Controlled Rectifiers (Line Commutated AC to DC converters)
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Transcript of Controlled Rectifiers (Line Commutated AC to DC converters)
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Power Electronics by Prof. M. Madhusudhan Rao 11
Controlled Rectifiers
(Line Commutated AC to DC converters)
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• Type of input: Fixed voltage, fixed frequency ac power supply.
• Type of output: Variable dc output voltage• Type of commutation: Natural / AC line commutation
LineC o m m uta te d
C o nve rte r
+
-
DC O utp utV0 (d c )
ACInp ut
Vo lta g e
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Different types of Line Commutated Converters
• AC to DC Converters (Phase controlled rectifiers)
• AC to AC converters (AC voltage controllers)• AC to AC converters (Cyclo converters) at low
output frequency.
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Differences Between Diode Rectifiers
& Phase Controlled Rectifiers
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• The diode rectifiers are referred to as uncontrolled rectifiers .
• The diode rectifiers give a fixed dc output voltage .
• Each diode conducts for one half cycle.• Diode conduction angle = 1800 or radians. • We can not control the dc output voltage or the
average dc load current in a diode rectifier circuit.
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Single phase half wave diode rectifier gives an
Average dc output voltage
Single phase full wave diode rectifier gives an 2Average dc output voltage
mO dc
mO dc
VV
VV
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Applications ofPhase Controlled Rectifiers
• DC motor control in steel mills, paper and textile mills employing dc motor drives.
• AC fed traction system using dc traction motor.• Electro-chemical and electro-metallurgical
processes.• Magnet power supplies.• Portable hand tool drives.
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Classification ofPhase Controlled Rectifiers
• Single Phase Controlled Rectifiers. • Three Phase Controlled Rectifiers.
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Different types of Single Phase Controlled Rectifiers.
• Half wave controlled rectifiers. • Full wave controlled rectifiers.
Using a center tapped transformer. Full wave bridge circuit.
Semi converter.Full converter.
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Different Types of Three Phase Controlled Rectifiers
• Half wave controlled rectifiers.• Full wave controlled rectifiers.
• Semi converter (half controlled bridge converter).
• Full converter (fully controlled bridge converter).
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Principle of Phase Controlled Rectifier Operation
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Single Phase Half-Wave Thyristor Converter with a Resistive Load
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Supply Voltage
Output Voltage
Output (load) Current
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Supply Voltage
Thyristor Voltage
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Equations
sin i/p ac supply voltagemax. value of i/p ac supply voltage
RMS value of i/p ac supply voltage2
output voltage across the load
s m
m
mS
O L
v V tV
VV
v v
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When the thyristor is triggered at sin ; to
Load current; to
sin sin ; to
Where max. value of load current
O L m
OO L
mO L m
mm
tv v V t t
vi i t
RV t
i i I t tRVIR
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To Derive an Expression for the Average (DC)
Output Voltage Across The Load
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2
0
1 . ; 2
sin
1 sin .2
1 sin .2
dc OO dc
O m
dc mO dc
mO dc
V V v d t
v V t for t to
V V V t d t
V V t d t
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Power Electronics by Prof. M. Madhusudhan Rao 1919
sin .2
cos2
cos cos ; cos 12
1 cos ; 22
mO dc
mO dc
mO dc
mm SO dc
VV t d t
VV t
VV
VV V V
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Power Electronics by Prof. M. Madhusudhan Rao 2020
max
max
Maximum average (dc) o/pvoltage is obtained when 0 and the maximum dc output voltage
1 cos 0 ; cos 0 12
mdmdc
mdmdc
VV V
VV V
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0
1 cos ; 22
The average dc output voltage can be varied by varying the trigger angle from 0 to a
maximum of 180 radians
We can plot the control characteristic
v by using the eq
mm SO dc
O dc
VV V V
V s
uation for O dcV
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Control Characteristic of
Single Phase Half Wave Phase Controlled Rectifier
with Resistive Load
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The average dc output voltage is given by the expression
1 cos2
We can obtain the control characteristic by plotting the expression for the dc output voltage as a function of trigger angle
mO dc
VV
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Control CharacteristicVO (dc)
Tr igger angle in degrees
0 60 120 180
Vdm
0.2 V dm
0.6Vdm
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Normalizing the dc output voltage with respect to , the Normalized output voltage
1 cos2
1 1 cos2
dm
m
dcn
mdm
dcn dcn
dm
V
VVV
VV
VV V
V
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To Derive An Expression for the
RMS Value of Output Voltage of a
Single Phase Half Wave Controlled Rectifier With Resistive Load
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22
0
12
2 2
The RMS output voltage is given by
1 .2
Output voltage sin ; for to
1 sin .2
OO RMS
O m
mO RMS
V v d t
v V t t
V V t d t
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2
12
2
12 2
12 2
1 cos 2By substituting sin , we get2
1 cos 21 .2 2
1 cos 2 .4
cos 2 .4
mO RMS
mO RMS
mO RMS
tt
tV V d t
VV t d t
VV d t t d t
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12
12
12
12
1 sin 222
sin 2 sin 21 ;sin2 02 2
1 sin 22 2
sin 222
mO RMS
mO RMS
mO RMS
mO RMS
V tV t
VV
VV
VV
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Performance Parameters Of
Phase Controlled Rectifiers
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Output dc power (avg. or dc o/ppower delivered to the load)
; . .,
Whereavg./ dc value of o/p voltage.
