Transcript Document
EE8407
Power Converter Systems
Topic 5
Graduate Course EE8407
Bin Wu
PhD, PEng
Professor
ELCE Department
Ryerson University
Contact Info
Office: ENG328
Tel:
(416) 979-5000 ext: 6484
Email:
[email protected]
http://www.ee.ryerson.ca/~bwu/
Ryerson Campus
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Topic 5
Two-Level Voltage Source Inverter (VSI)
Source:
Alstom
VDM5000 Two-level VSI
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Two Level Voltage Source Inverter
Topic 5
Lecture Topics
• Sinusoidal PWM
• Space vector modulation
Why Use PWM Techniques?
• To control inverter output frequency (fundamental)
• To control inverter output voltage (fundamental)
• To minimize harmonic distortion
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Sinusoidal PWM
• Inverter Configuration
P
S1
S3
S5
iA
A
Vd
iB
B
Cd
C
O
iC
LOAD
S4
S6
S2
N
Assumption:
dc capacitor very large dc voltage ripple free
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Sinusoidal PWM
• Modulating and Carrier Waves
v
v cr
v mB
vmA
vmC
Vˆm
Vˆcr
0
t
• vcr – Carrier wave (triangle)
• Amplitude modulation index
• vm – Modulating wave (sine)
• Frequency modulation index
Vˆm
ma
Vˆcr
mf
f cr
fm
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Sinusoidal PWM
• Gate Signal Generation
vmA
v cr
2
0
v g1
vg 4
v AN
Vd
0
Phase A
v mA v cr
v g1 0 (v g 4 0)
S1 on ( S 4 off )
v AN Vd
v mA v cr
v g 4 0 (v g1 0)
S 4 on ( S1 off )
v AN 0
Vg1 and Vg4 are complementary
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Sinusoidal PWM
• Line-to-Line Voltage vAB
v
vcr
vmA
vmB
vmC
Vˆm
Vˆcr
t
0
P
S1
S3
S5
v AN
Vd
A
t
B
Vd
C
vBN
Vd
S4
S6
S2
t
0
v AB
v AB1
N
Vd
0
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
2
t
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EE8407
Topic 5
Sinusoidal PWM
• Waveforms and FFT
v AB
THD = 92.07%
Vd
0
2
3
v AO
THD = 92.07%
2V d / 3
0
iA
• ma = 0.8, mf = 15,
fm = 60Hz, fcr = 900Hz
THD = 7.73%
0
2
3
V AB n / V d
• Switching frequency
fsw = fcr = 900Hz
V AB1 0.49 Vd
0.2
mf
THD = 92.07%
2m f 1
2
3m f 2
0.1
4m f 1
0
1
5
10
15
20
25
30
35
40
45
50
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
55
60
n
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EE8407
Topic 5
Sinusoidal PWM
• Harmonic Content
V AB n
THD
(%)
Vd
n 1
THD
• Low order harmonics
n < (mf -2) are eliminated
300
0.3
2m f 1
mf
0.2
200
• VAB1 versus ma is linear
• VAB1,max = 0.612Vd
2
3m f 2
4m f 1
0.1
100
3m f 4
0
0
0.2
0.4
0.6
0.8
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
ma
0
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EE8407
Topic 5
Sinusoidal PWM
• Over-Modulation
v mA
2
v mB
v mC
v cr
1
0
-1
-2
v AB
Vd
0
• Fundamental voltage ↑ i
2
3
A
• Low-order harmonics ↑ 0
2
3
V AB n / V d
V AB 1 0.744 Vd
0.2
0.1
0
1
5
10
15
20
25
30
35
40
45
50
55
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
60
n
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EE8407
Topic 5
Sinusoidal PWM
• Third Harmonic Injection PWM
v m1
v
v mA v m1 v m 3
vm 3
0
/3
Vˆm1
Vˆcr
VˆmA
2 / 3
2
t
• Vˆm1 Vˆcr - Fundamental voltage increased
• VˆmA Vˆcr - No low order harmonics produced
