DC-Choppers

Power Electronics by Prof. M. Madhusudhan Rao 11

DC Choppers

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

C hopper

• 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.

tO F F

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

ON OFF

or chopping period.

1 Freq. of chopper switching or chopping freq.f

Average Output Voltage

duty cycle

ON OFF

tV V V d

tbut d

Average Output Current

RMS value of output voltage

I dR T R

V v dtT

But during ,

Therefore RMS output voltage

ONO ON

V V dtT

tVV t V

Output power

Effective input resistance of chopper

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

tO N tO F F

tO F F

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

tO F F

Step-down ChopperWith R-L Load

C hopper

• 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.

O utpu tvo ltage

O utpu tcurrent

Im a x

tO F F

C ontinuouscurrent

O utpu tcurrent

D iscon tinuouscurrent

Expressions For Load Current

iO For Continuous Current Operation When

Chopper Is ON (0 t tON)

Taking Laplace Transform

At 0, initial current 0

diV i R L E

V ERI S L S I S i

IV EI S

RR SLS SLL

Taking Inverse Laplace Transform

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 t

V Ei t e I e

maxurrent is O ONi t I

When Chopper is OFF

When Chopper is OFF 0

Talking Laplace transform

Redefining time origin we have at 0,

initial current 0

diRi L E

ERI S L SI S i

Taking Inverse Laplace Transform

R Rt t

I EI S

R RS LS SL L

Ei t I e e

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

max min

From equation

To Find &

R Rt t

dRT dRT

V Ei t e I e

t t dT i t I

V EI e I e

From equation

R Rt t

OFF ON O

Ei t I e e

t t T t i t I

t t d T

min max

max min

Substituting for in equation

we get,

d RT d RT

dRT dRT

EI I e e

V EI e I e

V e EI

min max

max min

Substituting for in equation

we get,

is known as the steady state ripple.

d RT d RT

EI I e e

V e EI

max min

Therefore peak-to-peak ripple current

Average output voltage

Average output current

dc approx

min max

max minmin

Assuming load current varies linearly

from to instantaneous

load current is given by

. 0O ON

I ti I for t t dT

i I tdT

max minmin

2min max min2 2max min

RMS value of load current

I i dtdT

I I tI I dt

I I I tI II I t dt

dT dT dT

max min2min min max min

max minmin

RMS value of output current

RMS chopper current

I II I I I I

I i dtT

I II I t dt

max min2min min max min3

Effective input resistance is

CH O RMS

I II d I I I I

Average source currentS

Principle Of Step-up Chopper

C hopper

• 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

. ., O O

dIV V L i e V 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

during ON and OFF time of Chopper.

Voltage across inductor

Therefore energy stored in inductor

When Chopper

period of chopper.

(energy is supplied by inductor to load)

Voltage across

Energy supplied by inductor

where period of Chopper.

When Chopper

lecting losses, energy stored in inductor

is OFF

L V V It

= energy supplied by inductor L

T = Chopping period or period

of switching.

ON O OFF

ON OFFO

VIt V V It

V t tV

Where duty cyle

ON OFF

For variation of duty cycle ' ' in the

range of 0 1 the output voltage

will vary in the range O

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.

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 each cycle.

460 V, = 350 V, f = 2 kHz

1Chopping period

10.5 sec

Output voltage

Conduction period of thyristor

0.5 10 350

4600.38 msec

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 output voltage.

200 , 200 , 600

600 200200 10

Solving for

V V t s V V

Chopping frequency

300 10Pulse width is halved

200 10100

Frequency is constant

Output voltage =

300 10200 300 Volts

300 100 10

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 the chopper on time.

220 , 20 , 10

= Voltage drop across chopper = 1.5 volts

0.80 220 1.5 174.8 Volts

ONdc S ch

V V R f kHz

tV V V

Chopper ON time,

1Chopping period,

10.1 10 secs 100 μsecs

10 10Chopper ON time,

0.80 0.1 10

0.08 10 80 μsecs

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 is 2 ohms.

30 , 250 , 110 , 2

1 1Chopping period, 4 10 4 msecs

30 20.545

dcdc dc

I Amps f Hz V V R

VI V dV

Chopper ON period,

0.545 4 10 2.18 msecs

Chopper OFF period,

4 10 2.18 10

1.82 10 1.82 msec

OFF ON

• 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

– Average output voltage

– RMS value of output voltage

– Effective input resistance of chopper

– Chopper efficiency.

