Werner Leonhard Control of Electrical Drives

260

12.

Control

of

Induction

Motor

Drives

12

.2.2

Acquisition

of

Flux

Signals

Clearly, having up-to-date information

on

the

magnitude

and

phase

of

the

fundamental

fl.ux

wave

is

of

paramount

importance

since

this

is

the

basis

or

c

oordinate

transformation, leading to decoupled control of

the

currents

1

13

37,L7].

For

obtaining

a frequency-independent

fl.ux

measurement one could at-

t.(:mpt

to

measure

the

fl.ux

density in

the

airgap

of

the

machine directly by

p

la

ocing

suitably

spaced magneto-galvanic or magneto-resistive devices such

;lS

I{

all- sensors on

the

face of

stator

teethj by

interpolating

the

local samples

01'

llux density,

an

estimate of

the

magnitude

and

position of

the

airgap

fl.ux

IVa

ve

could be obtained.

Then

by adding a volt age component proportional

e

j

t.()

Lhe

stator

current vector, a signal representing

the

rotor

flux

'!f

or

the

f

R

11l<tf!:lletising

current

1 R would result, Eq. (12.22). However,

apart

from

the

m

"'tcl.

that

the

tiny

Hall sensors are mechanically fragile devices

that

would

"o\.

sta

nd up very well

under

severe vibrations

and

thermal

stress,

there

are

hrg(

: harmonics caused by

the

rotor

slots,

the

frequencies of which change

IV

i til speed.

This

calls for

adjustable

filters

that

would

be

difficult

to

design,

I ';trl.icularly

under

the

condition of zero phase shift. AIso,

the

torque signal

"olllputed from this information

is

likely

to

be unreliable since torque is a

';

lIlface-re

lated

integral

quantity

which

is

difficult

to

estimate

on

the

basis of

:t

r"w

local field measurements. Another disadvantage of

this

scheme

is

that

!.II<'

IIlO(

oor would have to

be

fitted with these sensors, so

that

it

would no

I" '

I/';('!"

!lI: a

standard

motor

that

could easily be exchanged for

another

motor

1.:..1\"11

rrmll

stock.

'I 'I

II'

;'o

di

vc

semiconductor elements

in

the

motor

could be avoided while

;

,.1.

LI",

';;

'"W

time suppressing

the

undesirable slot harmonics,

if

sensing coils

11

11.\1

1111'. a

widt.il

equal

to

full pole pitch would be installed in

the

stator,

for

,.

x

II

III

pJ.o

cllclosed in

the

wedges covering

the

stator

slotsj this geometrically

illl.

n s

til<'

d isturbances by

the

rotor

slots

and

produces signals proportional

1.

..

IIII

X

('!ta

ollge which, after integration, could serve as a measure

ofthe

main

1111

x. 1\

J'

;

a.i

11

lJy

using several sensing coils, displaced

around

the

circumference

,,r

1,

1,,

:

s[.;tLor,

and

adding voltages proportional

to

stator

currents, signals

1"

'1

" "';('

IILillg

rotor flux could be obtained.

'I'

hi

s s

dwrne

was tried in

the

laboratory

[G1,G2]

and

found

to

work well

"OWll

lo

v(:ry

low frequency (> 0.5 Hz), where

the

drift of

the

integrators

'·V"

IIL

lliI.I\y

lJccame

too

largej this limitation prec1udes

the

application of this

::

..

!t(:lII('

to dri

ves

requiring position controI. Again, a special1y prepared

motor

w",ild

llave

(;0

be used.

'I 'h,'

las!;

Ill

cntioned disadvantage

is

avoided by measuring

terminal

volt-

:

'1'

,":;, i

o':o

IlSillf!:

tile

stato

r windings as sensing coi

Is

. This, however, cornplicatcH

1.1

11'

,;

illl:l.Lioll

eve

ll

[llr1.b

er

l)(!

Cél

ll

S

(:

of

tlw

n:sistive volta

ge

dl'op, tilat dllll1"

i,,;!.I

."

:;

a

I.

low

J'n

'

<JIl(

\

lLcy

,

lll(\

llIU

s

l.

hc

(·olllJ)(:II:

;;

t1.(·d

prior to

illt.

q(

ratioll j a

.'i·

Lili '

!i

l

.;

do",. I'<',;i:;1.; I.LII·(' "halll!

;<'

S

wiLh

l<'nq

li'

1'11

1.1\1'1'

Ih

iN

IIH'

I\I

Hll'il;l

~

H

rlH'

IlH

: ClI,O

1""

'

1111

11'

",lIiLl

o

i

ll

v

,.J

v,·d

.

'1'1'

1'1

1.

:1

IV

tl.b,,"1.

~

o

l

·I

III"

'l(

l

l.\lrl

'

(

'

'''II~I(·I

HJ

~I.i

,,"

I

III.\f

I·

j

lld

i

12.2

Contro!

of

Current-fed

Induction

Motor

261

isa

imRa

a

iSb

b

Fig.

12.16.

Flux

mo

de! for

obtaining

the

magnetising

current

vector

(a)

in

stator

coordinates

and

(b)

in

fie!d

coordinates

cated

a

practical

lower frequency limit of

about

3 Hz

with

a 50 Hz motor.

The

situation

may be improved when performing

the

integration in field co-

ordinates, as discussed

in

8ect. 12.5.

Another

quite

different approach

is

based on

the

model equations of

the

motor.

The

equation representing

rotor

voltages, Eq.(12.29), a first

order

vectorial differential equation, may be used for computing 1

m

R(t)

in

stator

coordinates on- line.

The

measured

stator

currents is

and

speed w could serve

as

input

functions, with

the

motor

being described by a single

parameter,

the

rotor

time

constant

TR.

By

again introducing orthogonal two phase current components

ls(t)

=

is(t)

e

j

«t)

= isa(t) +j iSb(t) ,

(12.39)

1

m

R(t) = imR(t) e

j

e(t)

= imRa(t) +j imRb(t) ,

(12.40)

the

block

diagram

of Fig. 12.16 a results which illustrates

in

graphical

form

the interactions of Eq. (12.29).

The

structure

is similar

to

the

controllable

oscillator shown in Fig. 12.6 for

Yl

=

wT

R

, Y2

=-

1.

A more direct

method

of computing

the

magnitude

and

position of

the

fundamental

flux wave

is

to

immediately convert

the

flux model

into

field

coordinates, as described by Eqs. (12.33, 12.34) [841,842). Again,

stator

cur-

rents

and

speed serve as

input

signals while

the

transformed

stator

currents

is

d

,

iS

q

and

the

magnetising

current

i

mR

are

now directly available as

output

signals for controlling

fl.ux

and

torque.

The

fl.ux

model in field coordinates,

Fig. 12.16 b, is preferable because of its simplicity

and

potential

accuracyj

also

the

output

signals

are

constant

in steady

state.

Of

course,

the

infl.uence

of

the

rotor

time

constant

T

R

is still presentj this

parameter

may have

to

be

Ilpdated during

operation

. Fig.

12

.

16

b corresponds directly to

the

model of

lo

l,,

!

IllOtor

showll in Fig. 12.

12

and

is inc1uded as a "flux model" in Fig. 12.14.

