### Chapter 7

```Chapter 7
DC-to-AC Converters
“Introduction to Modern Power Electronics”, 2nd Ed., John Wiley 2010
by
1
Voltage-source inverter supplied form a diode
rectifier
INVERTER
AC LINE
RECTIFIER
Fig. 7.1
Chapter 7
2
Single-phase voltage-source inverter
ii
SA
DA
SB
DB
SB'
DB'
io
Vi
vo
SA'
DA'
Fig. 7.2
Chapter 7
3
TO INVERTER
FROM RECTIFIER
Circuit diagram of a Z-source
Fig. 7.3
Chapter 7
4
States, switching variables, and waveforms of
output voltage and current in a single-phase VSI
in the basic square-wave mode
STATE: 2
1
2
1
a
0
t
0
Vi
0
-
t
b
vo
io
4
2
t
3
Vi
Fig. 7.4
Chapter 7
5
States, switching variables, and waveforms of
output voltage and current in a single-phase VSI
in the optimal square-wave mode
STATE: 2
3
1
0
2
3
1
0
a
0
b
t
0
Vi
vo
io
2
0
Vi
4
t
3
0.81
-
t
Fig. 7.5
Chapter 7
6
Waveforms of output voltage and current in a
single-phase VSI in the PWM mode, N = 10: (a)
m = 1, (b) m = 0.5
Vi
vo
io
t
0
-
Vi
(a)
Vi
vo
io
t
0
-
Vi
(b)
Fig. 7.6
Chapter 7
7
Waveforms of output voltage and current in a
single-phase VSI in the PWM mode, N = 20: (a)
m = 1, (b) m = 0.5
Vi
vo
io
t
0
-
Vi
(a)
Vi
vo
io
t
0
-
Vi
(b)
Fig. 7.7
Chapter 7
8
Harmonic spectra of output voltage in a singlephase VSI: (a) basic square-wave mode, (b)
optimal square-wave mode
10
AMPLITUDE (pu)
1
0.1
0.01
0.001
0
20
40
60
80
100
80
100
HARMONIC NUMBER
(a)
10
AMPLITUDE (pu)
1
0.1
0.01
0.001
0
20
40
60
HARMONIC NUMBER
(b)
Fig. 7.8
Chapter 7
9
Harmonic spectra of output voltage in a singlephase VSI in the PWM mode (m = 1): (a) N =
10, (b) N = 20
10
AMPLITUDE (pu)
1
0.1
0.01
0.001
0
20
40
60
80
100
80
100
HARMONIC NUMBER
(a)
10
AMPLITUDE (pu)
1
0.1
0.01
0.001
0
20
40
60
HARMONIC NUMBER
(b)
Fig. 7.9
Chapter 7
10
Harmonic spectra of output current in a singlephase VSI: (a) basic square-wave mode, (b)
optimal square-wave mode
10
AMPLITUDE (pu)
1
0.1
0.01
0.001
0
20
40
60
80
100
80
100
HARMONIC NUMBER
(a)
10
AMPLITUDE (pu)
1
0.1
0.01
0.001
0
20
40
60
HARMONIC NUMBER
(b)
Fig. 7.10
Chapter 7
11
Harmonic spectra of output current in a singlephase VS in the PWM mode (m = 1): (a) N = 10,
(b) N = 20
10
AMPLITUDE (pu)
1
0.1
0.01
0.001
0
20
40
60
80
100
80
100
HARMONIC NUMBER
(a)
10
AMPLITUDE (pu)
1
0.1
0.01
0.001
0
20
40
60
HARMONIC NUMBER
(b)
Fig. 7.11
Chapter 7
12
Waveforms of input current in a single-phase
VSI: (a) optimal square-wave mode, (b) PWM
mode (m = 1, N = 20)
ii
t
0
(a)
ii
t
0
(b)
Fig. 7.12
Chapter 7
13
Harmonic spectra of input current in a single
phase VSI: (a) optimal square-wave mode, (b)
PWM mode (m = 1, N = 20)
1
AMPLITUDE (pu)
