Controlled Rectifiers
(Line Commutated AC to DC
converters)
Power Electronics by Prof. M. Madhusudhan Rao
1
+
AC
Input
Voltage
Line
Commutated
Converter
DC Output
V0(dc )
-
• Type of input: Fixed voltage, fixed frequency
ac power supply.
• Type of output: Variable dc output voltage
• Type of commutation: Natural / AC line
commutation
Power Electronics by Prof. M. Madhusudhan Rao
2
Different types of
Line Commutated Converters
• AC to DC Converters (Phase controlled
rectifiers)
• AC to AC converters (AC voltage controllers)
• AC to AC converters (Cyclo converters) at low
output frequency.
Power Electronics by Prof. M. Madhusudhan Rao
3
Differences Between
Diode Rectifiers
&
Phase Controlled Rectifiers
Power Electronics by Prof. M. Madhusudhan Rao
4
• The diode rectifiers are referred to as
uncontrolled rectifiers .
• The diode rectifiers give a fixed dc output
voltage .
• Each diode conducts for one half cycle.
• Diode conduction angle = 1800 or  radians.
• We can not control the dc output voltage or the
average dc load current in a diode rectifier
circuit.
Power Electronics by Prof. M. Madhusudhan Rao
5
Single phase half wave diode rectifier gives an
Average dc output voltage VO dc  
Vm

Single phase full wave diode rectifier gives an
Average dc output voltage VO dc  
Power Electronics by Prof. M. Madhusudhan Rao
2Vm

6
Applications of
Phase Controlled Rectifiers
• DC motor control in steel mills, paper and
textile mills employing dc motor drives.
• AC fed traction system using dc traction motor.
• Electro-chemical and electro-metallurgical
processes.
• Magnet power supplies.
• Portable hand tool drives.
Power Electronics by Prof. M. Madhusudhan Rao
7
Classification of
Phase Controlled Rectifiers
• Single Phase Controlled Rectifiers.
• Three Phase Controlled Rectifiers.
Power Electronics by Prof. M. Madhusudhan Rao
8
Different types of Single
Phase Controlled Rectifiers.
• Half wave controlled rectifiers.
• Full wave controlled rectifiers.
 Using a center tapped transformer.
 Full wave bridge circuit.
 Semi converter.
 Full converter.
Power Electronics by Prof. M. Madhusudhan Rao
9
Different Types of
Three Phase Controlled Rectifiers
• Half wave controlled rectifiers.
• Full wave controlled rectifiers.
• Semi converter (half controlled
bridge converter).
• Full converter (fully controlled bridge
converter).
Power Electronics by Prof. M. Madhusudhan Rao
10
10
Principle of Phase Controlled
Rectifier Operation
Power Electronics by Prof. M. Madhusudhan Rao
11
11
Single Phase Half-Wave Thyristor
Converter with a Resistive Load
Power Electronics by Prof. M. Madhusudhan Rao
12
12
Supply Voltage
Output Voltage
Output (load)
Current
Power Electronics by Prof. M. Madhusudhan Rao
13
13
Supply Voltage
Thyristor Voltage
Power Electronics by Prof. M. Madhusudhan Rao
14
14
Equations
vs  Vm sin  t  i/p ac supply voltage
Vm  max. value of i/p ac supply voltage
VS 
Vm
 RMS value of i/p ac supply voltage
2
vO  vL  output voltage across the load
Power Electronics by Prof. M. Madhusudhan Rao
15
15
When the thyristor is triggered at  t  
vO  vL  Vm sin  t ;  t   to 
vO
iO  iL 
 Load current;  t   to 
R
Vm sin  t
iO  iL 
 I m sin  t ;  t   to 
R
Vm
Where I m 
 max. value of load current
R
Power Electronics by Prof. M. Madhusudhan Rao
16
16
To Derive an Expression for the
Average (DC)
Output Voltage Across The Load
Power Electronics by Prof. M. Madhusudhan Rao
17
17
VO dc 
1
 Vdc 
2
2
 v .d t ;
O
0
vO  Vm sin  t for  t   to 

VO dc 
1
 Vdc 
V
sin

t
.
d

t


m

2 

VO dc 
1

V
sin

t
.
d

t


m

2 
Power Electronics by Prof. M. Madhusudhan Rao
18
18

VO dc 
VO dc 
VO dc 
VO dc 
Vm

sin

t
.
d

t



2 



Vm

  cos  t 
2 

Vm

  cos   cos   ; cos   1
2
Vm

1  cos   ; Vm  2VS
2
19
Power Electronics by Prof. M. Madhusudhan Rao
19
Maximum average (dc) o/p
voltage is obtained when   0
and the maximum dc output voltage
Vm
Vdc max   Vdm 
1  cos 0  ; cos  0   1
2
Vm
Vdc max   Vdm 