TIl<'

IIS(

:

<lI'

a dynamic

flllx

Il10del

slIr.h

as shown

in

Fig. 12.16 b offers

!i(

'v

I'

l'al

;\.(

lv:l.lIl.al

~

I'

~:

262 12.

Control

of

Induction

Motor

Drives

•

Flux

signals

are

not

based on local

measurements

and

are

not

affected by

slot

harmonics

and

stator

resistances,

• Use

of

a

standard

motor

without

additional sensors is possible.

•

Flux

sensing is

operative

down

to

zero frequency, because no

open

ended

integration

is needed which would

be

subject

to

dríft.

•

The

model

immediately generates

the

variables needed for feedback control.

Ilowever,

there

are

stringent

accuracy requirements, for example

with

respect

L()

Lh

e

modulo

27r

integration

of

lIj

this can

best

be

solved by digital com-

)llltation in a microprocessor as will

be

shown later.

The

dependence

of

the

roLor

model

on

the

time

constant

TR

constitutes a source

of

error

because

;\Il

illcorrect

orientation

li'

of

the

flux wave leads

to

undesirable coupling be-

Iwcen

the

d-

and

q-axes

and

could endanger

the

control in field coordinates,

CV(~

lltually

even resulting

in

instability

.

Another

possibility for

obtaining

a flux signal is

the

evaluation

of

the

sta-

Lor

voltage equation, Eq, (10.50), when sensing

the

terminal

voltages

and

cur-

II

I

IIL

5,

However, after eliminating

the

unaccessible

rotor

currents, Eq. (12.45)

n

ls

lllts which contains

the

rotor

flux in derivative form so

that

an

open

ended

illLegration would again

be

necessaryj because

of

the

necessary

isRs-

com-

IWHsation

and

integrator

drift

this

is likely

to

produce

unreliable results

at

low

speed.

This

option is

not

pursued

here,

it

will be

further

discussed in

~;(ICL.

12.5.

1

2.

2.:~

l

<:;

lfects

of

Residual

Lag

of

the

Current

Control

Loops

W11\'11 ex plaining

the

principie

of

control in

fi

eld coordinates, Fig. 12.13,

it

1111

::

1)(,

('

1I

;,

.ssllllled

that

the

stator

windings

are

supplied from perfect

current

::

0111'('(

'

::

, i.(I.

L1tat

the lag

ofthe

current

controlloops

can

be

ignored.

This

calls

1'11

1\ (''v''locollverter or a volt age source converter

with

high frequency pulse-

\Vi

d I.h

1111

)(llllation, allowing

rapid

access

to

the

currents

through

the

reference

1I

1!';lIil.l~;,

as well as

adequate

ceiling volt age

throughout

the

operating

range.

(:I(·;l.Ily

Lhe

seco

nd

condition is in conflict

with

an

economical design

of

the

('(111

wr!.cr uecause

it

would preclude a full utilisation

of

the

available voltage

III

higll speed.

On

the

other

hand,

if

the

lag of the

current

controlled converter

ii:

1I(

,i,

IIq

:

~

ligible,

the

decoupling by

the

inverse model becomes

inaccurate

and

111)(1('siraiJl

e coupling

terms

may

arise which will eventually

render

the

field

ol'J('ll!.al

,

(~d

contro! inoperative;

to

avoid this, two options

are

available:

• IlIdllsioll

of

a l

ea

d-

lag

network with

the

transfer

function

I

"

(.~)

-=

'1'1

S +1

'1'2

<

TI,

(12.41)

T

2

.9 -/-

1 '

iii

1.11(' 1:('/'1'1'1.'11('.(: ch;\IIJid

01'

t.Iw

sLa!.of

('llIT(~H(,

('.(lJl!.J.'o!!oops

.

•

t\ddil.i'llI

(II'

d('I'lllIpfillf:'

(.('1'111::

iII

lidd

(,ool'

dill

:iI,I'

':

,

i.I'.

prior

(,0

t.lH~

l.rau

I:

r'Il

'

llI

liI,i,

'1i1

1111

',0 ill,nl ... r

(·o"ldlllal."

I

i.

12.2

Control

of

Current-fed

Induction

Motor

263

For

the

following

it

is

assumed

that

the

first

approach

has

been

taken

but

that

its

potential

is

exhausted,

leaving a

residuallag

Te

that

cannot

be

reduced

any

furtherj hence

the

second

option

must

be

pursued.

The

situation

is depicted

in

Fig. 12.17 showing

the

two opposite transfor-

mations

which

are

supposed

to

cancel

and

the

unavoidable lag effects placed

in

between.

With

the

vectorial

notation

for

the

currents

in

stator-

and

field

Field coordinates + Stator coordinates + Field coordinates

p

iSqRef I

I

i'SqRef

II

iSbRef

~

iSb

from

Ie'

jp

controlfer

1+j

w

l

T

e

iSaRef

~

isa

i'SdRef

iSdRef

Decoupling

i

sq

iSd

F·

F·,

F·

LSRef

JSRef

Js

!s

Converter

Drive contrai

+ with + Motor

current control

Fig.

12.17.

Removal of

undesired

coupling effects

caused

by

the

residual lag

of

current

control loops

coordinates

is(t)

=

is(t)

eH

=iSa(t) +j iSb(t)

F

is(t)

=is

e-

j

(!

=iSd(t) +j isq(t)

and, correspondingly, for

the

reference signals,

. F ·' j

(!

(12.42)

lSRef

=

LSRef

e

lhe

lag effect

of

the

converter

may

be

described by

dis

. .

(12.43)

T

e

dI

+15 =15

Ref

.

WiLh

the

assumption

that

the

lag

time

constant

Te

has

already been reduced

Lo

a relatively small vai ue,

the

undesirable coupling is mainly

due

to

phase

Hh

ir!.

ra.

t.h

er

than

amplitude.

ln

steady

state

condition,

with

is

= const.,

(,!",/(

('-'I

and

ins

ert

ing Eqs. (12.42, 12.43),

this

yields

,..

./

"'

,

( 12.11)

'1

,,'\

1. -"

Ikf

I 1

.i

I.!

I 'I:.

264

12.

Control of Induction Motor Drives

when specifying a decoupled transmission,

F·

I F ·

'!.s

~

!SRef'

Lhe

res

ult

is

F 'I

(1'

T)F.

Ls

Ref

= + J

Wl

e

!S

Ref

.

,(,his

means

that

corrective

terms

should

be

applied

to

the

output

signals

of

I.he

controllers.

Written

in

orthogonal

components,

this

calls for

LSdRef

=

!SdRef

-

Wl

Te

iSqRef,

Ls

q

Ref

=

is

q

Ref

+

Wl

Te

is

d

Ref

.

Th

e

practical

realisation

of

this

additive

correction is

quite

easy since

DC

sig-

Ilals

are

involved in

steady

state.

For simplification,

the

speed signal W

may

Iw

used

instead

of

Wl

with

low slip motors.

ln

view

of

the

limited

ceiling volt-

age

of

the

converter,

the

residuallag

Te

of

the

current

controlloops

is likely

to

increase

with

the

stator

frequency

but

if

the

control

is

implemented

in

a

IlIir.rocomputer, this effect can be offset by varying

the

decoupling

parameter

'I;. as

the

speed changes.

