Werner Leonhard Control of Electrical Drives

:110

14. Variable Frequency Synchronous

Motor

Drives

n

min

-1

5000

Step size

32Rev

8 I 16

~

500 ms-----+l

t

Rev

32

16

8

4

Fig.

14.9.

Step

response

of

time-optimal

position

control

with

synchronous

motor

servo drive

at

no-Ioad

aclded to

the

speed- or position-control function

to

combine fast response

with aperiodic damping [L51].

The

speed response of

the

drive

is

limited, besides

the

inertia, by

the

llIéLximum

current

which

the

converter can supply. Given sufficient

stator

c1lfrent,

the

motors

have very high short-time overload capacity which

is

Ílllportant for servo drives designed for

intermittent

duty, Fig.

14.l.

Tile control circuits in Figs. 14.5

and

14.7 contain current

controlloops

in

::I.al.or

coordinates, producing approximately impressed

AC

stator

currents.

'I

'11<,

rderence

signals

are

sinusoidal in steady

state

which calls for careful

1.1111

i II!'; of

the

current controllers with regard

to

undesirable phase shifts. An

;dl.cruative

and

usually preferable arrangement is shown in its basic form in

I"il\.

14.10, where

the

currents are controlled in moving

rotor

coordinates;

this

\tas the advantage

that

the

controllers for

is

d

,

iS

q

are processing DC signals

ill

steady state.

The

effects

ofthe

induced voltages may again be compensated

I)y

L"eed

forward

at

the

outputs

of the current controllers;

the

control

can

also

Iw

cxtended for field weakening.

As

the phasor diagram

in

Fig. 14.6 b

and

the

parameters

of

the

experimen

..

Lal

lI1otor indicated,

the

increase of

the

stator

currents in

the

field weakening

r!'gion

is

due to

the

small

stator

inductance Ls, caused by

the

relatively largc

dh:ctive airgap as a consequence of

the

surface-mounted magnets.

This

enu

Iw illlproved with different

motor

designs, where

the

rotor

is

anisotropic, sim-

ilar

Lo

a rotor with salient poles, thus increasing

the

longitudinal illductallGC

I'S,1

colllpared with tbe

qlladrature

inductallce

LSI'

[B26,ll28,D29,J2]; pos

Ki

-

illl:

ÍUlpkJlWIlLatiollS

of

this

id

ca are seen in Pig.

1-1.11

a,b. 'I'lte

lll

a

l

~

U(

;

Ls

lJI:l,y

..

il.ll('l'

1)('

N

ILI

I'acn

IIIOllllLI:d

wiLh

UI('

:wi

ril

d,rop.v

clt

ll

scd

h.v

UI(

: i

111.1

'I'Jlal :·

dt:l./)("

0

11"

1.1)('

I'(d,I)I' I»

I.Iwy

1"lltld

11

)1'

!Ir);I.III

':I,d

illl.clllill!y

lf\,

u..,

II

~

w

)

lo·m

)

I\iI:1HI

;

iII l"d,11

14.1

Control

of

Synchronous

Motors

with

PM

Excitation

341

I

I PM synchronous

.-e

____

~

ú)

motor

I

US3 I I

~

AUSb

e

·jE

ejE

USdRef

USqR.f

Speed

control/er

ú)

Ú)Ref

--t

I

USa

I

r------

I

Voltage

source

Control

converter

Fig.

14.10.

PM-Synchronous

motor

drive

with

voltage source converter

and

current

control

in

rotor

coordinates

cases

laminated

rotor

constructions would be used. These designs

permit

an

easier displacement of

the

impressed flux by

the

direct

stator

current

com-

ponent

is

d

into

geometricalleakage

paths.

Of

course, a detailed modelling

of

the

machine is much more complex

but

in priniple

the

result would cor-

respond

to

the

simplified model in Fig. 14.10 where different values of

Ls

d

,

LSq

in direct

and

quadrature

axes are assumed, caused by varying cross sec-

tions

of

the

magnetic

paths

and, possibly,

saturation.

ln

the

design shown

in Fig. 14.11 b1 a cage winding

is

included for self-starting of

the

motor

on

a

constant

frequency supply.

With

these measures

PM

synchronous

motors

may exibit a

substantial

degree of field weakening

without

excessive

stator

eurrents;

this

is necessary for instance on vehicle drives, reducing

the

need

for a mechanical gear change.

Besides

the

PM

synchronous

motors

having sinusoidal

stator

voltages

and

eurrents

and

smooth

torque, i.e. low torque ripple in

steady

state,

there

are

also

ll\(»)'(:

ccoIlomica.l designs in

the

form of "brushless DC motors" , exhibit-

illg

t.rapczoid;t,\ Illlx dCllsity distribution

and

phase voltages [839, W14].

The

:,t.al.(lr

C·IIITI'II!.f;

!t;\VI'

ju prillciple a sl[u;ne waveform, as in Fig. 8.19 d, where

011<'

,,1

11111

" ,' (lrI"

'III,

\:;

'!,('rII

at,

1\.1I'y

I.illll';

l'iI.lIHI'c!

!ly

t.!tc'

finite

COlluIllltat.ion

in-

:)42

14. Variable Frequency Synchronous Motor Drives

tervals

the

currents

are

of

course continuous, i.e.

the

corners are

rounded

ofr.

The

main

advantage is

that

there

is no need for a pulse-

width-modulated

converter

and

maximum

power density is achievedj however,

due

to

imper-

fcct

commutation

there

is considerable

torque

ripple making these

motors

less

suited

for high precision servo drives.

S/a/or

6 - pole motor with

magnets

on

rotor surface

a)

-axis

Cage

M.agne/s

in

winding

Magne/s

S/a/or

....

)

~.

,

. x'

.•

·l

...

·:'·

,

aifga.p~

.

...

. ;,.

'i

,

-

,..

.

b1)

b2)

b 3)

4 - pole motors with rotor- internal magnets

"'i~.

14.11.