Power Electronics by Prof. M. Madhusudhan Rao
20
20
Vm
VO dc  
1  cos   ; Vm  2VS
2
The average dc output voltage can be varied
by varying the trigger angle  from 0 to a
maximum of 180  radians 
0
We can plot the control characteristic
V 
O dc 

vs  by using the equation for VO dc 
Power Electronics by Prof. M. Madhusudhan Rao
21
21
Control Characteristic
of
Single Phase Half Wave Phase
Controlled Rectifier
with
Resistive Load
Power Electronics by Prof. M. Madhusudhan Rao
22
22
The average dc output voltage is given by the
expression
Vm
VO dc  
1  cos  
2
We can obtain the control characteristic by
plotting the expression for the dc output
voltage as a function of trigger angle
Power Electronics by Prof. M. Madhusudhan Rao
23
23
Power Electronics by Prof. M. Madhusudhan Rao
24
24
Control Characteristic
VO(dc)
Vdm
0.6Vdm
0.2 Vdm
0
60
120
180
Trigger angle in degrees
Power Electronics by Prof. M. Madhusudhan Rao
25
25
Normalizing the dc output
voltage with respect to Vdm , the
Normalized output voltage
Vdc
Vn 
Vdm
Vm
1  cos  
2


Vm

Vdc 1
Vn 
 1  cos    Vdcn
Vdm 2
Power Electronics by Prof. M. Madhusudhan Rao
26
26
To Derive An
Expression for the
RMS Value of Output Voltage
of a
Single Phase Half Wave Controlled
Rectifier With Resistive Load
Power Electronics by Prof. M. Madhusudhan Rao
27
27
The RMS output voltage is given by
 1 2 2

VO RMS   
vO .d  t  

 2 0

Output voltage vO  Vm sin  t ; for  t   to 

VO RMS 
 1

2
2

Vm sin  t.d  t  

 2 

Power Electronics by Prof. M. Madhusudhan Rao
1
2
28
28
1  cos 2 t
By substituting sin  t 
, we get
2
2
VO RMS 
VO RMS 
VO RMS 
 1  2 1  cos 2 t 

   Vm
.d  t  
2
 2 

 Vm2

 4


 1  cos 2 t  .d  t 
1
2
1
2

 Vm2 

    d  t    cos 2 t.d  t  
 4 


Power Electronics by Prof. M. Madhusudhan Rao
1
2
29
29
VO RMS 
VO RMS 
VO RMS 
VO RMS 
Vm  1 

  t 
2   
Vm

2
Vm

2


 sin 2 t 


 2 


 


1
2
1
2
1 
sin 2  sin 2   

      
  ;sin2  0
2
  
 
1 
sin 2  
        2  

 
Vm 
sin 2 

     

2 
2  
Power Electronics by Prof. M. Madhusudhan Rao
1
2
1
2
30
30
Performance Parameters
Of
Phase Controlled Rectifiers
Power Electronics by Prof. M. Madhusudhan Rao
31
31
Output dc power (avg. or dc o/p
power delivered to the load)
PO dc   VO dc   I O  dc  ; i.e., Pdc  Vdc  I dc
Where
VO dc   Vdc  avg./ dc value of o/p voltage.
I O dc   I dc  avg./dc value of o/p current
Power Electronics by Prof. M. Madhusudhan Rao
32
32
Output ac power
PO ac   VO RMS   I O RMS 
Efficiency of Rectification (Rectification Ratio)
Efficiency  
PO dc 
PO ac 
; % Efficiency  
PO dc 
PO ac 
100
The o/p voltage consists of two components
The dc component VO dc 
The ac /ripple component Vac  Vr  rms 
Power Electronics by Prof. M. Madhusudhan Rao
33
33
The total RMS value of output voltage is given by
VO RMS   V
2
O  dc 

V
2
r  rms 
Vac  Vr  rms   V
2
O  RMS 
V
2
O  dc 
Form Factor (FF) which is a measure of the
shape of the output voltage is given by
FF 
VO RMS 
VO dc 

RMS output  load  voltage
DC load output  load  voltage
Power Electronics by Prof. M. Madhusudhan Rao
34
34
The Ripple Factor (RF) w.r.t. o/p voltage w/f
rv  RF 
rv 

Vr  rms 
Vac

Vdc
VO dc 
2
O  RMS 
V
V
VO dc 
2
O  dc 
2
VO RMS  
 
 1
 VO dc  
rv  FF  1
2
Power Electronics by Prof. M. Madhusudhan Rao
35
35
Current Ripple Factor ri 
Where I r  rms   I ac  I
I r  rms 
I O dc 
2
O  RMS 
I
I ac

I dc
2
O  dc 
Vr  pp   peak to peak ac ripple output voltage
Vr  pp   VO max   VO min 
I r  pp   peak to peak ac ripple load current
I r  pp   I O max   I O min 
Power Electronics by Prof. M. Madhusudhan Rao
36
36
Transformer Utilization Factor (TUF)
TUF 
PO dc 
VS  I S
Where
VS  RMS supply (secondary) voltage
I S  RMS supply (secondary) current
Power Electronics by Prof. M. Madhusudhan Rao
37
37
Power Electronics by Prof. M. Madhusudhan Rao
38
38
Where
vS  Supply voltage at the transformer secondary side
iS  i/p supply current
(transformer secondary winding current)
iS 1  Fundamental component of the i/p supply current
I P  Peak value of the input supply current
  Phase angle difference between (sine wave
components) the fundamental components of i/p
supply current & the input supply voltage.
Power Electronics by Prof. M. Madhusudhan Rao
39
39
  Displacement angle (phase angle)
For an RL load
  Displacement angle = Load impedance angle
L 
   tan 
 for an RL load
 R 
Displacement Factor (DF) or
1
Fundamental Power Factor
DF  Cos
Power Electronics by Prof. M. Madhusudhan Rao
40
40
Harmonic Factor (HF) or
Total Harmonic Distortion Factor ; THD
1
2
2


