III B. Tech I semester (JNTUH-R15) - iare.ac.in PPT.pdf•GATI . 4 Thyristor/Triac SCR1 2N3668 MT1 ... involved, and are often used ... The process of turning off an SCR is called

1

III B. Tech I semester (JNTUH-R15)

Prepared

By

Mr. S. Srikanth, Assistant Professor

ELECTRICAL AND ELECTRONICS ENGINEERING

INSTITUTE OF AERONAUTICAL ENGINEERING (AUTONOMOUS)

DUNDIGAL, HYDERABAD – 500 043

2

Power

Electronics (A50220)

3

Unit-I Power Semiconductor Devices &

Commutation Circuits

• Diodes

• Transistors

– Power BJTs

– Power MOSFETs

– Insulated-Gate BJT

• IGBT

– Static Induction

Transistors

• SITs

• Thyristors

– Force-Commutated

– Line-Commutated

– Gate Turn Off--GTO

– Reverse-Conducting

• RCT

– Gate-Assisted Turn-

off

• GATI

4

Thyristor/Triac

SCR1

2N3668

MT1

2N6346

5

Power Electronic Circuits

• Diode Rectifiers (AC to Fixed DC)

• AC-DC Converters (Controlled Rectifiers)

• AC-AC Converters (AC Voltage Controllers)

• DC-DC Converters (DC Choppers)

• DC-AC Converters (Inverters)

• Static Switches

SCR / Thyristor

• Circuit Symbol and Terminal Identification

SCR

2N3668

ANODE

CATHODE

GATE

6

SCR / Thyristor

• Anode and Cathode

terminals as

conventional pn

junction diode

• Gate terminal for a

controlling input signal

SCR

2N3668

ANODE

CATHODE

GATE

7

SCR/ Thyristor

• An SCR (Thyristor) is a “controlled”

rectifier (diode)

• Control the conduction under forward bias

by applying a current into the Gate terminal

• Under reverse bias, looks like conventional

pn junction diode

8

SCR / Thyristor

• 4-layer (pnpn) device

• Anode, Cathode as for a

conventional pn

junction diode

• Cathode Gate brought

out for controlling input

P

N

P

N

Anod

e

Cathod

e

Gate

9

Equivalent Circuit

Q2

BJT_NPN_VIRTUAL

Q1

BJT_PNP_VIRTUAL

ANODE

CATHODE

GATE

P

N

P

N

P

N

CATHOD

E

ANODE

GAT

E

10

Apply Biasing

With the Gate terminal OPEN,

both transistors are OFF. As

the applied voltage increases,

there will be a “breakdown”

that causes both transistors to

conduct (saturate) making IF >

0 and VAK = 0.

VBreakdown = VBR(F)

I

F

IC2=I

B1

I

F

IC1 =

IB2

Q2

BJT_NPN_VIRTUAL

Q1

BJT_PNP_VIRTUAL

ANODE (A)

CATHODE (K)

GATE (G)

Variable

50V

11

Volt-Ampere Characteristic

IF

VAK VBR(

F)

IH Holding

Current

Breakdown Voltage 12

Apply a Gate Current

Q2

BJT_NPN_VIRTUAL

Q1

BJT_PNP_VIRTUAL

ANODE (A)

CATHODE (K)

GATE (G)

Variable

50V

I

F

I

F

IB2

VG

For 0 < VAK < VBR(F),

Turn Q2 ON by applying a

current into the Gate

This causes Q1 to turn ON, and

eventually both transistors

SATURATE

VAK = VCEsat + VBEsat

If the Gate pulse is removed,

Q1 and Q2 still stay ON!

IC2 =

IB1

13

How do you turn it OFF?

• Cause the forward current to fall below the

value if the “holding” current, IH

• Reverse bias the device

14

When the anode is at a positive potential VAK with respect to the cathode with no voltage applied at the gate, junctions J1 and J3 are forward biased, while junction J2 is reverse biased. As J2 is reverse biased, no conduction takes place.

Now if VAK is increased beyond the breakdown voltage VBO of the thyristor, avalanche breakdown of J2 takes place and the thyristor starts conducting.

If a positive potential VG is applied at the gate terminal with respect to the cathode, the breakdown of the junction J2 occurs at a lower value of VAK. By selecting an appropriate value of VG, the thyristor can be switched into the on state suddenly.

Characteristics of thyristors

15

Reverse breakdown voltage

Holding current

Reverse leakage current

Latching current

Forward volt-drop (conducting)

Forward break-over voltage

Forward leakage current

Gate triggered

IH

IL

VBO VAK

IT

Switching Characteristic (IV) Forward breakdown voltage VBO

◦ The voltage of avalanche breakdown

Latching current IL

◦ The minimum anode current required to maintain the thyristor in the on-state immediately after it is turned on and the gate signal has been removed

Holding current IH

◦ The minimum anode current to maintain the thyristor in the on-state

IL > IH

16

Symbol and construction The thyristor is a four-layer, three terminal semiconducting device, with each layer consisting of alternately N-type or P-type material, for example P-N-P-N. The main terminals, labeled anode and cathode, are across the full four layers, and the control terminal, called the gate, is attached to p-type material near to the cathode.

17

• Silicon Controlled Rectifier (SCR).

• TRIAC.

• DIAC.

• Silicon Unilateral Switch (SUS) – has built

in low voltage avalanche diode

Different types of Thyristors

Construction of SUS

18

Application

• Mainly used where high currents and voltages are

involved, and are often used to control alternating currents,

where the change of polarity of the current causes the

device to switch off automatically; referred to as Zero

Cross operation.

• Thyristors can be used as the control elements for phase

angle triggered controllers, also known as phase fired

controllers.

19

Cntd…

• In power supplies for digital circuits, thyristor can be used

as a sort of "circuit breaker" or "crowbar" to prevent a

failure in the power supply from damaging downstream

components, by shorting the power supply output to

ground

Load voltage regulated by thyristor phase control. Red trace: load voltage Blue trace: trigger signal. 20

SCR Ratings

(a) SCR Current Ratings 1- Maximum Repetitive RMS current Rating

• Average on-state current is the maximum average current value that can be carried by the

SCR in its on state.

• RMS value of nonsinusoidal waveform is simplified by approximating it by rectangular

waveform.

• This approximation give higher RMS value, but leaves slight safety factor.

21

22

• Average value of pulse is

• Form factor is

• Knowing the form factor for given waveform, RMS current can be

obtained from

IRMS=fo(IAVE) • Maximum repetitive RMS current is given by

IT(RMS)=fo(IT(AVE)) • Conduction angle verses form factor

23

Conduction angle (θ) Form factor (fo)

20° 5.0

40° 3.5

60° 2.7

80° 2.3

100° 2.0

120° 1.8

140° 1.6

160° 1.4

180° 1.3

Conduction Angle

24

• Duration for which SCR is on. It is measured as

shown

2- Surge Current Rating

Peak anode current that SCR can handle for brief duration.

3- Latching current

Minimum anode current that must flow through the SCR in order for it to

stay on initially after gate signal is removed.

4- Holding Current

Minimum value of anode current, required to maintain SCR in conducting

state.

25

(b) SCR Voltage Ratings

1- Peak repetitive forward blocking voltage

Maximum instantaneous voltage that SCR can block in forward direction.

2- Peak Repetitive Reverse Voltage

Maximum instantaneous voltage that SCR can withstand, without

breakdown, in reverse direction.

3- Non-repetitive peak reverse voltage

Maximum transient reverse voltage that SCR can withstand.

26

(c) SCR Rate-of-Change Ratings

1- (di/dt rating)

Critical rate of rise of on-state current. It is the rate at which anode current increases and must be

less than rate at which conduction area increases.

To prevent damage to SCR by high di/dt value, small inductance is added in series with device.

Vaue of required inductance is

L>= Vp

(di/dt)max

2- dv/dt rating Maximum rise time of a voltage pulse that can be applied to the SCR in the off state without

causing it to fire. Unscheduled firing due to high value of dv/dt can be prevented by using RC

snubber circuit.

27

(d) Gate Parameters

1- Maximum Gate Peak Inverse Voltage Maximum value of negative DC voltage that can be applied without damaging the gate-cathode junction.

2-Maximum Gate Trigger Current Maximum DC gate current allowed to turn on the device.

3- Maximum gate trigger voltage DC voltage necessary to produce maximum gate trigger current.

4- Maximum Gate Power Dissipation

Maximum instantaneous product of gate current and gate voltage that can exist during forward-bias.

5- Minimum gate trigger voltage Minimum DC gate-to-cathode voltage required to trigger the SCR.

6-Minimum gate trigger current Minimum DC gate current necessary to turn SCR on.

28

29

Series and Parallel SCR

Connections

SCRs are connected in series and parallel to

extend voltage and current ratings.

For high-voltage, high-current applications,

series-parallel combinations of SCRs are

used.

