Transcript Step-down Chopper With RL Load

Subject :- Power Electronics-1
PREPARED BY:GUIDE BY:A.A.Shaikh
140073109006:- KATARIA KARAN
140073109007:-PARMAR HARDIK
140073109009:- PATEL URVI
140073109010:- PRAJAPATI SANKET
140073109011:- SIDDIQUI ZEESHAN
INTRODUCTION
•Chopper is a static device.
•A variable dc voltage is obtained from a
constant dc voltage source.
•Also known as dc-to-dc converter.
•Widely used for motor control.
•Also used in regenerative braking.
• Thyristor converter offers greater
efficiency, faster response, lower
maintenance, smaller size and smooth
control.
Choppers are of Two Types
 Step-down choppers.
 Step-up choppers.
 In step down chopper output voltage
is less than input voltage.
 In step up chopper output voltage is
more than input voltage.
Principle Of
Step-down Chopper
Chopper
i0
V
+
V0
R

• A step-down chopper with resistive
load.
• The thyristor in the circuit acts as a
switch.
• When thyristor is ON, supply voltage
appears across the load
• When thyristor is OFF, the voltage
across the load will be zero.
v0
V
Vdc
t
tOFF
tON
i0
V/R
Idc
t
T
Vdc  Average value of output or load voltage.
I dc  Average value of output or load current.
tON  Time interval for which SCR conducts.
tOFF  Time interval for which SCR is OFF.
T  tON  tOFF  Period of switching or chopping period.
1
f   Freq. of chopper switching or chopping freq.
T
Average Output Voltage
 tON

Vdc  V 

 tON  tOFF 
 tON 
Vdc  V 
  V .d
 T 
 tON
but 
 t

  d  duty cycle

Average Output Current
Vdc
I dc 
R
V  tON  V
I dc  
 d
R T  R
RMS value of output voltage
VO 
1
T
tON
 v dt
2
o
0
But during tON , vo  V
Therefore RMS output voltage
1
VO 
T
tON
V
dt

2
0
2
tON
V
VO 
tON 
.V
T
T
VO  d .V
Output power PO  VO I O
VO
But
IO 
R
 Output power
2
O
V
PO 
R
2
dV
PO 
R
Effective input resistance of chopper
V
Ri 
I dc
R
Ri 
d
The output voltage can be varied by
varying the duty cycle.
Methods Of Control
• The output dc voltage can be varied by the
following methods.
– Pulse width modulation control or
constant frequency operation.
– Variable frequency control.
 Pulse Width Modulation
• tON is varied keeping chopping frequency ‘f’
& chopping period ‘T’ constant.
• Output voltage is varied by varying the ON
time tON
V0
V
tON
tOFF
t
T
V0
V
t
tON
tOFF
Variable Frequency Control
• Chopping frequency ‘f’ is varied
keeping either tON or tOFF constant.
• To obtain full output voltage range,
frequency has to be varied over a wide
range.
• This method produces harmonics in
the output and for large tOFF load
current may become discontinuous
v0
V
tON
tOFF
t
T
v0
V
tON
tOFF
t
T
Step-down Chopper
With R-L Load
Chopper
i0
+
R
V
FWD
V0
L
E

• When chopper is ON, supply is
connected across load.
• Current flows from supply to load.
• When chopper is OFF, load current
continues to flow in the same direction
through FWD due to energy stored in
inductor ‘L’.
• Load current can be continuous or
discontinuous depending on the values
of ‘L’ and duty cycle ‘d’
• For a continuous current operation,
load current varies between two limits
Imax and Imin
• When current becomes equal to Imax
the chopper is turned-off and it is
turned-on when current reduces to
Imin.
v0
Output
voltage
V
tON
i0
tOFF
T
t
Imax
Output
current
Imin
Continuous
current
i0
t
Output
current
Discontinuous
current
t
 Expressions For Load Current iO For
Continuous Current Operation When Chopper
Is ON (0  t  tON)
i0
+
R
V
V0
L
E
-
diO
V  iO R  L
E
dt
Taking Laplace Transform
V
E

 RI O  S   L  S .I O  S   iO  0   
S
S

At t  0, initial current iO  0   I min
I min
V E
IO  S  

R
R

LS  S   S 
L
L

I max
E
 IO  S  

R
R

S 
LS  S 

L
L

Taking Inverse Laplace Transform
iO  t   I max e

R
t
L
E

R
R
 t 

L
1  e



The expression is valid for 0  t  tOFF ,
i.e., during the period chopper is OFF
At the instant the chopper is turned ON or at
the end of the off period, the load current is
iO  tOFF   I min
To Find I max & I min
From equation
At

