UNIT II
PHASE CONTROLLED
CONVERTERS
3/21/2016
Copyright by www.noteshit.com
1
Phase-Control Converters
Single-Phase
Three-Phase
Semiconverter Semiconverter
Full converter
Full converter
Dual converter Dual converter
3/21/2016
Copyright by www.noteshit.com
2
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
3/21/2016
Copyright by www.noteshit.com
3
3/21/2016
Copyright by www.noteshit.com
4
Average Output Voltage

Vm
1
1  cos 
Vdc 
Vm sin td t  

2 
2
Maximum
Output Voltage
Normalizing
Output Voltage
Vdm 
Vm

Vdc
Vn 
 0.51  cos  
Vdm
RMS Output Voltage

Vm 1 
1
sin 2 
2
2
Vrms 
Vm sin td t  
   


3/21/2016 2
Copyright by www.noteshit.com
2 
25 

If the converter has a purely resistive load of R and
the delay angle is ,    / 2 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
3/21/2016
Copyright by www.noteshit.com
6

Vm
1
Vdc 
Vm sin td t  

2 
2


1  cos 
2

2
Vdc  0.1592Vm
Vrms
Vm

2
2
dc
2
rms
V

V
3/21/2016


2 

1

2   0.3536V
    sin
m

2
2 





0.1592Vm 

2
0.3536Vm 
2
 20.27%
Copyright by www.noteshit.com
7
If the converter has a purely resistive load of R and
the delay angle is ,    / 2 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
Vrms 0.3536Vm
FF 

 2.221
Vdc 0.1592Vm
3/21/2016
Copyright by www.noteshit.com
8
If the converter has a purely resistive load of R and
the delay angle is ,    / 2 determine
(a) the rectification efficiency
(b) the form factor FF
(c) the ripple factor RF
RF  FF 1  2.221 1  1.983
2
2
and (d) the peak inverse voltage PIV of thyristor T1
PIV  Vm
3/21/2016
Copyright by www.noteshit.com
9
3/21/2016
Copyright by www.noteshit.com
Semiconverter
10
Single-Phase Semiconverter

Vm
2
1  cos  
Vdc 
Vm sin td t  

2 


Vrms
2
2
2

Vm sin td t 

2 
3/21/2016
Copyright by www.noteshit.com
11
Single-Phase Semiconverter (RL-load)
diL1
L
 Ri L1  E  0
0  t  
dt
Mode 1
R



E
L
I L1  iL1 t     I L 0 e
 1  e

R

Mode 2
2
2
1 L
  t  
Z  R  L   tan
R
di

L2
L
dt
I L2
R
L
 Ri L 2  E  2VS sin t
R 


2VS
2VS
E
E

sin t       I L1  
sin     e L  t
Z
R 
R
Z

3/21/2016
Copyright by www.noteshit.com
12
Single-Phase Semiconverter (RL-load)
RMS Current
for Thyristor
1
IR 
2
RMS Current
for Thyristor
1
IA 
2
RMS Output
1
I rms 
Current
2
1
AVG Output
I dc 
Current
2
3/21/2016
 2
 i d t 
L2

 i d t 
L2
 2

0


0
1
iL1d t  
2
1
i1d t  
2
Copyright by www.noteshit.com
 2
 i d t 
L2

 i d t 
2
13
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 t  0 , and the load
current IL1 at t    60 ,
(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
3/21/2016
Copyright by www.noteshit.com
14
Rectification
Mode
Inversion
Mode
Single-Phase
3/21/2016
Full
Converter
Copyright by www.noteshit.com
15
Single-Phase Full Converter
2
Vdc 
2
Vrms
3/21/2016
 
Vm sin td t  

2

2
 

2Vm

cos 
Vm
V sin td t  
2
2
m
2
Copyright by www.noteshit.com
16
Single-Phase Full Converter (RL-load)
Mode 1 = Mode 2
  tan
1
L
R
Z  R  L
2
2
R 


2VS
2VS
E
E
IL 
sin t       I L 0  
sin     e L  t
Z
R 
R
Z

3/21/2016
Copyright by www.noteshit.com
17
Single-Phase Full Converter (RL-load)
RMS Current
for Thyristor
1
IR 
2
RMS Current
for Thyristor
1
IA 
2
RMS Output
Current
AVG Output
Current
3/21/2016
  2

 

iL d t 
iL d t 
I rms  I R2  I R2  2 I R
I dc  I A  I A  2I A
Copyright by www.noteshit.com
18
3/21/2016
Dual
Copyright by www.noteshit.com
Converter
19
Single-Phase Dual Converter
Vdc1 
2Vm
cos 1
Vdc 2 
2Vm
cos  2


