Werner Leonhard Control of Electrical Drives

300

12. Control of

Indu

c

tion

Motor Drives

12.6 ControI of

an

Inducti

on Motor Using a Combined

FIux

ModeI

301

If

the

flux model is implemented in

stator

coordinates, processing variable

frequency AC quantities,

the

speed dependent

transition

of

the

estimates

from

the

current-based

to

the

voltage-based section could

be

done dynamically by

using

the

frequency response

of

the

observerj again,

at

low speed

the

results

of

the

current

model would

dominate

whereas

the

signals

obtained

from

the

voltages would prevail

at

elevated speed.

&!

~I

r

o::

c;)

CC

C\j

>-

C\,i

CC

C\j

>-

"-

vi

&"

8 1

81

.....

-

(l)

ê:

(l)

2

a

oS

.~

~

a

E:

(l)

Ol

~

-o...

~

'+-.

o::

Q

~Q

Q)

'-

~

iJ

ti

::J

&!

~

E

0lV)

.

S;;

c:~

I

l-E

:-...5'

~.~~

~

I~~~

8

~c:>-

~~

:s.

::J

-..;::

ço

cc

h~

1

h

~

L0

cc

C\j

>-

c:

"-

"Q

.g

vi

(l)

«l

&"

~.§

r.nVí

,

(l)

Q)

"Q

t t t

a

E:

......

c:

(l)

t::

::J

SJ

'-

~

<'A

'-

<'A

::J

.~

8

Meu

::;

urenll !/Its

l"

i

fl:.

I

:lA7.

(:"".1,;"",, V()Ii.:Ij·.'

'/

cIII

·,...·III.

111,,01,·'

f"r

r"L,,)'

IIIIX ,

·,;

L;lIlilL;()II

13.

Induction

Motor

Drive

with

Reduced

Speed

Range

Some mechanical loads, such as fans

or

centrifugaI pumps, exhibit a

strong

dependence

of

the

load torque

on

speed, so

that

a limited speed control

range suffices for achieving

the

desired effect.

The

sarne is

true

for

rotating

converters employing a flywheel, Sect. 7.4j since

the

kinetic energy

of

the

rotating

masses varies

with

the

square of

the

speed, there

is

little

incentive in

varying

the

speed by more

than,

say

20

or 25%. Similar

situations

exist if

an

electrical island grid with a fluctuating frequency, for instance a railway grid,

is

to

be supplied from

the

public

constant

frequency line

through

a

rotating

converter,

or

conversely, when a variable speed

generator

is feeding power

into

the

constant

frequency grid,

as

may be

the

case with wind energy

plants

or

pumped

storage hydro setsj using variable speed

there

would improve

the

aerodynamic

efficiency of

the

wind

rotor

with

changing wind velo city or

the

hydraulic efficiency

of

a

pumpjturbine

with varying head.

For applications

of

this

kind a wound-rotor induction

motor

drive presents

an interesting solutionj if

the

stator

is connected

to

the

constant

frequency

grid while

the

rotor

is

fed

with

slip frequency by a

static

converter,

its

rating

is

mainly

determined by

the

desired speed range

Llw

and

can be kept relatively

small. Still,

the

slip power

may

be

substantial

with

large machines, calling

for

an

efficient control scheme.

Beginning

at

about

the

tum

of

the

century, a variety of drive circuits has

been developed

that

made

use

of

auxiliary machines such as

rotary

frequency

changers [L23],

they

are

of

course obsolete todaYj

with

the

progress

of

power

electronics new solutions have become possible here too, one of which will

be

discussed in Sect. 13.1.

The

simplified

mathematical

mo deI

of

the

symmetrical

induction

machine derived in Chapo 10 can be used for

this

purpose with

minor modifications.

13.1

Doubly-fed

Induction

Machine

with

Constant

Stator

Frequency

and

Field-orientated

Rotor

Current

Whell

din

~

ct

<:111"1'('111:

is supplied

to

the

sliprings

of

a wound-rotor induction

ll\ol

,oJ') (.11(, :;!.i

Ü,,!'

"r which

is

C()ulwcl.(~d

to the COllstant frequency line,

the

I!lO!."!'

11

:

111

111111': 1

1./11'

Pl'lIpl'!'I,j(

' H

III'

il

fI

.Y11('!tr'

olloIlH

Hladtirl(~.

Constaul'.

(.orqlw

304

13.

Induction

Motor

Drive

with

Reduced

Speed

Range

can only

be

produced

if

the

rotor

is in synchronism

with

the

stator

field;

the

machine

can

also deliver reactive power,

but

at

the

sarne

time

the

problems

of

Lhe

line-fed synchronous machine become

apparent,

which includes

starting

:Iml

synchronisation as

we11

as oscillatory

transients

and

pu11-out torque.

This

i"

st,ill

true,

if

instead

of

the

direct current, a

constant

frequency

alternating

<"Ilrrent

excitation

is applied

to

the

rotor

winding; only

the

speed

ofthe

motor

IIIIIS!.

he

different for

the

stator

and

rotor

ampereturn

waves

to

move again

iii

sYllchronism. For these reasons doubly-fed machines

operated

at

constant

rol.or frequency

are

not

particularly

attractive.

'I'hc

situation

is different, however, if

the

AC

excitation

of

the

rotor

is

IIlad(' <lependent on

the

line volt age vector

and

the

angular

position

of

the

roLor.

The

machine

then

looses

its

synchronous characteristics entirely

and

call

operate

at

variable speed

and

reactive line current;

the

speed

transients

C<LJl

oe

we11

damped

[A13, A14, A31, D32, H36, K17, L13, L23, L27, L40,

Wll,

W'20,

W21, W22].