Cross sections of PM synchronous motors with

:\Ilisol.ropic rotor designs

for

extended

field

weakening range

L1.2

Cycloconverter-fed

Synchronous

Motors

with

Field-

and

Damper-

Windings

/\

\l(

)Lher

type

of

adjustable speed synchronous

motor

drives employs machines

01"

couventional design having in

the

rotor

a

symmetrical

damper

winding

aud

a.

single axis field winding fed

with

direct voltage

through

slíp rings 01:

rrolJl

:Ln

AC exciter

with

rotating

rectifiers. At low speed, for

instance

bdow

tOO

I /llIill,

Lhe

stator

can

be

supplied by a cycloconverter employillg

Iim~

C()1ll11l1l1.:üioll

which makes this scheme particu!arly aUractive for high

pOW

(>f

:l

ppli(";d,i()ll~;,

as

!Oll

g as

thc

[requency

mllg(~

of

t.hc

cycloconverter slIllire:j

OH'

Inr

\',"

('

11I11IIhcr

oF

t.hyriK!.or

brandl

cs

i~

!lOt.

()IJj

u

<:t.i(l

na

lJ!

~

:

a

!.

hi

gh

p()w(

~r

whnn'

1'1f.1

·n

ll

..ll.

h

v

ri

:

iI

.

"r

:: IJlil':ht.

()i.lJl"rwi

~;(

·11('

111'1,,,, ·

<1

.

'1'111'

nll,OI"

IIIIH

Il

lI

ill/(I,'

lI.X

iH

lidei

wl

od

l

lij/

. [

III"

II

, ::

vl'II'II"I

.

JÍ

,·,d

01

0 1111"'1

Willdillj

( whk

ll

1

111

1,,('ti

1'

''1

1I

IlI'pro

'

ll

n

illl

\

14.2 Synchronous Motor with Field- and Damper-Windings

343

harmonics

and

negative sequence

ampereturn

waves,

not

for

starting

the

motor

because this is now achieved

with

the

variable frequency supply.

The

basic circuit

of

this

type

of

drive is shown in Fig. 14.12.

References

Fig.

14.12.

Variable frequency synchronous motor drive with cycloconverter

Typical

applications

are

large gearless drives,

in

the

past

dominated

by

DC machines supplied by

dual

converters (Fig. 9.4), for example for reversing

rolling mil/s,

mine

hoists,

ore

mills

and

rotary

cement

kilnsj

at

lower power,

elevators

or

direct wheel drives

on

excavators in open-cast mines are also

possible applications.

The

drive

permits

4-quadrant

operation

with

smooth

transitions

including standstillj hence

it

is perfectly

suited

for speed- as well

as position- control requiring

rapid

response.

The

torque

harmonics

due

to

the

cycloconverter

are

small

and

of

relatively high frequency. An

additional

advantage

is

that

cycloconverters

with

air-

or

liquid- cooling

are

proven de-

signs from

the

DC

era

and

are readily available

up

to

MW

rating

.

A detailed analysis

of

the

drive calls for

an

extended

machine model in-

cluding

the

converter

that

could

not

be

dealt

with

manually

or

by

intuition

but

would require a

computer

simulation [M17]. For

qualitative

purposes,

however,

the

model derived

in

Sect. 10.1 still

remains

useful, as seen

in

Table

10.1 d. Rence

we

assume

that

the

motor

with

a nonsalient cylindrical

rotor

has

a

symmetrical

three-phase

rotor

winding into which, according

to

Fig.

14.13,

an

ideal source

of

direct volt age

UF

is

inserted

as field power supply.

Since

this

controllable voltage source contains no

internal

impedance,

the

damping

efrect

of

the

rotor

winding remains

unimpeded

and

the

symmetri-

cal

rot

or

winoing is used for DC excitation [L42].

The

simplified model is

not

ofFcrillg the sam e freedom for choosing

parameters

as a

separate

winding

arrallg<~IIj(

~

II[.

hut.

lIla

y

be

adcquate

for

the

design

of

the

control system.

To

a.da)'!.

1.111'

Illa!.lu'lllaI:Ícallllo,ld ,!priv<'d

in

Sect.

10

.1

to

this

constraint,

w,'

il

l"

".ln

d,

·

lill"

",11.h

·

'Y

211

;:

\ a vl'd.OI

(Ir

,' x 1.

1T1I

aliy

appJi(~d

I'ot.or

vo!t.a

.f'/'~;

:1'14

14. Variable Frequency Synchronous Motor Drives

. . 2

Y.R(t)

=

URl

+UR2 eJ'Y +UR3

e)

'Y

(14.16)

=

URl

-

~

(UR2 + UR3) +j

V;

(um

- UR3) .

I

kcause

of

the

short circuit between phases 2

and

3,

UR2 =

UR3,

Itolds, hence

(14.17)

Y.R(t)

=

URl

- UR2 =

up(t)

.

'1'

llUs

the

rotor

voltage vector is real, being identical

with

the

applied field

vo

ltage, Fig. 14.13.

URI

=i

F

Induced voltage

i

RI

ºSI

jmR

Rotor flux axis

L

R

RR

~

uF

í

R2

Rotor axis

Stator axis

UR2=

uR3

RF

='2

3

RR

I"if~'

14.13.

Symmetrical rotor winding

Fig.

14.14.

Definition

of

coordinate

\ViLl,

1)(

:

(

~

x:cita

tion

from

a voltage source system

TIl!'

rotor

currents have me

an

values,

to

which

transient

terms

iR

are

:;

lIpl

~l

illlposed.

Considering

the

isolated

neutral

of

the

winding,

we

find

Ip

).

(Ip

)

'2

"Íu

(t) =

(Ip

+i

Rl

)+ - 2 +i

R2

eJ'Y

+ - 2 + i

R3

e)

'Y

(

3

(I

./)

. J3 ('/

./)

(14.18)

=

'2

p +

2Rl

+J 2

2m

-

ZR3

.

'l'lte JIlcall of

the

rotor

current vector is also real,

. 3 3

Up

(14.

H»)

'lU

O =

'2

1

1"

-

'2

~RR

RR'

1'11l.

IlJld

(

~

r

dYIlamic conditions

the

vector can be deflc

cted

by indl1ced currelll.

1'

,1

'III

pl)Jl(

~

IIL

s.

I k s

l.

['1'"uILs

or

t.IlC drive c()ul.rnl

fIIay

h(

~

('

X:

I)(

~

d,ed

ir

tll(~

sLaLo1' C

llJ'lTlIL

H

'.1'

\'

H

' I

~ f

~ill

,'

III

T('

1I1.

il

UIII'CC'(

1

Ily

\.II<'

('yrl()((IIIV~·I

·

t'

· I ·

wi

l.

h t.lw

1tC'lp

III'

ff\)il,

CII!'

