Chapter 4

Report
“Introduction to Modern Power Electronics”, 2nd Ed., John Wiley 2010
by
Andrzej M. Trzynadlowski
1
SUPPLY LINE
A
B
C
N
iA
DA
iC
iB
DB
DC
io
vo
LOAD
Fig. 4.1
Chapter 4
2
vAN
vBN
vCN
0
iB = io
vBA
vBC
DB
io
vo = vBN
vBN
Fig. 4.2
Chapter 4
3
VLN,p
vo
io
t
0
2
-
VLN,p
vC
vA
vB
Fig. 4.3
Chapter 4
4
Fig. 4.4
Chapter 4
5
A
B
C
iC
iB
iA
io
DA
DB
R
DC
vo
DA'
DB'
L
DC'
E
Fig. 4.5
Chapter 4
6
vA
vB
vC
iA = i o
-i B = i o
vA
DA
io
R
vAC
vAB
vo = vAB
vAB
L
vCB
DB'
E
vB
Fig. 4.6
Chapter 4
7
Im

V^CA
V^CB
^
VCN
-V^BN
-V^AN
^
^
VAB
VBA
Re
^
VBN
^
VAN
^
-VCN
V^AC
^
VBC
Fig. 4.7
Chapter 4
8
vo
VLL,p
io
t
0
2
-
VLL,p
vBA vCA
vCB vAB vAC
vBC
Fig. 4.8
Chapter 4
9
^
V
C
SUPPLY LINE
A
^
V
F
B
^
V
D
C
^
V
A
D
E
F
^
V
B
^
V
E
io
vo
LOAD
Fig. 4.9
Chapter 4
10
1.00
DISCONTINUOUS CONDUCTION
LOAD EMF COEFFICIENT
0.95
0.90
CONTINUOUS CONDUCTION
0.85
0.80
0
15
30
45
60
75
90
LOAD ANGLE (deg)
Fig. 4.10
Chapter 4
11
vo
E
io
0
c
t
e
vBA vCA
2
vCB vAB vAC
vBC
Fig. 4.11
Chapter 4
12
iA,1
Io,dc
iA
5
_
3
0
2
t
_2
3
- Io,dc
Fig. 4.12
Chapter 4
13
10
AMPLITUDE (pu)
1
0.1
0.01
0.001
0
20
40
60
80
100
HARMONIC NUMBER
Fig. 4.13
Chapter 4
14
RECTIFIER
POWER SYSTEM
FILTER 1
(5th harmonic)
FILTER 2
(7th harmonic)
FILTER 3
(11th & 13th harmonics)
Fig. 4.14
Chapter 4
15
A
B
C
iC
iB
iA
io
TA
TB
R
TC
vo
TA'
TB'
L
TC'
E
Fig. 4.15
Chapter 4
16
Fig. 4.16
Chapter 4
17
vo
io
0
t
f
vBA vCA
2
vCB vAB vAC
vBC
Fig. 4.17
Chapter 4
18
1.00
MAGNITUDE CONTROL RATIO
0.75
0.50
0.25
0.00
-0.25
-0.50
-0.75
-1.00
0
30
60
90
120
150
180
FIRING ANGLE (deg)
Fig. 4.18
Chapter 4
19
A
B
C
io
R
Vo,dc
L
E
Fig. 4.19
Chapter 4
20
io
0
t
f
vBA vCA
vo 2
vCB vAB vAC
vBC
Fig. 4.20
Chapter 4
21
180
INFEASIBLE
FIRING ANGLE (deg)
150
120
90
60
FEASIBLE
30
0
-1.0
-0.5
0.0
0.5
1.0
LOAD EMF COEFFICIENT
Fig. 4.21
Chapter 4
22
1.00
o
0.75
ISCONTINUOUS
f=0
o
f=30
o
f=60
D
0.25
0.00
o
f=90
-0.50
f=120
o
f=150
o
ONTINUOUS
-0.25
-0.75
C
LOAD EMF COEFFICIENT
