### Chapter 5

```Chapter 5
AC-to-AC Converters
“Introduction to Modern Power Electronics”, 2nd Ed., John Wiley 2010
by
1
Single-phase ac voltage controller
T1
ii = io
io
T2
SOURCE
vo
vi
Fig. 5.1
Chapter 5
2
Waveforms of output voltage and current in a
single-phase ac voltage controller ( = 30 ): (a)
= 45 , (b)  = 135
vo
Vi,p
vi
e
0
-
io
2
4
f
t
Vi,p
(a)
Vi,p
vi
vo
e
0
-
io
2
f
4
t
Vi,p
(b)
Fig. 5.2
Chapter 5
3
Envelope of control characteristics,  = ( ),
of a single-phase ac voltage controller
1.0
MAGNITUDE CONTROL RATIO
0.8
0.6
0.4
0.2
0.0
0
30
60
90
120
150
180
FIRING ANGLE (deg)
Fig. 5.3
Chapter 5
4
Operation of a single-phase ac voltage
controller with (a) single-pulse gate signal, (b)
multipulse gate signal
vo
io ig2
ig1
0
ig2
ig1
2
4
t
f
vi
(a)
vi = vo
ig1 i
o
0
ig2
ig1
2
ig2
4
f
t
(b)
Fig. 5.4
Chapter 5
5
Definition of a control angle
vi
vo
io
e
0
f
2
t
'
Fig. 5.5
Chapter 5
6
Envelope of control characteristics,  = (′ ),
of a single-phase ac voltage controller
1.0
MAGNITUDE CONTROL RATIO
0.8
0.6
0.4
0.2
0.0
0
30
60
90
120
150
180
CONTROL ANGLE (deg)
Fig. 5.6
Chapter 5
7
Fully controlled
controller
three-phase
ac
voltage
SUPPLY LINE
A
B
C
iA
iB
TA
va
iC
TB
vb
vc
TC
Fig. 5.7
Chapter 5
8
Voltage and current distribution in a fully
controlled three-phase ac voltage controller: (a)
two triacs conducting, (b) three triacs
conducting
iA
TA
vA
vA
vB
vB
vC
vC
-iB
TB
iB
iA
TC
TA
TB
iC
TC
1
_v
2 BA
1
_
v
2 AB
vAB
vA
vB
vC
(b)
(a)
Fig. 5.8
Chapter 5
9
Output voltage waveforms in a fully controlled
three-phase ac voltage controller: (a)  = 0 ,
1
a
1
b 1
c
vA= va
vB
vC
0
0
30
60
90 120 150 180 210 240 270 300 330 360
f
t (deg)
(a)
a 0
b
c 1
1
1
0
1
2
vAB
0
vA
va
-1 vAC
2
0
0
30
f
60
90 120 150 180 210 240 270 300 330 360
t (deg)
(b)
Fig. 5.9
Chapter 5
10
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)
(+)
PHASE A
0
(-)
POLARITY
(+)
0
PHASE B
(-)
PHASE C
(+)
0
(-)
0
60
90
FIRING ANGLE (deg)
Fig. 5.10
Chapter 5
11
Output voltage waveforms in a fully controlled
three-phase ac voltage controller: (a)  = 75 ,
mode 2, (b)  = 120 ,  3
a 1
b 0
c
0
1
1
1
2
1
2
0
vAB
vA
va
vAC
0
90
60
30
0
120 150 180 210 240 270 300 330 360
f
t
(deg)
(a)
1
a
b
c
0
0
1
0
-1
2
1
vAB
vA
1
2
vAC
va
0
0
30
60
90
120 150 180 210 240 270 300 330 360
f
t
(deg)
(b)
Fig. 5.11
Chapter 5
12
Envelope of control characteristics,  = ( ),
of a fully controlled three-phase ac voltage
controller
1.0
MAGNITUDE CONTROL RATIO
0.8
0.6
0.4
0.2
0.0
0
30
60
90
120
150
180
FIRING ANGLE (deg)
Fig. 5.12
Chapter 5
13
Envelope of control characteristics,  = (′ ),
of a fully controlled three-phase ac voltage
controller
1.0
MAGNITUDE CONTROL RATIO
0.8
0.6
0.4
0.2
0.0
0
30
60
90
120
150
180
CONTROL ANGLE (deg)
Fig. 5.13
Chapter 5
14
Three-phase ac voltage controllers connected
before the load: (a) half-controlled, (b) deltaconnected
A
A
B
B
C
C
(a)
(b)
Fig. 5.14
Chapter 5
15
Three-phase ac voltage controllers connected
after the load: (a) wye-connected, (b) deltaconnected
A
A
B
B
C
C
(a)
(b)
Fig. 5.15
Chapter 5
16
Three-phase four-wire ac voltage controller
A
B
C
N
Fig. 5.16
Chapter 5
17
Single-phase ac chopper with an input filter
S1
i i'
ii
io
S2
S3
vi
S4
vo
Fig. 5.17
Chapter 5
18
Waveforms of voltages and currents in a singlephase ac chopper: (a) output voltage and
current, (b) input voltage and current after the
input filter, and the fundamental output current
vo
io
t
0
(a)