• 3rd harmonic – zero sequence (to appear in vAN and vBN )
• No triplen harmonics in vAB (vAB = vAN - vBN)
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Space Vector Modulation
• Switching States
P
S1
S3
S5
iA
A
iB
B
Vd
O
iC
C
LOAD
S4
S2
S6
N
Switching
State
Leg A
Leg B
S1
S4
V AN
S3
S6
P
On
Off
Vd
On
Off
O
Off
On
0
Off
On
Leg C
VBN
S5
Vd
0
S2
On
Off
Off
On
VCN
Vd
0
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Space Vector Modulation
Topic 5
• Switching States (Three-Phase)
P
S1
S3
S5
A
B
Vd
C
S4
S6
S2
N
• Eight switching states
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
13
EE8407
Topic 5
Space Vector Modulation
• Space Vector Diagram
jb
r
V3
r
V2
OPO
r
r
• Active vectors: V1 to V6
(stationary, not rotating)
r
• Zero vector: V0
• Six sectors: I to VI
PPO
SECTOR
II
SECTOR III
r
V4
r
Vref
SECTOR I
r
V1
q
PPP
OPP
OOO
a
POO
r
V0
SECTOR IV
SECTOR VI
SECTOR V
OOP r
V5
r POP
V6
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Space Vector Modulation
• Space Vectors
• Three-phase voltages
v AO (t ) vBO (t ) vCO (t ) 0
(1)
• Two-phase voltages
2
cos
0
cos
va (t )
2
3
v (t )
3 sin 0 sin 2
b
3
4 v AO (t )
3 v (t )
4 BO
sin
vCO (t )
3
cos
(2)
• Space
vector representation
r
V (t ) va (t ) j v b (t )
(2) (3)
r
2
V (t ) v AO (t ) e j 0 v BO (t ) e j 2 / 3 vCO (t ) e j 4 / 3
3
(3)
(4)
jx
where e cos x j sin x
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Space Vector Modulation
• Space Vectors (Example)
Switching state [POO] S1, S6 and S2 ON
2
1
v AO (t ) Vd , v BO (t ) Vd
3
3
1
v
(
t
)
Vd
and CO
3
r 2
V1 Vd e j 0
3
k 1, 2, ..., 6.
r
V2
OPO
(6)
PPO
SECTOR
II
SECTOR III
r
V4
Similarly,
r 2
j ( k 1)
3
Vk Vd e
3
jb
r
V3
(5) (4)
(5)
r
Vref
SECTOR I
r
V1
q
PPP
OPP
OOO
POO
r
V0
(7)
SECTOR IV
a
SECTOR VI
SECTOR V
OOP r
V5
r POP
V6
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Space Vector Modulation
• Active and Zero Vectors
P
Space Vector
S1
S3
S5
Zero
Vector
A
r
V1
B
Vd
r
V0
Switching State
(Three Phases)
[PPP]
S1 , S 3 , S 5
[OOO]
S4 , S6 , S2
[POO]
S1 , S 6 , S 2
C
S4
S6
S2
N
Active
Vector
• Active Vector: 6
• Zero Vector: 1
• Redundant switching
states: [PPP] and [OOO]
Vector
Definition
On-state Switch
r
V2
[PPO]
S1 , S 3 , S 2
r
V3
[OPO]
S 4 , S3 , S 2
r
V4
[OPP]
S 4 , S3 , S5
r
V5
[OOP]
S4 , S6 , S5
r
V6
[POP]
S1 , S 6 , S 5
r
V0 0
r 2
V1 Vd e j 0
3
r 2
j
V2 Vd e 3
3
2
r 2
j
V3 V d e 3
3
3
r 2
j
V4 Vd e 3
3
4
r 2
j
V5 V d e 3
3
5
r 2
j
V6 V d e 3
3
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Space Vector Modulation
• Reference Vector Vref
• Definition
r
Vref Vref e jq
SECTOR III
(8)
0 dt
PPO
SECTOR
II
r
V4
r
Vref
PPP
r
V1
OPP
OOO
a
POO
r
V0
SECTOR IV
t
SECTOR I
q
• Angular displacement
q (t )
r
V2
OPO
• Rotating in space at ω
2 f
jb
r
V3
SECTOR VI
SECTOR V
(9)
OOP r
V5
r POP
V6
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Space Vector Modulation
• Relationship Between Vref and VAB
• Vref is approximated by two active
and a zero vectors
• Vref rotates one revolution,
VAB completes one cycle
• Length of Vref corresponds to
magnitude of VAB
r
V2
r
Vref
Tb r
V2
Ts
SECTOR I
Q
q
