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UNIT II
PHASE CONTROLLED
CONVERTERS
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Phase-Control Converters
Phase-Control Converters
Single-Phase
Single-Phase
Semiconverter
Semiconverter
Three-Phase
Three-Phase
Full converter
Full converter
Dual converter
Dual converter
Semiconverter
Semiconverter
Full converter
Full converter
Dual converter
Dual converter
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Semiconverter
..is a one-quadrant converter and it has one polarity
Semiconverter
..is a one-quadrant converter and it has one polarity
Full converter..is a two-quadrant converter and the polarity of its
output can be either positive or negative.
Howeverthe output current of full converter has
one polarity only
Full converter..is a two-quadrant converter and the polarity of its
output can be either positive or negative.
Howeverthe output current of full converter has
one polarity only
Dual converter
..can operate in four quadrants ; both the output
voltage and current can be either positive or negative
Dual converter..can operate in four quadrants ; both the output
voltage and current can be either positive or negative
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( ) ( ) +==
cos12sin2
1 mmdc
V
ttdVV
( ) ( ) +==
cos12sin2
1 mmdc
V
ttdVV
Average Output Voltage
Average Output Voltage
mdm
VV =
mdm
VV =a!imum
Output Voltage
a!imum
Output Voltage
( )cos1"#$ +==dm
dcn
V
VV
( )cos1"#$ +==dm
dcn
V
VV%ormali&ing
Output Voltage
%ormali&ing
Output Voltage
( )
+==
22sin1
2
sin
2
1 22
mmrms
VttdVV
( )
+==
22sin1
2
sin
2
1 22
mmrms
VttdVV
'S Output Voltage
'S Output Voltage
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() the converter has a purel* resistive loa+ o) ' an+
the +ela* angle is , +etermine
a. the recti)ication e))icienc*
/. the )orm )actor FFc. the ripple )actor 'F
an+ +. the pea0 inverse voltage P(V o) th*ristor T1
() the converter has a purel* resistive loa+ o) ' an+
the +ela* angle is , +etermine
a. the recti)ication e))icienc*
/. the )orm )actor FFc. the ripple )actor 'F
an+ +. the pea0 inverse voltage P(V o) th*ristor T1
2=
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( )
( )
( )
23#2$
4"45#$
1"62#$
4"45#$2
22
sin2
1
2
1"62#$
2cos1
2sin
2
1
2
2
2
2
2
===
=
+=
=
+==
m
m
rms
dc
mm
rms
mdc
mmdc
V
V
V
V
VV
V
VV
VttdVV
( )
( )
( )23#2$
4"45#$
1"62#$
4"45#$2
22
sin2
1
2
1"62#$
2cos1
2sin
2
1
2
2
2
2
2
===
=
+=
=
+==
m
m
rms
dc
mm
rms
mdc
mmdc
V
V
V
V
VV
V
VV
VttdVV
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() the converter has a purel* resistive loa+ o) ' an+
the +ela* angle is , +eterminea. the recti)ication e))icienc*
/. the )orm )actor FF
c. the ripple )actor 'F
an+ +. the pea0 inverse voltage P(V o) th*ristor T1
() the converter has a purel* resistive loa+ o) ' an+
the +ela* angle is , +etermine
a. the recti)ication e))icienc*
/. the )orm )actor FF
c. the ripple )actor 'F
an+ +. the pea0 inverse voltage P(V o) th*ristor T1
2
=
221#21"62#$4"45#$ ===
m
m
dc
rms
VV
VVFF 221#2
1"62#$4"45#$ ===
m
m
dc
rms
VV
VVFF
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() the converter has a purel* resistive loa+ o) ' an+
the +ela* angle is , +eterminea. the recti)ication e))icienc*
/. the )orm )actor FF
c. the ripple )actor 'F
an+ +. the pea0 inverse voltage P(V o) th*ristor T1
() the converter has a purel* resistive loa+ o) ' an+
the +ela* angle is , +etermine
a. the recti)ication e))icienc*
/. the )orm )actor FF
c. the ripple )actor 'F
an+ +. the pea0 inverse voltage P(V o) th*ristor T1
2
=
674#11221#21 22 === FFRF 674#11221#21 22 === FFRF
mVPIV= mVPIV=
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Single-Phase Semiconverter R!-load"Single-Phase Semiconverter R!-load"
( )
===
=++
!R
!