The

basic circuit in Fig. 13.1 a shows a wound-rotor mo-

Lor,

the

stator

of which is connected

to

the

symmetrical

three-phase

supply

with

nominalline

volt age

Uso

and

frequency

Wo

while

the

rotor

is fed

with

illlpressed three-phase currents

of

variable

amplitude,

frequency

and

phase.

TI)(~

power supply

in

the

rotor-circuit could

either

be

a

current

contro11ed

qclocoIlverter

or

a DC- link converter, Chapo 11.

Thus

the

shaded

operating

r:l.Il{.';(~

of

the

torquejspeed

plane in Fig. 13.1 b becomes accessible. Voltage

r:d,ill{.';

alld

frequency

of

the

converter

are

directly

dependent

on

the

width

of

1,1

1<'

(i\>sircd

speed range.

'I'll(~

iilJpressed

rotor

currents

are

derived on

the

basis

of

the

rotor

angular

i'",

.;i

Lioll

'l.Ild

t.l)(~

vector of

the

line voltages; speed

and

reactive power control

wli,1!

('III'('('IlL

lilIlit

are

superimposed.

It

would also

be

possible

to

choose a

III,d,or

willl a

Lwo

phase

rotor

winding

instead

ofthe

usual

three

phases;

the

"11<'1":t.I,ioll

wOltld

oe the same, except for

the

harmonics

on

the

line side caused

I,,Y

III('

,;wil.chillg of

the

converter [B27]. For

the

fo11owing

considerations a

1.111"'1'

plrasc

rotor

with N

R

=

Ns

is assumed, as in Sect. 10.1.

'1'11<'

lllat.lwllIatical model

of

the

symmetrical

AC machine, Eqs. (10.50-

I

(I,~):\),

t.hat was derived

with

various simplifying assumptions can

be

em-

"Ioy(:d Itere also,

it

only needs to be

adapted

to

the

new constraints.

The

(oLor

willding

is

now fed by a converter,

,

di

R d

(.

- 'E)

/l/(ZI!

I·

L

R

dt

+

Lo

dt

'!:.s

e J = 'QR(t) ,

(13.1)

wlr(')"(~

'2

_.

'/l.I!.(t)

.~:

71Rl

+

71R2

eJ'Y

+

UR3

e

J

'Y

=

UR12

-

UR23

e J

'Y

(13.'2)

1::

Llre

vector

of

tlw

rotor

voItages suppliecl by

the

converter

to

the

sliprilll

(H

01'

IIH' 'llad,ÍiJ(',

W1Wll

ng

ain assulllillg thal.

Ul(~

COllV(~rt;er

is

c<jllipped

wit,h

I"n

nL

!"'

H

IHII

",

lilll',

("llnl'IIL

('oll(,J'

ol

J()()P~i,

I.he'

I'III.O!'

(".111'('1'111.:;

-i/{(t)

<l.n:

iII

dl'<-d

1'!',,<lIIi'I'<I

II,\'

"1111

"III.

H

ill

II

,.

"

,

~

;

h"III"',

ii:;

J""I', .l

::

1.111'

'·"/lV,'!'I.('I

' is I

lll1<-

1,0

illl

I""

ll

tl

UII"

1'1,(,111

l'

III

' I'

I'III,

!l

, i I '

,,"

;lI

I

I'

1

1111'I

1 11

<1"'111

1\

1.

" (,

,'il

l,'I',

\1

1\11.

,

'1

("

li

lld

"0111

1'

111

iS,

us,

OJ,

e

13.1 Doubly-fed

Induction

Machine

305

Wound rotor

induction motor

a

OJ

Operating range

FLlOJ

t

mM

b Generator

Motor

F i

g.

13.1.

Wound-rotor

induction

motor

with

variable frequency

rotor

supply

(a)

Circuit;

(b)

Operating

range

handwidth,

the

rotor

volt age

equation

Eq. (13.1)

has

no significance

with

re-

gard

to

the

dynamics

of

the

drive; this results in considerable simplification

of

the

drive controI.

The

situation

is

in

fact

quite

similar

to

the

case

of

the

stator-fed

induction

motor;

an

added

simplification is

that

now

both,

stator

;llld

rotor

currents,

can

be

readily measured.

It

is

thus

appropriate

to

fo11ow

;lg,ún

the

field

orientated

approach.

ln

analogy

to

Sec. 12.5

the

stator

volt age

equation

(10.50) is

written

in

Llle

form

Rsis

+

Lo

:t

[(1

+

O's)is

+

iR

ejE] ='Qs,

(13.3)

wl,,~r<~

acr.ording

to

Eq. (12.66)

i

.(t)

=

(l+O's)i

+i

ejE=i

s(t)eJI"(t)

(13.4)

m ,

o..;

-s

-R

m

\11

11.1

.1

('X

t.(~Jl(kd

lllagm:tising (:nrre

llt.

vc

rlol' r

f's

ponsiblc for

the

stator

flux

1

1I"ItIl!illl

':

!('

a

lla

)!.

.' ,

I"i

~,

10,7 Sholll,)

1.1,,'

I:YIlIlIld.r

ic

al

t.hre

e-phasc

HlIPP!Y

I'

Ln

wllil'll

1.11<'

n

l.

ft.l",,' in "'01111,','

1,,'<1

,

..

-dl

lhll ii

lI(d,

jc

"

I1.

I.I,'

illl.

e

rll

ll l i

lll]I<'dil.II('(',

306

13.

Induction

Motor

Drive

with

Reduced

Speed

Range

RN

+ jwoLN, for

instance

caused by a

transformer

or

a section

of

the

power

line,

it

can

be included

in

the

effective

stator

transient

impedance

Rs

+ j

Wo

as

Lo

==

Rso +

RN

+ j

Wo

(aso

Lo

+ LN) ,

(13.5)

with

Rso

+ jwoasoLo being

the

transient

impedance

of

the

machine proper.

