This document discusses three phase controlled rectifiers. It provides equations and diagrams for a three phase half-wave converter with an RL load operating under continuous and constant load current. The average output voltage is derived as one-third the peak phase voltage multiplied by 2/π. Waveforms at different trigger angles are shown. Methods for calculating the maximum, RMS, and normalized average output voltages are also presented.

1. 1
Three Phase Controlled
Rectifiers

2. 2
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. 3
• 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. 4
3-Phase Half Wave Converter
(3-Pulse Converter)
with RL Load
Continuous & Constant
Load Current Operation

5. 5

6. 6
Vector Diagram of
3 Phase Supply Voltages
VAN
VCN
VBN
120
0
120
0
120
0 RN AN
YN BN
BN CN
v v
v v
v v




7. 7
3 Phase Supply Voltage
Equations
We deifine three line to neutral voltages
(3 phase voltages) as follows

8. 8
 
 
 
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








 

 
   
 
 
 
   
 
 
 

9. 9
van vbn vcn van

10. 10
io=Ia
Constant Load
Current
Ia
Ia
Each thyristor conducts for 2/3 (1200)

11. 11
To Derive an Expression for
the Average Output Voltage of
a 3-Phase Half Wave
Converter with RL Load for
Continuous Load Current

12. 12
 
 
 
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

  

  

  

 
    
 
 
    
 
 
    
 

13. 13
 
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





 



 
 
 
  
  


14. 14
 
 
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








 



 
 





 
 
  
  
 
 
  
  
    
        
    


15. 15
   
   
   
       
   
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
 
 
  




 
  
    
     
    
    
     
   





    0
sin 30 sin 
 
 
 
 

16. 16
       
       
   
   
       
       
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
 
  
 
  
 
    
 
   
  
  
  





17. 17
   
 
   
 
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




 
 


   
 
  
 
   

 

18. 18
 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



 
  cosc
dmV


19. 19
   
 
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




 





 
 
  
  
 
  
 


20. 20
3 Phase Half Wave
Controlled Rectifier Output
Voltage Waveforms For RL Load
at Different Trigger Angles

21. 21
0
0
30
0
30
0
60
0
60
0
90
0
90
0
120
0
120
0
150
0
150
0
180
0
180
0
210
0
210
0
240
0
240
0
270
0
270
0
300
0
300
0
330
0
330
0
360
0
360
0
390
0
390
0
420
0
420
0
Van

V0

V0
Van


=30
0
=60
0
Vbn
Vbn
Vcn
Vcn
t
t
=300
=600

22. 22
=900

23. 23
3 Phase Half Wave
Controlled Rectifier With
R Load and RL Load with FWD

24. 24
a a
b b
c c
R
V0
L
R V0
+

T1
T2
T3
n n
T1
T2
T3

25. 25
3 Phase Half Wave
Controlled Rectifier Output
Voltage Waveforms For R Load
or RL Load with FWD
at Different Trigger Angles

26. 26
Prof. M.
0
0
30
0
30
0
60
0
60
0
90
0
90
0
120
0
120
0
150
0
150
0
180
0
180
0
210
0
210
0
240
0
240
0
270
0
270
0
300
0
300
0
330
0
330
0
360
0
360
0
390
0
390
0
420
0
420
0
Vs
V0
Van

=0
=150
Vbn Vcn
t
Van
Vbn Vcn
t
=00
=150

27. 27
0
0
30
0
30
0
60
0
60
0
90
0
90
0
120
0
120
0
150
0
150
0
180
0
180
0
210
0
210
0
240
0
240
0
270
0
270
0
300
0
300
0
330
0
330
0
360
0
360
0
390
0
390
0
420
0
420
0


V0
=30
0
Van
Vbn Vcn
t
V0
=600
Van
Vbn Vcn
t
=300
=600

28. 28
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. 29
 
 
 
 
 
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

  



  


 
    
 

 
 
    
 

  

30. 30
 
 
 
 
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

  



 
    
 

  
 

31. 31
 
   
 
 
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





  
 

 




 
  
  
   
 
  
  
 
  
  




32. 32
 
 
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








 
  
  
     
 
    

33. 33
Three Phase Semiconverters
• 3 Phase semiconverters are used in
Industrial dc drive applications up to
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. 34
3 Phase Half Controlled Bridge
Converter
(Semi Converter) with Highly
Inductive Load & Continuous
Ripple free Load Current

35. 35

36. 36
Wave forms of 3 Phase
Semiconverter for  > 600

37. 37

38. 38

39. 39
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
 

 

 
 

40. 40
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

 


 
  
 