R
!!!
!!
e
R
#eItiI
#Ridt
di
!
1
$
$11
11
( )
===
=++
!R
!
R
!!!
!
!
eR
#eItiI
#Ridt
di
!
1
$
$11
1
1
( ) ( ) t!R
$!
$!
$!
!
e%
V
R
#I
R
#t
%
VI
tV#Ridt
di
!
++=
=++
sin2
sin2
sin2
12
2
2
( ) ( ) t!R
$!
$!
$!
!
e%
V
R
#I
R
#t
%
VI
tV#Ridt
di
!
++=
=++
sin2
sin2
sin2
12
2
2
o+e 1o+e 1
t$
o+e 2o+e 2 t
R
! 1tan=
R
! 1tan=( ) 22 !R% += ( )
22 !R% +=
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Single-Phase Semiconverter R!-load"Single-Phase Semiconverter R!-load"
R&$ 'urrentfor (hyristorR&$ 'urrentfor (hyristor
( )=
tdiI !R
2
221
R&$ 'urrentfor (hyristor
R&$ 'urrent
for (hyristor ( )=
tdiI!) 2
2
1
R&$ *utput
'urrent
R&$ *utput
'urrent ( ) ( ) +=
tditdiI !!rms2
2$
2
1 2
1
2
1
)V+ *utput
'urrent
)V+ *utput
'urrent
( ) ( )
+=
tditdiIdc 2$
1
2
1
2
1
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The single-phase semiconverter has an '8 loa+ o)
8 9 5#"mH, ' 9 2#" Ohm, an+ : 9 1$ V# The input
voltage is VS9 12$ Vrms. at 5$ H Determine
a. the loa+ current (8$at , an+ the loa+
current (81at ,
/. the average th*ristor current (Ac. the rms th*ristor current ('+. the rms output current (rms
an+ e. the average output current (+c
The single-phase semiconverter has an '8 loa+ o)
8 9 5#"mH, ' 9 2#" Ohm, an+ : 9 1$ V# The input
voltage is VS9 12$ Vrms. at 5$ H Determine
a. the loa+ current (8$at , an+ the loa+
current (81at ,
/. the average th*ristor current (A
c. the rms th*ristor current ('+. the rms output current (rms
an+ e. the average output current (+c
$=t== 5$t
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Single-Phase
Full Converter
Rectification
Mode
Rectification
Mode
Inversion
Mode
Inversion
Mode
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Single-Phase Full ConverterSingle-Phase Full Converter
( )
( )2
sin
2
2
cos
2
sin2
2
22 mmrms
m
mdc
VtdtVV
V
tdtVV
==
==
+
+
( )
( )
2
sin
2
2
cos
2
sin2
2
22 mmrms
m
mdc
VtdtVV
V
tdtVV
==
==
+
+
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Single-Phase Full Converter R!-load"Single-Phase Full Converter R!-load"
( ) ( ) t!R
$!
$! e
%
V
R
#I
R
#t
%
VI
++=
sin2
sin2
$( ) ( ) t!
R
$!
$! e
%
V
R
#I
R
#t
%
VI
++=
sin2
sin2
$
o+e 1 9 o+e 2o+e 1 9 o+e 2 R
!
1
tan
= R!
1
tan
= ( )22
!R% += ( )22
!R% +=
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Single-Phase Full Converter R!-load"Single-Phase Full Converter R!-load"
R&$ 'urrentfor (hyristorR&$ 'urrentfor (hyristor
( ) +=
tdiI !R
2
21
R&$ 'urrentfor (hyristor
R&$ 'urrent
for (hyristor ( ) +
=
tdiI!)
2
1
R&$ *utput
'urrent
R&$ *utput
'urrent RRRrms IIII 2
22
=+=
)V+ *utput
'urrent
)V+ *utput
'urrent
)))dc IIII 2=+=02/20/16 18
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Dual
Converter02/20/16 19
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Single-Phase Dual ConverterSingle-Phase Dual Converter
,igh-Power Variable-$peed rives,igh-Power Variable-$peed rives
21
22
11
cos2
cos2
dcdc
mdc
mdc
VV
VV
VV
=
=
=
21
22
11
cos2
cos2
dcdc
mdc
mdc
VV
VV
VV
=
=
=
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Three-Phase
Semiconverter
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3 Phase Controe! "ecti#iers
$ %perate #rom 3 phase ac s&ppy 'otage.