30

SCRs in Series

• Unequal distribution of voltage across two series SCRs.

• Two SCRs do not share the same supply voltage. Maximum voltage

that SCRs can block is V1+V2, not 2VBO.

31

• Resistance equalization

• Voltage equalization

32

• RC equalization for SCRs connected in series.

33

SCRs In Parallel • Unequal current sharing between two SCRs is shown:

• Total rated current of parallel connection is I1+I2, not 2I2.

34

• With unmatched SCRs, equal current sharing is achieved by adding low

value resistor or inductor in series with each SCR, as shown below.

• Value of resistance R is obtained from:

R=V1-V2

I2-I1

35

Current sharing in SCRs with parallel reactors

Equalization using resistors is inefficient due to

Extra power loss

Noncompansation for unequal SCR turn-on and turn-off times.

Damage due to overloading

SCRs with center-tapped reactors is shown below.

36

37

SCR Gate-Triggering Circuits

Triggering circuits provide firing signal to

turn on the SCR at precisely the correct time.

Firing circuits must have following

properties 1. Produce gate signal of suitable magnitude and sufficiently short rise time.

2. Produce gate signal of adequate duration.

3. Provide accurate firing control over the required range.

4. Ensure that triggering does not occur from false signals or noise

5. In AC applications, ensure that the gate signal is applied when the SCR is

forward-biased

6. In three-phase circuits, provide gate pulses that are 120° apart with

respect to the reference point

7. Ensure simultaneous triggering of SCRs connected in series or

in parallel.

38

Types Of Gate Firing Signals

1. DC signals

2. Pulse signals

3. AC signals

39

(a) DC Gating Signal From

Separate Source

40

DC Gating signals from Same

Source

41

Disadvantage of DC gating

Signals

1. Constant DC gate signal causes gate

power dissipation

2. DC gate signals are not used for firing

SCRs in AC applications, because

presence of positive gate signal during

negative half cycle would increase the

reverse anode current and possibly

destroy the device. 42

(2) Pulse Signals

1. Instead of continuous DC signal, single

pulse or train of pulses is generated.

2. It provides precise control of point at

which SCR is fired.

3. It provides electrical isolation between

SCR and gate-trigger circuit.

43

SCR trigger circuits using UJT

oscillator Circuit A

44

Circuit B

45

SCR trigger circuit using DIAC

46

SCR trigger circuit using

Optocoupler

47

(c) AC Signals

48

Resistive phase control RC

phase control

Triggering SCRs in Series and in

Parallel

49

50

SCR Turnoff (Commutation)

Circuits

What is Commutation?

The process of turning off an SCR is

called commutation.

It is achieved by 1. Reducing anode current below holding current

2. Make anode negative with respect to cathode

Types of commutation are: 1. Natural or line commutation

2. Forced commutation 51

SCR Turnoff Methods

1. Diverting the anode current to an alternate path

2. Shorting the SCR from anode to cathode

3. Applying a reverse voltage (by making the cathode positive with

respect to the anode) across the SCR

4. Forcing the anode current to zero for a brief period

5. Opening the external path from its anode supply voltage

6. Momentarily reducing supply voltage to zero

52

(1) Capacitor Commutation

• SCR turnoff circuit using a transistor

switch

53

• SCR turnoff circuit using commutation

capacitor

• Value of capacitance is determined by:

C>= tOFF

0.693RL

54

(2) Commutation By External

Source

55

(3) Commutation by Resonance . Series resonant turnoff circuit

56

57

Parallel resonant turnoff circuit

(4) AC line commutation

58

59

Other members of Thyristor

Family

Power Semiconductor Switches

Power Diodes Power Transistors Thyristors

2 layer device 3 layer Device 4 layer Device

• Thyristor devices can convert and control large amounts of power in AC or DC systems while using very low power for control.

• Thyristor family includes

1- Silicon controlled switch (SCR)

2- Gate-turnoff thyristor (GTO)

3- Triac

4- Diac

5- Silicon controlled switch (SCS)

6- Mos-controlled switch (MCT)

60

Other Types of Thyristors

61

1. Silicon Controlled Switch (SCS)

2. Gate Turnoff Thyristor (GTO)

3. DIAC

4. TRIAC

5. MOS-Controlled Thyristor (MCT)

1. SCS

62

Structure

Symbol

Equivalent circuit

for SCS

(2) GTO

63

Structure

Symbol

GTO Ideal VI

characteristiccs

(3) DIAC

64

Structure

Symbol

VI characteristics

of diac

(4) Triac

65

Structure Symbol SCR

equivalent circuit

Triac VI characteristics

66

(5) MCT

67

Symbol equivalent

circuit

MCT VI

characteristics

UNIT-II AC-DC CONVERTERS (1-PHASE &

3-PHASE CONTROLLED RECTIFIERS)

Introduction to Line commutated Inverter

70

• Type of input: Fixed voltage, fixed frequency

ac power supply.

• Type of output: Variable dc output voltage

• Type of commutation: Natural / AC line

commutation

Line

CommutatedConverter

+

-

DC Output

V0(dc)

AC

Input

Voltage

71

Different types of

Line Commutated Converters

• AC to DC Converters (Phase controlled

rectifiers)

• AC to AC converters (AC voltage controllers)

• AC to AC converters (Cyclo-converters) at low

output frequency.

72

Differences Between

Diode Rectifiers

&

Phase Controlled Rectifiers

Cntd…

73

• The diode rectifiers are referred to as uncontrolled rectifiers .

• The diode rectifiers give a fixed dc output voltage .

• Each diode conducts for one half cycle.

• Diode conduction angle = 1800 or radians.

• We can not control the dc output voltage or the average dc load current in a diode rectifier circuit.

74

Single phase half wave diode rectifier gives an

Average dc output voltage

Single phase full wave diode rectifier gives an

2Average dc output voltage

m

O dc

m

O dc

VV

VV

Cntd…

75

Applications of


• DC motor control in steel mills, paper and

textile mills employing dc motor drives.

• AC fed traction system using dc traction motor.

• Electro-chemical and electro-metallurgical

processes.

• Magnet power supplies.

• Portable hand tool drives.

76

Classification of


• Single Phase Controlled Rectifiers.

• Three Phase Controlled Rectifiers.

77

Different types of Single

Phase Controlled Rectifiers.

• Half wave controlled rectifiers.

• Full wave controlled rectifiers.

Using a center tapped transformer.

Full wave bridge circuit.

Semi converter.

Full converter.

78

Different Types of

Three Phase Controlled Rectifiers

• Half wave controlled rectifiers.

• Full wave controlled rectifiers.

• Semi converter (half controlled

bridge converter).

• Full converter (fully controlled

bridge converter).

Principle of Phase Controlled Rectifier

Operation

80

Principle of Phase Controlled

Rectifier Operation

81

Single Phase Half-Wave Thyristor

Converter with a Resistive Load

82

Supply Voltage

Output Voltage

Output (load)

Current

83

Supply Voltage

Thyristor Voltage

84

Equations

sin i/p ac supply voltage

max. value of i/p ac supply voltage

RMS value of i/p ac supply voltage2

output voltage across the load

s m

m

mS

O L

v V t

V

VV

v v

85

When the thyristor is triggered at

sin ; to

Load current; to

sinsin ; to

Where max. value of load current

O L m

OO L

mO L m

mm

t

v v V t t

vi i t

R

V ti i I t t

R

VI

R

86

To Derive an Expression for the

Average (DC)

Output Voltage Across The Load

87

2

0

1. ;

2

sin

1sin .

2

1sin .

2

dc OO dc

O m

dc mO dc

mO dc

V V v d t

v V t for t to

V V V t d t

V V t d t

88

sin .2

cos2

cos cos ; cos 12

1 cos ; 22

m

O dc

m

O dc

m

O dc

mm SO dc

VV t d t

VV t

VV

VV V V

89

max

max

Maximum average (dc) o/p

voltage is obtained when 0

and the maximum dc output voltage

1 cos0 ; cos 0 12

mdmdc

mdmdc

VV V

VV V

90

0

1 cos ; 22

The average dc output voltage can be varied

by varying the trigger angle from 0 to a

maximum of 180 radians

We can plot the control characteristic

v by using the eq

mm SO dc

O dc

VV V V

V s

uation for

O dcV

Cntd…

91

Control Characteristic

of

Single Phase Half Wave Phase

Controlled Rectifier

with

Resistive Load

92

The average dc output voltage is given by the

expression

1 cos2

We can obtain the control characteristic by

plotting the expression for the dc output

voltage as a function of trigger angle

m

O dc

VV

Cntd…

93

94

Control Characteristic VO(dc)

Trigger angle in degrees

0 60 120 180

Vdm

0.2 Vdm

0.6Vdm

95

Normalizing the dc output

voltage with respect to , the

Normalized output voltage

1 cos2

11 cos

2

dm

m

dcn

mdm

dcn dcn

dm

V

V

VV

VV

VV V

V

96

To Derive An Expression for the RMS Value of

Output Voltage of a Single Phase Half Wave

Controlled Rectifier With Resistive Load

97

2

2

0

1

22 2

The RMS output voltage is given by

1.