The

rating

of

the

converter is

determined

by

the

specified values

of

stator

volt

ag

es,

currents

and

frequency. After

eliminating

the

rotor

current

from

I

';

qs. (10.50, 12.22),

the

stator

volt age reads

.

ilis

ili

mR

II

.

,>'

(/.)

=

Rs!s

+ u

Ls

dt

+

(1-

u)

Ls

dt

.

(12.45)

111

::

I.

c'

ady s

t.

a

te

condition, i.e.

with

constant

speed

and

sinusoidal currents,

1,1,,"1

=

Wl,

is

= const ,

imR

= const.,

11('11

C'C'

I,,:

;

(t

) =

(Rs

+ j

Wl

U

Ls}is

+ j

Wl

(1-

u)

Ls

i

mR

.

(12.46)

'I 'his (:()lIflrms

that

the

fundamental

component

of

the

stator

volt age rises

with

rr('<jl\c~nc:y,

Fig. 12.3 b.

When

the

available voltage

range

is near1y

exhausted

:d,

the

fr

equency WlO - some

margin

must

be left for control - a

further

illc['(

~

a

s

c

o

E"

the

sp

eed is only possible by reducing

the

magnetising

current

,

ic',

iJy

fidd w

ea

kening,

This

can

be achieved

with

•

:1.11

OpClJ

loop scheme employing a speed

depend

e

nt

reference

imRRer(w)

a

~

t

dlOWIJ

iII

Fi~

.

12

.1401'

•

:1.1\

ô\.lI

x

il

i

ary

("()lJlrollooJl

whidl

lilllits

Lhe

1J1

I\

f'

;J

lil.1Jde

of

th

e s

lalor

v()ll.agc

~

hy

J'(

'

cllI<:iIl,~

I.II(

~

flme r c fer C

lJc

:c '

i",.{l/i"J

;

il

silJlílllr

Ii

dwll\(: h:\,n

c

:

arlí(

~ I

'

1)

('1"'

11

clC'

H

e'I'i1lC'd

for

I){:

1I1:u,ltinc

'H,

I,'i"

, 7.

1:\

12,2 Control of Current-fed Induction Motor

265

When

the

field is reduced,

the

ceiling voltage

of

the

converter

should

nor-

mally be fully utilised,

resulting

in

gradual

cessation

of

pulse-width

modula-

tion

so

that

each leg

of

the

converter eventually

produces

square

wave

output

volt ages, Fig. 11.6.

The

stator

currents

would

then

be no longer sinusoidal

but

the

field

orientated

control

still

remains

functioning as

the

computation

of

the

flux

and

th

e

magnetising

current

is

based

on

the

measured

stator

currents, Because

of

the

limited

voltage

and

stator

currents,

the

maximum

torque

is,

of

course,

reduced

in

the

field weakening region, Eq, (10,85).

12.2.4

Digital

Signal

Processing

The

signal processing required for

the

field-orientated control, Fig, 12,14,

as

well

as

the

flux acquisition using a

dynamic

model, Fig. 12.16 b, is

of

consider-

able

complexity;

in

particular,

the

various multipliers

and

function

generators

needed for

the

coordinate

transformation

are

difficult

to

adjust

accurately

when realised

with

analogue

components.

On

the

other

hand,

on-line

digital

control

was economically

impractical

as

long as

it

had

to

be

performed

by

large

and

costly process

computers.

These

obstacles have delayed

widespread

application

of

the

sophisticated

control schemes needed for AC drives [L44].

However,

this

situation

has

changed

dramatically

since digital processors

have now s

hrunk

to

minute

size

thanks

to

the

progress

of

microelectronics.

The

reduction

in volume

and

cost

and

the

advances

in

processing power have

in

the

meanwhile reached a

point

where ali

the

signal processing

required

for

a

high

dynamic

performance

AC drive

can

be

executed by a single micro-

processor which,

together

with

the

associated

peripheral

components,

finds

room

on a

postcard

sized

printed

circuit

board.

The

main

advantage

of

digi-

tal

control

with

microprocessors is

that

the

sarne

standard

hardware

can

be

llsed for

many

different

appli

c

ations

because

the

function of

the

processor

is

determined

by a flexible

and

individually

adaptable

pr

o

gram,

i.e. by soft-

wa

re

; once

the

program

has

be

en

developed

and

verified

it

can

be

duplicated

at

negligible cost

and

transferred

to

a read-only

memory

chip c

onnected

to

Lhe

processor.

A

precondition

for

the

digitalisation of signal processing is,

of

course,

an

ade

quate

resolution of

the

signals

with

respect

to

amplitude

and

time,

Le.

sufficient word

length

and

computing

speed.

The

current

16 bit-processors

are

qllite

satisfactory

from these

points

of view; a 16-bit re

presentation

of

vari-

;

~blc

s

corr

e

sponds

to

an

internal

resolution

of

one

part

in

more

than

65,000;

ir 10-

or

12-

bit

analogue-to-digital converters

are

employed for converting

I.IJ(

~

analogue signals from

the

plant,

such as

stator

currents

or

motor

speed,

I.hc

: d fects

of

quantisation

are usual1y

unnoticeable

even

though

there

are

s

l.il!

exc

c ~

pti

o

n

s

)

when higher

internal

resolution, such as 32

bit,

proves

to

be

llC'

n'

ss

ar

y

wi

th s

om

e va

riabl

es. Most microprocessors still use

integer

valued

IIl'

il.hl\\(:(".l.i("

Inll

, pr

oo

,s

s

or

s witlt

Jloatinr

~

jJoint arit-hmctic

are

becoming

mor

e

{,

<l

I1IIJI"11

IICl

W,

pll.rticlILtrl

.v

ir

1.111'

rOlJtrol

pJ'()l~r;lII1

H

:U

'

('

to Iw writt.c

lI

in

hif

~

h(

~

r

266

12. Control of

Induction

Motor Drives

levellanguage such as in C,

to

make them independent of

the

processor

hard-

wa.re

used. Reduced word length, such as 10 bit, is usualIy

adequate

for

the

I)

IA-converters, i.e.

at

the

output

of

the

microprocessor because

the

DI

A-

converter

is

part

of

the

plant

and

thus

under

the

surveillance of

the

digital

controlIer, whereas errors in

the

AI

D-converter produce false signals.

The

choice of the required resolution in time

is

more complex as

it

depends

1101".

only on

the

type of drive

but

also on

the

particular

function within

the

drive controi. Clearly, when sampling

and

processing non-sinusoidal

currents

h;wing a fundamental frequency of 100 Hz, a higher sampling frequency

is

11("(

~

d

e

d

than

for the digital realisation of speed

or

position control, where

the

ral

.

(~

of change

is

restricted by

the

inertia of

the

drive.