1

"'11

'

1.

n

.,oI

.r..11

III

'

l[i

ll , lI ll wa.

li

11

["

)Wll

iu

:-\

",'1,. 1:

1.1

.

'1'1

';

11

1

\'

I

~W

I I

UIC'

l'

ul

.

1I

1'

vl,H

,/[I\

"

14.2

Synchronous Motor with Field- and Damper-Windings

345

equation

and

the

mechanical equations for modelling

the

drive dynamics,

Eqs,(10.51-1O.53),

·

L

di

R

L d ( ' - j

e)

Up

=

R

'!cR

+ R

dt

+ O

dt

'!cs

e ,

(14.20)

J

~

=

~

Lo

1m

[is

(iR

e

j

é)

*j

- m L ,

(14.21)

dE

(14.22)

dt

=

W.

The

design

of

a control scheme in field coordinates calls for

the

selection

of a suitable frame

of

reference.

ln

the

case of

the

synchronous

motor

with

permanent

magnets, Sect. 14.1,

the

rotor

position € was

the

natural

choice

as

this

was

the

orientation of

the

magnets producing

the

rotor

ampereturnsi

however,

the

situation

is different here, where

the

induced

currents

can

shift

the

ampereturns-wave

with

respect

to

the

rotor, Fig. 14.8.

It

is therefore

appropriate

to

employ a fiux vector as with

the

induction motor. A suitable

choice is

the

rotor

fiux, defined in Eq. (12.22),

i

mR

=

is

+

(1

+ IrR)

iR

e

j

e =

imR

e

j

e .

(14.23)

This

makes sense because

the

rotor

winding in Fig. 14.

13

has alI

the

features

of

an

induction machinei

the

only difference is

that

in

steady

state

the

mag-

netising current vector

imR

is in synchronism

with

the

rotor,

(!

- € = const.,

whereas

it

was moving with slip frequency across

the

rotor

of

the

induction

motor,

Fig. 12.11.

Eliminating

iR

from Eqs. (14.20,14.23)

dimR

(1

.

T)'

.

(1

)

Up

j e

T

R

~

+ - J W R

'!cmR

=

'!cS

+ +

Ir

R

RR

e ,

(14.24)

and

splitting

in two real differential equations yields

dimR.

. (

Up

(

TR

~

+ ZmR =

ZSd

+ 1 + IrR)

RR

cos

(!

-

€)

,

(14.25)

d

dt

((!

-

€)

=

WmR

- W

UP

=.

1T [i

S

q -

(1

+ IrR) R sin((! -

é)]

(14.26)

ZmR R R

where

is

e-·

j

(! =

is

e

i

(Ç-(J)

=

iSd

+ j iS

q

(14.27)

is

:~

g

aill

tiII' sl.:l.I.or C

llrr

e

nt

vector in

rot.

Qr {lIlX

c()ü

rclinates.

Sillc

'(' 1.

11<'

wc\.

..

,· i,,

"1I

\IIov

es ill

H\.c~:i.dy

,,

1.a

U'

sy

lldll'lHlOIISl

y

wit:h

til<'

rolor

,

\.11<'

I·

il,.lel.

le

ll

lld

l:

id

o

o"

I'

;

".

(l /

I.

'l

(i)

VIl

,

lI

i

N

llI'

~

,

346

14. Variable Frequency Synchronous

Motor

Drives

isql

Hoo

=

(1

+

UR)

~:

sin(º

- ê)IHoo .

(14.28)

The

equation

(12.27) for

the

driving

torque

remains unchanged,

mM

=

~

Lo

1m

[is (iR e

j

ê)*]

=

~

(1

-

u)

Ls

imR

iS

q

= k imR

iS

q

•

(14.29)

The

equations describing

the

synchronous machine in field coordinates are

graphically represented by

the

block diagram in

the

upper

part

of Fig. 14.15,

containing once more

the

transformations from

the

stator-

or rotor- orien-

tated

coordinate system

into

field coordinates.

The

diagram

corresponds

to

that

of

the

induction motor

with

the

exception of

the

field voltage

UF

which,

alter

transformation

into flux-orientated d - q-components, is

added

as

an

additional

input

signal

at

the

appropriate

points.

ln

practice

UF

may

be sup-

]llied by a

separate

two-quadrant converter with closed loop volt age control,

lhus underlining

the

characteristics of a low impedance source.

lt

would of

course also be possible

to

introduce a control loop for

the

field

current

to

eliminate

the

effect of changing field winding resistance due to

temperature

variations.

The

drive would

then

respond faster

in

the

field weakening range,

but

the

damping

effect by

transient

currents induced

in

the

low impedance

held circuit might be impeded; also

the

model of

the

machine would have

to

I

JC

Illodified.

ln

contrast

to

the

PM

excited machine

in

Fig. 14.6

there

is no need

to

apply

stator

current in

the

d-axis for field weakening, since this can now be

arhipved more efficiently by reducing

the

field voltage

rather

than

increas-

illf~

I.h

c s

tator

current.

The

need

to

reduce

the

field becomes manifest again

wll(~1l

lhe

magnitude

of

the

stator

volt age approaches its limit as sensed by a

I i Jlli

I.illg

voltage controllerj alternatively field weakening could be performed

wil.h

an

imwcontrolloop,

the

reference of which is generated as a nonlinear

J'lIllcl.ion of speed, imRRef(W), Fig. 12.14.

'fIte flux angle

{!

required for

modulation

and

for

computation

of i

m

R,

is

" alld

mM

is

again derived from a ftux model, processed on-line by a mi-

crocomputer. As in case of

the

induction machine,

the

model

may

be defined

ill

~

I.ator

or in field coordinates, Fig. 12.16 a,b.

Computational

advantages

are

gained by taking

the

second approach, referring

to

Eqs. (14.25, 14.26),

whidl

describe

the

magnitude

of

the

flux vector

and

its

position relative

to

1.Il<'

rotor.

This

is

represented by

the

block

diagram

in

Fig. 14.16 which is a

rop'y

()r

l/te motor model in Fig. 14.15. Clearly, with

UF

=

O,

the ftux mode!

