Power Electronics_DC Choppers New

8/12/2019 Power Electronics_DC Choppers New

1/120

DC Choppers


2/120

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.


3/120

Prof. T.K. Anantha Kumar, E&E Dept., MSRIT

Choppers are of Two Types

Step-down choppers.

Step-up choppers.

In step down chopper output voltage is lessthan input voltage.

In step up chopper output voltage is more

than input voltage.


4/120

Principle Of

Step-down Chopper

V

i0

V0

Chopper

R

+


5/120

A step-down chopper with resistive load.

The thyristor in the circuit acts as a switch.

When thyristor is ON, supply voltage appearsacross the load

When thyristor is OFF, the voltage across the

load will be zero.


6/120

Vdc

v0

V

V/R

i0

Idc

t

t

tON

T

tOFF


7/120

verage value of output or load voltage.

verage value of output or load current.

Time interval for which SCR conducts.

Time interval for which SCR is OFF.

Period of switching

dc

dc

ON

OFF

ON OFF

V A

I A

t

t

T t t

or chopping period.

1Freq. of chopper switching or chopping freq.f

T


8/120

Average Output Voltage

.

duty cycle

ONdc

ON OFF

ONdc

ON

tV V

t t

tV V V d

T

tbut d t


9/120

2

0

Average Output Current

RMS value of output voltage

1 ON

dcdc

ONdc

t

O o

VIR

tV V

I dR T R

V v dt T


10/120

2

0

2

But during ,

Therefore RMS output voltage

1

.

.

ON

ON o

t

O

ON

O ON

O

t v V

V V dt T

tV

V t VT T

V d V


11/120

2

2

Output power

But

Output power

O O O

OO

OO

O

P V I

VI

R

VP

RdV

PR


12/120

Effective input resistance of chopper

The output voltage can be varied by

varying the duty cycle.

i

dc

i

VR

I

RR

d


13/120

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 or frequency

modulation control.


14/120

Pulse Width Modulation

tONis varied keeping chopping frequency f&

chopping period T constant.

Output voltage is varied by varying the ON

time tON


15/120

V0

V

V

V0

t

ttON

tON tOFF

tOFF

T


16/120

Variable Frequency Control

Chopping frequency fis 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


17/120

v0

V

V

v0

t

t

tON

tON

T

T

tOFF

tOFF


18/120

Step-down Chopper

With R-L Load

V

i0

V0

Chopper

R

LFWD

E

+


19/120

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.


20/120

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 ImaxandImin

When current becomes equal to Imaxthechopper is turned-off and it is turned-on when

current reduces to Imin.


21/120

Outputvoltage

Outputcurrent

v0

V

i0

Imax

Imin

t

t

tON

T

tOFF

Continuouscurrent

Outputcurrent

t

Discontinuouscurrent

i0


22/120

22Prof. T.K. Anantha Kumar, E&E Dept., MSRIT

Expressions For

Load CurrentiOFor Continuous Current Operation When

Chopper Is ON (0 t tON)


23/120


V

i0

V0

R

L

E

+

-


24/120


min

min

Taking Laplace Transform

. 0

At 0, initial current 0

OO

O O O

O

O

diV i R L E

dt

V E

RI S L S I S iS S

t i I

IV EI SRR

SLS SLL


25/120


min

Taking Inverse Laplace Transform

1

This expression is valid for 0 ,

i.e., during the period chopper is ON.

