phase controlled-rectifiers (ac-dc coverters)
TRANSCRIPT
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1Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
UNIT-III
Phase Controlled Rectifiers
(Line Commutated AC to DC converters)
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2Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
• 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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3Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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4Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Differences Between Diode Rectifiers
& Phase Controlled Rectifiers
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5Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
• 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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6Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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7Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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8Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Classification ofPhase Controlled Rectifiers
• Single Phase Controlled Rectifiers. • Three Phase Controlled Rectifiers.
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9Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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10Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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11Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Principle of Phase Controlled Rectifier Operation
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12Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Single Phase Half-Wave Thyristor Converter with a Resistive Load
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13Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Supply Voltage
Output Voltage
Output (load)
Current
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14Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Supply Voltage
Thyristor Voltage
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15Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Equations
sin i/p ac supply voltage
max. 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 t
V
VV
v v
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16Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
When the thyristor is triggered at
sin ; to
Load current; to
sinsin ; to
Where max. value of load current
O L m
OO L
mO L m
mm
t
v v V t t
vi i t
RV t
i i I t tRV
IR
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17Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
To Derive an Expression for the Average (DC)
Output Voltage Across The Load
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18Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
2
0
1. ;
2
sin
1sin .
2
1sin .
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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19
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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20Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
max
max
Maximum average (dc) o/p
voltage is obtained when 0
and the maximum dc output voltage
1 cos0 ; cos 0 12
mdmdc
mdmdc
VV V
VV V
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21Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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22Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Control Characteristic of
Single Phase Half Wave Phase Controlled Rectifier
with Resistive Load
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23Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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24Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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25Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Control CharacteristicVO (dc)
Tr igger angle in degrees
0 60 120 180
Vdm
0.2 V dm
0.6Vdm
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26Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Normalizing the dc output
voltage with respect to , the
Normalized output voltage
1 cos2
11 cos
2
dm
m
dcn
mdm
dcn dcn
dm
V
VV
VVV
VV V
V
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27Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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28Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
22
0
1
22 2
The RMS output voltage is given by
1.
2
Output voltage sin ; for to
1sin .
2
OO RMS
O m
mO RMS
V v d t
v V t t
V V t d t
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29Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
2
1
22
12 2
12 2
1 cos 2By substituting sin , we get
2
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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30
1
2
1
2
1
2
1
2
1 sin 222
sin 2 sin 21;sin2 0
2 2
1 sin 2
2 2
sin 2
22
mO RMS
mO RMS
mO RMS
mO RMS
V tV t
VV
VV
VV
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31Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Performance Parameters Of
Phase Controlled Rectifiers
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32Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Output dc power (avg. or dc o/p
power delivered to the load)
; . .,
Where
avg./ 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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33Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Output ac power
Efficiency of Rectification (Rectification Ratio)
Efficiency ; % Efficiency 100
The o/p voltage consists of two components
The 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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34Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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35Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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 RMS
v
O dc O dc
v
V Vr RF
V V
V V Vr
V V
r FF
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36Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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 Ir
I I
I I I I
V
V V V
I
I I I
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37Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Transformer Utilization Factor (TUF)
Where
RMS supply (secondary) voltage
RMS supply (secondary) current
O dc
S S
S
S
PTUF
V I
V
I
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38Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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39Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
v
i
i
I
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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40Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
L
R
DF Cos
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41Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
112 22 2 2
121 1
1
Harmonic Factor (HF) or
Total Harmonic Distortion Factor ; THD
1
Where
RMS value of input supply current.
RMS value of fundamental component of
the i
S S S
S S
S
S
I I IHF
I I
I
I
/p supply current.
