Werner Leonhard Control of Electrical Drives

I1I1I

H,

Sl.atic Converter as a Power

Actuator

for

DC

Drives

(hll

.\'

Ily

)'('dllcing

the

load

current

i below a lower holding

threshold

iH

can

1.11<'

I.hyrist.or again

revert

to

blocking

statej

hence

it

represents a switch

that

,'

11.

11

1>('

('Ios(~d

by a low power control signal, whereas opening

it

requires

the

111

11

<1

('lllr(~l\t

to

become very

small

or

zero.

u

1\

K

i

-

"

A77

.

/u

9

K

b Ig

G

Fil

,(.

H

.2.

Thyristor

model

and

symbol

:-;illlplified characteristics

of

a

typical

power

thyristor

are

shown in Fig.

,

"{

.:\;

Lhe

scales

of

the

curves

are

different

to

emphasise

the

details.

While

the

kak

iW;

I'

cnrrent

in

both

directions could be below 100 mA,

the

load

current

in

l'lllldllcting

state

may

be

several

thousand

A.

The

voltage drop

of

the

(,()lIdlld.illg thyl'Ístor is

about

1.5 V

and

the

maximum

volt age in blocking

::I.:Ii.I'S call

Iw

lllore

than

8 kV.

W!II'II

tllC

lll<tximum reverse volt age is exceeded,

the

leakage

current

rises

li

l.pi<lly,

i~

'i

wiLh

semiconductor diodes, leading

to

break-down

and

thermal

<I,'::l.rtldillll

Ilr

t.he

thyristor.

ln

the

forward direction

(u

>

O)

the

effects

are

111111"

1'll

lIljllt-X,

Whcn

the

voltage reaches a breakover levei, which

depends

1111

1.11<'

I',ii

1.1'

(,\Irr(~lll.,

the

thyristor

switches spontaneously

to

the

conducting

: ,

1.:1i."

11,,\V('vI')',

1.11I'l1-OIl

by increased forward blocking volt age is

not

a

suitable

1111"1,,

"I'

('

IIliI.)'o!

for

a power

thyristor

because

the

"firing

instant"

(a

relict

I"

'III

pla:

:lll

i(, discharge valves) is

not

sufficiently well defined

and

there

may

I",

111

(':

11

Ilvel'iwal.iug of

the

semiconductor elemento

lnstead,

the

switching

L"

LI",

()rI

"

sl.ill.<:

should always

be

effected by a

gate

current

pulse

having

a

::1"

,rI.

11:;1'

I.ílll('

which

has

the

additional

advantage

that

the

thyristor

fires

at

a

1"1

'('

itl

,,

1y

ddiued

instant,

independent

of

the

individual

thyristor

parameters

.

11i)('

1.0

lhe

small dimensions

of

the

active

semiconductor

wafer

and

its

III

\V

1.I1I~l'Il1a!

capacity,

the

safe use of

thyristors

calls for observing some re-

::l.lldiIlIlS; apart, from limits

on

temperature,

volt age alld

current

there

are

IlIil

,X i

11IIIlll

values for

the

rate

of

the

current

rise

(di/

dt) while switching On, as

\1'1

,

II

i

l.

~

;

UIC

voltage

rate

(du/

dt)

during

and

aft(

~

r

tu

rll· OIf.

This

requires

the

ill('III:

:

il)ll

01'

prol.cctivl; circuitry such as a seri.::;

illdll('I.i\.IlC(

~

iUld

a parallel ca-

JI

,

)('iL(

II'

(.~llIlbl)(~r),

COllsi(kring

al:-;o

tlte

swil.chil'i

~

Hllq';<':, t.llat. i\.l'e llu<lvoidable

III

jlIIW('i'

:illi'ply

SYS

I,I

'

llI

S,

i!.

is

llcCI

'ssary

1,1)

lllailll.nill i1 prop(']'

safd-y

lllargill

" t

1.11('

"1H'1'

1i

!1,

.illll',

v

l

,llil

,

I

~

('

: ;

ag

aillst.

I.he

HIH

'd

l

kd

lH'

l

t!

t

V:t!llI':

).

1,'0)'

('xlwlpll',

a

I,

:

~

1"V

1.11,V11

::

I.III

lIili,Y

III'

iljll'('iJi"d iu n ("IIIV('rkl (·IIII1\('(' I.('d

1.11

1.111'

,

1110

V lilll'

11'110

'

1"

II",

III

/1X

1J

llllltI

"I"'I

II

UIII',

v"II

,'

IJ'.

n I

ii

IIIII

,V 1,IIh V

II"

WI' VI')',

\111"

'

11

itll

1.111'

8.1 Electronic Switching Devices

101

200A

,1,5VI

conducting

ig

i =100mA

-1kV

H

forward 1

kV

U

reverse

blocking

Fig,

8.3.

Static

and

dynamic

characteristics

of

thyristor

recommendations

by

the

supplier

are

observed,

the

thyristor

has

proved

to

be

a reliable

and

very

robust

switching element

that

can

stand

high

short

time

over-Ioad

current,

such as a 10 fold surge for one

cyde.

Persistent

overload

must

be

prevented

by a fast

acting

closed loop control

and

in

the

limit

by

fuselinks.

An

important

design

parameter

of

thyristors,

particularly

when

applied

in

force

commutated

converters, is

the

recovery

time

tr·

It

indicates

the

time

that

must

ela

ps e from

the

instant

when

the

load

current

has

reached zero,

until

the

thyristor

has

attained

full blocking

capability

in forward

direction

(u

>

O).

The

purpose

of

this

interval is

to

gi ve

the

residual charge carriers

accumulated

in region

nl

during

the

conduction

period

time

to

decay

through

diffusion

and

recombinationj

depending

on

the

type

of

thyristor,

reverse volt-

age

and

junction

temperature,

the

recovery

time

ranges from a few

Jls

for

a

high

frequency

thyristor

to

several

hundred

Jls

for a high power

thyristor

designed for low voltage drop.

t>

tr

/

I

/u(t)

u

/

o oi

r::.:J

sfored

I

charge

I

I,

....

_ /

\.

I

...I'~_I

-

..

I

b

a

Fig.

liA.

'1'lIrll

d

lfr

I.mllHil~nt

of

thyristor

(n)

(:1111"111.

i'

.

lId

v"It.II.I~"

(h)

I'roLeclive circllil

I I ) :

~

K.

