space vector modulation
TRANSCRIPT
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Power Converter Systems
Graduate Course EE8407
Ryerson Campus
Bin Wu PhD, PEng
ProfessorELCE DepartmentRyerson University
Contact Info Office: ENG328Tel: (416) 979-5000 ext: 6484Email: [email protected] http://www.ee.ryerson.ca/~bwu/
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VDM5000 Two-level VSI
Two-Level Voltage Source Inverter (VSI)
Source: Alstom
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• 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
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• Inverter Configuration
Assumption:
dc capacitor very large dc voltage ripple free
dC
1S
2S
3S 5S
4S 6S
A
B
C
P
N
LOAD
Ai
OBi
CidV
Sinusoidal PWM
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• Modulating and Carrier Waves
• vcr – Carrier wave (triangle) • Amplitude modulation index
cr
ma V
Vm
ˆ
ˆ
• Frequency modulation index
m
crf f
fm
0
v mAv Bmv Cmvcrv
crV̂ mV̂t
• vm – Modulating wave (sine)
Sinusoidal PWM
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• Gate Signal Generation
1gv
4gv
dV
0
ANv
2
mAv crv
0
crmA vv 01 gv )0( 4 gv 1S on )off( 4S dAN Vv Phase A
crmA vv 04 gv )0( 1 gv 4S on )off( 1S 0ANv
Vg1 and Vg4 are complementary
Sinusoidal PWM
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• Line-to-Line Voltage vAB
ABv
BNv
ANv
0
0
0
v mAv Bmv Cmvcrv
crV̂ mV̂
dV
dV
dV
2t
t
t
t
1ABv
1S
2S
3S 5S
4S 6S
B
C
P
N
dV
A
Sinusoidal PWM
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• 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%
dV
3/2 dV
ABv
AOv
Ai
2fm
12 fm
23 fm 14 fm
n
3
32
2
01 5 10 15 20 25 30 35 40 45 50 55 60
dVVAB 49.01
dn VVAB /
Sinusoidal PWM
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• Harmonic Content
• Low order harmonics n < (mf -2) are eliminated
• VAB1 versus ma is linear
• VAB1,max = 0.612Vd
am
12 fm2fm
14 fm23 fm
43 fm
d
nAB
V
V
1n
0.2 0.4 0.6 0.8
0.1
0.2
0.3
0
0
100
200
300
0
THD(%)
THD
Sinusoidal PWM
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• Over-Modulation
• Fundamental voltage ↑
• Low-order harmonics ↑
0
0.1
0.2
0dV
2 3
0
1
2
-1
-2
mAv mCvmBv
crv
ABv
n
0
Ai
2 3
dVVAB 744.01
dn VVAB /
n1 5 10 15 20 25 30 35 40 45 50 55 60
Sinusoidal PWM
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• Third Harmonic Injection PWM
crm VV ˆˆ1 • - Fundamental voltage increased
crmA VV ˆˆ • - 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
3mv
1mv
31 mmmA vvv
0
v
t
1ˆmV mAV̂ crV̂
Sinusoidal PWM
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• Switching States
Leg A Leg B Leg C Switching State
1S 4S ANV 3S 6S BNV 5S 2S CNV
P On Off dV On Off dV On Off dV
O Off On 0 Off On 0 Off On 0
1S
2S
3S 5S
4S 6S
B
C
P
N
dV
A
LOAD
Ai
OBi
Ci
Space Vector Modulation
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• Switching States (Three-Phase)
• Eight switching states
1S
2S
3S 5S
4S 6S
B
C
P
N
dV
A
Space Vector Modulation
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• Space Vector Diagram
1V
0V
3V
2V
4V
5V
6V
j
POO
PPOOPO
OPP
OOP POP
refV
OOOPPP
SECTOR ISECTOR III
SECTOR IV SECTOR VISECTOR V
SECTORII
• Active vectors: to (stationary, not rotating)
• Zero vector:
1V
6V
0V
• Six sectors: I to VI
Space Vector Modulation
