Post on 01-Jan-2016
EE8407 Topic 9
1 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
Power Converter Systems
Graduate Course EE8407
Ryerson Campus
Bin Wu PhD, PEng
ProfessorELCE DepartmentRyerson University
Contact Info Office: ENG328Tel: (416) 979-5000 ext: 6484Email: bwu@ee.ryerson.ca http://www.ee.ryerson.ca/~bwu/
EE8407 Topic 9
2 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
PWM CSI fed MV drive
Topic 9
PWM Current Source Inverters (CSI)
Courtesy of Rockwell Automation
EE8407 Topic 9
3 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
Lecture Topics
• Single Bridge Inverter
• Trapezoidal Modulation (TPWM)
• Selective Harmonic Elimination (SHE)
• Space Vector Modulation (SVM)
• Dual Bridge Inverter
PWM Current Source Inverters
EE8407 Topic 9
4 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Inverter Topology
Features:- Simple topology – no antiparallel diodes- Reliable short circuit protection – constant dc current- Very low dv/dt on motor terminals
Symmetrical GCTs1S
2S
3S 5S
4S 6S
dI
wi
ci
si
fC
4g 6g 2g
1g 3g 5g
A
B
C
fC fCLOAD
O
ABv
Function of Cf :
- Assist GCT commutation
- Reduce harmonic distortion
Single Bridge Inverter
EE8407 Topic 9
5 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• DC Current Source Id
Implementation of dc current source:
- use a large size dc choke – making Id smooth;
- use dc current feed back control – keeping Id constant
SCRor
PWMRectifier
PWMInverter
Controller
dIdL
*dI
UtilitySupply
M
asv
bsv
csv
fC
A
B
C
dI
Single Bridge Inverter
EE8407 Topic 9
6 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Trapezoidal PWM (TPWM)• Selective Harmonic Elimination (SHE)• Space Vector Modulation (SVM)
• Constraints on Switching Pattern Design
- dc current Id cannot be interrupted
- inverter output current waveform
must be defined.
• At any time instant, only two switches are
turned on, one connected to the positive
dc bus, and the other to the negative dc bus.
1S
2S
3S 5S
4S 6S
dI
wi
4g 6g 2g
1g 3g 5g
A
B
C
P
N
• Modulation Techniques
Single Bridge Inverter
EE8407 Topic 9
7 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Trapezoidal PWM (TPWM)
Number of pulses per half cycle: Np = 7
1gv
2gv
3gv
4gv
5gv
6gv
0
wi
3
3
2 2
t
t
t
t
t
t
tdI
2
3
3
2t
crv mv
mV̂ crV̂
0 2
Trapezoidal Modulation
EE8407 Topic 9
8 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Harmonic Content (TPWM)
• Np = 15
• Fundamental does not change much with ma
• ma = 0.85
am
n = 5
0.2 0.4 0.6 0.80
0.04
0.12
0.08
0.16
29
23
250
0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
n = 7n = 11
n = 17n = 13
19
n = 5
n = 7
n = 1
am
max,1wwn II
max,1wwn II
0
Trapezoidal Modulation
EE8407 Topic 9
9 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Waveforms (TPWM)
Hz180
,13,Hz8.131
sw
p
f
Nf
Hz155
,31,Hz55
sw
p
f
Nf
Trapezoidal Modulation
EE8407 Topic 9
10 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Principle
• Not all the switching angles are independent.
• Only two harmonics can be eliminated with Np = 5.
• No modulation index control – the magnitude of inverter output
current is controlled by Id
• Number of harmonics to be eliminated: 2/)1( pNk
3
3
2 21 2
6
23
dI
t
wi
13
0
Selective Harmonic Elimination (SHE)
EE8407 Topic 9
11 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Fourier Analysis
1)sin()(
nnw tnati
even.k )()sin(...)()sin(
)()sin(...)()sin(
;oddk )()sin(...)()sin(
)()sin(...)()sin(
4
2
3
3
6
2
3
3
3
6
1
1
2
1
1
1
2
1
tdtntdtn
tdtntdtn
tdtntdtn
tdtntdtn
Ia
k
k
k
k
k
k
dcn
2
0)()sin()(
4
tdtntia wn
Selective Harmonic Elimination
EE8407 Topic 9
12 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
even.k )6
cos()]3
(cos[)cos(
...)]3
(cos[)cos()]3
(cos[)cos(
;oddk )6
cos()]3
(cos[)cos(
...)]3
(cos[)cos()]3
(cos[)cos(
4
2211
2211
nnn
nnnn
nnn
nnnn
n
Ia
kk
kkdc
n
Expression for an
• Fourier Analysis
Selective Harmonic Elimination
EE8407 Topic 9
13 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Switching Angle Calculation
To Eliminate nth harmonic, set an = 0
kiF ki ..., ,2 ,1 0) ..., , , ,( 321
