research article transformer magnetizing inrush currents...

Hindawi Publishing CorporationISRN ElectronicsVolume 2013 Article ID 361643 8 pageshttpdxdoiorg1011552013361643

Research ArticleTransformer Magnetizing Inrush Currents Using a DirectlyCoupled Voltage-Source Inverter

Rickard Ekstroumlm Senad Apelfroumljd and Mats Leijon

Division of Electricity Department of Engineering Physics Swedish Centre for Renewable Electric Energy ConversionUppsala University PO Box 534 751 21 Uppsala Sweden

Correspondence should be addressed to Rickard Ekstrom rickardekstromangstromuuse

Received 20 July 2013 Accepted 19 September 2013

Academic Editors J Abu Qahouq and J Doval-Gandoy

Copyright copy 2013 Rickard Ekstrom et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The connection of a power transformer to the grid is associated with magnetizing inrush currents that may result in power qualityissues as well as faulty relay tripping In distributed generation the transformer may instead be premagnetized from the source toavoid this In this paper a VSI is directly coupled to a transformer Three different strategies of premagnetization are implementedinto the control system and the inrush currents are measured for various values of the remanent flux in the core The results showgood reduction in the peak magnetizing inrush currents without using any external circuitry

1 Introduction

When energizing a power transformer the magnetizinginrush currents that follow may be several times higher thanthe rated currents for the transformer The magnitude of theinrush currents may cause voltage dips in the local gridresulting in poor power quality [1] Also the magnetizinginrush currents are rich in harmonic content usually have ahigh direct current component and may erroneously triggertransformer overcurrent protections [2]Muchwork has beenconducted in making the protective relays recognize thedifference between overcurrents at a fault and a magnetizinginrush current [3]

Themagnitude of the inrush currents depends on the cir-cuit reactance the phase angle120572 of the voltage source and thetransformer remanent magnetic flux 120601

119903 The remanent flux

in the transformer is the flux that exists in the transformerafter it is powered down This phenomenon has long beenstudied and variousmethods andmodels can be found in theliterature To measure the remanent flux is not easy but maybe approximated with measurements of the voltage integralduring deenergization

Several ways to reduce or eliminate the inrush currentshave been presented Ways to handle the issues are throughcontrolled switching and removal of remanent flux [4 5]

sequential phase energization [6 7] insertion of dampingresistors [8] capacitive loading or thyristor switching control[9]

Work that uses PWM inverters to inject a cancelling-outcurrent via the inverter during powerup of the transformerhas also been presented [10] along with methods to detectthe remanent flux by analysing the DC component duringswitching [11]

Many renewable energy sources are nonsynchronouswith the grid which will require a power electronics conver-sion stage for grid connection A commonly used conversionis the voltage-source inverter (VSI) followed by an LCL-filterand a step-up transformer The full control of the VSI allowsthe transformer magnetization to be handled by the sourcerather than the grid which can give a great advantage inhandling the magnetizing inrush currents

In this paper the power transformer is directly magne-tized by a VSI The LCL filter is put on the secondary side ofthe transformer to reduce the ampacity of the filter inductorsas discussed in [12] No external circuitry is required forthe transformer magnetization Three different strategies ofmagnetization are experimentally evaluated with variationsin the remanent flux and the peak inrush currents aredetected

2 ISRN Electronics

Im

V1 120601

120601

120601min

120596t

120601max

Figure 1 The induced core flux 120601(119905) lags the induced voltage V1(119905) by almost 90∘ The resultant magnetizing current 119868

119898grows rapidly when

the transformer goes into saturation

Im

120601

(a) Strategy 1

Im

120601

(b) Strategy 2

Im

120601

(c) Strategy 3

Figure 2 Three different typical paths in the B-H plane 120601119903is assumed to be maximum for all cases In strategy 1 the core is directly pushed

into saturation and it can take a long time before it stabilizes In strategy 2120601119903is pulled down to zero for all phases which reduces themagnitude

of the inrush current In strategy 3 the voltage ramping will slowly converge to the stable B-H-path while avoiding large inrush currents

2 Theory

When a variable voltage source V1(119905) is applied to the trans-

former windings a resulting flux 120601(119905) will be induced in thetransformer core according to Faradayrsquos law as follows

V1(119905) = radic2

1003816100381610038161003816V1

1003816100381610038161003816cos (120596119905 + 120572) = 119873

119889120601 (119905)