I  I 
 IS 
HF  
     1
2
 I S 1 

 I S1 
Where
2
S
2
S1
1
2
I S  RMS value of input supply current.
I S 1  RMS value of fundamental component of
the i/p supply current.
Power Electronics by Prof. M. Madhusudhan Rao
41
41
Input Power Factor (PF)
VS I S 1
I S1
PF 
cos  
cos 
VS I S
IS
The Crest Factor (CF)
CF 
I S  peak 
IS
Peak input supply current

RMS input supply current
For an Ideal Controlled Rectifier
FF  1;   100% ; Vac  Vr  rms   0 ; TUF  1;
RF  rv  0 ; HF  THD  0; PF  DPF  1
Power Electronics by Prof. M. Madhusudhan Rao
42
42
Single Phase Half Wave
Controlled Rectifier
With
An
RL Load
Power Electronics by Prof. M. Madhusudhan Rao
43
43
Power Electronics by Prof. M. Madhusudhan Rao
44
44
Input Supply Voltage (Vs)
&
Thyristor (Output) Current
Waveforms
Power Electronics by Prof. M. Madhusudhan Rao
45
45
Power Electronics by Prof. M. Madhusudhan Rao
46
46
Output (Load)
Voltage Waveform
Power Electronics by Prof. M. Madhusudhan Rao
47
47
To Derive An Expression For
The Output
(Load) Current, During  t   to 
When Thyristor T1 Conducts
Power Electronics by Prof. M. Madhusudhan Rao
48
48
Assuming T1 is triggered  t   ,
we can write the equation,
 diO 
L
  RiO  Vm sin  t ;    t  
 dt 
General expression for the output current,
t
Vm
iO  sin  t     A1e 
Z
Power Electronics by Prof. M. Madhusudhan Rao
49
49
Vm  2VS  maximum supply voltage.
Z  R   L  =Load impedance.
2
2
L 
  tan 
  Load impedance angle.
 R 
L
   Load circuit time constant.
R
 general expression for the output load current
1
R
t
Vm
iO 
sin  t     A1e L
Z
Power Electronics by Prof. M. Madhusudhan Rao
50
50
Constant A1 is calculated from
 
initial condition iO  0 at  t   ; t=  
 
R
t
Vm
iO  0 
sin      A1e L
Z
R
t
Vm
L

A1e 
sin    
Z
We get the value of constant A1 as
A1  e
R  
L
 Vm

 Z sin     


Power Electronics by Prof. M. Madhusudhan Rao
51
51
Substituting the value of constant A1 in the
general expression for iO
R
 t  
L
Vm
 Vm

iO 
sin  t     e
sin






Z
 Z

 we obtain the final expression for the
inductive load current
Vm
iO 
Z
R
 t   

L
sin  t     sin     e
;


Where    t  
Power Electronics by Prof. M. Madhusudhan Rao
52
52
Extinction angle  can be calculated by using
the condition that iO  0 at  t  
R
 t   

Vm
L
iO 
sin

t



sin



e





0
Z 

 sin       e
R
   
L
 sin    
 can be calculated by solving the above eqn.
Power Electronics by Prof. M. Madhusudhan Rao
53
53
To Derive An Expression
For
Average (DC) Load Voltage of a
Single Half Wave Controlled
Rectifier with
RL Load
Power Electronics by Prof. M. Madhusudhan Rao
54
54
VO dc 
VO dc 
1
 VL 
2
2
 v .d t 
O
0


2


1
 VL 
  vO .d  t    vO .d  t    vO .d  t  
2  0



vO  0 for  t  0 to  & for  t   to 2



1
VO dc   VL 
  vO .d  t   ;
2 

vO  Vm sin  t for  t   to 
Power Electronics by Prof. M. Madhusudhan Rao
55
55
VO dc 



1
 VL 
  Vm sin  t.d  t  
2 




Vm
VO dc   VL 
  cos  t 
2 

Vm
VO dc   VL 
 cos   cos  
2
Vm
VO dc   VL 
 cos   cos  
2
Power Electronics by Prof. M. Madhusudhan Rao
56
56
Effect of Load
Inductance on the Output
During the period  t   to  the
instantaneous o/p voltage is negative and
this reduces the average or the dc output
voltage when compared to a purely
resistive load.
Power Electronics by Prof. M. Madhusudhan Rao
57
57
Average DC Load Current
I O dc   I L Avg  
VO dc 
RL
Power Electronics by Prof. M. Madhusudhan Rao
Vm

 cos   cos  
2 RL
58
58
Single Phase Half Wave Controlled
Rectifier
With RL Load
&
Free Wheeling Diode
Power Electronics by Prof. M. Madhusudhan Rao
59
59
T
i0
+
V0
+
Vs