C hopper

200 , 10 , 2

0.60, 1 .chV V R Chopper voltage drop V V

d f kHz

0.60 200 2 118.8 Volts

RMS value of output voltage

0.6 200 2 153.37 Volts

V d V V

Effective input resistance of chopper is

118.811.88 Amps

16.8311.88

Output power is

dT dTch

V VvP dt dt

T R T R

0.6 200 22352.24 watts

10Input power,

d V VP

P Vi dtT

V V VP dt

0.6 200 200 22376 watts

10Chopper efficiency,

2352.24100 99%

dV V VP

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 operating at a frequency of 1000 Hz. If the ON/OFF time ratio is 2:3. Calculate – Maximum and minimum values of load current

in one cycle of chopper operation.– Average load current

5 , 10 , 1000 ,

200 , : 2 : 3

Chopping period,

1 11 msecs

ON OFF

L H R f Hz

V V t t

1 10 0.6 msec5

ON OFF

OFF OFF

1 0.6 10 0.4 msec

Duty cycle,

0.4 100.4

1 10Maximum value of load current is given by

ON OFF

V e EI

0.4 10 1 10

max 10 1 10

Since there is no voltage source in

the load circuit, E = 0

0.8 10

max 2 10

8.0047A

Minimum value of load current with E = 0

is given by

0.4 10 1 10

min 10 1 10

max min

200 17.995 A

Average load current

28.0047 7.995

Problem• A chopper feeding on RL load is shown in

figure, 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.

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

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

Chopping period is

1 11 10 secs

C hopper

0.5 5 1 10

max 5 1 10

Maximum value of load current is given by

200 10

140 24.9 A

V e EI

0.5 5 1 10

min 5 1 10

Minimum value of load current is given by

200 10

140 15.1 A

V e EI

max min2min min max min

Average value of load current is

2for linear variation of currents

24.9 15.120 A

2RMS load current is given by

I II I I I I

24.9 15.115.1 15.1 24.9 15.1

96.04228.01 147.98 20.2 A

RMS chopper current is given by

0.5 20.2 14.28 A

ch O RMS

Effective input resistance is

= Average source current

0.5 20 10 A

Therefore effective input resistance is

Classification Of Choppers

• Choppers are classified as – Class A Chopper– Class B Chopper– Class C Chopper– Class D Chopper– Class E Chopper

Class A Chopper

C hopper

Power Electronics by Prof. M. Madhusudhan Rao 8585Prof. T.K. Anantha Kumar, E&E Dept., MSRIT

• When chopper is ON, supply voltage V is connected across the load.

• When chopper is OFF, vO = 0 and the load current continues to flow in the same direction through the FWD.

• The average values of output voltage and current are always positive.

• Class A Chopper is a first quadrant chopper .

• Class A Chopper is 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-L load can be used to study the performance of Class A Chopper.

O utpu t cu rren t

Thyristo rgate pu lse

O utpu t vo ltage

C H O N

FW D C onduc ts

Class B Chopper

C hopper

• When chopper is ON, E drives a current through L and R in a direction opposite to that shown in figure.

• During the ON period of the chopper, the inductance L stores energy.

• When Chopper is OFF, diode D conducts, and part of the energy stored in inductor L is returned to the supply.

• Average output voltage is positive.• Average output current is negative. • Therefore Class B Chopper operates in second

quadrant.• In this chopper, power flows from load to

source.• Class B Chopper is used for regenerative

braking of dc motor.• Class B Chopper is a step-up chopper.

O utpu t cu rren t

D con d u cts C h o pp e r

con d u cts

Thyristo rgate pu lse

O utpu t vo ltage

tO NtO F F

Expression for Output Current

For the initial condition i.e.,

During the interval diode 'D' conduc

The solution of the ab

voltage equation

ove equation is obtained

along similar lines as in s

is given by

LdiV Ri E

i t I t

tep-down chopper

with R-L load

max min

During the interval chopper is ON voltage

equation is g

iven by

OFF OFF

R Rt t

L LO OFF

R Rt t

V Ei t e I e t t

t t i t I

V EI e I e

LdiRi E

min max

Redefining the time origin, at 0

The solution for the stated initial condition is

1ON ON

R Rt t

L LO ON

R Rt t

t i t I

Ei t I e e t t

t t i t I

EI I e e

Class C Chopper

C hopper

D 2C H 2

• Class C Chopper is a combination of Class A and Class B Choppers.

• For first quadrant operation, CH1 is ON or D2 conducts.

• For second quadrant operation, CH2 is ON or D1 conducts.

• When CH1 is ON, the load current is positive.• The output voltage is equal to ‘V’ & the load

receives power from the source. • When CH1 is turned OFF, energy stored in

inductance L forces current to flow through the diode D2 and the output voltage is zero.

• Current continues to flow in positive direction.• When CH2 is triggered, the voltage E forces

current to flow in opposite direction through L and CH2 .

• The output voltage is zero.• On turning OFF CH2 , the energy stored in the

inductance drives current through diode D1 and the supply

• Output voltage is V, the input current becomes negative and power flows from load to source.

• Average output voltage is positive• Average output current can take both positive

and negative values.• Choppers CH1 & CH2 should not be turned

ON simultaneously as it would result in short circuiting the supply.

• Class C Chopper can be used both for dc motor control and regenerative braking of dc motor.

• Class C Chopper can be used as a step-up or step-down chopper.

G ate pu lseof C H 2

O utput cu rren t

O utpu t vo ltage

D 1 D 1D 2 D 2C H 1 C H 2 C H 1 C H 2

O N O N O N O N

Class D Chopper

V+ v 0

D 1 C H 2

L ER i0

• Class D is a two quadrant chopper.

• When both CH1 and CH2 are triggered simultaneously, the output voltage vO = V and 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, D1 and D2 , due to the energy stored in the inductor L.