119889119905

(1)

where 120596 is the natural frequency of the applied voltage 120572is the start angle and 119873 the number of winding turnsThe induced flux may be derived by computing the voltageintegral over time as follows

120601 (119905) = int

1199052

1199051

V1(119905)

1198731

119889119905 =

radic21003816100381610038161003816V1

1003816100381610038161003816

1205961198731

sin (120596119905) + 120601119903 (2)

where 120601119903is the remanent flux Figure 1 shows how this is used

to derive the classical 120601-119868119898-curve or 119861-119867-curve It is clear

how even a small saturation in themagnetic fluxmay result ina large magnitude of the magnetizing current 119868

119898 As a worst

case scenario the peak amplitude of 119868119898may be approximated

by [1]

119868119898=

1

119883 + 119883119901+ 119883119888(min)

[pu] (3)

where 119883 is the source impedance 119883119901

is the windingimpedance and 119883

119888(min) is the minimum magnetization

impedance When the core is completely saturated it may betreated as an air core and it has been shown that 119883

119888may be

approximated by the short-circuit impedance119883SC [13]More accurately the magnetizing inrush current is calcu-

lated by

119868119898=

radic21003816100381610038161003816V1

1003816100381610038161003816

radic(120596119871)2

+ 1198772

sdot (

2119861119873+ 119861119877minus 119861119878

119861119873

) (4)

where 119861119873is the normal rated flux density 119861

119903is the remanent

flux density and 119861119878is the saturation flux density For more

detailed analysis a finite-element method (FEM) model hasto be set up for the transformer

3 Magnetizing Strategies

With the VSI directly connected to the power transformerthree different magnetization strategies have been evaluatedfor start-up of the transformer

(1) step response with remanent flux(2) step response without remanent flux(3) voltage ramping with remanent flux

The general plots of the B-H-curves for the differentstrategies are illustrated in Figure 2 but they should only be

ISRN Electronics 3

(a) VSI (b) Power transformer

Figure 3 The VSI and the power transformer used in the experimental set-up

C

E

G

Ove

rcur

rent

desa

t pro

tect

ion

VCE

(a)

400

300

200

100

0

A

30 1 2 V

VCE

IC

tp = 80120583s

TJ = 25∘C

VGE = 15V

VGE = 17VVGE = 15VVGE = 11V

TJ = 125∘C

(b)

Figure 4 (a) De-sat protection circuit (b) 119881CE vs 119868119862 from datasheet

considered as rough estimates To vary the remanent flux overthe entire range the transformer is magnetized at 1 pu andthen abruptly stopped at different angles 120573 of the appliedvoltage Stopping at 120573 = 0∘ results in a maximum negativeflux 120601maxminus and stopping at 120573 = 180∘ results in a maximumpositive flux 120601max+

In the first strategy the inverter is started abruptly givingfullmagnetization to the transformerThis becomes similar toan immediate grid connection and will be used as a referencecase In Figure 2(a) the remanent flux was positive at start-up and the transformer core is pushed into saturation as thestarting angle 120572 = 0

∘ If instead 120572 = 180∘ for this case a

minimal inrush current would have been obtained for thisphase

In the second strategy the inverter is started at zeroamplitude modulation 119898

119886 which will slowly force the core

flux to zero for all the transformer legs The switchingfrequency of the inverter is much faster than the transformer

time constant resulting in only a small pulse ripple in thetransformer core flux This essentially results in a removal ofthe remanent flux that is 120601

119903= 0 and becomes a special case

of strategy 1 when 120572 = 90∘ or 270∘ Once the transformer hassettled a step response is made in the induced voltage to 1 puThis is illustrated in Figure 2(b) where the flux is forced tocircle around origo before energization

The third strategy starts at 119898119886= 0 and slowly increases

the applied voltagewith a constant ramping function until fullmagnetization is reached in the transformer coreThe appliedvoltage can be described as

V1(119905) = V

119873

119905 minus 1199050

119879119877

cos (120596 (119905 minus 1199050) + 120572) 119905

0le 119905 le 119879

119877 (5)

where V119873is the nominal voltage 119879

119877is the slope of the ramp

and 119905 minus 1199050is the duration of the voltage ramping The major

benefit of this method is that it becomes rather insensitiveto the initial 120601

119903 and the core flux will smoothly settle

4 ISRN Electronics

0 10 20 30 40 50 60 70 80 90 100

Overcurrent limit

Time (ms)