$ (hey pro'i!e higher !c o&tp&t 'otage.
$ )igher !c o&tp&t power.$ )igher o&tp&t 'otage rippe #re*&ency.
$ +itering re*&irements are simpi#ie! #or
smoothing o&t oa! 'otage an! oa!c&rrent.
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$ ,-tensi'ey &se! in high power 'ariabe
spee! in!&stria !c !ri'es.
$ (hree singe phase ha#wa'e con'erters
can be connecte! together to #orm a three
phase ha#wa'e con'erter.
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3Phase)a# a'e Con'erter
3P&se Con'erter
with
" oa!
Contin&o&s Constantoa! C&rrent %peration
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ector iagram o#
3 Phase &ppy otages
VA %
VC %
V; %
1 2 $
$
1 2 $
$
1 2 $$ R. ).
/. 0.
0. '.
v v
v v
v v
=
=
=
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3 Phase &ppy otage,*&ations
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( )
( )( )
$
$
$
sin =
a!# Phase Voltage
2sin
4
sin 12$2
sin4
sin 12$
sin 2>$
R. an m
m
/. bn m
m
0. cn m
m
m
v v V t
V
v v V t
V t
v v V t
V t
V t
= =
=
= =
= = = +
= +
=
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van
vbn
vcn
van
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io1Ia
Constant 8oa+
Current
Ia
Ia
:ach th*ristor con+ucts )or 24 12$$.
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(o eri'e an,-pression #or the
'erage %&tp&t otage o# a3Phase )a# a'e Con'erter
with " oa!
#or Contin&o&s oa! C&rrent
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( )
( )
( )
$1
$
2
$
4
$
4$5
" 1"$
5
3 23$
5
2:ach th*tistor con+ucts )or 12$ or ra+ians
4
( is triggered at t
( is triggered at t
( is triggered at t
= + = + = + = + = + = +
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( )
( )
"
5
5
"
5
5
4sin #
2
4
cos2
4 "cos cos2 5 5
mdc
mdc
mdc
VV t d t
V
V t
VV
+
+
+
+
=
=
= + + +
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( ) ( )
( ) ( )
( ) ( )
( ) ( ) ( ) ( )
( ) ( )
$ $
$
%ote )rom the trigonometric relationshipcos cos #cos sin #sin
" "cos cos sin sin
5 542
co
cos 1"$ cos sin 1"$ sin4
2 cos 4$
s #cos sin sin5 5
#cos
mdc
mdc
)
VV
0 ) 0 ) 0
VV
+ =
+ =
+
+
+=
( ) ( )$sin 4$ sin
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( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( )( ) ( )
( ) ( ) ( ) ( )( ) ( ) ( ) ( )
$ $
$ $ $ $
$ $
$ $
$
$
$
$
$ $
%ote? cos 1
cos 17$ 4$ cos sin 17$ 4$ sin4
2 cos 4$ #cos sin 4$ sin
cos 4$ cos sin 4$ sin42 cos 4$ #cos sin 4$ s
7$ 4$ cos 4$
sin 17$ 4$ sin 4$
in
mdc
mdc
VV
VV
=
+ = +
+ + =
+
=
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( ) ( )
( )
( ) ( )
( )
$4 2cos 4$ cos
24 4
2 cos2 2
4 4 44 cos cos
2 2
4cos
2
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( )ma!
The ma!imum average or +c output voltage is
o/taine+ at a +ela* angle $ an+ is given /*
4 4
2
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( ) ( )
( )
1" 25
2 2
5
1
2
The rms value o) output voltage is )oun+ /*
using the e@uation
4sin #
2
an+ we o/tain
1 44 cos 25 7
m* R&$
m* R&$
V V t d t
V V
+
+
=
= +
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3 Phase )a# a'eControe! "ecti#ier %&tp&t
otage a'e#orms +or "oa!