As

long as computa-

I.ioual speed of the processors was a

major

consideration which is no longer

I.

h(

: case with todays microprocessors,

an

advantage could be gained by em-

ploying different sampling periods for

the

different tasks. For example, for

an

('-"qJcrimental 1.5

kW

induction motor servo drive having a

PWM-transistor

power supply

and

an 8086 control unit,

the

folIowing sampling periods proved

cOlllmensurable with fast control transients [841].

a) Sampling period of 1 ms for

AI

D-conversion of

stator

currents

U

pdating

of fiux model

COllversion

to

field-coordinates

Cmrcnt

and

torque control

Couv(~rsion

of

diq-currents to

stator

coordinates

Olll.pUt.

of

current

references

1»

):;aIJlplin~

period of 5 ms for

1,'1,1

x

c01lt.rol

including field weakening

,',

pc

'c

,Ii

control

I'm:il.ioll control

fi

:;il.

1I1

pi

ill[';

time

of 1 ms for

the

stator

currents is

adequate

up

to

a

stator

r""I[IIC

:

llcy

uf

about

100 Hz, when the currents are sampled

and

processed

ten

l

.

illlC'

~:

per periodj

at

this frequency

the

fiux vector

is

computed

at

36° inter-

v:th

wllidl can make

the

use of a simple

extrapolation

scheme desirable. At

::

till

Ili

g

h(

~

r

stator

frequency, faster sampling of

the

variables

is

required. For

I.odays

hi,..;h

dynamic performance servo drives, a sampling period of

100JLs,

('oIT('spollding to a 10 kHz sampling frequency

may

be specifiedj this

can

be

adlil:v(~d

with signal processors. Another possibility are application specific

illl.l'l~ra

.

I,(~d

circuit (A8IC's), where ali the control software

is

incorporated as

I'II

S

t.Olll-

ltardware on special chips, [K34 - K38], [TU].

A

II

illcrelIlenta.1 position sensor as described in Chapo

15

.2 can serve for

:i<'lI::jllf~

i

LJlgular

position as

wdl

as speed; wlwn tlw [orward/reversc pulses

are

II.I

'

c

'

.

1I1111lIat.(

~

d

iII

a

r<~vcrsihlc

cOl.luter, which

is

illiLially s

et

hy

a.

rd(:n~llce

pulse,

LIli' :!.III-,lIla!' pw:itioll o[

lhe

shaft

call

1.1\'

cld,('d,c'd

,II.

1.

11<'

salllpliJlU

illSl.il.lll.

S hy

1.

111'

1'

11

ic

'r"l H'

IlC'

\'

:-lH

OI

',

[<'ol'll1il)

((

!.Ii<'

ditl"

'

I'\'III

'"

II('!.w('I'1I

I.WI)

Hl

rll

H

l'lflWUI.

Nn

lll(d('

N

1"

""icl,'

;!

II

14'

11

1

lI

'c' "r I,!t.,

II

V('l

lIf,\"

:1

1'1

"

1'01

i

II

1.1'1'

11

'

1.

illl

.\

'l'vnl.

~lI.l.lIndl'y,

fI,

1I

12.2 Control of Current-fed

Induction

Motor

267

encoder, delivering

at

any

instant

the

absolute angular position of

the

shaft

would be preferable for speed

and

position sensing as

it

removes

the

ambiguity

with regard

to

initial position,

but

this advantage has

to

be balanced

against

increased cost and complexity.

With

a high resolution incremental

speed/position

sensor producing 8000

increments

per

revolution,

the

speed signal

has

a frequency of 200 kHz

at

the

nominal speed of 1500

1/min

for a 4-pole, 50 Hz motor, Hence a 5 ms

sampling period of

the

speed controlIer results

in

a speed

measurement

of

1000 counts

at

nominal speed

but

correspondingly less

at

lower speed, 8ince

this

is

usualIy

inadequate

with

regard

to

resolution

and

accuracy, a quasi-

analogue sensing scheme providing finer resolution

at

low speed could

be

employed [845,

KU]j

another

option

is

to

convert

the

sensing scheme from

frequency-

to

time-measurements which alIows

better

resolution

at

low speedj

this

is

discussed

in

8ect, 15,2.

The

design of linear sampled

data

control systems is

part

of

the

general

control theory

that

has been exhaustively covered in

the

literaturej

there

is

no lack of proven design methods, e.g,

[43],

A look

at

Figs. 12,13

and

12,14

reveals

that

even

though

the

control plant is highly nonlinear, a considerable

degree of decoupling

and

linearisation is achieved

through

the

method

of

field orientation.

ln

addition,

the

principIe of cascade control, identical to

that

applied

with

DC

drives, serves for consolidation by allowing a step-by-

step

design of

the

control

structure.

All

that

has been said

about

the

design

of controlled

DC

drives, including

the

combination of feed-forward

and

feed-

back control, remains applicable here, because

the

difference between a

DC

and

an

AC drive is, besides

the

changed

parameters,

confined

to

the

block

"Torque

controlloop".

Further

simplification is due

to

the

fact

that

relatively

high sampling frequencies

can

be chosen with a suitable microprocessorj as a

result,

the

control

functions in

the

outer

loops are practically continuous so

that

the

added

complexity of sampled

data

design procedures is avoided.

As

an

example,

the

difference equation of a PID-controller relating

the

sampled

control

error e(v)

to

the

actuating

signal y(v)

may

be

written

in

straight

parallel

form

TV

T 1

(12.47)

y(v)=G

e(v)+Ti~e(JL)+

;[e(v)-e(v-1)],

[

where T

is

the

sampling interval, G

the

controlIer gain

and

Ti, T

d

the

time

collstants of

the

integrating

and

derivative channels respectively.

The

equa-

I.ioll

is

to

be solved

in

real

time

by the microcomputer.

The

integrating

term

would

normally

be

computed

recursively in

the

form

(12.48)

y,

(II)

dlt)

=

:'1

i('/ -

1)\

1'(1/)

.

--

'268

12.

Control

of

Induction

Motor

Drives

lt

is

important

that

all

the

variables are bounded to prevent numerical over-

flow

with

integer arithmetic, or undesirable signal overshoot if floating point

arithmetic

is

employed.

e

Ts

The

discrete transfer function of this controller is,

letting

z = ,

_

Y(z)

_ G

[1

T z T

d

Z -

1]

F

(

z

)

----

+---+---

(12.49)

E(z)

Ti

z-1

T z

\2

.2.5

Experimental

Results

1"i,;llre~

12.18

and

12.19 show speed

and

position control transients of a 1.5

k W induction

motor

with a switched

transistor

power supply

and

micropro-

('(~ssor

control;

the

motor

was

not

loaded during

the

tests.

The

8086-based

cOlll.rul

algorithm comprised altogether 8 k bytes of read-only-memory

[S44].

'I'lw response of

the

drive is illustrated by

the

fact

that

after a fraction of

(llle

revolution

the

motor

reaches field weakening speed.

The

smooth

and

rapid transients, resembling

the

simulated results in Fig. 12.15, indicate

that

tid<l orientation

is

indeed a powerful concept of controlling AC drives with

liigh dynamic performance. During

the

transients

the

waveforms

of

the

stator

cnr]"(~nts

are far from sinusoidal.

2

0ms

}-o

- - -

'"

i

sq

frL

(ú

10001lmin

/-

.

_ /

·1000

1Imin

.

VV

is,,,

=d

q

C\

/\.

~~

f

~

is,

. A

V

L\

V

A

\J

L"">'J/"""'.\.J

10"

1

1-<.

I'

...

.

IH

.

