power electronics by prof. m. madhusudhan rao 1 1 three phase controlled rectifiers

Power Electronics by Prof. M. Madhusudhan Rao 11

Three Phase Controlled Rectifiers


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.


• 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-Phase Half Wave Converter(3-Pulse Converter)

with RL Load

Continuous & ConstantLoad Current Operation


Vector Diagram of 3 Phase Supply Voltages

V A N

V C N

V B N

1 2 00

1 2 00

1 2 00 RN AN

YN BN

BN CN

v v

v v

v v


3 Phase Supply Voltage Equations

We deifine three line to neutral voltages

(3 phase voltages) as follows


0

0

0

sin ;

Max. Phase Voltage

2sin

3

sin 120

2sin

3

sin 120

sin 240

RN an m

m

YN bn m

m

BN cn m

m

m

v v V t

V

v v V t

V t

v v V t

V t

V t


van vbn vcn van


io=Ia

Constant Load Current

Ia

Ia

Each thyristor conducts for 2/3 (1200)


To Derive an Expression for the

Average Output Voltage of a 3-Phase Half Wave Converter

with RL Loadfor Continuous Load Current


01

02

03

0

306

5 150

6

7 270

6

2Each thytistor conducts for 120 or radians

3

T is triggered at t

T is triggered at t

T is triggered at t


5

6

6

If the reference phase voltage is

sin , the average or dc output

voltage for continuous load current is calculated

using the equation

3sin .

2

RN an m

dc m

v v V t

V V t d t


5

6

6

5

6

6

3sin .

2

3cos

2

3 5cos cos

2 6 6

mdc

mdc

mdc

VV t d t

VV t

VV


0 0

0

Note from the trigonometric relationship

cos cos .cos sin .sin

5 5cos cos sin sin

6 63

2co

cos 150 cos sin 150 sin3

2 cos 30

s .cos sin sin6 6

.cosm

dc

mdc

A

VV

B A B A B

VV

0sin 30 sin


0 0

0 0 0 0

0 0

0 0

0

0

0

0

0 0

Note: cos 1

cos 180 30 cos sin 180 30 sin3

2 cos 30 .cos sin 30 sin

cos 30 cos sin 30 sin3

2 cos 30 .cos sin 30 s

80 30 cos 30

sin 180 30 sin 30

in

mdc

mdc

VV

VV


032cos 30 cos

2

3 32 cos

2 2

3 3 33 cos cos

2 23

cos2

Where 3 Max. line to line supply voltage

mdc

mdc

m mdc

Lmdc

Lm m

VV

VV

V VV

VV

V V


max

The maximum average or dc output voltage is

obtained at a delay angle 0 and is given by

3 3

2Where is the peak phase voltage.

And the normalized average output voltage is

mdmdc

m

ddcn n

VV V

V

VV V

cosc

dmV


15 26

2 2

6

1

2

The rms value of output voltage is found by

using the equation

3sin .