1 1
ues to flow through FWD ;
and are turned off.
mD
T D

41. 41
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

 


 
  
 
 ach thyristor conducts
2
for and the FWD does not conduct.
3
mD


42. 42
 
 
 
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


 

 

  
 
     
 
 
     
 
 
is the peak phase voltage of a wye-connected sourcem

43. 43
 
 
 
 
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








 
     
 
 
     
 
 
     
 
 
     
 

44. 44
Wave forms of 3 Phase
Semiconverter for   600

45. 45

46. 46

47. 47

48. 48
To derive an Expression for the
Average Output Voltage
of 3 Phase Semiconverter
for  >  / 3 and
Discontinuous Output Voltage

49. 49
 
 
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











 




 
 
 
 
 
    
  
 



50. 50
 
 
 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






 
 
 

 

51. 51
 
   
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







  
 
 
 
 


52. Power Electronics 52
   
 
1
7 26
2 2
6
1
2
3
3 sin
2 6
3 sin2
3
4 2
mO rms
mO rms
V V t d t
V V




 


 


 
    
  
 
  
    
  


53. 53
Average or DC Output Voltage
of a 3-Phase Semiconverter for
 / 3,
and Continuous Output Voltage

54. 54
   
 
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


 



 






 
  
 
 
 
 

55. 55
 
     
 
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


 


 






  
 
  
 
 
  
   
  
 

56. 56
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. 57

58. 58

59. 59

60. 60
• The thyristors are triggered at an interval
of  / 3.
• The frequency of output ripple voltage is
6fS.
• T1 is triggered at t = (/6 + ), T6 is
already conducting when T1 is turned ON.
• During the interval (/6 + ) to (/2 + ),
T1 and T6 conduct together & the output
load voltage is equal to vab = (van – vbn)

61. 61
• T2 is triggered at t = (/2 + ), T6 turns
off naturally as it is reverse biased as soon
as T2 is triggered.
• During the interval (/2 + ) to (5/6 +
), 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. 62
 
 
 
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


 

 

  
 
     
 
 
     
 
 
is the peak phase voltage of a wye-connected sourcem

63. 63
 
 
 
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






 
     
 
 
     
 
 
     
 

64. 64
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. 65
 
2
6
6
. ;
2
3 sin
6
dc OO dc
O ab m
V V v d t
v v V t










 
 
   
 

The output load voltage consists of 6
voltage pulses over a period of 2 radians,
Hence the average output voltage is
calculated as

66. 66
 
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





 

 






 
  
 
 



  

L


67. 67
   
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









  
 
 
  
  


68. 68
   
   
 
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











 







 
 
  
  
 
  
    
  
 
   
 



69. Power Electronics 69
Vn/Vml-l for controlled 3-phase
full converter

70. Power Electronics 70
Example

71. Power Electronics 71
Continued..

72. 72
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.

73. 73

74. 74

75. 75

76. 76
Outputs of Converters 1 & 2
• During the interval (/6 + 1) to (/2 +
1), the line to line voltage vab appears
across the output of converter 1 and vbc
appears across the output of converter 2

77. 77
 
 
 
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


 

 

 

 
     
 
 
     
 
 

78. 78
 
 
 
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






 
     
 
 
     
 
 
     
 

79. 79
• 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
(/6 + 1)  t  (/2 + 1) is given by
To obtain an Expression for the
Circulating Current

80. 80
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
 
 


   
    
       
    
 
  
 

81. 81
   
   
 
 
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









 


 





 
  
 
  
    
  




82. 82
Four Quadrant Operation
Conv. 2
Inverting
2 > 900
Conv. 2
Rectifying
2 < 900
Conv. 1
Rectifying
1 < 900
Conv. 1
Inverting
1 > 900

83. 83
• There are two different modes of
operation.
 Circulating current free
(non circulating) mode of operation
 Circulating current mode of operation

84. 84
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 1 < 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

85. 85
• When the converter 1 is on,
For 1 > 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.

86. 86
• When the converter 2 is switched on,
For 2 < 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

87. 87
• When the converter 2 is switched on,
For 2 > 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.

88. 88
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 1 & 2 are adjusted such
that (1 + 2) = 1800

89. 89
• When 1 < 900, converter 1 operates as a
controlled rectifier. 2 is made greater
than 900 and converter 2 operates as an
Inverter.
• Vdc is positive & Idc is positive and Pdc is
positive.

90. 90
• When 2 < 900, converter 2 operates as a
controlled rectifier. 1 is made greater
than 900 and converter 1 operates as an
Inverter.
• Vdc is negative & Idc is negative and Pdc is
positive.