avg./dc value of o/p current
dc dc dcO dc O dc O dc
dcO dc
dcO dc
P V I i e P V I
V V
I I
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Output ac power
Efficiency of Rectification (Rectification Ratio)
Efficiency ; % Efficiency 100
The o/p voltage consists of two componentsThe dc component
The ac
O ac O RMS O RMS
O dc O dc
O ac O ac
O dc
P V I
P P
P P
V
/ripple component ac r rmsV V
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2 2
2 2
The total RMS value of output voltage is given by
Form Factor (FF) which is a measure of the shape of the output voltage is given by
RMS output l
O RMS O dc r rms
ac r rms O RMS O dc
O RMS
O dc
V V V
V V V V
VFF
V
oad voltage
DC load output load voltage
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22 2
2
The Ripple Factor (RF) w.r.t. o/p voltage w/f
1
1
r rms acv
dcO dc
O RMS O dc O RMSv
O dc O dc
v
V Vr RFV V
V V Vr
V V
r FF
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2 2
max min
max min
Current Ripple Factor
Where
peak to peak ac ripple output voltage
peak to peak ac ripple load current
r rms aci
dcO dc
acr rms O RMS O dc
r pp
r pp O O
r pp
r pp O O
I IrI I
I I I I
V
V V V
I
I I I
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Transformer Utilization Factor (TUF)
Where RMS supply (secondary) voltageRMS supply (secondary) current
O dc
S S
S
S
PTUF
V I
VI
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1
Where Supply voltage at the transformer secondary side i/p supply current (transformer secondary winding current) Fundamental component of the i/p supply current Peak value of the input s
S
S
S
P
vi
iI
upply current
Phase angle difference between (sine wave components) the fundamental components of i/p supply current & the input supply voltage.
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1
Displacement angle (phase angle)For an RL load
Displacement angle = Load impedance angle
tan for an RL load
Displacement Factor (DF) or Fundamental Power Factor
LR
DF Cos
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11 2 22 2 21
21 1
1
Harmonic Factor (HF) orTotal Harmonic Distortion Factor ; THD
1
WhereRMS value of input supply current.RMS value of fundamental component of the i
S S S
S S
S
S
I I IHFI I
II
/p supply current.
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1 1
Input Power Factor (PF)
cos cos
The Crest Factor (CF)
Peak input supply c
For an Ide
urrentRMS input supply current
1; 100% ; al Controlled Rectifier
0 ; 1;
S S S
S S S
S peak
S
ac r rms
V I IPFV I I
ICF
I
FF V V TUF
R
0 ; 0; 1vF r HF THD PF DPF
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Single Phase Half Wave Controlled Rectifier
With An
RL Load
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Input Supply Voltage (Vs)&
Thyristor (Output) Current Waveforms
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Output (Load) Voltage Waveform
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1
To Derive An Expression For The Output
(Load) Current, During to When Thyristor Conducts
tT
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1
1
Assuming is triggered ,we can write the equation,
sin ;
General expression for the output current,
sin
OO m
tm
O
T t
diL Ri V t tdt
Vi t A eZ
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22
1
1
2 maximum supply voltage.
=Load impedance.
tan Load impedance angle.