Eliminating

the

stator

current

fs from Eqs. (13.3, 13.4) leads

to

dfms " _ 1 +

as

" j

Ts

----;{t +

lms

-

~:l!s

+

IR

e

ê

.

(13.6)

Ts

=

Ls

/

Rs

is

the

main

time

constant

of

the

stator

circuito

The

expression

for

the

electrical

torque

is, Eq. (10.52),

mM

=

~

Lo

1m [fs

ÜR

e

j

ê)*]

=

~

1

!oas

1m

[fms (f

R

e

j

ê)*]

.

(13.7)

With

the

introduction

of

the

rotor

current

vector in

stator

coordinates,

f

R

e

j

ê = iR(t) e

j

(€+ê)

, (13.8)

the

torque

is

mM

=

-"3

2

(1

- a) L

R

ims

iR

sin(Ç'

+ e -

J.L)

=

-"3

2

(1

- a) LR

ims

iRq

.

(13.9)

Thc

position

of

the

rotor

current

vector

in

field coordinates,

ti'

t,+e-J.L,

(13.10)

rorf'('sponds

to

the

load angle.

The

angular

relations

of

the

various vectors

\

rc

SIIOWIl

in Fig. 13.2.

The

instantaneous

angular

velocities

are

dE,

de

dJ.L

dt-

=

W2,

dt =

w,

dt = Wms·

(13.11)

'L'h!~

rcal

and

imaginary

parts

of

iR

ej(.~+ê-J.')

= iR e

j

ó = iR cos 8 + j iR sin 8

=iRd +

jiRq

(13.12)

are defined as d - q-components

of

the

rotor

current

vector in a

stator

flux-

()['ieut.a.tcd reference frame

or

as direct

and

quadrature

components

of

the

rot.or

current

"in field coordinates";

they

are

DC

signals in steady

state.

WIl(

~

!l

assuming a

symmetrical

three-phase system

of

sinusoidalline

volt-o

HI-',C:;

bavillg

th

e COllstant frequency

wo,

the voltage

vc-

~

d.or

rotate

s 011 a circlllar

pal.h,

:~

J"

(/

::

/

.1

.

,'

" I ,

( 1:\1:1)

'I/. ' : (I )

' )

13.1 Doubly-fed

Induction

Machine

307

Stator flux

i e

ie

axis

-R

(Um5

f·

1mS

Rotor

u

"'"

e

-5

axis

Stator axis

•

Fig.

13.2.

Angular

relationships

of

current

vectors

for doubly-fed

induction

rnachine

where Us is

the

RMS-value

of

the

line-to-neutral voltages.

Transforming

Eq. (13.6)

into

field coordinates

with

the

help

of

Eqs. (13.4,

13.8, 13.11-13.13)

and

splitting

the

result into real

and

imaginary

compo-

nents

yields two real differential equations for

the

magnitude

and

angle

of

the

magnetising

current

vector,

dims.

1 +

as

.

Ts

----;{t +

~mS

=

~

USd

+

ZRd

,

(13.14)

dJ.L

1

[1

+

as

. ]

(13.15)

dt

=

WmS

=

Tsims

~USq

+ZRq

,

where

3V2

USd

=

-2-

Us

cos(wo

t -

J.L)

,

(13.16)

3/2

.

uS

q

=

-2-

Us sm(wo t -

J.L)

(13.17)

are

the

field

orientated

direct

and

quadrature

components

of

the

line voltages.

The

d - q-components

of

the

rotor

current

vector can be derived from

the

trleasured

rotor

currents

iRl,

iR2,

iR3

according

to

Eq. (13.12);

the

transition

is

again performed

in

two steps by first converting f

R

to

an

orthogonal

two

phase

AC

system

which is subsequently

transformed

into

field coordinates.

With

an

isolated

neutral

of

the

rotor

winding

we

have

with

'Y

=

2rr

/3

:

~n(t)

=

iu

ejÇ

= iRl +iR2

eh

+iR3 e

j2

'Y

:~

.

./3

(.

. ) . _.

.,' 1,/11

:J

T

1.J7.~

-

'/.11

.

:1

'1,11..,

I

.'I

Zn.I,

.

(13.18)

TI

...

1I

111,

1I

"qllO

,

"I

. 1.1

1I

1I:

:,r"IIIIHI.

i,,"

iul." li.·I,1 ,··

,,,,,,Iillnl

.

..

::

.yi..!'):;

:{08

13.

Induction Motor Drive with Reduced Speed Range

. j ("-JL)

_.

j (€+"-JL)

_.

j 8

!.R e - ZR e - ZR e

=

[iRa

+j

iRb][COS(t:

-

p,)

+j sin(t: -

p,)]

=

iRa

cos(t:

-

p,)

-

iRb

sin(t: -

p,)

+j

[iRa

sin(t: -

p,)

+

iRb

cos(t:

-

p,)]

=

iRd

+ j

iRq

;

(13.19)

Llw

angle t: -

p,

may

be

interpreted

as

the

rotor

position

in

field coordinates.

Wound rotor induction motor

(1+<3S)

3-{2 U

s

I

2

I , .

~

.,,-

,_

LI

~

-----

Rs

--~-------------

I

Converter with I

current contrai i

II

R3

i

Rb

II

i

Rq

e

j«.~)

iRai

iR~

Flux

msRef

Contrai

in

field

control/er

coordinates

e

.j(e'~)1

Torque

Speed

contraI/e r

contral/er

iRqRef

Fi~.

l:~.:i.

