This document discusses three phase controlled rectifiers. It explains that three phase controlled rectifiers operate from a three phase AC supply voltage, provide a higher DC output voltage and power, and have a higher output voltage ripple frequency which simplifies filtering requirements. Diagrams and equations are provided to illustrate the operation of a three phase half-wave converter, including expressions to derive the average and RMS output voltages for different trigger angles. Waveforms of the output voltage are shown for various trigger angles with resistive and RL loads.

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

2. Power Electronics by Prof. M. Madhusudhan Rao 22
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.

3. Power Electronics by Prof. M. Madhusudhan Rao 33
• 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.

4. Power Electronics by Prof. M. Madhusudhan Rao 44
3-Phase
Half Wave Converter
(3-Pulse Converter)
with
RL Load
Continuous & Constant
Load Current Operation

5. Power Electronics by Prof. M. Madhusudhan Rao 55

6. Power Electronics by Prof. M. Madhusudhan Rao 66
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
=
=
=

7. Power Electronics by Prof. M. Madhusudhan Rao 77
3 Phase Supply Voltage Equations
We deifine three line to neutral voltages
(3 phase voltages) as follows

8. Power Electronics by Prof. M. Madhusudhan Rao 88
( )
( )
( )
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
= =
=
 
= = − ÷
 
= −
 
= = + ÷
 
= +
= −

9. Power Electronics by Prof. M. Madhusudhan Rao 99
van vbn vcn van

10. Power Electronics by Prof. M. Madhusudhan Rao 1010
io=Ia
Constant Load
Current
Ia
Ia
Each thyristor conducts for 2π/3 (1200
)

11. Power Electronics by Prof. M. Madhusudhan Rao 1111
To Derive an
Expression for the
Average Output Voltage of a
3-Phase Half Wave Converter
with RL Load
for Continuous Load Current

12. Power Electronics by Prof. M. Madhusudhan Rao 1212
( )
( )
( )
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
 
= + = + ÷
 
 
= + = + ÷
 
 
= + = + ÷
 

13. Power Electronics by Prof. M. Madhusudhan Rao 1313
( )
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
+
+
= =
 
 
=  
  
∫

14. Power Electronics by Prof. M. Madhusudhan Rao 1414
( )
( )
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
+
+
+
+
 
 
=  
  
 
 
= − 
  
    
= − + + + ÷  ÷ 
    
∫

15. Power Electronics by Prof. M. Madhusudhan Rao 1515
( ) ( )
( ) ( )
( ) ( )
( ) ( ) ( ) ( )
( ) ( )
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
 
 
 
 

16. Power Electronics by Prof. M. Madhusudhan Rao 1616
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( )
( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
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
− =
 − − + −
 =
 + − 
 + +
 ∴ =
 + −
=

−
−

17. Power Electronics by Prof. M. Madhusudhan Rao 1717
( ) ( )
( )
( ) ( )
( )
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
 =  
 
= × 
 
 = = 
=
= =

18. Power Electronics by Prof. M. Madhusudhan Rao 1818
( )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=

19. Power Electronics by Prof. M. Madhusudhan Rao 1919
( ) ( )
( )
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
+
+
 
 
=  
  
 
= + 
 
∫

20. Power Electronics by Prof. M. Madhusudhan Rao 2020
3 Phase Half Wave
Controlled Rectifier Output Voltage
Waveforms For RL Load
at
Different Trigger Angles

21. Power Electronics by Prof. M. Madhusudhan Rao 2121
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

22. Power Electronics by Prof. M. Madhusudhan Rao 2222
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

23. Power Electronics by Prof. M. Madhusudhan Rao 2323
3 Phase Half Wave
Controlled Rectifier With
R Load
and
RL Load with FWD

24. Power Electronics by Prof. M. Madhusudhan Rao 2424
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

25. Power Electronics by Prof. M. Madhusudhan Rao 2525
3 Phase Half Wave
Controlled Rectifier Output Voltage
Waveforms For R Load
or RL Load with FWD
at
Different Trigger Angles

