Three phase-controlled-rectifiers

Power Electronics by Prof. M. Madhusudhan Rao 11
Three Phase Controlled
Rectifiers

3 Phase Controlled Rectifiers
• Operate from 3 phase ac supply voltage.
• They provide higher dc output voltage.
• Higher dc output power.
• Higher output voltage ripple frequency.
• Filtering requirements are simplified for
smoothing out load voltage and load current.

• Extensively used in high power variable speed
industrial dc drives.
• Three single phase half-wave converters can be
connected together to form a three phase half-
wave converter.

3-Phase
Half Wave Converter
(3-Pulse Converter)
with
RL Load
Continuous & Constant
Load Current Operation

Vector Diagram of
3 Phase Supply Voltages
V A N
V C N
V B N
1 2 0
0
1 2 0
0
1 2 0
0 RN AN
YN BN
BN CN
v v
v v
v v
=
=
=

3 Phase Supply Voltage Equations
We deifine three line to neutral voltages
(3 phase voltages) as follows

( )
( )
( )
0
0
0
sin ;
Max. Phase Voltage
2
sin
3
sin 120
2
sin
3
sin 120
sin 240
RN an m
m
YN bn m
m
BN cn m
m
m
v v V t
V
v v V t
V t
v v V t
V t
V t
ω
π
ω
ω
π
ω
ω
ω
= =
=
 
= = − ÷
 
= −
 
= = + ÷
 
= +
= −

van vbn vcn van

io=Ia
Constant Load
Current
Ia
Ia
Each thyristor conducts for 2π/3 (1200
)

To Derive an
Expression for the
Average Output Voltage of a
3-Phase Half Wave Converter
with RL Load
for Continuous Load Current

( )
( )
( )
0
1
0
2
0
3
0
30
6
5
150
6
7
270
6
2
Each thytistor conducts for 120 or radians
3
T is triggered at t
T is triggered at t
T is triggered at t
π
ω α α
π
ω α α
π
ω α α
π
 
= + = + ÷
 
 
= + = + ÷
 
 
= + = + ÷
 

( )
5
6
6
If the reference phase voltage is
sin , the average or dc output
voltage for continuous load current is calculated
using the equation
3
sin .
2
RN an m
dc m
v v V t
V V t d t
π
α
π
α
ω
ω ω
π
+
+
= =
 
 
=  
  
∫

( )
( )
5
6
6
5
6
6
3
sin .
2
3
cos
2
3 5
cos cos
2 6 6
m
dc
m
dc
m
dc
V
V t d t
V
V t
V
V
π
α
π
α
π
α
π
α
ω ω
π
ω
π
π π
α α
π
+
+
+
+
 
 
=  
  
 
 
= − 
  
    
= − + + + ÷  ÷ 
    
∫

( ) ( )
( ) ( )
( ) ( )
( ) ( ) ( ) ( )
( ) ( )
0 0
0
Note from the trigonometric relationship
cos cos .cos sin .sin
5 5
cos cos sin sin
6 63
2
co
cos 150 cos sin 150 sin3
2 cos 30
s .cos sin sin
6 6
.cos
m
dc
m
dc
A
V
V
B A B A B
V
V
π π
α α
π π π
α
α
α
α
π α
+ = −
    
− + ÷  ÷ 
    =
    
+ −  ÷  ÷
   
−
+

+
=
− ( ) ( )0
sin 30 sin α
 
 
 
 

( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( )
( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
0 0
0 0 0 0
0 0
0 0
0
0
0
0
0 0
Note: cos 1
cos 180 30 cos sin 180 30 sin3
2 cos 30 .cos sin 30 sin
cos 30 cos sin 30 sin3
2 cos 30 .cos sin 30 s
80 30 cos 30
sin 180 30 sin 30
in
m
dc
m
dc
V
V
V
V
α α
π α α
α α
π α α
− =
 − − + −
 =
 + − 
 + +
 ∴ =
 + −
=

−
−

( ) ( )
( )
( ) ( )
( )
03
2cos 30 cos
2
3 3
2 cos
2 2
3 3 3
3 cos cos
2 2
3
cos
2
Where 3 Max. line to line supply voltage
m
dc
m
dc
m m
dc
Lm
dc
Lm m
V
V
V
V
V V
V
V
V
V V
α
π
α
π
α α
π π
α
π
 =  
 