SI.;tLic

Converter as a Power

Actuator

for

DC

Drives

fi Ly

pi

cal

tr

ansient of

the

volt age u(t)

and

the

current

i(t)

of

a

thyristor

dlllilll ': Lllrn-Off is depicted in Fig. 8.4 a. As

the

load

current

i reaches zero,

1,

11\"

I.hyri

stor remains conducting for a

short

period with reverse current,

thus

('

1

(";

Llill

~

the

charge-carriers from the junction. After this charge

has

disap-

P(

';

II

('

<I,

current

flow

decays rapidly causing high reverse blocking volt age due

lo

UI

C circuit inductancej this voltage

peak

must

be

limited by

the

protec-

I.i

V(

~

parallel

capacitor

indicated

in

Fig. 8.4

b;

in

the

subsequent interval

the

(('v

erse volt age is

determined

by

the

external

load circuito

When

the

recov-

I'ry

I.illl

e tr has elapsed,

the

volt age can again become positive

without

the

11;1.1

1/'

:

<:

r of breakover

and

unwanted

forward conduction.

The

recovery

time

i

:i

('

llll

siderably reduced

if

reversed volt age U < O exists after

current

zero.

'I'

IH'

['('sistor in

the

snubbing circuit, Fig. 8.4 b, is required for limiting

the

di

:;

dlarge

current

of

the

capacitor

at

tum-On;

frequently

the

resistor

has

a

diode

ill

par

allel to make

the

capacitor

more effective

at

limiting

dujdt

in

(orward direction.

H.2

Line-commutated

Converter

iII

Single-phase

Bridge

Connection

'I'ilyrisl.ors, which

are

available in a variety

of

voltage

and

current

ratings,

;1./

('

e'Jlllhille

cl

to

converter circuits

to

serve as highly efficient electronic power

::

lIl'l'li('s for a wide power range.

Of

particular

importance

for

the

supply

of

1)(

:

IIIOl.orS

are

the

so called line-commutated converter circuits fed from a

::iUI',

11'

o)'

Lhree

-

ph

ase AC supply of

constant

volt age

and

frequency.

They

are

'1I

Iil.:d,I"

ror sllpplying

adjustable

direct voltage

and

current

to

the

armature

1.1111

li

('ld willcliIlg of

the

motor,

either

directly

or

through

a transformer.

LA

a

.--o

io

U

o

!

UAi

iA

I

~

io

."

i U

o

fi

tJ

II

I1H!lt,at.

~

·

d

("O

IlV

I'

rf

,I11'

(

I\'

)

d

'

~

'

III

I

,

(I.)

l'

II

I,,'I:

II

Q

01

1'

,,

1I'

'I"

'I,

v

,.

I,'

1I

1.

2'

I

l'

i I

F l,(.

tl

.

li

.

:-;

ilfl

\~

"

111

;

1,1,,

:\'

l

,

i

.

l

w

"

""

8.2

Line-commutated

Converter

in

Single-phase Bridge Connection

103

The

single-phase circuits discussed first

are

of

interest,

apart

from railway

traction

drives, for low power applications

up

to

a few kW.

The

circuit

shown

in

Fig. 8.5 a contains four

thyristors,

which

are

made

conducting

or

"fired"

in diagonal

pairs

during

every

alternate

half

cyele

of

the

line voltage

UA·

Provided

there

is a continuous direct

current

iD,

the

function of

the

circuit

may

be

described by a mechanical

commutating

switch, connecting

the

DC

circuit

with

alternate

polarity

to

the

line voltage

(8.1)

UA

=

UA

sinT,

wt

=

T.

When

assuming

at

first

that

the

direct

current

is smooth, iD = ID, being

maintained

by

a fictitious

current

source,

and

that

the

impedance

of

the

AC circuit is negligible,

with

UA

coming from

an

ideal volt age source,

the

volt age

UD(T)

between

the

DC

terminals

consists

of

periodic sections of

the

AC voltage

or

its

inverse;

this

is seen

in

Fig. 8.6 for different firing angles

a,

which

determine

the

instant

at

which

the

other

diagonal

pair

of

thyristors

is

made

conducting.

The

firing angle represents

the

switching delay

with

respect

to

a

"natural"

firing

instant

that

would

be

valid for a circuit consisting of

diodes; for

the

thyristors

1,

l'

the

"natural"

firing

instants

are

T =

O,

27r,

...

when

the

volt age

UA

(T)

and

-

with

thyristors

2,

2' conducting -

the

voltages

UTl

(T)

,

UTI'

(T)

become positive.

The

maximum

firing delay is

ama",

=

7r;

for

a

>

7r,

the

thyristors

1,

l'

cannot

be

made

conducting

since

they

are

reversely

biased.

This

is also seen from

the

curve of

the

volt age across

the

thyristor,

UTI

(T),

drawn

in

Fig

. 8.6 c for different firing angles

a.

Later

the

range

of

the

control angle will have

to

be

further

narrowed.

The

trace

of

the

thyristor

current

iTl

(T),

also shown

in

Fig. 8.6 c, elearly

indicates

the

switching

action

of

the

thyristors;

at

any

time

at

least

one of

the

quantities

UTl

(T),

iTl

(T)

is zero.

ln

steady

state

condition

with

a =

consto

the

volt ages

and

currents

in thyristors

2,

2'

pertaining

to

the

opposite

diagonal

pair

are

identical, being shifted by a

half

period.

Finally, in Fig. 8.6 d

the

input

current

iA(T) for

the

three

different values

of

the

firing angle a is drawn.

As

a consequence of

the

periodic

commuta-

tion

between

the

two

pairs

of

switches

the

impressed continuous

current

ID

appears

at

the

line side

of

the

converter as a square wave

alternating

current

iA(T), whose

phase

lag

ep

with

respect

to

the

line volt age

UA(T)

is prescribed

by

the

firing delay,

ep

=

a.

The

active power (mean

of

the

instantaneous

7r

power)

at

the

line side is - assuming

sinusoidalline

volt age -

determined

by

the

fundamental

component

iAl

(T)

of

the

line

current

2V2

PA

C =

UA

IAI cosep =

--

UA

ID

cosa,

(8.2)

whe['(

~

(J

II,

I

II'

are

H.MS-values of

the

line voltage

and

the

fundamental

cur-

n:lll.

('.OIIlj>OIlC·I\I

,. For

LI

< a <

~

,

the power flows from

the

AC -

to

the

DC -

:;id", wilil., ("r :: .

11

'

n""",,,

(./1I

~

(lO

WN

f10w

is

ITv(

~

r

s

(

:

d.

c

104

8.

Static

Converter

as a Power

Actuator

for

DC

Drives

rot

a

IX

1

=

30

°

lX.2=

90°

(X3=150

°

rot

U

o

rot

lX.2

a

3

'II

I .

I-----

_'AI

/

\

I

\

iA

I

\

I

~

7C

\

I

rol

\

I

~

I

'_I

~

,.

~Al

.

~

/II

I ----T-J

IA

I \

I

\

-,

1\

rot

Ir

I

~Tr

t7'

,

,~

\ /

d

1"'1(' H.G. V

()

lt

ages

and

currents

of

an

ideal single

phase

converter

'I'II(~

fir

st

mode

corresponds

to

controlled rectifier-,

the

other

to

inverter

"llCral.iof! .

111

Fig.

