8407 Slides Topic9 Current CSI

5/21/2018 8407 Slides Topic9 Current CSI

1/16

1

Topic 9

PWM Current Source Inverters (CSI)

Textbook: Bin Wu, High-Power Converters and AC Drives, Wiley-IEEE Press, 2006

EE8407

Power Converter Systems

PWM CSI fed MV drive Courtesy of Rockwell Automation

2

Lecture Topics

Single Bridge Inverter

Trapezoidal Modulation (TPWM)

Selective Harmonic Elimination (SHE)

Space Vector Modulation (SVM) Dual Bridge Inverter

Topic 9PWM Current Source Inverters (CSI)


EE8407


2/16

3

Inverter Topology

Features:- Simple topology no antiparallel diodes

- Reliable short circuit protection constant dc current

- Very lowdv/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 fC

LOAD

O

ABv

Function of Cf:

- Assist GCT commutation

- Reduce harmonic distortion


Topic 9 PWM CSI


EE8407

4

DC Current SourceId

Implementation of dc current source:

- use a large size dc chokemakingId smooth;

- use dc current feed back controlkeepingIdconstant

SCR

or

PWM

Rectifier

PWM

Inverter

Controller

dIdL

*dI

Utility

Supply

M

asv

bsv

csv

fC

A

B

C

dI


Topic 9 PWM CSI


EE8407


3/16

5

Trapezoidal PWM (TPWM)


Space Vector Modulation (SVM)

Constraints on Switching Pattern Design

- dc currentIdcannot be interrupted

- inverter output current waveform

must be defined.

At any time instant, only two switches are

turned on, one connected to the positivedc 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


Topic 9 PWM CSI


EE8407

6

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

mV crV

0 2


Topic 9 PWM CSI

Trapezoidal Modulation

EE8407


4/16

7

Harmonic Content (TPWM)

Np = 15

Fundamental does not

change much with ma

ma = 0.85am

am

max,1wwn II

max,1wwn II


Topic 9 PWM CSI


EE8407

8

Waveforms(TPWM)

Hz180

,13,Hz8.131

=

==

sw

p

f

Nf

Hz155

,31,Hz55

=

==

sw

p

f

Nf


Topic 9 PWM CSI


EE8407


5/16

9


Not all the switching angles are independent.

Only two harmonics can be eliminated withNp = 5.

No modulation index control the magnitude of inverter output

current is controlled byId

Number of harmonics to be eliminated: 2/)1( = pNk

3

3

2 21 2

6

23

dI

t

wi

13

0


Topic 9 PWM CSI

Selective Harmonic Modulation

EE8407

10

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

= 20 )()sin()(4

tdtntia wn


Topic 9 PWM CSI


EE8407


6/16

11

=+

++

=++

++

=

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 foran

Fourier Analysis


Topic 9 PWM CSI


EE8407

12

Switching Angle Calculation

To Eliminatenthharmonic, setan = 0

kiF ki ...,,2,10)...,,,,( 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


Topic 9 PWM CSI


EE8407


7/16

13

Switching Angles (SHE)

Switching Angles Switching AnglesHarmonicsEliminated 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 23.255,7,17 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


Topic 9 PWM CSI


EE8407

14

Inverter Waveforms (SHE)

Harmonic eliminated: 5th, 7th and 11th; fsw = 420Hz

wi

2 4

dI

max,1wwn II

1)1(3 pN 1)1(3 +pN

6


Topic 9 PWM CSI


EE8407


8/16

15

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


Topic 9 PWM CSI


EE8407

16

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

r

2Ir

3Ir

6Ir

5I

r

4Ir

refIr

0Ir


Topic 9 PWM CSI


EE8407


9/16

17

Switching State

Leg ASwitching

State1S 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


Topic 9 PWM CSI


EE8407

18

Switching States and Space Vectors

Space Vector Switching State On-state SwitchVector

Definition

[2 0 0] 41 S,S

[0 2 0] 63 S,S Zero

Vector 0Ir

[0 0 2] 25 S,S

00 =Ir

1Ir

[1 -1 0] 16 S,S 6/

13

2 = jdeIIr

2Ir

[1 0 -1] 21 S,S 6/

23

2 = jdeIIr

3Ir

[0 1 -1] 32 S,S 6/3

23

2 = jdeIIr

4Ir

[-1 1 0] 43 S,S 6/5

43

2 = jdeIIr

5Ir

[-1 0 1] 54 S,S 6/7

53

2 = jdeIIr

Active

Vector

6Ir

[0 -1 1] 65 S,S 6/9

63

2 = jdeIIr

[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)


