Industrial Electrical Engineering and AutomationLund University, Sweden

Power electronicsSolution to examination 2016-05-30

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Examination 2016-05-30 1a

U

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Examination 2016-05-30 1b

VVU dc 5662400max Maximum dc voltage

Average dc voltage VVU avedc 54024003

_

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Examination 2016-05-30 1cPhase current

-500-400-300-200-100

0100200300400500

0 0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 0,018 0,02

time [s]

[A]

1.63ms

AIrmsdiode

2.1142

400

02.0

00163.022

A

dxx

usofAverageIavediode

5.41400637.002.0

00163.02637.0

2cos0cos)sin(

sin 0

Rectifier diodeThreshold voltage 1.1 VDifferential resistance 2.0 mohmIrms 114.2 AAverage current 41,5 A

WIRIVP rmsdiffavethresholddioderectifier7.712.114002.05.411.1 22 Rectifier diode power loss

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Examination 2016-05-30 1d0

0,5

1

1,5

2

2,5

3

0 0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 0,018 0,02

AI

AI

AAcurrenthighestdiodeandTransistor

AAcurrentlowestdiodeandTransistor

AitL

Ui

t

iLUripplecurrentdiodeandTransistor

dioderms

transistorrms

2.703

8.1904.1208.1904.1202.0

4.1403

8.1904.1208.1904.1208.0

8.1904.704.120

4.1204.705.06.155

4.70105.0

1032.0430540

22

_

22

_

3

3

AAconductingwhencurrentaverageTransistor

msmsmstimeconductionDiode

msmstimeconductionTransistor

msperiodtimeditto

kHzfreq

AA

I

cycleDuty

AI

AAI

switch

diodeavg

transistoravg

converterbuckdc

6.15580.0

5.124

08.032.04.0

32.04.08.0

4.0

5.2

1.314

5.124

80.0540

430

5.124

5.1245.413

_

_

_

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Examination 2016-05-30 1dTransistorThreshold voltage 1.4VDifferential resistance 1.0 mohmIavg_trans 124.5 AIrms_trans 140.4 AIturnon_trans 120.4 AIturnoff_trans 190.8 ATurn on energy at 900 V and 180 A 60 mJTurn off energy at 900 V and 180 A 80 mJ

WP

WPlossesswitchTransistor

WrIUIPlossesconductionTransistor

transtotal

switch

trdifftrrmstrthtravgcond

4.381

4.187900180

54010808.190604.1202500

194001.04.1404.15.124

_

3

2_

2___

Diode Threshold voltage 1.6 VDifferential resistance 1.5 mohm Iavg_diode 31.1 AIrms_diode 70.2 AIturnoff_diode 120.4 AIturnon_diode 190.8 ATurn on energy at 900 V and 180 A 0 mJTurn off energy at 900 V and 180 A 25 mJ

WP

WPlossesswitchDiode

WrIUIPlossesconductionDiode

diodetotal

switch

trdifftrrmstrthtravgcond

3.82

1.25900180

54010254.12008.1902500

2.570015.02.706.11.31

_

3

2_

2___

Examination 2016-05-30 1dRMS value of a straight line

Industrial Electrical Engineering and AutomationLund University, Sweden

33

3332

22

3

2

2

;

222222

2

22

2

3

32

200

2

30

2

2

0

22

2

abbaaabaabab

T

Taab

T

Ta

T

Tab

T

dtt

aabT

dta

T

dtt

ab

T

dtatT

abat

Tab

dtT

ti

I

atT

abaL

T

abkLtkti

TTT

T

TRMS

0

2

4

6

8

10

12

0 0,005 0,01 0,015 0,02 0,025

a

b

T

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Examination 2016-05-30 1e

Rectifier diode (6)Loss each 71.7WRth diode 0.15 K/WTemp diff 10.8 oC

IGBT transistorLoss 381.4 WRth trans 0.1K/WTemp diff 38.1 oC

HeatsinkContribution fron 6 rectifier diodes and from one IGBT. Ambient temperature 35 oC Total loss to heatsink 6*71.7+82.3+381.4=893.9 WRth heatsink 0.05 K/WTemperature heatsink 893.9 *0.05+35=80 oC

Junction temperatureRectifier diode 80 +10.8 = 90.8 oCDiode 80 +16.4 = 96.4 oC Transistor 80 +38.1 = 118.1 oC