vi
ii,1
ii
t
0
1
(b)
Fig. 5.18
Chapter 5
19
Control characteristic of an ac chopper
1.0
MAGNITUDE CONTROL RATIO
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
MODULATION INDEX
Fig. 5.19
Chapter 5
20
Wye-connected three-phase ac choppers: (a)
three-wire, (b) four wire
A
A
B
B
C
C
N
S2
S3
S1
S2
S4
S3
S1
S4
(b)
(a)
Fig. 5.20
Chapter 5
21
Delta-connected three-phase ac chopper
S1
S4
S2
S3
Fig. 5.21
Chapter 5
22
Changes in the firing angle in a cycloconverter
180
M=1
150
M=0.75
M=0.5
M=0.25
90
M=0
f
(deg)
120
60
30
0
0
60
120
180
ot
240
300
360
(deg)
Fig. 5.22
Chapter 5
23
Output voltage waveforms in a six-pulse
cycloconverter: (a) M = 1, (b) M = 0.5
(  = 5)
vo1
ot
0
(a)
vo1
ot
0
(b)
Fig. 5.23
Chapter 5
24
Three-phase three-pulse cycloconverter
Fig. 5.24
Chapter 5
25
Three-phase six-pulse cycloconverter with
Fig. 5.25
Chapter 5
26
Three-phase six-pulse cycloconverter
with
Fig. 5.26
Chapter 5
27
Three-phase to three-phase (3-3) matrix
converter
SUPPLY LINE
INPUT FILTER
iA
iB
iC
vA
SAa
MATRIX
CONVERTER SAb
SAc
A
vB
SBa
SBb
SBc
vC
a
SCa
SCb
SCc
B
C
b
c
ia
ib
ic
va
vb
vc
vn
Fig. 5.27
Chapter 5
28
Arrangement of 3-1 and 1-3 matrix
converters, equivalent to a 3-3 matrix
converter
a
Idc
CONV 1
SAP
SBP
SCP
SAN
SBN
SCN
A
B
Vdc
c
b
CONV 2
SPa
SPb
SPc
SNa
SNb
SNc
P
N
C
Fig. 5.28
Chapter 5
29
State AAB as realized by activation od switches
in (a) virtual rectifier and inverter, (b) matrix
converter
A
B
C
P
SAP
SBP
SCP
SAN
SBN
SCN
N
SPa
SPb
SPc
SNa
SNb
SNc
b
a
c
(a)
B
A
C
SAa
SBa
SCa
SAb
SBb
SCb
SAc
SBc
SCc
a
b
c
(b)
Fig. 5-29
Chapter 5
30
Reference current vector in the vector space of
input currents of the virtual rectifier
jq
j 3 IDC I 0PN
I NP0
III
II
i*
I P0N
I*


IV
_3 I
2 DC
d
I
I N0P
VI
V
IPN0
I0NP
Fig. 5-30
Chapter 5
31
Reference voltage vector in the vector space of
line-to-neutral output voltages of the virtual
inverter
jq
VNPN
III
VNPP
v*
_
V3
j_
2
VDC

VPPN
II

I
V*
VDC
VI
IV
d
VPNN
V
VPNP
VNNP
Fig. 5-31
Chapter 5
32
TABLE 5.1 Switching Pattern for 3Φ-3Φ Matrix Converter with Space Vector PWM
Switching Subcycle
1
2
3
4
5
6
7
8
9
Rectifier State
XI
XI
YI
YI
ZI
YI
YI
XI
XI
Inverter State
XV
YV
YV
XV
ZV
XV
YV
YV
XV
Chapter 5

dXIdXV/2
dXIdYV/2
dYIdYV/2
dYIdXV/2
1 – (dXI + dYI )( dXV + dYV)
dYIdXV/2
dYIdYV/2
dXIdYV/2
dXIdXV/2
33
Output voltage and current waveforms in a 33 matrix converter: (a) N = 48, m = 0.7,
= 2.8, (b) N = 12, m = 0.35,   = 0.7
vo
0
ot
io
(a)
vo
o
t
io
(b)
Fig. 5-32
Chapter 5
34
Bidirectional semiconductor power switches: (a)
two IGBTs and two diodes, (b) one IGBT and
four diodes
(b)
(a)
Fig. 5-33
Chapter 5
35
TABLE 5.2 Switching Pattern for the Example Matrix Converter
Switching Subcycle
1
2
3
4
5
6
7
8
9
Rectifier State
0PN
0PN
NP0
NP0
Z00 or 0Z0
NP0
NP0
0PN
0PN
Inverter State
PPN
NPN
NPN
PPN
PPP
PPN
NPN
NPN
PPN

0.156
0.035
0.009
0.057
0.486
0.057
0.009
0.035
0.156
TABLE 5.3 Activation of Switches in the Example Matrix Converter
Switching Subcycle
1
2
3
4
5
6
7
8
9
State of Matrix Converter
BBC
CBC
ABA
BBA
BBB
BBA
ABA
CBC
BBC
Chapter 5
Activated Switches
SBa, SBb, SCc
SCa, SBb, SCc
SAa, SBb, SAc
SBa, SBb, SAc
SBa, SBb, SBc
SBa, SBb, SAc
SAa, SBb, SAc
SCa, SBb, SCc
SBa, SBb, SCc
Duration (µs)
31.2
7.0
1.8
11.4
97.2
11.4
1.8
7.0
31.2
36
Switching signals for individual switches in a
matrix converter in Example 5.4
SAa
SAb
SAc
S Ba
SBb
SBc
SCa
SCb
SCc
0
50
100
150
200
TIME, s
Fig. 5-34
Chapter 5
37
```