Power electronics Solution to examination 2012-05-21 Tenta 20120521_final.pdf · Industrial...

Industrial Electrical Engineering and Automation

Lund University, Sweden

Power electronics

Solution to examination 2012-05-21

© Namn Namn Föredragstitel

Examination 2012-05-21 1a


Examination 2012-05-21 1b

VU QCdc 4304 4QC average bridge voltage

Average dc voltage VVU avedc 54024003

_

4QC duty cycle 8.0540

430D


Examination 2012-05-21 1c

Rectifier diode current 172 A

Rectifier diode threshold voltage 1.0 V

Rectifier diode diff resistance 2.2 mohm

Rectifer diode on state voltage 1+172*0.0022=1.38 V

Rectifier diode power loss 1.38*172*0.33=79 W

(conducting 33% of time)

Continous rectifier output current 172 A

The 4QC continous load current 172/0.8=215 A (to maintain the power)

Assume load constant voltage 0 V (not stated in the text)



AA

i

AA

i

AmsimHLVUtL

Ui

t

iL

dt

diLU

rippleCurrent

8.1932

4.42215

2.2362

4.42215

4.42102101.5

8.05404.0

102

8.0,1.5,540

min

max

333

Examination 2012-05-21 1d

RMS value of a straight line

Industrial Electrical Engineering and Automation

Lund University, Sweden

33

3332

22

3

2

2

;

222222

2

22

2

3

32

00

2

2

0

2

2

0

2

22

babaaabaabab

T

Taab

T

Ta

T

Tab

T

dtt

T

aab

T

dta

T

dtt

T

ab

T

dtatT

abat

T

ab

dtT

ti

I

atT

abaL

T

abkLtkti

TTT

T

TRMS

a

bT

i

t



4QC transistor threshold voltage 1.4 V

4QC transistor diff resistance 12 mohm

Transistor conducting 80%+0.5*20%=90%)

4QC Transistor turn-on losses 65 mJ

4QC Transistor turn-off losses 82 mJ

4QC diode threshold voltage 1.1 V

4QC diode diff resistance 9.5 mohm

4QC diode turn-on losses 0 mJ

4QC diode turn-off losses 25 mJ


Examination 2012-05-21 1c cont’d

WWWlosstotalDiode

WlossswitchstateonDiode

WlosspowerstateonDiode

Aiiii

currentrmsDiode

Aii

currentaverageDiode

WWWlosstotalTransistor

WlossswitchTransistor

WlosspowerstateonTransistor

Aiiii

currentrmsTransistor

Aii

currentaverageTransistor

Ai

Ai

1073968

39900180

540025.02.2362000

680095.01.685.211.1

1.683

1.0

5.212

1.0

985213772

213900180

540082.02.236065.08.1932000

772012.03.2045.1934.1

3.2043

9.0

5.1932

9.0

8.193

2.236

2

min2

minmaxmax2

minmax

2

min2

minmaxmax2

minmax

min

max


Examination 2012-05-21 1c cont’d Upper left IGBT transistor loss 985 W

Upper right IGBT transistor loss 0 W

Lower left IGBT transistor loss 0 W

Lower right IGBT transistor loss 985 W

Upper left IGBT diode loss 0 W

Upper right IGBT diode loss 107 W

Lower left IGBT diode loss 107 W

Lower right IGBT diode loss 0 W


Examination 2012-05-21 1d

Rectifier diode (6)

Loss each 79 W

Rth diode 0.12 K/W

Temp diff 9.5 oC

IGBT transistor (2)

Loss each 985 W

Rth trans 0.043 K/W

Temp diff 42.4 oC

Heatsink

Contribution fron 6 rectifier diodes and from two IGBT.

Ambient temperature 42 oC

Total loss to heatsink 6*79+2*107+2*985=2658 W

Temp diff over heatsink 2642*0.025=66.5 oC

Junction temperature

Rectifier diode 42+66.5 +9.5=118 oC

IGBT diode 42+66.5 +8.4=117 oC

IGBT transistor 42+66.5 +42.4=151 oC

IGBT diode (2)

Loss each 107 W

Rth diode 0.078K/W

Temp diff 8.4 oC

Examination 2012-05-21 2a The buck converter with RCD snubber

D R

C

T

FD

i

At transistor T turn off, the current i commtutates over to the capacitor C via diode

D. The capacitor C voltages increases until the freewheeling diode FD becomes

forward biased and thereafter the load current iload flows through diode FD and the

current i=0.