26. Power Electronics by Prof. M. Madhusudhan Rao 2626
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

27. Power Electronics by Prof. M. Madhusudhan Rao 2727
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

28. Power Electronics by Prof. M. Madhusudhan Rao 2828
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

29. Power Electronics by Prof. M. Madhusudhan Rao 2929
( )
( )
( )
( )
( )
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
 
= + = + ÷
 
+
= =
 
= + = + ÷
 
+
= = −

30. Power Electronics by Prof. M. Madhusudhan Rao 3030
( )
( )
( )
( )
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
 
= + = + ÷
 
+
= = −
= +

31. Power Electronics by Prof. M. Madhusudhan Rao 3131
( )
( ) ( )
( )
( )
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
+
+
+
 
=  
  
= = = +
 
=  
  
 
=  
  
∫
∫
∫

32. Power Electronics by Prof. M. Madhusudhan Rao 3232
( )
( )
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

33. Power Electronics by Prof. M. Madhusudhan Rao 3333
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.

34. Power Electronics by Prof. M. Madhusudhan Rao 3434
3 Phase
Half Controlled Bridge Converter
(Semi Converter)
with Highly Inductive Load &
Continuous Ripple free Load Current

35. Power Electronics by Prof. M. Madhusudhan Rao 3535

36. Power Electronics by Prof. M. Madhusudhan Rao 3636
Wave forms of 3 Phase Semiconverter
for
α > 600

37. Power Electronics by Prof. M. Madhusudhan Rao 3737

38. Power Electronics by Prof. M. Madhusudhan Rao 3838

39. Power Electronics by Prof. M. Madhusudhan Rao 3939
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
≤ <
≤ <

40. Power Electronics by Prof. M. Madhusudhan Rao 4040
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

41. Power Electronics by Prof. M. Madhusudhan Rao 4141
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

42. Power Electronics by Prof. M. Madhusudhan Rao 4242
( )
( )
( )
0
0
0
We deifine three line neutral voltages
(3 phase voltages) as follows
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

43. Power Electronics by Prof. M. Madhusudhan Rao 4343
( )
( )
( )
( )
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
 
= = − = − ÷
 
 
= = − = − ÷
 
 
= = − = + ÷
 
 
= = − = + ÷
 

44. Power Electronics by Prof. M. Madhusudhan Rao 4444
Wave forms of 3 Phase Semiconverter
for
α ≤ 600

45. Power Electronics by Prof. M. Madhusudhan Rao 4545

46. Power Electronics by Prof. M. Madhusudhan Rao 4646

47. Power Electronics by Prof. M. Madhusudhan Rao 4747

48. Power Electronics by Prof. M. Madhusudhan Rao 4848
To derive an
Expression for the
Average Output Voltage
of 3 Phase Semiconverter
for α > π / 3
and Discontinuous Output Voltage

49. Power Electronics by Prof. M. Madhusudhan Rao 4949
( )
( )
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
+
+
≥
 
 =
 
 
 
  = − ÷
  
 
∫
∫

50. Power Electronics by Prof. M. Madhusudhan Rao 5050
( )
( )
( )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
= +
= +
= =
=
= =

51. Power Electronics by Prof. M. Madhusudhan Rao 5151
( )
( ) ( )
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
+
= = +
 
 =
 
 
∫

52. Power Electronics by Prof. M. Madhusudhan Rao 5252
( ) ( )
( )
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
+
 
  = − ÷
  
 
  
= − + ÷ 
  
∫

53. Power Electronics by Prof. M. Madhusudhan Rao 5353
Average or DC Output Voltage
of a
3-Phase Semiconverter
for α≤π / 3,
and Continuous Output Voltage

54. Power Electronics by Prof. M. Madhusudhan Rao 5454
( ) ( )
( )
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
+
+
≤
 
 = +
 
 
= +
∫ ∫

55. Power Electronics by Prof. M. Madhusudhan Rao 5555
( )
( ) ( ) ( )
( )
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
+
+
= = +
 
 = +
 
 
  
