rejinpaul - fatima michael college of engineering and …fmcet.in/eee/ee6503(r-13)_auque.pdf ·...

$: rejinpaul - Fatima Michael College of Engineering and …fmcet.in/EEE/EE6503(R-13)_auque.pdf · · 2015-08-31Important Parameters { Breakdown voltage. { On -resistance. Trade-off$
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EE2301 POWER ELECTRONICS

Unit-1

Introduction

• What are Power Semiconductor Devices (PSD)?

They are devices used as switches or rectifiers in

power electronic circuits

• What is the difference of PSD and low-power

semiconductor device?

Large voltage in the off state

High current capability in the on state

Classification

Fig. 1. The power semiconductor devices family

Important Parameters

• Breakdown voltage.

• On-resistance.

Trade-off between breakdown voltage and on-resistance.

• Rise and fall times for switching between on

and off states.

• Safe-operating area.

Power MOSFET: Structure

Power MOSFET has much higher current handling capability in

ampere range and drain to source blocking voltage(50-100V)

than other MOSFETs.

Fig.2.Repetitive pattern of the cells structure in power MOSFET

Power MOSFET: R-V Characteristics

An important parameter of a power MOSFET is on resistance:

L R R R R = + + , where R W C V V =

µ on S CH D ( ) - CH

n ox GS T

Fig. 3. Typical RDS versus ID characteristics of a MOSFET.

Thyristor: Structure • Thyristor is a general class of a four-layer pnpn

semiconducting device.

Fig.4 (a) The basic four-layer pnpn structure.

(b) Two two-transistor equivalent circuit.

Thyristor: I-V Characteristics

Three States:

Reverse Blocking

Forward Blocking

Forward Conducting

Fig.5 The current-voltage

characteristics of the pnpn device.

Applications

Power semiconductor devices have widespread applications:

Automotive

Alternator, Regulator, Ignition, stereo tape

Entertainment

Power supplies, stereo, radio and television

Appliance

Drill motors, Blenders, Mixers, Air conditioners and Heaters

Thyristors

• Most important type of power semiconductor device.

• Have the highest power handling capability.they have a rating of 1200V / 1500A with switching frequencies ranging from 1KHz to 20KHz.

• Is inherently a slow switching device compared to BJT or MOSFET.

• Used as a latching switch that can be turned on by the control terminal but cannot be turned off by the gate.

Different types of Thyristors

• Silicon Controlled Rectifier (SCR).

• TRIAC.

• DIAC.

• Gate Turn-Off Thyristor (GTO).

SCR

Symbol of

Silicon Controlled Rectifier

Structure

Cathode Gate

} 19 -3 19 -3 10 cm 10 cm 10 m µ n+ n+

} J3

} 17 -3

10 cm 30-100 m µ p-

J2

50-1000 m µ 13 14 -3 10 -5 x 10 cm n–

} J1 30-50 m µ 17 -3 p 10 cm

19 -3 10 cm p+

Anode

Device Operation

Simplified model of a

thyristor

V-I Characteristics

Effects of gate current

Two Transistor Model of SCR

Considering PNP transistor

of the equivalent circuit,

a a , , , I I I I = = = 1 E A C C 1 1

, I I I I = = CBO CBO B B

1 1

( ) ( ) a 1 1 I I I = - - - - - 1 B A CBO 1 1

Considering NPN transistor

of the equivalent circuit,

, , I I I I I I I I = = = = + C C B B E K A G

2 2 2

a I I I = + 2 C k CBO

2 2

( ) ( ) a 2 I I I I = + + - - - 2 C A G CBO 2 2

From the equivalent circuit,

we see that

I I = C B

2 1

I I I + + I a = 2 1 2 g CBO CBO

( ) a a 1 - + A

1 2

Case 1: When 0 I = g

I I + I = - + CBO CBO

( ) 1 2

a a 1 A

1 2

Case 2: When 0 I G

I I I + + I a = 2 1 2 g CBO CBO

( ) a a 1 - + A

1 2

Turn-on Characteristics

t t t = + o n d r

VAK

tC

tq

t

IA

Commutationdi dt Anode current

begins to

decrease Recovery Recombination

t1 t2 t3 t4 t5

Turn-off t

tq=device off time

Characteristi trr tgr

tc=circuit off time tq

c tc

Methods of Thyristor Turn-on

• Thermal Turn-on.