2

Output voltage sin ; for to

1sin .

2

OO RMS

O m

mO RMS

V v d t

v V t t

V V t d t

Cntd…

98

2

1

22

1

2 2

1

2 2

1 cos 2By substituting sin , we get

2

1 cos 21.

2 2

1 cos 2 .4

cos 2 .4

mO RMS

m

O RMS

m

O RMS

tt

tV V d t

VV t d t

VV d t t d t

Cntd…

99

1

2

1

2

1

2

1

2

1 sin 2

22

sin 2 sin 21;sin2 0

2 2

1 sin 2

2 2

sin 2

22

m

O RMS

m

O RMS

m

O RMS

m

O RMS

V tV t

VV

VV

VV

Cntd…

100

Performance Parameters

Of


101

Output dc power (avg. or dc o/p

power delivered to the load)

; . .,

Where

avg./ dc value of o/p voltage.

avg./dc value of o/p current

dc dc dcO dc O dc O dc

dcO dc

dcO dc

P V I i e P V I

V V

I I

Cntd…

102

Output ac power

Efficiency of Rectification (Rectification Ratio)

Efficiency ; % Efficiency 100

The o/p voltage consists of two components

The dc component

The ac

O ac O RMS O RMS

O dc O dc

O ac O ac

O dc

P V I

P P

P P

V

/ripple component ac r rms

V V

Cntd…

103

2 2

2 2

The total RMS value of output voltage is given by

Form Factor (FF) which is a measure of the

shape of the output voltage is given by

RMS output l

O RMS O dc r rms

ac r rms O RMS O dc

O RMS

O dc

V V V

V V V V

VFF

V

oad voltage

DC load output load voltage

Cntd…

104

22 2

2

The Ripple Factor (RF) w.r.t. o/p voltage w/f

1

1

r rms acv

dcO dc

O RMS O dc O RMS

v

O dc O dc

v

V Vr RF

V V

V V Vr

V V

r FF

Cntd…

105

2 2

max min

max min

Current Ripple Factor

Where

peak to peak ac ripple output voltage

peak to peak ac ripple load current

r rms aci

dcO dc

acr rms O RMS O dc

r pp

r pp O O

r pp

r pp O O

I Ir

I I

I I I I

V

V V V

I

I I I

Cntd…

106

Transformer Utilization Factor (TUF)

Where

RMS supply (secondary) voltage

RMS supply (secondary) current

O dc

S S

S

S

PTUF

V I

V

I

Cntd…

107

Cntd…

108

1

Where

Supply voltage at the transformer secondary side

i/p supply current

(transformer secondary winding current)

Fundamental component of the i/p supply current

Peak value of the input s

S

S

S

P

v

i

i

I

upply current

Phase angle difference between (sine wave

components) the fundamental components of i/p

supply current & the input supply voltage.

Cntd…

109

1

Displacement angle (phase angle)

For an RL load

Displacement angle = Load impedance angle

tan for an RL load

Displacement Factor (DF) or

Fundamental Power Factor

L

R

DF Cos

Cntd…

110

11

2 22 2 21

2

1 1

1

Harmonic Factor (HF) or

Total Harmonic Distortion Factor ; THD

1

Where

RMS value of input supply current.

RMS value of fundamental component of

the i

S S S

S S

S

S

I I IHF

I I

I

I

/p supply current.

Cntd…

111

1 1

Input Power Factor (PF)

cos cos

The Crest Factor (CF)

Peak input supply c

For an Ide

urrent

RMS input supply current

1; 100% ;

al Controlled Rectifier

0 ; 1;

S S S

S S S

S peak

S

ac r rms

V I IPF

V I I

ICF

I

FF V V TUF

R

0 ; 0; 1vF r HF THD PF DPF

Cntd…

112

Single Phase Half Wave Controlled Rectifier

With An RL Load

113

Cntd…

114

Input Supply Voltage (Vs)

&

Thyristor (Output) Current

Waveforms

115

Cntd…

116

Output (Load)

Voltage Waveform

117

1

To Derive An Expression For

The Output

(Load) Current, During to

When Thyristor Conducts

t

T

Cntd…

118

1

1

Assuming is triggered ,

we can write the equation,

sin ;

General expression for the output current,

sin

OO m

t

mO

T t

diL Ri V t t

dt

Vi t A e

Z

Cntd…

119

22

1

1

2 maximum supply voltage.

=Load impedance.

tan Load impedance angle.

Load circuit time constant.

general expression for the output load current

sin

m S

Rt

m LO

V V

Z R L

L

R

L

R

Vi t A e

Z

Cntd…

120

1

1

1

1

1

Constant is calculated from

initial condition 0 at ; t=

0 sin

sin

We get the value of constant as

sin

O

Rt

m LO

Rt

mL

R

mL

A

i t

Vi A e

Z

VA e

Z

A

VA e

Z

Cntd…

121

1Substituting the value of constant in the

general expression for

sin sin

we obtain the final expression for the

inductive load current

sin sin

O

Rt

m mLO

Rt

m LO

A

i

V Vi t e

Z Z

Vi t e

Z

;

Where t

Cntd…

122

Extinction angle can be calculated by using

the condition that 0

sin sin 0

sin sin

can be calculated by solving the above eqn.

O

Rt

m LO

R

L

i at t

Vi t e

Z

e

Cntd…

123

To Derive An Expression

For

Average (DC) Load Voltage of a

Single Half Wave Controlled

Rectifier with

RL Load

124

2

0

2

0

1.

2

1. . .

2

0 for 0 to & for to 2

1. ;

2

sin for to

L OO dc

L O O OO dc

O

L OO dc

O m

V V v d t

V V v d t v d t v d t

v t t

V V v d t

v V t t

125

1sin .

2

cos2

cos cos2

cos cos2

L mO dc

mLO dc

mLO dc

mLO dc

V V V t d t

VV V t

VV V

VV V

126

During the period to the

instantaneous o/p voltage is negative

reduces the average or the dc output

vo

and

this

when compared to a purely

resist

ltage

ive load.

t

Effect of Load

Inductance on the Output

127

Average DC Load Current

cos cos

2

O dc m

O dc L Avg

L L

V VI I

R R

Single Phase Half Wave Controlled Rectifier

With RL Load & Free Wheeling Diode

129

V0

i0

T

R

L

Vs ~+

+

FWD

130

0

0

0

0

vS

iG

vO

t

t

t

t

Supply voltage

Load current

Load voltage

t=

2

Gate pulses

iO

131

The followi

The average

ng points a

output voltage

1 cos which is the same as that 2

of a purely resistive load.

For low value of inductance, the load current

tends to become dis

re to be noted

cont

mdc

VV

inuous.

132

During the period to

the load current is carried by the SCR.

During the period to load current is

carried by the free wheeling diode.

The value of depends on the value of

R and L and the forwa

rd resistance

of the FWD.

133

For Large Load Inductance

the load current does not reach zero, &

we obtain continuous load current

0 t

2

t1

i0

SCR SCRFWD FWD

t3t2 t4

134

Single Phase Half Wave

Controlled Rectifier With

A

General Load

135

R

vS~+

L

E+

vO

iO

136

1sin

For trigger angle ,

the Thyristor conducts from to

For trigger angle ,

the Thyristor conducts from to

m

E

V

t

t

137

0

0

iO

t

t

Load current

E

vO

Load voltage

Vm

Im

138

Equations

sin Input supply voltage.

sin o/p load voltage

for to .

for 0 to &

for to 2 .

S m

O m

O

v V t

v V t

t

v E t

t

139

Expression for the Load Current

When the thyristor is triggered at a delay angle of

, the eqn. for the circuit can b

sin +E

e written as

The general expression for the output load

current can be writte

;

n

Om O

diV t i R L t

dt

s

as

int

mO

V Ei t Ae

Z R

140

22

1

Where

= Load Impedance.



The general expression for the o/p current can

be written as sinR

tm L

O

V Ei t Ae

Z

Z R

L

R

L

R

R

L

141

To find the value of the constant

'A' apply the initial conditions at ,

load current 0, Equating the general

expression for the load current to zero at

, we get

0 sinR

mO

O

L

t

i

t

V Ei Ae

Z R

142

We obtain the value of constant 'A' as

Substituting the value of the constant 'A' in the

expression for the load current; we get the

complete expression for the output load c

si

ur

nR

m LVE

A eR Z

sin

rent

in

s

as

Rt

m m LO

V VE Ei t e

Z R R Z

143

To Derive

An

Expression For The Average

Or

DC Load Voltage

144

2

0

2

0

2

0

sin Output load voltage

1.