()f

1.1t<'

imludion

machine, Fig.

12

.

16

b, results.

The

angle

º-

ê is approximately

(,()ll~;talll

ill st.eady

state.

'I'/te

;u

:

r.

uracy with which

th

e

stator

cllHcnls are tmdcinp; thc

refcrenq

:

1i

IIJlty

;\

'I1

;

ain

h

t:

c()lIsi(I(~rn.hly

illlproved

uy

(

~

mpl()yil1f

~

voll.ag<: f

Cüd

-

fofward;

il

,

fI

pllrp

OIi

(' i:i

t"

('

auc<'!

thl'

V()!1.

"~I

_

~

t'

('

....

h(

'hilld 1.l1('

'ntll

~

ienl.

n 'li.t'.I,llI 1('(:

whidl

li

1Ilcllll'

('

c!

I,

y

1.1,..

1I1

:

If

~

nd.

lní

lll',

(·ul

' r

l'II!.,

Lo.

UI<'

11IiI~1I

UI

! X.

14.2 Synchronous

Motor

with

Field-

and

Damper-Windings

347

I

Converters I

Field I

supply I

Synchronous motor

u~

II

(

~

I •

iS!

Rol I

i

S2Ro

I I

iS3R611

Fig.

14.15.

Control of synchronous

motor

in field-coordinates

The

stator

voltage was derived

in

Eq. (12.45)

.

~s

~mR

1is (t) =

Rs

1s +u

Ls

dt

+

(1

-

u)

Ls

&-

'

(14.30)

which in

steady

state,

Le.

with

WmR

=

Wl

=W = const, imR = const,

is

= const

assumes

the

form

llS(t)

=

(Rs

+ j W u

Ls}is

+

~s(t)

;

(14.31)

hence

the

induced voltage is

§.s(t) = j W

(1

-

u)

Ls

i

mR

.

(14.32)

If

the

control functions are performed by a microcomputer,

the

sinusoidal

three-phase components of

~s

can be easily

computed

and

fed

into

the

current

loops behind

the

current controllers as is shown in Fig. 14.17.

Experimental

rcsults were seen in Fig. 13.8.

If

the

rurrClIt

co

ntrollers

are

of

the

analogue version, being

part

of

the

i>ow(~r

(·(llIV(:rl.(:1's,

the

schenw

in

Pir

~

.

]4 .

.1.

7 a wOllld call for a second

DIA

('OIJVmi,l

lI

' Um!. (

'1

\.11

IJ<:

OJllit.t

:

(

~

d

hy

IIlixilll'

:

1,[1('

t-/igua!s wil.hi.ll.

t!t(:

IIlinoco)ll

-

PIlI.

...

I',

11

·1.

:

1\"

'WII

i

II

'<'ii',

. 14.17 h.

()J'

('(Jllf

li

(',

jll'l'l'l

:

<'I.

1':I.II<

:

dl

:

t.l.ioll

(lI'

I

':

:

iI!

Il(ll.

:\t\tl 14. Variable Frequency Synchronous Motor Drives

t'::J

i.

;

,-

p-e

e

Fi~.

14.16.

Dynamic

model for

computing

the

rotor

fiux

of

synchronous machine

I

<"SI

O IA

Feed

- forward

Current

Fc

.

-J-:

Mlcroco

mputer

I Converter

and

motor

.I

Ts+1

Fc=G

cTs

ti:

..

I

/". , :;

(1/1

I

Current

Lêw

dlLag

II

Fig. I 'J

.]

7.

Current

control with voltage feed-forward

pos

,:

ihlc

with any of the schemes since

the

nonlinear control dynamics of

th

e

(·ollv(:rl.(:r

s(~i>arate

the point of compensation from

the

actual

entry point of

!.II('

di.~l.llrhnllcc.

3till, considerabIe improvements are possiblc, as was

ShOWll

j

II

I,·jl

~

..

1

:\.

8.

Thr

residual lag of the

curnmt

loops lIlay

be

furt-her reduced

1,

.

\,

i

1I~:(

·

I'I.ill!';

[('ad.

laf.!;

liIt.c:rs

:1t the refcrcllcc

inpllts

of

the

currcnt

controllcrsj

I.II

i

l-!

íH i

lldk:iI,('d

ilJ

Fil~

.

11.17,

14.3 Synchronous Motor

with

Load-commutated

Inverter

349

An

altemative

approach

to

the

controI shown

in

Fig. 14.15 wouId

again

be

to

controI

the

stator

currents

in

fieId coordinates, according

to

Fig. 12.27

where

the

current

controllers are processing

De

signaIs in

steady

state.

14.3

Synchronous

Motor

with

Load-commutated

Inverter

(LeI-Drive)

The

variabIe frequency synchronous

motor

drive with cycloconverter sup-

pIy discussed in

the

preceding

paragraph

is suitabIe for Iarge drives with

high

dynamic

performance. 8ince

the

cycloconverter is line-commutated, onIy

converter-grade thyristors are needed,

although

in

a Iarge quantity.

On

the

other

hand

there

is

the

frequency

limitation

of cycloconverters; with a 50

Hz supply

and

6-puIse circuits

the

range extends

to

about

h = 20 H z.

This

is

sufficient for a rolling mill

motor

having a base speed of 60

l/min

and

a

maximum

speed of 120

l/min;

it

could be realised with up

to

20

poles

at

practically any power

rating

[84,879].

However, when Iarge high speed drives are needed, for exampIe 4500

l/min

on

a compressor for a pipe-line

or

a bIast fumace, a

maximum

stator

fre-

quency of

75

Hz wouId

be

needed even

with

a two poIe motor, so a cyclo-

converter

can

offer no solution; neither could a

De

drive have been

built

for

this

duty.

The

rotor

of

the

synchronous

motor

is

made

of solid steeI, similar

to

that

of a

turbogenerator.

The

simplest way

to

eliminate the restrictions imposed by

the

line fre-

quency

is

a two-stage conversion, inserting a

De

link for decoupling of

the

line-

and

the

machine-side converters. Fig. 11.14 showed such a circuit con-

taining

only 12 thyristors;

the

machine-side converter can be

further

simpli-

fied with a synchronous

motor

because

the

stator

winding contains a volt-

age source

fs

in

series with a

transient

impedance,

Eq

. (14.31). Hence the

machine-side converter can be

commutated

by

the

Ioad

without

resorting

to

forced

commutation

as was necessary with

the

induction motor;

in

other

words

the

synchronous machine is

operated

in

the

overexcited region so

that

it

can supply

the

reactive current neeeded by

the

phase-controlled machine-side

converter.

