1. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
1
Power Converter Systems
Graduate Course EE8407
Ryerson Campus
Bin Wu PhD, PEng
Professor
ELCE Department
Ryerson University
Contact Info
Office: ENG328
Tel: (416) 979-5000 ext: 6484
Email: bwu@ee.ryerson.ca
http://www.ee.ryerson.ca/~bwu/

2. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
2
VDM5000 Two-level VSI
Topic 5
Two-Level Voltage Source Inverter (VSI)
Source:
Alstom

3. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
3
• Sinusoidal PWM
• Space vector modulation
Lecture Topics
• To control inverter output frequency (fundamental)
• To control inverter output voltage (fundamental)
• To minimize harmonic distortion
Why Use PWM Techniques?
Two Level Voltage Source Inverter

4. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
4
• Inverter Configuration
Assumption:
dc capacitor very large  dc voltage ripple free
d
C
1
S
2
S
3
S 5
S
4
S 6
S
A
B
C
P
N
LOAD
A
i
O
B
i
C
i
d
V
Sinusoidal PWM

5. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
5
• Modulating and Carrier Waves
• vcr – Carrier wave (triangle) • Amplitude modulation index
cr
m
a
V
V
m
ˆ
ˆ

• Frequency modulation index
m
cr
f
f
f
m 
0
v mA
v B
m
v C
m
v
cr
v
cr
V
ˆ m
V
ˆ
t

• vm – Modulating wave (sine)
Sinusoidal PWM

6. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
6
• Gate Signal Generation
1
g
v
4
g
v
d
V
0
AN
v
 
2
mA
v cr
v
0
cr
mA v
v  0
1 
g
v )
0
( 4 
g
v 1
S on )
off
( 4
S d
AN V
v 
Phase A
cr
mA v
v  0
4 
g
v )
0
( 1 
g
v 4
S on )
off
( 1
S 0

AN
v
Vg1 and Vg4 are complementary
Sinusoidal PWM

7. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
7
• Line-to-Line Voltage vAB
AB
v
BN
v
AN
v
0
0
0
v mA
v B
m
v C
m
v
cr
v
cr
V
ˆ m
V
ˆ
d
V
d
V
d
V
 
2
t

t

t

t

1
AB
v
1
S
2
S
3
S 5
S
4
S 6
S
B
C
P
N
d
V
A
Sinusoidal PWM

8. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
8
• Waveforms and FFT
• ma = 0.8, mf = 15,
fm = 60Hz, fcr = 900Hz
• Switching frequency
fsw = fcr = 900Hz 0.1
0.2
0
0
0
THD = 92.07%
THD = 92.07%
THD = 7.73%
THD = 92.07%
d
V
3
/
2 d
V
AB
v
AO
v
A
i
2

f
m
1
2 
f
m
2
3 
f
m 1
4 
f
m
n

3

3

2

2


0
1 5 10 15 20 25 30 35 40 45 50 55 60
d
V
VAB 49
.
0
1 
d
n V
VAB /
Sinusoidal PWM

9. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
9
• Harmonic Content
• Low order harmonics
n < (mf -2) are eliminated
• VAB1 versus ma is linear
• VAB1,max = 0.612Vd
a
m
1
2 
f
m
2

f
m
1
4 
f
m
2
3 
f
m
4
3 
f
m
d
n
AB
V
V
1

n
0.2 0.4 0.6 0.8
0.1
0.2
0.3
0
0
100
200
300
0
THD
(%)
THD
Sinusoidal PWM

10. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
10
• Over-Modulation
• Fundamental voltage ↑
• Low-order harmonics ↑
0
0.1
0.2
0
d
V

2 
3

0
1
2
-1
-2
mA
v mC
v
mB
v
cr
v
AB
v
n
0
A
i

2 
3

d
V
VAB 744
.
0
1 
d
n V
VAB /
n
1 5 10 15 20 25 30 35 40 45 50 55 60
Sinusoidal PWM

11. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
11
• Third Harmonic Injection PWM
cr
m V
V ˆ
ˆ 1 
• - Fundamental voltage increased
cr
mA V
V ˆ
ˆ 
• - No low order harmonics produced
• 3rd harmonic – zero sequence (to appear in vAN and vBN )
• No triplen harmonics in vAB (vAB = vAN - vBN)
3
/
 3
/
2  
2
3
m
v
1
m
v
3
1 m
m
mA v
v
v 

0
v
t

1
ˆ
m
V mA
V
ˆ cr
V
ˆ
Sinusoidal PWM

12. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
12
• Switching States
Leg A Leg B Leg C
Switching
State
1
S 4
S AN
V 3
S 6
S BN
V 5
S 2
S CN
V
P On Off d
V On Off d
V On Off d
V
O Off On 0 Off On 0 Off On 0
1
S
2
S
3
S 5
S
4
S 6
S
B
C
P
N
d
V
A
LOAD
A
i
O
B
i
C
i
Space Vector Modulation

13. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
13
• Switching States (Three-Phase)
• Eight switching states
1
S
2
S
3
S 5
S
4
S 6
S
B
C
P
N
d
V
A
Space Vector Modulation

14. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
14
• Space Vector Diagram
a
1
V
r
0
V
r
3
V
r
2
V
r
4
V
r
5
V
r
6
V
r
b
j
POO
PPO
OPO
OPP
OOP POP
ref
V
r
q
OOO
PPP
SECTOR I
SECTOR III
SECTOR IV SECTOR VI
SECTOR V
SECTOR
II

• Active vectors: to
(stationary, not rotating)
• Zero vector:
1
V
r
6
V
r
0
V
r
• Six sectors: I to VI
Space Vector Modulation

15. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
15
• Space Vectors
• Three-phase voltages
0
)
(
)
(
)
( 

 t
v
t
v
t
v CO
BO
AO
• Two-phase voltages



























)
(
)
(
)
(
3
4
sin
3
2
sin
0
sin
3
4
cos
3
2
cos
0
cos
3
2
)
(
)
(
t
v
t
v
t
v
t
v
t
v
CO
BO
AO




b
a
• Space vector representation
)
(
)
(
)
( t
v
j
t
v
t
V b
a 

r
(2)  (3)
 
3
/
4
3
/
2
0
)
(
)
(
)
(
3
2
)
( 
 j
CO
j
BO
j
AO
e
t
v
e
t
v
e
t
v
t
V 


r
where x
j
x
ejx
sin
cos 

(3)
(1)
(2)
(4)
Space Vector Modulation

16. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
16
• Space Vectors (Example)
Switching state [POO]  S1, S6 and S2 ON
d
BO
d
AO
V
t
v
V
t
v
3
1
)
(
,
3
2
)
( 

 d
CO
V
t
v
3
1
)
( 

and
(5)  (4)
(7)
(5)
(6)
0
1
3
2 j
d
e
V
V 
r
Similarly,
3
)
1
(
3
2 


k
j
d
k e
V
V
r
.
6
...,
,
2
,
1

k
a
1
V
r
0
V
r
3
V
r
2
V
r
4
V
r
5
V
r
6
V
r
b
j
POO
PPO
OPO
OPP
OOP POP
ref
V
r
q
OOO
PPP
SECTOR I
SECTOR III
SECTOR IV SECTOR VI
SECTOR V
SECTOR
II