0.50
-1.00
0
15
30
45
60
75
90
LOAD ANGLE (deg)
Fig. 4.22
Chapter 4
23
vo
E
io
0
f
t
e
vBA vCA
2
vCB vAB vAC
vBC
(a)
io
0
f
t
e
2
E
vo
vBA vCA
vCB vAB vAC
vBC
(b)
Fig. 4.23
Chapter 4
24
iA,1
Io,dc
0
iA
t
f
_5
3
_2
3
2
- Io,dc
Fig. 4.24
Chapter 4
25
vAB
vAC
vBC
vBA
vCA
vCB
Rs
Rs
Rs
Rs
Rs
Rs
Ls
Ls
Ls
Ls
Ls
Ls
E
vo
L
R
T1
T2
i1
i2
io
Fig. 4.25
Chapter 4
26
vAB
vo
i1
i2
0
f
f+
ii
t
1 (vAB+v )
_
CB
2
vCB
Fig. 4.26
Chapter 4
27
vo
io
0
t
f
vBA vCA
2
vCB vAB vAC
vBC
(a)
io
0
t
f
2
vo
vBA vCA
vCB vAB vAC
vBC
(b)
Fig. 4.27
Chapter 4
28
vab
t
0
2
Fig. 4.28
Chapter 4
29
Vo,dc
INVERTER
RECTIFIER
POSITIVE VOLTAGE
POSITIVE VOLTAGE
II
I
I o,dc
III
IV
INVERTER
NEGATIVE VOLTAGE
RECTIFIER
NEGATIVE VOLTAGE
Fig. 4.29
Chapter 4
30
A
B
C
io
vo
i'o
v'o
Fig. 4.30
Chapter 4
31
A1
B1
C1
A2
B2
C2
io1
io
vo1 vo
vo2
io2
Fig. 4.31
Chapter 4
32
A
B
C
iA
iB
iC
io
TA1
TA2'
TB1
TB2'
TC1
R
TC2'
vo
TA1'
TA2
TB1'
TB2
TC1'
TC2
L
E
Fig. 4.32
Chapter 4
33
A B C
i o + i cr
i o + i cr
i cr
i o + i cr
L1
TA1
vo1
TB1'
i cr
icr
R
L2
TA2'
io
vo L vo2
TC2
E
RCT1
RCT2
Fig. 4.33
Chapter 4
34
vo1
0
f1
t
f2
2
vo2
vBA vCA
vCB vAB vAC
vBC
Fig. 4.34
Chapter 4
35
vo
icr
t
0
2
Fig. 4.35
Chapter 4
36
vo
icr
t
0
2
Fig. 4.36
Chapter 4
37
A B C
io + i cr1
io + i cr2
icr1
io + i cr1
L1
TA1
vo1
TB1'
RCT1
icr2
icr1
R
L2
io
vo L vo2
TA2'
TC2
E
io + i cr2
L3
L4
icr2
RCT2
Fig. 4.37
Chapter 4
38
i i,1
Lf
i i,h
Cf
ii
PWM RECTIFIER
vo
Fig. 4.38
Chapter 4
39
x1
t (s)
STATE:
2
0
3
2
0
x2
t (  s)
0
50
90
110
150
200
Fig. 4.39
Chapter 4
40
q
iA
A'
C
iC
B
iB
d
iB
B'
iC
C'
A
iA
Fig. 4.40
Chapter 4
41
s
jq
Im
C
A'
^
IA
C
^
IC
B
B
A
d
Re
B'
C'
^
IB
A
(a)
(b)
Fig. 4.41
Chapter 4
42
jq
s
qs
s
j

s
d
ds
Fig. 4.42
Chapter 4
43
jq
IY
dY I
Y
I*
i*
I*ma

x
I
IX
d
dX IX
Fig. 4.43
Chapter 4
44

jq
jQ
v
jvq
D
jv Q
vD
t
vd
d
Fig. 4.44
Chapter 4
45
SA
Io
iA
ia
v BN i
B
vCN
SC
ib
iC
LOAD
vAN
SB
Vo
ic
SA'
SB'
SC'
Fig. 4.45
Chapter 4
46
jq
j
3 Io
I3
II
III
I4
i*
I2