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42Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
1 1
Input Power Factor (PF)
cos cos
The Crest Factor (CF)
Peak input supply c
For an Ide
urrent
RMS input supply current
1; 100% ;
al Controlled Rectifier
0 ; 1;
S S S
S S S
S peak
S
ac r rms
V I IPF
V I I
ICF
I
FF V V TUF
R
0 ; 0; 1vF r HF THD PF DPF
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43Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Single Phase Half Wave Controlled Rectifier
With An
RL Load
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44Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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45Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Input Supply Voltage (Vs)&
Thyristor (Output) Current Waveforms
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46Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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47Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Output (Load) Voltage Waveform
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48Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
1
To Derive An Expression For
The Output
(Load) Current, During to
When Thyristor Conducts
t
T
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49Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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 t
dt
Vi t A e
Z
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50Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
Rt
m LO
V V
Z R L
L
R
L
R
Vi t A e
Z
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51Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
Rt
m LO
Rt
mL
RmL
A
i t
Vi A e
Z
VA e
ZA
VA e
Z
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52Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
Rt
m mLO
Rt
m LO
A
i
V Vi t e
Z Z
Vi t e
Z
;
Where t
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53Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Extinction angle can be calculated by using
the condition that 0
sin sin 0
sin sin
can be calculated by solving the above eqn.
O
Rt
m LO
R
L
i at t
Vi t e
Z
e
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54Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
To Derive An Expression For
Average (DC) Load Voltage of a Single Half Wave Controlled
Rectifier withRL Load
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55Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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56Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
1sin .
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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57Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
During the period to the
instantaneous o/p voltage is negative
reduces the average or the dc output
vo
and
this
when compared to a purely
resist
ltage
ive load.
t
Effect of Load Inductance on the Output
![Page 58: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/58.jpg)
58Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Average DC Load Current
cos cos
2O dc m
O dc L AvgL L
V VI I
R R
![Page 59: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/59.jpg)
59Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Single Phase Half Wave Controlled Rectifier
With RL Load &
Free Wheeling Diode
![Page 60: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/60.jpg)
60Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
V 0
i0T
R
L
V s ~+
+
FW D
![Page 61: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/61.jpg)
61Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
0
0
0
0
vS
iG
vO
t
t
t
t
Supp ly vo ltage
Load curren t
Load vo ltage
t=
2
G ate pu lses
iO
![Page 62: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/62.jpg)
62Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/63.jpg)
63Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/64.jpg)
64Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/65.jpg)
65Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Single Phase Half Wave Controlled Rectifier With
A General Load
![Page 66: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/66.jpg)
66Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
R
vS~+
L
E+
vO
iO
![Page 67: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/67.jpg)
67Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
1sin
For trigger angle ,
the Thyristor conducts from to
For trigger angle ,
the Thyristor conducts from to
m
E
V
t
t
![Page 68: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/68.jpg)
68Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/69.jpg)
69Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
t
v E t
t
![Page 70: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/70.jpg)
70Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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 Ae
Z R
![Page 71: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/71.jpg)
71Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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 sinR
tm L
O
V Ei t Ae
Z
Z R
L
R
L
R
R
L
![Page 72: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/72.jpg)
72Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
t
i
t
V Ei Ae
Z R
![Page 73: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/73.jpg)
73Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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 LVE
A eR Z
sin
rent
in
s
asR
tm m L
O
V VE Ei t e
Z R R Z
![Page 74: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/74.jpg)
74Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
To Derive An
Expression For The Average Or
DC Load Voltage
![Page 75: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/75.jpg)
75
2
0
2
0
2
0
sin Output load voltage
1.
2
1.
for 0 to & for to 2
for
. .
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 t
v E t t
t
![Page 76: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/76.jpg)
76Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
2
0
1cos
2
10 cos cos 2
2
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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/77.jpg)
77Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/78.jpg)
78Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Single Phase Full Wave Controlled Rectifier
Using A Center Tapped Transformer
![Page 79: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/79.jpg)
79Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
ACSupply
O
A
B
T 1
T2
R L
vO
+
![Page 80: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/80.jpg)
80Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Discontinuous Load Current Operation
without FWDfor
![Page 81: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/81.jpg)
81Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
vOV m
0
( ) ( )
iO
t
t0
![Page 82: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/82.jpg)
82Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
1
To Derive An Expression For
The Output
(Load) Current, During to
When Thyristor Conducts
t
T
![Page 83: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/83.jpg)
83Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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 t
dt
Vi t A e
Z
![Page 84: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/84.jpg)
84
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
Rt
m LO
V V
Z R L
L
R
L
R
Vi t A e
Z
![Page 85: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/85.jpg)
85Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
Rt
m LO
Rt
mL
RmL
A
i t
Vi A e
Z
VA e
ZA
VA e
Z
![Page 86: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/86.jpg)
86Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
Rt
m mLO
Rt
m LO
A
i
V Vi t e
Z Z
Vi t e
Z
;
Where t
![Page 87: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/87.jpg)
87Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Extinction angle can be calculated by using
the condition that 0
sin sin 0
sin sin
can be calculated by solving the above eqn.