2

1.

for 0 to & for to 2

for

. .

to

2

1. sin .

2

O

OO dc

O O OO d

m

m

c

O dc

O

V v d t

V v d t v d t v d t

V E d t V t E d t

v V t

v E t t

t

145

2

0

1cos

2

10 cos cos 2

2

cos cos 22 2

2cos cos

2 2

mO dc

mO dc

m

O dc

m

O dc

V E t V t E t

V E V E

V EV

VV E

146

2

2

0

Conduction angle of thyristor

RMS Output Voltage can be calculated

by using the expres

1.

sion

2OO RMS

V v d t

Single Phase Full Wave Controlled Rectifier

Using A Center Tapped Transformer

148

ACSupply

O

A

B

T1

T2

R L

vO

+

149

Discontinuous

Load Current Operation

without FWD

for

150

vOVm

0

( ) ( )

iO

t

t0

151

1


The Output



t

T

152

1

1



sin ;


sin

OO m

t

mO

T t

diL Ri V t t

dt

Vi t A e

Z

153

22

1

1


=Load impedance.




sin

m S

Rt

m LO

V V

Z R L

L

R

L

R

Vi t A e

Z

154

1

1

1

1

1



0 sin

sin


sin

O

Rt

m LO

Rt

mL

R

mL

A

i t

Vi A e

Z

VA e

Z

A

VA e

Z

155



sin sin



sin sin

O

Rt

m mLO

Rt

m LO

A

i

V Vi t e

Z Z

Vi t e

Z

;

Where t

156



sin sin 0

sin sin


O

Rt

m LO

R

L

i at t

Vi t e

Z

e

157

To Derive An Expression For The

DC Output Voltage Of

A Single Phase Full Wave

Controlled Rectifier With RL Load

(Without FWD)

158

vOVm

0

( ) ( )

iO

t

t0

159

1.

1sin .

cos

cos cos

dc OO dc

t

dc mO dc

mdcO dc

mdcO dc

V V v d t

V V V t d t

VV V t

VV V

160

When the load inductance is negligible i.e., 0

Extinction angle radians

Hence the average or dc output voltage for R load

cos cos

cos 1

1 cos ; for R load, when

m

O dc

m

O dc

m

O dc

L

VV

VV

VV

161

2 2

To calculate the RMS output voltage we use

the expression

1sin .mO RMS

V V t d t

162

Discontinuous Load Current

Operation with FWD

163

vOVm

0

( ) ( )

iO

t

t0

164

2

2

1

1

Thyristor is trigger

Thyristor is triggered at ;

conducts from to

FWD conducts from to &

0 during discontinuous loa

ed at ;

conducts from t

d current.

o 2

O

T t

T

T t

t

T t

t

v

165

To Derive an Expression

For The

DC Output Voltage For

A

Single Phase Full Wave Controlled

Rectifier

With RL Load & FWD

166

0

1.

1sin .

cos

cos cos ; cos 1

1 cos

dc OO dc

t

dc mO dc

mdcO dc

mdcO dc

mdcO dc

V V v d t

V V V t d t

VV V t

VV V

VV V

167

• The load current is discontinuous for low values

of load inductance and for large values of

trigger angles.

• For large values of load inductance the load

current flows continuously without falling to

zero.

• Generally the load current is continuous for

large load inductance and for low trigger angles.

168

Continuous Load Current

Operation

(Without FWD)

169

vOVm

0

( )

iO

t

t0

( )

170

To Derive

An Expression For

Average / DC Output Voltage

Of


Rectifier For Continuous Current

Operation without FWD

171

vOVm

0

( )

iO

t

t0

( )

172

1.

1sin .

cos

dc OO dc

t

dc mO dc

mdcO dc

V V v d t

V V V t d t

VV V t

173

cos cos ;

cos cos

cos cos

2cos

dcO dc

m

mdcO dc

mdcO dc

V V

V

VV V

VV V

174

• By plotting VO(dc) versus ,

we obtain the control characteristic of a

single phase full wave controlled rectifier

with RL load for continuous load current

operation without FWD

175

cosdc dmV V

176

VO(dc)


030 60 90

Vdm

0.2 Vdm

0.6Vdm

-0.6 Vdm

-0.2Vdm

-Vdm

120 150 180

cosdc dmV V

177

00

By varying the trigger angle we can vary the

output dc voltage across the load. Hence we can

control the dc output power flow to the load.

For trigger a . ., ngle , 0 to 90

cos is positive

0 90 ;

i e

and hence is positive

Converter

& are positive ; is positive

Controlled Rectif operates as a

Power flow is from the

ie

ac source to the d.

r.

loa

dc dc dc dc d

d

c

cV

V I P V I

178

0

0

0

0. ., 90 180 ,

is negative; is positive

For trigger angle , 90

;

is negative.

Line

to 180

cos is negative and hence

In this case the conve

Co

rte

mmutated In

r operates

s vea a

dc dc

dc dc dc

i e

V I

P V I

Power flows from the load ckt. to the i/p ac source.

The inductive load energy is fed back to the

i/p sou

rter.

rce.

179

Drawbacks Of Full Wave


With Centre Tapped Transformer • We require a centre tapped transformer which

is quite heavier and bulky.

• Cost of the transformer is higher for the

required dc output voltage & output power.

• Hence full wave bridge converters are

preferred.

Single Phase

Full Wave Bridge Controlled Rectifier

181

Single Phase

Full Wave Bridge Controlled

Rectifier 2 types of FW Bridge Controlled Rectifiers are

Half Controlled Bridge Converter

(Semi-Converter)

Fully Controlled Bridge Converter

(Full Converter)

The bridge full wave controlled rectifier does not

require a centre tapped transformer

182

Single Phase

Full Wave Half Controlled Bridge

Converter

(Single Phase Semi Converter)

183

184

Trigger Pattern of Thyristors

1

2

0

1 2

, 2 ,...

, 3 ,...

& 180

Thyristor T is triggered at

t at t


t at t

The time delay between the gating

signals of T T radians or

185

Waveforms of

single phase semi-converter

with general load & FWD

for > 900

186

Single Quadrant

Operation

187

188

189

1 1

2 2

Thyristor & conduct

from

Thyristor & conduct

from 2

FWD conducts during

0 to , ,...

T D

t to

T D

t to

t to

190

Load Voltage & Load Current

Waveform of Single Phase Semi

Converter for

< 900

& Continuous load current operation

191

vOVm

0

iO

t

( )

t0

( )

192


For The

DC Output Voltage of

A

Single Phase Semi-Converter With

R,L, & E Load & FWD

For Continuous, Ripple Free Load

Current Operation

193

0

1.

1sin .

cos

cos cos ; cos 1

1 cos

dc OO dc

t

dc mO dc

mdcO dc

mdcO dc

mdcO dc

V V v d t

V V V t d t

VV V t

VV V

VV V

194

max

can be varied from a max.

2value of 0 by varying from 0 to .

For 0, The max. dc o/p voltage obtained is

Normalized dc o/p voltage is

2

11 cos

2

dc

m

m

dc

mdn

mdmdc

dcn n

V

Vto

V

V

V V

VVV

V

V

1 cos2

195

RMS O/P Voltage VO(RMS)

1

22 2

1

2 2

1

2

2sin .

2

1 cos 2 .2

1 sin 2

22

mO RMS

m

O RMS

m

O RMS

V V t d t

VV t d t

VV

196

Single Phase Full Wave


197

Single Phase Full Wave Controlled Rectifier

Using A Center Tapped Transformer

198 198

ACSupply

O

A

B

T1

T2

R L

vO

+

Single Phase Midpoint type

Fully controlled Rectifier

199

199

Discontinuous


without FWD

for

200

200

vOVm

0

( ) ( )

iO

t

t0

201

201

1


The Output



t

T

202

202

1

1



sin ;


sin

OO m

t

mO

T t

diL Ri V t t

dt

Vi t A e

Z

203

203

22

1

1


=Load impedance.




sin

m S

Rt

m LO

V V

Z R L

L

R

L

R

Vi t A e

Z

204

204

1

1

1

1

1



0 sin

sin


sin

O

Rt

m LO

Rt

mL

R

mL

A

i t

Vi A e

Z

VA e

Z

A

VA e

Z

205

205



sin sin



sin sin

O

Rt

m mLO

Rt

m LO

A

i

V Vi t e

Z Z

Vi t e

Z

;

Where t

206

206



sin sin 0

sin sin


O

Rt

m LO

R

L

i at t

Vi t e

Z

e

207 207

To Derive An Expression For The DC Output

Voltage Of

A Single Phase Full Wave Controlled

Rectifier With RL Load

(Without FWD)

208

208

vOVm

0

( ) ( )

iO

t

t0

209

209

1.

