Werner Leonhard Control of Electrical Drives

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320 13.

Induction

Motor

Drive

with

Reduced

Speed

Range

y (v+

jWot

PWM

sector

Ref e-j wot

y(v-l)

e- jwot

13.16.

Volt age vectors of

converter

line-voltage

coordinates

l/lN

(iNd

+ jiNq) dt =

3.J2/2

(INact + jINreacd

(13.38)

t-T

holds. For

the

purpose

offast

control,

the

instantaneous values iNd(t), iNq (t)

llIay

be used as feedback signals

place of active

and

reactive currents,

"VI'H

though

they

are only identical as

mean

values and with high switching

fJ'c<[llcncy,

i.e. low harmonic contento

The

converter

acts

as a reactive com-

1)(

llsator

by producing a controllable reactive line current, whereas

the

active

I iII\: c

mrent

has

the

task

of controlling

the

DC link volt age

UD.

The

mesh equation for

the

DC link volt age is, combining

the

chine-side

;\.lId

the line-side link currents iDM, iDN,

dUD.

= tDN -

tDM;

(13.39)

·i

a disturbance in

the

voltage

controlloop.

When

the

converter is used

(!xdusivelyas a reactive compensator, i.e.

without

a machine-side converter,

I.be

constraint

iDM

The

available voltage vectors

moving coordinates

the

terminaIs

1.11('

line-side converter are indicated in Fig. 13.16, from which

the

PWM

collvcrlcr selects by vectorial modulation in each

intervall

the

two

neigh

"O\lriIl~\

vec.tors.

e switching fllIlctions Si

±1 correspond again

ti\('

!'ol.(:II(.ial

(;11(

: (".()\lvcr!;(!r

lel"llliual

i, as Hl1oWI\

ill

Fig.

11.R; t:lw Jlla

gnitlldc

01'

1,111'

voll

iI,/'

V('('!.!)!":;

i:;

dd.<

rlllill('d

LI\('

1>(;

lilll(

VO]l.i

;<',

13,2 Line-side voltage source converter

321

I +

)

Nq'

control/er

<n.,

I~I~

ó+~-:

----'-

Ir:: ~

NdR

•

'control/er

iNb

iNd

Fig.

13.17.

BIock

diagram

the

orthogonal

controI

the

line-side

converter

= v

+ j

V12

v23

e-h

=uD/2[(Sl -

S2)

(S2

S3)e-

]

jvrr

= uD/4[(2S

- S3) +

jV3(S2

S3)]

e , (13.40)

where

0,1,2

The

switching combinations result in a six-pointed

star

for

the

voltage vector

1L(

t);

in addition

there

are

the

two zero vectors

(SI, S2,

S3)

(-1,

-1,

-1)

and

(1,1,1),

when

the

converter terminaIs are

short

circuited

the

upper

or lower DC bus.

When

neglecting

the

protective intervals

and

applying

the

equivalences

given in Eqs. 13.21,

the

link

current

iDN

may

be expressed by

the

line cur-

rents,

iDN =

SliNl

+ S2iN2 + S3iN3

1/3

[(2S

- S3)iNa +

(S2

- S3)iNb];

(13.41 )

during

the

zero vector intervals

the

line currents

are

bypassing

the

DC-link,

iDN =

The

six-pointed

star

the

available converter volt ages in line-voltage

coordinates, Fig. 13.16,

1L(t)

)..

+ jV

(vrr

/3-w

(13.42)

rotates with

the

angular

velo city W

in c10ckwise direction

and

the

task

thc

current eontrollers

generate

the

needed direct

and

quadrature

volt-

;lj

;(!

lllpüUClltS

('li

,l + jVq)Rc! for tran5fo

rmation

into

the

AC components

(

'(I"

-1-

J V

I1)lkj';

til(!

~do

rial

Illodlllat,or

1,11(

dd<!rlllines for each switching

lH:l'io.] '

I:,

LI\('

1l"(

1iflit

I'Y

lii

i')

lIi1h (SI

"r..,'

,.:,S:I).

III

vi,

e tI:a.} voltag

V('('

1.01' '/l N

(/.),

' 1,\ (1) :I

J'2

ali,]

1.1«'

lol,;d

il'/'

, /i L

I\,

I' '/I(t)

)..

!.II(! 1I10<1I1];d.11I1I

:~22

13.

Induction

Motor

Drive

with

Reduced

Speed

Range

is mainly performed

the

vicinity of

the

real axis, using

the

two adjacent

available voltage vectors.

Vd(t)

and

vq(t) are in steady

state

voltages

wit.h

PWM-related

noise; because of

the

transformation,

they contain no line

I'requency components.