• Light.

• High Voltage.

• Gate Current.

• dv/dt.

Thyristor Types

• Phase-control Thyristors SCR’s . • Fast-switching Thyristors SCR’s . • Gate-turn-off Thyristors (GTOs).

• Bidirectional triode Thyristors (TRIACs).

• Reverse-conducting Thyristors (RCTs).

• Static induction Thyristors (SITHs).

• Light-activated silicon-controlled rectifiers (LASCRs).

• FET controlled Thyristors (FET-CTHs).

• MOS controlled Thyristors (MCTs).

Phase Control Thyristor • These are converter thyristors.

• The turn-off time tq is in the order of 50 to

100µsec.

• Used for low switching frequency.

• Commutation is natural commutation

• On state voltage drop is 1.15V for a 600V device.

• They use amplifying gate thyristor.

Fast Switching Thyristors

• Also called inverter thyristors.

• Used for high speed switching applications.

• Turn-off time tq in the range of 5 to 50µsec.

• On-state voltage drop of typically 1.7V for

2200A, 1800V thyristor.

• High dv/dt and high di/dt rating.

Bidirectional Triode Thyristors (TRIAC)

Mode-I Operation

(+) MT2

P1

N1

P2 Ig

MT2 Positive, N2

Gate Positive ( ) - MT1 G

V (+)

Ig

Mode-II Operation

(+) MT2

P1

Final Initial N1 conduction conduction

P2

MT2 Positive, N2 N3

Gate Negative ( ) - MT1 G

V

Ig

Mode-III Operation ( ) - MT2

N4

P1

N1

P2

MT2 Negative, N2

(+) G Gate Positive

MT1

(+)

Ig

Mode-IV Operation ( ) - MT2

N4

P1

N1

MT2 Negative, P2

N3

Gate Negative (+) G MT1

(-)

Ig

Triac Characteristics

BJT structure heavily doped ~ 10^15 provides the carriers lightly doped ~ 10^8 lightly doped ~ 10^6

note: this is a current of electrons (npn case) and so the conventional current flows from collector to emitter.

BJT characteristics

BJT modes of operation

Mode EBJ CBJ

Cutoff Reverse Reverse

Forward Forward Reverse

active

Reverse Reverse Forward

active

Saturation Forward Forward

BJT modes of operation

Cutoff: In cutoff, both junctions reverse biased. There is very little current flow, which corresponds to a logical "off", or an open switch. Forward-active (or simply, active): The emitter-base junction is forward biased and the base-collector junction is reverse biased. Most bipolar transistors are designed to afford the greatest common-emitter current gain, f in forward-active mode. If this is the case, the collector-emitter current is approximately proportional to the base current, but many times larger, for small base current variations. Reverse-active (or inverse-active or inverted): By reversing the biasing conditions of the forward-active region, a bipolar transistor goes into reverse-active mode. In this mode, the emitter and collector regions switch roles. Since most BJTs are designed to maximise current gain in forward-active mode, the f in inverted mode is several times smaller. This transistor mode is seldom used. The reverse bias breakdown voltage to the base may be an order of magnitude lower in this region. Saturation: With both junctions forward-biased, a BJT is in saturation mode and facilitates current conduction from the emitter to the collector. This mode corresponds to a logical "on", or a closed switch.

UNIT II

PHASE CONTROLLED

CONVERTERS

Phase-Control Converters

Single-Phase

Semiconverter

Three-Phase

Full converter

Dual converter

Semiconverter

Full converter

Dual converter


Semiconverter

..is a one-quadrant converter and it has one polarity

Full converter

..is a two-quadrant converter and the polarity of its

output can be either positive or negative.