Cur

rent

(A)

300

200

100

0

minus100

minus200

minus300

(a) 120572 = 180∘ 120573 = 0∘

0 10 20 30 40 50 60 70 80 90 100Time (ms)

Cur

rent

(A)

100

50

0

minus50

minus100

(b) 120572 = 180∘ 120573 = 180∘

0 10 20 30 40 50 60 70 80 90 100Time (ms)

Phase APhase BPhase C

0 10 20 30 40 50 60 70 80 90 10Time (ms)


Overcurrent limit

Cur

rent

(A)

300

200

100

0

minus100

minus200

minus300

(c) 120572 = 0∘ 120573 = 180∘

0 10 20 30 40 50 60 70 80 90 100Time (ms)


0 10 20 30 40 50 60 70 80 90 10Time (ms)


Cur

rent

(A)

100

50

0

minus50

minus100

(d) 120572 = 0∘ 120573 = 0∘

Figure 5 Strategy 1 time plots for different firing angles 120572 and stop angles 120573

according to Figure 2(c) while the largest inrush currentsmay be avoided

4 Experimental Set-Up

41 Hardware Implementation A three-phase two-levelvoltage-source inverter (VSI) has been designed as shown inFigure 3(a) It is made from three dual-package 400GB126Dinsulated-gate bipolar transistor (IGBT) modules with2SC0108T2Ax-17 driver boards mounted on top Thesehave in-built desaturation (desat) protections set to trigger25 120583s after a fault detection of an overcurrent of 250A orabove The de-sat protection circuit is shown in Figure 4(a)The collector-emitter voltage 119881CE across the IGBT iscontinuously detected and if it goes above a set thresholdvalue 119881th during conduction this is recognized as a faultycurrent and the IGBT is turned off 119881CE is a function of thethe collector current 119868

119862as shown in Figure 4(b) The IGBT

will be turned on again after a delay time but after multiplefault detections it will stop to avoid overheating

The inverter is directly connected to a three-phase345V1 kV YY-connected transformer shown in Figure 3(b)The transformer ratings are given in Table 1

Table 1 Transformer rating

Power rating 80 kVAVoltage ratio 138V1 kVPrimary winding resistance 68mΩPrimary leakage reactance 04mHSecondary winding resistance 48mΩSecondary leakage reactance 88mHMagnetizing impedance (50Hz) 0368HMagnetizing resistance (50Hz) 2768Ω

42 Software Implementation A compactRIO NI-9014 mod-ule with integrated RT-controller and FPGA chip has beenused to implement grid control strategies and the proposedtransformer magnetization strategies The FPGA chip is ofmodel Xilinx-5 [14] with an internal clock frequency of40MHz The RT-controller is of the model NI-9022

The VSI is controlled by sinusoidal pulse-width modu-lation (SPWM) where a sinusoidal reference waveform iscompared with sawtooth carrier waveforms to generate theoutput logic to the IGBTs It is possible to control the startangle 120572 and stop angle 120573 as well as the voltage rampingslope

ISRN Electronics 5

0 50 100 150 200 250 300 350

Peak

curr

ent (

A)

Firing angle 120572 (∘)

250200150100

500

minus50

minus100

minus150

minus200

minus250

(a) 120573 = 0∘

0 50 100 150 200 250 300 350Firing angle 120572 (∘)

Peak

curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus250

(b) 120573 = 90∘


0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(c) 120573 = 180∘


0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(d) 120573 = 270∘

Figure 6 Strategy 1 varying the firing angle 120572 for different stop angles 120573

0 10 20 30 40 50 60 70 80 90 100Time (ms)

Curr

ent (

A)

200

150

100

50

0minus50

minus100

minus150

minus200


(a) 120572 = 0∘

Curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus2500 10 20 30 40 50 60 70 80 90 100

Time (ms)


(b) 120572 = 180∘

Figure 7 Strategy 2 time plots

6 ISRN Electronics

Peak

curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus250


0 50 100 150 200 250 300 350Firing angle 120572 (∘)

Figure 8 Strategy 2 varying the firing angle 120572 with zero initial core flux

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

100

50

0

minus50

minus100

(a) 1 cycle

0

20

40

60

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

minus20

minus40

minus60

(b) 3 cycles

0

10

20

30

40

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

minus10

minus20

minus30

minus40

(c) 5 cycles

Figure 9 Strategy 3 varying the number of cycles from zero to full magnetization

ISRN Electronics 7

0 1 2 3 4 5 6 7 8 9 10Number of cycles

Peak

curr

ent (

A)