N,)

IO

~

L

"

>1

1"'('.1

f

('v('r~al

"I" 1.:' I'

,W

illdlldiollllllll.or

wl

LlI

1.'

"

11

1

11

,1

1.'"

, ,·

,,"v,'rl.,·r

lIlI<1

IIli(

'r

"l"u

("'ll

l1

'"

' ('

(IId,r,d

12.2

Control

of

Current-fed

Induction

Motor

269

1-

500 ms

-----I

1j

!l

~

;eVOlutions

vrvv

i

IL3500 l/min \

ro

•

1

b

~

V

iSq

mR

Field weakening./

i

~

liRM'/'

,.,

ln

"i

".wHil\4~'IH

li

,

....

i

S2

~

1"lfIM

••

I

lU."

,:rt

....

..

AIlU\~11I

\

==

Fig.

12.19.

Step-response

of

a

position

controlled 1.5

kW

induction

motor

drive

12.2.6

Effects

of

a

Detuned

Flux

Model

The

parameter

TR

can

be expected

to

change slowly due

to

changes of

rotor

t(~:nperature,

but

instantaneously when

operating

into

the

field weakening

range, when

the

motor

core becomes desaturated.

The

interaction is described

b.Y

Fig. 12.20, where

it

is seen

that

the

flux model

ofFig.

12.16 b, controlled by

t1w

Ill

c<tsmed

stator

c

urrents

and

speed, functions as

an

open loop observer

iII para)l,,1

to

tlw

motor

dynamics.

It

produces estimates of

the

flux angle

II' .tlid til(' .li('ld

()ri(~"l.;t(.ed

clIrr('JlL

("OJllpOJlCIII.S

"<;t/

,

i~r,tJ

and

i:

nn

to be

mwd

/11-.

j'(

·

(·dl'il,

..

li

viI.rinhl<-:

:

ror

/.Iw

(·ol)!.ro!.

'l'1)(~

,':iI,illlll.l,,'d

(

·(~

dha('1<

:;il';II.t1s

C;~iI

01'

270 12. Control

of

lnduction

Motor

Drives

course only

be

correct if

the

parameters

of

the

flux model are in agreement

with

the

parameters

of

the

control plant; this

may

require on-Une

tuning

of

the

model.

C'Ontr'Ol

-l-M'Ot'Or

I

UsbRel I

"~'~Q

iSb

e'

Jp

e~'

I

~

Q

c:

o

"

I

isa

!I"lrtn~

L'

\

UsaReI I

1--

I

p'

1'0

c'Onlr'OIIers

Fil

C(

·

12.20.

Flux

model

as

an

open

loop observer for

the

motor

flux,

1.1

... li

,·

ld o

rientated

currents

and

the

electrical

torque

Elevated

rotor

i

Sq

temperature

Desaturation

( (Field weakening)

sd

n)

" li)

FI

l-(

.

I~.

:lI.

VC'No!'

clil~J\I"

I\

1I1

01'

dn

t.lll1c·cI

1111

x '''Cld..!

12.2

Control

of

Current-fed

lnduction

Motor

271

W

min

o'

" /

"

WRe/

1500

T

' - -

1 T

R

R - 2

ai

•

Flux

modeltuned,

p'

=p

·1500

R'Ol'Or

winding

sh'Ol1

circuiled, TR = T

RO

o

Flux

model

deluned

W

T

'R

• (m'Odel)

min-

t

/

,c

3

WRe/

T

RO

lR

'Ol'Or

winding

15'0'0

1

--si

'011

circuiled

'2

TRO

4 2

o I

(m'OI'Or)

ffi

T

R

1

'2

TRO

with

extemal

r'Ol'Or

resisl'Or

·15'00

a

b

Fig.

12.22.

Reversing

transients

of

22

kW

wound

rotor

motor

with

correctly

set

and

with

detuned

flux model.

(a)

Reversing

transients

with

current

limit;

(b)

operating

points

in

TR,

T~-

plane

The

vector

diagram

in Fig. 12.21 indicates

the

deviation

of

the

load

angle

o'

= arctan

w2TR

produced

by

a flux model,

that

may

have been

tuned

to

the

motor

at

nominal

temperature

and

flux leveI,

and

the

actual

load

angle

of

the

motor

o=arctanw2TR.

The

deviation is

w2(T

R

-

T

R

)

.do

=

o'

- o=

arctan

1 +W2

2T

R

R '

(12.50)

T

.do

> O für T

R

< T

R

caused by overheated

motor

.do

< Ofür T

R

> T

R

caused by cold

or

desaturated

motor

(field weakening)

If

the

flux model is

tuned

at

rated

load

of

the

motor

the

maximum

de-

viation

may

cover a

range

of

0.75T

RO

<

TR

< 1.

5TRO

with

a converter-fed

motor

where full line voltage

starts

do

not

occur.

The

effect

of

a

detuned

flux model is concealed

as

long as

the

motor

is

only

partially

loaded, because

the

speed controller

would

generate

the

quadrature

c

urrent

reference iSqRef needed for producing

the

torque,

even

though

the

nux

may

be

somewhat increased

or

reduced.

However,

when

the

motor

is

flllly

Jond(~d

iLlul

<'

.;

,,/I.,.!

ifi

damped,

there is

an

actualloss

of

torque, i.e.

the

lll

(l

l.or

'"

ILIl

IIOI.

1)('

flllly

load(~d.

This

is

dernollstrated

in

Fi~.

12.22, where a

22

kW

W()llfld

1'101,(11

' /l1C.l.or wil.h a

dd

il,joll/l.l

i/l<'l'l.ia

W fU, cOlIl.roll(·c!

t1lf'(l1lf~h

n

273

272 12. Control

of

Induction

Motor

Drives

speed reversal with tuned and detuned flux model.

The

tests were performed

with two values of rotor resistance

and

corresponding

rotor

time

constants

Tu, [H31, H32).

When

the

flux mo deI

is

correctly set

(1

and 4 in Fig. 12.22

;~,IJ),

full

torque

is

produced, whatever

the

rotor

resistancej with detuned

(11Ix

model

(2

and

3 in Fig. 12.22 a,b),

the

torque is reduced, resulting in a

[ower acceleration.

Of

course,

with

an

increased

rotor

resistance

the

motor

opcrates

at

higher

rotor

frequency

and

lower efficiency when producing

the

sa

IllC

torque, as was shown in Fig. 10.11.

I----------------~

I I

i:;

1

iSb

í'sq

RR

RRO

e'

jp

'

(Temperature)

I I

T

RO

._t.

- m

mM

I

j'Sd

ísa

i"

3

I

im:~:)::-

-

t-

+i

l2..

~

-L

~

Fl'mRO 'I"mR I - - - I

i'mR

I

mL

Inverse magnetising curve

(('I'

mR)

1"il',.12.23.

Nonlinear flux model, containing a nonlinear function for

saturation

..11','<"1,

,,

;

,.11<1

a control

input

for on- line

tuning

the

rotor

resistance

'I'hc

flux

mo dei in Fig. 12.16 b may

be

further refined by including a

110111 i

upar

function representing

saturation

[844)

and

an

additional

input

for

a

(.(

~

lllpcrature-

dependent

rotor

resistance, as shown in Fig. 12.23 [H32).

