Power Electronics

1. UNIT II
PHASE CONTROLLED
CONVERTERS

2. Phase-Control Converters
Single-Phase
Semiconverter
Three-Phase
Full converter
Dual converter
Semiconverter
Full converter
Dual converter

3. Semiconverter
..is a one-quadrant converter and it has one polarity
Full converter
..is a two-quadrant converter and the polarity of its
output can be either positive or negative.
However
the output current of full converter has
one polarity only
Dual converter
..can operate in four quadrants ; both the output
voltage and current can be either positive or negative

5.    
 









cos
1
2
sin
2
1 m
m
dc
V
t
td
V
V
Average Output Voltage

m
dm
V
V 
Maximum
Output Voltage
 

cos
1
5
.
0 


dm
dc
n
V
V
V
Normalizing
Output Voltage
  








  2
2
sin
1
2
sin
2
1 2
2 








m
m
rms
V
t
td
V
V
RMS Output Voltage

6. If the converter has a purely resistive load of R and
the delay angle is , determine
(a) the rectification efficiency
(b) the form factor FF
(c) the ripple factor RF
and (d) the peak inverse voltage PIV of thyristor T1
2
/

 

7.  
 
 
%
27
.
20
3536
.
0
1592
.
0
3536
.
0
2
2
2
sin
2
1
2
1592
.
0
2
cos
1
2
sin
2
1
2
2
2
2
2





























 
m
m
rms
dc
m
m
rms
m
dc
m
m
dc
V
V
V
V
V
V
V
V
V
V
t
td
V
V













8. If the converter has a purely resistive load of R and
the delay angle is , determine
(a) the rectification efficiency
(b) the form factor FF
(c) the ripple factor RF
and (d) the peak inverse voltage PIV of thyristor T1
2
/

 
221
.
2
1592
.
0
3536
.
0



m
m
dc
rms
V
V
V
V
FF

9. If the converter has a purely resistive load of R and
the delay angle is , determine
(a) the rectification efficiency
(b) the form factor FF
(c) the ripple factor RF
and (d) the peak inverse voltage PIV of thyristor T1
2
/

 
983
.
1
1
221
.
2
1 2
2




 FF
RF
m
V
PIV 

10. Semiconverter

11. Single-Phase Semiconverter
   
 


















t
td
V
V
V
t
td
V
V
m
rms
m
m
dc
2
2
sin
2
2
cos
1
sin
2
2

12. Single-Phase Semiconverter (RL-load)
  




















 L
R
L
R
L
L
L
L
L
e
R
E
e
I
t
i
I
E
Ri
dt
di
L
1
0
0
1
1
1
1
    t
L
R
S
L
S
L
S
L
L
e
Z
V
R
E
I
R
E
t
Z
V
I
t
V
E
Ri
dt
di
L
























sin
2
sin
2
sin
2
1
2
2
2
Mode 1

 
 t
0
Mode 2


 
 t
R
L

 1
tan

 2
2
L
R
Z 



13. Single-Phase Semiconverter (RL-load)
RMS Current
for Thyristor
 






t
d
i
I L
R
2
2
2
1
RMS Current
for Thyristor
 






t
d
i
I L
A 2
2
1
RMS Output
Current
   

 








t
d
i
t
d
i
I L
L
rms
2
2
0
2
1
2
1
2
1
AVG Output
Current
   

 








t
d
i
t
d
i
Idc 2
0
1
2
1
2
1

14. The single-phase semiconverter has an RL load of
L = 6.5mH, R = 2.5 Ohm, and E = 10 V. The input
voltage is VS = 120 V(rms) at 60 Hz. Determine
(a) the load current IL0 at , and the load
current IL1 at ,
(b) the average thyristor current IA
(c) the rms thyristor current IR
(d) the rms output current Irms
and (e) the average output current Idc
0

t



 60

t

15. Single-Phase
Full Converter
Rectification
Mode
Inversion
Mode

16. Single-Phase Full Converter
 
 
2
sin
2
2
cos
2
sin
2
2
2
2 m
m
rms
m
m
dc
V
t
d
t
V
V
V
t
d
t
V
V























17. Single-Phase Full Converter (RL-load)
    t
L
R
S
L
S
L e
Z
V
R
E
I
R
E
t
Z
V
I 












 