8.7 a

phasor

diagram

is showing

the

phasors

of

the

line

volt

-

!l~

"

I J A

aud

of

the

fundamental

component

of

the

line

current,

I

Al

. Clearly,

a cllul.roUcd c

onverter

appears

as

an

inductive load

at

the

line side,

drawing

Ja.j'

:I':illp;

J'(

~

a("t.iv(

!

cunent;

this is

du

e

to

the

control

principIe allowing only

,kla

.y

( ~

d

lirill,

~.

Firiup; adv;mce is

uot

possible with

line-commutatcd

convcrt

-

!'I

ii

1

H"

.ct

Ul

s('

Lhe

jiriug

plllses would bc

appli(~d

(.0 tltyristors

having

rcv

e

r

s

(~

Ilta

!-l

volL

i'lt'í<

' whirll i'f('v('uLH

tlH:lll

[('IIJH

(·OJldlld.illg;

advaúC(~

firillg

iR

ollly

!,o

wd

ld

('

wi

l.h

·

r"I"

'"

,·o)[)l

ll

u(.n.I.('d

'~OIlV

..

[ I.'·

lii

,

wI","

:

illI

iul.<'rval wil,h rorw<I.rd

«(

I

8.2

Line-commutated

Converter

in Single-phase Bridge

Connection

105

Inverter I Rectifier

a=7C

2

Fig.

8.7.

Phasor

diagram

of

a single

phase

converter

blocking voltage

V,T

> O is

created

for a <

O,

during

which

the

thyristor

can

be

fired. Forced

commutation

calls for

additional

components

and

thyristors

with

short

recovery

time

which involves

increased

cost

and

complexity;

this

wiU

be

discussed

later.

Ü

o

2 .

-u

11:

Reclifier

a

Inverter

........

-

Fig.

8.8.

Control

curve

of

phase

controlled converter

The

possibility

of

reversing

the

power flow

by

electronic

control

is of

importance

if '

the

converter

is

to

suppIy a

DC

motor

since

it

permits

regen-

eration.

It

is

pointed

out,

however,

that

firing controI affects

not

onIy

the

active

but

also

the

reactive

power flow

at

the

line side. At a =

~

the

reactive

power

assumes

a

maximum

value (for I

D

= const.) while

the

active power is

zero;

this

is

the

case

when

the

motor

produces

torque

at

standstill.

Identical

results

are

obtained

when

examining

the

DC

side of

the

con-

vert

er, where

the

mean

voltage is

tt

u

o+rr

1 !

'It

A sin T

dT

2

= -

í/,

A cos a

2)2

= - - UA cos a = U

DO

COS a

71'

7r 7r

UU)

fi

I U I I

I

,

~

C

f\

1.06

8.

Static Converter

as

a Power Actuator

for

DC Drives

This

is described by

the

control characteristic

UD(Ú)

seen in Fig. 8.8; for

reasons discussed

later

the

curve

is

only valid in

the

interval O< Ú < ú

max

,

with Ú

max

~

150°. Because

of

i

D

= I

D

= const.,

the

mean of

the

output

jJower

is

2..)2

F

DC

=

UD

I

D

=

--

UA I

D

cos Ú ,

(8.4)

7r

which

is

in agreement with Eq. (8.2).

This

is

so because

the

idealised switch-

iii!

;

co

nverter consumes no power; it functions by shifting

the

180

0

-blocks

()r

Lh

e direct current with respect

to

the

line voltage.

The

transferred

mean

p

..

wcr changes sign in accordance with

the

direct voltage as

the

firing angle

II"

exceeds i. Since

the

current

cannot change sign because of

the

unidirec-

Liolla[

thyristors,

the

line-commutated converter circuit in Fig. 8.5 represents

;t

cO

l1

trolled power supply operable in

the

two

quadrants

of

the

ID, uD-plane,

;

lS

seen in Fig. 8.9.

The

control is performed by electronically delaying

the

li

r

ill

f.!;

pulses

to

the

thyristors by

the

firing angle

ú.

U

o

'.

"

'/1

' (//1

a=O

Rectifier

lO

Inverter

a=

a

max

/I

1//1

I"il~

·

1'1.0.

'I

'wo

quadrant operation of line-commutated converter

(;Icarly,

a switched converter causes interactions with

the

line, involving

I;I./',I

~

illg

reactive power as well as current harmonics. Because of

the

supply-

/1,11(1

1.11('

Lrau

sformer l

ea

kage impedances this causes voltage fluctuations

and

hlu'IJlollic

([i

st

ortion which

must

be

taken into consideration as

the

rating

of

1,

1"

,

('()Ilv(~rt(']"

inereases. While

the

harmonics problem may be relieved by

I',(JIII,

~

t,o

Illlllt,i-phasp. circuit

,s,

th

e reactive power is a characteristic feature of

allli

ll(

'-cOllllllllt

,a

l(

:d

CO

llverter

::;

with

dday

c

cl

firillg control;

it

is independent

of

LI", 11111111)('1' 0

1'

pha

~.,

\,s

alld call ollly

1)('

(:(lllllLt'racl

,

cd

hy

reactive c

omp

ou:m

tioJl,

AI.

ili!'

.h

pm

v

"1

II()i.h

,,11"

'

1'1.

:1

IIln

.v

J'(

~

qll

,

ij'('

C"l'I'l'djoll

I,y

hi\.J'IIl()I;icJill

,

·

r

~i

havillJ>;

II, I"

'"

dill!,,

IIII'IIL

,""V"I'

1'111'1

,

01'

u.t.

lill(' 1''''

'111

1\

11'

'

.1'

8.2 Line-commutated Converter in Single-phase Bridge Connection

107

Controlling a converter by electronic phase shift

of

firing pulses requires

little control power

and

involves only very

short

delay.

This

is

seen in Fig.

8.10 showing

the

output

voltage

uD(r)

with

the

firing angle being switched

between

Ú = 30°

and

Ú = 150°. Since only one diagonal

pair

of

thyristors

can be fired in

ea

ch

half

period,

there

is a

maximum

delay of

10

ms

with

a

50

Hz supply until

the

converter

output

responds

to

a command calling for

a chang e in firing angle. Hence a

static

converter represents

an

actuator

of

high dynamic performance combining

- high power

gain

- large

output

power

and

low los ses

- very fast response.

These

features

may

yet

be

enhanced by employing multi-phase circuits, as

will be shown in

the

next section.

(Ut

= r

Fig.

8.10.

Output volt

age

of single phase converter with changing firing angle

One drawback, though

of

little practical importance,

is

the

fact

that

th

e

steady-state

and

the

dynamic behaviour of

the

converter

is

highly nonlinear,

corresponding

to

a nonlinear sampled

data

system

with

one firing

transient

in each

half

period, From Fig. 8.10 it is

apparent

that,

following a changing

firing command,

the

result may

not

become effective immediately because

there

are

variable waiting intervals.