However

the output current of full converter has

one polarity only

Dual converter ..can operate in four quadrants ; both the output

voltage and current can be either positive or negative


cos12

sin2

1 mmdc

VttdVV

Average Output Voltage

m

dm

VV Maximum

Output Voltage

cos15.0 dm

dcn

V

VVNormalizing

Output Voltage

2

2sin1

2sin

2

1 22

mmrms

VttdVV

RMS Output Voltage

If the converter has a purely resistive load of R and

the delay angle is , determine (a) the rectification efficiency

(b) the form factor FF (c) the ripple factor RF

and (d) the peak inverse voltage PIV of thyristor T1

2/


%27.203536.0

1592.0

3536.02

22

sin2

1

2

1592.0

2cos1

2sin

2

1

2

2

2

2

2

m

m

rms

dc

mm

rms

mdc

mmdc

V

V

V

V

VV

V

VV

VttdVV



(b) the form factor FF

(c) the ripple factor RF and (d) the peak inverse voltage PIV of thyristor T1

2/

221.21592.0

3536.0

m

m

dc

rms

V

V

V

VFF



(b) the form factor FF

(c) the ripple factor RF

and (d) the peak inverse voltage PIV of thyristor T1

2/

983.11221.21 22 FFRF

mVPIV

www.Vidyarthiplus.com Semiconverter

Single-Phase Semiconverter

ttdVV

VttdVV

mrms

mmdc

22 sin2

2

cos1sin2

2


Single-Phase Semiconverter (RL-load)

L

R

L

R

LLL

LL

eR

EeItiI

ERidt

diL

1

0

011

11

tL

R

SL

SL

SLL

eZ

V

R

EI

R

Et

Z

VI

tVERidt

diL

sin2

sin2

sin2

12

22

Mode 1

t0

Mode 2

tR

L 1tan 22LRZ


Single-Phase Semiconverter (RL-load)

RMS Current

for Thyristor

tdiI LR

2

22

1

RMS Current

for Thyristor

tdiI LA 2

2

1

RMS Output

Current

tditdiI LLrms

2

20

2

12

1

2

1

AVG Output

Current

tditdiIdc 2

01

2

1

2

1

The single-phase semiconverter has an RL load of

L = 6.5mH, R = 2.5 Ohm, and E = 10 V. The input

voltage is VS = 120 V(rms) at 60 Hz. Determine

(a) the load current IL0 at , and the load

current IL1 at , (b) the average thyristor current IA

(c) the rms thyristor current IR (d) the rms output current Irms

and (e) the average output current Idc

0t 60t


Single-Phase

Full Converter

Rectification

Mode

Inversion

Mode

Single-Phase Full Converter

2

sin2

2

cos2

sin2

2

22 mmrms

mmdc

VtdtVV

VtdtVV

Single-Phase Full Converter (RL-load)

tL

R

SL

SL e

Z

V

R

EI

R

Et

Z

VI

sin2

sin2

0

Mode 1 = Mode 2 R

L 1tan 22LRZ


Single-Phase Full Converter (RL-load)

RMS Current

for Thyristor

tdiI LR

2

2

1

RMS Current

for Thyristor

tdiI LA

2

1

RMS Output

Current RRRrms IIII 222

AVG Output

Current AAAdc IIII 2


Dual Converter


Single-Phase Dual Converter

High-Power Variable-Speed Drives

21

22

11

cos2

cos2

dcdc

mdc

mdc

VV

VV

VV


Three-Phase Semiconverter

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 & Constant Load Current Operation

Vector Diagram of 3 Phase Supply Voltages

VAN

VCN

VBN

1200

1200

1200 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 Load

for Continuous Load Current

0

1

0

2

0

3

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

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

.cos

mdc

mdc

A

VV

B A B A B

VV

0sin 30 sin

032cos 30 cos

2

3 32 cos

2 2

3 3 33 cos cos

2 2

3cos

2

Where 3 Max. line to line supply voltage

mdc

mdc

m mdc

Lmdc

Lm m

VV

VV

V VV

VV

V V

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

Van

V0

V0

Van

=300

=600

Vbn

Vbn

Vcn

Vcn

t

t

=300

=600

030

060

090

0120

0150

0180

0210

0240

0270

0300

0330

0360

0390

0420

0

V0

Van

=900

Vbn Vcn

t

=900

3 Phase Half Wave Controlled Rectifier With

R Load and

RL Load with FWD

a a

b b

c c

R

V0

L

R V0

+

T1

T2

T3

n n

T1

T2

T3

3 Phase Half Wave

Controlled Rectifier Output

Voltage Waveforms For R Load

or RL Load with FWD

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

Vs

V0

Van

=0

=150

Vbn Vcn

t

VanVbn Vcn

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

V0

=300

VanVbn Vcn

t

V0

=600

VanVbn Vcn

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

0

1

0 0

1

0

2

0 0

2

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

0

3

0 0

3

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

Q

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.

6

The 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.