The

block

diagram

the

orthogonal control

drawn

Fig. 13.17 show-

iug in

the

upper

left

comer

demodulator

for identifying

the

line vector from

I.wo

the

line volt ages

and

the

usual transformations.

The

transformed cur-

IltS,

representing DC signals

steady

state,

are controlled in two channels,

with

the

undesired interactions removed again by feed-forward

the

output

()f

the

current

controllers.

Experimental

results

obtained

with a 20

kVA

IGBT

reactive

compensator

are depicted in Fig. 13.18 employing vectorial

PWM

with 4 kHz clock fre-

qllency [H36).

The

line currents shown

Fig. 13.18 a are nearly sinusoidal

aud

the

transition

from leading

lagging reactive current takes only a

few

ms.

Changing

the

link volt age reference

UDRef

in Fig. 13.18 b results in a

hrief active

current

component for charging

the

link capacitor, while

the

re-

active

current

remains nearly undisturbed; clearly

the

decoupling control

dfective.

link voltage

Reactive companent af

fine

current

350

INq/A

Ir(j

e·/

urfV

300

. 'Ia

• t

20ms

___

-i

-I-

....l-

I~I

-i

W-\

ff-

"1\

..,.,

, i

N t

1.'11)

ilA

uD"

20ms

JActl

iNd

Reac

ive

'\,:;

om,

one

fine

urre t

il A

()

/lIV

; I.',()

·50

·30

Fi~

13.18.

Measured s

tep

responses on a line-side

IGBT

converter

wil.h

v,~ct.orial

PWM

4 kHz clock frequency

(a)

Itc·

versa.1

Lhe

rea.ctive

current,

(b)

Change

ofDe

link voltage

TIl<'

f')(;l.lll[lI,~

l1\akf~S

iI.

(~vid(:lI1.

Uml. pow(:r

kd.rol\ics,

()rl.(

look('d

aI.

II. '

·'

bll! i

01'

I.l'ollld

" H

JlI('

lill(,

-lii

illl.f'l'af'i.ioll~;

iII

!.lI('

fU)'I1I

·;

"f'I.iv(' ('111'1"':111.1'

1.11<1

,I"

"IO'f1

í(

II,

nll

provi

.!,'

:;,dlll.illll

rol'

\'("'I<'Villl',

:·

"1<'1,

..t["'(,!.I'i;

I.lIÍ

13.3

Wound-Rotor

Induction

with

Slip-Power Recovery

323

due

the

emergence of semiconductor devices

with

adequate switching

frequency.

The

cost

and

complexity associated

with

the

line-side converter

will

future

be tolerable even with lower power equipment as

industrial

drives. At higher power

the

:fI.exibility will be

important

for

the

stable

and

economical

operation

the

supply grid.

13.3

Wound-Rotor

Induction

Motor

with

Slip-Power

Recovery

The

doubly-fed machine described

the

Sect. 13.1 can

operate

as a

motor

generator

a speed

band

above or below synchronism, drawing leading

or lagging

stator

current

from

the

line. Depending

the

operating

condi-

tion

power

:fI.ows

from

the

converter

the

rotor or

the

reverse direction.

This

high degree of :fI.exibility calls for a relatively costly converter

but

sim-

plifications are possible when

the

specifications are relaxed. For example,

when rectifying

the

three-phase

rotor

currents

with

diodes and feeding a DC

link,

the

power flow becomes unidirectional.

This

is so because

both

volt age

and

current

the

DC side of

the

rectifier are restricted

positive valuesj

seen from

the

AC side

the

rectifier

appears

like a nonlinear, purely resistive

network.

The

purpose of this scheme may therefore be

recover

the

slip

power

that

would otherwise be lost in external

rotor

resistorsj

can

either

converted

mechanical power in a DC

motor

coupled to

the

shaft of

the

induction

motor

(Kramer-drive) or fed back to

the

AC line with

the

help

a line-commutated or

other

type

of inverter

(static

Scherbius-drive) as

explained

Fig. 13.19 a.

Scherbius

(j)

ÜDmax

IS'

UR=O

)

---.L

(j)

o -

UDmax

Loadcurve

a b

Fig.

13.19.

Wound-rotor

motor

with

slip power recovery scheme.

(

Circuit;

(b)

Operating

range

Ag;ülI,

~;[ip

POW(~l"

rc:c()very is of part.icular in(;erest

high power such as

I\(

(!ded

for

)'ul.;~l.illl·.

COllVf:

I·l"rs

with

H.Yw1lf'd

:iI

o)'al

rollin

g llIill driv('

UI'

for

1,,

1"1

"",.,,

plllll

n!.f'lIdilll';

iII!."

1.11<'

:~I)

1'11,<',

('(.1..

7.1\

, Whii<-

iiI<'