Transcript xslides_topic9 - Ryerson University

EE8407
Power Converter Systems
Topic 9
Graduate Course EE8407
Bin Wu
PhD, PEng
Professor
ELCE Department
Ryerson University
Contact Info
Office: ENG328
Tel:
(416) 979-5000 ext: 6484
Email:
[email protected]
http://www.ee.ryerson.ca/~bwu/
Ryerson Campus
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
1
EE8407
Topic 9
Topic 9
PWM Current Source Inverters (CSI)
PWM CSI fed MV drive
Courtesy of
Rockwell Automation
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
2
EE8407
PWM Current Source Inverters
Topic 9
Lecture Topics
• Single Bridge Inverter
• Trapezoidal Modulation (TPWM)
• Selective Harmonic Elimination (SHE)
• Space Vector Modulation (SVM)
• Dual Bridge Inverter
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
3
EE8407
Single Bridge Inverter
Topic 9
• Inverter Topology
S1
g1
S3
g3
S5
g5
Symmetrical GCTs
is
iw
A
Id
v AB
ic
O
B
C
S6
S4
g4
g6
LOAD
S2
g2
Cf
Cf
Cf
Function of Cf :
- Assist GCT commutation
- Reduce harmonic distortion
Features:
- Simple topology – no antiparallel diodes
- Reliable short circuit protection – constant dc current
- Very low dv/dt on motor terminals
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
4
EE8407
Single Bridge Inverter
Topic 9
• DC Current Source Id
Ld
vas
vbs
vcs
Utility
Supply
SCR
or
PWM
Rectifier
Id
A
PWM
Inverter
B
M
C
Cf
Controller
Id
I d*
Implementation of dc current source:
- use a large size dc choke – making Id smooth;
- use dc current feed back control – keeping Id constant
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
5
EE8407
Single Bridge Inverter
Topic 9
• Modulation Techniques
• Trapezoidal PWM (TPWM)
• Selective Harmonic Elimination (SHE)
• Space Vector Modulation (SVM)
P
S1
g1
S3
g3
S5
g5
iw
Id
A
• Constraints on Switching Pattern Design
B
- dc current Id cannot be interrupted
- inverter output current waveform
C
must be defined.
S6
S4
g4
g6
N
S2
g2
• 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.
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
6
EE8407
Topic 9
Trapezoidal Modulation
• Trapezoidal PWM (TPWM)
vm
vcr
Vˆcr
Vˆm
0

2
3
3

v g1
2
2
vg 2
t
t
t
vg 3
t
vg 4
t
vg5
t
vg 6
t
iw
0
Id

3
2
3

2
t
Number of pulses per half cycle: Np = 7
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
7
EE8407
Trapezoidal Modulation
Topic 9
• Harmonic Content (TPWM)
I wn I w1, max
n=1
0.8
0.6
• Np = 15
0.4
0.2
n=5
n=7
0
0
0.2
0.4
0.6
0.8
ma
• Fundamental does not
change much with ma
I wn I w1, max
• ma = 0.85
n=5
0.16
0.12
0.08
n=7
n = 11
29
23
0.04
n = 17
n = 13
19
0
25
0
0.2
0.4
0.6
0.8
ma
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
8
EE8407
Trapezoidal Modulation
Topic 9
• Waveforms
(TPWM)
f1  13.8Hz, N p  13,
f sw  180Hz
f 5  5Hz, N p  31,
f sw  155Hz
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
9
EE8407
Selective Harmonic Elimination (SHE)
Topic 9
• Principle
iw

3
0
1  2 
6

3
 1
Id

2
3
3
2

2
t
• Not all the switching angles are independent.
• Only two harmonics can be eliminated with Np = 5.
• Number of harmonics to be eliminated:
k  ( N p  1) / 2
• No modulation index control – the magnitude of inverter output
current is controlled by Id
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
10
EE8407
Selective Harmonic Elimination
Topic 9
• Fourier Analysis

iw (t )   an sin( nt )
n1
an 
4


2i (
0 w
t ) sin( nt )d (t )