The

basic circuit

of

a Ioad-commutated inverter drive (LeI-drive)

is

seen

in

Fig. 14.18.

This

leaves

the

problem of

commutation

at

start-up,

where

the

induced

volt age

is

insufficient,

but

this

can be circumvented by

intermittently

bIank-

ing

th

e link

current

with

the

heIp of

the

line-side converter. This produces

Lorqnc

pulsations,

but

there

are

many

applications where

smooth

operation

ill

tlw

very low speed range, say beIow

10%

of nominal speed, is

not

neces-

s

ary;

examples are the turbo-compressors mentioned before, also gas-turbine

01'

PlllllP(~d

storage sets, which

are

started

with

the

synchronous generator

a.diJlI'.

a.

s

ii.

11101.01'.

()III.

Ni

d('

a.

V('ry

low

s

p

~

't:d

l'l1,

1I

J«:

, wli!'!'(·

UI<'

('

IIITl'lIl

'i

I>

IIIllsl

.

),('

IIlad('

illl.('l'I

l

liu(·,d

, 1,,,

»11"\\1

(·

"IIIllIlll.lll.

l.

'l1 01' 1.

11

"

"'

/ir

llÍl

...

lI

id,· (·""V(',·I.<-I',

I.!

...

d"

lv

('

:350

14. Variable Frequency Synchronous

Motor

Drives

Supply

Shunt Thyristor

Line-side

Machine-side

converter

References

F

ig.

14.18.

Six-pulse converter

with

De

link

ror

supplying

a synchronous

machine

i -

(ú

omax'

uo

,

max

\

~

-'

'n

I u

o

> O "

max

(ÚS ''

Pulsafing

forque

•

__

~_

m

,

.,.

;--'Omax

Uo> O

Uo

< O

,

.)

"

,

\

,

Fig.

14.19.

Operating

range

of

synchronous

motor

drive

with

direct

current

link

can

operate

smoothly in all four

quadrants

of

the

torquejspeed

plane, as

is

illust.rated in Fig. 14.19.

During

regeneration

the

voltage

tiD

is

reversed by

ddayed

firing of

the

line-side converter whereas

the

direction of

rotation

is

dctcnuined

by

the

sequence of

the

firing pulses for

the

machine-side converter.

'l'lw voltage

UD

rises with the speed up to

the

li.mit given by

the

converter,

II

furt.hnr incrcase of speed is then achieved by reducing

the

field currcnt, i.e.

I.y

lidd

weakeuing

as

with a

De

drive.

The

line interactiow; of this

tyP(~

(II'

drive

ar<

:

ó\.I.~()

slt\lilar

to

th()s(~

of a convert.cr-fcd

reversihl

e DC drivn, Chapo

~.

'I'It" I,II

:-l

i(' 1110,11' of operat.ioll

01'

(.\11:

11

tncli'i

1I(

··

jo

;Jd,·

COI\V(:ft.,·L'

COI'I'UR

I)(llld:,

Ir,I)

tI,

!!

1

d"

Il

('l

ilwd

iII

S,'~'f..

~

.

:

I,

,'x

'l''''pl,

1.1.,

11,1', til,'

1Ir'Í1I

1

',

01'

I.Ii

,vrli1tor

ll

11111:

1

1.

I"

,

14.3

Synchronous

Motor

with

Load-commutated

Inverter

351

synchronised to

the

variable frequency source voltage

~s

which is perform-

ing

the

commutation. Outside

the

commutation

intervals

the

stator

current,

flowing

through

two phases of

the

motor,

is

current-sourced by

the

DC

linkj

its

magnitude

is

maintained

by closed loop control

via

the

line-side converter.

The

stator

current

has approximately

the

sarne waveform consisting

of

120

0

blocks as seen in Fig. 11.15 aj one

stator

phase carries

no

current.

The

distorted

waveform of

the

currents, which also produces

torque

pulsations,

and

the

need for low

impedance

commutating

paths

make

it

desirable

to

provide continuous

damper

windings which assist

the

formation

of

a

smoothly

moving

rotational

flux wave, as was shown in Fig. 12.30 and 12.37.

The

combination of

•

current

sources in

the

stator

(except during commutation, where two ter-

minaIs

are

short-cicuited

through

the

converter),

and

• low impedance rotor circuit

indicates

that

a detailed analysis of

the

system is complex

and

could only

be

handled

by digital simulation [M17]j however, by approximation

the

sarne

mathematical

model of

the

machine can be employed as in

the

preceding

section, Eqs. (14.20-14.22).

The

flux vector, Eq. (14.23),

the

induced voltage,

Eq. (14.32)

and

the

computational

model for

the

rotor

flux, Fig. 14.16, also

remain

valido

Despite

this

similarity of

the

plant

structure

the

field

orientated

control

strategies

illustrated

in Figs. 12.33

and

14.15 are

not

directly applicablej

this

is so because

the

stator

currents

cannot

be

determined

at

will, as was

possible with

the

current

source converter employing forced

commutation

or

the

cycloconverter with line

commutation

and

current

controI. Instead, firing

of

the

thyristors

in

the

machine-side converter

must

now be so

timed

as

to

•

permit

safe

commutation,

• result in

minimum

link

current

for a given torquej

the

line-side converter

would otherwise

operate

at

an

unnecessarily low power factor.

These

are overriding conditions which can

best

be fulfilled by always

operat-

ing

the

machine-side converter

at

the

limits of

the

control range, i.e.

• zero firing delay (a

=

O)

when regenerating or

•

maximum

firing delay

(ama",)

in

the

motoring region.

The

firing delay a is defined with respect

to

the

induced voltages

es

behind

the

transient

impedance.

The

two modes of

operation

are sketched in Fig. 14.20 a,b. Clearly

the

commutation

interval

and

the

fact

that

the

commutation

must

be completed

before

T =

7r,

prevent

operation

with purely

quadrature

current.