IV
_3 I
2
o
d
I
I5
VI
V
I
I1
I6
Fig. 4.46
Chapter 4
47
2
STATE:
3
9
3
2
9
a
0
b
0
c
1
a'
0
b'
0
c'
1
0.0
0.2
0.4
0.6
0.8
1.0
t / Tsw
Fig. 4.47
Chapter 4
48
RECTIFIER
vA
LOAD
vB
a...c'
VOLTAGE VECTOR
CALCULATOR

SVPWM
MODULATOR
m
Fig. 4.48
Chapter 4
49
vo
io
t
0
(a)
vo
io
t
0
(b)
Fig. 4.49
Chapter 4
50
Fig. 4.50
Chapter 4
51
io
t
0
vo
(a)
ia
ia,1
t
0
(b)
Fig. 4.51
Chapter 4
52
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. 4.52
Chapter 4
53
SA
SB
SC
Io
vAN
A iA
A'
v BN
B iB
B'
N
Vo
vCN
C iC
C'
SA'
SB'
SC'
Fig. 4.53
Chapter 4
54
Vo
SA
N'
A'
va
DA'
iA
SA'
DA
0
Fig. 4.54
Chapter 4
55
_
jq
j V3 Vo
jq
V6'
_
V2
V4'
V2'
_3
2
Vo
d
V3
j_
V
2
o
V6
V3
Vo
d
V4
V 5'
V3'
V5
V1
V1'
(b)
(a)
Fig. 4.55
Chapter 4
56
jq
V2
III
V3
v*
_
V3
j_
2

Vo
V6
II

I
Vo
VI
IV
d
V4
V
V5
V1
Fig. 4.56
Chapter 4
57

jq
jQ
i
jiq
ji Q
vD
jvq
D
iD
v

t
id
vd
d
Fig. 4.57
Chapter 4
58
RECTIFIER
iA
vA
LOAD
iB
vB
ABC
a, b, c
dq
SVPWM
MODULATOR
id
iq
vd
dq
DQ
vq
dq
DQ
vQ*
*
iQ
vD*
iQ
+-
iD*
-
+
Vo*
vd*
vq*
iD
+-
Vo
Fig. 4.58
Chapter 4
59
RECTIFIER
iA
LOAD
iB
vB
a, b, c
POWER
CALCULATOR
q
x
+
Vo
-
vA
*
Vo
STATE
SELECTOR
p
vA
y
vB
z
V'o
ABC
dq
p
p*
SECTOR
IDENTIFIER
q
+
p
q
-
-
vq
+
vd
Vo
q*
Fig. 4.59
Chapter 4
60
TABLE 4.1 State Selection in the Voltage-Type PWM Rectifier with Direct Power Control
x:
y=0
y=1
z=0
z=1
z=0
z=1
1
6
2
0
0
2
4
6
4
0
3
4
6
7
7
4
5
4
5
7
5
5
4
0
0
6
1
5
1
0
Chapter 4
7
1
5
7
7
8
3
1
3
7
9
3
1
0
0
10
2
3
2
0
11
2
3
7
7
12
6
2
6
7
61
vAN
v BN
vCN
iA
iB
iC
t
2
Fig. 4.60
Chapter 4
62
vo
io
t
Fig. 4.61
Chapter 4
63
ia
DC MACHINE
Ra
va
T n
LOAD
La
Ea
Fig. 4.62
Chapter 4
64
n
GENERATING
COUNTERCLOCKWISE
II
n
T
MOTORING
CLOCKWISE
I
T
III
MOTORING
COUNTERCLOCKWISE
IV
GENERATING
CLOCKWISE
Fig. 4.63
Chapter 4
65
A
B
C
ia
 f < 90
io
o
Ra
Vo,dc
va
Tn
La
Ea
Fig. 4.64
Chapter 4
66
A
B
C
ia
 f > 90
io
o
Ra
Vo,dc
va
n
La
Ea
T
Fig. 4.65
Chapter 4
67
RCT1
L1
L2
TR1
RCT2
TR2
SYSTEM 2
SYSTEM 1
DC LINE
L3
L4
Fig. 4.66
Chapter 4
68
a
0
b
0
c
1
a'
0
b'
0
c'
0
0
50
100
t
150
200
s
Fig. 4.67
Chapter 4
69

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