at
i##erent (rigger nges
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$
$
4 $ $
4 $ $
5 $ $
5 $ $
6 $ $
6 $ $
1 2 $ $
1 2 $ $
1 " $$
1 " $$
1 7 $ $
1 7 $ $
2 1 $ $
2 1 $ $
2 > $ $
2 > $ $
2 3 $ $
2 3 $ $
4 $ $ $
4 $ $ $
4 4 $ $
4 4 $ $
4 5 $ $
4 5 $ $
4 6 $$
4 6 $$
> 2 $ $
> 2 $ $
V a n
V
$
V
$
V a n
9 4 $ $
9 5 $ $
V / n
V / n
V c n
V c n
t
t
300
600
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$
4 $ $
5 $ $
6 $ $
1 2 $ $
1 " $ $
1 7 $ $
2 1 $ $
2 > $ $
2 3 $ $
4 $ $ $
4 4 $ $
4 5 $ $
4 6 $ $
> 2 $ $
V
$
V a n
9 6 $ $
V / n
V c n
t
900
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3 Phase )a# a'e
Controe! "ecti#ier ith
" oa!an!
" oa! with +
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a a
/ /
c c
'
V$
8
' V $
T1
T2
T4
n n
T1
T2
T4
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3 Phase )a# a'eControe! "ecti#ier %&tp&t
otage a'e#orms +or " oa!or " oa! with +
at
i##erent (rigger nges
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$
$
4 $ $
4 $ $
5 $ $
5 $ $
6 $ $
6 $ $
1 2 $ $
1 2 $ $
1 " $ $
1 " $ $
1 7 $$
1 7 $$
2 1 $ $
2 1 $ $
2 > $ $
2 > $ $
2 3 $ $
2 3 $ $
4 $ $ $
4 $ $ $
4 4 $ $
4 4 $ $
4 5 $ $
4 5 $ $
4 6 $$
4 6 $$
> 2 $ $
> 2 $ $
Vs
V$
Va n
9 $
9 1 " $
V/ n V c n
t
Va n
V / n V c n
t
00
150
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$
$
4 $ $
4 $ $
5 $ $
5 $ $
6 $ $
6 $ $
1 2 $ $
1 2 $ $
1 " $ $
1 " $ $
1 7 $ $
1 7 $ $
2 1 $ $
2 1 $ $
2 > $$
2 > $$
2 3 $$
2 3 $$
4 $ $ $
4 $ $ $
4 4 $ $
4 4 $ $
4 5 $ $
4 5 $ $
4 6 $ $
4 6 $ $
> 2 $ $
> 2 $ $
V$
9 4 $ $
Va n
V/ n V c n
t
V$
9 5 $ $
Va n
V/ n V c n
t
300
600
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(o eri'e n
,-pression +or (he 'erage %r
c %&tp&t otage %#
3 Phase )a# a'e Con'erterith "esisti'e oa!
%r" oa! ith +
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( )
( )
( )
( )( )
$
1
$ $
1
$
2
$ $
2
$
4$5
4$ 17$ =
sin
" 1"$
5
1"$ 4$$ =sin 12$
* an m
* bn m
( is triggered at t
( conducts from to
v v V t
( is triggered at t
( conducts from tov v V t
= + = +
+
= =
= + = +
+= =
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( )
( )( )
( )
$
4
$ $
4
$
$
3 23$5
23$ >2$ =
sin 2>$
sin 12$
* cn m
m
( is triggered at t
( conducts from to
v v V t
V t
= + = +
+= =
= +
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( )
( ) ( )
( )
( )
$
$
$
$
$
$
17$
4$
$ $
17$
4$
17$
4$
4#
2
sin = )or 4$ to 17$
4 sin #2
4 sin #2
dc *
* an m
dc m
mdc
V v d t
v v V t t
V V t d t
VV t d t
+
+
+
=
= = = +
=
=
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( )
( )
$
$
17$
4$
$ $
$
$
4cos
2
4cos17$ cos 4$
2
cos17$ 1, we get
4 1 cos 4$2
m
dc
m
dc
mdc
VV t
VV
VV
+
=
= + +
=
= + +
Q
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(hree Phase emicon'erters
$ 3 Phase semicon'erters are &se! in n!&stria
!c !ri'e appications &pto 120: power o&tp&t.
$ inge *&a!rant operation is possibe.$ Power #actor !ecreases as the !eay ange
increases.
$ Power #actor is better than that o# 3 phase ha#wa'e con'erter.
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3 Phase)a# Controe! ;ri!ge Con'erter
emi Con'erter
with )ighy n!&cti'e oa! Contin&o&s "ippe #ree oa!