Control of doubly-fed induction machine in stator fiux coordinates

'l'ile block

diagram

of

the

doubly-fed machine is contained

in

the

upper

part.

of Fig. 13.3, showing

the

interactions described by

the

preceding equét-

Liolls.

COIlsiderable similarity exists

with

the

block

diagram

of

the

induction

11101.01',

Fig. 12.12, except

that

there

is

an

additional

electrical

input

in

the

rOrJlI

of

the

line voltage

USo

The

angle

wot

-

p,

constitutes

the

advance of

l.!Ip voltagc vector

lL-s

against

the

magnetising vector

!mS'

Since

the

stator

rirclIiL

is

couflcctcd

to

a low impedance source,

the

angle

wot

-

p,

~

expc·,

ricll('(':;

ollly slllaU cltanges.

As

in

the

case

of

the

stator-fecl induction

lllot'lr

1'

'\1('

lll;q~llil.lId(~

of

!.lte

fillx cau only be altcrcd t:llrollgh

t.!w

la

g

1'

5,

Wlt

C[

(,iI

.H

!.lH'

qlJ;ldrn,L1JJ'<'

clJrJ'(~JlL

'i/(I{

i:-;

availahk

[01'

rapidJy

(;

olll.rollilll

<

t.orqll

C.

1'[

!.II('

('

oflv

,

'rl.n

wi th ('111'('('111. C

OJlI.

!'

01 i

II

I

I.i>p

rold

lllal.('d

hy

ii.

t.1m'('

pIl

HH"

,'III. 1"

'1\

1,

/)( ,

111'

<'''

wl',

1\

1I

I'I

',

l

ip

,Hdi' Il

tr

"

1,111'

, j

d"

I\

,

II

r(' ,

111(1

,'

11

1 i

II

li('ld

"" ol'.llllíd

,,·

/I

,'

iI,

11

13.1

Doubly-fed Induction Machine

309

again

be

applied.

ln

this case

it

means

that

the

coordinate

transformation

ej("-JL)

inside

the

machine should

be

cancelled by

an

external

transforma-

tion

e-j("-JL);

with

the

subsequent phase split a

balanced

three-phase

system

of

current

references is generated. This is seen

in

the

lower left

portion

of

Fig. 13.3.

The

angle

of

transformation,

t: -

p"

is readily available from

mea-

surements

of

rotor

position as well as

the

stator

and

rotor

currents.

The

transformation

from field into

rotor

coordinates,

in

effect a

modulation,

is

based

on

the

following

algorithm

j2

!RRef

=

[iRl

+i

R2

eh

+

iR3

e

']Ref

'

,.]

['

,.]

-j

("-JL)

=

[

Z

Ra

+J ZRb

Ref

= Z

Rd

+J Z

Rq

Ref

e ,

(13.20)

which

results

in

iRaRef

=

iRdRef

cos(t: -

p,)

+

iRqRef

sin(t: -

p,)

,

iRbRef

=

-iRdRef

sin(t: -

p,)

+

iRqRef

cos(t: -

p,)

.

The

equivalent balanced three-phase system of

current

references is, Eq.

(12.37) ,

. 2 '

ZRIRef

=

"3

ZRaRef,

. 1 . 1 .

ZR2Ref

=

-"3

ZRaRef

+

v'3

ZRbRef,

(13.21)

, 1 ' 1 '

ZR3Ref

=

-"3

ZRaRef

-

v'3

ZRbRef·

Clear1y

the

decoupled control scheme offers direct access

to

the

d - q-current

components.

There

are

various possibilities for designing

the

higher levei

control as

can

be

deduced from a discussion

of

the

steady

state

characteristics

of

the

drive.

At

constant

load

torque

and

speed

the

rotor

angle is t: = wt

and

the

flux

vector

rotates

in

synchronism

with

the line voltage vector,

WmS

=

Wo.

Anal-

ogous

to

Eq.

(13.13)

the

vector

of

the

stator

currents

is, ignoring harmonics,

2

Is

=

is(t)

= 3

V2

Is

e

J

'

Wo

t

,

Is

ej'Ps

,

(13.22)

where

Is

is a complex phasor. Similarly

the

rotor

current

vector

in

stator

coordinates

is

i

(t)e

j

,,=3V2

I

e

j

(w2+

w

)t=3V2

I

e

jwot

IR

= IR

ej'PR

.

-R

2

-R

2

-R

,

(13.23)

Illscrting these definitions into Eq. (13.3) leads

to

an

algebraic

phasor

equa-

I.ioll

Rs

~

s

-I-

.i

Wo

I,s

Is

+ j

Wo

Lo

ln

= U

50

,

(13,24)

Wllich, wil.h L

...

,

(I

I

(7,';)

T'II!

i~j

illllsl.J'II,kd hy Uw ('qllivaklll. circlIil.

iII

Fil',.

I :

\.

,'

I.

:no

13.

Induction

Motor Drive

with

Reduced

Speed

Range

J.s

RS

(JS

LO

1R

U

so

LO

Fi

g.

13.4.

Steady

state

equivalent circuit of doubly- fed

induction

machine

w

ith

impressed

rotor

currents

'Rd

'ms

2~--~--~

r-

--.---.-

I over excited

~

, -

lls"U

s

({JS

'

~

I under excíted

'41s

1so

o

-t-I

-

-1

r---+----r--t-

o

-1

I

nq

III

.'>

"'í,

~

.

1;1.5. Decoupled orthogonal control of

stator

current

TIl(' st.ator resistance may be neglected with larger machines,

Rs «

wo

Ls,

~j()

Lh

at

the

phasor of

the

magnetising current

is

determined by

the

impressed

s

l.aLor

voltage,

Uso

)

1

+1

~

-~.