Vdc1  Vdc 2
High-Power
Variable-Speed
Drives
3/21/2016
Copyright by www.noteshit.com
20
Three-Phase
Semiconverter
3/21/2016
Copyright by www.noteshit.com
21
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.
3/21/2016
Copyright by www.noteshit.com
22
• 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.
3/21/2016
Copyright by www.noteshit.com
23
3-Phase
Half Wave Converter
(3-Pulse Converter)
with
RL Load
Continuous & Constant
Load Current Operation
3/21/2016
Copyright by www.noteshit.com
24
3/21/2016
Copyright by www.noteshit.com
25
Vector Diagram of
3 Phase Supply Voltages
VCN
0
120
120
v
VAN RN
0
0
120
VBN
3/21/2016
 v AN
vYN  vBN
vBN  vCN
Copyright by www.noteshit.com
26
3 Phase Supply Voltage
Equations
We deifine three line to neutral voltages
(3 phase voltages) as follows
3/21/2016
Copyright by www.noteshit.com
27
vRN  van  Vm sin  t ;
Vm  Max. Phase Voltage
vYN
2 

 vbn  Vm sin   t 

3 

 Vm sin  t  1200 
vBN
3/21/2016
2 

 vcn  Vm sin   t 

3 

 Vm sin  t  120
0

sin  t  240 
 Vm
0
Copyright by www.noteshit.com
28
van
3/21/2016
vbn
vcn
Copyright by www.noteshit.com
van
29
Each thyristor conducts for 2/3 (1200)
Constant Load
Current
io=Ia
Ia
Ia
3/21/2016
Copyright by www.noteshit.com
30
To Derive an
Expression for the
Average Output Voltage of a
3-Phase Half Wave Converter
with RL Load
for Continuous Load Current
3/21/2016
Copyright by www.noteshit.com
31


T1 is triggered at  t        300   
6

 5

T2 is triggered at  t  
    1500   
 6

 7

0
T3 is triggered at  t  
     270   
 6

2
0
Each thytistor conducts for 120 or
radians
3
3/21/2016
Copyright by www.noteshit.com
32
3Vm
Vdc 
2
3Vm
Vdc 
2
3Vm
Vdc 
2
3/21/2016
5

6




  sin  t.d  t  
 6 

5
 

6



cos

t





 

6


 5



  cos  6     cos  6    





Copyright by www.noteshit.com
33
Note from the trigonometric relationship
cos  A  B    cos A.cos B  sin A.sin B 
3Vm
Vdc 
2
3Vm
Vdc 
2
3/21/2016


 5 
 5 
  cos  6  cos    sin  6  sin  

 
 




 
 
 cos   .cos    sin   sin   

6
6


  cos 1500  cos    sin 1500  sin  



0
0



cos
30
.cos


sin
30
sin











Copyright by www.noteshit.com
34
0
0
0
0



cos
180

30
cos


sin
180

30
sin









3Vm


Vdc 
0
0
2 


cos
30
.cos


sin
30
sin











Note:
cos 1800  300    cos  300 
sin 1800  300   sin  300 
0
0



cos
30
cos


sin
30
sin  
 




3Vm


Vdc 
0
0
2 


cos
30
.cos


sin
30
s
in











3/21/2016
Copyright by www.noteshit.com
35
3Vm
 2 cos  300  cos   
Vdc 

2 

3Vm 
3
Vdc 
cos   
2 
2 
2

3Vm 
3
3
V
m

Vdc 
3
cos


cos







2
2
3VLm
Vdc 
cos  
2
Where VLm  3Vm  Max. line to line supply voltage
3/21/2016
Copyright by www.noteshit.com
36
The maximum average or dc output voltage is
obtained at a delay angle   0 and is given by
3 3 Vm
Vdc max   Vdm 
2
Where Vm is the peak phase voltage.
And the normalized average output voltage is
Vdc
Vdcn  Vn 
 cos 
Vdm
3/21/2016
Copyright by www.noteshit.com
37
The rms value of output voltage is found by
using the equation
VO RMS 

 3

2

5

6


2
2
Vm sin  t.d  t  




6
1
2
and we obtain
VO RMS 
3/21/2016
1

3
 3Vm  
cos 2 
 6 8

Copyright by www.noteshit.com
1
2
38
3 Phase Half Wave
Controlled Rectifier Output
Voltage Waveforms For RL
Load
at
Different Trigger Angles
3/21/2016
Copyright by www.noteshit.com
39

Van
Vbn
Vcn

V0
=30
0
0
30
0
60
0
90
0
120

0
0
0
0
0
0
0
0
150 180 210 240 270 300 330 360
Van
Vbn
0
0
3/21/2016
0
60
0
90
0
120
0
0
0
0
t
0
Vcn
=60
30
=300
390 420