The

situa-

tiol\

is

crit.ical in

motor

operation

with

the

machine-side converter serving as

ali

illvI:rt.er

h

ec;

w

~p

the extinction

angle"

explained

in

Fig. 8.17, should be

"'II;dl

j(\

'"

'

d"l'

1101.

1.0

J'(

:

dllce

tlw

t.lll'qllC

IIlHwc(!Hsa,rily

Illlt

OH

th0.

other

ha.no

ii,

111111

1

1.

h"

11

',,;,·,

"IIIIIII~h

1.11

II,

I,I<tw

~m

f

"

n,,

'IIv,'J'Y itf

I,I\(

:

1l1lt.1

(

(liJlI

~

f.hyl'iHt.itl'.

Ir

S1

352

14. Variable Frequency Synchronous Motor Drives

a=O

UO

<O

Regenerating

o

r I

~

'"<

I/!

:

'. '.

""'

1\.)

•

't

i

~

a

I

~"

~

/ \

a

wt

='t

max

Uo>O

Motoring

't

b

Fi

g.

14.20.

Current

and

voltage waveforms of machine-side converter

with

natural

commutation.

(a)

regenerating,

(b)

motoring

i.Iw extinction angle becomes

too

small, a

commutation

failure may be

the

colIsequence; while this would

not

constitute a

major

disturbance,

with

the

lillk reactor preventing excessive rise of

the

current,

it

would still cause a

:;cvcrc

torque

transient until

the

current control loop has restored

the

link

l"1ll"rellt

and

the

inverter

returns

to

its regular firing sequence; the incident

is

Sillli

la.r

to

the

misfiring of a six-cylinder combustion engine.

Another problem is

the

synchronisation

of

the

machine side converter;

t.illlÍug of

the

firing circuit

with

respect

to

the

terminal

volt ages of

the

machine

would be unsatisfactory since these volt ages are highly distorted

and

out

of

pll<ts

e with

the

nearly sinusoidal induced voltages es.

There are two possibilities for detecting es,

the

driving voltages of

the

colIlJnutating circuits. One is based on Eq. (14.31),

ili

mR

.

~s

fs

(t) =

(1

-

0")

Ls

dt

= 1!s(t) -

Rs

"'-s

-

O"

Ls

dt

'

(14.

3:1)

wltich

cOllld

l,e evalllated with analogue eircuitry

or

a microcomplltcr.

1\

~

(~cnlld

opt.ioll

is

t.o

use

the

flux

lllodd

iJl

Vigo

111.

Ili,

wlw)"(~

l.wo

orl.hog

on

al

:

ll.

n

t.or

(.

I I

rrl

'11

Ls

'i

s

" , 'is /"

t.h(~

'.

tlll',ular

I'O(,Ul"

pO

l:l

i t.ioa f' i

wdt.hc

lidd

vol(

,

Il.I

~

t>

"/1./

,>

['(

>111"'

1"

'111,

1.111'

illplll.

i1i

l'

:naINj t.hiH

wOllld

l

d\'lir

d Ld,Y f"f>qllin> ,t

Itli('l

>

()('or

~

ll)lII

>

,

>

q

1,,1

"

~

"(,III

if!f', I,II!'

\llI

l

i"lI

:i

lIuld

i

l\

('r

tr

>

rlll,l('

l.If

'll

lI

'I'ft",

[iI

II

I.

"r

UI<'

l.

wtI

Il

fllll

'

tl

H

dl\

"l

14.3 Synchronous Motor

with

Load-commutated

Inverter

353

was chosen for a

laboratory

drive, as

it

seems

to

be more

straight

forward

and

less sensitive

to

uncertain

parameters

of

the

motor.

If

the

reconstruction

of

the

induced

motor

voltages es is of sufficient accu-

racy, a c10sed loop control for

the

extinction angle could aIs o be envisaged, as

is

common practice

on

high voltage DC transmissions (HVDC). However,

the

draw-back even of sophisticated nonlinear extinction angle control schemes

is

that

they

cannot

entirely exclude

commutation

failures because

there

may

always be

late

disturbances

that

are

not

taken

into

account when

the

firing

instant

is

determined [F21,77].

The

problem with every extinction

margin

control

is

that

only hindsight can tell with certainty, whether

the

previously

calculated firing angle was adequate.

A

major

difference between

the

firing control schemes for

the

line-

and

the

machine-side converters is

that

the

latter

has

to

function with

both

directions

of sequence

and

over a wide frequency range;

this

is a

strong

incentive

to

employ digital methods, where a variable clock frequency

may

be used

to

chang e

the

slope of

saw-tooth

signals etc.

The

commutation

itself

is

nearly frequency independent, as long as

the

resistance of

the

commutation

circuit can be neglected, because

the

driv-

ing volt ages increase with speed

and

the

time

available for

commutation

is

reduced inversely with speed, resulting in

an

approximately

constant

com-

mutation

angle Tc over a wide speed range.

At

very low speed, however,

this

is

no longer

true

because

the

resistive

voltage component consumes

an

increasing

portion

of

the

available voltage-

time

area;

the

minimal speed, where

natural

commutation

ce ases

to

func-

tion

is usually below 10% of nominal speed.

Operation

in

this speed

range

is

still possible when reverting

to

intermittent

link current;

this

is achieved by

commanding

zero link current,

to

which

the

current

controller responds by

temporarily

shifting

the

firing pulses of

the

line-side converter

to

the

commu-

tation

limit, i.e. applying

maximum

negative volt age

to

the

DC-link. As soon

as

the

current

in

the

stator

windings has decayed

to

zero

and

the

recovery

time

for

the

thyristors

has elapsed,

the

of

the

machine-side

converter

is

made

conducting

and

the

link current

can

be

restored.

The

delay necessary for reducing

and

building up

the

link

current

can

be

considerably reduced if a shunt

thyristor

in

parallel with

the

link inductor,

Fig. 14.18,

is

fired

at

the

time, when

the

current

reference

is

blanked [LI];

this

short-circuits

the

link

inductor

and

allows

the

current

to

circulate freely

without

affecting

the

commutation; as soon as

the

machine-side converter

is

switched

to

the

new conducting

state

and

the

line-side converter

is

reacti-

vated,

the

shunting

thyristor

is quickly blocked by

the

volt ages in

the

DC

link.