(13.25)

11/

IS =

(1

+ (JS - S

-R

~

j

Wo

Lo

'I 'he lIo-loa.d s

tator

current (IR =

O)

is

Uso

(13.2(i)

' so

~

j

Wo

Ls

'

IU:ll

co'

I':q. (

1:1./.;')

;L~S

I\'II(

:~;

Lhe

!"mlll

13.1 Doubly-fed

Induction

Machine

311

Is

~

Iso

[

1-

IR

] =

[1

_

ei

(Hé-/ll]

Iso

IR

ImS ImS

IR

e

J

.

ó]

[I

Rd

. IRq]

=

Iso

1 -

---

=

Iso

1 -

---

- J -

(13.27)

[

ImS ImS

ImS

This

indicates

that

the

decoupled control

of

the

rotor

current in d - q-

components corresponds directly

to

orthogonal control of

the

active

and

re-

active currents as

is

shown by

the

orthogonal grid in Fig. 13.5. Note

that

this

operation in ali four

quadrants

of

the

current plane is

not

limited

to

constant

speed

but

applies to

the

whole

torque/speed

area, Fig. 13.1 b, accessible with

the

voltage, Current

and

frequency limits of

the

converter. Depending on

the

operating

condition of

the

drive, power is flowing from

the

rotor

via

the

con-

verter

to

the

line or vice versa as is shown in Fig. 13.6.

The

phase sequence

of

the

rotor

currents is inverted below

and

above synchronism.

Supply

Ps

RI

Mech.

power

P

1L

)

I

Mech.

power

w<w

o

w <w

o

Fig.

13.6.

Power

flow

of

doubly-fed induction

motor

drive

below

and

above synchronism

When

assessing

the

reactive power balance,

the

reactive power drawn by

the converter from

the

line

must

also be

taken

into account.

If

a cycloconverter

is

used, its lagging reactive

input

current may

be

substantial; it could

impair

the

ability of

the

drive

to

operate

with overallleading power factor. Measures

for reducing

the

lagging reactive line current

of

the

converter such as

the

reduction of its supply volt age with a transformer when operating

the

drive

at low slip are frequently applied.

Starting

the

drive is accomplished with

the

help of resistors, as seen in

Fig. 13.1 a; as soon as

the

motor

has reached

the

operating speed range

the

current-controlied converter

is

switched in.

The

orthogonal grid in Fig. 13.5 provides a clear indication of how

the

higher le

veI

control should be arranged. As

the

stator

flux (ims) is essen-

I.i

ally prescri bed by

the

line volt age U

s,

the

d-component of

the

rotor

current

wlII<l be used to maintain

the

reactive

stator

current

at

a fixed value or pos-

~

:

ihl'y

a

VltlrW

,!<op"Il(I(

:

nl

(ln

M.at.or voltag'!

(n:act

.

iv(

~

power bias). On

the

other

h

11

.

11<\

,

1.111'

IJ

"<lII'IHlIWIIL i:: 1.

11(

:

i<\I'

",

1

illpllt

for 1.<lnpH: c()lIl.rol t.o

whidt

~pc

(

~(

l

,·

olll.ml

LUI

1)<"

::

III"TIIIII

HJ

II

Cd

Ali

",,!" 'r"

II<"I

'

'I11I1.1I1

.

il.i'

·I

: !IIl1ll1ld

1,(,

lilllil

...

<\

Lo

(ú

ReI

úl

's act

Active

Reactive

current

's react

I

!,.Js

I

iSI

.---::,------,-

isI

iRI

E I

I

,-------''---,

U

s

iS

converter

Rotor coordinates

312 13.

Induction

Motor

Drive

with

Reduced

Speed

Range

I.

Microcomputer 8086

-I

control/er

: Coordinate ,

Field coordinates

:transformation:

Fig.

13.7.

Contrai

scheme

of

doubly-fed

induction

motor

drive

with

microcomputer

avoid undesirable

operating

conditions

and

to

protect

the

equipment.

The

cOlltroI section in

the

Iower

part

of

Fig. 13.3 represents only one

of

severaI

[JossibiIities; yielding

torque

/ speed curves with

torque

limit as in Fig. 13.1 b.

Figure

13.7 depicts

the

controI scheme

of

an

experimental

22

kW

drive

wi[,1J

microprocessor controI [AI3].

The

rotor

winding is supplied from a

6-

Pllbe

cycloconverter

with

analogue current controI;

the

converter was chosen

1.0

Ilave

adequate

power

rating

up

to

7.5

Hz

corresponding

to

15% sIip. To

illlprovc

the

steady

state

accuracy

of

the

current

controlloops,

feed-forward

voll.age :;ignals were

added

for counteracting

the

slip-proportionaI induced

voll.agcs in

the

rotor

windings.

As was mentioned before,

the

angIe

f.J,

of

the

magnetising current

(stator

flll

x)

UUl

either

be

computed

from measurements

of

the

currents, Eq.(13.4),

or

fr()J\J

stator

voItages

and

currents; in combination with a measurement

of

the

]"o[,or

position ê this provides

the

information for

the

modulation

producing

1.11('

reference signaIs for

the

rotor

currents.

Wit.1J

field

orientated

controI

an

excellent

dynamic

performance

of

the

dri

ve

is achieved, even

though

this

may not

be

essentiaI for some

of

the

ap-

plications rnentioned,

but

the

transparent

structure

of

the controI is beneficial

a~;

i

t.

ofrcrs a

great

degree

of

flexibiIity.

I<'igll[(:

13

.8 shows

the

effect

of

voItage feed-forward on

the

performaucc

01'"

I\. ("II1TI'III. loop ill stl'ady.,state.