80

60

40

20

0minus20

minus40

minus60

minus80


(a) 120573 = 0∘

Number of cycles0 1 2 3 4 5 6 7 8 9 10

Peak

curr

ent (

A)

80

60

40

200

minus20

minus40

minus60

minus80


(b) 120573 = 180∘

Figure 10 Strategy 3 varying the number of cycles to full magnetization The start angle 120572 is always set to 0∘ but it will have little impact onthe current peaks for the voltage ramping strategy

5 Results and Discussion

The transformer was magnetized to its rated voltage of 1 kVusing the three different strategies proposed above whilemeasuring the peak magnetizing inrush currents In strategy1 the transformerwas stopped at different angles120573 to evaluatethe variations in the remanent flux In strategy 2 this becomesredundant as 120601

119903always converges to zero before start-up In

strategy 3 120573 = 0∘ and 120573 = 180∘ are used to evaluate 120601maxminusand 120601max+

51 Strategy 1 Results In Figure 5 the magnetizing inrushcurrents are plotted for two different 120572 and 120573 in phase AThese samples are shown to illustrate the worst scenarios withmaximum remanent flux in the core As expected the highestinrush currents are obtained when 120572 is shifted half a periodfrom 120573 and here the peak currents easily reach above 250ATo minimize the peak currents for this strategy 120572 shouldbe in phase with 120573 which here results in peak currents ofabout 100A It is clear from Figures 5(a) and 5(c) how de-satprotection is activated which otherwise could have resultedin much higher currents

In Figure 6 the peak current values are sampled anddisplayed for fixed values of 120573 The variation between phasesis due to not only 120572 and 120573 but also unbalances in thetransformer core where the center leg will have a lowerreluctance path than the outer legsThiswas not compensatedfor in the transformer design

52 Strategy 2 Results In strategy 2 the remanent flux isessentially removed resulting in the special case of strategy 1when 120573 = 0∘ for phase A Also the remanent fluxes for phasesB and C are removed which was not the case in strategy 1In Figure 7 currents are displayed for the two worst casescenarios in phase A 120572 = 0∘ and 120572 = 180∘ The worst inrushcurrents are less than half compared to those in strategy 1

and never sufficiently high to trigger the de-sat protectionIn Figure 8 the peak phase currents are shown while varying120572

53 Strategy 3 Results In Figure 9 the applied voltage startsfrom zero and is linearly ramped to 1 pu In Figure 9(a) theramping time duration is one fundamental cycle (20ms)in Figure 9(b) this is increased to 3 cycles (60ms) and inFigure 9(c) 5 cycles 120573 was set to 0∘ for all cases but it hasnegligible impact for this strategy Already at 1 cycle rampingtime the peak current has reduced by half compared to that instrategy 1 and it continues to drop for longer time durations

Inrush current peak vs number of cycles is displayed inFigure 10 As the ramping time increases the inrush currentsare effectively removed

6 Conclusions

The magnitude of the magnetizing inrush currents for apower transformer with direct VSI connection has beenevaluated where no external circuitry for the grid connec-tion is required Three magnetization strategies have beensuggested and experimentally investigated step responsewith remanent flux step response without remanent fluxand voltage ramping A de-sat protection is used to limitthe highest currents By removing the remanent flux thepeak inrush current is reduced to at least half in the worstcases However with voltage ramping the peak currentsmay be more or less completely removed depending on thetime duration of voltage ramping All strategies are easy toimplement in the FPGA-based control system

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

8 ISRN Electronics

Acknowledgments

This project is supported by Statkraft AS KIC InnoEnergy-CIPOWER Fortum oy the Swedish Energy Agency DrakaCable AB the Gothenburg Energy Research FoundationFalkenberg EnergyAB theWallenius FoundationHelukabelProEnviro Seabased AB the Olle Engkvist Foundationthe J Gust Richert Foundation A ngpanneforeningenrsquosFoundation for Research and Development CF Environ-mental Fund the Goran Gustavsson Research Foundationand Vargons Research Foundation This support is gratefullyacknowledged

References

[1] M Nagpal T G Martinich A Moshref K Morison and PKundur ldquoAssessing and limiting impact of transformer inrushcurrent on power qualityrdquo IEEE Transactions on Power Deliveryvol 21 no 2 pp 890ndash896 2006