 sin
2
sin
2
0
Mode 1 = Mode 2
R
L

 1
tan
  2
2
L
R
Z 



18. Single-Phase Full Converter (RL-load)
RMS Current
for Thyristor
 








t
d
i
I L
R
2
2
1
RMS Current
for Thyristor
 








t
d
i
I L
A
2
1
RMS Output
Current R
R
R
rms I
I
I
I 2
2
2



AVG Output
Current A
A
A
dc I
I
I
I 2




19. Dual
Converter

20. Single-Phase Dual Converter
High-Power Variable-Speed Drives
2
1
2
2
1
1
cos
2
cos
2
dc
dc
m
dc
m
dc
V
V
V
V
V
V









21. Three-Phase
Semiconverter

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.

23. • 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.

24. 3-Phase
Half Wave Converter
(3-Pulse Converter)
with
RL Load
Continuous & Constant
Load Current Operation

26. 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




27. 3 Phase Supply Voltage
Equations
We deifine three line to neutral voltages
(3 phase voltages) as follows

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

29. van vbn vcn van

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

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

32.  
 
 
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

  

  

  

 
   
 
 
 
   
 
 
 
   
 
 

33.  
 
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








 



 
 





 
 
  
 
 
 
 
 
 
 
 
 
   
    
   
 
   
 


34.    
   
   
       
   
0 0
0
Note from the trigonometric relationship
cos cos .cos sin .sin
5 5
cos cos sin sin
6 6
3
2
co
cos 150 cos sin 150 sin
3
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 
 
 
 
 

35.        
       
   
   
       
       
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 sin
3
2 cos 30 .cos sin 30 sin
cos 30 cos sin 30 sin
3
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
 
  
 
  
 
 
   
 

 
 
 
 
 
 
 
 
 






36.    
 
   
 
0
3
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




 
 


 
  
 
 
 
 
 
 
 

 

37.  
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
dm
dc
m
d
dcn n
V
V V
V
V
V V



 
  cos
c
dm
V



38.    
 
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
m
O RMS
m
O RMS
V V t d t
V V




 





 
 
  
 
 
 
 
 
 


39. 3 Phase Half Wave
Controlled Rectifier Output
Voltage Waveforms For RL
Load
at
Different Trigger Angles

40. 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

41. 0
30
0
60
0
90
0
120
0
150
0
180
0
210
0
240
0
270
0
300
0
330
0
360
0
390
0
420
0

V0
Van

=90
0
Vbn Vcn
t
=900

42. 3 Phase Half Wave
Controlled Rectifier With
R Load
and
RL Load with FWD

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

44. 3 Phase Half Wave
Controlled Rectifier Output
Voltage Waveforms For R Load
or RL Load with FWD
at
Different Trigger Angles

45. 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

46. 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

47. 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

48.  
 
 
 
 
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

  



  


 
   
 
 

 
 
   
 
 

  

49.  
 
 
 
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

  



 
   
 
 

  
 

50.  
   
 
 
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





  
 

 




 
  
 
 
   
 
  
 
 
 
  
 
 




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

52. 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.

53. 3 Phase
Half Controlled Bridge Converter
(Semi Converter)
with Highly Inductive Load &
Continuous Ripple free Load
Current

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

58. 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
S
f
t
t
 

 

 
 

59. 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.
m
D
T D

60. 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
m
D T
T
t
T D

 


 
 
 
 
 ach thyristor conducts
2
for and the FWD does not conduct.
3
m
D


61.  
 
 
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 source.
m

62.  
 
 
 
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








 
    
 
 
 
    
 
 
 
    
 
 
 
    
 
 

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

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

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

69.  
 
 
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
dm
dc
V
V
V
V
V V
V
V V






 
 
 

 

70.  
   
1
7 2
6
2
6
The normalized average output voltage is
0.5 1 cos
The rms output voltage is found from
3
.
2
dc
n
dm
ac
O rms
V
V
V
V v d t







  
 
 

 
 


71. 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.

75. 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

76.  
 
 
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


 

 

 

 
    
 
 
 
    
 
 
 

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. To obtain an Expression for the Circulating
Current
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

79. 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
 
 


   
 
   
   
   
 
   
 
 
 
 
 

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

81. Four Quadrant Operation

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

83. 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

84. • 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.

85. • 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

86. • 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.

87. • 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
Circulating Current
Mode Of Operation

88. 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.

89. • 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.