Load circuit time constant.
general expression for the output load current
sin
m S
R tm LO
V V
Z R L
LR
LR
Vi t A e
Z
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1
1
1
1
1
Constant is calculated from
initial condition 0 at ; t=
0 sin
sin
We get the value of constant as
sin
O
R tm L
O
RtmL
RmL
A
i t
Vi A eZ
VA eZ
A
VA eZ
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1Substituting the value of constant in the general expression for
sin sin
we obtain the final expression for the inductive load current
sin sin
O
R tm mL
O
R tm L
O
Ai
V Vi t eZ Z
Vi t eZ
;
Where t
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Extinction angle can be calculated by usingthe condition that 0
sin sin 0
sin sin
can be calculated by solving the above eqn.
O
R tm L
O
RL
i at t
Vi t eZ
e
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To Derive An Expression For
Average (DC) Load Voltage of a Single Half Wave Controlled
Rectifier withRL Load
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2
0
2
0
1 .2
1 . . .2
0 for 0 to & for to 2
1 . ;2
sin for to
L OO dc
L O O OO dc
O
L OO dc
O m
V V v d t
V V v d t v d t v d t
v t t
V V v d t
v V t t
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1 sin .2
cos2
cos cos2
cos cos2
L mO dc
mLO dc
mLO dc
mLO dc
V V V t d t
VV V t
VV V
VV V
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During the period to the instantaneous o/p voltage is negative
reduces the average or the dc outputvo
and this
when compared to a purely resist
ltageive load.
t
Effect of Load Inductance on the Output
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Average DC Load Current
cos cos
2O dc m
O dc L AvgL L
V VI IR R
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Single Phase Half Wave Controlled Rectifier
With RL Load &
Free Wheeling Diode
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V 0
i0T
R
L
V s ~+
+
FW D
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Power Electronics by Prof. M. Madhusudhan Rao 6161
0
0
0
0
vS
iG
vO
t
t
t
t
Sup ply vo ltage
Lo ad curren t
Load v o ltage
t=
2
G ate p u lses
iO
![Page 62: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/62.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 6262
The followi
The average
ng points a
output voltage
1 cos which is the same as that 2
of a purely resistive load.
For low value of inductance, the load current tends to become dis
re to be noted
cont
mdc
VV
inuous.
![Page 63: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/63.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 6363
During the period to the load current is carried by the SCR.During the period to load current is carried by the free wheeling diode.The value of depends on the value of R and L and the forwa
rd resistance
of the FWD.
![Page 64: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/64.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 6464
For Large Load Inductancethe load current does not reach zero, & we obtain continuous load current
0 t
2
t1
i0
S C R S C RF W D F W D
t3t2 t4
![Page 65: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/65.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 6565
Single Phase Half Wave Controlled Rectifier With
A General Load
![Page 66: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/66.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 6666
R
vS~+
L
E+
vO
iO
![Page 67: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/67.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 6767
1sin
For trigger angle ,the Thyristor conducts from to For trigger angle , the Thyristor conducts from to
m
EV
t
t
![Page 68: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/68.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 6868
0
0
iO
t
t
L o a d c u rr en t
E
v O
L o a d v o lt a g e
V m
I m
![Page 69: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/69.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 6969
Equations
sin Input supply voltage.
sin o/p load voltage for to .
for 0 to & for to 2 .
S m
O m
O
v V t
v V t
tv E t
t
![Page 70: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/70.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 7070
Expression for the Load CurrentWhen the thyristor is triggered at a delay angle of
, the eqn. for the circuit can b
sin +E
e written as
The general expression for the output load current can be writte
;
n
Om O
diV t i R L t
dt
s
as
int
mO
V Ei t AeZ R
![Page 71: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/71.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 7171
22
1
Where
= Load Impedance.
tan Load impedance angle.
Load circuit time constant.
The general expression for the o/p current can
be written as sinRt
m LO
V Ei t AeZ
Z R
LR
LR
R
L
![Page 72: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/72.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 7272
To find the value of the constant 'A' apply the initial conditions at , load current 0, Equating the general expression for the load current to zero at
, we get
0 sinR
mO
O
L
ti
t
V Ei AeZ R
![Page 73: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/73.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 7373
We obtain the value of constant 'A' as
Substituting the value of the constant 'A' in the expression for the load current; we get the complete expression for the output load c
si
ur
nR
m LVEA eR Z
sin
rent
in
s
asR t
m m LO
V VE Ei t eZ R R Z
![Page 74: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/74.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 7474
To Derive An
Expression For The Average Or
DC Load Voltage
![Page 75: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/75.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 7575
2
0
2
0
2
0
sin Output load voltage
1 .2
1 .