2

and we obtain

1 33 cos 2

6 8

mO RMS

mO RMS

V V t d t

V V


3 Phase Half Wave Controlled Rectifier Output Voltage

Waveforms For RL Load at

Different Trigger Angles


0

0

300

300

600

600

900

900

1200

1200

1500

1500

1800

1800

2100

2100

2400

2400

2700

2700

3000

3000

3300

3300

3600

3600

3900

3900

4200

4200

V an

V 0

V 0

V an

= 300

= 600

V bn

V bn

V cn

V cn

t

t

=300

=600


030

060

090

0120

0150

0180

0210

0240

0270

0300

0330

0360

0390

0420

0

V 0

V an

= 900

V bn V cn

t

=900


3 Phase Half Wave Controlled Rectifier With

R Load and

RL Load with FWD


a a

b b

c c

RV 0

L

R V 0

+

T 1

T 2

T 3

n n

T 1

T 2

T 3


3 Phase Half Wave Controlled Rectifier Output Voltage

Waveforms For R Load or RL Load with FWD

atDifferent Trigger Angles


0

0

300

300

600

600

900

900

1200

1200

1500

1500

1800

1800

2100

2100

2400

2400

2700

2700

3000

3000

3300

3300

3600

3600

3900

3900

4200

4200

V s

V 0

V a n

= 0

= 1 5 0

V b n V c n

t

V a n V b n V c n

t

=00

=150


0

0

300

300

600

600

900

900

1200

1200

1500

1500

1800

1800

2100

2100

2400

2400

2700

2700

3000

3000

3300

3300

3600

3600

3900

3900

4200

4200

V 0

= 3 0 0

V a nV b n V c n

t

V 0

= 6 0 0

V a nV b n V c n

t

=300

=600


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


01

0 01

02

0 02

0

306

30 180 ;

sin

5 150

6

150 300 ;

sin 120

O an m

O bn m

T is triggered at t

T conducts from to

v v V t

T is triggered at t

T conducts from to

v v V t


03

0 03

0

0

7 270

6

270 420 ;

sin 240

sin 120

O cn m

m

T is triggered at t

T conducts from to

v v V t

V t


0

0

0

0

0

0

180

30

0 0

180

30

180

30

3.

2

sin ; for 30 to 180

3sin .

2

3sin .

2

dc O

O an m

dc m

mdc

V v d t

v v V t t

V V t d t

VV t d t


0

0

180

30

0 0

0

0

3cos

2

3cos180 cos 30

2

cos180 1, we get

31 cos 30

2

mdc

mdc

mdc

VV t

VV

VV


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 Phase Half Controlled Bridge Converter

(Semi Converter)with Highly Inductive Load &

Continuous Ripple free Load Current


Wave forms of 3 Phase Semiconverter for

> 600


0 0

1

3 phase semiconverter output ripple frequency of

output voltage is 3

The delay angle can be varied from 0 to

During the period

30 210

7, thyristor T is forward biased

6 6

Sf

t

t


1

1 1

If thyristor is triggered at ,6

& conduct together and the line to line voltage

appears across the load.

7At , becomes negative & FWD conducts.

6The load current contin

ac

ac m

T t

T D

v

t v D

1 1

ues to flow through FWD ;

and are turned off.mD

T D


1

2

1 2

If FWD is not used the would continue to

conduct until the thyristor is triggered at

5, and Free wheeling action would

6

be accomplished through & .

If the delay angle , e3

mD T

T

t

T D

ach thyristor conducts

2for and the FWD does not conduct.

3 mD


0

0

0

We deifine three line neutral voltages


sin ; Max. Phase Voltage

2sin sin 120

3

2sin sin 120

3

sin 240

RN an m m

YN bn m m

BN cn m m

m

v v V t V

v v V t V t

v v V t V t

V t

V

is the peak phase voltage of a wye-connected source.m


3 sin6

53 sin

6

3 sin2

3 sin6

RB ac an cn m

YR ba bn an m

BY cb cn bn m

RY ab an bn m

v v v v V t

v v v v V t

v v v v V t

v v v v V t


Wave forms of 3 Phase Semiconverter for

600


To derive an Expression for the

Average Output Voltage of 3 Phase Semiconverter

for > / 3 and Discontinuous Output Voltage


76

6

76

6

For and discontinuous output voltage:3

the Average output voltage is found from

3.

2

33 sin

2 6

dc ac

dc m

V v d t

V V t d t


max

3 31 cos

23

1 cos2

3 Max. value of line-to-line supply voltage

The maximum average output voltage that occurs at

a delay angle of 0 is

3 3

mdc

mLdc

mL m

mdmdc

VV

VV

V V

VV V


17 26

2

6

The normalized average output voltage is

0.5 1 cos

The rms output voltage is found from

3.

2

dcn

dm

acO rms

VV

V

V v d t


17 26

2 2

6

1

2

33 sin

2 6

3 sin 23

4 2

mO rms

mO rms

V V t d t

V V


Average or DC Output Voltage of a

3-Phase Semiconverter for / 3,

and Continuous Output Voltage


562

6 2

For , and continuous output voltage3

3. .

2

3 31 cos

2

dc ab ac

mdc

V v d t v d t

VV


15 262

2 2

6 2

1

22

0.5 1 cos

RMS value of o/p voltage is calculated by using

the equation

3. .