 2
6
 1 sin( nt )d (t )  ...    k sin( nt )d (t ) 
 

 3  k 1
sin( nt )d (t )  ...   2 sin( nt )d (t )



1
4 I dc  3  k
3
an 

k
  2
sin( nt )d (t )  ...   sin( nt )d (t ) 


 k 1
 1

   k
 3 sin( nt )d (t )  ...   2 sin( nt )d (t )
1
 6
3
k  odd;
k  even.
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
11
EE8407
Selective Harmonic Elimination
Topic 9
• Fourier Analysis
Expression for an



cos(
n

)

cos[
n
(


)]

cos(
n

)

cos[
n
(
  2 )]  ...
1
1
2

3
3

 cos(n )  cos[n(   )]  cos(n  )
k  odd;
k
k
4 I dc 
3
6
an 



n 
cos(n1 )  cos[n(  1 )]  cos(n 2 )  cos[n(   2 )]  ...

3
3



k  even.
 cos(n k )  cos[n(   k )]  cos(n )

3
6
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
12
EE8407
Selective Harmonic Elimination
Topic 9
• Switching Angle Calculation
To Eliminate nth harmonic, set an = 0
Fi (1 ,  2 ,  3 , ..., k )  0
i  1, 2, ..., k
For 5th, 7th and 11th harmonic elimination:


F1  cos(51 )  cos[5(  1 )]  cos(5 2 )  cos[5(   2 )] 
3
3

5
 cos(5 3 )  cos[5(   3 )]  cos( )  0
3
6


F2  cos(71 )  cos[7(  1 )]  cos(7 2 )  cos[7(   2 )]
3
3

7
 cos(7 3 )  cos[7(   3 )]  cos( )  0
3
6


F3  cos(111 )  cos[11(  1 )]  cos(11 2 )  cos[11(   2 )]
3
3

11
 cos(11 3 )  cos[11(   3 )]  cos(
)0
3
6
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
13
EE8407
Selective Harmonic Elimination
Topic 9
• Switching Angles (SHE)
Harmonics
Switching Angles
Eliminated 1
2
3
5
7
11
13
5,7
5,11
5,13
7,11
7,13
7,17
11,13
11,17
11,19
13,17
13,19
5,7,11
5,7,13
5,7,17
5,11,13
5,11,17
5,13,17
7,11,13
18.00
21.43
24.55
25.38
7.93
12.96
14.48
15.23
16.58
18.49
19.00
20.51
21.10
21.19
21.71
2.24
4.21
6.91
7.81
10.16
11.24
9.51
13.75
19.14
21.12
19.37
20.79
23.08
21.74
23.14
23.75
23.45
23.94
5.60
8.04
11.96
11.03
14.02
14.92
11.64
21.26
22.45
25.57
22.13
23.34
22.98
23.27
Harmonics
Eliminated1
7,11,17
7,13,17
7,13,19
11,13,17
11,13,19
13,17,19
13,17,23
5,7,11,13
5,7,11,17
5,7,11,19
5,7,13,17
5,7,13,19
5,7,17,19
5,11,13,17
5,11,13,19
5,11,17,19
5,13,17,19
7,11,13,17
7,11,13,19
7,11,17,19
7,13,17,19
11,13,17,19
Switching Angles
2
3
4
11.70
12.69
13.49
14.55
15.24
17.08
18.03
0.00
0.07
1.11
1.50
2.56
4.59
4.16
5.13
6.93
7.80
5.42
6.35
8.07
8.88
10.39
14.12
14.97
15.94
15.97
16.71
18.23
19.22
1.60
2.63
4.01
4.14
5.57
7.96
6.07
7.26
9.15
9.82
6.65
7.69
9.44
10.12
11.14
24.17
24.16
24.53
25.06
25.32
25.84
26.16
15.14
16.57
18.26
16.40
17.82
17.17
16.79
17.57
17.85
18.01
18.03
18.67
19.09
19.35
20.56
20.26
21.80
23.60
21.12
22.33
20.55
22.04
22.72
22.77
23.25
22.17
22.74
22.93
23.22
23.60
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
14
EE8407
Selective Harmonic Elimination
Topic 9
• Inverter Waveforms (SHE)
iw
Id
0
2
6
4
I wn I w1, max
3( N p  1)  1
3( N p  1)  1
0.2
0.1
0
1
5
10
15
20
25
30
35
40
45
n
Harmonic eliminated: 5th, 7th and 11th; fsw = 420Hz
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
15
EE8407
Selective Harmonic Elimination
Topic 9
• Waveforms (SHE)
(a)
f1  20Hz, N p  7
I w5  I w7  I w11  0
(b)
f1  35Hz, N p  5
I w5  I w 7  0
(c )
f1  60Hz, N p  3
I w5  0
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
16
EE8407
Space Vector Modulation
Topic 9
• Space Vector Modulation
j