[2] L-C Wu C-W Liu S-E Chien and C-S Chen ldquoThe effect ofinrush current on transformer protectionrdquo in Proceedings of the38th Annual North American Power Symposium (NAPS rsquo06) pp449ndash456 Carbondale Ill USA September 2006

[3] F Mekic R Girgis Z Gajic and E Nyenhuis ldquoPower trans-former characteristics and their effect on protective relaysrdquo inProceedings of the 33rd Western Protective Relay ConferenceOctober 2006

[4] J H Brunke and K J Frohlich ldquoElimination of transformerinrush currents by controlled switching I theoretical consid-erationsrdquo IEEE Transactions on Power Delivery vol 16 no 2pp 276ndash280 2001

[5] J H Brunke and K J Frohlich ldquoElimination of transformerinrush currents by controlled switching II application and per-formance considerationsrdquo IEEETransactions on PowerDeliveryvol 16 no 2 pp 281ndash285 2001

[6] Y Cui S G Abdulsalam S Chen and W Xu ldquoA sequentialphase energization technique for transformer inrush currentreduction I simulation and experimental resultsrdquo IEEE Trans-actions on Power Delivery vol 20 no 2 pp 943ndash949 2005

[7] W Xu S G Abdulsalam Y Cui and X Liu ldquoA sequentialphase energization technique for transformer inrush currentreduction II theoretical analysis and design guiderdquo IEEETransactions on PowerDelivery vol 20 no 2 pp 950ndash957 2005

[8] L Cipcigan W Xu and V Dinavahi ldquoA new technique tomitigate inrush current caused by transformer energizationrdquoin Proceedings of the IEEE Power Engineering Society SummerMeeting vol 1 pp 570ndash574 Chicago ILL USA July 2002

[9] M S J Asghar ldquoElimination of inrush current of transformersand distribution linesrdquo in Proceedings of the 1996 InternationalConference on Power Electronics Drives amp Energy Systems forIndustrial Growth (PEDES rsquo96) vol 2 pp 976ndash980 New DelhiIndia January 1996

[10] K Shinohara K Yamamoto K Iimori YMinari O Sakata andM Miyake ldquoCompensation for magnetizing inrush currents intransformers using a PWM inverterrdquo Electrical Engineering inJapan vol 140 no 2 pp 53ndash64 2002

[11] A Rasic G Herold and U Krebs ldquoFast connection recon-nection of the VSC to the power networkrdquo in Proceedings ofthe European Conference on Power Electronics and Applications(EPE rsquo07) Aalborg Denmark September 2007

[12] R Ekstrom S Apelfrojd and M Leijon ldquoTransformer mag-netization losses using a non-filtered voltage-source inverterrdquoAdvances in Power Electronics vol 2013 Article ID 261959 7pages 2013

[13] D Povh and W Schultz ldquoAnalysis of overvoltages caused bytransformer magnetizing inrush currentrdquo IEEE Transactions onPower Apparatus and Systems vol 97 no 4 pp 1355ndash1365 1978

[14] Xilinx Data Book 2006 httpwwwxilinxcom

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2 ISRN Electronics

Im

V1 120601

120601

120601min

120596t

120601max

Figure 1 The induced core flux 120601(119905) lags the induced voltage V1(119905) by almost 90∘ The resultant magnetizing current 119868

119898grows rapidly when

the transformer goes into saturation

Im

120601

(a) Strategy 1

Im

120601

(b) Strategy 2

Im

120601

(c) Strategy 3

Figure 2 Three different typical paths in the B-H plane 120601119903is assumed to be maximum for all cases In strategy 1 the core is directly pushed

into saturation and it can take a long time before it stabilizes In strategy 2120601119903is pulled down to zero for all phases which reduces themagnitude

of the inrush current In strategy 3 the voltage ramping will slowly converge to the stable B-H-path while avoiding large inrush currents

2 Theory

When a variable voltage source V1(119905) is applied to the trans-

former windings a resulting flux 120601(119905) will be induced in thetransformer core according to Faradayrsquos law as follows

V1(119905) = radic2

1003816100381610038161003816V1

1003816100381610038161003816cos (120596119905 + 120572) = 119873

119889120601 (119905)

119889119905

(1)

where 120596 is the natural frequency of the applied voltage 120572is the start angle and 119873 the number of winding turnsThe induced flux may be derived by computing the voltageintegral over time as follows

