1

Chapter 5

AC-to-AC Converters

“Introduction to Modern Power Electronics”, 2nd Ed., John Wiley 2010by

Andrzej M. Trzynadlowski

Single-phase ac voltage controller

v

v

S O U R C E L O A D

T 1

T 2

i o

o

= i o i i i

Chapter 5 2

Fig. 5.1

Waveforms of output voltage and current in a single-phase ac voltage controller (): (a) , (b)

Chapter 5 3

Fig. 5.2

Vi,p-

Vi,p

vi

42

vi

Vi,p

4

0 t

(b)

io

vo

e

f

(a)

-

Vi,p

0

f

e

io

vo

2 t

Envelope of control characteristics, ), of a single-phase ac voltage controller

Chapter 5 4

Fig. 5.3

FIRING ANGLE (deg)

0 30 60 90 120 150 180

MA

GN

ITU

DE

CO

NT

RO

L R

AT

IO

0.0

0.2

0.4

0.6

0.8

1.0

Operation of a single-phase ac voltage controller with (a) single-pulse gate signal, (b) multipulse gate signal

Chapter 5 5

Fig. 5.4

ig2 ig1 ig2 io ig1

ig2 ig2 ig1 ig1

vi

42

vi

4

0 t

(b)

vo

f

(a)

0 f

io

vo

2 t

=

Definition of a control angle

Chapter 5 6

Fig. 5.5

vi

20 t

io

vo

e

f

'

Envelope of control characteristics, ), of a single-phase ac voltage controller

Chapter 5 7

Fig. 5.6

CONTROL ANGLE (deg)

0 30 60 90 120 150 180

MA

GN

ITU

DE

CO

NT

RO

L R

AT

IO

0.0

0.2

0.4

0.6

0.8

1.0

Fully controlled three-phase ac voltage controller

Chapter 5 8

Fig. 5.7

av v vb c

T A T B T C

LO A D

A

B

C

Ai i iB C

S U P P L Y L IN E

Voltage and current distribution in a fully controlled three-phase ac voltage controller: (a) two triacs conducting, (b) three triacs conducting

Chapter 5 9

Fig. 5.8

v

v

v

B

A

v_1

(a) (b)

C

TBTA TC

vAB

Ai -iB

vAB BA

2 _ 21

TBTA TC

Ai i iB C

Av v vB C

v

v

v

B

A

C

Output voltage waveforms in a fully controlled three-phase ac voltage controller: (a) , (b) (R load)

Chapter 5 10

Fig. 5.9

vAC

vA=

vAB21

21

0

111

vB vCva

cba

f

t (deg)

(a)

t (deg)

(b)

va

0 30 60 90 120 150 180 210 240 270 300 330 360

-

-

f

0

0101

10

cba

vA

0 30 60 90 120 150 180 210 240 270 300 330 360

Polarities of output voltages and currents in a fully controlled three-phase ac voltage controller in mode 2 before firing triac TA (solid line) and following the firing (broken line)

Chapter 5 11

Fig. 5.10

(-)

0

(+)

(-)

0

(+)

FIRING ANGLE (deg)

0 60

PO

LAR

ITY

90

PHASE C

PHASE B

PHASE A

(-)

0

(+)

Output voltage waveforms in a fully controlled three-phase ac voltage controller: (a) , mode 2, (b)

Chapter 5 12

Fig. 5.11

vACvAB

21

21

12

1

1

0 10

01

vAC

vABvA

0

va

cba

f

0

t (deg)

(a)

t (deg)

(b)

va

0 30 60 90 120 150 180 210 240 270 300 330 360

--

f

0

1

011

0

cba

vA

0 30 60 90 120 150 180 210 240 270 300 330 360

-2

-

Envelope of control characteristics, ), of a fully controlled three-phase ac voltage controller

Chapter 5 13

Fig. 5.12

FIRING ANGLE (deg)

0 30 60 90 120 150 180

MA

GN

ITU

DE

CO

NT

RO

L R

AT

IO

0.0

0.2

0.4

0.6

0.8

1.0

Envelope of control characteristics, ), of a fully controlled three-phase ac voltage controller

Chapter 5 14

Fig. 5.13

CONTROL ANGLE (deg)

0 30 60 90 120 150 180

MA

GN

ITU

DE

CO

NT

RO

L R

AT

IO

0.0

0.2

0.4

0.6

0.8

1.0

Three-phase ac voltage controllers connected before the load: (a) half-controlled, (b) delta-connected

Chapter 5 15

Fig. 5.14

A

B

C

A

B

C

(a )

(b )

Three-phase ac voltage controllers connected after the load: (a) wye-connected, (b) delta-connected

Chapter 5 16

Fig. 5.15

(a)

(b)

A

B

C

A

B

C

Three-phase four-wire ac voltage controller

Chapter 5 17

Fig. 5.16

A

B

C

N

Single-phase ac chopper with an input filter

Chapter 5 18

Fig. 5.17

i i i i'

vov i

i o

S 1

S 2

S 3 S 4

Waveforms of voltages and currents in a single-phase ac chopper: (a) output voltage and current, (b) input voltage and current after the input filter, and the fundamental output current

Chapter 5 19

Fig. 5.18

ii,1ii

io

vo

vi

t0

(a)

1

t0

(b)

Control characteristic of an ac chopper

Chapter 5 20

Fig. 5.19

MODULATION INDEX

0.0 0.2 0.4 0.6 0.8 1.0

MA

GN

ITU

DE

CO

NT

RO

L R

AT

IO

0.0

0.2

0.4

0.6

0.8

1.0

Wye-connected three-phase ac choppers: (a) three-wire, (b) four wire

Chapter 5 21

Fig. 5.20

(b )