V0
0
0
0
0
0
0
150 180 210 240 270 300 330 360
0
0
0
=600
t
390 420
Copyright by www.noteshit.com
40

Vbn
Van
Vcn
=900

V0
=90
0
0
30
3/21/2016
0
60
0
90
0
120
0
0
0
0
0
0
0
0
150 180 210 240 270 300 330 360
Copyright by www.noteshit.com
0
0
0
t
390 420
41
3 Phase Half Wave
Controlled Rectifier With
R Load
and
RL Load with FWD
3/21/2016
Copyright by www.noteshit.com
42
T1
T1
a
a
T2
T2
b
b
T3
+
T3
c
c
R V0
R
V0
L
n

n
3/21/2016
Copyright by www.noteshit.com
43
3 Phase Half Wave
Controlled Rectifier Output
Voltage Waveforms For R Load
or RL Load with FWD
at
Different Trigger Angles
3/21/2016
Copyright by www.noteshit.com
44
Vbn
Van
Vcn
=0
Vs
0
30
0
0
60
0
90
0
0
120 150

0
0
0
0
0
0
180 210 240 270 300 330 360
0
Vbn
Van
0
390 420
0
0
=0
t
Vcn
=150
=150
V0
3/21/2016
0
30
0
0
60
0
90
0
0
120 150
0
0
0
0
0
0
180 210 240 270 300 330 360
0
0
390 420
Copyright by www.noteshit.com
0
t
45

Vbn
Van
Vcn
=30
V0
0
0
0
30
0
60
0
90
0
0
0
0
120 150 180 210

0
0
0
0
0
Vbn
Van
0
240 270 300 330 360 390 420
0
0
0
30
3/21/2016
0
60
0
90
0
0
0
0
120 150 180 210
0
0
t
Vcn
=600
V0
=300
0
0
0
0
240 270 300 330 360 390 420
Copyright by www.noteshit.com
0
=600
t
46
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
3/21/2016
Copyright by www.noteshit.com
47


0
T1 is triggered at  t        30   
6

T1 conducts from  300    to 1800 ;
vO  van  Vm sin  t
 5

T2 is triggered at  t  
    1500   
 6

T2 conducts from 150    to 300 ;
0
0
vO  vbn  Vm sin  t  1200 
3/21/2016
Copyright by www.noteshit.com
48
 7

0
T3 is triggered at  t  
     270   
 6

T3 conducts from  270    to 420 ;
0
0
vO  vcn  Vm sin  t  240
 Vm sin  t  120
3/21/2016
Copyright by www.noteshit.com
0
0


49
3
Vdc 
2


  vO .d  t  
 300

1800
vO  van  Vm sin  t ; for  t    300  to 1800 


  Vm sin  t.d  t  
 300

0
180

3Vm 
Vdc 
  sin  t.d  t  
2  300

3
Vdc 
2
3/21/2016
1800
Copyright by www.noteshit.com
50
3Vm
Vdc 
2

  cos  t



  300 

1800
3Vm
0
0


Vdc 

cos180

cos


30




2
0
cos180  1, we get
3Vm
0


Vdc 
1

cos


30



2 
3/21/2016
Copyright by www.noteshit.com
51
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.
3/21/2016
Copyright by www.noteshit.com
52
3 Phase
Half Controlled Bridge Converter
(Semi Converter)
with Highly Inductive Load &
Continuous Ripple free Load
Current
3/21/2016
Copyright by www.noteshit.com
53
3/21/2016
Copyright by www.noteshit.com
54
Wave forms of 3 Phase
Semiconverter for
 > 600
3/21/2016
Copyright by www.noteshit.com
55
3/21/2016
Copyright by www.noteshit.com
56
3/21/2016
Copyright by www.noteshit.com
57
3 phase semiconverter output ripple frequency of
output voltage is 3 f S
The delay angle  can be varied from 0 to 
During the period
30   t  210

7
 t 
, thyristor T1 is forward biased
6
6
0
3/21/2016
0
Copyright by www.noteshit.com
58


If thyristor T1 is triggered at  t      ,

6
T1 & D1 conduct together and the line to line voltage
vac appears across the load.
7
, vac becomes negative & FWD Dm conducts.
At  t 
6
The load current continues to flow through FWD Dm ;
T1 and D1 are turned off.
3/21/2016
Copyright by www.noteshit.com
59
If FWD Dm is not used the T1 would continue to
conduct until the thyristor T2 is triggered at
 5

 t      , and Free wheeling action would
 6

be accomplished through T1 & D2 .
If the delay angle  

3
, each thyristor conducts
2
for
and the FWD Dm does not conduct.
3
3/21/2016
Copyright by www.noteshit.com
60
We deifine three line neutral voltages
(3 phase voltages) as follows
vRN  van  Vm sin  t ;
Vm  Max. Phase Voltage
2 