DiodeLoss 82.3 WRth diode 0.2 K/WTemp diff 16.4 oC

Examination 2016-05-30 2a The buck converter with RCD snubber

D R

C

T

FD

i

At turn off of transistor T, the current i commtutates over to the capacitor C via diode D. The capacitor C charges until the potential of the transistor emitter reduces till the diode FD becomes forward biased and thereafter the load current iload flows through diode FD and the current i=0. A turn on of the transistor T, the capacitor C is discharged via the the transistor T and resistor R. The diode FD becomes reverse biased and the current i commutates to the transistor T.

iload

Examination 2016-05-30 2b i

A turn on of the transistor 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 150V the duty cycle is 75%. The switching frequency is 2 kHz and the on state time is 0.375 ms, and thus the time constant =0.125 ms

D R

CT

FD

iload

At turn off of transistor T, the capacitor C charges until the potential of the transistor emitter reduces till the diode FD becomes forward biased and thereafter the load current commutates to the freewheeling diode.

Load current 9 ASupply voltage 200 VLoad voltage 150 VCommutation time 0.015 msSwitching frequency 2 kHz

200 V

Fdu

dtiC

dt

duCi 675.0

200

10159 6

150 V

18510675.0

101256

6

CRRC

Examination 2016-05-30 2c Fly-back converter with snubbers and

common mode (CM) and differential mode (DM) filter

vD

DM-filter CM-filter

doublevoltage

Examination 2016-05-30 2d Fly-back converter withSnubber operation

L1

C1

D2

R1

L2

C2

R2

T1

D3

L3

C3

R3

D0

ip is

For the description of the snubber operation the stray inductance L1 between the switch transistor and the supply/dclink, and the transformer leakage inductance, L2

on primary side and L3 on secondary side are added as discrete component in the circuit drawing above.

• Snubber R1C1 in parallel with the switch transistor T1. The stray inductance L1 keeps the current flowing, and the RC snubber offers an alternative path. The current will flow until the magnetic energy in the stray incuctance is consumed in the snubber resistor.

• The primary winding leakage inductance will keep the current flowing. The snubberr R2C2D2 offers an alternative path, the current circulated

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Examination 2016-05-30 2d cont’d Fly-back converter withSnubber operation

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Examination 2016-05-30 3a

)3

4(ˆ

)3

2(ˆ

)(ˆ

tCOSee

tCOSee

tCOSee

c

b

a

tjtjtjjtjtjjtjtjtjtj

jjtjjjtjjjtjjjtjtjtjjtjtj

jtjtj

tjtj

jxjxjjj

c

j

ba

tj

j

c

j

ba

eeeeeeeeeeeeee

eeeeeeee

eee

eeeee

eexetetteeeeeee

solutioneAlternativ

eetjte

jttejjtjjte

jttjttte

jttjttte

jtjtteeeeeee

2

3ˆ

2

3

2

1

2

3

2

113

3

2

2

1ˆ

3

2

2

1ˆ

2223

2ˆ

2223

2ˆ

2)cos(

3

4cos

3

2coscos

3

2ˆ

3

2

2

3ˆsincos

2

3ˆ

2

3sin

2

3cos

3

2ˆ

4

3

4

3

4

3

4

3sin

4

3

4

1

4

3

4

11cos

3

2ˆ

2

3

2

1

2

3sin

2

1cos

2

3

2

1

2

3sin

2

1coscos

3

2ˆ

2

3

2

1

3

4sinsin

3

4coscos

2

3

2

1

3

2sinsin

3

2coscoscos

3

2ˆ

2

3

2

1

3

4cos

2

3

2

1

3

2coscos

3

2ˆ

3

2

0

3

8

3

4

3

4

3

4

3

4

3

4

3

2

3

2

3

2

3

2

3

43

4

3

4

3

23

2

3

2

3

4

3

2

3

4

3

2

3

4

3

2

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Examination 2016-05-30 3b

a/b< a/b/cvect

d/q >a/bd-comp vectq-compangle

a/b >a/b/cid PI-controllerrefactemf

3-phase modulator

3-phase inverter

Ts/2-advance

a/b > d/qVectangle

a/b > d/qVectangle

Flux-angleFlux emf

angle

-1

iq PI-controllerrefactemf

3-phase current measurement

e e e

3-phase load

udclink

i*ab

iact

psi