0.1
0.01
0.001
0.0001
0
10
20
30
40
50
40
50
HARMONIC NUMBER
(a)
1
AMPLITUDE (pu)
0.1
0.01
0.001
0.0001
0
10
20
30
HARMONIC NUMBER
(b)
Fig. 7.13
Chapter 7
14
Three-phase voltage-source inverter
ii
SA
DA
SB
DB
SC
DC
SA'
DA'
SB'
DB'
SC'
DC'
Vi
vAB
vBC
A
B
iA
vAN
vCA
C
iB
vBN
iC
vCN
N
Fig. 7.14
Chapter 7
15
TABLE 7.1 States and Voltages of the Three-Phase Voltage-Source Inverter
______________________________________________________________________________
State
abc

____________________________________________________________________________________________________________________
0
000
0
0
0
0
0
0
1
001
0
-1
1
-1/3
-1/3
2/3
2
010
-1
1
0
-1/3
2/3
-1/3
3
011
-1
0
1
-2/3
1/3
1/3
4
100
1
0
-1
2/3
-1/3
-1/3
5
101
1
-1
0
1/3
-2/3
1/3
6
110
0
1
-1
1/3
1/3
-2/3
7
111
0
0
0
0
0
0
______________________________________________________________________________
Chapter 7
16
Switching variables and waveforms of output
voltages in a three-phase VSI in the squarewave mode
STATE: 5
4
6
2
3
1
a
t
b
t
c
t
vAB
Vi
t
vBC
t
vCA
t
vAN
t
vBN
t
vCN
t
0
_1
3
_4
3
_2
3
_5
3
2
Fig. 7.15
Chapter 7
17
Waveforms of output voltage (line-to-neutral)
and current in a three-phase VSI in the squarewave mode (RL load)
_2 Vi
3
vAN
iA
0
2
3
4
t
2
- _ Vi
3
Fig. 7.16
Chapter 7
18
Waveforms of input current in a three-phase VSI
in the square-wave mode (RL load)
ii
t
0
2
Fig. 7.17
Chapter 7
19
Switching variables and waveforms of output
voltages in a three--phase VSI in the PWM
mode
a
t
b
t
c
t
vAB
t
vBC
t
vCA
t
vAN
t
vBN
t
vCN
t
0
2
Fig. 7.18
Chapter 7
20
Waveforms of the output voltage and current in
an RL load of a three-phase VSI in the PWM
60
_2 Vi
3
vAN
iA
t
0
2
- _ Vi
3
(a)
_2 Vi
3
vAN
iA
t
0
2
- _ Vi
3
(b)
Fig. 7.19
Chapter 7
21
Waveforms of input current in a three-phase VSI
in the PWM mode (a) load angle of 30 , (b) load
angle of 60
ii
t
0
(a)
ii
t
0
(b)
Fig. 7.20
Chapter 7
22
Carrier-comparison PWM technique (N = 12, m =
0.75)
rA
y
rB
rC
t
a
t
b
t
c
t
0
2
Fig. 7.21
Chapter 7
23
Third-harmonic modulating
components at m = 1
function
and
its
1st
1
F(1, t )
3
rd
2
0
t
-1
Fig. 7.22
Chapter 7
24
Voltage space vector plane of a three-phase VSI
(per-unit)
jq
V2
III
_
2_
V3
v*
V6
1

II

I
_
2_
V3
m
V3
VI
IV
d
V4
V
V1
-1
V5
Fig. 7.23
Chapter 7
25
High-quality space sequence
STATE:
1
X
(4)
Y
(6)
100
110
a
Z1
(7)
Y
(6)
X
(4)
Z2
(0)
111
110
100
000
T_X
2
T_Z
2
0
b
1
0
c
1
0
T_X
2
T_Y
2
T_Z
2
T_Y
2
Tsw
Fig. 7.24
Chapter 7
26
High-efficiency space sequence
STATE:
1
X
(4)
Y
(6)
100
110
a
Z
(7)
Y
(6)
X
(4)
111
110
100
0
b
1
0
c
1
0
T_X
2
T_Y
2
TZ
T_Y
2