 R
 R


t




 t
V E
L
 L
iO  t  
1  e
  I min e  
R 

t  tON  dT , iO  t   I max
I max
V E

R
dRT
dRT




L
L
1  e
  I min e


From equation
iO  t   I max e
At

R
t
L
R
 t 

L
1  e



iO  t   I min
E

R
t  tOFF  T  tON ,
t  tOFF  1  d  T
1 d  RT


1 d  RT




E

I min  I max e L  1  e L 
R 

Substituting for I min in equation
I max
dRT
dRT




V E
L
L

1

e

I
e

 min
R 

I max
dRT


V 1  e L

RT


R
L
1

e

we get,

 E
 R

Substituting for I max in equation
I min  I max e

1 d  RT
L
1 d  RT 


E
 1  e L 
R 

we get,


V  e  1 E
I min 

RT
 R
R L
 e  1 
 I max  I min  is known as the steady state ripple.
dRT
L
Therefore peak-to-peak ripple current
I  I max  I min
Average output voltage
Vdc  d .V
Average output current
I
 I min
I dc approx   max
2
Assuming load current varies linearly
from I min to I max instantaneous
load current is given by
iO  I min
iO  I min
I  .t


for 0  t  tON
dT
 I max  I min 

t
dT


 dT 
RMS value of load current
I O RMS  
I O RMS  
I O RMS  
1
dT
dT
1
dT
dT
1
dT
dT
 i dt
2
0
0

0

0

 I max  I min  t  dt
I

 min

dT


2
2
 2
 I max  I min  2 2 I min  I max  I min  t 
 I min  
 dt
 t 
dT
dT




RMS value of output current
 2

I max  I min 

I O  RMS    I min 
 I min  I max  I min  
3




RMS chopper current
2
I CH 
I CH 
1
T
dT
1
T
dT

i02 dt
0

0
2

 I max  I min  
I

 t  dt
 min 
dT

 

1
2
I CH
2
 2

I max  I min 

 d  I min 
 I min  I max  I min  
3


1
2
I CH  d I O RMS 
Effective input resistance is
V
Ri 
IS
Where
I S  Average source current
I S  dI dc

V
Ri 
dI dc
Principle Of Step-up Chopper
I
L
+
D
+

C
V
Chopper
L
O
A
D
VO

• Step-up chopper is used to obtain a load
voltage higher than the input voltage V.
• The values of L and C are chosen
depending upon the requirement of
output voltage and current.
• When the chopper is ON, the inductor L
is connected across the supply.
• The inductor current ‘I’ rises and the
inductor stores energy during the ON
time of the chopper, tON.
• When the chopper is off, the inductor current I is forced
to flow through the diode D and load for a period, tOFF.
• The current tends to decrease resulting in reversing the
polarity of induced EMF in L.
• Therefore voltage across load is given by
dI
VO  V  L
dt
i.e., VO  V
• A large capacitor ‘C’ connected across the load, will
provide a continuous output voltage .
• Diode D prevents any current flow from capacitor to the
source.
• Step up choppers are used for regenerative braking of dc
motors.
Expression For Output Voltage
Assume the average inductor current to be
I during ON and OFF time of Chopper.
When Chopper is ON
Voltage across inductor L  V
Therefore energy stored in inductor
= V .I .tON
Where tON  ON period of chopper.
When Chopper is OFF
(energy is supplied by inductor to load)
Voltage across L  VO  V
Energy supplied by inductor L  VO  V  ItOFF
where tOFF  OFF period of Chopper.
Neglecting losses, energy stored in inductor
L = energy supplied by inductor L
 VItON  VO  V  ItOFF
VO 
V tON  tOFF 
tOFF
 T 
VO  V 

 T  tON 
Where
T = Chopping period or period
of switching.
T  tON  tOFF


 1 
VO  V 
tON 
 1


T 
 1 

VO  V 

1

d


tON
Where d 
 duty cyle
T
For variation of duty cycle ' d ' in the
range of 0  d  1 the output voltage VO
will vary in the range V  VO  
Performance Parameters
• The thyristor requires a certain minimum
time to turn ON and turn OFF.
• Duty cycle d can be varied only between a
min. & max. value, limiting the min. and
max. value of the output voltage.
• Ripple in the load current depends
inversely on the chopping frequency, f.
• To reduce the load ripple current,
frequency should be as high as possible.