This

is

particularly

pronounced when

the

firing angle is increased for inverter

operation

because it is necessary

to

allow for

the

relatively "slow" reversal of

the

line voltage.

When

going

to

rectifier

operation,

i.e. reducing

the

firing angle,

the

converter

may

re-

spond instantaneously. An

accurate

analysis

of

dynamic converter

operation

is quite complex; for small

perturbations

linearised difference equations can

be derived

but

large signal dynamics are governed by non-linear difference

equations

for which

th

ere is

no

analyti

ca

l solution [F12,L34,P46].

Fortunately

the

converter is usually followed by

an

inductive load having low-pass transfer

characteristics, such as

the

armature

circuit of a DC machine which smoothes

the

current; therefore

the

converter dynamics may be

approximated

by very

simple models when designing

the

inner

current

controlloop.

Anot,lwr Jloint where high power converters

may

occasionally cause prob-

kws

is a

djj'(~ct.

collscquence of

its

advantages mentioned before;

the

power

HIIJ)pli,:

cI

Lo

LIli'

lo

n

tl

IIlw;t

, iu

sta

lltarwo

ll

sly

COIIIO

frOITl

th

e

AC

líne.

Th

ere

is

II

I)

d'

·(O"

"plllll'.

1'1("

'(

I.

t,

.y

illt,I

'

l'llaJl

y

sl,(

IITt!

(

'

IlC'1')

~'v

hl·I

':\.

II

S(·

ali

id('al

C()

ll

v(~

r"

,(~

r

lOS

S.

Static Converter

as

a Power Actuator

for

DC Drives

("ontains only loss-free switches. As was

mentioned

before,

the

importance

of

Lhese

effects has receded as

the

capacity

of

the

interconnected

supply

systems

Itas increased

and

is

more

closely meshed.

The

control

of

the

converter is normally

performed

by

the

output

signal

I)r

an

electronic controller influencing

the

phase

of

the

firing pulses

through

ii,

firing control device.

Its

basic function is explained

with

the

help

of

Fig.

!:UI.

The

output

signal

Yl

(t)

of

the

innermost controller, usually

the

current

coutroller, is

compared

with

a

saw-tooth-shaped

periodic

ramp

function YT

which is synchronised by

the

zero intersections

of

the

line voltage

UA.

When-

eVI'r

the

difference becomes positive for

the

first

time

in

each

half

period,

lhe diagonal

pair

of

thyristors,

Fig. 8.5, having forward bias voltage is fired.

'!'/te selection is done by

alternately

activating one

of

two

monostable

trigger

circllits

MT

1

,

MT

2

.

One

ofthe

trigger

circuits

produces

a

short

pulse which,

;IJt,I~r

amplification, is passed

through

a small

isolating

transformer

to

the

1~"Lcs

of

the

thyristors

to

be

fired (only one

of

the

output

windings is

drawn).

ILL

high voltage applications, such as high voltage

DC-transmission

or

static

n:<l,ctive

power

compensators,

optical

fibres

may

be

used for

transmitting

the

I i r i llg pulses,

thus

preventing

electromagnetic interference.

It

is seen

that

the

coLllparison

of

the

control signal

Yl

with

the

saw-tooth

function

represents

a

,';;\.Illpling

method,

at

the

sarne

time

providing a voltage-to-phase conversion.

'l'hc

basic principie

of

control described can

be

modified in various ways. If,

1lI.';1,l:ad

of a

saw-tooth

function, sections

of

cos-functions

are

employed,

as

is

illdl<:al.l:d

by dashed lines in Fig. 8.11 b,

the

control curve

UD(Yl)

seen in Fig.

fi,

,'i

l,cc()Ll\cS

a

straight

line, i.e.

the

converter assumes

constant

volt age

gain

<111/1/1':1/1.

Tll(~

sarne effect is achieved,

at

least

in

steady

state,

by

inserting

,III

arc:iill-rllllction

generator

Yl

=

arcsiny

into

the

input

channel

of

the

firing

('íITllil;

I./tis

is

indicated

in Fig. 8.11 a. Control devices for converters

are

I.IIII:LY

av.ti labll: in a variety

of

integrated

circuits.

I"

()nl<:!'

Lo

gain a

better

insight

into

the

principie

of

converter

opera-

IIIIIL,

é:lIlIJ<:

simplifications

that

are

not

fully realised

in

practice

have

been

IIIII'IIIIILCI:<I;

one is

the

assumption

of

a

smooth

current

ID'

the

other

of

an

iLII]lI'(':;:;('<I

voltage

UA,

neglecting

the

line impedance.

These

points

will now

1,('

li

iSCllsscd

in a

little

more

detail.

When

a resistor

RD

is connected

to

the

11111.]1111.

()f

Lhe

converter in Fig. 8.5,

UD

=

RDiD

holds

in

the

DC

branch,

with

thl',

('.ILrn~nt

ltaving

the

sarne waveform as

the

voltage. Hence

the

conducting

Lllyrisl.ors

wiU

be blocked when

the

driving volt age

UA

becomes negative;

I.h

iH

is

so

llCcallse

iD

cannot

change sign

and

the

passive

DC

circuit

cannot

('VI'II

iusl.<1lltaneously - feed power back

to

the

line.

Thus

the

current

will

I'X

hil,il.

LILI:

plllsating

shape

seen in Fig. 8.12;

during

the

zero

current

inter-

V;I,!ci

Lhe

vo!Lagc

a:cross the series connected non-conducting valves is divided

,(('1'111

<I

i

III';

LI,

(,\l(,j

l'

lli()cki\l~;

l'(:sistances.

'I'I\('

dh

('olll.ill'lliLy

or

LlI<'

]o;td

CllIT<:UI:

iI-!

:\1'('1:1I(,1Ia(;(:d

ii'

a,

h;tck

vo!L;lj';<:

«I)

,I)

i::

(""11-1<;('11'<1

\

11

::lTil':

:

wiLlJ

UI('

IT::i:-:l.or

IIi>-

Now

a

I.ltyriHL()r

pai r

1::1,11

S.2

Line-commutated Converter in Single-phase Bridge Connection

109

(rom

2

Y1

=]iarc

.

!.

__

.

sm Y

controller

rl~LL~~

~I~I:

T-

Y I;====IJ

Il0u

g

,

~IIOug2

a

0:

1

0:

2

0:

1

0:

2

-Y

1

(7:)

wt=7:

~

b

Fig.

8.11.

Principie of

an

electronic firing control circuito

(a) Block diagram;

(b)

Mode of operation

U

o

=

ROiO

"

,.

,"

a

(\

1~

1\

I~\

..

' _ ' . I I " I \

'"

l,

'. I ; " I \

UD~

/";{t

;'

'.

.'.

;....

. • I !-

(,o

. I F I

_"">L-_

..

\

I

\

rot

= r

\ I \

\ /

~

\

,/

Fig.

8.12.