T_X
2
Tsw
Fig. 7.25
Chapter 7
27
Switching pattern with half- and quarter-wave
symmetries
a
1
0
0
_1
2
3
_
2
t
2
Fig. 7.26
Chapter 7
28
Optimal primary switching angles as functions of
the magnitude control ratio (K = 5)
90
OPTIMAL PRIMARY SWITCHIN
75
60
45
30
15
0
0.0
0.2
0.4
0.6
0.8
1.0
MAGNITUDE CONTROL RATIO
Fig. 7.27
Chapter 7
29
Harmonic spectrum of line-to-neutral voltage with
the harmonic-elimination technique (K = 5, M = 1)
1
AMPLITUDE (pu)
0.1
0.01
0.001
0.0001
0
20
40
60
80
100
HARMONIC NUMBER
Fig. 7.28
Chapter 7
30
Switching patterns and output voltage and current
waveforms; (1) carrier-comparison PWM with
sinusoidal reference, (2) space vector PWM with
high-efficiency state sequence, (3) programmed
PWM with harmonic elimination
a
0
t
vAN
iA
(1)
t
0
a
0
t
vAN
iA
(2)
t
0
a
0
(3)
vAN
t
iA
t
0
0
2
Fig. 7.29
Chapter 7
31
Waveforms of output current in a three-phase VSI:
(a) regular PWM, (b) random PWM
iA
iB
iC
t
0
(a)
iA
iB
iC
t
0
(b)
Fig. 7.30
Chapter 7
32
Frequency spectra of the line-to-neutral output
voltage in a three-phase VSI: (a) regular PWM, (b)
random PWM
1
AMPLITUDE (pu)
0.1
0.01
0.001
0.0001
0
48
96
144
192
144
192
HARMONIC NUMBER
(a)
1
AMPLITUDE (pu)
0.1
0.01
0.001
0.0001
0
48
96
HARMONIC NUMBER
Fig. 7.31
Chapter 7
33
Comparison of random PWM techniques with the
regular PWM
SAMPLING/SWITCHINGCYCLES
n
n+1
n+2
n+4
n+3
...
t
PWM
SAMPLING/SWITCHINGCYCLES
n
n+1
n+3
n+2
n+4
...
t
RPWM
T smp
SAMPLINGCYCLES
n
n+1
n+2
n+4
n+3
...
t
SWITCHINGCYCLES
n-1
n
n+1
n+2
n+3
n+4
...
t
VD-RPWM
t del
T sw,n
Fig. 7.32
Chapter 7
34
Hysteresis current control scheme
A
B
N
C
iA
 iA
i A*
iB
 iB
i B*
iC
 iC
i C*
Fig. 7.33
Chapter 7
35
Characteristic of the hysteresis current controller
a
1
0
h
h
2
2
 iA
Fig. 7.34
Chapter 7
36
Waveforms of output currents in a VSI with
hysteresis current control: (a) 20% tolerance, (b)
10% tolerance
iA
iB
iC
t
0
(a)
iA
iB
iC
t
0
(b)
Fig. 7.35
Chapter 7
37
Waveform of output currents in a VSI with
hysteresis current control at a rapid change in the
magnitude, frequency, and phase of the reference
current
iA
t
0
Fig. 7.36
Chapter 7
38
Space vector version of the hysteresis current
control scheme
A
B
N
C
 id
i d*
id
 iq
i q*
a
zd
b
c
SWITCHING
TABLE
zq
iq
iC
dq
abc
iA
Fig. 7.37
Chapter 7
39
Characteristic of a current controller for the space
vector version of the hysteresis current control
scheme
zd
1
h
2
h
0
4
h
h
4
2
 id
-1
Fig. 7.38
Chapter 7
40
Characteristic of a current controller for the space
vector version of the hysteresis current control
scheme
RAMP GENERATOR
y
CONTROLLER
iA