3mD

0

0

0

We deifine three line neutral voltages

(3 phase voltages) as follows

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

To derive an

Expression for the


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

2

31 cos

2

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 2

62

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

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.

Four Quadrant Operation

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 tON tOFF

i0

V/R

Idc

t T

verage value of output or load voltage. V A = dc

verage value of output or load current. I A = dc

Time interval for which SCR conducts. t = ON

Time interval for which SCR is OFF. t = OFF

Period of switching T t t = + = or chopping period. ON OFF

1 Freq. of chopper switching or chopping freq. f T = =


t V V t t = ON

+ dc

ON OFF

t . V V V d = = ON

T dc

t duty cycle but d = = ON

t

Average Output Current

V I R = dc dc

t V V I d = = ON

R T R dc

RMS value of output voltage

t

V v dt = 1 ON 2

T O o

0

But during , t v V = ON o

Therefore RMS output voltage

1 t ON

V V dt = 2

T O

0

t V 2

. V t V = = ON

T T O ON

. V d V = O

Output power P V I = O O O

V But I R = O

O

Output power

V 2

P R = O O

dV 2

P = R O

Effective input resistance of chopper

V R I =

i

dc

R R d =

i

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 pe iod 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 f e uency f is va ied 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

V0 V FWD 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 inducto 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 T tOFF

t

Output i0

current Imax

Continuous current Imin

t Output i0 current

Discontinuous current

t

Expressions For

Load Current

iO For Continuous Current Operation When

Chopper Is ON (0 = t = tON)

i0 +

R

V0 V L

E

-

di V i R L E = + + O

dt O

Taking Laplace Transform

V E ( ) ( ) ( ) . 0 RI S L S I S i = + - + -

S S O O O

( ) At 0, initial current 0 t i I = = - min O

I V E - ( ) I S = + min

R R S O

+ LS S + L L

Taking Inverse Laplace Transform

R R V E - ( ) t t - -

1 i t e I e = - + L L

R min O

This expression is valid for 0 , t t = = ON

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

At the instant the chopper is turned off,

load c urrent is i t I = ( ) max O ON

When Chopper is OFF

i0

R

L

E

( ) When Chopper is OFF 0 t t = = OFF

di 0 Ri L E = + + O

dt O

Talking Laplace transform

( ) ( ) E ( ) 0 0 RI S L SI S i = + - + -

S O O O

Redefining time origin we have at 0, t =

initial current 0 i I = - ( ) max O

I E ( ) I S = - max

R R O

S + LS S + L L

Taking Inverse Laplace Transform

E R R

( ) t t - - 1 i t I e e = - - L L

R max O

The expression is valid for 0 , t t = = OFF

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

i t I = ( ) min O OFF

To Find & I I max min

From equation

R R V E - ( )

