Werner Leonhard Control of Electrical Drives

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2./'

- ó

:HO

11. Power Supplies for

Adjustable

Speed

AC Drives

Ul2

/1pply

U23

-o

3.,,101

2 t 3

Load

D Principie

a cross

bar

connection

b Example

switching arrangement

U,2

(1)

w,t

c Selection

fine

voltages

d Bidirectional switches

I;'i~.

11.20.

Principie

PWM

matrix

converter for

generating

viLri

frequency voltages

directly

from

the

line volt ages

lU . '

voi(

thus

facilitating large scale

integration

with semiconductors.

TIl!' prillciple of a

matrix

converter is shown

Fig.11.20 a in

the

form

crel

;;S

;1.1'

al'rangement, where

the

three

load

terminals

are

alternatively

(·

"I!II!'cl.I

1.0

the

three

supply terminals.

This

requires nine bidirectional

Íl

.dl\

·:

t"Íf.(

.11.20 d,

pulse-width-modulated

some kHzj a possible

;

••

' :

\lII

',1'

III('Il[.

is seen in Fig. 11.20 b, where

each

time

interval

t = 1r/6

iiI<'

il';

lwsl.

tine-to-line voltage assumes

the

role

the

former

link volt-

.•

;I.

shown in Fig. 11.20

This switching

strategy

permit

the

highest

: ; : :

lhl(

output

voltagej

the

sarne

time

the

reactive line-side

current

n'd

u('(

sillce

the

current

flows only in

the

centre

region of

the

line volt-

." p

rioc!

The

higher frequency components of

the

line

currents

can

l('lll()v(~d

hy capacitive filters. As usual,

must

prevented

that

the

line

v()ll.;q

;

are

temporarily

short

circuited

but

this

is excluded

with

the

arrange-

1II

lll.

itcbes in Fig. 11.20 b.

The

equivalence for vectorial

modulation

Iii.:" w rrcsponds

. (11.2),

then

reads

s I

!.,

.r =

(USa

+ j

USb)Rer

=U ik (r)

(

~~)

_ e

,,/3

)

(11.8)

1'0

wll(

l'!

'II

id'1')

t.lw

hil

cst

1i\H

I,()

lin

voll.lIl

'·

iII

('jL('h

j (j

illt

nva

.l.

ln a

dcli

tillll

1' 1 I I .

....

I 2/'0 'III Ilolds,

wlwn

1'0 i

i-!

1.110'

'1.

('1'0

vI'cl,or i

lll.<

;rval , wbclI

I.hc

11I1I!.

!,r

....

h"rI

. dl'('uil.l·

0111'

01'

11('

lill!' 1.(·I·

IÍ

llill

rI,

f i/\,

II)!.

12.

Control

Induction

Motor

Drives

When

comparing

the

dynamic

model

of a

separately

excited DC machine,

Eqs.

1-5.4),

Fig

. 5.4,

with

that

induction

machine, Eqs, (10.50-

10.53), Fig. 10.16,

obvious

that

the

latter

represents a much

com-

plex cOntrol planto

This

is caused by

the

fact

that

the

main

flux

and

armature

current

distribution

of a DC machine

are

fixed in space

and

can

directly

and

independently

controlled while

with

AC machine these

quan-

tities

are

strongly

interacting

and

move with respect

the

stator,

the

rotor

as well as each otherj

they

are

determined

the

instantaneous

values

t,he

stator

currents,

two

which represent

independent

control variables. An

dditional

complication

stems

from

the

fact

the

rotor

currents

cannot

measured

with

ordinary

cage rotors. Hence

the

motor

is a nonlinear

multi-variable control

plant

that

kept

cOntrol engineers puzzling for a long

time.

The

differences in control

dynamics

and

motor

are

best

<~xplained

the

mechanical mo deIs shown in Fig.

Fig

.1 a, cor-

ponding

a DC

motor

with

a mechanical load, a disk is driven by

I.angential force

acting

P which can

moved in a

radial

slot

I,y

radial

force

acting

against

a springj caused by velocity-dependent

I'ri

ctio

the

radial

motion

the

is assumed

relatively slow.

Between this mechanical

arrangement

and

the

electric model

a DC

I<l<:hine

the

following analogies

hold

armature

current,

R h

electrical torque,

main

fiux,

R W

induced voltage (e.m.f.),

field voltage, RW

electrical power.

Controlling torque, speed

and

angular

position

the

disk is

straight-

IllI'w

ard

and

can

independ

ently chosenj

the

analogy applies

"pI'I'atioll below base speed as well as in

the

eld-weakening range

with

lill,il.a

l.i

bcing e

ither

saturation

(length of

the

radial

slot) or

maximum

·'I

,dll

('.(

age (circumferential velo city of pin).

illlil

arra

nge

ment

applics

the

motor,

Fig.12.1 bj however,

;

drivc

three

llllecting rods

that

apply

forces h ,

III

l'I'I'

x(·d

din'

l'.l

iollS Rp

a.<:ed

°. To procluce a

smooth

circular

III,tI

l,'

11.1.

II!'

/la

lIlC'

t.il1w

<l.:

I,.,illl', (,

II!'

pill

;d,

p;ivI'1I

radius, a

J!'~

I ,

n I.," I i Id . "r I

tll.,

'1·IH

.i II

,rC

'II

ln I

"1(

iI"d r, I I' I"

II.'

iI 'I';

l'Oll

I ial