Space Vector Modulation

17. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
17
• Active and Zero Vectors
Space Vector
Switching State
(Three Phases)
On-state Switch
Vector
Definition
[PPP] 5
3
1 ,
, S
S
S
Zero
Vector 0
V
r
[OOO] 2
6
4 ,
, S
S
S
0
0 
V
r
1
V
r
[POO] 2
6
1 ,
, S
S
S 0
1
3
2 j
d e
V
V 
r
2
V
r
[PPO] 2
3
1 ,
, S
S
S 3
2
3
2


j
d e
V
V
r
3
V
r
[OPO] 2
3
4 ,
, S
S
S 3
2
3
3
2


j
d e
V
V
r
4
V
r
[OPP] 5
3
4 ,
, S
S
S 3
3
4
3
2


j
d e
V
V
r
5
V
r
[OOP] 5
6
4 ,
, S
S
S 3
4
5
3
2


j
d e
V
V
r
Active
Vector
6
V
r
[POP] 5
6
1 ,
, S
S
S 3
5
6
3
2


j
d e
V
V
r
• Active Vector: 6
• Zero Vector: 1
• Redundant switching
states: [PPP] and [OOO]
1
S
2
S
3
S 5
S
4
S 6
S
B
C
P
N
d
V
A
Space Vector Modulation

18. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
18
(8)
• Reference Vector Vref
• Definition
a
1
V
r
0
V
r
3
V
r
2
V
r
4
V
r
5
V
r
6
V
r
b
j
POO
PPO
OPO
OPP
OOP POP
ref
V
r
q
OOO
PPP
SECTOR I
SECTOR III
SECTOR IV SECTOR VI
SECTOR V
SECTOR
II

• Angular displacement


t
dt
t
0
)
( 
q (9)
q
j
ref
ref e
V
V 
r
• Rotating in space at ω
Space Vector Modulation
f

 2


19. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
19
• 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
1
V
r
2
V
r
ref
V
r
q
1
V
T
T
s
a
r
2
V
T
T
s
b
r
SECTOR I
Q
Space Vector Modulation

20. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
20
• Dwell Time Calculation
• Volt-Second Balancing









0
0
0
2
1
T
T
T
T
T
V
T
V
T
V
T
V
b
a
s
b
a
s
ref
r
r
r
r
(10)
• Ta, Tb and T0 – dwell times for and
, 2
1
V
V
r
r
0
V
r
• Ts – sampling period
• Space vectors
d
j
ref
ref
V
V
e
V
V
3
2
, 1


r
r q 3
2
3
2 
j
d
e
V
V 
r
0
0 
V
r
, and
(11)  (10)










b
d
s
ref
b
d
a
d
s
ref
T
V
T
V
T
V
T
V
T
V
3
1
)
(sin
3
1
3
2
)
(cos
q
q
:
Im
:
Re
(11)
(12)
1
V
r
2
V
r
ref
V
r
q
1
V
T
T
s
a
r
2
V
T
T
s
b
r
SECTOR I
Q
Space Vector Modulation

21. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
21
• Dwell Times
Solve (12)

















b
a
s
d
ref
s
b
d
ref
s
a
T
T
T
T
V
V
T
T
V
V
T
T
0
sin
3
)
3
(
sin
3
q
q

3
/
0 
q 
 (13)
Space Vector Modulation

22. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
22
• Vref Location versus Dwell Times
ref
V
r
Location 0

q
6
0

q 

6

q 
3
6

q



3

q 
Dwell Times
0
0


b
a
T
T
b
a T
T  b
a T
T  b
a T
T 
0
0


b
a
T
T
1
V
r
2
V
r
ref
V
r
q
1
V
T
T
s
a
r
2
V
T
T
s
b
r
SECTOR I
Q
Space Vector Modulation

23. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
23
• Modulation Index













c
b
s
a
s
b
a
s
a
T
T
T
T
m
T
T
m
T
T
0
sin
)
3
(
sin
q
q

(15)
d
ref
a
V
V
m
3
 (16)
Space Vector Modulation

24. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
24
• Modulation Range
• Vref,max
3
2
3
3
2
max
,
d
d
ref
V
V
V 

 (17)
a
1
V
r
0
V
r
3
V
r
2
V
r
4
V
r
5
V
r
6
V
r
b
j
POO
PPO
OPO
OPP
OOP POP
ref
V
r
q
OOO
PPP
SECTOR I
SECTOR III
SECTOR IV SECTOR VI
SECTOR V
SECTOR
II