O
Rt
m LO
R
L
i at t
Vi t e
Z
e
![Page 88: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/88.jpg)
88Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
To Derive An Expression For The DC Output Voltage Of
A Single Phase Full Wave Controlled Rectifier With RL Load
(Without FWD)
![Page 89: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/89.jpg)
89Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
vOV m
0
( ) ( )
iO
t
t0
![Page 90: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/90.jpg)
90Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
1.
1sin .
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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/91.jpg)
91Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
When the load inductance is negligible i.e., 0
Extinction angle radians
Hence 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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/92.jpg)
92Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
2 2
To calculate the RMS output voltage we use
the expression
1sin .mO RMSV V t d t
![Page 93: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/93.jpg)
93Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Discontinuous Load Current Operation with FWD
![Page 94: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/94.jpg)
94
vOV m
0
( ) ( )
iO
t
t0
![Page 95: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/95.jpg)
95Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
t
v
![Page 96: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/96.jpg)
96Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
To Derive an Expression For The
DC Output Voltage For A
Single Phase Full Wave Controlled Rectifier
With RL Load & FWD
![Page 97: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/97.jpg)
97
0
1.
1sin .
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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/98.jpg)
98Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
• 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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/99.jpg)
99Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Continuous Load Current Operation
(Without FWD)
![Page 100: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/100.jpg)
100Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
vOV m
0
( )
iO
t
t0
( )
![Page 101: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/101.jpg)
101Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
To Derive An Expression For
Average / DC Output VoltageOf
Single Phase Full Wave Controlled Rectifier For Continuous Current
Operation without FWD
![Page 102: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/102.jpg)
102Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
vOV m
0
( )
iO
t
t0
( )
![Page 103: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/103.jpg)
103Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
1.
1sin .
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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/104.jpg)
104Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
cos cos ;
cos cos
cos cos
2cos
dcO dc
m
mdcO dc
mdcO dc
V V
V
VV V
VV V
![Page 105: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/105.jpg)
105Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
• 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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/106.jpg)
106
cosdc dmV V
![Page 107: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/107.jpg)
107Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
VO(dc)
Trigger angle in degrees
030 60 90
Vdm
0.2 Vdm
0.6Vdm
-0.6 Vdm
-0.2Vdm
-Vdm
120 150 180
cosdc dmV V
![Page 108: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/108.jpg)
108
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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/109.jpg)
109Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
rte
mmutated 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 the
i/p sou
rter.
rce.
![Page 110: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/110.jpg)
110Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/111.jpg)
111Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/112.jpg)
112Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Single Phase Full Wave Half Controlled Bridge
Converter (Single Phase Semi Converter)
![Page 113: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/113.jpg)
113Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
![Page 114: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/114.jpg)
114Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Trigger Pattern of Thyristors
1
2
01 2
, 2 ,...
, 3 ,...
& 180
Thyristor T is triggered at
t at t
Thyristor T is triggered at
t at t
The time delay between the gating
signals of T T radians or
![Page 115: Phase Controlled-Rectifiers (AC-DC Coverters)](https://reader037.vdocuments.site/reader037/viewer/2022102713/55cf9820550346d03395be44/html5/thumbnails/115.jpg)
115Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Waveforms of single phase semi-converter
with general load & FWDfor > 900
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116Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Single Quadrant Operation
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117Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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118Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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119Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
1 1
2 2
Thyristor & conduct
from
Thyristor & conduct
from 2
FWD conducts during
0 to , ,...