for 0 to & for to 2for
. .
to
2
1 . sin .2
O
OO dc
O O OO d
m
m
c
O dc
O
V v d t
V v d t v d t v d t
V E d t V t E d t
v V tv E t t
t
![Page 76: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/76.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 7676
2
0
1 cos2
1 0 cos cos 22
cos cos 22 2
2cos cos
2 2
mO dc
mO dc
mO dc
mO dc
V E t V t E t
V E V E
V EV
VV E
![Page 77: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/77.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 7777
2
2
0
Conduction angle of thyristor
RMS Output Voltage can be calculated by using the expres
1 .
sion
2 OO RMSV v d t
![Page 78: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/78.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 7878
Single Phase Full Wave Controlled Rectifier
Using A Center Tapped Transformer
![Page 79: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/79.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 7979
ACSupply
O
A
B
T 1
T2
R L
vO
+
![Page 80: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/80.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 8080
Discontinuous Load Current Operation
without FWDfor
![Page 81: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/81.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 8181
vOV m
0
( ) ( )
iO
t
t0
![Page 82: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/82.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 8282
1
To Derive An Expression For The Output
(Load) Current, During to When Thyristor Conducts
tT
![Page 83: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/83.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 8383
1
1
Assuming is triggered ,we can write the equation,
sin ;
General expression for the output current,
sin
OO m
tm
O
T t
diL Ri V t tdt
Vi t A eZ
![Page 84: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/84.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 8484
22
1
1
2 maximum supply voltage.
=Load impedance.
tan Load impedance angle.
Load circuit time constant.
general expression for the output load current
sin
m S
R tm LO
V V
Z R L
LR
LR
Vi t A e
Z
![Page 85: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/85.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 8585
1
1
1
1
1
Constant is calculated from
initial condition 0 at ; t=
0 sin
sin
We get the value of constant as
sin
O
R tm L
O
RtmL
RmL
A
i t
Vi A eZ
VA eZ
A
VA eZ
![Page 86: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/86.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 8686
1Substituting the value of constant in the general expression for
sin sin
we obtain the final expression for the inductive load current
sin sin
O
R tm mL
O
R tm L
O
Ai
V Vi t eZ Z
Vi t eZ
;
Where t
![Page 87: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/87.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 8787
Extinction angle can be calculated by usingthe condition that 0
sin sin 0
sin sin
can be calculated by solving the above eqn.
O
R tm L
O
RL
i at t
Vi t eZ
e
![Page 88: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/88.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 8888
To Derive An Expression For The DC Output Voltage Of
A Single Phase Full Wave Controlled Rectifier With RL Load
(Without FWD)
![Page 89: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/89.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 8989
vOV m
0
( ) ( )
iO
t
t0
![Page 90: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/90.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 9090
1 .
1 sin .
cos
cos cos
dc OO dct
dc mO dc
mdcO dc
mdcO dc
V V v d t
V V V t d t
VV V t
VV V
![Page 91: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/91.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 9191
When the load inductance is negligible i.e., 0
Extinction angle radiansHence the average or dc output voltage for R load
cos cos
cos 1
1 cos ; for R load, when
mO dc
mO dc
mO dc
L
VV
VV
VV
![Page 92: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/92.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 9292
2 2
To calculate the RMS output voltage we usethe expression
1 sin .mO RMSV V t d t
![Page 93: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/93.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 9393
Discontinuous Load Current Operation with FWD
![Page 94: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/94.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 9494
vOV m
0
( ) ( )
iO
t
t0
![Page 95: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/95.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 9595
2
2
1
1
Thyristor is trigger
Thyristor is triggered at ; conducts from to
FWD conducts from to &0 during discontinuous loa
ed at ;
conducts from t
d current.
o 2
O
T t
T
T t
t
T t
tv
![Page 96: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/96.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 9696
To Derive an Expression For The
DC Output Voltage For A
Single Phase Full Wave Controlled Rectifier
With RL Load & FWD
![Page 97: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/97.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 9797
0
1 .
1 sin .
cos
cos cos ; cos 1
1 cos
dc OO dct
dc mO dc
mdcO dc
mdcO dc
mdcO dc
V V v d t
V V V t d t
VV V t
VV V
VV V
![Page 98: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/98.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 9898
• The load current is discontinuous for low values of load inductance and for large values of trigger angles.