The

cyclocollv

ertc

r

is

operatillg

at

a

freqll(~nl'y

clr

(i.'{

11'1.

c'C))TI':q,()l\dilll~

to a

sp'~I:d

of

1.700

l / ll1ill

01'

I.h

(~

I\

-polf: llIH.r.hiw:.

Tlle

c!loi

..

c'

01'

I.!II'

II'c'eI

rorwllrd Sr.lII'IIW is

lJ

.t

SI'

d

OH

I.IH'

. l'Ot.or

v()lI.n

,~

I:

cqllat.iolJ

I';q,

(1:1

I)

wllll'!I,

i

1I1

.l'ocl

IlC'

i

1'1',

1.llI' JlHI,,:

lJdi

:I

I!

'I'.

"111

1'

('11

1" ill

wil,h

[,Ii/

/(11

'1'/1

13.1 Doubly-fed

Induction

Machine

313

Voltage feed-forward

iRIA

.

Off

t. On

In1

iR1Rel

100

50

o I

\\

H

~

H

II

H

~I

I I \ , I I I \

Vs

o 0,25

0,5 0,75

Fig.

13.8.

Effect

of

voltage feed-forward

on

current

control

with

a cycloconverter

di

R

.

1 ( ) T d

('

-J'

E)

(J

T

R

dt

+

~R

=

RR

Y.R - 1 -

(J

R dt

~mS

e .

(13.28)

The

Iast

term

may be

expanded

in the form

d .

~R

=

(1

-

(J)

L

R

dt

(i.mS

e-

J

E)

=

(1

-

(J)

LR

:t

(imS

e

i

(J.I-E))

(13.29)

=

(1

-

(J)

LR

[d~~s

+ j

(wmS

-

w)

i

m

s

]

ei

(J.I-ê)) ;

with

ims

:::::;

const., this represents

the

sIip-proportionaI voltage

acting

as a

Ioad

disturbance

in

the

current

controIIoop; its effect is

compensated

by feed-

forward

with

the

necessary signaIs being

generated

in

the

microprocessor, Fig.

14.17.

Ps Os

Pr'

asO

P

SRef

\.

0.8

'"

=const

0.5

,"'

...

'a

._

.......

• ' ...

-"

ú)

tI

o I _

..

•

ov;:/""9'

·(.....,·-

..

I

..

tI--1P....í>·V·=:ff'

*{P

*

.....

'"""1'

..

tlms

o 100 200

300

400

FiK.

1:1.11.

Ik,:cHlpl, ·d

rnntrol

of

Il.ctive/rcn.çtivc powcr

with

a cycloconverter

:

H4

13.

Induction

Motor

Drive

with

Reduced

Speed

Range

The

measured

step

response

of

the

control loop for active

stator

power

(with

the

speed control disabled) is seen in Fig. 13.9j

it

exhibits good dynamic

pcrformance

and

little cross coupling with

the

reactive power control loop.

'l'he ripple

on

the

recorded traces is caused by

harmonics

of

the

cycloconverter

a.lI(!

quantisation

effects.

30

V'

16 A

OJ

O

1

10ms

1

30 V 115 A

OJ

O

30 V I 16 A

OJ O

I"i

r.:;

. I:J.10. Waveforms of

totalline-side

current

of

a

22

kW

doubly-fed drive

with

::Y

"IIII<'I.ri

ca

l

GTO

voltage source converter

at

different reactive power setpoints.

I.ill

<:

C1ment

(a)

in

phase,

(b)

lagging,

(c)

leading

Whcn employing a

De

link

PWM-

converter

instead

of

a cycloconverter

for

sllpplying

the

rotor-winding, the performance

of

the

drive c

an

be

further

illlproved in view of

the

higher switching frequency

and

the

reduced

harmonk

illt.(~raction

s

on the line-

and

motor-side.

The

reactive power drawn

by

tlw

collverl.er from the line

ca

n also

be

greatly

reduced. Fig. 13.10 displays

the

to-

t.

al

Iill!:

currcnt, comprising the

stator

as well as

the

conve

rter

input

currents,

Wll

C

lI

a sYlfunetrical volt age source converter with

GTO

thyristors, as s

howl1

i

II

ICi

g. 11. I

:3,

is

used. By designing a decollpled orthogonal control

stnl(:tlln~

;d

liO for

(.jl<~

líH

e side

co

nv

erte

r,

ha:wr!

OH

tJl<~

v()lt,:q

~

(

~

vector,

th(~

active

fUld

l"C

°ndi

VI'

p:

....

't

.K

0

1'

t.Il(

~

t.ot.nlliJl(

~

Cllrr(~I1t.

c;t.u

h(~

e

Olltl'oll(

~

d,

as

di

:

~ct

H

;se

d

il1

S

oei.

.

r:!:

.!.j

I.hi

!1

1'

I'

lJ

vid.

,:;

('o"lpld('

[n

'

('d""1

wit

\h

1 '

('

I

~n

,

l'd

t.o

1.111'

liIH

Hlíd., chnrad .• 'r.

13.1 Doubly-fed

Induction

Machine 315

istics

of

the

drive, which

may

also

be

employed for power factor correction,

apart

from high dynamic performance drive control [A31, H36, H37, K17].

Even

though

this

type

of

drive shows very interesting characteristics,

the

amount

of

hardware

for

the

rotor

si de converter is considerable which is likely

to

limit

the

use

to

higher power

and

special applications, where

the

added

flexibility provided by two-axes control is

important.

One

prominent

area

of

application

is

that

of

generators

in

large wind power

stations

operating

on

the

constant

frequency gridj

the

variable speed

operation

uses

the

high-inertia

wind

rotor

effectively as a flywheel

in

gusty

wind conditions.