t t - -

1 i t e I e = - + L L

R min O

( ) At , t t dT i t I = = = max ON O

V E - dRT dRT - -

1 I e I e = - + L L

R max min

From equation

E R R

( ) t t - - 1 i t I e e = - - L L

R max O

( ) At , t t T t i t I = = - = min OFF ON O

( ) 1 t t d T = = - OFF

( ) ( ) E 1 1 d RT d RT - - - -

1 I I e e = - - L L

R min max

Substituting for in equation I min

V E - dRT dRT - -

1 I e I e = - + L L

R max min

we get,

dRT -

1 V e E - L

I R = - R max RT

- 1 e - L

Substituting for in equation I max

( ) ( ) E 1 1 d RT d RT - - - -

1 I I e e = - - L L

R min max

we get,

dRT

1 V e E - L

I R = - R min RT

1 e - L

( ) is known as the steady state ripple. I I - max min

Therefore peak-to-peak ripple current

I I I = - max min

Average output voltage

. V d V = dc

Average output current

I I + I = max min

( ) 2 dc approx

Assuming load current varies linearly

from to instantaneous I I min max

load current is given by

( ) . 0 I t ( ) i I for t t dT = + = =

dT min O ON

I I - i I t = + max min

dT min O

RMS value of load current

1 dT

I i dt = 2 ( ) dT 0 O RMS

0

( ) 2 I I t - 1 dT

I I dt = + max min ( ) dT dT min O RMS

0

( ) 2 I I I t - 1 I I - 2 dT

I I t dt = + + min max min 2 2 max min ( ) dT dT dT min O RMS

0

RMS value of output current

( ) I I - 2 2

( I I I I I = + + - ) 1 max min 2

( ) 3 min min max min O RMS

RMS chopper current

1 dT

I i dt = 2

T 0 CH

0

2 I I - 1 dT

I I t dt = + max min

T dT min CH

0

1

( ) I I - 2 2

( ) I d I I I I = + + - max min 2

3 min min max min CH

I d I = ( ) CH O RMS

Effective input resistance is

V R I =

i

S

Where

Average source current I = S

I dI = S dc

V R dI =

i

dc

Principle Of Step-up Chopper

L I D

+ + -

L O C V VO A D

Chopper

-

• 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 inducto cu ent I ises 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 . ., V V L i e V V = + >

dt O O

• A la ge capacito C connected ac oss 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. I

When Chopper is ON

Voltage across inductor L V =

Therefore energy stored in inductor

= . . V I t ON

Where period of chopper. t ON = ON

When Chopper is OFF

(energy is supplied by inductor to load)

Voltage across L V V = - O

( ) Energy supplied by inductor L V V It = - O OFF

where period of Chopper. t OFF = OFF

Neg lecting losses, energy stored in inductor

L = energy supplied by inductor L

( ) VIt V V It = - ON O OFF

[ ] V t t + V = ON OFF

t O

OFF

T V V T t =

- O

ON

Where

T = Chopping period or period

of switching.

T t t = + ON OFF

1 V V t =

O

1 - ON

T

1 V V d = -

1 O

t Where duty cyle d T = = ON

For variation of duty cycle ' ' in the d

range of 0 1 the output voltage d V < < O

will vary in the range V V < < 8 O

INTRODUCTION

AC voltage controllers are thyristor based devices which convert fixed alternating voltage directly to variable alternating voltage without change in frequency.

Using these controllers, rms value of the voltage across the load is steplessly varied from a maximum value to zero.

The simplest way to control AC voltage to the load is by using AC switch (bidirectional).

The bi-directional conducting property can be achieved by simply connecting two unidirectional thyristors in inverse parallel to each other.

AC voltage controllers are naturally commutated. 1

AC POWER CONTROL

Control of AC voltage controllers is of two

kinds.

1. On-Off Control (Integral Cycle Control)

2. Phase Control

2

Single Phase AC voltage Controller

1- On-Off Control (Integral Cycle Control)

The load power can be controlled by connecting the source to

the load for few complete cycles then disconnecting the

source from the load for another number of cycles, and

repeating the switching cycle.

Suitable for systems with large time constants.

Average power to the load can be varied from 0% through

100%

Integral cycle control finds applications in heating loads and

for motor speed control.

(In industry, there are several applications in which mechanical time constant

or thermal time constant is of the order of several seconds. For example,

mechanical time constant for many of the speed-control drives, or thermal

time constants for most of the heating loads is usually quite high. For such

applications, almost no variation in speed or temperature will be noticed if

control is achieved connecting the load to source for some on cycles and then

disconnecting the load for some off cycles.)

3

4

For resistive load

Voltage

across thyristors

2 2

1 1

T

T

Average load power is given by:

Po(avg.) = Vi² TON = Vi² d = Po(max) d

RT R

RMS value of output voltage is:

Vo= Vm √(TON /T) = Vi √d

√2

Ratio of on time to total cycle time controls

average load power as well as rms output voltage.

5

Power factor is:

PF=√(TON/T) = √d Source current is always in time phase with source voltage.

This does not mean that integral cycle control circuit

operates at unity power factor- for part of time, the source

current is not present at all and therefore is not in phase

with source voltage.

6

d

PF=√d

2- AC Phase Control Phase control is kind in which thyristors are fired once every

cycle and the instant of firing can be delayed from the zero

crossing. By this, only a part of the voltage waveform appears

across the load, providing voltage control. The load current

appears in pulses, the zero crossing of which can be used for

turn-off of the thyristors.

Suitable for loads with short time constants.

Firing instants of thyristors are 180° apart, each occuring in

its respective half cycle.

By controlling this instant of firing, the effective voltage

occuring across the load can be varied.

As the two thyristors have firing pulses delayed by 180° , the

AC current pulses are periodic and symmetrical and there is

no DC current component. The load voltage also does not have

any DC component.