• For large values of load inductance the load current flows continuously without falling to zero.
• Generally the load current is continuous for large load inductance and for low trigger angles.
![Page 99: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/99.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 9999
Continuous Load Current Operation
(Without FWD)
![Page 100: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/100.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 100100
vOV m
0
( )
iO
t
t0
( )
![Page 101: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/101.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 101101
To Derive An Expression For
Average / DC Output VoltageOf
Single Phase Full Wave Controlled Rectifier For Continuous Current
Operation without FWD
![Page 102: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/102.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 102102
vOV m
0
( )
iO
t
t0
( )
![Page 103: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/103.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 103103
1 .
1 sin .
cos
dc OO dct
dc mO dc
mdcO dc
V V v d t
V V V t d t
VV V t
![Page 104: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/104.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 104104
cos cos ;
cos cos
cos cos
2cos
dcO dc
m
mdcO dc
mdcO dc
V V
V
VV V
VV V
![Page 105: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/105.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 105105
• By plotting VO(dc) versus ,
we obtain the control characteristic of a single phase full wave controlled rectifier with RL load for continuous load current operation without FWD
![Page 106: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/106.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 106106
cosdc dmV V
![Page 107: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/107.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 107107
VO(dc)
Trigger angle in degrees
0 30 60 90
Vdm
0.2 Vdm
0.6Vdm
-0.6 Vdm
-0.2Vdm
-Vdm
120 150 180
cosdc dmV V
![Page 108: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/108.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 108108
00
By varying the trigger angle we can vary the output dc voltage across the load. Hence we can control the dc output power flow to the load.
For trigger a . ., ngle , 0 to 90
cos is positive
0 90 ;
i e
and hence is positive
Converter
& are positive ; is positive
Controlled Rectif operates as a Power flow is from the
ie ac source to the d.
r.loa
dc dc dc dc d
d
c
cV
V I P V I
![Page 109: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/109.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 109109
0
0
0
0. ., 90 180 ,
is negative; is positive
For trigger angle , 90
; is negative.
Line
to 180
cos is negative and hence
In this case the conve Co
rtemmutated In
r operates s vea a
dc dc
dc dc dc
i e
V I
P V I
Power flows from the load ckt. to the i/p ac source.The inductive load energy is fed back to thei/p sou
rter.
rce.
![Page 110: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/110.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 110110
Drawbacks Of Full Wave Controlled Rectifier With Centre Tapped Transformer
• We require a centre tapped transformer which is quite heavier and bulky.
• Cost of the transformer is higher for the required dc output voltage & output power.
• Hence full wave bridge converters are preferred.
![Page 111: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/111.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 111111
Single Phase Full Wave Bridge Controlled Rectifier2 types of FW Bridge Controlled Rectifiers are
Half Controlled Bridge Converter (Semi-Converter)
Fully Controlled Bridge Converter (Full Converter)
The bridge full wave controlled rectifier does not require a centre tapped transformer
![Page 112: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/112.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 112112
Single Phase Full Wave Half Controlled Bridge
Converter (Single Phase Semi Converter)
![Page 113: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/113.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 113113
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Power Electronics by Prof. M. Madhusudhan Rao 114114
Trigger Pattern of Thyristors
1
2
01 2
, 2 ,...
, 3 ,...
& 180
Thyristor T is triggered att at t
Thyristor T is triggered att at t
The time delay between the gating
signals of T T radians or
![Page 115: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/115.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 115115
Waveforms of single phase semi-converter
with general load & FWDfor > 900
![Page 116: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/116.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 116116
Single Quadrant Operation
![Page 117: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/117.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 117117
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Power Electronics by Prof. M. Madhusudhan Rao 118118
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Power Electronics by Prof. M. Madhusudhan Rao 119119
1 1
2 2
Thyristor & conduct from
Thyristor & conduct from 2
FWD conducts during 0 to , ,...
T Dt to
T Dt to
t to
![Page 120: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/120.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 120120
Load Voltage & Load Current Waveform of Single Phase Semi
Converter for < 900
& Continuous load current operation
![Page 121: Controlled Rectifiers (Line Commutated AC to DC converters)](https://reader036.fdocuments.us/reader036/viewer/2022081502/56815cc9550346895dcad409/html5/thumbnails/121.jpg)
Power Electronics by Prof. M. Madhusudhan Rao 121121
vOV m
0
iO
t
( )
t0
( )
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Power Electronics by Prof. M. Madhusudhan Rao 122122
To Derive an Expression For The
DC Output Voltage of A
Single Phase Semi-Converter With R,L, & E Load & FWD
For Continuous, Ripple Free Load Current Operation
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0
1 .