= × 
 
 = = 
=
= =

( )max
The maximum average or dc output voltage is
obtained at a delay angle 0 and is given by
3 3
2
Where is the peak phase voltage.
And the normalized average output voltage is
m
dmdc
m
d
dcn n
V
V V
V
V
V V
α
π
=
= =
= = cosc
dmV
α=

( ) ( )
( )
1
5 2
6
2 2
6
1
2
The rms value of output voltage is found by
using the equation
3
sin .
2
and we obtain
1 3
3 cos2
6 8
mO RMS
mO RMS
V V t d t
V V
π
α
π
α
ω ω
π
α
π
+
+
 
 
=  
  
 
= + 
 
∫

3 Phase Half Wave
Controlled Rectifier Output Voltage
Waveforms For RL Load
at
Different Trigger Angles

0
0
3 0
0
3 0
0
6 0
0
6 0
0
9 0
0
9 0
0
1 2 0
0
1 2 0
0
1 5 0
0
1 5 0
0
1 8 0
0
1 8 0
0
2 1 0
0
2 1 0
0
2 4 0
0
2 4 0
0
2 7 0
0
2 7 0
0
3 0 0
0
3 0 0
0
3 3 0
0
3 3 0
0
3 6 0
0
3 6 0
0
3 9 0
0
3 9 0
0
4 2 0
0
4 2 0
0
V a n
↑
V 0
↑
V 0
V a n
α
α
α = 3 0
0
α = 6 0
0
V b n
V b n
V c n
V c n
ω t
ω t
α=300
α=600

0
3 0
0
6 0
0
9 0
0
1 2 0
0
1 5 0
0
1 8 0
0
2 1 0
0
2 4 0
0
2 7 0
0
3 0 0
0
3 3 0
0
3 6 0
0
3 9 0
0
4 2 0
0
↑
V 0
V a n
α
α = 9 0
0
V b n V c n
ω t
α=900

3 Phase Half Wave
Controlled Rectifier With
R Load
and
RL Load with FWD

a a
b b
c c
R
V 0
L
R V 0
+
−
T 1
T 2
T 3
n n
T 1
T 2
T 3

3 Phase Half Wave
Controlled Rectifier Output Voltage
Waveforms For R Load
or RL Load with FWD
at
Different Trigger Angles

0
0
3 0
0
3 0
0
6 0
0
6 0
0
9 0
0
9 0
0
1 2 0
0
1 2 0
0
1 5 0
0
1 5 0
0
1 8 0
0
1 8 0
0
2 1 0
0
2 1 0
0
2 4 0
0
2 4 0
0
2 7 0
0
2 7 0
0
3 0 0
0
3 0 0
0
3 3 0
0
3 3 0
0
3 6 0
0
3 6 0
0
3 9 0
0
3 9 0
0
4 2 0
0
4 2 0
0
V s
V 0
V a n
α
α = 0
α = 1 5 0
V b n V c n
ω t
V a n
V b n V c n
ω t
α=00
α=150

0
0
3 0
0
3 0
0
6 0
0
6 0
0
9 0
0
9 0
0
1 2 0
0
1 2 0
0
1 5 0
0
1 5 0
0
1 8 0
0
1 8 0
0
2 1 0
0
2 1 0
0
2 4 0
0
2 4 0
0
2 7 0
0
2 7 0
0
3 0 0
0
3 0 0
0
3 3 0
0
3 3 0
0
3 6 0
0
3 6 0
0
3 9 0
0
3 9 0
0
4 2 0
0
4 2 0
0
α
α
V 0
α = 3 0
0
V a n
V b n V c n
ω t
V 0
α = 6 0
0
V a n
V b n V c n
ω t
α=300
α=600

To Derive An
Expression For The Average Or
Dc Output Voltage Of A
3 Phase Half Wave Converter With
Resistive Load
Or
RL Load With FWD

( )
( )
( )
( )
( )
0
1
0 0
1
0
2
0 0
2
0
30
6
30 180 ;
sin
5
150
6
150 300 ;
sin 120
O an m
O bn m
T is triggered at t
T conducts from to
v v V t
T is triggered at t
T conducts from to
v v V t
π
ω α α
α
ω
π
ω α α
α
ω
 
= + = + ÷
 
+
= =
 
= + = + ÷
 
+
= = −

( )
( )
( )
( )
0
3
0 0
3
0
0
7
270
6
270 420 ;
sin 240
sin 120
O cn m
m
T is triggered at t
T conducts from to
v v V t
V t
π
ω α α
α
ω
ω
 