Single phase converter with l'esistive load

only

begin

to

conduct

if

the

line volt age exceeds

the

back voltage,

IUAI

>

e,

because

otherwise

the

thyristors

would

be

reversely biased;

the

current

ceases

to

flow as soon as

this

condition

is violatedj Fig. 8.13 shows

the

effect.

A furtlu:r cornplication arises,

if

the

DC

circuit contains

an

inductance

J~

II

in

,t<ldi

Lioll

1.0

l.he

resistor

RD

and

the

back

voltage

e,

.which is

the

case

01';\

COlLvITI.I'r

fl'l:dillf',

I.h<:

mmature

of a

DC

motor.

Now

the

current

iD

may

1)('

('0

111('

l'Olll.il

,

III<lII::

('VI'II

for o >

()

!lecami(: th('

arlllatlLre

indllctance

with

its

110 8. Static Converter

as

a Power Actuator

for

DC Drives

8

/

~

,

e

\

UI)

\

I

\

I

rot

= r

I

\

I

,

/

~

1"i

lJ:.

8.13.

Single phase converter with back volt

age

and resistive load

c

;I.()II~d

energy

can

maintain

the

current

iD

during

part

of

the

interval where

1"11

A 1 <

e.

This

is drawn

in

Fig. 8.14 for different values of

the

firing angle a

;tlld

assuming

e = E = const

..

The

internal

impedance

of

the

line voltage is

~;I.ill

neglected.

lO

I I I

~3+n

/ I '\.

J/

1

",

E

/1

rl

I

rot

=r

~31a1

I

,I

I /

I'

l I

//

III)

I'

I /

I I, I /

I I

I

'"

I'

......

__

......

--ú

A

I '

I...

1

......

_

......

--

U

A

I I

I

o

:a

1

a

2

a

· 1

I

",..-'

2n

rot

=r

I"i!;.

tl.14.

Discontinuous and continuous current

Lct

115

assume

an

initial zero

current

state,

iD

=diD/dt

= O

and

conse-

(lll(~ntly

'/Lo

= E,

At

time

wt

= r =

aI,

with

the

condition

UA

sin

aI

> E,

1,11<:

I,hyrisl:ors 1,

l'

are fired so

that

the

current

iD begins to rise

with

finite

:,Io(l(:

and lIuickly exceeds the latching value

iL.

With

the

thyristors

1,

l'

('olld

udi

II"; ;wd

;11,

/I

(

1'

)

'Il

A (r), the following diffcrential

equation

holds,

,b

:" , '

/,

/. 1

r,

I

{"

J , I

/{

JI

1

/I

'U

,\ H

III

,

<tI'

I '

~

/1

1

•

(I)};)

rll

8,2 Line-commutated Converter in Single-phase Bridge Connection

111

The

solution, satisfying

the

initial condition

iD(al)

=

O,

and

with

the

abbre-

viation

LD/

R

D

= TD is

UA

1

iD(r)

=

--

\

RD

VI

+

(wT

D

)2

[sin(r

-

arctanwT

D

) -

e-(r-a,)!wT

D

sin(al

-

arctanwT

D

)]

-

.!!...-

[1-

e-(r-a')!'OTD]

(8.6)

R

D

At

f31

<

aI

+ 7r

the

current

iD becomes zero, iD(f31) =

O,

see Fig. 8.14,

at

which

time

the

thyristors

return

to

blocked condition;

the

current

remains

zero

until

r =

aI

+

7r,

when

the

thyristors

2,

2'

are

fired

and

the

sarne

transient

is

repeated.

Thus

in

steady-state

the

direct

current

is discontinuous,

consisting

of

separate

pulses.

The

mean

of

the

current

is a function

of

all

pararneters,

_ 1

j{3'

iD = ;:

iD(r)

dr

=

F[a,

UA,

wT

D

, R

D

,

E].

(8.7)

a,

When

evaluating

Eq. (8.5)

the

impedance

(RD,

LD)

must

be

augmented

by

a

smallline-side

impedance

as is shown lateI'.

A

similar

expression holds for

the

mean

voltage

0.,+11"

UD

=

~

j

uD(r)

dr

.

(8.8)

a,

This

integral

may

be

simplified

with

the

help of Eq. (8.5) considering

the

periodic

boundary

condition

iD(aI)

=

iD(al

+

7r)

= O;

(8.9)

thus

it

assumes

the

form

UD

= E +

RDiD

(8.10)

where iD is given by Eq. (8.7).

This

load

characteristic

uD(iD)

for a = const.

and

different values

of

the

back volt age E is highly nonlinear as long as

the

current

is discontinuous;

this

is due

to

the

variable

period

of

conduction,

f31

-

aI

<

7r,

as is seen in Fig. 8.14.

When

graduaJly reducing

the

firing angle, a <

aI,

with

the

same

initial

conditiolls as 1wfore,

the

amplitude

and

the

duration

of

the

current

pulses

illc\,(',

as(:

1IIII.il

:I

, lilllitiug case occurs, a = a2, where one

pair

of

thyristors

in

lir('d

;11,

UI(' 111.111]('111.

(,]1('

other

pair ceases conducting,

f32

=

a2

+

7r;

the

('1111"1'111.

1.11<'11

ollly

t,i1lwlll':;

'I,('II~

OIlC(~

(:v('ry

IIn,lr

p(:riod.

112

8.

Static

Converter

as a Power

Actuator

for

DC

Drives

If

the

firing angle is still

further

reduced, a < a2,

the

current

will

not

II

;

tvC

reached zero by

the

time

the

other

thyristors

are

fired.

This

then

con-

:;

LiLntes

the

region

of

continuous conduction, where

the

current

is

transferred

iII

a

commutation

transient

directly from

the

outgoing

thyristors

2, 2'

to

the

illCOllling

thyristors

1,

l'

and

the

current

is no longer discontinuous.

Th

e

bordering

case

to

continuous conduction follows

with

the

periodic

J,ollll(lary condition

-lo(a2) = iD(a2 +

'Ir)

= O (8.11)

I'rolll Eq. (8.6),

UA

wTD

) i +

(wT

)2

(1

+

e-

7r

/

) sin(a2 -

arctanwT

D

)

D

7r

wTD

+ E

(1

-

e-

/

) = O. (8.12)

Sol

ving

for a2,

the

condition for continuous conduction can

be

written

as

[

E.)1

+

(w

T

D

)2

tanhC

W'lr

TD

) 1 .

(t

<

a2

=

arctan

w

TD

- arcsin

UA

. (8.13)

l<'oJ"

(~ach

value of

the

back

voltage E a firing angle

a2

exists,

at

which

1.11<"

1;1.1\1',<:

0[" colltinuous conduction begins.

With

WTD

» 1, i.e. assuming a

I1<'1

1'1

'c

1.1

y sllJool.h current, Eq. (8.13) yields

the

obvious result

"2

ú;\

co

s a > E

(8.14)

/fI!