S 2 S 1

S 4S 3

S 2 S 1

S 4S 3

(a)

A

B

C

A

B

C

N

Delta-connected three-phase ac chopper

Chapter 5 22

Fig. 5.21

S1 S4

S2 S3

Changes in the firing angle in a cycloconverter

Chapter 5 23

Fig. 5.22

M=0.5

(deg

)

0 60 120 180 240 300 360

0

30

60

90

120

150

180

M=0

M=0.25

M=0.75

M=1

(deg)ot

f

Output voltage waveforms in a six-pulse cycloconverter: (a) M = 1, (b) M = 0.5 (

Chapter 5 24

Fig. 5.23

vo1

vo1

ot

ot0

(a)

0

(b)

Three-phase three-pulse cycloconverter

Chapter 5 25

Fig. 5.24

Three-phase six-pulse cycloconverter with isolated phase loads

Chapter 5 26

Fig. 5.25

Three-phase six-pulse cycloconverter with interconnected phase loads

Chapter 5 27

Fig. 5.26

Three-phase to three-phase (3-3) matrix converter

Chapter 5 28

Fig. 5.27

SUPPLY LINE

INPUT FILTER

LOAD

A B C

a

b

cS A b

S A c S C c

S A a

S B b

S B a

S B c

S C a

S C b

iA i iB C

vA v vB C

i i ia b c

v v va b c

vn

MATRIXCONVERTER

Arrangement of 3-1 and 1-3 matrix converters, equivalent to a 3-3 matrix converter

Chapter 5 29

Fig. 5.28

A B C

a b c

S S

S S

S

SP a P b P c

N a N b N c

P

N

I

V

C O N V 1 C O N V 2

dc

dc

S AP S B P S C P

S AN S B N S C N

State AAB as realized by activation od switches in (a) virtual rectifier and inverter, (b) matrix converter

Chapter 5 30

Fig. 5-29

S S

S S

S

S

A B C

S S

S S

S

S

ba c

AP BP CP

AN BN CN

Pa Pb Pc

Na Nb Nc

S S

S S

S

S

A B C

S SS

a

b

c

Aa Ba Ca

Ab Bb Cb

Ac Bc Cc

(a)

(b)

P

N

Reference current vector in the vector space of input currents of the virtual rectifier

Chapter 5 31

Fig. 5-30

d

jq

i*

I

I

I

I

I

I II II

IV

V V I

I*

2_3 I

0PN

PN0IN0P

0NP

INP0

Ij 3 DC

DC

P0N

Reference voltage vector in the vector space of line-to-neutral output voltages of the virtual inverter

Chapter 5 32

Fig. 5-31

V

V

jq

d

VI

I

IV

II

V

III V *v *

V

V

V

DC

__V 3

2j VDC PPN

PNN

PNPNNP

VNPP

VNPN

Chapter 5 33

TABLE 5.1 Switching Pattern for 3Φ-3Φ Matrix Converter with Space Vector PWM

Switching Subcycle Rectifier State Inverter State 𝒕𝒏 𝑻𝒔𝒘Τ 1 XI XV dXIdXV/2 2 XI YV dXIdYV/2 3 YI YV dYIdYV/2 4 YI XV dYIdXV/2 5 ZI ZV 1 – (dXI + dYI )( dXV + dYV) 6 YI XV dYIdXV/2 7 YI YV dYIdYV/2 8 XI YV dXIdYV/2 9 XI XV dXIdXV/2

Output voltage and current waveforms in a 3-3 matrix converter: (a) N = 48, m = 0.7, (b) N = 12, m = 0.35,

Chapter 5 34

Fig. 5-32

0

(a)

(b)

i

vo

vo

io

o

o

o

t

t

Bidirectional semiconductor power switches: (a) two IGBTs and two diodes, (b) one IGBT and four diodes

Chapter 5 35

Fig. 5-33

(a ) (b )

Chapter 5 36

TABLE 5.2 Switching Pattern for the Example Matrix Converter

Switching Subcycle Rectifier State Inverter State 𝒕𝒏 𝑻𝒔𝒘Τ 1 0PN PPN 0.156 2 0PN NPN 0.035 3 NP0 NPN 0.009 4 NP0 PPN 0.057 5 Z00 or 0Z0 PPP 0.486 6 NP0 PPN 0.057 7 NP0 NPN 0.009 8 0PN NPN 0.035 9 0PN PPN 0.156

TABLE 5.3 Activation of Switches in the Example Matrix Converter

Switching Subcycle State of Matrix Converter Activated Switches Duration (µs) 1 BBC SBa, SBb, SCc 31.2 2 CBC SCa, SBb, SCc 7.0 3 ABA SAa, SBb, SAc 1.8 4 BBA SBa, SBb, SAc 11.4 5 BBB SBa, SBb, SBc 97.2 6 BBA SBa, SBb, SAc 11.4 7 ABA SAa, SBb, SAc 1.8 8 CBC SCa, SBb, SCc 7.0 9 BBC SBa, SBb, SCc 31.2

Switching signals for individual switches in a matrix converter in Example 5.4

Chapter 5 37

Fig. 5-34

TIME, s

0 50 100 150 200

S

Aa

Ab

Ac

Ba

Bb

Bc

Ca

Cb

Cc

S

S

S

S

S

S

S

S