= + = + ÷
 
+
= = −
= +

( )
( ) ( )
( )
( )
0
0
0
0
0
0
180
30
0 0
180
30
180
30
3
.
2
sin ; for 30 to 180
3
sin .
2
3
sin .
2
dc O
O an m
dc m
m
dc
V v d t
v v V t t
V V t d t
V
V t d t
α
α
α
ω
π
ω ω α
ω ω
π
ω ω
π
+
+
+
 
=  
  
= = = +
 
=  
  
 
=  
  
∫
∫
∫

( )
( )
0
0
180
30
0 0
0
0
3
cos
2
3
cos180 cos 30
2
cos180 1, we get
3
1 cos 30
2
m
dc
m
dc
m
dc
V
V t
V
V
V
V
α
ω
π
α
π
α
π
+
 
= − 
  
 = − + + 
= −
 = + + 
Q

Three Phase Semiconverters
• 3 Phase semiconverters are used in Industrial
dc drive applications upto 120kW power
output.
• Single quadrant operation is possible.
• Power factor decreases as the delay angle
increases.
• Power factor is better than that of 3 phase half
wave converter.

3 Phase
Half Controlled Bridge Converter
(Semi Converter)
with Highly Inductive Load &
Continuous Ripple free Load Current

Wave forms of 3 Phase Semiconverter
for
α > 600

0 0
1
3 phase semiconverter output ripple frequency of
output voltage is 3
The delay angle can be varied from 0 to
During the period
30 210
7
, thyristor T is forward biased
6 6
Sf
t
t
α π
ω
π π
ω
≤ <
≤ <

1
1 1
If thyristor is triggered at ,
6
& conduct together and the line to line voltage
appears across the load.
7
At , becomes negative & FWD conducts.
6
The load current contin
ac
ac m
T t
T D
v
t v D
π
ω α
π
ω
 
= + ÷
 
=
1 1
ues to flow through FWD ;
and are turned off.
mD
T D

1
2
1 2
If FWD is not used the would continue to
conduct until the thyristor is triggered at
5
, and Free wheeling action would
6
be accomplished through & .
If the delay angle , e
3
mD T
T
t
T D
π
ω α
π
α
 
= + ÷
 
≤ ach thyristor conducts
2
for and the FWD does not conduct.
3
mD
π

( )
( )
( )
0
0
0
We deifine three line neutral voltages
sin ; Max. Phase Voltage
2
sin sin 120
3
2
sin sin 120
3
sin 240
RN an m m
YN bn m m
BN cn m m
m
v v V t V
v v V t V t
v v V t V t
V t
V
ω
π
ω ω
π
ω ω
ω
= = =
 
= = − = − ÷
 
 
= = + = + ÷
 
= −
is the peak phase voltage of a wye-connected sourcem

( )
( )
( )
( )
3 sin
6
5
3 sin
6
3 sin
2
3 sin
6
RB ac an cn m
YR ba bn an m
BY cb cn bn m
RY ab an bn m
v v v v V t
v v v v V t
v v v v V t
v v v v V t
π
ω
π
ω
π
ω
π
ω
 
= = − = − ÷
 
 
= = − = − ÷
 
 
= = − = + ÷
 
 
= = − = + ÷
 

Wave forms of 3 Phase Semiconverter
for
α ≤ 600

To derive an
Expression for the
Average Output Voltage
of 3 Phase Semiconverter
for α > π / 3
and Discontinuous Output Voltage

( )
( )
7
6
6
7
6
6
For and discontinuous output voltage:
3
the Average output voltage is found from
3
.
2
3
3 sin
2 6
dc ac
dc m
V v d t
V V t d t
π
π
α
π
π
α
π
α
ω
π
π
ω ω
π
+
+
≥
 
 =
 
 
 
  = − ÷
  
 
∫
∫

( )
( )
( )max
3 3
1 cos
2
3
1 cos
2
3 Max. value of line-to-line supply voltage
The maximum average output voltage that occurs at
a delay angle of 0 is
3 3
m
dc
mL
dc
mL m
m
dmdc
V
V
V
V
V V
V
V V
α
π
α
π
α
π
= +
= +
= =
=
= =

( )
( ) ( )
1
7 26
2
6
The normalized average output voltage is
0.5 1 cos
The rms output voltage is found from
3
.
2
dc
n
dm
acO rms
V
V
V
V v d t
π
π
α
α
ω
π
+
= = +
 