R
~
FWD
L

Power Electronics by Prof. M. Madhusudhan Rao
60
60
vS
Supply voltage
0




t
iG
Gate pulses
0
iO
t

Load current

t=
0

vO
0
t


2
Load voltage



Power Electronics by Prof. M. Madhusudhan Rao

t
61
61
The average output voltage
Vm
Vdc 
1  cos   which is the same as that
2
of a purely resistive load.
The following points are to be noted
For low value of inductance, the load current
tends to become discontinuous.
Power Electronics by Prof. M. Madhusudhan Rao
62
62
During the period  to 
the load current is carried by the SCR.
During the period  to  load current is
carried by the free wheeling diode.
The value of  depends on the value of
R and L and the forward resistance
of the FWD.
Power Electronics by Prof. M. Madhusudhan Rao
63
63
For Large Load Inductance
the load current does not reach zero, &
we obtain continuous load current
i0
0

t1
t2
t3
t4
SCR
FWD
SCR
FWD


Power Electronics by Prof. M. Madhusudhan Rao
2
t

64
64
Single Phase Half Wave
Controlled Rectifier With
A
General Load
Power Electronics by Prof. M. Madhusudhan Rao
65
65
iO
R
+
~

vS
L
+

Power Electronics by Prof. M. Madhusudhan Rao
vO
E
66
66
 E
  sin  
 Vm 
For trigger angle    ,
1
the Thyristor conducts from  t   to 
For trigger angle    ,
the Thyristor conducts from t   to 
Power Electronics by Prof. M. Madhusudhan Rao
67
67
Vm
vO
Load voltage
E
0 
iO




t


Im
Load current
0



Power Electronics by Prof. M. Madhusudhan Rao

t

68
68
Equations
vS  Vm sin  t  Input supply voltage.
vO  Vm sin  t  o/p  load  voltage
for  t   to  .
vO  E for  t  0 to  &
for  t   to 2 .
Power Electronics by Prof. M. Madhusudhan Rao
69
69
Expression for the Load Current
When the thyristor is triggered at a delay angle of
   , the eqn. for the circuit can be written as
 diO 
Vm sin  t  iO  R  L 
 +E ;    t  
 dt 
The general expression for the output load
current can be written as
t
Vm
E
iO 
sin  t      Ae 
Z
R
Power Electronics by Prof. M. Madhusudhan Rao
70
70
Where
Z  R   L  = Load Impedance.
2
2
L 
  tan 
  Load impedance angle.
 R 
L
   Load circuit time constant.
R
The general expression for the o/p current can
1
be written as
Vm
E
iO 
sin  t      Ae
Z
R
Power Electronics by Prof. M. Madhusudhan Rao
R
t
L
71
71
To find the value of the constant
'A' apply the initial conditions at  t   ,
load current iO  0, Equating the general
expression for the load current to zero at
 t   , we get
Vm
E
iO  0 
sin       Ae
Z
R
Power Electronics by Prof. M. Madhusudhan Rao
R 

L 
72
72
We obtain the value of constant 'A' as
 E Vm

A    sin      e
R Z

Substituting the value of the constant 'A' in the
R

L
expression for the load current; we get the
complete expression for the output load current as
Vm
E  E Vm

iO  sin  t        sin      e
Z
R R Z

Power Electronics by Prof. M. Madhusudhan Rao
R
 t  
L
73
73
To Derive
An
Expression For The Average
Or
DC Load Voltage
Power Electronics by Prof. M. Madhusudhan Rao
74
74
VO dc 
1

2
2
 v .d t 
O
0


2


1
VO dc  
  vO .d  t    vO .d  t    vO .d  t  
2  0



vO  Vm sin  t  Output load voltage for  t   to 
vO  E for  t  0 to  & for  t   to 2
VO dc 


2


1

  E.d  t    Vm sin  t   E.d  t  
2  0



Power Electronics by Prof. M. Madhusudhan Rao
75
75
VO dc 
VO dc 
VO dc 
VO dc 
2




1

 Vm   cos  t 
 E  t 
 E  t 

2 
 
0


1

 E   0   Vm  cos   cos    E  2    
2
Vm
E

 cos   cos    
 2      
2
2
 2       
Vm

 cos   cos    
E
2
2


Power Electronics by Prof. M. Madhusudhan Rao
76
76
Conduction angle of thyristor       
RMS Output Voltage can be calculated
by using the expression
2
VO RMS 

1  2

  vO .d  t  
2  0

Power Electronics by Prof. M. Madhusudhan Rao
77
77
Single Phase
Full Wave Controlled Rectifier
Using A
Center Tapped Transformer
Power Electronics by Prof. M. Madhusudhan Rao
78
78
T1
A
+
vO
AC
Supply
O
L
R
T2
B
Power Electronics by Prof. M. Madhusudhan Rao
79
79
Discontinuous
Load Current Operation
without FWD
for
       
Power Electronics by Prof. M. Madhusudhan Rao
80
80
vO
Vm
t
0
iO



t
0


()
Power Electronics by Prof. M. Madhusudhan Rao


()
81
81
To Derive An Expression For
The Output
(Load) Current, During  t   to 
When Thyristor T1 Conducts
Power Electronics by Prof. M. Madhusudhan Rao
82
82
Assuming T1 is triggered  t   ,
we can write the equation,
 diO 
L
  RiO  Vm sin  t ;    t  
 dt 
General expression for the output current,
t
Vm
iO  sin  t     A1e 
Z
Power Electronics by Prof. M. Madhusudhan Rao
83
83
Vm  2VS  maximum supply voltage.
Z  R   L  =Load impedance.
2
2
L 
  tan 
  Load impedance angle.
 R 
L
   Load circuit time constant.
R
 general expression for the output load current
1
R
t
Vm
iO 
sin  t     A1e L
Z
Power Electronics by Prof. M. Madhusudhan Rao
84
84
Constant A1 is calculated from
 
initial condition iO  0 at  t   ; t=  
 
R
t
Vm
iO  0 
sin      A1e L
Z
R
t
Vm
L

A1e 
sin    
Z
We get the value of constant A1 as
A1  e
R  
L
 Vm

 Z sin     


Power Electronics by Prof. M. Madhusudhan Rao
85
85
Substituting the value of constant A1 in the
general expression for iO
R
 t  
L
Vm
 Vm

iO 
sin  t     e
sin






Z
 Z

 we obtain the final expression for the
inductive load current
Vm
iO 
Z
R
 t   

L
sin  t     sin     e
;