120601 (119905) = int

1199052

1199051

V1(119905)

1198731

119889119905 =

radic21003816100381610038161003816V1

1003816100381610038161003816

1205961198731

sin (120596119905) + 120601119903 (2)

where 120601119903is the remanent flux Figure 1 shows how this is used

to derive the classical 120601-119868119898-curve or 119861-119867-curve It is clear

how even a small saturation in themagnetic fluxmay result ina large magnitude of the magnetizing current 119868

119898 As a worst

case scenario the peak amplitude of 119868119898may be approximated

by [1]

119868119898=

1

119883 + 119883119901+ 119883119888(min)

[pu] (3)

where 119883 is the source impedance 119883119901

is the windingimpedance and 119883

119888(min) is the minimum magnetization

impedance When the core is completely saturated it may betreated as an air core and it has been shown that 119883

119888may be

approximated by the short-circuit impedance119883SC [13]More accurately the magnetizing inrush current is calcu-

lated by

119868119898=

radic21003816100381610038161003816V1

1003816100381610038161003816

radic(120596119871)2

+ 1198772

sdot (

2119861119873+ 119861119877minus 119861119878

119861119873

) (4)

where 119861119873is the normal rated flux density 119861

119903is the remanent

flux density and 119861119878is the saturation flux density For more

detailed analysis a finite-element method (FEM) model hasto be set up for the transformer

3 Magnetizing Strategies

With the VSI directly connected to the power transformerthree different magnetization strategies have been evaluatedfor start-up of the transformer

(1) step response with remanent flux(2) step response without remanent flux(3) voltage ramping with remanent flux

The general plots of the B-H-curves for the differentstrategies are illustrated in Figure 2 but they should only be

ISRN Electronics 3



C

E

G

Ove

rcur

rent

desa

t pro

tect

ion

VCE

(a)

400

300

200

100

0

A

30 1 2 V

VCE

IC

tp = 80120583s

TJ = 25∘C

VGE = 15V


TJ = 125∘C

(b)














V1(119905) = V

119873

119905 minus 1199050

119879119877

cos (120596 (119905 minus 1199050) + 120572) 119905

0le 119905 le 119879

119877 (5)






4 ISRN Electronics

0 10 20 30 40 50 60 70 80 90 100

Overcurrent limit

Time (ms)

Cur

rent

(A)

300

200

100

0

minus100

minus200

minus300

(a) 120572 = 180∘ 120573 = 0∘

0 10 20 30 40 50 60 70 80 90 100Time (ms)

Cur

rent

(A)

100

50

0

minus50

minus100

(b) 120572 = 180∘ 120573 = 180∘

0 10 20 30 40 50 60 70 80 90 100Time (ms)


0 10 20 30 40 50 60 70 80 90 10Time (ms)


Overcurrent limit

Cur

rent

(A)

300

200

100

0

minus100

minus200

minus300

(c) 120572 = 0∘ 120573 = 180∘

0 10 20 30 40 50 60 70 80 90 100Time (ms)


0 10 20 30 40 50 60 70 80 90 10Time (ms)


Cur

rent

(A)

100

50

0

minus50

minus100

(d) 120572 = 0∘ 120573 = 0∘












ISRN Electronics 5

0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(a) 120573 = 0∘

0 50 100 150 200 250 300 350Firing angle 120572 (∘)

Peak

curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus250

(b) 120573 = 90∘


0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(c) 120573 = 180∘


0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(d) 120573 = 270∘


0 10 20 30 40 50 60 70 80 90 100Time (ms)

Curr

ent (

A)

200

150

100

50

0minus50

minus100

minus150

minus200


(a) 120572 = 0∘

Curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus2500 10 20 30 40 50 60 70 80 90 100

Time (ms)


(b) 120572 = 180∘


6 ISRN Electronics

Peak

curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus250


0 50 100 150 200 250 300 350Firing angle 120572 (∘)


0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

100

50

0

minus50

minus100

(a) 1 cycle

0

20

40

60

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

minus20

minus40

minus60

(b) 3 cycles

0

10

20

30

40

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

minus10

minus20

minus30

minus40

(c) 5 cycles


ISRN Electronics 7

0 1 2 3 4 5 6 7 8 9 10Number of cycles

Peak

curr

ent (

A)