!T

- ,

wllidl

IIW<l.ll

S

Lltat

the

mean

output

volt age

UD

must

exceed

the

back voltage

ror

CIlIll.illllOU

S load

current

to

flow.

>

!\

II

L!t(

'

pr

eceding equations

are

valid for E <

O,

that

is, for rectifier as

wdL as

illv(~rter

operation.

!\ s

wa

.';

Ill

cntioned before, continuous

current

flow occurs if

the

firing angle

is

rl

~

<lllc

c

d

beyond

the

bordering

case,

a3

<

a2j

lowering

the

back voltage E

(l

I

illClTit

sing the lag

term

wT

D

would have a similar effect.

With

the

current

IlowiJlg colltinuously,

Eq

.

(8

.

5)

is valid

during

the

full

half

period following

I.IlI' lirillg of

th

e

thyristors

1,

1',

a3

:S

T

:S

a3

+

'lrj

in

steady

state

the

periodic

J,olllldary nmrlition is

'

in

(

It

:,) =

iJ)(ü

a

-+-

'Ir)

> O ;

(8

.

15)

lu

'

[IC

('

\.1[('

S

ollll.ipll

IIl;ty

1)('

writl:clI as

8,2

Line-commut~ted

Converter

in

Single-phase Bridge

Connection

113

iD(T) =

_UA_

1

R

D

-,,;c

1

=+==;(=w=;;:T

:===;)""'2

D

[sin(T -

arctanwTD)

-

e-(T-

0

3) /

wTD

sin(a3 ;- arctanwTD)]

-!

[1-

e-(T-

0

3) /

wTD]

+ i

D

(a3)

e-(T

-

0

3) /

wTD,

(8.16)

where

the

initial

value

iD(a

3) in

steady-state

is

obtained

with

the

help

of

Eq.

(8.15).

li

the

mean

value of

the

current

is mainly

of

interest

as is

the

case

with

drives, a much simpler solution exists for continuous

current

in

steady-state

.

By

integrating

Eq

. (8.5) over a

half

period

and

inserting

the

condition

(8.15)

for periodicity, we find

-

iD(a3)

1

=

:;

0 3 +

7r

J 1

RD

(UA

sin T -

1

E)

dT

= R

D

(uD(a3) -

E)

,

(8.17)

0 3

where

the

average voltage

UD

is given by Eq.

(8

.

3)

. Hence

the

converter

acts

as a linear

controllable

voltage source only if

the

current

in

the

load

branch

is continuous.

The

mean

current

i

D

(a2),

at

which discontinuous

operation

sets in, Eq.

(8.13), is

an

important

design

parameter

for

the

possible selection

of

a

smoothing

choke, resulting in

an

adequate

value

of

the

normalised

time

con-

stant

wT

D

.

As is shown in Fig. 8.16

this

current

also depends on

the

back

volt age E,

its

peak

occurs

around

E

~

O,

where

the

AC

component

contained

in

UD(T)

assumes a

maximum.

With

large drives

the

specification

may

call for

the

maximum

discontinuous

current

to

be

less

than

10%

of

nominal

current,

i

D

(a2) < O.

lIDr,

to

limit

the

ripple

current

which produces

additionallosses

in

the

armature

and

may

impair

commutation.

However,

with

medium

and

smaller drives

the

smoothing

choke is frequently

omitted

for reasons

of

cost,

so

that

only

the

armature

inductance

is left for filtering

the

current.

This

may

result

in

discontinuous

current

of

half

nominal value, affecting

not

only

the

los ses

but

also

the

design of

the

current

controller, as will be explained

in

Sect. 8.5.

Another

important

effect neglected so far is

the

finite

commutation

in-

terval

caused by

the

impedance

in

the

AC circuit, which consists

mainly

of

the

leakage

inductance

and

winding resistance of

the

transformerj also, line

inductances

may

have been

inserted

for protective reasons

to

limit

the

rate

of change

of

currents

(including fault currents)

through

the

thyristors. At

medium

and

larger

power

rating,

the

line

impedance

is

predominantly

induc-

tive,

R;1

::<::

O.lwL;\, which for

approximate

calculations justifies neglecting

the

f('sisl.iv(~

cOlllponnnt,

Tlt(, li

uI'

:-l

ide illdllcLallce L;\, even thollgh

it,

is small whcn compa

red

with

UI('

i

llllllri..'I.JlIT

I ,,)

'ill

UI('

1011,<1

circllil., cn

Il

SI'

J»

\.IIC

liJlI

~

('.IIIT(

~

1l1.

to !>(!

('.

O

lll

l:

a

11'1

8.

Static

Converter

as a Power

Actuator

for

DC

Drives

sLat.e

variable

subject

to

continuous

change onlYi

hence

iA(T)

and

the

cur-

)"('Ilt.S

in

the

thyristor

branches

can

no

longer

exhibit

the

discontinuities seen

iii

Fig. 8.6.

Instead,

the

rise

and

decay

of

the

thyristor

currents

and,

cor-

f"(~spondingly,

the

reversal

of

the

alternating

current

iA(T) now

assume

the

f"mlll

of

continuous

commutating

transients

requiring

a finite

time,

called

the

coJJlmutation

interval

Tc

or overlapi

naturally,

this

effect occurs

only

with

nllltinuous

load

current

because

in

discontinuous

current

mo

de

the

currents

h"gill in

each

period

with

zero

initial

condition.

For

example

it

may

be

assumed

that

the

thyristors

2, 2'

of

the

circuit

iII

F'ig.

8.15 a

are

initially

conducting

and

that

at

T =

0:,

Le.

with

positive

lill(,

voltage

UA,

the

thyristors

1,

l'

are

fired. Since

the

currents

iD

and

iA

;\.IC

c()lltinuous

on

account

of

L

D

and

LA,

the

thyristors

2, 2'

remain

also

mlld

IlcLing

at

first, so

that

the

four

thyristors

represent

temporarily

a

short

circllit

connection,

UD

=

UB

=

O,

decoupling

the

line

current

from

the

load

circllit.

Hence, from Kirchhoffs laws,

it

follows

with

wt =

T,

(8.18)

'iTi +iT2 =

iD

,

'Í'Fl

-

'i

T2

=iA ,

(8.19)

diA

R'

(8.20)

LU

LA b + A tA =

UA

,

.

diD

. E

(8.21)

w

Lo

- - + RD

ZD

= - .

.

dT

TIl\" illiCial conditions

are

io'/'I (o) cc. O,

10'/,::(11')

- - iA

(o:)

= iD(O:) .

It

..