1 sin .
cos
cos cos ; cos 1
1 cos
dc OO dct
dc mO dc
mdcO dc
mdcO dc
mdcO dc
V V v d t
V V V t d t
VV V t
VV V
VV V
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max
can be varied from a max. 2value of 0 by varying from 0 to .
For 0, The max. dc o/p voltage obtained is
Normalized dc o/p voltage is
2
11 cos
2
dc
m
m
dc
mdn
mdmdc
dcn n
VV to
VV
V V
VVV
V
V
1 cos2
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RMS O/P Voltage VO(RMS)
12
2 2
12 2
12
2 sin .2
1 cos 2 .2
1 sin 222
mO RMS
mO RMS
mO RMS
V V t d t
VV t d t
VV
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Single Phase Full Wave Full Converter
(Fully Controlled Bridge Converter)
With R,L, & E Load
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Waveforms of Single Phase Full Converter
Assuming Continuous (Constant Load Current)
& Ripple Free Load Current
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i OC o n s ta n t L o a d C u rr e n t i = IO a
ii
T 1
T 2&
I a
t
t
tI ai
iT 3
T 4&
I a
I a
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To Derive An Expression For
The Average DC Output Voltage of a Single Phase Full Converter
assuming Continuous & Constant Load Current
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2
0
The average dc output voltage can be determined by using the expression
1 . ;2
The o/p voltage waveform consists of two o/p pulses during the input supply time period of 0 to 2 r
dc OO dcV V v d t
adians. Hence the Average or dc o/p voltage can be calculated as
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2 sin .2
2 cos22 cos
dc mO dc
mdcO dc
mdcO dc
V V V t d t
VV V t
VV V
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0
max
max
Maximum average dc output voltage is
calculated for a trigger angle 0and is obtained as
2 2cos 0
2
m mdmdc
mdmdc
V VV V
VV V
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max
The normalized average output voltage is given by
2 coscos2
O dc dcdcn n
dmdc
m
dcn nm
V VV VV V
V
V V V
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By plotting VO(dc) versus ,
we obtain the control characteristic of a single phase full wave fully controlled bridge converter
(single phase full converter) for constant & continuous
load current operation.
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To plot the control characteristic of a Single Phase Full Converter for constant& continuous load current operation.We use the equation for the average/ dc output voltage
2 cosmdcO dc
VV V
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VO(dc)
Trigger angle in degrees
0 30 60 90
Vdm
0.2 Vdm
0.6Vdm
-0.6 Vdm
-0.2Vdm
-Vdm
120 150 180
cosdc dmV V
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• During the period from t = to the input voltage vS and the input current iS are both positive and the power flows from the supply to the load.
• The converter is said to be operated in the rectification mode
Controlled Rectifier Operationfor 0 < < 900
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• During the period from t = to (+), the input voltage vS is negative and the input current iS is positive and the output power becomes negative and there will be reverse power flow from the load circuit to the supply.
• The converter is said to be operated in the inversion mode.
Line Commutated Inverter Operationfor 900 < < 1800
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Two Quadrant Operation of a Single Phase Full Converter
0< < 900
Controlled Rectifier Operation
900< <1800
Line CommutatedInverter Operation
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To Derive An Expression For The RMS Value Of The Output Voltage
2
2
0
The rms value of the output voltage is calculated as
1 .2 OO RMSV v d t
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The single phase full converter gives two output voltage pulses during the input supply time period and hence the single phase full converter is referred to as a two pulse converter. The rms output vo
2
ltage can be calculated as
2 .2 OO RMSV v d t
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2 2
22
2
2
1 sin .
sin .
1 cos 2.