0
vYN  vbn  Vm sin   t 

V
sin

t

120


 m
3 

2 

0
vBN  vcn  Vm sin   t 
  Vm sin  t  120 
3 

 Vm sin  t  240
0

Vm is the peak phase voltage of a wye-connected source.
3/21/2016
Copyright by www.noteshit.com
61


vRB  vac   van  vcn   3Vm sin   t  
6

5 

vYR  vba   vbn  van   3Vm sin   t 

6 

vBY
vRY


 vcb   vcn  vbn   3Vm sin   t  
2



 vab   van  vbn   3Vm sin   t  
6

3/21/2016
Copyright by www.noteshit.com
62
Wave forms of 3 Phase
Semiconverter for
  600
3/21/2016
Copyright by www.noteshit.com
63
3/21/2016
Copyright by www.noteshit.com
64
3/21/2016
Copyright by www.noteshit.com
65
3/21/2016
Copyright by www.noteshit.com
66
To derive an
Expression for the
Average Output Voltage
of 3 Phase Semiconverter
for  >  / 3
and Discontinuous Output Voltage
3/21/2016
Copyright by www.noteshit.com
67
For  

and discontinuous output voltage:
3
the Average output voltage is found from
7
3
Vdc 
2
3
Vdc 
2
3/21/2016
 6



v
.
d

t


ac



 6

7
 6






3
V
sin

t

d

t


m



6



 6

Copyright by www.noteshit.com
68
VmL
3 3Vm
Vdc 
1  cos  
2
3VmL
Vdc 
1  cos  
2
 3Vm  Max. value of line-to-line supply voltage
The maximum average output voltage that occurs at
a delay angle of   0 is
Vdc max   Vdm 
3/21/2016
3 3Vm

Copyright by www.noteshit.com
69
The normalized average output voltage is
Vdc
Vn 
 0.5 1  cos  
Vdm
The rms output voltage is found from
VO rms 
3/21/2016
 3

 2

7

2

v
.
d

t


ac



6 

6
Copyright by www.noteshit.com
1
2
70
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.
3/21/2016
Copyright by www.noteshit.com
71
3/21/2016
Copyright by www.noteshit.com
72
3/21/2016
Copyright by www.noteshit.com
73
3/21/2016
Copyright by www.noteshit.com
74
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
3/21/2016
Copyright by www.noteshit.com
75
We deifine three line neutral voltages
(3 phase voltages) as follows
vRN  van  Vm sin  t ;
Vm  Max. Phase Voltage
2 

0
vYN  vbn  Vm sin   t    Vm sin  t  120 
3 

2 

0
vBN  vcn  Vm sin   t    Vm sin  t  120 
3 

 Vm sin  t  240
3/21/2016
Copyright by www.noteshit.com
0

76
We deifine three line neutral voltages
(3 phase voltages) as follows
vRN  van  Vm sin  t ;
Vm  Max. Phase Voltage
2 

vYN  vbn  Vm sin   t    Vm sin  t  1200 
3 

2 

vBN  vcn  Vm sin   t    Vm sin  t  1200 
3 

 Vm sin  t  2400 
3/21/2016
Copyright by www.noteshit.com
77
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
3/21/2016
Copyright by www.noteshit.com
78
vr  vO1  vO 2  vab  vbc
 

 

vr  3Vm sin   t    sin   t   
6
2 

 


vr  3Vm cos   t  
6

The circulating current can be calculated by
using the equation
3/21/2016
Copyright by www.noteshit.com
79
t
1
ir  t  
 Lr


6


6
3/21/2016
1


3Vm cos   t   .d  t 
6



 
sin   t  6   sin 1 


 
3Vm
ir  t  
 Lr
ir  max 
1
t
1
ir  t  
 Lr
vr .d  t 
3Vm

 Lr
Copyright by www.noteshit.com
80
Four Quadrant Operation
3/21/2016
Copyright by www.noteshit.com
81
• There are two different modes of
operation.
 Circulating current free
(non circulating) mode of operation
 Circulating current mode of operation
3/21/2016
Copyright by www.noteshit.com
82
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
3/21/2016
Copyright by www.noteshit.com
83
• 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.
3/21/2016
Copyright by www.noteshit.com
84
• 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
3/21/2016
Copyright by www.noteshit.com
85
• 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.
3/21/2016
Copyright by www.noteshit.com
86
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
3/21/2016
Copyright by www.noteshit.com
87
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.
3/21/2016
Copyright by www.noteshit.com
88
• 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.
3/21/2016
Copyright by www.noteshit.com
89