'I'lw

saturation

curve could

be

identified for a given

motor

in

the

factory

<ll'

prior to commissioning in

the

field, whereas

the

slow variations

of

the

I(

II.(

n'

rcsist,ance can be tuned on- line, based on

temperature

measurements

or

sOlJle idcntification procedure. An experimental result is seen in Fig. 12.24,

w

lIcrc

t.h(~

sarne

motor

used before is accelerated

at

current limit

through

a

wid(~

sp(~(

~

d

range with a linear flux model according to Fig. 12.16 b and with

1.11<'

lIolllin

ea

r model of Fig. 12.23j

the

variation of

the

magnetising current

i,,,

11

i:

; also sllowlI

ia

both

cases. Clearly,

taking

the

magnetic nonlinearity

illl.o

;Lc'('Ollllt. l'<'HlIltS in a bel;ter trackillg of tlw

fillx

and again increases th('

lI"

lx

illllllll lorqu(:

at

tiw

given

currenllevel.

1\

vll,riC'l.y

01'

:;r!I<'IIWS

has

IIc:(

:

1\

SIlC,J

{(

::-;

(.('c\

for

idclIl.il'yiJl

g

I.hc

varyinl',

lllo(.or

P:

l.

f'I'

l.lIwl

r

.('I' '['u,

11i'(I

S

l.

01'

whidl

ndl

fo

I'

n(ldiI.iOllH.llllc'

~ I

S

lll'f'lIlC'lIl

s

hy

IIll\,kill

~

II/i('

"r

i.I

tt' Il

l.n

l.,

li

'

voll.

l

lf

'\

'·

<"fi

II

iI.U",

II.

('

.

r,.

IC:

~I

.

I T I

12.2 Control

of

Current-fed

Induction

Motor

n

1/min

2S00

ímR/A

isq/A

a 18si

o

[

.

\

/

.....

aI

ísq/A

5:~

\-b

_.

Fig.

12.24.

Reversing

transients

of

22

kW

induction

motor

between field weakening

speeds,

(a)

with

constant

and

(b)

with

saturation-dependent

flux model

MS

dRe

'

~e'

úl

Speed

control/er

Field

weakening

Torque

control/er

m'd

MS

dRe

'

e

§

]l

§}

8

~

i'mR

Contrai

•:• Converter

and

motor

Fig.

12.25.

TR- Identification

through

correlation

An identification

method

without

the

need

of

a voltage measurement

[G5,

GG)

is

ba

sed

on

the

fact

that

the

output

signals iSdRef' iSqRef

of

the

controllcrs

iII

Ji'if~·

12.25

a.llow

decoupled control

of

the

plant

in

the

d-,

q_

il)((~0

CJlIly

ir

I.hc

'

;U

ll(\(~

fi

lls(~d

for the

modulation

is

in

agreement

with

the

H.C'I.II

:d

pCl:

lil.iClII I'

C1i'

I.h,'

f1l1x

wav('.

1I"II('c'

;1.

\ow

\cvd

dlil.r;\.d.eristic:

tc-~st

dis-.

274

12.

Control

of

Induction

Motor

Drives

Lurbance injected

into

the

presumed

iSdRef

channel

must

be uncorrelated

with

the

noise in

the

real isq-channel, expressed for example by

the

speed

error

at

the

input

of

the

speed controller.

If

there

is

noticeable correlation it

c

an

serve as

an

indication

that

the

supposed d'-axis

is

not

orthogonal

with

the

actual

q-axis and, disregarding other sources of error,

the

parameter

T.k

in

the

flux model needs

to

be

corrected

to

track

the

planto

The

correlation

process is manageable when it

can

be performed in

the

microprocessor used

for controlling the drive. For example, by employing a pseudo-random

binary

sequence (PRBS) as a

test

disturbance,

the

generation of

the

signal,

its

cor-

relation

with

the

speed

error

and

the

adjustment

of

the

parameter

in

the

flux

model

are

straight-forward,

requiring very little additional computing time.

The

sign of

the

cross correlation function points

to

the

direction in which

T.k

should be adjusted.

The

sampling

time

of

the

PRBS

should be chosen

sufficiently small

to

allow

the

field lag

to

attenuate

the

signal, i.e.

to

avoid

an

immediate

effect on

the

torque through variation of

imR'

On

the

other

hand,

building

up

a meaningful correlation function requires sufficient averaging

time

for suppressing irrelevant noise components.

Another

RR-

adaptation

method

that

is

somewhat easier

to

implement

was described in [H31,H32,S42];

it

is

based

On

a comparison

of

volt age signals

obtained

by measurements

and

derived from

the

flux model.

Eq

. (12.45)

may

1>

e

written

in

the

form

di.mR

()

R'

L di.s

(

5,5

()

t =

(

1 -

(J"

)

L S

~

=

l!s

t - s

:?os

- (J' S

dt

'

(12.51)

w

hcn

~

c.

dt)

is

the

"volt age

behind

the

transient

stator

impedance". Assuming

/l .,;

to

i>

c kllown, for instance from a

temperature

senSor in

the

stator

winding,

"".!

(/

/' S

to

be relatively unaffected by

saturation,

~

s

(t)

may be derived

ri

(" II a

111(

~

a

S

llrement

of

terminal

volt ages

and

currentS.

When

converting this

(·

qll

i

tl

.

ioll

lo

field coordinates defined by

the

rotor

flux mo dei in Fig. 12.20 or

1

'L.

'2

:1

, wc nnd for

the

direct component

of

the

volt age

dimR

.

disd

.

Co

d =

(

1 - (J"

)

L s

--

= USd -

Rs

tSd

- (J'

Ls

--

+

WmR

(J' L s

ts

q

,

. & &

(12.52)

wlaiell reduces in steady

state

to

CSrl

~

'USd

-

Rs

iSd

+WmR (J" Ls

iS

q

:::::J

O.

(12.53)

tu; I.be angle of transformation p', being derived from an initially

detuned

JllOdd,

rnay be incorrect this condition

is

not

automatically

satisfied

but

may

1)('

Ils(~d

for

sdf-

tuning

the

model according

to

, ,

(I(UII;Rj{

u) _ CSd

(12.Gt1)

/",<l",!,1

II

-

fi,.

("

, '

'lf

l

12.3

Control

of

Voltage-fed

Induction

Motor

275

RR

TR

s

0.200

0.150

0.100

s

o j

5

10

Fig.

12.26.

Rw

self-

tuning

employing

terminal

voltages.

(a)

Self-tuning

schem

ej

(b)

experimental

results

with

22

kW

wound-rotor

motor

This

scheme

is

shown in Fig.

12

.

26

a;

to

obtain

convergence,

the

signs

of

WmR

and

iS

q

have

to

be correctly chosen. AIso,

there

are

lower

practical

limits

of

speed

and

load, for which

the

adaptation

yields reliable results.

When

the

rotor

current

is

dose

to

zero

at

low load, a correct

setting

of

T.k

is

not

important

, provided

the

parameter

is

quickly

adjusted

when

load

is

applied. A

test

result is seen in Fig.

12

.

26

b

taken

on

a

22

kW

wound

rotor

motor,

with

external

rotor

resistors being switched in

and

out.

