr.Pan has been twice the recipient of the A ward fo r Excellence

in Teaching, presented by ihe Min ister of Ministry of Educa-tion and the University President, respectively. He also

received Research Awards from the National ScienceCouncil in 1986-1992. Dr. Pan is a member of IEEE, ICE,

IEE, Phi Tau Phi, Eta Kapp a Nu, and Phi K appa Phi.

A Novel Vector Control Hysteresis Current Controller for Induction Motor Drives

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