For 5th, 7th and 11th harmonic elimination:
0)6
11cos()]
3(11cos[)11cos(
)]3
(11cos[)11cos()]3
(11cos[)11cos(
0)6
7cos()]
3(7cos[)7cos(
)]3
(7cos[)7cos()]3
(7cos[)7cos(
0)6
5cos()]
3(5cos[)5cos(
)]3
(5cos[)5cos()]3
(5cos[)5cos(
33
22113
33
22112
33
22111
F
F
F
Selective Harmonic Elimination
EE8407 Topic 9
14 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Switching Angles (SHE) Switching Angles Switching Angles Harmonics
Eliminated 1 2 3 Harmonics Eliminated 1 2 3 4
5 18.00 - - 7,11,17 11.70 14.12 24.17 - 7 21.43 - - 7,13,17 12.69 14.97 24.16 - 11 24.55 - - 7,13,19 13.49 15.94 24.53 - 13 25.38 - - 11,13,17 14.55 15.97 25.06 - 5,7 7.93 13.75 - 11,13,19 15.24 16.71 25.32 - 5,11 12.96 19.14 - 13,17,19 17.08 18.23 25.84 - 5,13 14.48 21.12 - 13,17,23 18.03 19.22 26.16 - 7,11 15.23 19.37 - 5,7,11,13 0.00 1.60 15.14 20.26 7,13 16.58 20.79 - 5,7,11,17 0.07 2.63 16.57 21.80 7,17 18.49 23.08 - 5,7,11,19 1.11 4.01 18.26 23.60 11,13 19.00 21.74 - 5,7,13,17 1.50 4.14 16.40 21.12 11,17 20.51 23.14 - 5,7,13,19 2.56 5.57 17.82 22.33 11,19 21.10 23.75 - 5,7,17,19 4.59 7.96 17.17 20.55 13,17 21.19 23.45 - 5,11,13,17 4.16 6.07 16.79 22.04 13,19 21.71 23.94 - 5,11,13,19 5.13 7.26 17.57 22.72 5,7,11 2.24 5.60 21.26 5,11,17,19 6.93 9.15 17.85 22.77 5,7,13 4.21 8.04 22.45 5,13,17,19 7.80 9.82 18.01 23.25 5,7,17 6.91 11.96 25.57 7,11,13,17 5.42 6.65 18.03 22.17 5,11,13 7.81 11.03 22.13 7,11,13,19 6.35 7.69 18.67 22.74 5,11,17 10.16 14.02 23.34 7,11,17,19 8.07 9.44 19.09 22.93 5,13,17 11.24 14.92 22.98 7,13,17,19 8.88 10.12 19.35 23.22 7,11,13 9.51 11.64 23.27 11,13,17,19 10.39 11.14 20.56 23.60
Selective Harmonic Elimination
EE8407 Topic 9
15 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Inverter Waveforms (SHE)
Harmonic eliminated: 5th, 7th and 11th; fsw = 420Hz
0
wi
2 4
dI
max,1wwn II
1)1(3 pN 1)1(3 pN
n1 5 10 15 20 25 30 35 40 450
0.1
0.2
6
Selective Harmonic Elimination
EE8407 Topic 9
16 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Waveforms (SHE)
0
7,20
)(
1175
1
www
p
III
NHzf
a
0
3,60
)(
5
1
w
p
I
NHzf
c
0
5,35
)(
75
1
ww
p
II
NHzf
b
Selective Harmonic Elimination
EE8407 Topic 9
17 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Space Vector Modulation
• Six active current vectors and one zero vector
• Six sectors
SECTOR I
SECTOR III
SECTOR IV
SECTOR VISECTOR V
j
SECTOR II
1I
2I
3I
6I
5I
4I
refI
0I
Space Vector Modulation
EE8407 Topic 9
18 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Switching State
Leg A Switching State
1S 4S wI
[1] On Off dI
[-1] Off On dI
[0] Off Off 0
[2] On On 0
1S
2S
3S 5S
4S 6S
dI
LOAD
wi
ci
oi
fC
4g 6g 2g
1g 3g 5g
A
B
C
fC fC
Z
Space Vector Modulation
EE8407 Topic 9
19 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Switching States & Space Vectors
Space Vector Switching State On-state Switch Vector
Definition
[2 0 0] 41 S,S
[0 2 0] 63 S,S Zero
Vector 0I
[0 0 2] 25 S,S
00 I
1I
[1 -1 0] 16 S,S 6/1
3
2 jd eII
2I
[1 0 -1] 21 S,S 6/2
3
2 jd eII
3I
[0 1 -1] 32 S,S 6/32
3
2 jd eII
4I
[-1 1 0] 43 S,S 6/54
3
2 jd eII
5I
[-1 0 1] 54 S,S 6/75
3
2 jd eII
Active
Vector
6I
[0 -1 1] 65 S,S 6/96
3
2 jd eII
[1]: Upper switch on
[-1]: Lower switch on
[0]: None of the switches
in a leg turned on
[2]: Both switches in a
leg turned on
(bypass mode)
Space Vector Modulation
EE8407 Topic 9
20 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Dwell Time Calculation
021
002211
TTTT
TITITITI
s
sref
2I
refI
22 I
T
T
s
11 I
T
T
s
1I
)(3
1)(sin
)()(cos
21
21
TTITI
TTITI
dsref
dsref
:Im
:Re
Following the same principleof SVM for the NPC inverter
Space Vector Modulation
EE8407 Topic 9
21 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Dwell Time Calculation
210
2
1
)6
(sin
)6
(sin
TTTT
TI
IT
TI
IT
s
sd
ref
sd
ref
210
2
1
)6
(sin
)6
(sin
TTTT
TmT
TmT
s
sa
sa
d
w
d
refa I
I
I
Im 1
ˆ
Space Vector Modulation
EE8407 Topic 9
22 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Switching Sequence
Requirements:
1) Transition from one switching state to the next involves only
two switches
2) At any time only two switches are on.