Ta r
V1
Ts
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
r
V1
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EE8407
Topic 5
Space Vector Modulation
• Dwell Time Calculation
r
V2
• Volt-Second Balancing
r
r
r
r
Vref Ts V1 Ta V2 Tb V0 T0
Ts Ta Tb T0
(10)
r r
r
Vref
Tb r
V2
Ts
r
• Ta, Tb and T0 – dwell times for V1 , V2 and V
0
• Ts – sampling period
SECTOR I
Q
q
Ta r
V1
Ts
r
V1
• Space vectors
r
r 2
r 2
r
j
jq
Vref Vref e , V1 Vd , V2 Vd e 3 and V0 0
3
3
(11)
(11) (10)
2
1
Re
:
V
(cos
q
)
T
V
T
Vd Tb
ref
s
d
a
3
3
Im : Vref (sin q ) Ts 1 Vd Tb
3
(12)
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Space Vector Modulation
• Dwell Times
Solve (12)
Ta
Tb
T0 Ts
3 Ts Vref
Vd
3 Ts Vref
Vd
sin (
sin q
3
q )
0 q /3
(13)
Ta Tb
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
21
EE8407
Topic 5
Space Vector Modulation
• Vref Location versus Dwell Times
r
V2
r
Vref
Tb r
V2
Ts
SECTOR I
Q
q
r
V1
Ta r
V1
Ts
r
V ref
Location
Dwell Times
q 0
Ta 0
Tb 0
0 q
Ta Tb
6
q
6
6
Ta Tb
q
Ta Tb
3
q
3
Ta 0
Tb 0
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Space Vector Modulation
• Modulation Index
Ta Ts ma sin ( 3 q )
Tb Ts ma sin q
T0 Ts Tb Tc
ma
3 Vref
(15)
(16)
Vd
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Space Vector Modulation
• Modulation Range
jb
r
V3
OPO
• Vref,max
2
3 Vd
Vref , max Vd
3
2
3
(17)
PPO
SECTOR
II
SECTOR III
r
V4
r
Vref
PPP
r
V1
OOO
a
POO
r
V0
SECTOR IV
(17) (16)
SECTOR I
q
OPP
• ma,max = 1
r
V2
SECTOR VI
SECTOR V
• Modulation range: 0 ma 1
r POP
V6
OOP r
V5
(18)
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Space Vector Modulation
Topic 5
• Switching Sequence Design
• Basic Requirement:
Minimize the number of switchings per
sampling period Ts
• Implementation:
Transition from one switching state to
the next involves only two switches in
the same inverter leg.
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
25
EE8407
Topic 5
Space Vector Modulation
• Seven-segment Switching Sequence
r
V0
r
V1
OOO POO
• Selected vectors:
V0, V1 and V2
v AN
• Dwell times:
Ts = T0 + Ta + Tb
vBN
r
V2
r
V0
r
V2
r
V1
r
V0
PPO
PPP
PPO
POO OOO
Vd
0
Vd
0
vCN
Vd
0
T0
4
Ta
2
Tb
2
T0
2
Tb
2
Ta
2
T0
4
Ts
• Total number of switchings: 6
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Space Vector Modulation
Topic 5
• Undesirable Switching Sequence
• Vectors V1 and V2 swapped
r
V0
r
V2
OOO PPO
r
V1
r
V0
r
V1
POO
PPP
POO
v AN
r
V2
r
V0
PPO OOO
Vd
0
vBN
Vd
0
vCN
Vd
0
T0
4
Tb
2
Ta
2
T0
2
Ta
2
Tb
2
T0
4
Ts
• Total number of switchings: 10
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Space Vector Modulation
Topic 5
• Switching Sequence Summary (7–segments)
Sector
I
II
Switching Sequence
r
V0
r
V1
r
V2
PPO
r
V0
PPP
r
V2
r
V0
OOO
r
V0
POO
r
V3
r
V2
OOO
r
V0
OPO
r
V3
rPPO rPPP rPPO rOPO rOOO
V4
V0
V4
V3
V0
OOO
r
OPO
r
V5
rOPP rPPP rOPP rOPO rOOO
V4
V0
V4
V5
V0
r
OOO
V0
r
OOP
V5
rOPP rPPP rOPP rOOP rOOO
V6
V0
V6
V5
V0
r
OOO
rOOP
V1
rPOP rPPP rPOP r OOP rOOO
V6
V0
V6
V1
V0
OOO
POO
r
V0
PPO
r
V1
r
V2
POO
r
V3
OOO
r
V0
III
V0
IV
V
V0
VI
POP
PPP
POP
POO
OOO
Note: The switching sequences for the odd and ever sectors are different.