iA*
iA
COMPARATOR
zA
a
iA
Fig. 7.39
Chapter 7
41
Waveforms of the output current in a VSI with the
ramp
comparison
current
control:
(a)  1 = 10, (b)  1 = 20
iA
iB
iC
t
0
(a)
iA
iB
iC
t
0
(b)
Fig. 7.40
Chapter 7
42
Current-regulated delta modulation scheme for a
current-controlled VSI
iA
iA*
S&H
a
iA
Fig. 7.41
Chapter 7
43
Linear current control scheme for a VSI
A
B
N
C
LINEAR
CONTROLLERS
id
i d*
id
 iq
i q*
a
v*d
v*q
b
c
PULSE
WIDTH
MODULATOR
iq
iC
dq
abc
iA
Fig. 7.42
Chapter 7
44
Current-source inverter supplied from a controlled
rectifier
INVERTER
AC LINE
RECTIFIER
CURRENT FEEDBACK
Fig. 7.43
Chapter 7
45
Three-phase current-source inverter
ii
SA
SB
SC
SA'
SB'
SC'
Ii
vAB
vBC
A
B
iA
vAN
vCA
iB
vBN
C
iC
vCN
N
Fig. 7.44
Chapter 7
46
Switching variables in a three-phase CSI in the
square-wave mode
a
t
a'
t
b
t
b'
t
c
t
c'
t
0
_1
3
_4
3
_2
3
_5
3
2
Fig. 7.45
Chapter 7
47
Idealized waveforms of output currents in a threephase CSI in the square-wave mode
iA
Ii
t
iB
t
iC
t
iAB
t
iBC
t
iCA
t
0
_1
3
_4
3
_2
3
_5
3
2
Fig. 7.46
Chapter 7
48
Waveforms of output voltage and current in a threephase CSI in the square-wave mode: (a) RL load,
vAN
t
0
iA
(a)
vAN
iA
t
0
(b)
Fig. 7.47
Chapter 7
49
Three-phase PWM current-source inverter
RECTIFIER
INVERTER
A i'A
iA
AC LINE
i C,AB
B i'B
iB
N
iC,BC
i C,CA
C i'C
iC
CURRENT FEEDBACK
Fig. 7.48
Chapter 7
50
Carrier-comparison method for the PWM CSI
Fig. 7.49
Chapter 7
51
Optimal switching pattern for the PWM CSI with two
primary switching angles
Fig. 7.50
Chapter 7
52
Waveforms of the output current, capacitor current,
and output voltage in a three-phase PWM CSI
(wye-connected RL load, P = 9)
iA'
t
0
iA
t
0
iC,AB
t
0
vAN
t
0
0
2
Fig. 7.51
Chapter 7
53
Generic five-level inverter
S1
V1
C1
Vi
4
S2
V2
C2
Vi
Vi
4
V3
C3
Vi
4
S3
S4
V4
C4
V5
vo
Vi
4
S5
Fig. 7.52
Chapter 7
54
Half-bridge voltage-source inverter
ii
Vi
io
vo
Fig. 7.53
Chapter 7
55
Three-level neutral-clamped inverter
ii
S1
D1
S2
D2
S3
D3
D5
C1
Vi
G
C2
vBN
D6
S4
D4
vBC
vAB
A
B
iA
iB
vAN
vBN
vCA
C
iC
vCN
N
Fig. 7.54
Chapter 7
56
Voltage space vectors of a three-level neutralclamped inverter
V6
V7
V8
jq
_
_
V3
2
V15
V3 = V16
V24
V12 = V25
V21
V9 = V22
V4 = V17
V18
1
-1
V5
V1 = V14
V2
V10 = V23
_
V3
-j _
2
V11
d
V19
V20
Fig. 7.55
Chapter 7
57
States, switching variables, and waveforms of
output voltage in a three-level neutral-clamped
inverter in the square-wave mode
STATE: 18 21 24 15 6 7 8 5 2 11 20 19
a
t
b
t
c
t
vAB
Vi
t
vBC
t
vCA
t
vAN
t
vBN
t
vCN
t
0
2
Fig. 7.56
Chapter 7
58