1I
16 , SS
1gv
2I
0I
1I
2I
0I
21 , SS 41 , SS 16 , SS 21 , SS 41 , SS
1T 2T 0T6gv5gv4gv3gv2gv
sT sT
Space Vector Modulation
EE8407 Topic 9
23 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Switching Sequence (Over one cycle)
1gv
Sector
1 0 6 1 06
VI I II III IV V
2 0 1 2 01 3 0 2 3 02
wi
0 2dI
...3,2,1I
sT sT
)( 6I
2gv
3gv
4gv
5gv
6gv
Space Vector Modulation
EE8407 Topic 9
24 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Inverter Output Waveforms (SVM)
0
wi
si
ABv
0
1.0
-1.0
(pu)
-2.0
0
1.0
-1.0
(pu)
-2.0
1.5
-1.5
(pu)
-3.0
(a) Waveforms
2 4
2 4
f1 = 60Hz, fsw = 540Hz, Np = 9 and ma = 1
Space Vector Modulation
EE8407 Topic 9
25 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Harmonic Spectrum (SVM)
THD = 45.7%
THD = 6.36%
THD =8.77%
max,1/ ABABn VV
max,1/ ssn II
max,1/ wwn II
(b) Spectrum
0
0.05
0.10
0.15
0.20
0
0.05
0.10
0.15
0.20
0
0.05
0.10
0.15
0.20
5 10 15 20 25 30 35 40 45 50 55 60 n
5 10 15 20 25 30 35 40 45 50 55 60 n
5 10 15 20 25 30 35 40 45 50 55 60 n
f1 = 60Hz, fsw = 540Hz, Np = 9 and ma = 1
Space Vector Modulation
EE8407 Topic 9
26 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Harmonic Content (SVM)
0
0.1
0.2
0.3
0.4
n = 19
n = 5
n = 17
n = 13n = 7
n = 11
THD
300%
200%
100%
0%
400%
Iwn / Iw1,max0.5
THD
0.2 0.4 0.6 0.8 ma0
9,Hz540(a) psw Nf
n = 1
Space Vector Modulation
EE8407 Topic 9
27 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Converter Configuration
CSI-1
M
fC
CSI-2
1i1L 2L
2i
dv
3i
4i
1S 5S3S 1S 5S3S
4S 2S6S 4S 2S6S
A
B
C
wi si
Dual-Bridge Inverter
EE8407 Topic 9
28 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Space Vector Diagram
[56;56]
[16;16]
[12;12]
[32;32]
[34;34]
[54;54]
[16;56][56;16]
[12;16][16;12]
[32;12][12;32]
[32;34][34;32]
[34;54][54;34]
[54;56][56;54]
Sector I
Sector IISector III
Sector IV
Sector V Sector VI
1I
7I
2I
8I
9I
10I
17I
16I
15I
18I
11I
12I
3I
4I
5I
6I
14I
13I
0I
refI
19 vectors and 51 switching states
Dual-Bridge Inverter
EE8407 Topic 9
29 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
CSI-1 CSI-2
1i1L 2L
2i
dv
3i
4i
Load andFilter Capacitor
A
B
C
O
~
~
~
1S 5S3S 1S 5S3S
4S 2S6S 4S 2S6S
Current paths with switching state [16;56]
• DC Current Balance Control
Dual-Bridge Inverter
EE8407 Topic 9
30 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• DC Current Balance Control
Current paths with switching state [16;56]
Dual-Bridge Inverter
EE8407 Topic 9
31 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• Space Vector Diagram
i1
i3
0
i
vAB
is
Timebase: 1.0sec/div Timebase: 4ms/div
(a) dc current transient response (b) Steady state ac waveforms
No balancecontrol
Dual-Bridge Inverter
EE8407 Topic 9
32 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
• PWM Scheme Comparison
Item SVM TPWM SHE
DC Current Utilization
dw II /max,1 0.707 0.74 0.73 to 0.78
Dynamic performance High Medium Low
Digital Implementation Real time Real time or look-up table
Look-up table
Harmonic Performance Adequate Good Best
dc Current Bypass Operation Yes No Optional
Summary
EE8407 Topic 9
33 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006