Where    t  
Power Electronics by Prof. M. Madhusudhan Rao
86
86
Extinction angle  can be calculated by using
the condition that iO  0 at  t  
R
 t   

Vm
L
iO 
sin

t



sin



e





0
Z 

 sin       e
R
   
L
 sin    
 can be calculated by solving the above eqn.
Power Electronics by Prof. M. Madhusudhan Rao
87
87
To Derive An Expression For The DC
Output Voltage Of
A Single Phase Full Wave Controlled
Rectifier With RL Load
(Without FWD)
Power Electronics by Prof. M. Madhusudhan Rao
88
88
vO
Vm
t
0
iO



t
0


()
Power Electronics by Prof. M. Madhusudhan Rao


()
89
89
VO dc   Vdc 
VO dc 
VO dc 
VO dc 
1


 
vO .d  t 
t



1
 Vdc    Vm sin  t.d  t  
 




Vm
 Vdc 
  cos  t 
 

Vm
 Vdc 
 cos   cos  

Power Electronics by Prof. M. Madhusudhan Rao
90
90
When the load inductance is negligible  i.e., L  0 
Extinction angle    radians
Hence the average or dc output voltage for R load
VO dc  
Vm
 cos   cos  
VO dc  
Vm
 cos    1 
VO dc  
Vm
1  cos   ; for R load,



Power Electronics by Prof. M. Madhusudhan Rao
when   
91
91
To calculate the RMS output voltage we use
the expression

VO RMS 

1 2 2

  Vm sin  t.d  t  
 

Power Electronics by Prof. M. Madhusudhan Rao
92
92
Discontinuous Load Current
Operation with FWD
Power Electronics by Prof. M. Madhusudhan Rao
93
93
vO
Vm
t
0
iO



t
0


()
Power Electronics by Prof. M. Madhusudhan Rao


()
94
94
Thyristor T1 is triggered at  t   ;
T1 conducts from  t   to 
Thyristor T2 is triggered at  t      ;
T2 conducts from  t      to 2
FWD conducts from  t   to  &
vO  0 during discontinuous load current.
Power Electronics by Prof. M. Madhusudhan Rao
95
95
To Derive an Expression
For The
DC Output Voltage For
A
Single Phase Full Wave Controlled
Rectifier
With RL Load & FWD
Power Electronics by Prof. M. Madhusudhan Rao
96
96
VO dc   Vdc 
 VO dc   Vdc 
VO dc 
VO dc 

1
vO .d  t 
 
t 0
1

V


m
sin  t.d  t 



Vm
 Vdc 
  cos  t 
 

Vm
 Vdc    cos   cos   ; cos   1
 VO dc   Vdc 

Vm

1  cos  
Power Electronics by Prof. M. Madhusudhan Rao
97
97
• The load current is discontinuous for low values
of load inductance and for large values of
trigger angles.
• For large values of load inductance the load
current flows continuously without falling to
zero.
• Generally the load current is continuous for
large load inductance and for low trigger angles.
Power Electronics by Prof. M. Madhusudhan Rao
98
98
Continuous Load Current
Operation
(Without FWD)
Power Electronics by Prof. M. Madhusudhan Rao
99
99
vO
Vm
t
0
iO




t
0


()
Power Electronics by Prof. M. Madhusudhan Rao

()

100
100
To Derive
An Expression For
Average / DC Output Voltage
Of
Single Phase Full Wave Controlled
Rectifier For Continuous Current
Operation without FWD
Power Electronics by Prof. M. Madhusudhan Rao
101
101
vO
Vm
t
0
iO




t
0


()
Power Electronics by Prof. M. Madhusudhan Rao

()

102
102
VO dc   Vdc 
VO dc   Vdc 
VO dc 
1
  
vO .d  t 


 
1
  


t

 


Vm sin  t.d  t  

Vm 
 Vdc 
  cos  t
 
Power Electronics by Prof. M. Madhusudhan Rao
   



103
103
VO dc   Vdc


Vm
cos   cos      ;

cos       cos 
VO dc   Vdc 
Vm
VO dc   Vdc 
2Vm

Power Electronics by Prof. M. Madhusudhan Rao

cos   cos  
cos 
104
104
• By plotting VO(dc) versus ,
we obtain the control characteristic of a single
phase full wave controlled rectifier with RL
load for continuous load current operation
without FWD
Power Electronics by Prof. M. Madhusudhan Rao
105
105
Vdc  Vdm  cos 
Power Electronics by Prof. M. Madhusudhan Rao
106
106
Vdc  Vdm  cos 
V O(dc)
Vdm
0.6Vdm
0.2 Vdm
0
-0.2Vdm