80

60

40

20

0minus20

minus40

minus60

minus80


(a) 120573 = 0∘

Number of cycles0 1 2 3 4 5 6 7 8 9 10

Peak

curr

ent (

A)

80

60

40

200

minus20

minus40

minus60

minus80


(b) 120573 = 180∘












6 Conclusions




8 ISRN Electronics

Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Electronics 3



C

E

G

Ove

rcur

rent

desa

t pro

tect

ion

VCE

(a)

400

300

200

100

0

A

30 1 2 V

VCE

IC

tp = 80120583s

TJ = 25∘C

VGE = 15V


TJ = 125∘C

(b)














V1(119905) = V

119873

119905 minus 1199050

119879119877

cos (120596 (119905 minus 1199050) + 120572) 119905

0le 119905 le 119879

119877 (5)






4 ISRN Electronics

0 10 20 30 40 50 60 70 80 90 100

Overcurrent limit

Time (ms)

Cur

rent

(A)

300

200

100

0

minus100

minus200

minus300

(a) 120572 = 180∘ 120573 = 0∘

0 10 20 30 40 50 60 70 80 90 100Time (ms)

Cur

rent

(A)

100

50

0

minus50

minus100

(b) 120572 = 180∘ 120573 = 180∘

0 10 20 30 40 50 60 70 80 90 100Time (ms)


0 10 20 30 40 50 60 70 80 90 10Time (ms)


Overcurrent limit

Cur

rent

(A)

300

200

100

0

minus100

minus200

minus300

(c) 120572 = 0∘ 120573 = 180∘

0 10 20 30 40 50 60 70 80 90 100Time (ms)


0 10 20 30 40 50 60 70 80 90 10Time (ms)


Cur

rent

(A)

100

50

0

minus50

minus100

(d) 120572 = 0∘ 120573 = 0∘












ISRN Electronics 5

0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(a) 120573 = 0∘

0 50 100 150 200 250 300 350Firing angle 120572 (∘)

Peak

curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus250

(b) 120573 = 90∘


0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(c) 120573 = 180∘


0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(d) 120573 = 270∘


0 10 20 30 40 50 60 70 80 90 100Time (ms)

Curr

ent (

A)

200

150

100

50

0minus50

minus100

minus150

minus200


(a) 120572 = 0∘

Curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus2500 10 20 30 40 50 60 70 80 90 100

Time (ms)


(b) 120572 = 180∘


6 ISRN Electronics

Peak

curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus250


0 50 100 150 200 250 300 350Firing angle 120572 (∘)


0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

100

50

0

minus50

minus100

(a) 1 cycle

0

20

40

60

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

minus20

minus40

minus60

(b) 3 cycles

0

10

20

30

40

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

minus10

minus20

minus30

minus40

(c) 5 cycles


ISRN Electronics 7

0 1 2 3 4 5 6 7 8 9 10Number of cycles

Peak

curr

ent (

A)

80

60

40

20

0minus20

minus40

minus60

minus80


(a) 120573 = 0∘

Number of cycles0 1 2 3 4 5 6 7 8 9 10

Peak

curr

ent (

A)

80

60

40

200

minus20

minus40

minus60

minus80


(b) 120573 = 180∘












6 Conclusions




8 ISRN Electronics

Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









4 ISRN Electronics

0 10 20 30 40 50 60 70 80 90 100

Overcurrent limit

Time (ms)

Cur

rent

(A)

300

200

100

0

minus100

minus200

minus300

(a) 120572 = 180∘ 120573 = 0∘

0 10 20 30 40 50 60 70 80 90 100Time (ms)

Cur

rent

(A)

100

50

0

minus50

minus100

(b) 120572 = 180∘ 120573 = 180∘

0 10 20 30 40 50 60 70 80 90 100Time (ms)


0 10 20 30 40 50 60 70 80 90 10Time (ms)


Overcurrent limit

Cur

rent

(A)

300

200

100

0

minus100

minus200

minus300

(c) 120572 = 0∘ 120573 = 180∘

0 10 20 30 40 50 60 70 80 90 100Time (ms)


0 10 20 30 40 50 60 70 80 90 10Time (ms)


Cur

rent

(A)

100

50

0

minus50

minus100

(d) 120572 = 0∘ 120573 = 0∘












ISRN Electronics 5

0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(a) 120573 = 0∘

0 50 100 150 200 250 300 350Firing angle 120572 (∘)