1sin .

cos

cos cos

dc OO dc

t

dc mO dc

mdcO dc

mdcO dc

V V v d t

V V V t d t

VV V t

VV V

210

210

When the load inductance is negligible i.e., 0

Extinction angle radians

Hence the average or dc output voltage for R load

cos cos

cos 1

1 cos ; for R load, when

m

O dc

m

O dc

m

O dc

L

VV

VV

VV

211

211

2 2

To calculate the RMS output voltage we use

the expression

1sin .mO RMS

V V t d t

212

212

Discontinuous Load Current

Operation with FWD

213

213

vOVm

0

( ) ( )

iO

t

t0

214

214

2

2

1

1

Thyristor is trigger

Thyristor is triggered at ;

conducts from to

FWD conducts from to &

0 during discontinuous loa

ed at ;

conducts from t

d current.

o 2

O

T t

T

T t

t

T t

t

v

215

215

To Derive an Expression For The DC Output

Voltage For A Single Phase Full Wave


RL Load & FWD

216

216

0

1.

1sin .

cos

cos cos ; cos 1

1 cos

dc OO dc

t

dc mO dc

mdcO dc

mdcO dc

mdcO dc

V V v d t

V V V t d t

VV V t

VV V

VV V

217

217

• The load current is discontinuous for low values

of load inductance and for large values of

trigger angles.

• For large values of load inductance the load

current flows continuously without falling to

zero.

• Generally the load current is continuous for

large load inductance and for low trigger angles.

218

218

Continuous Load Current

Operation

(Without FWD)

219

219

vOVm

0

( )

iO

t

t0

( )

220

220

To Derive

An Expression For

Average / DC Output Voltage

Of


Rectifier For Continuous Current

Operation without FWD

221

221

vOVm

0

( )

iO

t

t0

( )

222

222

1.

1sin .

cos

dc OO dc

t

dc mO dc

mdcO dc

V V v d t

V V V t d t

VV V t

223

223

cos cos ;

cos cos

cos cos

2cos

dcO dc

m

mdcO dc

mdcO dc

V V

V

VV V

VV V

224

224

• By plotting VO(dc) versus ,


single phase full wave controlled rectifier

with RL load for continuous load current

operation without FWD

225

225

cosdc dmV V

226

226

VO(dc)


030 60 90

Vdm

0.2 Vdm

0.6Vdm

-0.6 Vdm

-0.2Vdm

-Vdm

120 150 180

cosdc dmV V

227

227

00

By varying the trigger angle we can vary the

output dc voltage across the load. Hence we can

control the dc output power flow to the load.

For trigger a . ., ngle , 0 to 90

cos is positive

0 90 ;

i e

and hence is positive

Converter

& are positive ; is positive

Controlled Rectif operates as a

Power flow is from the

ie

ac source to the d.

r.

loa

dc dc dc dc d

d

c

cV

V I P V I

228

228

0

0

0

0. ., 90 180 ,

is negative; is positive

For trigger angle , 90

;

is negative.

Line

to 180

cos is negative and hence

In this case the conve

Co

rte

mmutated In

r operates

s vea a

dc dc

dc dc dc

i e

V I

P V I

Power flows from the load ckt. to the i/p ac source.

The inductive load energy is fed back to the

i/p sou

rter.

rce.

229

Single Phase

Full Wave Bridge Controlled Rectifier

230

230

Drawbacks Of Full Wave


With Centre Tapped Transformer • We require a centre tapped transformer which

is quite heavier and bulky.

• Cost of the transformer is higher for the

required dc output voltage & output power.

• Hence full wave bridge converters are

preferred.

231

231

Single Phase Full Wave Bridge


2 types of FW Bridge Controlled Rectifiers are


(Semi-Converter)

Fully Controlled Bridge Converter

(Full Converter)

The bridge full wave controlled rectifier does not

require a centre tapped transformer

232

232

Single Phase

Full Wave Half Controlled Bridge

Converter

(Single Phase Semi Converter)

233

233

Single Phase Full Wave Half Controlled

Bridge Converter

234

234

Trigger Pattern of Thyristors

1

2

0

1 2

, 2 ,...

, 3 ,...

& 180


t at t


t at t

The time delay between the gating

signals of T T radians or

235

235

Waveforms of

single phase semi-converter

with general load & FWD

for > 900

236

236

Single Quadrant

Operation

237

237

238

238

239

239

1 1

2 2

Thyristor & conduct

from

Thyristor & conduct

from 2

FWD conducts during

0 to , ,...

T D

t to

T D

t to

t to

240

240

Load Voltage & Load Current Waveform of

Single Phase Semi Converter for

< 900 & Continuous load current

operation

241

241

vOVm

0

iO

t

( )

t0

( )

242

242


For The

DC Output Voltage of

A

Single Phase Semi-Converter With

R,L, & E Load & FWD

For Continuous, Ripple Free Load

Current Operation

243

243

0

1.

1sin .

cos

cos cos ; cos 1

1 cos

dc OO dc

t

dc mO dc

mdcO dc

mdcO dc

mdcO dc

V V v d t

V V V t d t

VV V t

VV V

VV V

244

244

max

can be varied from a max.

2value of 0 by varying from 0 to .

For 0, The max. dc o/p voltage obtained is

Normalized dc o/p voltage is

2

11 cos

2

dc

m

m

dc

mdn

mdmdc

dcn n

V

Vto

V

V

V V

VVV

V

V

1 cos2

245

245

RMS O/P Voltage VO(RMS)

1

22 2

1

2 2

1

2

2sin .

2

1 cos 2 .2

1 sin 2

22

mO RMS

m

O RMS

m

O RMS

V V t d t

VV t d t

VV

246

Single Phase Full Converter

247


247

248

248

Waveforms of


Assuming Continuous (Constant

Load Current)

&

Ripple Free Load Current

249

249

250

250

251

251

iOConstant Load Current i =IO a

i

iT1

T2&

Ia

t

t

t

Iai

iT3

T4&

Ia

Ia

252

252

To Derive An Expression For The Average DC

Output Voltage of a Single Phase Full Converter

assuming Continuous & Constant Load Current

253

253

2

0

The average dc output voltage

can be determined by using the expression

1. ;

2

The o/p voltage waveform consists of two o/p

pulses during the input supply time period of

0 to 2 r

dc OO dcV V v d t

adians. Hence the Average or dc

o/p voltage can be calculated as

254

254

2sin .

2

2cos

2

2cos

dc mO dc

mdcO dc

mdcO dc

V V V t d t

VV V t

VV V

255

255

0

max

max

Maximum average dc output voltage is

calculated for a trigger angle 0

and is obtained as

2 2cos 0

2

m mdmdc

mdmdc

V VV V

VV V

256

256

max

The normalized average output voltage is given by

2cos

cos2

O dc dcdcn n

dmdc

m

dcn nm

V VV V

V V

V

V VV

257

257

By plotting VO(dc) versus ,


single phase full wave fully controlled

bridge converter

(single phase full converter)

for constant & continuous

load current operation.

258

258

To plot the control characteristic of a

Single Phase Full Converter for constant

& continuous load current operation.

We use the equation for the average/ dc

output voltage

2cosm

dcO dc

VV V

259

259

260

260

VO(dc)


030 60 90

Vdm

0.2 Vdm

0.6Vdm

-0.6 Vdm

-0.2Vdm

-Vdm

120 150 180

cosdc dmV V

261

261

• During the period from t = to the input

voltage vS and the input current iS are both

positive and the power flows from the supply

to the load.

• The converter is said to be operated in the

rectification mode

Controlled Rectifier Operation

for 0 < < 900

262

262

• During the period from t = to (+), the input voltage vS is negative and the input current iS is positive and the output power becomes negative and there will be reverse power flow from the load circuit to the supply.

• The converter is said to be operated in the inversion mode.

Line Commutated Inverter Operation

for 900 < < 1800

263

Two Quadrant Operation

of a Single Phase Full Converter

264

264

Two Quadrant Operation

of a Single Phase Full Converter

0< < 900


Operation

900< <1800

Line Commutated

Inverter Operation

265

265

To Derive An

Expression For The

RMS Value Of The Output Voltage

2

2

0

The rms value of the output voltage

is calculated as

1.

2OO RMS

V v d t

266

266

The single phase full converter gives two

output voltage pulses during the input supply

time period and hence the single phase full

converter is referred to as a two pulse converter.

The rms output vo

2

ltage can be calculated as

2.

2OO RMS

V v d t

267

267

2 2

22

2

2

1sin .

sin .

1 cos 2.