This

helps

to

smooth

the

power fluctuations

and

reduces

the

rating

of

the

generator

as well

as stresses

on

mechanical components such as

shaft

and

gears.

Another

ex-

ample

are

constant

frequency ship-

board

generators, driven

at

variable

speed

by

the

main

Diesel engine with its low fuel cost, so called shaft generators.

Contrai

p-ê

w,

URq

URd

Variable speed

generator

, i

,-

:_--(~~;-.--+-

p

Load

impedance j

Driving forque

(Mo dei

of

AG

grid) I

OlmR

p

~'-------------------------------------------'

S/a/or coordina/8S

--+--

Field coordina/8s

Fig.

13.11.

Block

diagram

of

a variable speed AC

generator

with

impressed

rotor

voltages feeding

an

island grid

at

constant

frequency

If

the

doubly-fed machine is normally

acting

as a generator, is is prefer-

able

to

operate

the

rotor

side converter as a variable frequency volt age source,

i.(·.

wit.ll<llll

,

CIIIT

(!

llt.

control, in order not to

impede

transient

currents

in

th

e

rot.or

Willdil1f',:;

wllich are

c

a.

lul(

~

d

hy díst.llrh:wces OH the

stator

side.

Thi

s is

illll:it.r;d .•

'd

iII LlI('

I"ud

t diaf

!;

r:l.Il1

iII

,I,'il',.

1:

1.

11,

Wh('JT

t.\\(

~

('.ollvnt.(·]"

is

drawll

jlJ

316 13.

Induction

Motor

Drive

with

Reduced

Speed

Range

f~'

fI

~

~~

~==:;;

0,5

1,5

2

2,5

tis

~

US~

,

~

fV-

0,5 1,5 2

2,5

tis

U

RA

' U

RB

r··

~

0,5 1 1,5 2

2,5

tis

U

RD

u

RQ

~~.-:

0,5 1 1,5 2

2,5

tis

F

ig.

13.12.

Simulation

results

of a variable

speed

AC

generator

with

impressed

"d,!lr voltages.

Transients

following

step

changes

of

the

volt age reference

and

a

ramp

(:

IJa.lIge

of

speed

1'(

,I.(

,I"

coordinates;

the

stator-

fed

AC

grid is represented by a load impedance

/I

/"

/,

f, in

stator-

and

the

electromagnetic interactions in

rotor

flux- coordi-

II;t.I

,C

S.

The

structure

of

the

diagram

is similar

to

that

shown in Fig. 12.38.

f\

I.w,,- axes control

is

indicated for

the

stator

voltage

and

stator

frequency;

will, the help of two

separate

PI-

controllers,

the

simulated results in

Fig

.

I:\. 1

'2.

are obtained, showing

the

transients after

step

changes of

the

voltage

l'(,r(~l"ence

with

regard

to

frequency

and

amplitude

and

when

the

mechanical

spccd follows a

ramp

change;

the

sequence

of

the

rotor

voltages reverses as

I.ltc

rotor passes through

the

synchronous speed.

Future high power applications for this

type

of control are found in

IHllllpcd storage hydro power stations for changing

the

speed of

the

tur-

bilw/

pump

when

it

operates with varying head,

thus

improving

the

hydraulic

dli(:icm:y. AIso, changing

the

speed of

the

motor-generator-set by small

alllollllts

allows to activate kinetic energy

and

thus offers

the

option of COI1-

I.lilHll

,illg to thc dynamic stability of

the

powcr grid

[H36,

H52,

H75,I<17, T3i .

13.2 Line-side voltage source

converter

317

13.2

Control

of

a

Line-side

Volt

age

Source

Converter

as

a

Reactive

Power

Compensator

The

principIe of field

orientated

control as discussed in Chapo 12

with

the

example of machine-side volt age source converters

can

equally be applied

to

line-side converters for achieving high dynamic performance.

This

is

shown

in Fig. 13.13 a, where a symmetrical voltage source

PWM

converter serves

to

connect

the

DC link

of

a doubly-fed machine

through

a

transformer

to

the

constant

frequency grid. Line-side

PWM

converters are applicable whenever

a DC bus

is

to

be

coupled with

the

AC grid, such as fuel cells

or

variable

Supply

---

.....

-------_

.......................

.....

.

~

~~

YN=Y

o

.

"mM,O)

l

s=p+jQ

N N N

«Moto~\\::::~::

.

,,'.,~~\\

Gen

..

:/",1.'..

"

y

'OM

-,'

'-:

',---.'

"

iON /

ma;~ine

sid~1onverter

':

r-~__1,..~r_~__\----<r_~-tI-~~...-

~

-o .. ·· ..

···:····

, ...•... f····

...

···,

J

• , I r I , I ,

• I I I

I'

, I I I I

) , " I ,

:(

'

.,

;:

:

lt'

-

,

~;

l( -J:

_II'.

<-

....

' •

_II'.

I-r

' t.

r

,

_II~

U

o

I

I.

I

'.

I

1 , I I , , I • I

t--~---'

~--~---

+---+--_.

I I I I

II) I

II):

II)'

:(

:/~:

:(

:/~,-

:( :{:

_II'

-1-\

_II'

-:-'

_II'

-r'

I I I I

I I I I I

I I I I

I,

J

a

L-

...

---

.....

>-

....

---

...

-

....

---

...... --o-..

--.--------~---~--------

..

---'

line side

converter

solar

converter

.. ~·o

+.

-

;~"..

..•

-['::::":0

-.

................

_.,.

..

,

Solar radiation

I'

/'

" I '

\.

::

i '

~

.I

~

:..t

~

:

..