Waveforms of output voltage and current in a threelevel neutral-clamped inverter in the square-wave
mode
_2 Vi
3
vAN
iA
0
2
3
4
t
2
- _ Vi
3
Fig. 7.57
Chapter 7
59
One phase of a multilevel cascaded H-bridge
inverter
Fig. 7.58
Chapter 7
60
Switched network for illustration of the operating
principle of a resonant dc link
R
ii
L
iC
Vi
C
iS
iD
S
D
vo
Io
Fig. 7.59
Chapter 7
61
Waveforms of voltage and current in the resonant
g
t
0
ii
I2
Io
t
0 i
S
0
iD
t0
0
t
t
iC
t
0
vo
Vi
t1
t2
t3
t
0
0
Fig. 7.60
Chapter 7
62
Three-phase resonant dc link inverter with an active
clamp
C cl
D
S
L
Vi
C
A
B
C
N
Fig. 7.61
Chapter 7
63
Waveforms of line-to-line output voltages in a
vAB
t
0
vBC
t
0
vCA
t
0
Fig. 7.62
Chapter 7
64
Auxiliary resonant commutated pole inverter: (a)
one phase with the auxiliary circuit, (b) the entire
inverter
Ci
D1
S1
Cr
S2
Cr
AC
Lr
Vi
S
Lf
Ci
D2
A
(a)
AC
AC
AC
B
A
C
(b)
Fig. 7.63
Chapter 7
65
Idealized line-to-neutral voltage and line current
waveforms in a VSI in the square-wave mode
vAN
iSA
a
t
0
iSA'
0
(a)
vAN
iSA
iDA'
a
t
0
iSA'
iDA
0
(b)
Fig. 7.64
Chapter 7
66
Block diagram of a photovoltaic utility interface
PV ARRAY
INVERTER
TRANSFORMER
DIODE RECTIFIER
CONTROLLED RECTIFIER
FILTER
GRID
Fig. 7.65
Chapter 7
67
Block diagram of an active power filter
Fig. 7.66
Chapter 7
68
Waveforms of voltage and current in an active
power filter
Fig. 7.67
Chapter 7
69
UPS System
STATIC SWITCH
RECTIFIER
INVERTER
FILTER
GRID
LINE
FILTER
BATTERY
Fig. 7.68
Chapter 7
70
Block diagram of an ac drive system with scalar
speed control
RECTIFIER
INVERTER
MOTOR
AC LINE
SPEED
SENSOR
*
v*
p
VOLTAGE CONTROLLER
*syn
*
M
*sl
SLIP CONTROLLER
*
 M
M
M
Fig. 7.69
Chapter 7
71
Use of the modular frequency changer of Figure
2.24 in an ac drive: (a) system with a braking
resistor, (b) system with a step-up chopper
BRAKING
RESISTOR
INVERTER
AC LINE
RECTIFIER
TO MOTOR
(a)
RECTIFIER
INVERTER
AC LINE
BOOST
INDUCTOR
(b)
TO MOTOR
Fig. 7.70
Chapter 7
72
power flow in ac motor drives: (a) current-type
rectifier, inductive dc link, and current-source
inverter, (b) voltage-type-rectifier, capacitive dc link,
and voltage-source inverter
RECTIFIER
INVERTER
LINE
FILTER
AC LINE
MOTOR
(a)
RECTIFIER
LINE
FILTER
INVERTER
AC LINE
MOTOR
(b)
Fig. 7.71
Chapter 7
73
Switching pattern of the inverter in Example 7.2
STATE:
1
X
(1)
Y
(5)
001
101
a
Z
(7)
Y
(5)
X
(1)
111
101
001
t ( s)
0
b
1
t ( s)
0
c
1
t ( s)
0
0
32
157.5
92.5
218
250
Fig. 7.72
Chapter 7
74
Per-unit voltage vectors of the three-level inverter in
Example 7.3
jq
V24
j 23
V15
j 43
V12 = V25
V21
v*

0
V9 = V22
0.5
V18
1
d
Fig. 7.73
Chapter 7
75
```