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• Space Vectors
• Three-phase voltages
0)()()( tvtvtv COBOAO
• Two-phase voltages
)(
)(
)(
3
4sin
3
2sin0sin
3
4cos
3
2cos0cos
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
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• Space Vectors (Example)
Switching state [POO] S1, S6 and S2 ON
dBOdAO VtvVtv3
1)(,
3
2)(
dCO Vtv3
1)( and
(5) (4)
(7)
(5)
(6)0
1 3
2 j
d eVV
Similarly,
3)1(
3
2
kj
dk eVV
.6...,,2,1k
1V
0V
3V
2V
4V
5V
6V
j
POO
PPOOPO
OPP
OOP POP
refV
OOOPPP
SECTOR ISECTOR III
SECTOR IV SECTOR VISECTOR V
SECTORII
Space Vector Modulation
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• 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 00 V
1V
[ P O O ] 261 ,, SSS 01 3
2 jd eVV
2V
[ P P O ] 231 ,, SSS 32 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
5V
[ 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]
1S
2S
3S 5S
4S 6S
B
C
P
N
dV
A
Space Vector Modulation
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(8)
• Reference Vector Vref
• Definition
1V
0V
3V
2V
4V
5V
6V
j
POO
PPOOPO
OPP
OOP POP
refV
OOOPPP
SECTOR ISECTOR III
SECTOR IV SECTOR VISECTOR V
SECTORII
• Angular displacement
t
dtt0
)( (9)
jrefref eVV
• Rotating in space at ω
Space Vector Modulation
f 2
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• 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
1V
2V
refV
1VT
T
s
a
2VT
T
s
b
SECTOR I
Q
Space Vector Modulation
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• Dwell Time Calculation• Volt-Second Balancing
0
0021
TTTT
TVTVTVTV
bas
basref
(10)
• Ta, Tb and T0 – dwell times for and , 21 VV
0V
• Ts – sampling period
• Space vectors
d
j
refref VVeVV3
2, 1
3
2 3
2 j
d eVV
00 V
, and
(11) (10)
bdsref
bdadsref
TVTV
TVTVTV
3
1)(sin
3
1
3
2)(cos
:Im
:Re
(11)
(12)
1V
2V
refV
1VT
T
s
a
2VT
T
s
b
SECTOR I
Q
Space Vector Modulation
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• Dwell Times
Solve (12)
bas
d
refs
b
d
refs
a
TTTT
V
VTT
V
VTT
0
sin3
)3
(sin3
3/0 (13)
Space Vector Modulation
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• Vref Location versus Dwell Times
refV Location 0
60
6
36
3
Dwell Times 0
0
b
a
T
T baTT baTT baTT 0
0
b
a
T
T
1V
2V
refV
1VT
T
s
a
2VT
T
s
b
SECTOR I
Q
Space Vector Modulation
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• Modulation Index
cbs
asb
asa
TTTT
mTT
mTT
0
sin
)3
(sin
(15)
d
ref
a V
Vm
3 (16)
Space Vector Modulation
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• Modulation Range
• Vref,max
32
3
3
2max,
ddref
VVV (17)
1V
0V
3V
2V
4V
5V
6V
j
POO
PPOOPO
OPP
OOP POP
refV
OOOPPP
SECTOR ISECTOR III
SECTOR IV SECTOR VISECTOR V
SECTORII
(17) (16)
• ma,max = 1
• Modulation range: 0 ma 1 (18)
Space Vector Modulation
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• 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
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• Seven-segment Switching Sequence
dV
20T
2aT
2bT
2aT
BNv
ANv
CNv
0
1V
1V
2V
0V
2V
POOOOO PPO PPP PPO POO OOO
dV
dV
40T
40T
2bT
sT
0
0
0V
0V
• Total number of switchings: 6
• Selected vectors: V0, V1 and V2
• Dwell times: Ts = T0 + Ta + Tb
Space Vector Modulation
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• Undesirable Switching Sequence
• Vectors V1 and V2 swapped
dV
20T
2aT
2bT
2aT
BNv