This

allows a

substantial

reduction of

th

e blanking

time

intervals in

the

low

sp

ced region and reduces

Lhe

effccts of pulsating torque.

Tt

wn.s

JlI(~nt.io!l(~d

above ill

COJ1lH

~

d,iol1

with

Pi!!:.

14.20 Lhat

the

machine-

sidc cOllvnl.('t',

oIH'

.rat.illg

wil.lt

lIai.llr;d

('OIlIIlIIIt.al.iol1,

illvaria,hly

C;\.IIS(~S

a

c(~r

Laill

ll.lll"lI

I ii, "r ('111' 1"'111.

iII

tI)('''

!lxi::, I

,>

1I11;lIl.t>IILillllalloa,d dqwlld.>1I1.

:1.1'111;1

:

154

14. Variable Frequency Synchronous Motor Drives

Lme

reaction.

This

can

be

offset by a corresponding change

of

field

current.

Olle possibility is

to

control

the

magnitude

of

the

induced

motor

voltages

es

1.0

a reference value rising

with

speedj when limiting

the

voltage reference

above

base

speed, field weakening is initiated.

Supp/y

Microcomputer

_1_

Converter

and

motor

8085

~

Line-side

Minimum

Link current Firing

current

control/er circuit

converter

Machine-side

converter

Jo'i~.

14.21.

Microcomputer

based

speed

control

of

LeI

synchronous

motor

drive

wil.h

I)C

link

converter

A control scheme

incorporating

these features is shown in Fig. 14.21.

The

p()w(~r

cil'cuit contains four converters of different types

and

sizes.

• Linc-side converter,

• Machinc-side converter,

• ShUllt thyristor,

• J,'idd power supply,

f'lI' which

the

microcomputer

is producing

coordinated

control comman(h;.

'l'IH'y

;1.1'('

t:he

refercncc values for

the

De

link

current

and

field voltage

as

wdJ

II:

·;

:;i,~lIals

for

lhe

digital firing circuit of

the

machine-side cOllvertcr

a.nel

tIl('

li

dllllll.illg

I,hyrislol', 'l'he function gmleralor

1)t'(~scl'Íhillg

lhe

Jillk cnlTcnt

rd

'

er

('II«T

Iaa:;

(.llI'

pllrpO:

j(;

()r

a

:;

snl'ing

cont.iulIOtlH

ClllT(~llt;

iu

t\w

lllillÍlllal

c·.tlrrell!.

1IlOdc'

('(,"!.r()1

1Ül d lh'l.('d

t.llrOIlI~h

1./1

0

Jirillf

~

I

lll!

'

;IC~

(

,r

II.ilc'

HlII.dlÍll

C:

~

H

iel('

C(

'IlV

(',

['i,(

' 1

w!.ic'h

c.ptl

,'hl

.v

ll

!l~H

II"

( 'I

:

il

tl

IIppC'

1'

III' l"wC'r

111111

",

"

(I

CW

(\

1

n"

'

ilHI

I,I

J

II

H

1.1.,.

14.3

Synchronous

Motor

with

Load-commutated

Inverter

355

link

current

reference begins

to

respond

to

increased

torque

demand,

The

in-

verter

limit angle

Qmax

must

be

continuously

adjusted

to

achieve

minimal

but

safe

extinction

timej

it

can

be

determined

either

by

open

loop

computation

based

on

current,

voltage

and

speed

or

by closed loop control, possibly with

feed-forward

compensation

from

the

current.

The

control loop for

the

field

voltage

Up

is included

in

Fig. 14.21 which corresponds

to

the low

impedance

rotor

model in Fig. 14.13. AIso, control of

the

field voltage responds

more

favourably when

transient

currents

are

induced in

the

field winding when

load

is applied. A control loop for

the

field

current

ip

would

tend

to

tem-

porarily

reduce

the

field voltage

at

a time, when

it

should be increased.

On

the

other

hand,

control

of

the

field

current

would

eliminate

the

effect

of

changing field winding resistance due

to

temperature

variations

and

improve

the

dynamic

response

in

the

field weakening region.

The

sequence

of

the

firing pulses for

the

machine-side converter

can

be

based

on

the

estimated

angular

position

of

the

flux model, Fig. 14.16,

or

on

the

rotor

position

ê,

if

a voltage model according

to

Eq. (14.33) is used, whose

accuracy is questionable

at

low speed,

An

important

feature is

the

starting

control

algorithm

in

the

very low

speed

range

by

temporarily

blanking

the

link

current

via

the

line-side con-

verter

and

firing

the

shunt

thyristor.

This

is a convenient way

of

quickly

altering

the

mode

of

operation,

such as

torque

reversal

at

low speed which

could

take

too

long when waiting for

the

commutation.

n

1/min

800

600

400

200

o

~

,/

-200

- 400

- 600

- 800

i..Q

Intermittent

A

Link current

40

20

1

IIII,II~"

11111

,"

0;5

1;0

1;5 2;0

2;5

3;0

3;5

4;0 1

5

Fig.

14.22.

Reversing

transient

of

a

20

kW

synchronous

motor

drive

at

half

nominal

speed

/I.

:W

kW s

yllchrouous

Illotor drive

wit.h

microcomputer

control

has

heen

c\c'si

)

.{

lIrt!

iii

UI('

lahonüol'Y

aliei

t.(~sl.(~d

l1un,lu7,IUH1·

Fjr;lln

~

11.22 ckpic:t.s a

n·nll,I,·,llc

'

vc

·I'nÍtlg 1,1'

1I.

1I:

1'

iC'llt.nt iraI!' IICIIIJillll.l :iJltTCI wi

l.lr

1.1iC'

IIlC'J'tiacl!'

LliC'

clriv\'

__

_

356 14. Variable Frequency Synchronous

Motor

Drives

increased

by

a

dynamometer

without

load.

The

intermittent

link

current

at

low speed as well as

the

upper

and

lower

current

limits

are

clearly visible.