At the instant the chopper is turned off,

load c

R Rt tL L

O

ON

V Ei t e I e

R

t t

maxurrent is O ONi t I


26/120


When Chopper is OFF

i0

R

L

E


27/120


max

When Chopper is OFF 0

0

Talking Laplace transform

0 0

Redefining time origin we have at 0,

initial current 0

OFF

OO

O O O

O

t t

diRi L E

dt

ERI S L SI S i

S

t

i I


28/120


max

max

Taking Inverse Laplace Transform

1

O

R Rt tL L

O

I EI SR R

S LS S

L L

Ei t I e eR


29/120


min

The expression is valid for 0 ,

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

OFF

O OFF

t t

i t I


30/120


min

max

max

max min

min

From equation

1

At ,

To Find &

1

R Rt t

L L

O

ON O

dRT dRT

L L

V E

i t e I eR

t t dT i t I

V EI e I e

I I

R


31/120


max

min

From equation

1

At ,1

R Rt t

L LO

OFF ON O

OFF

Ei t I e eR

t t T t i t I t t d T


32/120


1 1

min max

min

max min

max

1

Substituting for in equation

1

we get,

1

1

d RT d RT

L L

dRT dRT

L L

dRT

L

RT

L

EI I e e

R

I

V EI e I eR

V e EI

R Re


33/120


max

1 1

min max

min

max min

Substituting for in equation

1

we get,

1

1

is known as the steady state ripple.

d RT d RT

L L

dRT

L

RTL

I

EI I e e

R

V e EI

R Re

I I


34/120


max min

max min

Therefore peak-to-peak ripple current

Average output voltage

.

Average output current

2

dc

dc approx

I I I

V d V

I II


35/120


min max

min

max minmin

Assuming load current varies linearly

from to instantaneous

load current is given by

. 0O ON

O

I I

I ti I for t t dT

dT

I Ii I tdT


36/120


2

0

0

2

max min

min

0

2

min max min2 2max min

min

0

RMS value of load current

1

1

21

dT

O RMS

dT

O RMS

dT

O RMS

I i dtdT

I I tI I dt

dT dT

I I I tI I

I I t dtdT dT dT


37/120


1

2 2max min2

min min max min

2

0

0

2

max minmin

0

RMS value of output current

3

RMS chopper current

1

1

O RMS

dT

CH

dT

CH

I II I I I I

I i dtT

I II I t dt

T dT


38/120


12 2

max min2

min min max min3

Effective input resistance is

CH

CH O RMS

i

S

I II d I I I I

I d I

VR

I


39/120

39

Where

Average source currentS

S dc

i

dc

I

I dI

VR

dI


40/120


Principle Of Step-up Chopper

+

VOV

Chopper

CLOAD

DLI

+


41/120


Step-up chopper is used to obtain a load

voltage higher than the input voltage V. The values of Land Care chosen depending

upon the requirement of output voltage andcurrent.

When the chopper is ON, the inductor Lisconnected across the supply.

The inductor current Irises and the inductor

stores energy during the ONtime of thechopper, tON.


42/120


When the chopper is off, the inductor current Iis forced to flow through the diode Dand load

for a period, tOFF.

The current tends to decrease resulting inreversing the polarity of induced EMF in L.

Therefore voltage across load is given by

. .,O OdI

V V L i e V V dt


43/120


A large capacitor C connected across the

load, will provide a continuous output voltage.

Diode Dprevents any current flow from

capacitor to the source.

Step up choppers are used for regenerative

braking of dc motors.


44/120


Expression For Output Voltage

Assume the average inductor current to be

during ON and OFF time of Chopper.

Voltage across inductor

Therefore energy stored in inductor

= . .

Where

When Chopper

period of chopper.

is ON

ON

ON

I

L V

V I t

t ON


45/120


(energy is supplied by inductor to load)

Voltage across

Energy supplied by inductor

where period of Chopper.

Neg

When Chopper

lecting losses, energy stored in inductor

is OFF

O

O OFF

OFF

L V V

L V V It

t OFF

L

= energy supplied by inductor L


46/120


WhereT = Chopping period or period

of switching.

ON O OFF

ON OFF

O

OFF

O

ON

VIt V V It

V t tV

t

TV V

T t


47/120


1

1

1

1

Where duty cyle

ON OFF

OON

O

ON

T t t

V Vt

T

V Vd

td

T


48/120


For variation of duty cycle ' ' in the

range of 0 1 the output voltage

will vary in the range

O

O

d

d V

V V


49/120


Performance Parameters

The thyristor requires a certain minimum time toturn ONand turn OFF.

