8/18/2019 [doi 10.1109_IEMDC.1999.769200] Jun-Koo Kang, ; Dae-Woong Chung, ; Seung-Ki Sul, -- [IEEE Electric Machines a…

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Direct Torque Control

of

Induction Machine with Variable Am plitude

Control

of

Flux and Torqu e Hysteresis Bands

Jun-Koo Kang Dae-Woong Chung and Seung-Ki

SUI

School o f Elec t r ica l Engineering

Seoul Nat ional Univers i ty

S a n 56-1, Shi l l im-Dong, Kwanak-Ku, Seoul , Korea , 151-742

Ph o n e : 82-2-880-7243, Fa x :+82-2-878-1452 e-mail : ulsk@plaza.snu.ac.kr,

httD://eeDel.snu.ac.kr

Ab s t ra c t

-

In th i s paper, e ffec ts o f the hysteresi s bands on the

Di re c t To rq u e C o n t ro l (DTC ) o f a n i n d u c t i o n ma c h i n e a re

invest iga ted , and a method to cont ro l the swi tch ing frequenc y of

inverter by a variab le ampl i tude of the hysteresi s band i s

proposed for D TC of an induct ion machine.

A

m a j o r d r a w b a c k

of thc convent ional DTC is an unpred ic tab le inverter swi tch ing

frequency which varies due to opera t ing speed , load condi t ion

a n d p a ra me t e r s of t h e i n d u ct i o n ma c hi n e . Th e re fo re t h e

amp l i tude of the hysteresi s band should be la rge enough to avoid

excessive inverter swi tch ing a t any opera t ing reg ion , which

inev itab ly causes re la t ive ly la rge to rq ue r ipp le especial ly in the

low speed reg ion . This paper p roposes an effec t ive swi tch ing

frequency regula t ion method which consis t s o f hysteresi s band

c o n t ro l l e r a n d swi t c h i n g f re q u e n c y c o mma n d g e n e ra t o r . Th e

effec t iveness o f the proposed s t ra tegy i s analyzed and compared

wi th the convent ional method .

1. INTRODUCTION

Since the innovative studies in the mid-1980’s [I]-[2],

application fields of the Direct Torque Control (DTC)

strategy have been increased including paper machines,

traction and mill drives. DTC provides a fast dynamic

response of torque and a robustness to machine parameter

variations without current regulators. Among several DTC

strategies [3

1

the voltage vector selection strategy using

switching table has been widely used because it is easy in

concept and simple in implementation, only using torque and

flux hysteresis comparato rs. The amplitude of hysteresis band

strongly influences the inverter performances such as flux and

torque ripples, current harmonics and switching frequency of

power device. A major drawback of the conventional DTC is

unpredictable variation of switching frequency according to

machine parameters and operating speed conditions even

though the amplitude of hysteresis band set to constant value.

Therefore the hysteresis band has to be set large enough to

limit the inverter switching frequency below a certain level

that is usually determined by thermal restriction of power

devices. Since the hysteresis bands are set to cope with the

worst case, the system performance is inevitably degraded in

a certain operating range, especially in a

low

speed region.

In this paper, a new DTC control strategy with variable

hysteresis bands is presented. The proposed strategy modifies

the hysteresis bands

so

that the inverter switching frequency

can follow a given command frequency. The switching

frequency variation characteristic of the flux hysteresis

controller is different from that of torque hysteresis controller.

This phenomenon makes flux and torq ue hysteresis controller

to

have different contributions to the total switching

frequency. It means that the amplitude of flux and torque

hysteresis controller should be regulated separately for

effective utilization of given total switching frequency

comman d. In this paper, total switching frequency command

f, is divided into

two

components, i.e., f s i and j,:, and

then each command frequency is separately regulated by

switching frequency controller which modifies the amplitude

of flux and torque hysteresis comparators.

11. SWITCHING FREQUENCY VARIATION IN DTC

An induction machine can be modeled with stator and

rotor fluxes as state variables by the following equation.

0-7803-5293-9199 10.00 1999 IEEE

640

where os nd or are stator and rotor flux complex vectors,

v, is stator voltage complex vector, R ,

and

R, are stator and

rotor resistances,

L ,

and

L~

are stator and rotor self

inductances,

L

is a mutual inductance, c is leakage

coefficient with CT =

- L:

/

L L

and 0 is rotor angular

velocity. The electromagnetic torque can be expressed in

te rn s of stator and rotor flux as

where P is the number of poles of the machine and “ t ”

denotes the complex conjugate. Using (1) and (2), variations

of torque and flux during control sam pling time t s p t (k+l)‘h

sampling instant can be expressed as follow :

[4]

4)

As can be seen from (3), the variation of torque

A<

during

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t s p

i.e., torque slope is a function of stator voltage, stator and

rotor fluxes, and motor speed. Therefore, in a torque

hysteresis controller, an elapsing time to move from lower to

upper limit, and vice versa can be changed according to

operating conditions. This characteristic makes the variation

of the switching frequency according to various load and

speed operating conditions. In case of stator flux, as can be

seen from 4), the angle between stator voltage vector and

flux vector determines the rate of flux variation. As this angle

varies with a rotating stator flux in the space vector plane,

flux slope is changed. Therefore the rotating speed o f stator

flux proportion ally affects the variation cycle of flux slope.

Fig. shows the switching frequencies of the torque and

flux hysteresis controllers versus motor speed with different

hysteresis band amplitude, where p 7 denotes the size of

hysteresis band of torque controller in per unit and p

denotes that of flux controller. As can be seen,

fi has

maximum value in a medium speed range while switching

frequency of the flux hysteresis controller fa s proportional

to the rotating speed

con .