I3
SECTOR III

I4

SECTOR II

I ref

I2

SECTOR IV

I0

SECTOR I

I1

I5
SECTOR V

I6
SECTOR VI
• Six active current vectors and one zero vector
• Six sectors
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
17
EE8407
Topic 9
Space Vector Modulation
• Switching State
S1
Switching
State
g1
Leg A
S1
S4
Iw
[1]
On
Off
Id
[-1]
Off
On
 Id
S3
g3
S5
g5
iw
A
Id
io
ic
LOAD
B
C
[0]
Off
Off
0
[2]
On
On
0
S6
S4
g4
g6
S2
g2
Cf
Cf
Cf
Z
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
18
EE8407
Space Vector Modulation
Topic 9
• Switching States & Space Vectors
Space Vector
Zero
Vector
On-state Switch
[2 0 0]
S1 , S 4
[0 2 0]
S3 , S6
[0 0 2]
S5 , S2
[1 -1 0]
S 6 , S1

2
I1 
I d e  j / 6
3
[1 0 -1]
S1 , S 2

2
I2 
I d e j / 6
3
[0 1 -1]
S2 , S3

2
I2 
I d e j 3 / 6
3
[-1 1 0]
S3 , S4

2
I4 
I d e j 5 / 6
3

I5
[-1 0 1]
S4 , S5

2
I5 
I d e j7 / 6
3

I6
[0 -1 1]
S5 , S6

2
I6 
I d e j 9 / 6
3

I0

I1

I2
Active
Vector
Vector
Definition
Switching State

I3

I4

I0  0
[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)
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
19
EE8407
Topic 9
Space Vector Modulation
• Dwell Time Calculation
T2 
I2
Ts
Following the same principle
of SVM for the NPC inverter




I ref Ts  I1 T1  I 2 T2  I 0 T0

Ts  T1  T2  T0

I2


I ref

T1 
I1
Ts
Re : I ref (cos ) Ts  I d (T1  T2 )


1
Im
:
I
(sin

)
T

I d (T1  T2 )
ref
s

3


I1
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
20
EE8407
Space Vector Modulation
Topic 9
• Dwell Time Calculation
I ref


T

sin
(
  ) Ts
1
Id
6


I ref

sin (   ) Ts
T2 
Id
6



T0  Ts  T1  T2



T

m
sin
(
  ) Ts
a
1
6

T  m sin (   ) T
a
s
 2
6


T  T  T  T
 0
s
1
2
Iˆw1
ma 

Id
Id
I ref
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
21
EE8407
Space Vector Modulation
Topic 9
• Switching Sequence

I1

I2

I0

I1

I2

I0
S 6 , S1
S1 , S 2
S1 , S 4
S 6 , S1
S1 , S 2
S1 , S 4
v g1
vg 2
vg 3
vg 4
vg 5
vg 6
T1
T2
Ts
T0
Ts
Requirements:
1)
Transition from one switching state to the next involves only
two switches
2)
At any time only two switches are on.
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
22
EE8407
Topic 9
Space Vector Modulation
• Switching Sequence (Over one cycle)
Sector