Duty cycle d can be varied only between a min.

& max. value, limiting the min. and max. valueof 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.


50/120


Problem

A Chopper circuit is operating on TRC at a

frequency of 2 kHz on a 460 V supply. If the

load voltage is 350 volts, calculate the

conduction period of the thyristor in eachcycle.


51/120


3

460 V, = 350 V, f = 2 kHz

1Chopping period

10.5 sec

2 10

Output voltage

dc

ONdc

V V

T

f

T m

tV VT


52/120


3

Conduction period of thyristor

0.5 10 350

4600.38 msec

dc

ON

ON

ON

T V

t V

t

t


53/120


Problem

Input to the step up chopper is 200 V. The

output required is 600 V. If the conducting time

of thyristor is 200 sec. Compute Chopping frequency,

If the pulse width is halved for constant

frequency of operation, find the new outputvoltage.


54/120


6

200 , 200 , 600

600 200200 10

Solving for

300

ON dc

dc

ON

V V t s V V

TV V

T tT

T

T

T s


55/120


6

6

Chopping frequency

1

1 3.33300 10

Pulse width is halved

200 10100

2ON

fT

f KHz

t s


56/120


6

6

Frequency is constant

3.33

1300

Output voltage =

300 10200 300 Volts

300 100 10

ON

f KHz

T sf

TV

T t


57/120


Problem

A dc chopper has a resistive load of 20 and

input voltage VS= 220V. When chopper is ON,its voltage drop is 1.5 volts and chopping

frequency is 10 kHz. If the duty cycle is 80%,

determine the average output voltage and thechopper on time.


58/120


220 , 20 , 10

0.80

= Voltage drop across chopper = 1.5 voltsAverage output voltage

0.80 220 1.5 174.8 Volts

S

ON

ch

ONdc S ch

dc

V V R f kHz

td

T

V

t

V V VT

V


59/120


3

3

3

3

Chopper ON time,

1Chopping period,

1

0.1 10 secs 100 secs10 10

Chopper ON time,

0.80 0.1 10

0.08 10 80 secs

ON

ON

ON

ON

t dT

Tf

T

t dT

t

t


60/120


Problem

In a dc chopper, the average load current is 30

Amps, chopping frequency is 250 Hz, supply

voltage is 110 volts. Calculate the ON and OFF

periods of the chopper if the load resistance is2 ohms.


61/120


3

30 , 250 , 110 , 2

1 1Chopping period, 4 10 4 msecs

250

&

30 20.545

110

dc

dcdc dc

dc

dc

I Amps f Hz V V R

Tf

VI V dVR

dVI

RI R

dV


62/120


3

3 3

3

Chopper ON period,

0.545 4 10 2.18 msecs

Chopper OFF period,

4 10 2.18 10

1.82 10 1.82 msec

ON

OFF ON

OFF

OFF

t dT

t T t

t

t


63/120


A dc chopper in figure has a resistive load of R= 10 and input voltage of V = 200 V. When

chopper is ON, its voltage drop is 2 V and the

chopping frequency is 1 kHz. If the duty cycle is

60%, determine


RMS value of output voltage

Effective input resistance of chopper

Chopper efficiency.


64/120


V

i0Chopper

+

R v0

200 , 10 , 2

0.60, 1 .