 =
 
 
∫

( ) ( )
( )
1
7 26
2 2
6
1
2
3
3 sin
2 6
3 sin 2
3
4 2
mO rms
mO rms
V V t d t
V V
π
π
α
π
ω ω
π
α
π α
π
+
 
  = − ÷
  
 
  
= − + ÷ 
  
∫

Average or DC Output Voltage
of a
3-Phase Semiconverter
for α≤π / 3,
and Continuous Output Voltage

( ) ( )
( )
5
62
6 2
For , and continuous output voltage
3
3
. .
2
3 3
1 cos
2
dc ab ac
m
dc
V v d t v d t
V
V
ππ
α
π π
α
π
α
ω ω
π
α
π
+
+
≤
 
 = +
 
 
= +
∫ ∫

( )
( ) ( ) ( )
( )
1
5 262
2 2
6 2
1
2
2
0.5 1 cos
RMS value of o/p voltage is calculated by using
the equation
3
. .
2
3 2
3 3 cos
4 3
dc
n
dm
ab acO rms
mO rms
V
V
V
V v d t v d t
V V
ππ
α
π π
α
α
ω ω
π
π
α
π
+
+
= = +
 
 = +
 
 
  
= + ÷ 
  
∫ ∫

Three Phase Full Converter
• 3 Phase Fully Controlled Full Wave Bridge
Converter.
• Known as a 6-pulse converter.
• Used in industrial applications up to 120kW
output power.
• Two quadrant operation is possible.

• The thyristors are triggered at an interval of
π / 3.
• The frequency of output ripple voltage is 6fS.
• T1 is triggered at ωt = (π/6 + α), T6 is already
conducting when T1 is turned ON.
• During the interval (π/6 + α) to (π/2 + α),
T1 and T6 conduct together & the output load
voltage is equal to vab= (van– vbn)

• T2 is triggered at ωt = (π/2 + α), T6 turns off
naturally as it is reverse biased as soon as T2 is
triggered.
• During the interval (π/2 + α) to (5π/6 + α), T1
and T2 conduct together & the output load
voltage vO = vac = (van – vcn)
• Thyristors are numbered in the order in which
they are triggered.
• The thyristor triggering sequence is 12, 23,
34, 45, 56, 61, 12, 23, 34, ………

( )
( )
( )
0
0
0
sin ; Max. Phase Voltage
2
sin sin 120
3
2
sin sin 120
3
sin 240
RN an m m
YN bn m m
BN cn m m
m
v v V t V
v v V t V t
v v V t V t
V t
V
ω
π
ω ω
π
ω ω
ω
= = =
 
= = − = − ÷
 
 
= = + = + ÷
 
= −
is the peak phase voltage of a wye-connected sourcem

( )
( )
( )
The corresponding line-to-line
supply voltages are
3 sin
6
3 sin
2
3 sin
2
RY ab an bn m
YB bc bn cn m
BR ca cn an m
v v v v V t
v v v v V t
v v v v V t
π
ω
π
ω
π
ω
 
= = − = + ÷
 
 
= = − = − ÷
 
 
= = − = + ÷
 

To Derive An Expression For The
Average Output Voltage Of
3-phase Full Converter
With Highly Inductive Load
Assuming Continuous And
Constant Load Current

( )
2
6
6
. ;
2
3 sin
6
dc OO dc
O ab m
V V v d t
v v V t
π
α
π
α
ω
π
π
ω
+
+
= =
 
= = + ÷
 
∫
The output load voltage consists of 6 voltage
pulses over a period of 2π radians, Hence the
average output voltage is calculated as

( )
2
6
mL
max
3
3 sin .
6
3 3 3
cos cos
Where V 3 Max. line-to-line supply vo
The maximum average dc output voltage is
obtained for a delay angle
ltage
3 3
0,
3
dc m
m mL
dc
m
m m
dmdc
V V t d t
V V
V
V
V V
V V
π
α
π
α
π
ω ω
π
α α
π
α
π
π
+
+
 
= + ÷
 
= =
=
=
=
= = =
∫
L
π

( ) ( )
1
2
2
2
6
The normalized average dc output voltage is
cos
The rms value of the output voltage is found from
6
.
2
dc
dcn n
dm
OO rms
V
V V
V
V v d t
π
α
π
α
α
ω
π
+
+
= = =
 
 
=  
  
∫

( ) ( )
( ) ( )
( )
1
2
2
2
6
1
2
2
2 2
6
1
2
6
.
2
3
3 sin .
2 6
1 3 3
3 cos2
2 4
abO rms
mO rms
mO rms
V v d t
V V t d t
V V
π
α
π
α
π
α
π
α
ω
π
π
ω ω
π
α
π
+
+
+
+
 
 
=  
  
 
  
= + ÷  
  
 
= + ÷ ÷
 
∫
∫

Three Phase Dual Converters
• For four quadrant operation in many industrial
variable speed dc drives , 3 phase dual
converters are used.
• Used for applications up to 2 mega watt output
power level.
• Dual converter consists of two 3 phase full
converters which are connected in parallel & in
opposite directions across a common load.