T D
t to
T D
t to
t to
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120Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Load Voltage & Load Current Waveform of Single Phase Semi
Converter for < 900
& Continuous load current operation
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121Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
vOV m
0
iO
t
( )
t0
( )
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122Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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123Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
0
1.
1sin .
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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124Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
V
Vto
VV
V V
VVV
V
V
1 cos2
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125Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
RMS O/P Voltage VO(RMS)
1
22 2
12 2
1
2
2sin .
2
1 cos 2 .2
1 sin 2
22
mO RMS
mO RMS
mO RMS
V V t d t
VV t d t
VV
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126Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Single Phase Full Wave Full Converter
(Fully Controlled Bridge Converter)
With R,L, & E Load
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127Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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128Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Waveforms of Single Phase Full Converter
Assuming Continuous (Constant Load Current)
& Ripple Free Load Current
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129
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130Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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131Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
i OC o n s t a n t L o a d C u rr e n t i = IO a
ii
T 1
T 2&
I a
t
t
t
I aii
T 3
T 4&
I a
I a
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132Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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133Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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134Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
2sin .
2
2cos
22
cos
dc mO dc
mdcO dc
mdcO dc
V V V t d t
VV V t
VV V
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135Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
0
max
max
Maximum average dc output voltage is
calculated for a trigger angle 0
and is obtained as
2 2cos 0
2
m mdmdc
mdmdc
V VV V
VV V
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136Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
max
The normalized average output voltage is given by
2cos
cos2
O dc dcdcn n
dmdc
m
dcn nm
V VV V
V V
V
V VV
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137Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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138Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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
2cosm
dcO dc
VV V
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139Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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140Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
VO(dc)
Trigger angle in degrees
030 60 90
Vdm
0.2 Vdm
0.6Vdm
-0.6 Vdm
-0.2Vdm
-Vdm
120 150 180
cosdc dmV V
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141Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
• 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 Operation
for 0 < < 900
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142Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
• 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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143Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Two Quadrant Operation of a Single Phase Full Converter
0< < 900
Controlled Rectifier Operation
900< <1800
Line Commutated
Inverter Operation
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144Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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145
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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146Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
2 2
22
2
2
1sin .
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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147
2
2
2
sin 222
sin 2 sin 2
2 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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148Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
2
2 2
sin 2 sin 2
2 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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149Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Thyristor Current Waveforms
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150Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
i OC o n s t a n t L o a d C u rr e n t i = IO a
ii
T 1
T 2&
I a
t
t
t
I aii
T 3
T 4&
I a
I a
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151Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
The rms thyristor current can be
calculated as
2The average thyristor current can be
calculated as
2
O RMS
T RMS
O dc
T Avg
II
II
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152Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Single Phase Dual Converter
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153
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154Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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155Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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156Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
1 1
2 2
The average dc output voltage of converter 1 is
2cos
The average dc output voltage of converter 2 is
2cos
mdc
mdc
VV
VV
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157Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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158Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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159Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
To Obtain an Expression for the
Instantaneous Circulating Current
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160Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
• 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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161Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
1
1
1 2
2
2
1 2
1 2
2
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
v
v v v
i v v d tL
v V t t
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162Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
1 12 2
1
sin . sin .
2cos cos
The instantaneous value of the circulating current
depends on the delay angle.
t tm
rr
mr
r
Vi t d t t d t
L
Vi t
L
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163Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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 n
t n n
I
the
converters that controls the power flow
may carry a peak current of
4,m
pr
VI
L
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164Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
max
max
where
,
&
4 max. circulating current
mp L
L
mr
r
VI I
R
Vi
L
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165Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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166Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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167Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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168Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
• 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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169Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
Four Quadrant OperationConv. 2 Inverting
2 > 900
Conv. 2 Rectifying
2 < 900
Conv. 1 Rectifying
1 < 900
Conv. 1 Inverting
1 > 900
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170Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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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171Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
• 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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172Prof. M. Madhusudhan Rao, E&C Dept., MSRIT
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.