chV V R Chopper voltage drop V V

d f kHz


65/120



0.60 200 2 118.8 VoltsRMS value of output voltage

0.6 200 2 153.37 Volts

dc ch

dc

O ch

O

V d V V

V

V d V V

V


66/120


22

0

0 0

Effective input resistance of chopper is

118.811.88 Amps

10200

16.8311.88

Output power is

1 1

i

S dc

dcdc

i

S dc

dT dT

ch

O

V VR I I

VI

RV V

RI I

V VvP dt dt

T R T R


67/120


2

2

0

0

0.6 200 22352.24 watts

10

Input power,

1

1

ch

O

O

dT

i O

dT

ch

O

d V VP

R

P

P Vi dtT

V V VP dt

T R


68/120


0.6 200 200 22376 watts

10

Chopper efficiency,

100

2352.24100 99%

2376

ch

O

O

O

i

dV V V P

R

P

P

P


69/120


Problem

A chopper is supplying an inductive load with a

free-wheeling diode. The load inductance is 5 H

and resistance is 10.. The input voltage to the

chopper is 200 volts and the chopper is operatingat a frequency of 1000 Hz. If the ON/OFF time

ratio is 2:3. Calculate

Maximum and minimum values of load currentin one cycle of chopper operation.

Average load current


70/120


5 , 10 , 1000 ,

200 , : 2 :3Chopping period,

1 1

1 msecs1000

2

32

3

ON OFF

ON

OFF

ON OFF

L H R f Hz

V V t t

T f

t

t

t t


71/120


3

23

5

3

3

53

1 10 0.6 msec5

ON OFF

OFF OFF

OFF

OFF

T t t

T t t

T t

t T

T


72/120


3

3

3

max

1 0.6 10 0.4 msecDuty cycle,

0.4 10

0.41 10

Maximum value of load current is given by

1

1

ON OFF

ON

ON

dRT

L

RT

L

t T t

t

t

d T

V e EI

R Re


73/120


3

3

max

0.4 10 1 10

5

max 10 1 10

5

Since there is no voltage source in

the load circuit, E = 0

1

1

200 110

1

dRT

L

RTL

V eI

R e

eI

e


74/120


75/120

75


3

3

0.4 10 1 10

5

min 10 1 10

5

max min

200 17.995 A10

1

Average load current

2

8.0047 7.9958 A

2

dc

dc

eI

e

I II

I


76/120

76


Problem

A chopper feeding on RL load is shown infigure, with V = 200 V, R = 5, L = 5 mH, f

= 1 kHz, d = 0.5 and E = 0 V. Calculate

Maximum and minimum values of load

current.

Average value of load current.

RMS load current.

Effective input resistance as seen by source.

RMS chopper current.


77/120

77


3

3

V = 200 V, R = 5 , L = 5 mH,

f = 1kHz, d = 0.5, E = 0

Chopping period is

1 11 10 secs

1 10T

f

i0

v0

Chopper

R

LFWD

E

+


78/120

78


3

3

3

3

max

0.5 5 1 10

5 10

max 5 1 10

5 10

0.5

max 1

Maximum value of load current is given by

1

1

200 10

51

140 24.9 A

1

dRT

L

RT

L

V e EI

R Re

eI

e

eI

e


79/120

79


3

3

3

3

min

0.5 5 1 105 10

min 5 1 10

5 10

0.5

min 1

Minimum value of load current is given by

1

1

200 10

51

140 15.1 A

1

dRT

L

RT

L

V e EIR R

e

eI

e

eI

e


80/120

80


1 2

12 2

max min2

min min max min

Average value of load current is

2

for linear variation of currents

24.9 15.1 20 A2

RMS load current is given by

3

dc

dc

O RMS

I II

I

I II I I I I


81/120

81


12 2

2

1

2

24.9 15.115.1 15.1 24.9 15.1

3

96.04228.01 147.98 20.2 A

3

RMS chopper current is given by

0.5 20.2 14.28 A

O RMS

O RMS

ch O RMS

I

I

I d I


82/120

82


Effective input resistance is

= Average source current

0.5 20 10 A

Therefore effective input resistance is

20020

10

i

S

S

S dc

S

i

S

VRI

I

I dI

I

VR

I

Cl ifi i Of Ch


83/120

Classification Of Choppers

Choppers are classified as

Class A Chopper

Class B Chopper

Class C Chopper

Class D Chopper

Class E Chopper

Cl A Ch


84/120

Class A Chopper

V

Chopper

FWD

+

v0

v0

i0

i0

L

OAD

V


85/120

When chopper is ON,supply voltage Visconnected across the load.