Peak

curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus250

(b) 120573 = 90∘


0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(c) 120573 = 180∘


0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(d) 120573 = 270∘


0 10 20 30 40 50 60 70 80 90 100Time (ms)

Curr

ent (

A)

200

150

100

50

0minus50

minus100

minus150

minus200


(a) 120572 = 0∘

Curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus2500 10 20 30 40 50 60 70 80 90 100

Time (ms)


(b) 120572 = 180∘


6 ISRN Electronics

Peak

curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus250


0 50 100 150 200 250 300 350Firing angle 120572 (∘)


0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

100

50

0

minus50

minus100

(a) 1 cycle

0

20

40

60

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

minus20

minus40

minus60

(b) 3 cycles

0

10

20

30

40

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

minus10

minus20

minus30

minus40

(c) 5 cycles


ISRN Electronics 7

0 1 2 3 4 5 6 7 8 9 10Number of cycles

Peak

curr

ent (

A)

80

60

40

20

0minus20

minus40

minus60

minus80


(a) 120573 = 0∘

Number of cycles0 1 2 3 4 5 6 7 8 9 10

Peak

curr

ent (

A)

80

60

40

200

minus20

minus40

minus60

minus80


(b) 120573 = 180∘












6 Conclusions




8 ISRN Electronics

Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Electronics 5

0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(a) 120573 = 0∘

0 50 100 150 200 250 300 350Firing angle 120572 (∘)

Peak

curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus250

(b) 120573 = 90∘


0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(c) 120573 = 180∘


0 50 100 150 200 250 300 350

Peak

curr

ent (

A)


250200150100

500

minus50

minus100

minus150

minus200

minus250

(d) 120573 = 270∘


0 10 20 30 40 50 60 70 80 90 100Time (ms)

Curr

ent (

A)

200

150

100

50

0minus50

minus100

minus150

minus200


(a) 120572 = 0∘

Curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus2500 10 20 30 40 50 60 70 80 90 100

Time (ms)


(b) 120572 = 180∘


6 ISRN Electronics

Peak

curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus250


0 50 100 150 200 250 300 350Firing angle 120572 (∘)


0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

100

50

0

minus50

minus100

(a) 1 cycle

0

20

40

60

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

minus20

minus40

minus60

(b) 3 cycles

0

10

20

30

40

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

minus10

minus20

minus30

minus40

(c) 5 cycles


ISRN Electronics 7

0 1 2 3 4 5 6 7 8 9 10Number of cycles

Peak

curr

ent (

A)

80

60

40

20

0minus20

minus40

minus60

minus80


(a) 120573 = 0∘

Number of cycles0 1 2 3 4 5 6 7 8 9 10

Peak

curr

ent (

A)

80

60

40

200

minus20

minus40

minus60

minus80


(b) 120573 = 180∘












6 Conclusions




8 ISRN Electronics

Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









6 ISRN Electronics

Peak

curr

ent (

A)

250200150100

500

minus50

minus100

minus150

minus200

minus250


0 50 100 150 200 250 300 350Firing angle 120572 (∘)


0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

100

50

0

minus50

minus100

(a) 1 cycle

0

20

40

60

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

minus20

minus40

minus60

(b) 3 cycles

0

10

20

30

40

0 20 40 60 80 100 120 140 160 180 200Time (ms)


0 20 40 60 80 100 120 140 160 180 20Time (ms)


Cur

rent

(A)

minus10

minus20

minus30

minus40

(c) 5 cycles


ISRN Electronics 7

0 1 2 3 4 5 6 7 8 9 10Number of cycles

Peak

curr

ent (

A)

80

60

40

20

0minus20

minus40

minus60

minus80


(a) 120573 = 0∘

Number of cycles0 1 2 3 4 5 6 7 8 9 10

Peak

curr

ent (

A)

80

60

40

200

minus20

minus40

minus60

minus80


(b) 120573 = 180∘












6 Conclusions




8 ISRN Electronics

Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









ISRN Electronics 7

0 1 2 3 4 5 6 7 8 9 10Number of cycles

Peak

curr

ent (

A)

80

60

40

20

0minus20

minus40

minus60

minus80


(a) 120573 = 0∘

Number of cycles0 1 2 3 4 5 6 7 8 9 10

Peak

curr

ent (

A)

80

60

40

200

minus20

minus40

minus60

minus80


(b) 120573 = 180∘












6 Conclusions




8 ISRN Electronics

Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









8 ISRN Electronics

Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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