2

cos 2 .2

mO RMS

m

O RMS

m

O RMS

m

O RMS

V V t d t

VV t d t

tVV d t

VV d t t d t

268

268

2

2

2

sin 2

22

sin 2 sin 2

2 2

sin 2 2 sin 2;

2 2

sin 2 2 sin 2

m

O RMS

m

O RMS

m

O RMS

V tV t

VV

VV

269

269

2

2 2

sin 2 sin 2

2 2

02 2 2

2

Hence the rms output voltage is same as the

rms input supply voltage

m

O RMS

m m m

O RMS

mSO RMS

VV

V V VV

VV V

270

270

Thyristor Current Waveforms

271

271

iOConstant Load Current i =IO a

i

iT1

T2&

Ia

t

t

t

Iai

iT3

T4&

Ia

Ia

272

272

The rms thyristor current can be

calculated as

2

The average thyristor current can be

calculated as

2

O RMS

T RMS

O dc

T Avg

II

II

273

THREE PHASE LINE

COMMUTATED CONVERTERS

274

Introduction to

Three phase converters

275

3 Phase Controlled Rectifiers

• Three phase converters are 3-

phase controlled rectifiers which

are used to convert ac input power

supply into dc output power across

the load

276

276

Features of 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.

277

277

• 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.

278

Classification of 3-phase converters

• 3-phase half wave converter

• 3-phase semi converter

• 3-phase full converter

• 3- phase dual converter

279

Classification according to

no of pulses in the output wave

• 3- pulse converter

• 6-pulse converter

• 12- pulse converter

280

280

3-Phase

Half Wave Converter

(3-Pulse Converter)

with

R-L Load

Continuous & Constant


281

281

Circuit Diagram of 3- pulse converter

282

282

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

283

283

3 Phase Supply Voltage Equations

We deifine three line to neutral voltages

(3 phase voltages) as follows

284

284

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

285

285

van vbn vcn van

286

286

io=Ia

Constant Load

Current

Ia

Ia

Each thyristor conducts for 2/3 (1200)

287

287

To Derive an

Expression for the

Average Output Voltage of a

3-Phase Half Wave Converter

with RL Load

for Continuous Load Current

288

288

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

289

289

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

290

290

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

291

291

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

292

292

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

293

293

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

294

294

max

The maximum average or dc output voltage is

obtained at a delay angle 0 and is given by

3 3

2

Where is the peak phase voltage.

And the normalized average output voltage is

mdmdc

m

ddcn n

VV V

V

VV V

cosc

dmV

295

295

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

296

296

3 Phase Half Wave

Controlled Rectifier Output

Voltage Waveforms For RL Load

at

Different Trigger Angles

297

297

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

298

298

030

060

090

0120

0150

0180

0210

0240

0270

0300

0330

0360

0390

0420

0

V0

Van

=900

Vbn Vcn

t

=900

299

299

3 Phase Half Wave


R Load

and

RL Load with FWD

300

300

a a

b b

c c

R

V0

L

R V0

+

T1

T2

T3

n n

T1

T2

T3

301

301

3 Phase Half Wave

Controlled Rectifier Output

Voltage Waveforms For R Load

or RL Load with FWD

at

Different Trigger Angles

302

302

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

303

303

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

304

304

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

305

305

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

306

306

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

307

307

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

308

308

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

309

Three Phase Semi-converters

310

310

Three Phase Semi-converters

• 3 Phase semi-converters 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.

311

311

3 Phase


(Semi Converter)

with Highly Inductive Load &

Continuous Ripple free Load Current

312

312

313

313

Wave forms of 3 Phase Semiconverter

for

> 600

314

314

315

315

316

316

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

317

317

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

318

318

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

319

319

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

320

320

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

321 321

Wave forms of 3 Phase Semiconverter

for

600

322

322

323

323

324

324

325 325

To derive an Expression for the

Average Output Voltage of 3 Phase

Semi-converter for > / 3

and Discontinuous Output Voltage

326

326

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

327

327

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

328

328

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

329

329

17 2

62 2

6

1

2

33 sin

2 6

3 sin 23

4 2

mO rms

mO rms

V V t d t

V V

330

330

Average or DC Output Voltage

of a

3-Phase Semi-converter

for / 3,

and Continuous Output Voltage

331

331

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

332

332

15 2

622 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

333

Three Phase Full Converter

334

334

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.

335

335

336

336

337

337

338

338

• 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)

339

339

• 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, ………

340

340

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

341

341

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

342

342


The Average Output Voltage Of

3-phase Full Converter

With Highly Inductive Load

Assuming Continuous And

Constant Load Current

343

343

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

344

344

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

345

345

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

346

346

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

347

Single Phase Dual Converter

348

348

Single Phase Dual Converter

349

349

350

350

351

351

352

352

1 1

2 2

The average dc output voltage of converter 1 is

2cos

The average dc output voltage of converter 2 is

2cos

mdc

mdc

VV

VV

353

353

0

0

1

In the dual converter operation one

converter is operated as a controlled rectifier

with 90 & the second converter is

operated as a line commutated inverter

in the inversion mode with 90

dcV V

2dc

354

354

1 2 2

1 2

2 1 1

2 1

1 2

2 1

2 2 2cos cos cos

cos cos

or

cos cos cos

or

radians

Which gives

m m mV V V

355

355

To Obtain an Expression

for the

Instantaneous Circulating Current

356

356

• vO1 = Instantaneous o/p voltage of converter 1.

• vO2 = Instantaneous o/p voltage of converter 2.

• The circulating current ir can be determined by

integrating the instantaneous voltage difference

(which is the voltage drop across the circulating

current reactor Lr), starting from t = (2 - 1).

• As the two average output voltages during the

interval t = (+1) to (2 - 1) are equal and

opposite their contribution to the instantaneous

circulating current ir is zero.

357

357

1

1

1 2

2

2

1 2

1 2

2

1 1

1. ;

As the o/p voltage is negative

1. ;

sin for 2 to

t

r r r O O

r

O

r O O

t

r O O

r

O m

i v d t v v vL

v

v v v

i v v d tL

v V t t

358

358

1 12 2

1

sin . sin .

2cos cos

The instantaneous value of the circulating current

depends on the delay angle.

t t

mr

r

mr

r

Vi t d t t d t

L

Vi t

L

359

359

1For trigger angle (delay angle) 0,

the magnitude of circulating current becomes min.

when , 0, 2,4,.... & magnitude becomes

max. when , 1,3,5,....

If the peak load current is , one of p

t n n

t n n

I

the

converters that controls the power flow

may carry a peak current of

4,m

p

r

VI

L

360

360

max

max

where

,

&

4 max. circulating current

mp L

L

m

r

r

VI I

R

Vi

L

361

361

Different Modes Of Operation of

Dual converter

• Non-circulating current (circulating current

free) mode of operation.

• Circulating current mode of operation.

362

362

Non-Circulating

Current Mode of Operation

• In this mode only one converter is operated

at a time.

• When converter 1 is ON, 0 < 1 < 900

• Vdc is positive and Idc is positive.

• When converter 2 is ON, 0 < 2 < 900

• Vdc is negative and Idc is negative.

363

363

Circulating

Current Mode Of Operation

• In this mode, both the converters are switched

ON and operated at the same time.

• The trigger angles 1 and 2 are adjusted such

that (1 + 2) = 1800 ; 2 = (1800 - 1).

364

364

• When 0 <1 <900, converter 1 operates as a

controlled rectifier and converter 2 operates as

an inverter with 900 <2<1800.

• In this case Vdc and Idc, both are positive.

• When 900 <1 <1800, converter 1 operates as

an Inverter and converter 2 operated as a

controlled rectifier by adjusting its trigger

angle 2 such that 0 <2<900.

• In this case Vdc and Idc, both are negative.

365

365

Four Quadrant Operation

Conv. 2

Inverting

2 > 900

Conv. 2

Rectifying

2 < 900

Conv. 1

Rectifying

1 < 900

Conv. 1

Inverting

1 > 900

366

366

Advantages of Circulating


• The circulating current maintains

continuous conduction of both the

converters over the complete control range,

independent of the load.

• One converter always operates as a rectifier

and the other converter operates as an

inverter, the power flow in either direction

at any time is possible.

367

367

• As both the converters are in continuous

conduction we obtain faster dynamic response.

i.e., the time response for changing from one

quadrant operation to another is faster.

368

368

Disadvantages of Circulating

Current Mode Of Operation • There is always a circulating current flowing

between the converters.

• When the load current falls to zero, there will be a

circulating current flowing between the converters

so we need to connect circulating current reactors in

order to limit the peak circulating current to safe

level.

• The converter thyristors should be rated to carry a

peak current much greater than the peak load

current.

369

Three Phase Dual Converters

370

370

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.

371

371

372

372

373

373

374

374

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

375

375

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

376

376

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

377

377

• 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

378

378

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

379

379

1

1

6

6

1

max

1.

13 cos .

6

3sin sin

6

3

t

r r

r

t

r m

r

mr

r

m

r

r

i t v d tL

i t V t d tL

Vi t t

L

Vi

L

380

380

Four Quadrant Operation

Conv. 2

Inverting

2 > 900

Conv. 2

Rectifying

2 < 900

Conv. 1

Rectifying

1 < 900

Conv. 1

Inverting

1 > 900

381

381

Contd…

• There are two different modes of operation.