At transistor T turn on, the capacitor C is discharged via the the transistor T and

resistor R. The diode FD becomes reverse biased and the current iload commutates to

the transistor T and the current i= iload.

iload

Examination 2012-05-21 2b i

At transistor T turn on, the current i commutates to the transistor T, and the capacitor C is

discharged via the the transistor T and resistor R. As the load voltage is 160V the duty cycle is

64%. The switching frequency is 1 kHz and the on state time is 0.64 ms.

The time constant =0.64/3 ms =0.213 ms

D R

CT

FD

iload

At transistor T turn off, the capacitor C charges and its voltage increases until the diode FD

becomes forward biased and thereafter the load current commutates to the freewheeling

diode.

Load current Iload i=15 A

Supply voltage 250 V

Load voltage 160 V

Commutation time 0.012 ms250 V

Fdu

dtiC

dt

duCi 72.0

250

101215 6

160 V

2961072.0

102136

6

CRRC


Forward converter with snubber

vC

Rload

VDcCdc

vS

CD2

D1D3

Z

L

S

N1 N2

C1

R1

Examination 20120521 2d

Examination 20120521 2e

Drift region n-

Examination 20120521 3a The buck converter as battery charger

198 VL I

L= 4 mH

R=0 ohm

Switching frequency 4 kHz

Period time 0.25 ms

Load current=0-10 A

Duty cycle 100/198=0.505

On pulse 0.25 *0.505=0.13 ms

R

a3

Peak rectifier dc-voltage 220*1.414=311 V

Average rectifier dc-voltage 311*2/3.14=198 V

220 V,

50Hz

Examination 20120521 3b

The buck converter as battery charger


A

L

TeUi

kekikiT

LkU

RkeniniRTL

TRkiki

R

T

L

keniniT

R

L

Tkiki

R

T

LkUb

s

s

k

ns

s

s

k

ns

s

s

125.6004.0

00025.0100198

ˆˆ

0ˆˆ2

2ˆ2

ˆˆ

2

ˆ2

3

**

1

0

**

1

0

***

Examination 20120521 3c The buck converter as battery charger

L= 4 mH

R=0 ohm

Switching frequency 4 kHz

Period time 0.25 ms

Sampling time is set to 0.25 ms

Load current=0 to 10 A

Duty cycle with 0 A 100/311=0.32

On pulse 0.25 *032=0.08 ms

Voltage ref with const 0 A =100 V

Duty cycle with >0 A = 100/198=0.505

On pulse 0.25 *0.505=0.13 ms

Current increase/sample =6.125 A (se 3b)

Time to reach 10 A=10/6.125=0.4 ms

Current derivative at current step =24.5*103

Inductive voltage drop at current step =98 V

Voltage ref at current step= 100+98=198 V

Voltage ref at const 10 A=100 V

10A

6.125A

0A

0.25 msDuty cycle 0.32Duty cycle 0.505

100 V

198 V

0V

Uref

Uref

198 V

311V

0V

100V

Modulation

Phase current

Ud

0

dV

1V2V

Fig 1

as

d

sa

d

d

ddavgavg

ddavg

ddavg

as

d

as

d

as

d

sa

dLL

dddddL

d

dddddavgavg

dddavg

davg

s

pers

Lf

V

fL

ViripplecurrentMax

VVVVVe

VVV

VVVatvoltagesPhase

xatLf

V

x

iderivativeondsit

xwhenx

ix

Lf

V

x

iderivativesit

Lf

xxV

f

x

L

xVi

L

tVi

dt

diLVequationviarippleCurrent

xVVxVVeVVeVVinductoroverVoltage

V

VVonturnedareand

switchrisecurrentAt

VxVVxVVxVVemotoroverVoltage

VxVVxV

VxVvoltagesPhase

f

xTxtdurationpulseOn

xratioControl

2

5.05.012

005.0

5.05.01

5.05.0max

5.0max04

sec'

5.00212

'

212

122

0

4

1,

2

1

max

_2_1

_2

_1

2

2

2

21

2

1

_2_1

_2

_1

_

La

e

1

2

3

4

Examination 20120521 4a


Examination 20120521 4c

a/b< a/b/c

vect

d/q >a/b

d-comp vect

q-comp

angle

a/b >a/b/cid PI-controller

ref

act

emf

3-phase

modulator

3-phase

inverter

Ts/2-advance

a/b > d/q

Vect

angle

a/b > d/q

Vect

angle

Flux-angle

Flux emf

angle

-1

iq PI-controller

ref

act

emf

3-phase

current

measurement

e e e

3-phase

load

udclink

i*ab

iact

psi


Examination 20120521 5

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