(17)  (16)
• ma,max = 1 
• Modulation range: 0  ma  1 (18)
Space Vector Modulation

25. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
25
• 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.
Space Vector Modulation

26. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
26
• Seven-segment Switching Sequence
d
V
2
0
T
2
a
T
2
b
T
2
a
T
BN
v
AN
v
CN
v
0
1
V
r
1
V
r
2
V
r
0
V
r
2
V
r
POO
OOO PPO PPP PPO POO OOO
d
V
d
V
4
0
T
4
0
T
2
b
T
s
T
0
0
0
V
r
0
V
r
• Total number of switchings: 6
• Selected vectors:
V0, V1 and V2
• Dwell times:
Ts = T0 + Ta + Tb
Space Vector Modulation

27. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
27
• Undesirable Switching Sequence
• Vectors V1 and V2 swapped
d
V
2
0
T
2
a
T
2
b
T
2
a
T
BN
v
AN
v
CN
v
0
1
V
r
1
V
r
2
V
r
2
V
r
POO
OOO PPO PPP PPO
POO OOO
d
V
d
V
4
0
T
4
0
T
2
b
T
s
T
0
0
0
V
r
0
V
r
0
V
r
• Total number of switchings: 10
Space Vector Modulation

28. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
28
• Switching Sequence Summary (7–segments)
Sector Switching Sequence
0
V
r
1
V
r
2
V
r
0
V
r
2
V
r
1
V
r
0
V
r
I
OOO POO PPO PPP PPO POO OOO
0
V
r
3
V
r
2
V
r
0
V
r
2
V
r
3
V
r
0
V
r
II
OOO OPO PPO PPP PPO OPO OOO
0
V
r
3
V
r
4
V
r
0
V
r
4
V
r
3
V
r
0
V
r
III
OOO OPO OPP PPP OPP OPO OOO
0
V
r
5
V
r
4
V
r
0
V
r
4
V
r
5
V
r
0
V
r
IV
OOO OOP OPP PPP OPP OOP OOO
0
V
r
5
V
r
6
V
r
0
V
r
6
V
r
5
V
r
0
V
r
V
OOO OOP POP PPP POP OOP OOO
0
V
r
1
V
r
6
V
r
0
V
r
6
V
r
1
V
r
0
V
r
VI
OOO POO POP PPP POP POO OOO
Note: The switching sequences for the odd and ever sectors are different.
Space Vector Modulation

29. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
29
• Simulated Waveforms
AB
v
AO
v
0
0
0
A
i
d
V
3
/
2 d
V
 
2 
3
 
2 
3
VI
VI
Sector
I
II
III
IV
V
I
II
III
IV
V
f1 = 60Hz, fsw = 900Hz, ma = 0.696, Ts = 1.1ms
Space Vector Modulation

30. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
30
• Waveforms and FFT
0
0.1
0.2
n
0
0
AB
v
AO
v
A
i
THD =80.2%
THD =80.2%
THD =8.37%
THD =80.2%
d
V
3
/
2 d
V

2
d
V
VAB 566
.
0
1 
1 5 10 15 20 25 30 35 40 45 50 55 60
d
n V
VAB /
0

2
 
3
Space Vector Modulation

31. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
31
• Waveforms and FFT (Measured)
23
AO
v
AB
v d
n
V
VAB
0.2
0.1
0
(a) Waveforms 2ms/div (b) Spectrum (500Hz/div)
14
34
10 47
58
THD = 80.3%
8
16 29 43
Space Vector Modulation

32. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
32
0 0.2 0.4 0.6 0.8
0
0.05
0.10
0.15
10 16 20
d
n
AB V
V /
a
m
1

n
2

n 4 8
14
(a) Even order harmonics
5
7
11
13
17
n = 19
0.05
0.10
0.15
d
n
AB V
V /
0 0.2 0.4 0.6 0.8 a
m
1

n
(b) Odd order harmonics
0
100
200
300
0
THD
(%)
THD
• Waveforms and FFT (Measured)
Hz
60
1 
f sec
720
/
1

s
T
( and )
Space Vector Modulation

33. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
33
• Even-Order Harmonic Elimination
BN
v
AN
v
CN
v
0
5
V
r
4
V
r
0
V
r
OOP
OOO OPP PPP OPP OOP OOO
0
0
0
V
r
0
V
r
AB
v
0
d
V