30
60
90
120
150
180
-0.6 V dm
-Vdm
Trigger angle in degrees
Power Electronics by Prof. M. Madhusudhan Rao
107
107
By varying the trigger angle we can vary the
output dc voltage across the load. Hence we can
control the dc output power flow to the load.
For trigger angle  , 0 to 90
0
 i.e., 0    90  ;
0
cos  is positive and hence Vdc is positive
Vdc & I dc are positive ; Pdc  Vdc  I dc  is positive
Converter operates as a Controlled Rectifier.
Power flow is from the ac source to the load.
Power Electronics by Prof. M. Madhusudhan Rao
108
108
For trigger angle  , 900 to 1800
0
0
i
.
e
.,
90



180

,
cos is negative and hence
Vdc is negative; I dc is positive ;
Pdc  Vdc  I dc  is negative.
In this case the converter operates
as a Line Commutated Inverter.
Power flows from the load ckt. to the i/p ac source.
The inductive load energy is fed back to the
i/p source.
Power Electronics by Prof. M. Madhusudhan Rao
109
109
Drawbacks Of Full Wave
Controlled Rectifier
With Centre Tapped Transformer
• We require a centre tapped transformer which
is quite heavier and bulky.
• Cost of the transformer is higher for the
required dc output voltage & output power.
• Hence full wave bridge converters are
preferred.
Power Electronics by Prof. M. Madhusudhan Rao
110
110
Single Phase
Full Wave Bridge Controlled Rectifier
2 types of FW Bridge Controlled Rectifiers are
 Half Controlled Bridge Converter
(Semi-Converter)
 Fully Controlled Bridge Converter
(Full Converter)
The bridge full wave controlled rectifier does not
require a centre tapped transformer
Power Electronics by Prof. M. Madhusudhan Rao
111
111
Single Phase
Full Wave Half Controlled Bridge
Converter
(Single Phase Semi Converter)
Power Electronics by Prof. M. Madhusudhan Rao
112
112
Power Electronics by Prof. M. Madhusudhan Rao
113
113
Trigger Pattern of Thyristors
Thyristor T1 is triggered at
 t   , at  t   2    ,...
Thyristor T2 is triggered at
 t      , at  t   3    ,...
The time delay between the gating
signals of T1 & T2   radians or 180
Power Electronics by Prof. M. Madhusudhan Rao
0
114
114
Waveforms of
single phase semi-converter
with general load & FWD
for  > 900
Power Electronics by Prof. M. Madhusudhan Rao
115
115
Single Quadrant
Operation
Power Electronics by Prof. M. Madhusudhan Rao
116
116
Power Electronics by Prof. M. Madhusudhan Rao
117
117
Power Electronics by Prof. M. Madhusudhan Rao
118
118
Thyristor T1 & D1 conduct
from  t   to 
Thyristor T2 & D2 conduct
from  t      to 2
FWD conducts during
 t  0 to  ,  to     ,...
Power Electronics by Prof. M. Madhusudhan Rao
119
119
Load Voltage & Load Current
Waveform of Single Phase Semi
Converter for
 < 900
& Continuous load current operation
Power Electronics by Prof. M. Madhusudhan Rao
120
120
vO
Vm
t
0

iO



t
0




()
Power Electronics by Prof. M. Madhusudhan Rao
()
121
121
To Derive an Expression
For The
DC Output Voltage of
A
Single Phase Semi-Converter With
R,L, & E Load & FWD
For Continuous, Ripple Free Load
Current Operation
Power Electronics by Prof. M. Madhusudhan Rao
122
122
VO dc   Vdc 
 VO dc   Vdc 
VO dc 
VO dc 

1
vO .d  t 
 
t 0
1

V


m
sin  t.d  t 



Vm
 Vdc 
  cos  t 
 

Vm
 Vdc    cos   cos   ; cos   1
 VO dc   Vdc 

Vm

1  cos  
Power Electronics by Prof. M. Madhusudhan Rao
123
123
Vdc can be varied from a max.
value of
2Vm

to 0 by varying  from 0 to  .
For   0, The max. dc o/p voltage obtained is
Vdc max   Vdm 
2Vm

Normalized dc o/p voltage is
Vm
Vdcn
1  cos  
Vdc  
1
 Vn 

 1  cos  
Vdn
2
 2Vm 


  
Power Electronics by Prof. M. Madhusudhan Rao
124
124
RMS O/P Voltage VO(RMS)

VO RMS 
VO RMS 
VO RMS 
 2

2
2
   Vm sin  t.d  t  
 2 

 Vm2

 2
1
2


 1  cos 2t  .d t 
Vm  1 
sin 2  

      2 
2 

Power Electronics by Prof. M. Madhusudhan Rao
1
2
1
2
125
125
Single Phase Full Wave
Full Converter
(Fully Controlled Bridge
Converter)
With R,L, & E Load
Power Electronics by Prof. M. Madhusudhan Rao
126
126
Power Electronics by Prof. M. Madhusudhan Rao
127
127
Waveforms of
Single Phase Full Converter
Assuming Continuous (Constant
Load Current)
&
Ripple Free Load Current
Power Electronics by Prof. M. Madhusudhan Rao
128
128
Power Electronics by Prof. M. Madhusudhan Rao
129
129
Power Electronics by Prof. M. Madhusudhan Rao
130
130
Constant Load Current
iO=Ia
iO
Ia
t

iT1

Ia
Ia
t
& iT2

iT3
 
Ia
t
& iT4
  
Power Electronics by Prof. M. Madhusudhan Rao
131
131
To Derive
An Expression For
The Average DC Output Voltage of a
Single Phase Full Converter
assuming
Continuous & Constant Load Current
Power Electronics by Prof. M. Madhusudhan Rao
132
132
The average dc output voltage
can be determined by using the expression
2

