slides_topic5.pptde concours recrutementg

bon cours

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

2. 2
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
VDM5000 Two-level VSI
Topic 5

Two-Level Voltage Source Inverter (VSI)
Source:
Alstom

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

5. 5
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Modulating and Carrier Waves
• v
cr
– 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 mAv
Bm
v
Cm
v
cr
v
crV
ˆ
m
V
ˆ
t
• v
m
– Modulating wave (sine)
Sinusoidal PWM

6. 6
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Gate Signal Generation
1gv
4gv
d
V
0
ANv
 2
mAv
crv
0





crmAvv 0
1

g
v )0(
4

g
v
1
S on )off(
4
S
dANVv
Phase A
crmAvv 0
4

g
v )0(
1

g
v
4S on )off(
1S 0
ANv

V
g1 and V
g4 are complementary
Sinusoidal PWM

7. 7
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Line-to-Line Voltage v
AB
ABv
BNv
AN
v
0
0
0
v mAv
Bmv
Cmv
crv
crV
ˆ
mV
ˆ
dV
d
V
d
V
 2
t
t
t
t
1ABv
1S
2S
3S
5S
4S
6S
B
C
P
N
d
V
A
Sinusoidal PWM

8. 8
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Waveforms and FFT
• m
a
= 0.8, m
f
= 15,
f
m
= 60Hz, f
cr
= 900Hz
• Switching frequency
f
sw = f
cr = 900Hz 0.1
0.2
0
0
0
THD = 92.07%
THD = 92.07%
THD = 7.73%
THD = 92.07%
d
V
3/2
dV
AB
v
AO
v
Ai
2
f
m
12
fm
23
f
m 14
fm
n
3
32
2

0
151015202530354045505560
d
VV
AB
49.0
1
dn
VV
AB
/
Sinusoidal PWM

9. 9
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Harmonic Content
• Low order harmonics
n < (m
f -2) are eliminated
• V
AB1
versus m
a
is linear
• V
AB1,max
= 0.612V
d
a
m
12
fm
2
fm
14
fm
23
fm
43
fm
d
nAB
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. 10
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• 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
ABv
n
0
A
i
2 3
d
VV
AB
744.0
1
dnVV
AB/
n151015202530354045505560
Sinusoidal PWM

11. 11
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Third Harmonic Injection PWM
crm
VV ˆˆ
1
• - Fundamental voltage increased
crmAVV ˆˆ• - No low order harmonics produced
• 3
rd
harmonic – zero sequence (to appear in v
AN and v
BN
)
• No triplen harmonics in v
AB (v
AB = v
AN - v
BN)
3/ 3/2  2
3m
v
1mv
31 mmmA vvv 
0
v
t
1
ˆ
m
V mAV
ˆ
crV
ˆ
Sinusoidal PWM

12. 12
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• 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

1S
2S
3S
5S
4
S
6
S
B
C
P
N
dV
A
LOAD
Ai
O
Bi
Ci
Space Vector Modulation

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

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

15. 15
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Space Vectors
• Three-phase voltages
0)()()(  tvtvtv
COBOAO
• Two-phase voltages



























)(
)(
)(
3
4
sin
3
2
sin0sin
3
4
cos
3
2
cos0cos
3
2
)(
)(
tv
tv
tv
tv
tv
CO
BO
AO




• Space vector representation
)()()( tvjtvtV



(2)  (3)
 
3/43/20
)()()(
3
2
)(
 j
CO
j
BO
j
AO
etvetvetvtV 

where xjxe
jx
sincos
(3)
(1)
(2)
(4)
Space Vector Modulation

16. 16
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Space Vectors (Example)
Switching state [POO]  S
1
, S
6
and S
2
ON
dBOdAO
VtvVtv
3
1
)(,
3
2
)( 
dCO Vtv
3
1
)(and
(5)  (4)
(7)
(5)
(6)
0
1
3
2
j
deVV

Similarly,
3
)1(
3
2



kj
dk
eVV

.6...,,2,1k

1
V

0
V

3
V

2
V

4
V

5V

6V

j
POO
PPOOPO
OPP
OOP POP
ref
V


OOOPPP
SECTOR ISECTOR III
SECTOR IV SECTOR VI
SECTOR V
SECTOR
II

Space Vector Modulation

17. 17
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Active and Zero Vectors
S p a c e V e c t o r
S w it c h in g S t a t e
( T h r e e P h a s e s )
O n-s t a t e S w it c h
V e c t o r
D e f in it io n
[ P P P ]
531
,,SSS
Z e r o
V e c t o r
0V