2

3 23 3 cos

4 3

dcn

dm

ab acO rms

mO rms

VV

V

V v d t v d t

V V


Three Phase Full Converter

• 3 Phase Fully Controlled Full Wave Bridge Converter.

• Known as a 6-pulse converter.

• Used in industrial applications up to 120kW output power.

• Two quadrant operation is possible.


• The thyristors are triggered at an interval of / 3.

• The frequency of output ripple voltage is 6fS.

• T1 is triggered at t = (/6 + ), T6 is already conducting when T1 is turned ON.

• During the interval (/6 + ) to (/2 + ), T1 and T6 conduct together & the output load voltage is equal to vab = (van – vbn)


• T2 is triggered at t = (/2 + ), T6 turns off naturally as it is reverse biased as soon as T2 is triggered.

• During the interval (/2 + ) to (5/6 + ), T1 and T2 conduct together & the output load voltage vO = vac = (van – vcn)

• Thyristors are numbered in the order in which they are triggered.

• The thyristor triggering sequence is 12, 23, 34, 45, 56, 61, 12, 23, 34, ………


0

0

0



sin ; Max. Phase Voltage

2sin sin 120

3

2sin sin 120

3

sin 240

RN an m m

YN bn m m

BN cn m m

m

v v V t V

v v V t V t

v v V t V t

V t

V

is the peak phase voltage of a wye-connected source.m


The corresponding line-to-line

supply voltages are

3 sin6

3 sin2

3 sin2

RY ab an bn m

YB bc bn cn m

BR ca cn an m

v v v v V t

v v v v V t

v v v v V t


To Derive An Expression For The Average Output Voltage Of

3-phase Full Converter With Highly Inductive Load Assuming Continuous And

Constant Load Current


2

6

6. ;

2

3 sin6

dc OO dc

O ab m

V V v d t

v v V t

The output load voltage consists of 6 voltage pulses over a period of 2 radians, Hence the average output voltage is calculated as


2

6

mL

max

33 sin .

6

3 3 3cos cos

Where V 3 Max. line-to-line supply vo

The maximum average dc output voltage is

obtained for a delay angle

ltage

3 3

0,

3

dc m

m mLdc

m

m mdmdc

V V t d t

V VV

V

V VV V

L


1

22

2

6

The normalized average dc output voltage is

cos

The rms value of the output voltage is found from

6.

2

dcdcn n

dm

OO rms

VV V

V

V v d t


1

22

2

6

1

22

2 2

6

1

2

6.

2

33 sin .

2 6

1 3 33 cos 2

2 4

abO rms

mO rms

mO rms

V v d t

V V t d t

V V


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.


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


0

0

0



sin ;

Max. Phase Voltage

2sin sin 120

3

2sin sin 120

3

sin 240

RN an m

m

YN bn m m

BN cn m m

m

v v V t

V

v v V t V t

v v V t V t

V t


The corresponding line-to-line

supply voltages are

3 sin6

3 sin2

3 sin2

RY ab an bn m

YB bc bn cn m

BR ca cn an m

v v v v V t

v v v v V t

v v v v V t


• 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

To obtain an Expression for the Circulating Current


1 2

3 sin sin6 2

3 cos6

The circulating current can be calculated by

using the equation

r O O ab bc

r m

r m

v v v v v

v V t t

v V t


1

1

6

6

1

max

1.

13 cos .

6

3sin sin

6

3

t

r rr

t

r mr

mr

r

mr

r

i t v d tL

i t V t d tL

Vi t t

L

Vi

L


Four Quadrant OperationConv. 2 Inverting

2 > 900

Conv. 2 Rectifying

2 < 900

Conv. 1 Rectifying

1 < 900

Conv. 1 Inverting

1 > 900


• There are two different modes of operation. Circulating current free

(non circulating) mode of operation Circulating current mode of operation


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


• 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.



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



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.


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


• 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.


• 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.

power electronics by prof. m. madhusudhan rao 1 1 three phase controlled rectifiers

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