2
cos 2 .2
mO RMS
mO RMS
mO RMS
mO RMS
V V t d t
VV t d t
tVV d t
VV d t t d t
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2
2
2
sin 222
sin 2 sin 22 2
sin 2 2 sin 2;
2 2
sin 2 2 sin 2
mO RMS
mO RMS
mO RMS
V tV t
VV
VV
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2
2 2
sin 2 sin 22 2
02 2 2
2Hence the rms output voltage is same as the rms input supply voltage
mO RMS
m m mO RMS
mSO RMS
VV
V V VV
VV V
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Thyristor Current Waveforms
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i OC o n s ta n t L o a d C u rr e n t i = IO a
ii
T 1
T 2&
I a
t
t
tI ai
iT 3
T 4&
I a
I a
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The rms thyristor current can be calculated as
2The average thyristor current can be calculated as
2
O RMST RMS
O dcT Avg
II
II
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Single Phase Dual Converter
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1 1
2 2
The average dc output voltage of converter 1 is2 cos
The average dc output voltage of converter 2 is2 cos
mdc
mdc
VV
VV
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0
0
1
In the dual converter operation one converter is operated as a controlled rectifier
with 90 & the second converter is operated as a line commutated inverter
in the inversion mode with 90
dcV V
2dc
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1 2 2
1 2
2 1 1
2 1
1 2
2 1
2 2 2cos cos cos
cos cos or
cos cos cos
or
radians
Which gives
m m mV V V
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To Obtain an Expression for the
Instantaneous Circulating Current
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• vO1 = Instantaneous o/p voltage of converter 1.
• vO2 = Instantaneous o/p voltage of converter 2.
• The circulating current ir can be determined by integrating the instantaneous voltage difference (which is the voltage drop across the circulating current reactor Lr), starting from t = (2 - 1).
• As the two average output voltages during the interval t = (+1) to (2 - 1) are equal and opposite their contribution to the instantaneous circulating current ir is zero.
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1
1
1 22
2
1 2
1 22
1 1
1 . ;
As the o/p voltage is negative
1 . ;
sin for 2 to
t
r r r O Or
O
r O O
t
r O Or
O m
i v d t v v vL
vv v v
i v v d tL
v V t t
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1 12 2
1
sin . sin .
2 cos cos
The instantaneous value of the circulating current depends on the delay angle.
t tm
rr
mr
r
Vi t d t t d tL
Vi tL
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1For trigger angle (delay angle) 0,the magnitude of circulating current becomes min. when , 0,2, 4,.... & magnitude becomes max. when , 1,3,5,....If the peak load current is , one of p
t n nt n n
I
the
converters that controls the power flow may carry a peak current of
4 ,mp
r
VIL
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max
max
where
,
& 4 max. circulating current
mp L
L
mr
r
VI IR
ViL
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The Dual Converter Can Be Operated In Two Different Modes Of Operation
• Non-circulating current (circulating current free) mode of operation.
• Circulating current mode of operation.
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Non-Circulating Current Mode of Operation
• In this mode only one converter is operated at a time.
• When converter 1 is ON, 0 < 1 < 900
• Vdc is positive and Idc is positive.
• When converter 2 is ON, 0 < 2 < 900
• Vdc is negative and Idc is negative.
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Circulating Current Mode Of Operation
• In this mode, both the converters are switched ON and operated at the same time.
• The trigger angles 1 and 2 are adjusted such that (1 + 2) = 1800 ; 2 = (1800 - 1).
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• When 0 <1 <900, converter 1 operates as a controlled rectifier and converter 2 operates as an inverter with 900 <2<1800.
• In this case Vdc and Idc, both are positive.• When 900 <1 <1800, converter 1 operates as
an Inverter and converter 2 operated as a controlled rectifier by adjusting its trigger angle 2 such that 0 <2<900.
• In this case Vdc and Idc, both are negative.
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Four Quadrant OperationConv. 2 Inverting2 > 900
Conv. 2 Rectifying2 < 900
Conv. 1 Rectifying1 < 900
Conv. 1 Inverting1 > 900
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Advantages of Circulating Current Mode Of Operation
• The circulating current maintains continuous conduction of both the converters over the complete control range, independent of the load.
• One converter always operates as a rectifier and the other converter operates as an inverter, the power flow in either direction at any time is possible.
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• As both the converters are in continuous conduction we obtain faster dynamic response. i.e., the time response for changing from one quadrant operation to another is faster.
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Disadvantages of Circulating Current Mode Of Operation
• There is always a circulating current flowing between the converters.
• When the load current falls to zero, there will be a circulating current flowing between the converters so we need to connect circulating current reactors in order to limit the peak circulating current to safe level.
• The converter thyristors should be rated to carry a peak current much greater than the peak load current.