[ O O O ]
264 ,, SSS
0
0V


1
V

[ P O O ]
261 ,, SSS
0
1
3
2
j
d
eVV


2
V

[ P P O ]
231 ,,SSS 3
2
3
2


j
d
eVV


3V

[ O P O ]
234
,,SSS 3
2
3
3
2


j
d
eVV


4V

[ O P P ]
534
,,SSS 3
3
4
3
2


j
d
eVV


5
V

[ O O P ]
564 ,, SSS 3
4
5
3
2


j
d
eVV


A c t iv e
V e c t o r
6V

[ P O P ]
561
,, SSS 3
5
6
3
2


j
d
eVV



• Active Vector: 6
• Zero Vector: 1
• Redundant switching
states: [PPP] and [OOO]
1
S
2S
3
S
5
S
4S
6S
B
C
P
N
dV
A
Space Vector Modulation

18. 18
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
(8)
• Reference Vector V
ref
• Definition

1
V

0
V

3
V

2
V

4V

5
V

6V

j
POO
PPOOPO
OPP
OOP POP
ref
V


OOOPPP
SECTOR ISECTOR III
SECTOR IV SECTOR VI
SECTOR V
SECTOR
II


• Angular displacement


t
dtt
0
)( 
(9)
j
refref eVV

• Rotating in space at ω
Space Vector Modulation
f2

19. 19
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Relationship Between V
ref
and V
AB
• V
ref
is approximated by two active
and a zero vectors
• V
ref
rotates one revolution,
V
AB
completes one cycle
• Length of V
ref
corresponds to
magnitude of V
AB
1
V

2
V

refV


1V
T
T
s
a

2V
T
T
s
b

SECTOR I
Q
Space Vector Modulation

20. 20
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Dwell Time Calculation
• Volt-Second Balancing





0
0021
TTTT
TVTVTVTV
bas
basref

(10)
• T
a
, T
b
and T
0
– dwell times for and ,
21
VV

0
V

• T
s – sampling period
• Space vectors
d
j
refref
VVeVV
3
2
,
1



3
2
3
2

j
d
eVV

0
0V

, and
(11)  (10)









bdsref
bdadsref
TVTV
TVTVTV
3
1
)(sin
3
1
3
2
)(cos


:Im
:Re
(11)
(12)
1V

2
V

refV


1V
T
T
s
a

2V
T
T
s
b

SECTOR I
Q
Space Vector Modulation

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

22. 22
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• V
ref
Location versus Dwell Times
refV

Location 0
6
0


6


36




3


Dwell Times
0
0


b
a
T
T

baTT
baTT
baTT
0
0


b
a
T
T


1V

2
V

ref
V


1V
T
T
s
a

2V
T
T
s
b

SECTOR I
Q
Space Vector Modulation

23. 23
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Modulation Index










cbs
asb
asa
TTTT
mTT
mTT
0
sin
)
3
(sin



(15)
d
ref
a
V
V
m
3

(16)
Space Vector Modulation

24. 24
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Modulation Range
• V
ref,max
32
3
3
2
max,
d
dref
V
VV  (17)

1
V

0
V

3V

2V

4
V

5
V

6
V

j
POO
PPOOPO
OPP
OOP POP
ref
V


OOOPPP
SECTOR ISECTOR III
SECTOR IV SECTOR VI
SECTOR V
SECTOR
II

(17)  (16)
• m
a,max = 1 
• Modulation range: 0  m
a
 1
(18)
Space Vector Modulation

25. 25
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Switching Sequence Design
• Basic Requirement:
Minimize the number of switchings per
sampling period T
s
• Implementation:
Transition from one switching state to
the next involves only two switches in
the same inverter leg.
Space Vector Modulation

26. 26
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Seven-segment Switching Sequence
d
V
2
0T
2
aT
2
bT
2
aT
BNv
ANv
CNv
0
1V

1V

2V

0V

2V

POOOOO PPO PPP PPO POOOOO
dV
dV
4
0T
4
0T
2
bT
s
T
0
0
0V

0V

• Total number of switchings: 6
• Selected vectors:
V
0
, V
1
and V
2
• Dwell times:
T
s
= T
0
+ T
a
+ T
b
Space Vector Modulation

27. 27
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Undesirable Switching Sequence
• Vectors V
1 and V
2 swapped
d
V
2
0
T
2
a
T
2
b
T
2
a
T
BNv
ANv
CNv
0
1V

1V

2V

2V

POOOOOPPO PPP PPOPOO OOO
d
V
d
V
4
0
T
4
0
T
2
b
T
s
T
0
0
0V

0V

0V

• Total number of switchings: 10
Space Vector Modulation

28. 28
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Switching Sequence Summary (7–segments)
Sector Switching Sequence
0V