1 
VO dc   Vdc 
  vO .d  t   ;
2  0

The o/p voltage waveform consists of two o/p
pulses during the input supply time period of
0 to 2 radians. Hence the Average or dc
o/p voltage can be calculated as
Power Electronics by Prof. M. Madhusudhan Rao
133
133
 
VO dc 
VO dc 
VO dc 

2 
 Vdc 
  Vm sin  t.d  t  
2  

2Vm
 
 Vdc 
  cos  t 
2
2Vm
 Vdc 
cos 

Power Electronics by Prof. M. Madhusudhan Rao
134
134
Maximum average dc output voltage is
calculated for a trigger angle   0
0
and is obtained as
Vdc max   Vdm 
2Vm

Vdc max   Vdm 
 cos  0  
2Vm

2Vm

Power Electronics by Prof. M. Madhusudhan Rao
135
135
The normalized average output voltage is given by
Vdcn  Vn 
VO dc 
Vdc

Vdm
Vdc max 
2Vm
Vdcn  Vn  
cos 
2Vm
 cos 

Power Electronics by Prof. M. Madhusudhan Rao
136
136
By plotting VO(dc) versus ,
we obtain the control characteristic of a
single phase full wave fully controlled
bridge converter
(single phase full converter)
for constant & continuous
load current operation.
Power Electronics by Prof. M. Madhusudhan Rao
137
137
To plot the control characteristic of a
Single Phase Full Converter for constant
& continuous load current operation.
We use the equation for the average/ dc
output voltage
VO dc   Vdc 
Power Electronics by Prof. M. Madhusudhan Rao
2Vm

cos 
138
138
Power Electronics by Prof. M. Madhusudhan Rao
139
139
Vdc  Vdm  cos 
V O(dc)
Vdm
0.6Vdm
0.2 Vdm
0
-0.2Vdm

30
60
90
120
150
180
-0.6 V dm
-Vdm
Trigger angle in degrees
Power Electronics by Prof. M. Madhusudhan Rao
140
140
• During the period from t =  to  the input
voltage vS and the input current iS are both
positive and the power flows from the supply
to the load.
• The converter is said to be operated in the
rectification mode
Controlled Rectifier Operation
for 0 <  < 900
Power Electronics by Prof. M. Madhusudhan Rao
141
141
• During the period from t =  to (+), the
input voltage vS is negative and the input
current iS is positive and the output power
becomes negative and there will be reverse
power flow from the load circuit to the supply.
• The converter is said to be operated in the
inversion mode.
Line Commutated Inverter Operation
for 900 <  < 1800
Power Electronics by Prof. M. Madhusudhan Rao
142
142
Two Quadrant Operation
of a Single Phase Full Converter
0< < 900
Controlled Rectifier
Operation
900< <1800
Line Commutated
Inverter Operation
Power Electronics by Prof. M. Madhusudhan Rao
143
143
To Derive An
Expression For The
RMS Value Of The Output Voltage
The rms value of the output voltage
is calculated as
2
VO RMS 

1  2

  vO .d  t  
2  0

Power Electronics by Prof. M. Madhusudhan Rao
144
144
The single phase full converter gives two
output voltage pulses during the input supply
time period and hence the single phase full
converter is referred to as a two pulse converter.
The rms output voltage can be calculated as
VO RMS 
 


2
2

  vO .d  t  
2  

Power Electronics by Prof. M. Madhusudhan Rao
145
145
VO RMS 
 


1
2
2

  Vm sin  t.d  t  


VO RMS 
 


V
2

  sin  t.d  t  
 

VO RMS 
 


1  cos 2 t 

V

.d  t  
 
 
2

VO RMS 
 
 


V

  d  t    cos 2 t.d  t  
2  


2
m
2
m
2
m
Power Electronics by Prof. M. Madhusudhan Rao
146
146
VO RMS 
V 

 t 
2 
2
m
2
m
VO RMS 
V

2
VO RMS 
Vm2

2
 

 sin 2 t 


2


 





 sin 2      sin 2  
       

2


 

 sin  2  2   sin 2  
   
 ;
2


 
sin  2  2   sin 2
Power Electronics by Prof. M. Madhusudhan Rao
147
147
VO RMS 
V 
 sin 2  sin 2  

   


2 
2


2
m
2
m
2
m
V
V
Vm
VO RMS  

   0 
2
2
2
Vm
VO RMS  
 VS
2
Hence the rms output voltage is same as the
rms input supply voltage
Power Electronics by Prof. M. Madhusudhan Rao
148
148
Thyristor Current Waveforms
Power Electronics by Prof. M. Madhusudhan Rao
149
149
Constant Load Current
iO=Ia
iO
Ia
t

iT1

Ia
Ia
t
& iT2

iT3
 
Ia
t
& iT4
  
Power Electronics by Prof. M. Madhusudhan Rao
150
150
The rms thyristor current can be
calculated as
IT  RMS  
I O RMS 
2
The average thyristor current can be
calculated as
IT  Avg  
Power Electronics by Prof. M. Madhusudhan Rao
I O dc 
2
151
151
Single Phase Dual Converter
Power Electronics by Prof. M. Madhusudhan Rao
152
152
Power Electronics by Prof. M. Madhusudhan Rao
153
153
Power Electronics by Prof. M. Madhusudhan Rao
154
154
Power Electronics by Prof. M. Madhusudhan Rao
155
155
The average dc output voltage of converter 1 is
Vdc1 
2Vm

cos 1
The average dc output voltage of converter 2 is
Vdc 2 
2Vm

Power Electronics by Prof. M. Madhusudhan Rao
cos  2
156
156
In the dual converter operation one
converter is operated as a controlled rectifier
with  90 & the second converter is
0
operated as a line commutated inverter
in the inversion mode with   90