I 1, 2, 3...
VI
I
II
III
IV
V
6 1 0 6 1 0 1 2 0 1 2 0 2 3 0 2 3 0
( I6 )
v g1
vg 2
vg 3
Ts
Ts
vg 4
vg 5
vg 6
iw
0
Id

Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
2
23
EE8407
Space Vector Modulation
Topic 9
• Inverter Output Waveforms (SVM)
iw (pu)
1.0
0
-1.0
2
4
2
4
-2.0
is (pu)
1.0
0
-1.0
-2.0
v AB (pu)
1.5
0
-1.5
-3.0
(a) Waveforms
f1 = 60Hz, fsw = 540Hz, Np = 9 and ma = 1
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
24
EE8407
Space Vector Modulation
Topic 9
• Harmonic Spectrum (SVM)
I wn / I w1,max
THD = 45.7%
0.20
0.15
0.10
0.05
0
I sn / I s1,max
5
10
15
20
25
30
35
40
45
50
55
60
n
THD = 6.36%
0.20
0.15
0.10
0.05
0
5
10
15
20
25
30
35
40
45
50
55
60
n
V ABn / V AB1,max
THD =8.77%
0.20
0.15
0.10
0.05
0
5
10
15
20
25
30
35
(b) Spectrum
40
45
50
55
60
n
f1 = 60Hz, fsw = 540Hz, Np = 9 and ma = 1
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
25
EE8407
Topic 9
Space Vector Modulation
• Harmonic Content (SVM)
Iwn / Iw1,max
THD
400%
0.5
THD
n = 19
n=1
0.4
300%
0.3
200%
n = 17
0.2
100%
0.1
0%
n=5
n=7
n = 13
n = 11
0
0
0.2
0.4
0.6
(a) f sw  540Hz, N p  9
0.8
ma
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
26
EE8407
Topic 9
Dual-Bridge Inverter
• Converter Configuration
L1
i1
L2
S1
S3
S5
i3
S1
S 3
S 5
iw
is
A
vd
M
B
C
S4
S6
S2
S 4
S 6
S 2
Cf
i4
i2
CSI-1
CSI-2
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
27
EE8407
Topic 9
Dual-Bridge Inverter
• Space Vector Diagram
[32;32]
Sector III
[32;34]
[34;32] 
I9
[32;12]
 [12;32]
I8

I 15

I4
[34;34]
Sector II

I3

I2

I 16
Sector IV

I
[34;54] 10
[54;34]

I0


I 17

I5
[54;54]

I 14

I 13
[54;56]
[56;54]
Sector V

I 12

I6
[56;56]

I ref
Sector I
[12;16]
 [16;12]
I7

I1

I 18

I 11
[12;12]
[16;16]
[16;56]
[56;16]
Sector VI
19 vectors and 51 switching states
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
28
EE8407
Topic 9
Dual-Bridge Inverter
• DC Current Balance Control
i3
L1
i1
S1
S3
S5
S1
L2
S 3
S 5
~
A
B
vd
~
C
S4
S6
S2
S 4
S 6
i2
S 2
O
~
Load and
Filter Capacitor
i4
CSI-1
CSI-2
Current paths with switching state [16;56]
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
29
EE8407
Dual-Bridge Inverter
Topic 9
• DC Current Balance Control
Current paths with switching state [16;56]
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
30
EE8407
Dual-Bridge Inverter
Topic 9
• Space Vector Diagram
vAB
i1
is
i
i3
0
No balance
control
Timebase: 1.0sec/div
(a) dc current transient response
Timebase: 4ms/div
(b) Steady state ac waveforms
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
31
EE8407
Topic 9
Summary
• PWM Scheme Comparison
Item
SVM
TPWM
SHE
DC Current Utilization
I w1,max / I d
0.707
0.74
0.73 to 0.78
Dynamic performance
High
Low
Digital Implementation
Real time
Harmonic Performance
dc Current Bypass Operation
Adequate
Yes
Medium
Real time or
look-up table
Good
No
Look-up table
Best
Optional
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
32
EE8407
Topic 9
Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006
33