C&rrent
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a'e #orms o# 3 Phase
emicon'erter #or< 600
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$ $
1
4 phase semiconverter output ripple )re@uenc* o)
output voltage is 4
The +ela* angle can /e varie+ )rom $ to
During the perio+
4$ 21$
3 , th*ristor T is )orwar+ /iase+5 5
$f
t
t
se! #or appications &p to 2 mega watt o&tp&t
power e'e.
$ &a con'erter consists o# two 3 phase #&
con'erters which are connecte! in parae in
opposite !irections across a common oa!.
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%&tp&ts o# Con'erters 1 2
$ &ring the inter'a /6 ? 1 to /2 ? 1=the ine to ine 'otage vabappears across
the o&tp&t o# con'erter 1 an! vbcappearsacross the o&tp&t o# con'erter 2
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( )
( )
( )
$
$
$
$
R. an m
m
/. bn m m
0. cn m m
m
v v V t
V
v v V t V t
v v V t V t
V t
= ==
= = = = = + = +
=
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( )
( )
( )
$
$
$
$
R. an m
m
/. bn m m
0. cn m m
m
v v V t
V
v v V t V t
v v V t V t
V t
= ==
= = = = = + = +
=
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(o obtain an ,-pression #or the Circ&ating
C&rrent
# vO1an! vO2are the o&tp&t 'otages o#
con'erters 1 an! 2 respecti'ey= theinstantaneo&s 'otage across the c&rrent
imiting in!&ctor !&ring the inter'a
/6 ? 1 t /2 ? 1 is gi'en by
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1 2
4 sin sin5 2
4 cos5
The circulating current can /e calculate+ /*using the e@uation
r * * ab bc
r m
r m
v v v v v
v V t t
v V t
= + =
= +
=
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( ) ( )
( ) ( )
( )
( )
1
1
5
5
1
ma!
1#
14 cos #
5
4sin sin
5
4
t
r r
r
t
r m
r
m
r
r
m
r
r
i t v d t
!
i t V t d t !
Vi t t
!
Vi!
+
+
=
=
=
=
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+o&r @&a!rant %peration
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$ (here are two !i##erent mo!es o#
operation. Circ&ating c&rrent #ree
non circ&ating mo!e o# operation
Circ&ating c&rrent mo!e o# operation
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Aon Circ&ating
C&rrent Bo!e %# %peration$ n this mo!e o# operation ony one con'erter is
switche! on at a time
$ hen the con'erter 1 is switche! on=
+or 1 900the con'erter 1 operates in the"ecti#ication mo!e
!cis positi'e= !cis positi'e an! hence the
a'erage oa! power P!cis positi'e.$ Power #ows #rom ac so&rce to theoa!
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$ hen the con'erter 1 is on=
+or 1< 900the con'erter 1operates in the n'ersion mo!e
!cis negati'e= !cis positi'e an! the
a'erage oa! power P!cis negati'e.
$ Power #ows #rom oa! circ&it to ac
so&rce.
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$ hen the con'erter 2 is switche! on=
+or 2 900the con'erter 2 operates inthe "ecti#ication mo!e
!cis negati'e= !cis negati'e an! the
a'erage oa! power P!cis positi'e.$ (he o&tp&t oa! 'otage oa! c&rrent
re'erse when con'erter 2 is on.
$ Power #ows #rom ac so&rce to the oa!
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$ hen the con'erter 2 is switche! on=
+or 2< 900the con'erter 2 operates in then'ersion mo!e
!cis positi'e= !cis negati'e an! the a'erage
oa! power P!cis negati'e.
$ Power #ows #rom oa! to the ac so&rce.
$ ,nergy is s&ppie! #rom the oa! circ&it to the ac
s&ppy.
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$ ;oth the con'erters are switche! on at the same
time.
$ %ne con'erter operates in the recti#ication mo!e
whie the other operates in the in'ersion mo!e.
$ (rigger anges 1 2are a!D&ste! s&ch that 1? 2 1800
Circ&ating C&rrent
Bo!e %# %peration
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hen 1 900= con'erter 1 operatesas a controe! recti#ier. 2 is ma!egreater than 900 an! con'erter 2
operates as an n'erter.$ !cis positi'e !cis positi'e an! P!c
is positi'e.
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$ hen 2 900= con'erter 2 operatesas a controe! recti#ier. 1 is ma!egreater than 900 an! con'erter 1
operates as an n'erter.
$ !cis negati'e !cis negati'e an!
P!cis positi'e.