• Output voltage vO = - V .

• Average load voltage is positive if chopper ON time 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.

O utpu t curren t

O utpu t vo ltage

Average v 0

C H ,C HO N1 2 D 1,D 2 Conducting

O utpu t curren t

O utpu t vo ltage

Average v 0

C HC H

D , D1 2

Class E Chopper

i0L ER

C H 2 C H 4D 2 D 4

D 1 D 3C H 1 C H 3

Four Quadrant Operationv 0

C H - C H O NC H - D C onduc ts

D D2 3 - C onductsC H - D C onduc ts4 2

C H - C H O NC H - D C onduc ts

C H - D C onduc tsD - D C onducts

• 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 CH4 are OFF, the energy stored in the inductor L drives iO through D2 and D3 in the same direction, but output voltage vO = -V.

• Therefore the chopper operates in the fourth quadrant.

• When CH2 and CH3 are triggered, the load current iO flows in opposite direction & output voltage vO = -V.

• Since both iO and vO are negative, the chopper operates in third quadrant.

• When both CH2 and CH3 are OFF, the load current iO continues to flow in the same direction D1 and D4 and the output voltage vO = V.

• Therefore the chopper operates in second quadrant as vO is positive but iO is negative.

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 the problem of source inductance.

• 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.

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.

C hopper

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

tV V dV

R Rt t

oltage at that instant.

Free wheeling diode (FWD) will never

conduct in a resistive load.

Average & RMS free wheeling diode

currents are zero.

But during

V v dtT

Where duty cycle,

ONO RMS

V V dtT

RMS value of thyristor current

= RMS value of load current

Average value of thyristor current

= Average value of load current

O RMSV

Impulse Commutated Chopper

• Impulse commutated choppers are widely used in high power circuits where load fluctuation is not large.

• This chopper is also known as

– Parallel capacitor turn-off chopper

– Voltage commutated chopper

– Classical chopper.

• To start the circuit, capacitor ‘C’ is initially charged with polarity (with plate ‘a’ positive) by triggering the thyristor T2.

• Capacitor ‘C’ gets charged through VS, C, T2 and load.

• As the charging current decays to zero thyristor T2 will be turned-off.

• With capacitor charged with plate ‘a’ positive the circuit is ready for operation.

• Assume that the load current remains constant during the commutation process.

• For convenience the chopper operation is divided into five modes.– Mode-1

– Mode-2

– Mode-3

– Mode-4

– Mode-5

Mode-1 Operation

V C iC

• Thyristor T1 is fired at t = 0.

• The supply voltage comes across the load.

• Load current IL flows through T1 and load.

• At the same time capacitor discharges through T1, D1, L1, & ‘C’ and the capacitor reverses its voltage.

• This reverse voltage on capacitor is held constant by diode D1.

Capacitor Discharge Current

1Where

& Capacitor Voltage

Ci t V t

V t V t

Mode-2 Operation

• Thyristor T2 is now fired to commutate thyristor T1.

• When T2 is ON capacitor voltage reverse biases T1 and turns if off.

• The capacitor discharges through the load from –V to 0.

• Discharge time is known as circuit turn-off time.

Circuit turn-off time is given by

Where is load current.

t depends on load current, it must be designed

for the worst case condition which occur at the

maximum value of load current and mini

value of capacitor voltage.

• Capacitor recharges back to the supply voltage (with plate ‘a’ positive).

• This time is called the recharging time and is given by

• The total time required for the capacitor to discharge and recharge is called the commutation time and it is given by

r C dt t t

• At the end of Mode-2 capacitor has recharged to VS and the free wheeling diode starts conducting.

Mode-3 Operation

T 2V S

• FWD starts conducting and the load current decays.

• The energy stored in source inductance LS is transferred to capacitor.

• Hence capacitor charges to a voltage higher than supply voltage, T2 naturally turns off.

The instantaneous capacitor voltage is

SC S L S

LV t V I t

Mode-4 Operation

• Capacitor has been overcharged i.e. its voltage is above supply voltage.

• Capacitor starts discharging in reverse direction.

• Hence capacitor current becomes negative. • The capacitor discharges through LS, VS, FWD,

D1 and L. • When this current reduces to zero D1 will stop

conducting and the capacitor voltage will be same as the supply voltage

Mode-5 Operation

• Both thyristors are off and the load current flows through the FWD.

• This mode will end once thyristor T1 is fired.

C a p a c i to r C u rr e n tI L

I p C u r r e n t t h r o u g h T 1

Vo l ta g e a c r o s s T 1

O u tp u t Vo l t a g e

C a p a c i to r Vo l t a g e

V s c+ V

Disadvantages• A starting circuit is required and the starting circuit

should be such that it triggers thyristor T2 first.

• Load voltage jumps to almost twice the supply voltage when the commutation is initiated.

• The discharging and charging time of commutation capacitor are dependent on the load current and this limits high frequency operation, especially at low load current.

• Chopper cannot be tested without connecting load.

• Thyristor T1 has to carry load current as well as resonant current resulting in increasing its peak current rating.

DC-Choppers

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