= + ÷ 
  
∫ ∫

56. Power Electronics by Prof. M. Madhusudhan Rao 5656
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.

57. Power Electronics by Prof. M. Madhusudhan Rao 5757

58. Power Electronics by Prof. M. Madhusudhan Rao 5858

59. Power Electronics by Prof. M. Madhusudhan Rao 5959

60. Power Electronics by Prof. M. Madhusudhan Rao 6060
• 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)

61. Power Electronics by Prof. M. Madhusudhan Rao 6161
• 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, ………

62. Power Electronics by Prof. M. Madhusudhan Rao 6262
( )
( )
( )
0
0
0
We deifine three line neutral voltages
(3 phase voltages) as follows
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

63. Power Electronics by Prof. M. Madhusudhan Rao 6363
( )
( )
( )
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
 
= = − = + ÷
 
 
= = − = − ÷
 
 
= = − = + ÷
 

64. Power Electronics by Prof. M. Madhusudhan Rao 6464
To Derive An Expression For The
Average Output Voltage Of
3-phase Full Converter
With Highly Inductive Load
Assuming Continuous And
Constant Load Current

65. Power Electronics by Prof. M. Madhusudhan Rao 6565
( )
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

66. Power Electronics by Prof. M. Madhusudhan Rao 6666
( )
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

67. Power Electronics by Prof. M. Madhusudhan Rao 6767
( ) ( )
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
+
+
= = =
 
 
=  
  
∫

68. Power Electronics by Prof. M. Madhusudhan Rao 6868
( ) ( )
( ) ( )
( )
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
+
+
+
+
 
 
=  
  
 
  
= + ÷  
  
 
= + ÷ ÷
 
∫
∫

69. Power Electronics by Prof. M. Madhusudhan Rao 6969
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.

70. Power Electronics by Prof. M. Madhusudhan Rao 7070

71. Power Electronics by Prof. M. Madhusudhan Rao 7171

72. Power Electronics by Prof. M. Madhusudhan Rao 7272

73. Power Electronics by Prof. M. Madhusudhan Rao 7373
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

74. Power Electronics by Prof. M. Madhusudhan Rao 7474
( )
( )
( )
0
0
0
We deifine three line neutral voltages
(3 phase voltages) as follows
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
= =
=
 
= = − = − ÷
 
 
= = + = + ÷
 
= −

75. Power Electronics by Prof. M. Madhusudhan Rao 7575
( )
( )
( )
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
 
= = − = + ÷
 
 
= = − = − ÷
 
 
= = − = + ÷
 

76. Power Electronics by Prof. M. Madhusudhan Rao 7676
• 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

77. Power Electronics by Prof. M. Madhusudhan Rao 7777
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
= + = −
    
= + − − ÷  ÷ 
    
 
= − ÷
 

78. Power Electronics by Prof. M. Madhusudhan Rao 7878
( ) ( )
( ) ( )
( )
( )
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
+
+
=
 
= − ÷
 
  
= − − ÷ 
  
=
∫
∫

79. Power Electronics by Prof. M. Madhusudhan Rao 7979
Four Quadrant Operation
Conv. 2
Inverting
α2> 900
Conv. 2
Rectifying
α2< 900
Conv. 1
Rectifying
α1< 900
Conv. 1
Inverting
α1> 900

80. Power Electronics by Prof. M. Madhusudhan Rao 8080
• There are two different modes of operation.
 Circulating current free
(non circulating) mode of operation
 Circulating current mode of operation

81. Power Electronics by Prof. M. Madhusudhan Rao 8181
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

82. Power Electronics by Prof. M. Madhusudhan Rao 8282
• When the converter 1 is on,
For α1 > 900
the converter 1 operates in the
Inversion mode
Vdc is negative, Idc is positive and the average
load power Pdc is negative.
• Power flows from load circuit to ac source.

83. Power Electronics by Prof. M. Madhusudhan Rao 8383
• When the converter 2 is switched on,
For α2 < 900
the converter 2 operates in the
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

84. Power Electronics by Prof. M. Madhusudhan Rao 8484
• When the converter 2 is switched on,
For α2 > 900
the converter 2 operates in the
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.

85. Power Electronics by Prof. M. Madhusudhan Rao 8585
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

86. Power Electronics by Prof. M. Madhusudhan Rao 8686
• 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.

87. Power Electronics by Prof. M. Madhusudhan Rao 8787
• 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.