Circulating current free

(non circulating) mode of operation

Circulating current mode of operation

382

382

Non Circulating


• 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

383

383

• 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.

384

384


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

385

385


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.

386

386

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

387

387

• 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.

UNIT-III

DC-DC CONVERTERS (CHOPPERS)

388

389

DC-DC Converters

• Convert a fixed DC Source into a Variable

DC Source

• DC equivalent to an AC transformer with

variable turns ratio

• Step-up and Step-down versions

• Applications

– Motor Control

– Voltage Regulators

390

Step-down Operation

• Switch SW is known as a “Chopper”

• Use BJT, MOSFET, or IGBT

• Close for time t1

– VS appears across R

• Open for time t2

– Voltage across R = 0

• Repeat

• Period T = t1 + t2

391

Waveforms for the Step-Down Converter

392

Average Value of the Output Voltage

1

1

0

0

11

1

1

t

a O

t

a S

a S S

a S

V v dtT

V V dtT

tV V ft V

T

V kV

393

Average Value of the Load Current

1

a Sa

V kVI

R R

T period

tk dutycycle

T

f frequency

394

rms Value of the output voltage

1

22

0

1

22

0

1

1

kT

O O

kT

O S

O S

V v dtT

V V dtT

V kV

395

If the converter is “lossless”, Pin = Pout

0

2

0

2

2

1

1

1

kT

in O

kT

Oin

Sin

Sin

P v idtT

vP dt

T R

VP kT

T R

VP k

R

396

Effective Input Resistance seen by VS

S Si

Sa

i

V VR

VIk

R

RR

k

397

Modes of Operation

• Constant – frequency operation

– Period T held constant, t1 varied

– Width of the pulse changes

– “Pulse-width modulation”, PWM

• Variable -- frequency operation

– Change the chopping frequency (period T)

– Either t1 or t2 is kept constant

– “Frequency modulation”

398

Generation of Duty Cycle

• Compare a dc reference signal with a saw-

tooth carrier signal

DC Reference Signal Carrier Signal

399

rr

Vv k

T

@r cr

rcr

cr

r

v V t kT

VV kT

T

Vk M

V

k

T

400

To generate the gating signal

• Generate the triangular waveform of period T, vr, and

the dc carrier signal, vcr

• Compare to generate the difference vc - vcr

• Apply to a “hard limiter” to “square off”

401

Step-Down Converter with RL Load

402

Mode 1: Switch Closed

1

1S

diV Ri L E

dt

1 1( ) 1

R Rt t

L LSV E

i t I e eR

1( )t t kT

1 ( 0 ) 1( )

ti t I

1

1 2( )

t t kT

i kT I

403

Mode 2: Switch Open

2

2

2 2

2 2

0

( 0)

( ) 1R R

t tL L

diR i L E

dt

i t I

Ei t I e e

R

2

2

2 2 3 1

0 (1 )

@ (1 )

( )

t t k T

t t K T

i t I I

404

Current for “Continuous” Mode

405

1

2

( 1 )

max

1

1

1

1

1

1

4

kz

S

z

kz

S

z

kz z k z

S

z

S

V e EI

R e R

V e EI

R e R

T Rz

L

V e e eI

R e

VI

fL

406

10

10

1

kz

z

S

I

e E

e V

For Continuous Current

407

Define the load emf ratio

1

1

S

kz

z

S

Ex

V

E ex

V e

408

UNIT-IV

AC-AC CONVERTERS (AC

VOLTAGE CONTROLLERS) &

FREQUENCY CHANGERS

(CYCLO-CONVERTERS)

409

Ac Voltage controller circuits

(RMS voltage controllers)

An ac voltage controller is a type of thyristor

power converter which is used to convert a

fixed voltage, fixed frequency ac input supply

to obtain a variable voltage ac output

410

Applications Of Ac Voltage

Controllers

•Lighting / Illumination control in ac power

circuits.

•Induction heating.

•Industrial heating & Domestic heating.

•Transformer tap changing (on load

transformer tap changing).

•Speed control of induction motors C

magnet controls.

411

Type Of Ac Voltage Controllers

• Single phase half wave ac voltage controller (Uni-directional controller).

• Single phase full wave ac voltage controller (Bi-directional controller).

• Three phase half wave ac voltage controller (Uni-directional controller).

• Three phase full wave ac voltage controller (Bi-directional Controller)

412

A.C voltage control technique

413

Principle of ON-OFF Control

Technique

414

Vs

Vo

io

ig1

ig2

wt

wt

wt

wt

Gate pulse of T1

Gate pulse of T2

n m

415

416

417

418

Expression For The RMS Value Of

Output Voltage, For ON-OFF

Control Method

419

420

421

422

423

424

RMS Out put voltage

425

Duty cycle

426

427

Input Power factor

428

429

The Average Current Of Thyristor

430

Waveform of Thyristor current

431

432

RMS Thyristor Current

433

Principle Of AC Phase Control

And

Operation of single Phase half-Wave

A.C Phase controller

Power Electronics Unit-6 434

Principle Of AC Phase Control

435

436

Equations

437

Output Load Voltage

438

Out Put Load Current

439

Expression For RMS Out put Load

Voltage

440

441

442

443

444

Control Characteristics

445

Average Value of Out put Voltage

446

447

448

Disadvantages

449

Single Phase Full Wave Ac Voltage

Controller (Bidirectional Controller)

With R-Load

450


Controller With R-Load

Fig.: Single phase full wave ac voltage controller

(Bi-directional Controller) using SCR

451

Waveforms of single phase full

wave ac voltage controller

452

Expression for RMS output voltage

2 2 2

0

1sin .mL RMS

V V t d t

2

2 2

0

1.

2LL RMS

V v d t

2

2 22 1sin sin

2m mL RMS

V V t d t V t d t

453

Contd…

2

2 2 2 21sin . sin .

2m mV t d t V t d t

2

2 2 2 21sin . sin .

2m mV t d t V t d t

22

1 cos 2 1 cos 2

2 2 2

mV t td t d t

2 22

cos 2 . cos 2 .2 2

mVd t t d t d t t d t

454

2 22

sin 2 sin 2

4 2 2

mV t tt t

2

1 1sin 2 sin 2 sin 4 sin 2

4 2 2

mV

2

1 12 0 sin 2 0 sin 2

4 2 2

mV

2 sin 2sin 2

24 2 2

mV

455

2 sin 2 2sin 2

24 2 2

mV

2

sin 2 12 sin 2 .cos 2 cos 2 .sin 2

4 2 2

mV

sin 2 0 & cos2 1

Therefore,

2

2 sin 2 sin 22

4 2 2

m

L RMS

VV

2

2 2 2 sin 24

m

L RMS

VV

456

• Taking the square root, we get

2 2 sin 22

m

L RMS

VV

2 2 sin 22 2

m

L RMS

VV

1

2 2 sin 222

m

L RMS

VV

1 sin 2

22 22

m

L RMS

VV

457

1 sin 2

22

m

L RMS

VV

1 sin 2

2L RMS i RMS

V V

1 sin 2

2SL RMS

V V

458



With R-L Load

459



With R-L Load


Input supply voltage & Thyristor

current waveforms

461

Gating Signals


Waveforms For RL load for and

for Discontinuous Conduction

463

sin sinR

tm L

O

Vi t e

Z

Expression for the inductive load

current of a single phase full wave

ac voltage controller with RL load

22Z R L

1tanL

R

Where

= Load impedance angle (power factor

angle of load).

464

Output voltage and output current waveforms

for a single phase full wave

ac voltage controller with RL load for

vO

2

3

t

Vm

0

Im

t

v =vO S

iO

465

TRIAC and Its Modes of Operation

466

TRIAC

MT2

MT1G

P2

P2 N1

N4

N3

G N2

N1P1

MT1

MT2

P1

Fig.1 : Triac Structure Fig. 2 : Triac

Symbol

467

TRIGGERING MODES OF TRIAC

• MODE 1 : MT1 positive, Positive gate current

( I+ mode of operation)

P1

N1

N2

P2Ig

Ig

MT2 (+)

MT1 ( )G

V(+)

468

• When and gate current are positive with respect

to MT1, the gate current flows through P2-N2 junction

• The junction P1-N1 and P2-N2 are forward

biased but junction N1-P2 is reverse biased.

• When sufficient number of charge carriers are injected in P2 layer by the gate current the junction N1-P2 breakdown and triac starts conducting through P1N1P2N2 layers.

• Once triac starts conducting the current increases and its V-I characteristics is similar to that of thyristor. Triac in this mode operates in the first-quadrant.