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Space Vector Modulation
• Simulated Waveforms
Sector
V
VI
V
IV
VI
IV
III
II
I
II
I
III
v AB
Vd
0
2
3
v AO
2Vd / 3
0
iA
0
2
3
f1 = 60Hz, fsw = 900Hz, ma = 0.696, Ts = 1.1ms
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
29
EE8407
Topic 5
Space Vector Modulation
• Waveforms and FFT
v AB
THD =80.2%
Vd
0
2
v AO
THD =80.2%
2V d / 3
0
iA
THD =8.37%
0
3
2
V AB n / V d
THD =80.2%
V AB 1 0.566V d
0.2
0.1
0
1
5
10
15
20
25
30
35
40
45
50
55
60
n
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Space Vector Modulation
• Waveforms and FFT (Measured)
V AB n
Vd
v AB
THD = 80.3%
23
0.2
14
0.1
v AO
47
10
16
29 34
43
58
8
0
(a) Waveforms 2ms/div
(b) Spectrum (500Hz/div)
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
31
EE8407
Topic 5
Space Vector Modulation
• Waveforms and FFT (Measured)
V AB n / Vd
V AB n / Vd
THD
(%)
n 1
n 1
300
0.15
0.15
10
14
16
20
THD
0.10
0.10
n2
4
200
n = 19
8
17
13
11 7
100
0.05
0.05
0
0
0.2
0.4
0.6
0.8
0
ma
0
0.2
0.4
0.6
0.8
ma
0
(b) Odd order harmonics
(a) Even order harmonics
( f1 60Hz
5
and
Ts 1 / 720 sec )
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Topic 5
Space Vector Modulation
• Even-Order Harmonic Elimination
r
V0
r
V5
r
V4
r
V0
r
V4
OOO
OOP
OPP
PPP
OPP
v AN
r
V5
r
V0
OOP OOO
Vd
0
vBN
Vd
0
0
vBN
r
V4
r
V5
r
V0
r
V5
r
V4
r
V0
PPP
OPP
OOP
OOO
OOP
OPP
PPP
Vd
Vd
0
vCN
Vd
0
vCN
0
0
v AB
v AN
r
V0
Vd
0
v AB
Vd
Type-A sequence
(starts and ends with [OOO])
Vd
Type-B sequence
(starts and ends with [PPP])
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
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EE8407
Space Vector Modulation
Topic 5
• Even-Order Harmonic Elimination
r
V3
b
SECTOR III
r
V4
a
a
30
30
a
a
b
a
b
a
r
V5
SECTOR I
b
b
SECTOR IV
r
V2
SECTOR II
SECTOR VI
b
SECTOR V
r
V1
Type-A sequence
Type-B sequence
r
V6
Space vector Diagram
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
34
EE8407
Topic 5
Space Vector Modulation
• Even-Order Harmonic Elimination
V AB n
Vd
v AB
THD = 80.5%
23
0.2
17
v AO
47
13
0.1
41
7
5
65
35
0
(a) Waveforms 2ms/div
(b) Spectrum (500Hz/div)
• Measured waveforms and FFT
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
35
EE8407
Topic 5
Space Vector Modulation
• Even-Order Harmonic Elimination
V AB n / Vd
THD
(%)
0.3
THD
300
n 1
200
0.2
17
19
13
0.1
7
0
0
0.2
( f1 60Hz
0.4
0.6
and
100
5
11
0.8
ma
0
Ts 1 / 720 sec )
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
36
EE8407
Topic 5
Space Vector Modulation
• Five-segment SVM
r
V0
r
V1
r
V2
r
V1
r
V0
r
V0
r
V2
r
V1
r
V2
r
V0
OOO
POO
PPO
POO
OOO
PPP
PPO
POO
PPO
PPP
Tb
2
T0
2
v AN
Vd
Vd
0
vBN
Vd
Vd
0
vCN
Vd
0
T0
2
Ta
2
Tb
Ts
(a) Sequence A
Ta
2
T0
2
T0
2
Tb
2
Ta
Ts
(b) Sequence B
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
37
EE8407
Space Vector Modulation
Topic 5
• Switching Sequence ( 5-segment)
Sector
I
Switching Sequence (A)
r
V0
OOO
II
r
V1
POO
r
V2
PPO
r
V1
POO
r
V0
OOO
r
V0
r
V3
r
V2
r
V3
OOO
r
OPO
r
rPPO
V4
rOPO rOOO
V3
V0
rOPP
V4
rOPO rOOO
V5
V0
rOOP rOOO
V5
V0
V0
V3
OOO
r
OPO
r
r
V0
III
V0
V5
r
OOO
r
OOP
IV
V
V0
V5
rOPP
V6
r
OOO
rOOP
V1
rPOP r OOP rOOO
V6
V1
V0
OOO
POO
V0
v CN 0
v CN 0
v AN 0
v AN 0
v BN 0
v BN 0
VI
POP
POO
OOO
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
38
EE8407
Space Vector Modulation
Topic 5
• Simulated Waveforms ( 5-segment)
v g1
2 / 3
vg 3
2
vg 5
vAB
0
4
Vd
2
4
iA
0
2
4
• f1 = 60Hz, fsw = 600Hz, ma = 0.696, Ts = 1.1ms
• No switching for a 120° period per cycle.
• Low switching frequency but high harmonic distortion
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
39
EE8407
Topic 5
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
40