4
V
r
5
V
r
d
V
d
V
d
V
Type-A sequence
(starts and ends with [OOO])
BN
v
AN
v
CN
v
0
0
0
AB
v
0
d
V

5
V
r
OOP
4
V
r
OPP
d
V
d
V
d
V
4
V
r
OPP
5
V
r
OOP
PPP
0
V
r
0
V
r
OOO PPP
0
V
r
Type-B sequence
(starts and ends with [PPP])
Space Vector Modulation

34. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
34
• Even-Order Harmonic Elimination
1
V
r
3
V
r
2
V
r
4
V
r
5
V
r
6
V
r
SECTOR I
SECTOR III
SECTOR IV SECTOR VI
SECTOR V
SECTOR II
a
b
a
a
a
a
a
b
b
b
b
b
Type-A sequence
Type-B sequence

30

30
Space vector Diagram
Space Vector Modulation

35. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
35
• Even-Order Harmonic Elimination
(a) Waveforms 2ms/div
AO
v
AB
v
0.2
0.1
0
d
n
V
VAB
(b) Spectrum (500Hz/div)
23
13 47
35
7
17
65
THD = 80.5%
41
5
• Measured waveforms and FFT
Space Vector Modulation

36. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
36
• Even-Order Harmonic Elimination
17
19
13
7
5
11
100
200
300
0
THD
(%)
0 0.2 0.4 0.6 0.8 a
m
0
0.1
0.2
0.3
d
n
AB V
V /
1

n
THD
Hz
60
1 
f sec
720
/
1

s
T
( and )
Space Vector Modulation

37. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
37
• Five-segment SVM
d
V
2
a
T
b
T
2
a
T
BN
v
AN
v
CN
v
0
1
V
r
1
V
r
2
V
r
0
V
r
POO
OOO PPO POO OOO
d
V
s
T
0
0
0
V
r
2
0
T
2
0
T
d
V
a
T
1
V
r
2
V
r
0
V
r
PPP PPO POO PPP
d
V
s
T
0
V
r
2
0
T
2
0
T
(a) Sequence A
2
V
r
PPO
d
V
2
b
T
2
b
T
(b) Sequence B
Space Vector Modulation

38. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
38
• Switching Sequence ( 5-segment)
Sector Switching Sequence (A)
0
V
r
1
V
r
2
V
r
1
V
r
0
V
r
I
OOO POO PPO POO OOO
0

CN
v
0
V
r
3
V
r
2
V
r
3
V
r
0
V
r
II
OOO OPO PPO OPO OOO
0

CN
v
0
V
r
3
V
r
4
V
r
3
V
r
0
V
r
III
OOO OPO OPP OPO OOO
0

AN
v
0
V
r
5
V
r
4
V
r
5
V
r
0
V
r
IV
OOO OOP OPP OOP OOO
0

AN
v
0
V
r
5
V
r
6
V
r
5
V
r
0
V
r
V
OOO OOP POP OOP OOO
0

BN
v
0
V
r
1
V
r
6
V
r
1
V
r
0
V
r
VI
OOO POO POP POO OOO
0

BN
v
Space Vector Modulation

39. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
39
• Simulated Waveforms ( 5-segment)
d
V

2 
4
1
g
v
3
g
v
5
g
v
AB
v
0
0
A
i
3
/
2

2 
4

2 
4
• No switching for a 120° period per cycle.
• Low switching frequency but high harmonic distortion
• f1 = 60Hz, fsw = 600Hz, ma = 0.696, Ts = 1.1ms
Space Vector Modulation

40. Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
40