7

8

Single-phase AC voltage controller with resistive load

Load power can be

varied by changing α

over the full range from zero to 180°

9

RMS value of output voltage is:

RMS value of output current is:

Output power is:

Po(avg.) = I²o(RMS) (R) Or V²o(RMS) /R

Power factor is given by:

Power factor is unity when firing angle (α) is zero; it becomes

progressively smaller as α increases, becoming approximately zero for α=180°

10

Variation of output voltage and power

With delay angle for resistive load

11

Single-phase AC voltage controller with inductive (RL) load

CYCLOCONVERTERS

12

INTRODUCTION Cycloconverter is frequency changer that converts AC power at one input

frequency to AC output power at a different frequency.

Variable frequency output can be obtained by AC DC AC using phase-

controlled converters (rectifier followed by inverter). This is two stage

frequency conversion.

Single-stage frequency conversion is called cycloconversion.

Cycloconversion can be anyone of following:

1- conversion of variable frequency to fixed one (aircraft or shipboard power

supplies or wind generators)

2- conversion of fixed frequency to a variable one (AC motor speed control)

Cycloconverters can be step-up or step-down

For efficient operation, cycloconverters are usually operated in frequency

range of zero to less than one-third the source frequency.

13

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B.E. / B.Tech. Degree Examination, April / May 2011

Sixth Semester

Electrical and Electronics Engineering

EE 2351 – Power System Analysis

(Regulation 2008)

Time: Three hours Maximum: 100 marks

Answer all questions

Part A – (10 × 2 = 20 marks)

1. Draw a simple per-phase model for a cylindrical rotor synchronous machine?

2. What are the advantages of per unit system?

3. What is Jacobian matrix?

4. What is a slack bus?

5. Mention the objectives of short circuit analysis.

6. Write down the balanced and unbalanced faults occurring in a power system.

7. What is sequence network?

8. Write the symmetrical components of a three phase system?

9. Define critical clearing angle.

10. Write swing equation.

Part B – (5 × 16 = 80 marks)

11. (a) (i) With the help of single line diagram, explain the basic components of a power system. (8)

(ii) Write detailed notes about the per-phase model of a three phase transformer. (8)

(OR)

(b) Draw the impedance diagram for the electric power system shown in given figure showing all

impedance in per unit on a 100 MVA base.

Choose 20 KV as the voltage base for generator. The tree-phase power and line-lie ratings are given

below. (16)

Generator G1: 90 MVA 20 KV X = 9 %

Transformer T1: 80 MVA 20 / 200 KV X = 16 %

Transformer T2: 80 MVA 200 / 20 KV X = 20 %

Generator G2: 90 MVA 18 KV X = 9 %

Line: 200 KV X = 120

Load: 200 KV, S = 48 MW + j64 MVAr

12 (a) With neat flow chart explain the computational procedure for load flow solution using fast

decoupled method when the system contains all types of buses.

(OR)

(b) Explain the step by step computational procedure for Gauss-Seidel method of load flow studies.

13 (a) Explain symmetrical fault analysis using Zbus matrix with eat flow chart.

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(OR)

(b) A 11 KV, 100 MVA alternator having a sub-transient reactance of 0.25 p.u is supplying a 50

MVA motor having a sub-transient reactance of 0.2 p.u through a transmission line. The line

reactance is 0.05 p.u on a base of 100 MVA. The motor is drawing 40 MW at 0.8 p.f leading with a

terminal voltage of 10.95 KV when a 3-phase fault occurs at the generator terminals. Calculate the

total current in generator and motor under fault condition.

14. (a) What are the assumptions to be made in short circuit studies? Deduces and thaw the

sequence network for a line fault at the terminal of an unloaded generator.

(OR)

(b) Two 11 KV, 20 MVA, three phase, star connected generator operate in parallel as shown in

given figure the positive, negative and zero sequence reactances of each being, respectively, j0.18,

j0.15, j0.10 p.u. The star point of one of the generators is isolated and that of the other is earthed

through a 2.0 O resistor. A single line to ground fault occurs at the terminals of one of the

generators.

Estimate (i) The fault current

(ii) Current in grounding resistor, and

(iii) The voltage across grounding resistor.

15. (a) Describe the Runge-Kutta method of solution of swing equation for multi-machine systems.

(OR)

(b) Derive an expression for the critical clearing angle and clearing time.

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