1V


2V


0V


2V


1V


0V


I
OOO POO PPO PPP PPO POO OOO
0V


3V


2V


0V


2V


3V


0V


II
OOO OPO PPO PPP PPO OPO OOO
0V


3V


4V


0V


4V


3V


0V


III
OOO OPO OPP PPP OPP OPO OOO
0V


5V


4V


0V


4V


5V


0V


IV
OOO OOP OPP PPP OPP OOP OOO
0V


5V


6V


0V


6V


5V


0V


V
OOO OOP POP PPP POP OOP OOO
0V


1V


6V


0V


6V


1V


0V


VI
OOO POO POP PPP POP POO OOO

Note: The switching sequences for the odd and ever sectors are different.
Space Vector Modulation

29. 29
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Simulated Waveforms
ABv
AO
v
0
0
0
Ai
dV
3/2
dV
 2 3
 2 3
VIVI
Sector
I
II
III
IV
V
I
II
III
IV
V
f
1 = 60Hz, f
sw = 900Hz, m
a = 0.696, T
s = 1.1ms
Space Vector Modulation

30. 30
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Waveforms and FFT
0
0.1
0.2
n
0
0
AB
v
AO
v
Ai
THD =80.2%
THD =80.2%
THD =8.37%
THD =80.2%
d
V
3/2
d
V
2
d
VV
AB
566.0
1

151015202530354045505560
dnVV
AB/
0
2 3
Space Vector Modulation

31. 31
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Waveforms and FFT (Measured)
23
AOv
ABv
d
n
V
V
AB
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. 32
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
0 0.2 0.4 0.6 0.8
0
0.05
0.10
0.15
10 1620
dnABVV/
am
1n
2n 48
14
(a) Even order harmonics
57111317n = 19
0.05
0.10
0.15
dnABVV/
0 0.2 0.4 0.6 0.8
am
1n
(b) Odd order harmonics
0
100
200
300
0
THD
(%)
THD
• Waveforms and FFT (Measured)
Hz60
1f sec720/1
s
T ( and )
Space Vector Modulation

33. 33
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Even-Order Harmonic Elimination
BNv
ANv
CNv
0
5V

4V

0V

OOPOOO OPP PPP OPP OOPOOO
0
0
0V

0V

ABv
0
d
V
4V

5V

dV
dV
dV
Type-A sequence
(starts and ends with [OOO])
BNv
ANv
CNv
0
0
0
ABv
0
dV
5V

OOP
4V

OPP
dV
dV
d
V
4V

OPP
5V

OOPPPP
0V

0V

OOO PPP
0V

Type-B sequence
(starts and ends with [PPP])
Space Vector Modulation

34. 34
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Even-Order Harmonic Elimination
1
V

3
V

2
V

4
V

5V

6V

SECTOR ISECTOR 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. 35
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Even-Order Harmonic Elimination
(a) Waveforms 2ms/div
AOv
ABv
0.2
0.1
0
d
n
V
V
AB
(b) Spectrum (500Hz/div)
23
13 47
35
7
17
65
THD = 80.5%
41
5
• Measured waveforms and FFT
Space Vector Modulation

36. 36
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Even-Order Harmonic Elimination
17
19
13
7
5
11
100
200
300
0
THD
(%)
0 0.2 0.4 0.6 0.8 am
0
0.1
0.2
0.3
dnAB
VV/
1n
THD
Hz60
1f sec720/1
s
T ( and )
Space Vector Modulation

37. 37
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Five-segment SVM
dV
2
a
T
b
T
2
a
T
BNv
ANv
CNv
0
1V

1
V

2V

0V

POOOOO PPO POOOOO
d
V
sT
0
0
0V

2
0
T
2
0
T
d
V
a
T
1
V

2
V

0
V

PPP PPO POO PPP
d
V
sT
0
V

2
0
T
2
0
T
(a) Sequence A
2
V

PPO
d
V
2
b
T
2
b
T
(b) Sequence B
Space Vector Modulation

38. 38
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Switching Sequence ( 5-segment)
Sector Sw itching Sequence (A)
0V


1V


2V


1V


0V


I
O O O PO O PPO PO O O O O
0
CN
v
0
V


3
V


2
V


3
V


0
V


II
O O O O PO PPO O PO O O O
0
CN
v
0V


3V


4V


3V


0V


III
O O O O PO O PP O PO O O O
0
AN
v
0
V


5
V


4
V


5
V


0
V


IV
O O O O O P O PP O O P O O O
0
AN
v
0V


5V


6V


5V


0V


V
O O O O O P PO P O O P O O O
0
BN
v
0V


1V


6V


1V


0V


VI
O O O PO O PO P PO O O O O
0
BN
v

Space Vector Modulation

39. 39
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
EE8407 Topic 5
• Simulated Waveforms ( 5-segment)
dV
2 4
1g
v
3gv
5g
v
ABv
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
• f
1 = 60Hz, f
sw = 600Hz, m
a = 0.696, T
s = 1.1ms
Space Vector Modulation

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