Topic 9 PWM CSI


EE8407


10/16

19

Dwell Time Calculation

++=

++=

021

002211

TTTT

TITITITI

s

sref

rrrr

2Ir

refIr

22 IT

T

s

r

11 IT

T

s

r

1Ir

+=

+=

)(3

1

)(sin

)()(cos

21

21

TTITI

TTITI

dsref

dsref

:Im

:Re

Following the same principle

of SVM for the NPC inverter


Topic 9 PWM CSI


EE8407

20

Dwell Time Calculation

=

+=

=

210

2

1

)6

(sin

)6

(sin

TTTT

TI

IT

TI

IT

s

s

d

ref

s

d

ref

=

+=

=

210

2

1

)6

(sin

)6

(sin

TTTT

TmT

TmT

s

sa

sa

d

w

d

ref

aI

I

I

Im 1

==


Topic 9 PWM CSI


EE8407


11/16

21

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.

1Ir

16 ,SS

1gv

2Ir

0Ir

1Ir

2Ir

0Ir

21 ,SS 41 ,SS 16 ,SS 21 ,SS 41 ,SS

1T 2T 0T

6gv

5gv

4gv

3gv

2gv

sT sT


Topic 9 PWM CSI


EE8407

22

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 2

dI

...3,2,1Ir

sT sT

)( 6Ir

2gv

3gv

4gv

5gv

6gv


Topic 9 PWM CSI


EE8407


12/16

23

Inverter Output Waveforms (SVM)

wi

si

ABv

2 4

2 4

f1 = 60Hz, fsw = 540Hz,Np = 9 andma = 1


Topic 9 PWM CSI


EE8407

24

Harmonic Spectrum (SVM)

max,1/ ABABn VV

max,1/ ssn II

max,1/ wwn II

f1 = 60Hz, fsw = 540Hz,Np = 9 andma = 1


Topic 9 PWM CSI


EE8407


13/16

25

Harmonic Content (SVM)

9,Hz540(a) == psw Nf


Topic 9 PWM CSI


EE8407

26

Converter Configuration


Topic 9 PWM CSI

Dual Bridge Inverter

EE8407

fC

1i1L 2L

2i

dv

3i

4i

1S 5S3S 1S 5S3S

4S 2S6S 4S 2S6S

wi si


14/16

27


Space Vector Diagram

Topic 9 PWM CSI


EE8407

1Ir

7Ir

2Ir

8Ir

9Ir

10Ir

17Ir

16Ir

15Ir

18Ir

11Ir

12Ir

3Ir

4Ir

5Ir

6Ir

14Ir

13Ir

0Ir

refIr

19 vectors and 51 switching states

28


Topic 9 PWM CSI


EE8407

1i1L 2L

2i

dv

3i

4i

1S 5S3S 1S 5S3S

4S 2S6S 4S 2S6S

Current paths with switching state [16;56]

DC Current Balance Control


15/16

29


DC Current Balance Control

Topic 9 PWM CSI


EE8407

Current paths with switching state [16;56]

30


Space Vector Diagram

Topic 9 PWM CSI


EE8407


16/16

31

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 timeReal time or

look-up tableLook-up table

Harmonic Performance Adequate Good Best

dc Current Bypass Operation Yes No Optional


Topic 9 PWM CSI

Summary

EE8407

32


EE8407

Topic 9PWM Current Source Inverters (CSI)

8407 Slides Topic9 Current CSI

Documents