0
Vdc1  Vdc 2
Power Electronics by Prof. M. Madhusudhan Rao
157
157
2Vm


cos 1 
2Vm

cos  2 
2Vm
cos 1   cos  2

  cos  2 
or
cos  2   cos 1  cos   1 

 2    1  or
1   2   
radians
Which gives
 2     1 
Power Electronics by Prof. M. Madhusudhan Rao
158
158
To Obtain an Expression
for the
Instantaneous Circulating Current
Power Electronics by Prof. M. Madhusudhan Rao
159
159
• vO1 = Instantaneous o/p voltage of converter 1.
• vO2 = Instantaneous o/p voltage of converter 2.
• The circulating current ir can be determined by
integrating the instantaneous voltage difference
(which is the voltage drop across the circulating
current reactor Lr), starting from t = (2 - 1).
• As the two average output voltages during the
interval t = (+1) to (2 - 1) are equal and
opposite their contribution to the instantaneous
circulating current ir is zero.
Power Electronics by Prof. M. Madhusudhan Rao
160
160
t


1
ir 
  vr .d  t   ; vr   vO1  vO 2 
 Lr   2 1 

As the o/p voltage vO 2 is negative
vr   vO1  vO 2 

t


1
ir 
   vO1  vO 2  .d  t   ;
 Lr   2 1 

vO1  Vm sin  t for  2  1  to  t
Power Electronics by Prof. M. Madhusudhan Rao
161
161
t
t


Vm
ir 
   sin  t.d  t    sin  t.d  t  
 Lr   2 1 

 2 1 
2Vm
ir 
 cos  t  cos 1 
 Lr
The instantaneous value of the circulating current
depends on the delay angle.
Power Electronics by Prof. M. Madhusudhan Rao
162
162
For trigger angle (delay angle) 1  0,
the magnitude of circulating current becomes min.
when  t  n , n  0, 2, 4,.... & magnitude becomes
max. when  t  n , n  1,3,5,....
If the peak load current is I p , one of the
converters that controls the power flow
may carry a peak current of

4Vm
 Ip 
 Lr


,

Power Electronics by Prof. M. Madhusudhan Rao
163
163
where
I p  I L max 
Vm

,
RL
&
ir  max 
4Vm

 max. circulating current
 Lr
Power Electronics by Prof. M. Madhusudhan Rao
164
164
The Dual Converter
Can Be Operated
In Two Different Modes Of Operation
• Non-circulating current (circulating current
free) mode of operation.
• Circulating current mode of operation.
Power Electronics by Prof. M. Madhusudhan Rao
165
165
Non-Circulating
Current Mode of Operation
• In this mode only one converter is operated at a
time.
• When converter 1 is ON, 0 < 1 < 900
• Vdc is positive and Idc is positive.
• When converter 2 is ON, 0 < 2 < 900
• Vdc is negative and Idc is negative.
Power Electronics by Prof. M. Madhusudhan Rao
166
166
Circulating
Current Mode Of Operation
• In this mode, both the converters are switched
ON and operated at the same time.
• The trigger angles 1 and 2 are adjusted such
that (1 + 2) = 1800 ; 2 = (1800 - 1).
Power Electronics by Prof. M. Madhusudhan Rao
167
167
• When 0 <1 <900, converter 1 operates as a
controlled rectifier and converter 2 operates as
an inverter with 900 <2<1800.
• In this case Vdc and Idc, both are positive.
• When 900 <1 <1800, converter 1 operates as
an Inverter and converter 2 operated as a
controlled rectifier by adjusting its trigger
angle 2 such that 0 <2<900.
• In this case Vdc and Idc, both are negative.
Power Electronics by Prof. M. Madhusudhan Rao
168
168
Four Quadrant Operation
Conv. 2
Inverting
2 > 900
Conv. 1
Rectifying
1 < 900
Conv. 2
Rectifying
2 < 900
Conv. 1
Inverting
1 > 900
Power Electronics by Prof. M. Madhusudhan Rao
169
169
Advantages of Circulating
Current Mode Of Operation
• The circulating current maintains continuous
conduction of both the converters over the
complete control range, independent of the
load.
• One converter always operates as a rectifier
and the other converter operates as an inverter,
the power flow in either direction at any time is
possible.
Power Electronics by Prof. M. Madhusudhan Rao
170
170
• As both the converters are in continuous
conduction we obtain faster dynamic response.
i.e., the time response for changing from one
quadrant operation to another is faster.
Power Electronics by Prof. M. Madhusudhan Rao
171
171
Disadvantages of Circulating Current Mode
Of Operation
• There is always a circulating current flowing
between the converters.
• When the load current falls to zero, there will be a
circulating current flowing between the converters
so we need to connect circulating current reactors in
order to limit the peak circulating current to safe
level.
• The converter thyristors should be rated to carry a
peak current much greater than the peak load
current.
Power Electronics by Prof. M. Madhusudhan Rao
172
172