469

MODE 2

• MT2 positive, Negative gate current

(I- mode of operation)

P1

N1

N2N3

P2

Ig

MT2 (+)

MT1 ( )G

V

Finalconduction

Initialconduction

470

• When MT2 is positive and gate G is negative with

respect to MT1 the gate current flows through P2-N3

junction

• The junction P1-N1 and P2-N3 are forward biased

but junction N1-P2 is reverse biased. Hence, the triac

initially starts conducting through P1N1P2N3 layers.

• As a result the potential of layer between P2-N3 rises

towards the potential of MT2.

• Thus, a potential gradient exists across the layer P2

with left hand region at a higher potential than the

right hand region.

471

• This results in a current flow in P2 layer from left to right, forward biasing the P2N2 junction. Now the right hand portion P1-N1 - P2-N2 starts conducting.

• The device operates in first quadrant. When compared to Mode 1, triac with MT2 positive and negative gate current is less sensitive and therefore requires higher gate current for triggering.

472

MODE 3

• MT2 negative, Positive gate current

(III+ mode of operation)

P1

N1

N4

N2

P2

Ig

MT2 ( )

MT1 (+)G(+)

473

• When MT2 is negative and gate is positive with respect to MT1 junction P2N2 is forward biased and junction P1-N1 is reverse biased.

• N2 layer injects electrons into P2 layer as shown by arrows in figure below.

• This causes an increase in current flow through junction P2-N1. Resulting in breakdown of reverse biased junction N1-P1.

• Now the device conducts through layers P2N1P1N4 and the current starts increasing, which is limited by an external load.

• The device operates in third quadrant in this mode. Triac in this mode is less sensitive and requires higher gate current for triggering.

474

MODE 4

• MT2 negative, Negative gate current

(III+ mode of operation)

P1

N1

N4

P2

Ig

MT2 ( )

MT1 (+)

N3

G(+)

475

• In this mode both MT2 and gate G are negative with

respect to MT1, the gate current flows through P2N3

junction as shown.

• Layer N3 injects electrons as shown by arrows into

P2 layer. This results in increase in current flow

across P1N1 and the device will turn ON due to

increased current in layer N1.

• The current flows through layers P2N1P1N4. Triac is

more sensitive in this mode compared to turn ON

with positive gate current. (Mode 3).

476

• Triac sensitivity is greatest in the first quadrant when

turned ON with positive gate current and also in third

quadrant when turned ON with negative gate current.

when is positive with respect to it is recommended

to turn on the triac by a positive gate current.

• When is negative with respect to it is recommended

to turn on the triac by negative gate current.

Therefore Mode 1 and Mode 4 are the preferred

modes of operation of a triac (mode and mode of

operation are normally used).

477

Triac characteristics RL

MT1

MT2

Rg

Vs

Vgg

I

A

A

VG

+

+

++

+

-

-

-

-

-

478

V-I Characteristics of a triac

VB02

MT2( )

G( )

MT2(+)

G(+)

VB01

VB01, V

- Breakover voltages B01

Ig1

Ig2I

VV

I > Ig2 g21

479

Single phase full wave ac

voltage controller

(Bi-directional Controller) using

TRIAC

480

Single phase full wave ac voltage

controller (Bi-directional Controller)

using TRIAC

481

Waveforms of single phase full

wave ac voltage controller

482

Single phase full wave ac controller with

common cathode

(Bidirectional controller in common

cathode configuration)

483


Controller Using A Single Thyristor

RL

T1

ACSupply

-

D1

D4

D3

D2

+

484

CYCLOCONVERTER

485

CYCLOCONVERTER

• A device which converts input power at one

frequency to the out put power at different

frequency with one stage conversion is called

a cycloconverter.

• A cycloconverter requires one stage frequency

conversion.

• Cycloconverter of two types

(i) Step-Up Cycloconverter ( fo > s)

(ii) step-Down Cycloconverter ( fo < fs)


Single phase to single phase Mid point type

step-up Cycloconverter

with R load

487


Single phase to single phase Bridge

type step-up

Cycloconverter with R load

489


1-φ to 1-φ Mid point type step-Down


491

Output voltage (Vo) and current (Io) waveform

492

1-φ to 1-φ Bridge type Cyclo-

converter with R and R-L load


1-φ to 1-φ Bridge type step-Down



Output voltage (Vo) and current (Io) waveform


1-φ to 1-φ Midpoint type step-Down

Cycloconverter with R-L load


Output voltage (Vo) and current (Io)

waveform for Discontinuous

Conduction mode



waveform for Continuous Conduction mode


1-φ to 1-φ Bridge-type step-Down

Cycloconverter with R-L load



waveform for Discontinuous

Conduction mode



waveform for Continuous Conduction

mode

UNIT-V

DC-AC CONVERTERS

(INVERTERS)

501

502

Single-phase half-bridge inverter

503

Operational Details

• Consists of 2 choppers, 3-wire DC source

• Transistors switched on and off alternately

• Need to isolate the gate signal for Q1 (upper device)

• Each provides opposite polarity of Vs/2 across the load

3-wire DC

source

504

Q1 on, Q2 off, vo = Vs/2

Peak Reverse Voltage of Q2 = Vs

505

Q1 off, Q2 on, vo = -Vs/2

506

Waveforms with resistive load

507

Look at the output voltage

1

222

0

2

4 2

oT

s so

o

V VV dt

T

rms value of the output voltage, Vo

508

Fourier Series of the instantaneous output

voltage

1

0

0

1,3,5,..

cos( ) sin( )2

, 0

1sin( ) ( ) sin( ) ( )

2 2

21,3,5,...

2sin( )

oo n n

n

o n

s sn

sn

so

n

av a n t b n t

a a

V Vb n t d t n t d t

Vb n

n

Vv n t

n

509

rms value of the fundamental component

1,3,5,..

1

1

2sin

21

2

0.45

so

n

so

o s

Vv n t

n

VV

V V

510

When the load is highly inductive

511

Turn off Q1 at t = To/2

Current falls to 0 via D2, L, Vs/2 lower

+

Vs/

2

- +

Vs/2

-

512

Turn off Q2 at t = To

Current falls to 0 via D1, L, Vs/2 upper

+

Vs/

2

- +

Vs/2

-

513

Load Current for a highly inductive load

Transistors are only switched on for a quarter-cycle, or 90

514

Fourier Series of the output current for an RL

load

2 21,3,5,...

1

2sin( )

( )

tan ( )

o o so n

n

n

v v Vi n t

Z R jn L n R n L

n L

R

515

Fundamental Output Power

In most cases, the useful power

2

1 1 1 1 1

2

12 2

cos

2

2 ( )

o o o o

so

P V I I R

VP R

R L

516

DC Supply Current

• If the inverter is lossless, average power absorbed by the load equals the average power supplied by the dc source.

• For an inductive load, the current is approximately sinusoidal and the fundamental component of the output voltage supplies the power to the load. Also, the dc supply voltage remains essentially at Vs.

0 0

( ) ( ) ( ) ( )

T T

s s o ov t i t dt v t i t dt

517

1 1

0 0

11

1( ) 2 sin( ) 2 sin( )

cos( )

T T

s o o s

s

os o

s

i t dt V t I t dt IV

VI I

V

DC Supply Current (continued)

518

Performance Parameters

• Harmonic factor of the nth harmonic (HFn)

1

onn

o

VHF

V for n>1

Von = rms value of the nth harmonic component

V01 = rms value of the fundamental component

519

Performance Parameters (continued)

• Total Harmonic Distortion (THD)

• Measures the “closeness” in shape between a

waveform and its fundamental component

1

2 2

2,3,...1

1( )on

no

THD VV

520


• Distortion Factor (DF)

• Indicates the amount of HD that remains in a

particular waveform after the harmonics have been

subjected to second-order attenuation.

12 2

22,3,...1

2

1

1 on

no

onn

o

VDF

V n

VDF

V n

for n>1

521


• Lowest order harmonic (LOH)

• The harmonic component whose frequency

is closest to the fundamental, and its

amplitude is greater than or equal to 3% of

the amplitude of the fundamental

component.

522

Single-phase full-bridge inverter

523

Operational Details

• Consists of 4 choppers and a 3-wire DC source

• Q1-Q2 and Q3-Q4 switched on and off alternately

• Need to isolate the gate signal for Q1 and Q3 (upper)

• Each pair provide opposite polarity of Vsacross the load

524

Q1-Q2 on, Q3-Q4 off, vo = Vs

+ Vs -

525

Q3-Q4 on, Q1-Q2 off, vo = -Vs

- Vs +

526

When the load is highly inductive

Turn Q1-Q2 off – Q3-Q4 off

527

Turn Q3-Q4 off – Q1-Q2 off

528

Load current for a highly inductive load

Documents

III B. Tech I semester (JNTUH-R15) - iare.ac.in PPT.pdf•GATI . 4 Thyristor/Triac SCR1 2N3668 MT1 ... involved, and are often used ... The process of turning off an SCR is called