Post on 26-Oct-2014
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PWM Inverters
Inverters
ClassificationsSingle phase & three phase
Voltage Source & Current source
Two-level & Multi-level
Voltage Source Inverter
Sinusoidal PWM
Space vector modulation
Topics
To control inverter output frequency (fundamental)
To control inverter output voltage (fundamental)
To minimize harmonic distortion
Why Use PWM Techniques?
Voltage Source Inverter
Open loop voltage control
Closed loop current-control
VSIAC
motorPWMiref
if/back
VSI ACmotor
PWMvref
Voltage Source Inverter
Inverter Configuration
4
Voltage Source Inverter (VSI) Six-Step VSI
Waveforms of gating signals, switching sequence, line to negative voltages for six-step voltage source inverter.
Gating signals, switching sequence and line to negative voltages
where, 561 means that S5, S6 and S1 are switched on
Six inverter voltage vectors for six-step voltage source inverter.
Switching Sequence:
561 (V1) 612 (V2) 123 (V3) 234 (V4) 345 (V5) 456 (V6) 561 (V1)
5
Voltage Source Inverter (VSI) Six-Step VSI
Waveforms of line to neutral (phase) voltages and line to line voltagesfor six-step voltage source inverter.
Line to line voltages (Vab, Vbc, Vca) and line to neutral voltages (Van, Vbn, Vcn)
Vab = VaN - VbN
Vbc = VbN - VcN
Vca = VcN - VaN
Line to line voltages
Van = 2/3VaN - 1/3VbN - 1/3VcN
Phase voltages
Vbn = -1/3VaN + 2/3VbN - 1/3VcN
Vcn = -1/3VaN - 1/3VbN + 2/3VcN
6
Voltage Source Inverter (VSI) Six-Step VSI
Harmonic spectrum of a square wave
Voltage Source Inverter (VSI)
Six-Step VSI
Amplitude of line to line voltages (Vab, Vbc, Vca)
Fundamental Frequency Component (Vab)1
Harmonic Frequency Components (Vab)h
: amplitudes of harmonics decrease inversely proportional to their harmonic order
dcdcdc V78.0V
6
2
V4
2
3
(rms))(V 1ab
3,.....)2,1,(n16nhwhere,
V78.0
dcab
h
(rms))(V h
7
Voltage Source Inverter (VSI) Six-Step VSI
AB DC4
V (1) V cos (4(b))n 2
8
Characteristics of Six-step VSI
It is called “six-step inverter” because of the presence of six “steps”
in the line to neutral (phase) voltage waveform
Harmonics of order three and multiples of three are
absent from both the line to line and the line to
neutral voltages and consequently absent from the
currents Output amplitude in a three-phase inverter can be controlled
by only change of DC-link voltage (Vdc)
Voltage Source Inverter (VSI) Six-Step VSI
Sinusoidal PWMModulating 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 mf should be an odd integer
if mf is not an integer, there may exist sub-hamonics at output voltage
if mf is not odd, DC component may exist and even harmonics are present at output voltage
mf should be a multiple of 3 for three-phase PWM inverter
An odd multiple of 3 and even harmonics are suppressed
Sinusoidal PWM
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 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
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 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
(a)
c c m1 AO DC
c m2 c c AO DC
c c m c c m DCAO c
c c c
DC m
c
T V v (t)S ON period = 2 V is V 2
2 2Vc
V v (t)S ON period = T T V is V 2
2Vc
T T v (t) T T v (t) V1V average for a period T + +
T 2 2V 2 2V 2
V v (t)..........(5)
2 V
Space Vector ModulationSwitching States (Three-Phase)
Eight switching states
1S
2S
3S 5S
4S 6S
B
C
P
N
dV
A
Space Vector ModulationSpace 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 ModulationSpace 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 Space Vectors (Example)
Switching state [POO] S1, S6 and S2 ON
dCOdBOdAO VtvVtvVtv3
1)(,
3
1)(,
3
2)(
(5) (4)
0
1 3
2 j
d eVV
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 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
(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
f 2
Space Vector Modulation
Relationship Between Vref and VAB
Vref is approximated by two active and 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 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
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
d
j
refref VVeVV3
2, 1
32 3
2 j
d eVV
Space Vector Modulation
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 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
Modulation Index
cbs
asb
asa
TTTT
mTT
mTT
0
sin
)3
(sin
(15)
d
ref
a V
Vm
3 (16)
Space Vector Modulation
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
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 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 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 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 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 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
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
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