ANv
CNv
0
1V
1V
2V
2V
POOOOO PPO PPP PPOPOO OOO
dV
dV
40T
40T
2bT
sT
0
0
0V
0V
0V
• Total number of switchings: 10
Space Vector Modulation
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• 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
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• Simulated Waveforms
ABv
AOv
0
0
0
Ai
dV
3/2 dV
2 3
2 3
VIVISector
III
IIIIV
V
III
IIIIV
V
f1 = 60Hz, fsw = 900Hz, ma = 0.696, Ts = 1.1ms
Space Vector Modulation
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• Waveforms and FFT
0
0.1
0.2
n
0
0
ABv
AOv
Ai
THD =80.2%
THD =80.2%
THD =8.37%
THD =80.2%
dV
3/2 dV
2
dVVAB 566.01
1 5 10 15 20 25 30 35 40 45 50 55 60
dn VVAB /
0 2 3
Space Vector Modulation
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• Waveforms and FFT (Measured)
23
AOv
ABv d
n
V
VAB
0.2
0.1
0
(a) Waveforms 2ms/div (b) Spectrum (500Hz/div)
14
34
10 4758
THD = 80.3%
8
16 29 43
Space Vector Modulation
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0 0.2 0.4 0.6 0.80
0.05
0.10
0.15
10 16 20
dnAB VV /
am
1n
2n 4 8
14
(a) Even order harmonics
57111317n = 19
0.05
0.10
0.15
dnAB VV /
0 0.2 0.4 0.6 0.8 am
1n
(b) Odd order harmonics
0
100
200
300
0
THD(%)
THD
• Waveforms and FFT (Measured)
Hz601 f sec720/1sT ( and )
Space Vector Modulation
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• Even-Order Harmonic Elimination
BNv
ANv
CNv
0
5V
4V
0V
OOPOOO OPP PPP OPP OOP OOO
0
0
0V
0V
ABv0
dV
4V
5V
dV
dV
dV
Type-A sequence (starts and ends with [OOO])
BNv
ANv
CNv
0
0
0
ABv0
dV
5V
OOP4V
OPP
dV
dV
dV
4V
OPP5V
OOPPPP0V
0V
OOO PPP0V
Type-B sequence (starts and ends with [PPP])
Space Vector Modulation
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• Even-Order Harmonic Elimination
1V
3V
2V
4V
5V
6V
SECTOR ISECTOR III
SECTOR IV SECTOR VI
SECTOR V
SECTOR II
a
ba
a
a
aa
b
b
bb
b
Type-A sequence
Type-B sequence
30
30
Space vector Diagram
Space Vector Modulation
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• Even-Order Harmonic Elimination
(a) Waveforms 2ms/div
AOv
ABv
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
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• Even-Order Harmonic Elimination
17
1913
75
11
100
200
300
0
THD(%)
0 0.2 0.4 0.6 0.8 am0
0.1
0.2
0.3
dnAB VV /
1nTHD
Hz601 f sec720/1sT ( and )
Space Vector Modulation
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• Five-segment SVM
dV
2aT
bT2aT
BNv
ANv
CNv
0
1V
1V
2V
0V
POOOOO PPO POO OOO
dV
sT
0
0
0V
20T
20T
dV
aT
1V
2V
0V
PPP PPO POO PPP
dV
sT
0V
20T
20T
(a) Sequence A
2V
PPO
dV
2bT
2bT
(b) Sequence B
Space Vector Modulation
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• Switching Sequence ( 5-segment)
S ector S w itch in g S eq u en ce (A )
0V
1V
2V
1V
0V
I
O O O P O O P P O P O O O O O 0CNv
0V
3V
2V
3V
0V
II
O O O O P O P P O O P O O O O 0CNv
0V
3V
4V
3V
0V
III
O O O O P O O P P O P O O O O 0ANv
0V
5V
4V
5V
0V
IV
O O O O O P O P P O O P O O O 0ANv
0V
5V
6V
5V
0V
V
O O O O O P P O P O O P O O O 0BNv
0V
1V
6V
1V
0V
V I
O O O P O O P O P P O O O O O 0BNv
Space Vector Modulation
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• Simulated Waveforms ( 5-segment)
dV
2 4
1gv
3gv
5gv
ABv
0
0
Ai
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
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