Thus, for a regulation of switching

frequency, two variable amplitude hysteresis controllers are

required.

8

( r l l i 4 0 0 3 ib) i 4 U l ( r l P-aOZ

id1 p U O 7 i d g -OO5 in

8 A O i

a8

I v

0

(a) Torque hysteresis control.

0

M

m

lcel

1440 llD0

Motor spccd

o

dmin)

k x o r

spccd

mm

dn i in )

(b) Flux hysteresis control.

Fig. I . Simulated switching frequency o f hysteresis controllers versus

motor speed with different hysteresis bands of pa, and

PT

111.

THE PROPOSED SWITCHING FREQUENCY REGULATION

The basic implementation of the proposed

DTC

system is

presented in Fig.

2

The goal is to maintain the switching

frequency at a commanded value equal tot:. Fig 2  is a

diagram

of

flux hysteresis controller, but a torque controller

also has a same structure. The basic technique to achieve the

constant switching frequency is not quite different from the

case of hysteresis current controller which also modifies the

amplitude of hysteresis comparator

[5].

The proposed

switching frequency regulation strategy can be briefly

described as; pulse counter counts the output pulse of

hysteresis comparator S and the counter output is used as a

feedback to the

PI

controller. Frequency command, J,:, is

integrated to obtain a switching count command. Then PI

controller modifies the amplitude of hysteresis band in order

to drive feedback-switching count,

N

of flux controller to

commanded values, N ; . The dotted line indicates the

optional amplitude predictor which can be used as

a

feedforward compensation signal. But for an accuate

prediction, electical parameters and rotor speed are required

as can be seen from (3) and

4).

Fig. 3  shows a DTC control block diagram with the

proposed variable hysteresis band controller. Like hysteresis

bands setting procedure in the conventional DTC, the ratio

of

f ; and

f ;

should be determined depending on the

application requirement. A frequency command divider

calculates two frequency commands based on the ratio. Stator

voltage vector v, is selected by S

S ,

nd stator flux sector

.

A

voltage selection rule is same as the conventional DTC.

IV. SIMULATION RESULTS

Simulations have been carried out for the evaluation of a

proposed algorithm. Simulation parameters are as follows ;

Motor ra t ing

:

3 phase,

4

ole,

220V,

7.5kW,

40

N-m

Pa ra me t e r : Rs= 0 . 1 5 8 , Rr

=

0 .1 7 8 , Ls=3 5 mH, Lm= 3 3 .8mH,

Lr=35mH

load

inertia

=0.4 kg-m2.

PI

Control ler

Fig. 2. Flux hysteresis controller with switching frequency regulation.

641

8/18/2019 [doi 10.1109_IEMDC.1999.769200] Jun-Koo Kang, ; Dae-Woong Chung, ; Seung-Ki Sul, -- [IEEE Electric Machines a…

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vol tage

vector

Selection

Switching

Frequency

I 1 tmledor

I I I I

Fig. 3. Control block diagram of the Proposed DTC

Fig. 4 shows the torque control characteristic of the proposed

DTC method. At I = 0.02

s,

torque command is set to 50N-m,

120% of the rated value, and at motor speed U = 1750 r/min,

120

load torque is applied. As can be seen, the amplitudes

of torque and flux ripple vary according to operating speed .

For comparison igures of torque and flux are also presented

with constant hysteresis band. Fig. 5  shows the variation

of

hysteresis band under the same operating condition as Fig. 4.  

As can be seen, both torque and flux controllers maintain

their frequencies at command values (dotted lines)

whilep,. and pg are varied according to operating speed.

The fkequency errors of flux in low speed region and error

of

torque in high speed region come from the limitation

of

control cycle time (here 2 5 ~ s ) .

s

I

-

'i

5

e

0

.- I

I

0 0 0 4

0 8 1 2 1 6

2 0

time

s)

machine drive. (upper two; conventional DTC for comparison.)

Fig. 4.

Step torque characteristic of the proposed

DTC

induction

I I

ci

0

 

9

- -

0

.

0 0 0 4 0 8 1 2 1 6

2.0

time

(s)

Fig. 5 Switching frequency control characteristic of system

V.

CONCLUSION

In this paper, the switching frequency of DTC inverter is

controlled for the improvement

of

drive performance. The

main advantages of the proposed DTC method are

;

efficient

and s table utilization

of

power devices by regulating inverter

switching frequency, and improvement

of

torque ripple

characteristic in a low and high speed regions. The

differences between conventional and proposed DTC have

been investigated. The simulation results verify the feasibility

of the proposed control.

REFERENCES

[ l ]

I.Takahashi,T.Noguchi,

A

new quick-response and high-efficiency

control strategy of an induction motor, IEEE Trans. on

Ind.

M. Depenbrock, Direct self-control DSC )of inverter-fed induction

machine, IEEE

Trans.

on Power Elcr.,Vol.3, N o.4, pp.420-429,1988

G. Buja, D. Casadei, DTC-based strategies for induction motor

drives I, in Con

Rec.

IEEE-IECON, pp1506-1516,1997

J.K. Kang, S.K. SUI, Torque Ripple Minimization Strategy for

Direct Torque Control of Induction Motor, in Con Rec. IEEE-IAS,

pp. 438-443, 1998.

L.Males ani, P. Mattavelli, High-performance hysteresis modulation

technique for active filters, in Proc. IEEE-APEC, pp. 939-946, 1996

Appl V01.22

O.5 p.820-827,1986.

[2]

[3]

[4]

[5]

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