The

lag of

a

few

seconds would normally

be

acceptable for correcting a

temperature

induced variation

of

the

rotor resistance.

12.3

Rotor

FIux

Orientated

ControI

of

Voltage-fed

Induction

Motor

The

field

orientated

control scheme in Sect. 12.2 was introduced with

the

sim-

plifying

assumption

of

current

sources in

the

stator

circuits; this was achieved

by fast cOntrol loops for

the

stator

currents,

making

use

of

MOSFET-

or

IGBT-

converters with ample ceiling voltage

and

short

access

time

due

to

high

switching frequency.

Of

course, these conditions

cannot

be

met

at

maximum

speed, where

rectangular

volt age waveforms are desired for fully utilising

the

converter; hence

the

concept of impressing

currents

becomes impractical

in

the

field weakening speed range. Another

area

of application, where

the

approach

with

current

sources and, in

steady

state

condition, nearly sinu-

soidal

stator

currents

has

to

be abandoned

is

that

of pulse-width

modulated

voltage-soUl'ce converters for larger drives employing

thyristors

and

GTO-

thyri

stor

s.

Tlt

e

fi

witching frequency of such converters is usually below 1

kU'l"

as

colllJlar<

~

d

t.o

10

kHz for IGBT-

or

20

kH'l,

for

MOSFET-

converters.

A s

;t.

C

()Jl

:;

('(l'l('ll

C

(

~,

t1w

ltanllOlli('s

of

t.lw :;t.nt.oj' nllT('llts may bc

af

appr

c

ci

a-

1.1(,

111

1

11',11

\1.

11.1"

tl.lld

1.1)('

lI'if

illllll't

.

iotl

01'

II<':t.t'I.v

"ill

::

I.

I

IIII

.i

lllCOll

:;

"

(·

.

\lrl'(

~

llt

('.o!ll.rol

1"'("1111"

::

qll'

·l

l

l.i""

II.

loI

',',

276

12.

Control

of

Induction

Motor

Drives

As

a result,

the

stator

voItage equation (10.50) now has

to

be

taken

into

account as well; by inserting the magnetising current vector, Eq. (12.22),

representing

the

rotor flux, Eq. (12.45) results. Converting

the

volt age vector

to

field coordinates as in

Eq

. (12.26),

-j

(2

•

Y,s

(t)

e =

USd

+J

uS

q

,

(12.55)

and

splitting

in real

and

imaginary

components yields

disd

USd

dimR

.

(JTs

di

+

iSd

=

Rs

-

(1

- (J)

Ts

~

+

(JTSWmR

ZSq

,

(12.56)

dis

q

.

uS

q

()'

. ( )

(J

T

S

di

+

ZSq

=

Rs

- 1 -

(J

Ts

WmR

ZmR

-

(J

Ts

WmR

ZSd . 12.57

These

equations describe

the

interactions between

the

field-orientated sta-

tor

volt ages

and

currents;

together

with Eqs. (12.27, 12.33,

12

.34)

and

the

equations for

the

mechanical

part

of

the

plant

(10.52, 10.53) they form

the

mathematical

model of

the

voltage-fed induction

motor

in field coordinates.

Thi

s model is contained iu graphical form in

the

upper

part

of Fig. 12.27.

The

additional right-hand si de

terms

in Eqs. (12.56, 12.57)

constitute

undesirable

coupling

terms

which could be compensated by suitable feed-forward signals

aL

tI.e

output

side of

the

current

controllers [G3, G4].

The

principie of field orientated control, applied to this scheme, is shown

iII

I.

h(

! lower

part

of Fig. 12.27.

With

the

assumption

that

the

control dynamics

01'

I.

II<!

voltagc source converter can be

approximated

by a small delay

that

is

rda

.

I.I

!

.!

Lo

Lhe

clock frequency

of

the

modulator,

the

transformations within

1.11\'

pLud

.

are

again cancelled by inverse operations performed

ou

the

reference

:.Idl·

(;

t.llillg

for

a

transformation

from

the

field-orientated into

the

stator

(<I"r,lillal.l'

~

;yst

e

m

,

'

/1.:;

11<'1

'-= (-USd +j

USq)Ref

e

j

(2'

;

(12.58)

I'

I:

:

;

1I

~aill

the angle of

the

fundamental flux wave as determined by a flux

iI,('([llisitiOll

scheme, for instance

the

flux model shown in Fig. 12.16 b.

The

Jllaill dilrcrence between

the

control schemes in Fig. 12.14

and

Fig. 12.27 is

l.

h;tI,

I.he

current

control is now performed in field coordinates, where

the

con-

I.roll(

!rs are processing DC signals in steady

state,

thus

avoiding

the

problem

or

pltase shift of

AC

current loops. AIso, the digital

part

of

the

control

may

1I0W

illclude

the

pulse-width-modulator

and

can be extended down

to

thc

I

~

(!ll(!ration

of

the switching signals for

the

converter.

Th(!

rCllIaillder

of

the control system is similar

to

the

one shown in Fig.

I

:~.

1,1.

TI.e

~tructure

in Fig. 12.27 is somewhat

redundant

since

the

task of

is

d

-

1L

lld

isC/

-

mutrol

could also be assumed by the flux and torque controlknl,

(lrllil.i.illg

th(!

CIIIT('1I1;

COl1t,fo\l('rs.

Field weakening is adricvctl with a

fllllCt.ioll

r:

llIlt'J'ill.or

<I<'IllIi

lll

'( a

S

I)(

~

(

~

d

-

dq)(!lld('1I1.

r('r(~I'I'III'(\

for

t\w

lJ1agnl'tisilll';

CIlITI

!

IILi

li

lll

í

l.

l

ll

l',

LIli'

:·i

U,,I.1I1'

voll.

nW!H

wil.h

;~

li

llp"1

illlpO

:i

l'd

vo]I.;q

:.

,'

cOlll.l'ol

loop

wOIII.!

I"

, I\

ljll

lI

.I'

()t

l/atl

hl

..

.

12.3 Control

of

Voltage-fed

Induction

Motor

277

Us3

...

e sd

,

Rs

,

------f---

,

Flux

Contrai

control/er

U

S

1RfJ

I

U

S

2R(Jf

,

,E

U

3Re'

L-J-~·F::::·~

.

~

:"1.:.:.:.:.:::

~.

s

~L-:'-ó4-.

us

qRef

:.:

.

..

•

..

"

..

:_-.:

(J)Rel

:-------.:

€Re/

Phase Coordinate Current

Speed Angle

spllt

transformo

control/ers

control/er conlrol/er

Fig.

12.27.

Block

diagram

of

induction

motor

control

in

field coordinates,

assuming

volt age source converter (- - - optional)

A

22

kW

induction

motor

fed by a voltage source

transistor

converter

with

vectorial

PWM

and

controlled by a signal processor

programmed

in

C language has been designed

and

tested

in

the

laboratorYj

the

somewhat

modified control

structure

is seen in Fig.

12

.

28

[K52].

Field-weakening is now

performed by a voltage limiter, which corresponds to

the

solution shown in

Fig. 7.13 for a DC motor.