When chopper is OFF, vO= 0 and the loadcurrent continues to flow in the same directionthrough the FWD.

The average values of output voltage andcurrent are always positive.

Class A Chopper is a first quadrant chopper .


86/120

Class A Chopperis a step-down chopper in

which power always flows form source to load.

It is used to control the speed of dc motor.

The output current equations obtained in step

down chopper with R-Lload can be used to

study the performance of Class A Chopper.

i


87/120

Output current

Thyristorgate pulse

Output voltage

ig

i0

v0

t

t

ttON

T

CH ON

FWD Conducts

Cl B Ch


88/120

Class B Chopper

V

Chopper

+

v0

v0

i0

i0

L

E

R

D


89/120

When chopper is ON, Edrives a currentthrough L and R in a direction opposite to thatshown in figure.

During the ON period of the chopper, theinductance Lstores energy.

When Chopper is OFF, diode Dconducts, and

part of the energy stored in inductor Lisreturned to the supply.


90/120

Average output voltage is positive.

Average output current is negative.

Therefore Class B Chopperoperates in secondquadrant.

In this chopper, power flows from load tosource.

Class B Chopperis used for regenerativebraking of dc motor.

Class B Chopperis a step-up chopper.

Thyristorig


91/120

Output current

Dconducts Chopper

conducts

Thyristorgate pulse

Output voltage

i0

v0

t

t

t

Imin

Imax

T

tONtOFF


92/120

Expression for Output Current


93/120

min

For the initial condition i.e.,

During the interval diode 'D' conduc

at 0

The solution of the ab

ts

voltage equation

ove equation is obtainedalong similar lines as in s

is given by

OO

O

LdiV Ri E

dt

i t I t

tep-down chopper

with R-L load


94/120

min

max

max min

During the interval chopper is ON voltage

equation is g

1 0

At

1

0

iven by

OFF OFF

R Rt t

L LO OFF

OFF O

R Rt t

L L

OO

V Ei t e I e t t

Rt t i t I

V EI e I eR

LdiRi E

dt


95/120

max

max

min

min max

Redefining the time origin, at 0

The solution for the stated initial condition is

1 0

At

1ON ON

O

R Rt t

L LO ON

ON O

R Rt t

L L

t i t I

Ei t I e e t t R

t t i t I

EI I e e

R

Class C Chopper


96/120

Class C Chopper

V

Chopper

+

v0

D1

D2CH2

CH1

v0i0

i0

L

E

R


97/120

Class C Chopperis a combination of Class Aand Class B Choppers.

For first quadrant operation, CH1is ON or D2conducts.

For second quadrant operation, CH2 is ON orD1conducts.

When CH1is ON, the load current is positive. The output voltage is equal to V & the load

receives power from the source.

When CH1is turned OFF, energy stored ininductance Lforces current to flow throughthe diode D2 and the output voltage is zero.


98/120

Current continues to flow in positive direction.

When CH2is triggered, the voltage Eforcescurrent to flow in opposite direction through Land CH2.

The output voltage is zero.

On turning OFF CH2, the energy stored in theinductance drives current through diode D1

and the supply Output voltage is V, the input current becomes

negative and power flows from load to source.


99/120

Average output voltage is positive

Average output current can take both positiveand negative values.

Choppers CH1& CH2 should not be turned ON

simultaneously as it would result in shortcircuiting the supply.

Class C Choppercan be used both for dc motorcontrol and regenerative braking of dc motor.

Class C Choppercan be used as a step-up orstep-down chopper.

Gate pulseof CH

ig1


100/120

Gate pulseof CH2

of CH1

Output current

Output voltage

ig2

i0

V0

t

t

t

t

D1 D1D2 D2CH1 CH2 CH1 CH2ON ON ON ON

Class D Chopper


101/120

Class D Chopper

V+ v0

D2

D1 CH2

CH1

v0

i0

L ER i0


102/120

Class D is a two quadrant chopper.

