EE8407 Topic 9 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 1 Power Converter Systems Graduate Course EE8407 Ryerson

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: [email protected] http://www.ee.ryerson.ca/~bwu/

EE8407 Topic 9


PWM CSI fed MV drive

Topic 9

PWM Current Source Inverters (CSI)

Courtesy of Rockwell Automation

EE8407 Topic 9


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


• 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


• 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


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


• 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


EE8407 Topic 9


• Waveforms (TPWM)

Hz180

,13,Hz8.131

sw

p

f

Nf

Hz155

,31,Hz55

sw

p

f

Nf


EE8407 Topic 9


• 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


• 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


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


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


• 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


EE8407 Topic 9


• 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)


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


• 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


EE8407 Topic 9


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


EE8407 Topic 9


• DC Current Balance Control

Current paths with switching state [16;56]


EE8407 Topic 9


• 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


EE8407 Topic 9


• 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


Documents

EE8407 Topic 9 Textbook: Bin Wu, ‘High-Power Converters and AC Drives’, Wiley - IEEE Press, 2006 1 Power Converter Systems Graduate Course EE8407 Ryerson