,

01"':('

of"

Lhe

llIuch

smaller

inductance

LA,

the

line

current

changes

rapidly

wlll'f"(':ls

Llw load

current

may

be

assumed

to

be

approximately

constant

dur-

1111',

III('

shorL

commutation

interval, iD(T)

~

iD(O:). Hence,

with

the

abbre-

"I:d.ioJl '/';1

-,

L

A

/ RA we find for

o:

~

T

~

o:

+

Tc

iA(T)

~

iA sin(T -

arctanwTA)

-[iD(O:)

+iA sin(o: - arctanwTA)]

e-(T-a)/wT

A

(8.22)

wll(')"(:

UA

'tA

=

~

+

(wLAF

i;;

i\w

p(:ak valuc of

the

(steady

state)

short

circuit

current

at

the

line

termi-

lIalH.

1"1"0111

r'~qs.

(8.18), (8.19)

the

thyristor

currents

are

obtained,

I .

;',/"1 ( r) :

':1

')

f'in(n) 1

';'A(T)I

,

;

'

l

'~

( I')

~

l

i

r.((I

'

)

il

l( r

}l·

8.2

Line-commutated

Converter

in Single-phase Bridge

Connection

115

t1U

o

wt

=r

Lo

Ro

i I I I i ' I

T2111

TI

'I

'--~r

1'---

I

!e

/>,

O

ai

1\

--~,

II

wt=r

1 \ I I

c

I I

i I I I

DI

I I

I

---,-,,-

....

wt

=r

d

Fig.

8.15.

Commutation

of

a single

phase

converter

These

results

apply

only as long as

the

four

thyristors

are

conducting.

The

commutation

terminates

at

time

o:

+

Tc,

when

iT2(0: +

Tc)

= O

(8.23)

after

this

instant,

Eq. (8.5) is

again

valido

The

various volt ages

and

currents,

when

including

the

line

impedance,

are

seen

in

Fig.

8.15 a,b,

assuming

continuous

current

iDo

All

the

currents

are

now

continuous

functions

oftimei

in

contrast,

the

volt ages

UD(T)

and

UB(T)

exhibit

characteristic

discontinuities

during

commutation,

when

all

thyristors

are

conducting.

As a consequence

of

the

finite

commutation

interval,

the

line

current

ex-

periences

a

further

shift

in

time

resulting

in

an

additional

component

of

reactive

power

due

to

commutation,

increasing

the

reactive

power

caused

by

the

delayed

firing

control

as discussed before, Fig. 8.7

Another

effect

of

the

line

impedance

is a loss in

output

voltage

due

to

the

temporary

short

circuit,

1tO(T)

= 0,

a

~

T

~

o:

+

Tc

i

(8.24)

iI.

c;m;;(';;

ii

drop

01"

i.Il(~

JIlcan voltage

by

a

\

/1

ue I I

I I

I "

I

I,

a+r

c

U

o

I I

II(i

8. Static Converter

as

a Power Actuator

for

DC Drives

TC

_ 1

"J+

L1uD

~

1r

UA

dr

,

(8.25)

"

Wllich

may

be

estimated

from

the

current

change in

the

AC circuito

With

the

~;illl[llification

mentioned

before,

RA

«WLA,

\VI'

lilld

from Eq. (8.20)

TC

-

--

1

"J+

1

I"+TC

.d"lll)

~

-

UA

dr

~

-wLAiA(r)

1r

1r "

"

1

=

-WLA

[iA

(a +

rc)

-

iA(a)].

(8.26)

1r

1

kllce

the

voltage-time-area lost

during

commutation

is

the

flux

('liallgc in

the

line

inductance.

U

o

U

oo

n

discontinuous current

"2

a=

0°

continuous current

60°

0,5

1\\

':

' 900

":n

120°

r-

i

/ 150°

a

"'it~.

8.10.

Clmractcristics of single phase converter with inductive load

Ir

(I. f

;IIIIÍcÍI')lI,ly

1i~1'I',('

slIIooLhillP;

illdllct.:I.Il(,p

Ln

is employed, s\lell tllnt,

tltc

,I

ppll

' ('

llt

n'

I.

II.

'(

'I,"

I

.nilwcI

ill

i,,(

I)

lIItty IH'

IU'I',I<'d,'d,

i ,

1(n

,·1 r,,)

~

'I:,,((\')

:=::!

I

(/

;

I'

~

q

(H

.

~

~n

)

11,1'

11

.

I'

/I'ld

,I. !1

VI

,II.

ii

I'," <1m!,

pr"lll,d

.l

."ml

ln

!.II('

)1I

,

~d

('

111"1"1'111.

8.2

Line-conunutated Converter in Single-phase Bridge Connection

117

--

2 -

L1uD

~

-WLA

iD,

(8.27)

1r

which

indicates

that

the

line-commutated

converter

acts

like a controlled

volt

age

source having

an

apparent

internal

resistance

proportional

to

the

reactance

of

the

AC linej

of

course,

this

drop

of

the

terminal

volt age does

not

involve

real

power losses,

as

it

is caused by

commutation

at

the

AC side

of

the

converter. As a consequence,

the

load

curves

of

the

converter

uD(i

D

)

for

0'=

const.

are

drooping

in

the

continuous

current

region (Fig. 8.16), even

though

all

ohmic

resistances

apart

from

that

in

the

load

branch

have

been

neglected.

ln

contrast

to

the

intermittent

current

range

where

the

curves

are

strongly

nonlinear,

the

characteristics

in

the

continuous

current

region

are

linear,

exhibiting

only a slight droop.

By

normalising

Eq. (8.27)

with

the

no-Ioad volt age UDO

and

nominal

current

I

Dn

,

we

find

L1uD

~

wLAI

Dn

iD = k iD .

(8.28)

U

DO

.,fiUA

IDn

I

Dn

The

normalised

impedance

factor k is

mainly

determined

by

the

leakage

reactance

of

the

line

transformerj

a common value is k

~

0.05

to

0.10.

The

commutation

interval rc, which usually

lasts

only a few degrees, de-

pends

also

on

the

firing angle

aj

this

is seen from a rough

estimate

of

the

integral

in Eq. (8.25)

~

4.J.UD

~

1

-

"+T

c

J' . d

UA

sm

r r

~

M

v

2

U .

-

rc

A

sm

a

(8.29)

1r

"

which shows

that

for

constant

load

current

the

overlap is

minimal

at

a

~,

when

the

AC volt age has

its

peak

amplitude.

A

more

accurate

result

is

obtained

by

evaluating

the

integral, Eq. (8.25),

.,fiwLA-]

rc

~

arccos

cosa

-

UA

iD -

a.

(8.30)

[

The

knowledge

of

the

overlap is

of

particular

importance

when

the

con-

verter

operates

as

inverter, i.e.

with

large firing delay a, because

then

it

must

be

assured

that

the

commutation

is

completed

and

in

addition

the

outgoing

thyristors

have recovered

and

are

ready

to

block forward volt age when

the

line voltage changes signj otherwise

an

unintentional

refiring

may

occur. Since

the

back voltage is negative

during

inverter

operation,

E <

O,

this

would con-

nect in series two voltages (E,

UA)

having (for a

half

period)

the

sarne signj

the

result

wOllld

be

a

short

circuit condition

with

a fast

current

rise which

is only

limit<~d

by

the

smoothing

inductance.