The

converter was a 30

kVA

experimental

unit

with

540 V

DC

link voltage

and

a clock frequency

of

1.37 kHzj

the

sampling

frequency for

the

inner loops is twice

the

clock frequency, Fig. 11.8j

an

integer

fraction

of

this

frequency was used for

the

outer

control loops.

A reversing

transient

of

the

speed controlled drive is depicted

in

Fig. 12.29,

with

the

inertia

of

the

drive increased by a DC dynamometerj

it

confirms

the

expectations

by showing nearly perfect decoupling of

the

d - q- axeSj

I.\ti

s

is

manifested by

the

constant

magnetisiug

current

and

the

rapid

rise

1.0

lll

axilfllll/1 value

of

the

quadrature

current representing torque. While

the

s

tator

Cllrrcllts cxhihit large

transicnt

tenns,

the

magnetising

current

remains

pracl.ically

:

;

illll~;()idali

thiti is

dll(~

t.o

til<'

Iag

TR,

acting as a low pass filter.

'J'!H

!

J'i

~

('

I.illll'

"r

/.III'

I,o('qlll!

of

a

hulIl.

'2

1/1.8

COI'fl'sp

Ollds to the limits imposed

I,.\'

I.h, ·

(',,111.1'

..

1d

'y

II

fi

lII

i ('H

01'

/.IIC'

)'WM

('OIlV

I'I'I,"

r;

I.his

rnpid

I'

ns

poll:w

is

HIIP('

-

278

12

.

Control

or

Induction

Motor

Drives

Field

coordina/es

S/a/or coordina/es

Vol/age

Flux

PWM

Converter

limi/er

m

e

jp'

Speed

con/rol/er

u

VQ

lusaR,,11

I

I~

t

úl

mM

R.,

I I

mM

'",R"

I

úl

i",

-jP'

u

.~

e·

-,

Fig.

12.28.

Microcomputer

control

or

induction

motor

wilh

a voltage source

PWM-converter

rior to

that

of a high-performance

De

drive with a 6-pulse line-commutated

converter

at

50 Hz.

The

pertinent

loci of

the

stator-

and

the

magnetising

Clll'rent vectors

i.s

(t) , i.mR(t) are seen in Fig. 12.30. Again,

the

magnetis-

iIlg

c

mrent

vector reverses on a near perfect circular

path,

while

the

stator

('11

rrcllt vector

is

temporarily boosted

to

produ ce

the

desired torque.

'r1t(~

ulock diagram shown

in

Fig. 12.27

is

simplified in so far as

the

internal

!'c-('dh;lCk

signals seem

to

be derived directly from

the

motor, while in reality

I.Iwy

are

gcnerated by

the

flux model computed

in

parallel

to

the

motor,

I"i)',. 12.20.

This

observer-like

structure

is

shown

in

more detail

in

Fig. 12.31.

11,'(((',(

'

OIW

should distinguish between

the

real

but

not

accessible variables,

('or

illstallce p,

and

the model-based approximate signals such as p'. Since

the

coordillat.e transformations

at

the

input

of

the

converter

and

in

the

flux model

ilJ'(~

l)(~rformed

by

the

sarne angle

p',

the

actual

stator

frequency

Wl

is

in

exact

ll!-,:n~e1l1eIlt

with

the

frequency

WmR

generated

in

the

flux mode!.

ln

steady

~;

I.a(.c

~

it corresponds (assuming a two pole machine)

to

the

extrapolated

no-

loatl speed of

the

motor; if

the

measured speed signal W

is

correct,

then

the

csl.jllli\.ted rotor frequency

is

also in agreement

with

the

actual

rotor frequency,

C,)~~

=

W2

.

Of

course, should

the

model

parameter

TR be detuned,

the

flux could

(kvial,c~

from

the

desired value;

at

reduced flux,

the

rotor frequency would be

1.00

high alld vice versa,

but

the

torque would still be correct, unless

tlH~

CIII,(,C~J)(.S

an

~

liJllitcd, ot.herwise

the

speed controller (assuming

it

to

be frce of

dri!'t.)

illil.ia(.c

~ :

j

lhe

Ilece::;sary

changc~s.

lu

t.hc~

l"wl~r

[larl o[

Fig

. 12.31 lhe

Oll

c

.

lilll

~

Uwt.ulIillg scheme is

HPI~ll

t,hn.t.

W lu<

d"

::l'I'i[,,',]

iIi

ro'il';.

12

.

2(;;

ah;o ali all';llI'it.lllll

iH

illdi(';,i.<

~

d

for

c·

slilllat.il\/

-';

I.ho

.'1

111'.1('

,

/.

I)

IlI'l.w(

·

(·u

t.I,,~

"'"'1"'111

.

iI

.lld volt:q'.'· v,·,·t."!'!: iII

Ht.c'ady

H

t.Il.t.c;

I

I:

:

12.4

Induction

Motor

with

a

Current

Source

Converter

279

Jmin

'1

60~

, ,

~

, , , ,

,I/S

,600

0.1

0.2

O~

0.6

0.7 0.8 0

.9

1.0

1.1

1.2

l

t ".

I

sq

100 . .

O ,

__

.,

, , , , :

~,_

I ,... I

,tis

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.1

1.2

tA ImR

:1

, , , , , , , , , , , ,

ti

s

0.0

0.1

0

.2

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.1

1.2

100t

A Isa

o

C/

\J0.v

C

70\

A

I

f\

I

f\

-"/\'1

{\

('

\I

n

f\

1"\ A

yA

f\

Í\

ti

s\

P\1\\A74

f\ ){\,

\

\/~}\r\t

'\f

q

\I

\./

3~p

Af\

f\

f\1JLf\

fV)

(V)JV\

fi

f\1Jlf\

f\

f\JJLf\

tis

ImRa

'30VV

WIJ2J

V

rJJ

V

O

.4

~.6

VoV

VoWíJ

V}9V

IJ1YJ

Vlj,1V

V

112

Fig.

12.29.

Reversing

transient

or

22

kW

induction

motor

drive

with

voltage source

converter

and

signal processar control

at

no load

iSb

i

mRb

Current Iimit

t i

sq

100

75

i

mRa

50

25

i

mR

O j

30

.I

35

/

-100

a

b C

Fig.

12.30.

Stator

current

and

magnetising

current

vectors

of

PWM-converter

drive

during

the

speed

rever sal

shown

in

Fig. 12.29

(a),

(b)

Currents

in

stator

coordinates,

(c) in field

coordinates

shown

in

Fig. 12.32

the

needed signals are available in

the

control computer,

where

they

are generated with

the

sarne

transformation

angle p'.

With

the

help of Eqs. (10.72,10.76) this results

in

,

7r

,(1

-

(J)

W2

T

R

tau

(I(!

-I-

:-)

= cot (-<p ) = .

(T

)2

(12.59)

~

1 +

(J

W2

n

1'1'01"

UI('

...

·:ltdt.i/ll·; C[lIaclrat.i/: cCfllat.ioll for (w

'J

Tu)'

ltml

the

known

va.hlP

(Ir

w~

\

H

II.,U",

!'

(·

lI

t,

i

ll

uLl

./·

(lr

t.lw

11ICldd t"l.Il1.l1l1'l.(·r

'/';(

..

.,,,1<1

hc~

dC

'

rivc:c1

,

Werner Leonhard Control of Electrical Drives

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