Outputs of Converters 1 & 2
• During the interval (π/6 + α1) to (π/2 + α1), the
line to line voltage vab appears across the output
of converter 1 and vbc appears across the output
of converter 2

( )
( )
( )
0
0
0
sin ;
Max. Phase Voltage
2
sin sin 120
3
2
sin sin 120
3
sin 240
RN an m
m
YN bn m m
BN cn m m
m
v v V t
V
v v V t V t
v v V t V t
V t
ω
π
ω ω
π
ω ω
ω
= =
=
 
= = − = − ÷
 
 
= = + = + ÷
 
= −

( )
( )
( )
The corresponding line-to-line
supply voltages are
3 sin
6
3 sin
2
3 sin
2
RY ab an bn m
YB bc bn cn m
BR ca cn an m
v v v v V t
v v v v V t
v v v v V t
π
ω
π
ω
π
ω
 
= = − = + ÷
 
 
= = − = − ÷
 
 
= = − = + ÷
 

• If vO1 and vO2 are the output voltages of
converters 1 and 2 respectively, the
instantaneous voltage across the current
limiting inductor during the interval
(π/6 + α1) ≤ ωt ≤ (π/2 + α1) is given by
To obtain an Expression for the
Circulating Current

1 2
3 sin sin
6 2
3 cos
6
The circulating current can be calculated by
using the equation
r O O ab bc
r m
r m
v v v v v
v V t t
v V t
π π
ω ω
π
ω
= + = −
    
= + − − ÷  ÷ 
    
 
= − ÷
 

( ) ( )
( ) ( )
( )
( )
1
1
6
6
1
max
1
.
1
3 cos .
6
3
sin sin
6
3
t
r r
r
t
r m
r
m
r
r
m
r
r
i t v d t
L
i t V t d t
L
V
i t t
L
V
i
L
ω
π
α
ω
π
α
ω
ω
π
ω ω
ω
π
ω α
ω
ω
+
+
=
 
= − ÷
 
  
= − − ÷ 
  
=
∫
∫

Four Quadrant Operation
Conv. 2
Inverting
α2> 900
Conv. 2
Rectifying
α2< 900
Conv. 1
Rectifying
α1< 900
Conv. 1
Inverting
α1> 900

• There are two different modes of operation.
 Circulating current free
(non circulating) mode of operation
 Circulating current mode of operation

Non Circulating
Current Mode Of Operation
• In this mode of operation only one converter is
switched on at a time
• When the converter 1 is switched on,
For α1 < 900
the converter 1 operates in the
Rectification mode
Vdc is positive, Idc is positive and hence the
average load power Pdc is positive.
• Power flows from ac source to the load

• When the converter 1 is on,
For α1 > 900
Inversion mode
Vdc is negative, Idc is positive and the average
load power Pdc is negative.
• Power flows from load circuit to ac source.

For α2 < 900
Rectification mode
Vdc is negative, Idc is negative and the average
load power Pdc is positive.
• The output load voltage & load current reverse
when converter 2 is on.
• Power flows from ac source to the load

For α2 > 900
Inversion mode
Vdc is positive, Idc is negative and the average
load power Pdc is negative.
• Power flows from load to the ac source.
• Energy is supplied from the load circuit to the
ac supply.

Circulating Current
Mode Of Operation
• Both the converters are switched on at the
same time.
• One converter operates in the rectification
mode while the other operates in the inversion
mode.
• Trigger angles α1 & α2 are adjusted such that
(α1 + α2) = 1800

• When α1 < 900
, converter 1 operates as a
controlled rectifier. α2 is made greater than 900
and converter 2 operates as an Inverter.
• Vdc is positive & Idc is positive and Pdc is positive.

• When α2 < 900
, converter 2 operates as a
controlled rectifier. α1 is made greater than 900
and converter 1 operates as an Inverter.
• Vdc is negative & Idc is negative and Pdc is
positive.

Three phase-controlled-rectifiers

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