This

malfunction

is called a

COllllJllIl.al.ioll

hilllr<~.

III )"i,,;. H.

I'1

l,ltiH

di~t1Ll'b<\l\c

e

is

(kr-;cril)(

~

d

iu more detail.

The

invert(

~

r

i

fi

1I

!IH

lIlIl<'d

I.n 1'!,I

'I'Il

Ln

illil.in,lIy

aI.

I.ltl~

r;;IJ(,

IÍr

l

111',

il.ll/

~

l<-

n,

'(;:)0",

wll<'1l

nll

118

8.

Static

Converter as a Power

Actuator

for

DC

Drives

Commutating

voltage

,

-,

\

U

a , \

" \

I

){

I W

~

i

T1

' ! I

~

( !

~

"'

mt

=

"t"

c;

lJ

mt

=

"t"

U : Back commutation

T2

I

to

2,

2'

I

·-

---'-rf------==',.l...r.oL.,----

....

mt

=

"t"

c

Fi!;.

8.17.

Commutation

failure

due

to

late

firing

of

thyristors

1,

l'

;ulditiollal firing delay

..:1a

for

the

thyristors

1,

l'

is introduced. Due

to

the

I"w

voJl.agc

7J.A

(r)

in

this

interval

the

commutation

proceeds quite slowly as

ii

.

I.al\(

·.s

I.

illl!:

to accumulate

the

necessary voltage-time-area.

The

commutat-

"11',

1,

I'iI.lISi(

·

1I1.

is cventually completed

at

a + rc, when

the

current

through

I.lty,i:;I.ors 2,

:l'

liaS

become zero.

There

is

still some negative blocking volt age

11,/,

~

,

'

()

arross

the outgoing

thyristors

but

it is small

and

the

time

until

the

v"II.

II.

I'.<

· 'Ii /I chauges sign may be

too

short

for

the

thyristors

2,

2'

to

recover

1.llI'

il I'mwarcl blocking capability.

ln

other

words,

the

time

equivalent

of

the

t·

.

~

I.illrLioll

angle,

= 7r -

(a

+rc) no longe r exceeds

the

recovery time

tr

which

i

~

,

i

IIcr<~;t.scd

by

the

low reversed bias volt age across

the

outgoing thyristors.

Tllc

collscquence could be a spontaneous refiring of thyristors

2,

2'

and

IlI\ck-cOIlIIn\ltation, leading

to

the

series connection of

UA

< O

and

E < O

I.Ilro'lf

~

h

thyristors

2,

2'

and

a subsequent steep rise of

the

current.

The

the

inverter is possible one period after

the

attempted

fil'illf

~

(Ir

thyristors

1,

1', where

the

controller

must

now assure a sufficient1y

H.d

vallC(

·d timing of

the

firing pulses

to

successfully complete

the

commutation

d,

~

spil.<:

I.hc

irtcreased current. Otherwise a circuit breaker or fuse

wo

.uld have

1.0

d,~;t.['

lhe

fault.

II.

is

n(~('lI

that.

th(

~

danger of a

commutation

failure increases with

the

IlIiq·,I1il.lld(·

(I]'

lhe

c1lL'n~lll

and

thc line-side ['('ad.ance, since

both

effeds pro-

I""lí

1.1a('

(,Olllllllltatjoll

illl.(~rv;d

r,:

.

III

ord(~r

1.0

flllly Ill.Ílise nlc.

voH

agc of

lhe

lllv,·r

l.v

r, II ::ldlitl'·1I1. I

11

1'.

II

i I.lldn

of

t.l1(~

(·xl.lll<'l.

i,,"

1

1111',1

0

,lIlUy

h(·

a.'is

lIl·(·d

hy a

il

q'

III I' I."

",,"11'1>1

")('1'. 11"w"v"I',

iII

v

il·w

"r

1.III

',

"I,l

il

.I

,,,ml

'·'''"(1I<

·xity

1111.1

LIli'

8.3

Line-commutated

Converter

in

Three-phase

Bridge

Connection

119

remaining

uncertainty

in case of a sudden voltage dip of

the

AC line voltage

(which would unexpectedly increase

the

overlap), extinction angle control

is seldom used except

with

very high power installations, such as HVDC,

where

operation

of

the

inverter

at

the

maximum

firing angle is

important

for power factor considerations

and

the

cost of

the

control system is less sig-

nificant [F21,77].

The

usual practice with drives is

to

limit

the

firing angle

to

"safe" values, for instance a < a

max

= 150

0

,

and

to

prevent excessive

currents

by a fast acting

controlloop.

8.3

Line-commutated

Converter

in

Three-

phase

Bridge

Connection

With

the

exception of

traction

drives having a single phase supply

the

single

phase circuit discussed in

the

preceding section

is

normally used only for low

power applications, such as

the

supply of field windings. Beyond a

few

kW

there

are

strong

incentives for three-phase converter circuits.

The

bridge con-

nection shown in Fig. 8.18 is

the

circuit most commonly used

with

thyristors

or

power transistors;

it

requires two more

thyristors

but

has a

number

of

important

advantages:

•

The

three-phase line is symmetrically loaded in

steady

state.

•

The

line currents have a lower harmonic contentj as a consequence

there

is less

distortion

of

the

line volt ages

than

with

a single

phase

circuito

•

The

sarne is

true

for

the

direct voltage

uD(r)

which contains ripple com-

ponents

of higher frequencies

and

lower amplitudes, thereby

permitting

a

reduction of

the

filter components

and

causing lower losses in

the

load.

•

The

dynamic performance of three-phase converters

is

superior because

thyristors

are

fired

at

shorter

intervals; hence

the

reduced delay for control

signals

permits

more

rapid

controI.

ln

contrast

to

the

single-phase bridge circuit (Fig. 8.5) where

the

thyris-

tors

had

to

be

fired in pairs,

the

commutations in

the

three-phase circuit

(Fig. 8.18)

alternate

between

the

upper

and

lower row of thyristors, so

that

in

steady

state

six regularly spaced firing

transients

occur

during

each line

period. Hence

the

three-phase bridge

is

a "six-pulse converter" , whereas

the

single phase bridge

with

two firing

instants

per

period belongs

to

the

class of

"two-pulse converter" circuits.

With

Hg-arc valves, having a much higher volt age drop

than

thyristors,

center

tap

circuits

without

series connection of valves

had

been in widespread

use;

they

were

the

natural

choice with multi-anode valves

with

a common Hg-

cathode. However, since

the

introduction

of

thyristors

as individual switching

dp'vjc<

~s

witll sllla.ll physical dimensions

and

low voltage drop these aspects

hav

e hecllllu'

oh

s

old,·

.

Werner Leonhard Control of Electrical Drives

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