When both CH1 and CH2are triggered

simultaneously, the output voltage vO= Vand

output current flows through the load. When CH1 and CH2 are turned OFF, the load

current continues to flow in the same direction

through load, D1and D2, due to the energystored in the inductor L.

Output voltage vO= - V.


103/120

Average load voltage is positive if chopper ONtime is more than the OFF time

Average output voltage becomes negative if

tON < tOFF. Hence the direction of load current is always

positive but load voltage can be positive or

negative.

Gate pulseof CH1

ig1


104/120

Gate pulseof CH2

Output current

Output voltage

Average v0

ig2

i0

v0

V

t

t

t

t

CH ,CH

ON1 2 D1,D2 Conducting

Gate pulseof CH1

ig1


105/120

Gate pulseof CH2

Output current

Output voltage

Average v0

ig2

i0

v0

V

t

t

t

t

CH

CH1

2

D , D1 2

Class E Chopper


106/120

Class E Chopper

V

v0

i0L ER

CH2 CH4D2 D4

D1 D3CH1 CH3

+


107/120

Four Quadrant Operation

v0

i0

CH - CH ON

CH - D Conducts1 4

4 2

D D2 3- ConductsCH - D Conducts4 2

CH - CH ONCH - D Conducts

3 2

2 4

CH - D Conducts

D - D Conducts2 4

1 4


108/120


109/120


110/120

Class E is a four quadrant chopper

When CH1 and CH4 are triggered, output

current iO flows in positive direction through

CH1 and CH4, and with output voltage vO= V. This gives the first quadrant operation.

When both CH1 and CH4are OFF, the energy

stored in the inductor L drives iOthrough D2and D3 in the same direction, but output

voltage vO= -V.


111/120

Therefore the chopper operates in the

fourth quadrant. When CH2 and CH3are triggered, the load

current iO flows in opposite direction & output

voltage vO= -V.

Since both iO andvO are negative, the chopper

operates in third quadrant.


112/120

When both CH2 and CH3are OFF, the load

current iOcontinues to flow in the same

direction D1andD4and the output voltage

vO= V.

Therefore the chopper operates in second

quadrant as vO is positive but iOis negative.

Eff Of S &


113/120

Effect Of Source &

Load Inductance

The source inductance should be as small as

possible to limit the transient voltage. Also source inductance may cause

commutation problem for the chopper.

Usually an input filter is used to overcome theproblem of source inductance.


114/120

The load ripple current is inversely

proportional to load inductance and chopping

frequency. Peak load current depends on load inductance.

To limit the load ripple current, a smoothing

inductor is connected in series with the load.


115/120

Problem

For the first quadrant chopper shown in figure,express the following variables as functions of V,

R and duty cycle d in case load is resistive.

Average output voltage and current Output current at the instant of commutation

Average and RMS free wheeling diode current.

RMS value of output voltage RMS and average thyristor currents.


116/120

V

i0

v0

Chopper

FWD

+

LOAD


117/120

Average output voltage,

Average output current,

The thyristor is commutated at the instant

output current at the instant of commutation is

since V is the output v

ONdc

dc

dc

ON

tV V dV T

V dV

I R R

t t

V

R

oltage at that instant.


118/120

2

00

Free wheeling diode (FWD) will never

conduct in a resistive load.

Average & RMS free wheeling diode

currents are zero.

1

But during

ONt

O RMS

O ON

V v dt T

v V t


119/120

2

0

2

1

Where duty cycle,

ONt

O RMS

ON

O RMS

O RMS

ON

V V dt T

t

V V T

V dV

td

T

RMS value of thyristor current


120/120

RMS value of thyristor current

= RMS value of load current

Average value of thyristor current

= Average value of load current

O RMSV

R

dVR

dV

Power Electronics_DC Choppers New

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