The

oscillogram

demonstrates

that

the

dynamic response is slower

than

could

be

expected

with a field

orientated

type

of

controI. However,

there

are

many

applications

where fast response is

not

a

primary

concern.

n

min

-1

2000

Speed

1500

1000

io

Load

applíed

1/

A

:

De

Iínk current

50

40

30

20

10

O

1

I

I,

A

Field current

5

4

3

2

Firing angle

16;~

1400

.

of

machine-side converteI

1200

~

ms

2

Extinction time

~Ii<V

..

~~~

I

O

o

I

1,0

2,0

s

Fig.

14.23.

Loading

transient

of

a

20

kW

synchronous

motor

drive

Further

details

are

seen in Fig. 14.23 where load

torque

is applied; tlw

rise

of

the

field current is

initiated

by

a

transient

and

then

maintained

by

th(

~

controlloop

for

the

induced

motor

voltages es, thus neutralising the

effeds

of

armature

reaction.

The

trace

of

the

extinction time indicates the go

od

perfonnancc of

Lhis

crit.ical cont.rol function.

Fi

II

;tlly) I

"i

,,;

. 1·

1.21\

show

s

I.h(

~

dr('cl.

or

a

dd

i

I>

cm

tdy

l.rif(I

~~

m

d

COI II

III

II

tnt.joll

L,illll"

wlli"11 , ' :111::1': :

:t

1'1I1'id )'i:iI'

(Ir

UI(' lill

l\

1'11111'1'11

..

IloWI'VI')',

t.lw

1"111'1'1'111.

14.3 Synchronous Motor

with

Load-commutated

Inverter

357

UTh

-V-

200

Thyristor voltage

O

-200

-

400

aO

delayed firing causes

1600

/

commutation failure

1400

1200

ia

A

60

De

Iink current

40

20

O

b

10

20

30

40

50

t

ms

Fig.

14.24.

Intentional

commutation

failure

Df

machine-side converter

controller is able

to

quickly restore

the

link

current

so

that

the

machiuc

..

:-;idc

inverter

can

resume firing in

the

regular

pattern.

As

seen in Table 11.1 synchronous

motor

LCI-drives are being used

IIp

1.0

the

highest power

ratings,

mainly

for compressors, gas

turbines

and

j.>Ullllwd

storage

sets. Since

the

usual

method

of reducing resistive los ses by illc

n:a

Hilll'.

the

motor

volt ages

cannot

be

applied indefinitely because

of

the

windiJl

J-(

iH

,'

lation

of

the

motor

(the

usuallimit

is

around

10

kV), converters

iII

pn

m

lll'

I

connection

are

often chosen, as is shown in Fig. 14.25 for

12-puls(~

o»(:nl.l.Í()lI

,

at

the

sarne

time

reducing

torque

pulsations. For this purpose

the

llIol.o)'

wlI.I,

solid steel

rotor

is

built

with

two

separate

stator

windings, displaccd

11.1'

:111

"

electrically, which

are

fed from two

separate

DC link converters.

At

(.]1('

li

ll!'

side, a corresponding phase shift

may

be

produced

by a

starjdelta

colllu'dl'cI

transformeI.

Brushless excitation

of

the

motor

with

an

AC exciter and rol.al.

ing rectificrs,

common

on large

turbogencrators,

is also indicated.

Pi

JJ;

.

II\

.

Zfi

demons

tratcs

th

e cOlltrol scheme,

wl)(

~

f(

:

1.111:

S

]lCCC\

controller sUJlplics (:qll:d

C1JIT(~1l1.

n :

f"J'('llc(

';:

to

t.h(~

s(~pllrat(

~

lillk

nlJT('Ut.

ClwLrolkr

:-;

;

tll(~

hac\c

voll.a

.I'.'·:

·/I./ll

, ·

(t/l

'.)

:wl

,

iv"

iii

1.111"

I)C

lillk

1:i

, :\'1'"

}1

lJiJ'I

,

l'd

a'

"

I'<))"(liJl,

~

1.0 til\!

/;I;

colI\l"l.l'il'il.l

1)()

h

il.i()II:

~

"r

ii,,·

111"1.,,1'

willdill,'

.

~

.

1

358

14. Variable Frequency Synchronous Motor Drives

Machine-side

converter

Une-side

converter

fo= const

.---

i

02

fI =variable

:_~~

i

01

(1

'".

U

01

~--f!'~:-'

\ I a

21

r-----~----~~--------_,

a"

mM'w

Brushless excitation

with rotating rectifiers

6-phase

motor

Fig.

14.25.

High power

LeI-drive

with

6-phase

motor

ú)

Start

wilh

int

e

rmitlent

cu"enl

í

DI

je

LC;1

(1+

aR!LRe

I~SI

RS

1

@SI

mR

(I)Hül

---.

..:....H.J-I.-=l

{S2

(1+

aR)

iR

e

ii

e- rr/6)

I!!S2 RS(I 'O)L

S

Fig.

14.26.

Equivalent circuit

and

control of a 12-pulse

LeI-drive

14.3 Synchronous

Motor

with

Load-commutated

Inverter

359

iSI(t)

Stator winding 1

iS13

iRI

Rotor winding

n/6

(combined field and

JR(t)

damper winding)

Stator winding 2

Fig.

14.27.

Simplified winding scheme of a two pole, 6-pulse synchronous

motor

The

arrangement of

the

windings

is

demonstrated

in Fig. 14.27 in sim-

plified form; whereas in

the

rotor

a symmetrical AC winding serves as a

combined field-

and

damper- winding, there are two electrically isolated and

by

7r

/6

= 30° displaced two pole AC windings in

the

stator; in accordance

with

the

simplifications introduced in Sect. 10.1 they are modelled as airgap-

windings.

The

pertinent

ampereturns

waves are, as in Eq. 10.2,

8

S1

(0,

t)

= Ns[isl1(t)t9s(o) + iS12(t)t9S(0

-,)

+

+ iS13(t)t9S(0 - 2,)],

(14.34)

8s

2

(o, t) = N

S[iS21

(t)t9s (o -

7r

/6) + iS

22

(t)t9

s

(o -

7r

/6

-

,)

+

+ iS

23

(t)t9s(o - 7r/6 -

2,)],

(14.35)

whcl'e

- 1 <

79

s

(0) <

+1

are dimensionlcss periodic functions describiug

tJw

disiriblltiolls

()r

lh(~

windiJlgs.

Tw()

(·()\J1pl(·

.X'

Ktntor

cllrr

eut.

VC

cl

OI'H

aJ'(~

ddill(~d

ror

t;h(~

t.wo

Willdirl1';s,

Werner Leonhard Control of Electrical Drives

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