~)

~

..

y'

'OS

::

S :

::

:: :

: :

~-~

~

..

~

..

~

~-~

'S

:

:Jr.

~

~~

,

~

I

.,

'"

I

U :i'; .,:,- U

--!---

~1.~

~J~ ~;J

~;J

MPPl

O

_II",

'-

...

' S .

"'':'"

:""i:

:

~

:

~

, I

••

" ,

I I I I

I.

,.

,

I

-,,-

.,-

-'f-

--

-

:

~W:

:

~

:

~:

:

'~ :

•••

"

I,

,

, • ' j I

••

-----O

-.

-

-1-

-

i-

-------

~-

-1

..

---

~

[-

~

l~

-

~r-

~

I -

c

U

s

b

Step-up

chopper

Solar

panei

:Fig.

13.13.

Line-side voltage source

IGBT

converter

(II) in rol.m circllil.

01'

a doubly-fcd AC

motor,

(b)

for solar generatorj

(c)

"MHXilLIIIIII

I'ow(~r

PoillV' çonLro\

01'

~()Iu

.

r

pnlle1

--

--------------

--

----------

318 13.

Induction

Motor Drive

with

Reduced

Speed

Range

~peed

wind energy plants employing a DC Iinki a solar generator is indicated

in Fig. 13.13 b, where a step-up chopper raises

the

voltage Us of

the

solar

paneIs

at

the

irradiation-dependent maximum power point

to

the

leveI

of

the

Iink voltage UD.

i

ON

iOM

T

R L

íNl

o---CJ

-'í

N2

1

-I-

~_.

I

.

v

12

v

23

Il

J1

51

-1

'_f2

r

L

'----

53

l-I

t 1

ti

í I

ic

c,

-,-

Uo

iN3

-I-

U

j

1

N1

N3

U

N2

V

1

V

2

V

3

Fig.

13.14.

Equivalent switching circuit of

the

line-side converter

An equivalent switching circuit of

the

line-side converter is seen in Fig.

13

.14 corresponding to

the

circuit in Fig. 11.7 ai the transformer is rep-

resented by

its

line impedance.

The

time-dependent vector

of

the

sinusoidal

and

symmetricalline

voltages with constant frequency is

with

wNt =wot =

~

and , = 27r/3

Y,N(t) = UNi

+e

h

UN2

+e

j2

'UN3 =3../2/2

UNei>\(t)

=UNa(t) + jUNb(t)i

(13.30)

similar definitions hold for

the

PWM

volt ages

at

the secondary of

the

trans-

former, i.e.

at

the

input

of

the converter bridge,

j2

:11.(t)

=

Vi

+ e

h

v2

+ e

'v3

=

V12

-

V23

e-h

= va(t) + jVb(t)

(13.31)

and

the line-side currents

j2

iN(t)

=

iNl

+ e

h

iN2 + e

'iN3

= iNa(t) + jiNb(t).

(13.32)

Control of

the

currents is again carried out in a moving frame of coordinates so

that

the feedback signaIs are DC quantities in steady state. According to Sect.

10.3 a suitable reference frame are now line voltage coordinates, wherc tlw

vector

Y,N

assumes

the

role of the induced

motor

voltages

~s

anel

th

e

i>uls(

~



width-lIlodnlat.cd converter voltagcs y(t) serve a!i

Lhe

aetnaLiIlf( variabJes.

Fig.

13.

Ui

slIowH

Lhe

v

{:c

Lor

dia

g-ra

m of tlw

lill(

·~

·

sid(

~

C(>lIv(

~

rt.(

~

r.

'l'll(~

t.rallsforllwd

voll

.

;I./',""

;

lIId

'·III.,.c:"I.~l

.,,(1) ,.

1\

II"

I'

I'I,,,

' N

U)'

,·

,\

·

~N.

t

I 111V'1

( 1:

1.:\

:

1)

13.2 Line-side voltage source converter

319

Vector

o,

fine voltages

LJi

tJ

!N(t)

/.-.\.

d

/\

v\ V

/ I \ 'Nq

~

\ q

I \ Q

I',

/ \ h

LdiN

/ . h

...

/ '

.....

\

,

dt

~c~r~

/

dÓ

,

\

,

fine currents \

/.

l·6

'-

/ 'Nd 6

j

t.Nb

\

úJo .

A......

,6

/ ó

,

R'

,ó

\

'! (t)

I

.

jiNb

I

_'''!3

-.J

UNa

J

LN

Vector

o,

voltages

at

converter

terminaIs

Fig.

13.15.

Vector

diagram

of

the

line-side converter

may

be called line-orientated variables.

The

differentiaI equation for

the

line-side impedance

R,

L

diN .

L

dt

+ R

'!,.N

=

Y,N

-

:11.,

(13.34)

w here

R < < W N L holds for higher power, is transformed into

the

moving

coordinate system by multiplication with

e-

j

>..

and

subsequently split into

real

and

imaginary

parts,

diNd .

In/

L '

L--+R2Nd=3v2

2UN-Vd+Wo

2Nq,

(13.35)

dt

diNq R '

L'

L--

+

2Nq

=

-v

q

-W

o

2Nd,

(13.36)

dt

The

instantaneous direct

and

quadrature

components

ofthe

currents, iNd

and i

Nc11

are a measure for

the

active and reactive currents flowing from

the

line to

the

converter, as expressed by thc instantaneous complex power,

11."rv

'

lN

(

:

IJ:~/2)

lI

N

"

.

i>-'

i

N

-

:IJ:~/'2

(/NI'iNdU) I

jiN,,(l)Jj

(1:1.~7)

I"

!i

1.(

·ll.

dy

nUd,

<'

Werner Leonhard Control of Electrical Drives

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