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An improved spectral performance of SPWM inverter based on the time-sequence of chaos

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An improved spectral performance of SPWM inverter based on the time-sequence of chaos

    An improved spectral performance of

    SPWM inverter based on the

    time-sequence of chaos

    JournalofHarbinInstituteofTechnolo(NewSeries),Vo1.14,No.1,2007 AnimprovedspectralperformanceofSPWMinverter

    basedonthetimesequenceofchaos

    LIGuanlin|

    .

    CHENXiyou2

    ,

    LIUttongchen.YANGWei|

    李冠林,陈希有,刘洪臣,杨伟

    (1.Dept.ofElectricalEngineering,HarbinInstituteofTechnology,Harbin150001,China; 2.Dept.ofElectricalandElectronicsEngineering,DalianUniversityofTechnology,Dalian116023,China)

    Abstract:AnovelapproachforimprovingthespectralperformanceofsinusoidalPulseWidthModulation(SP.

    WM)inverterispresented.ByvaryingthecarrierDequencyaccordingtochaotictime

    sequence,thediscrete

    spectrumoftheoutputvoltageistransformedintothecontinuousspectrum,whichcouldreducetheacoustic

    noiseconcentratedatspecifictonesinaninverter

    drivenelectricmachine.Fourieranalysisshowsthatthehar.

    monicatthefixedfrequencyhasbeenrestrained

    range.Besides,anovelvariableisintroducedfor

    effectivelyandthedistributionofthespectrumisinawider

theevaluationoftheoutputvoltagespectruminSPWMinvert

    er.SimulationsandexperimentswithDSPconfirmtheadvantagesofthenovelapproach.Exp

    erimentalresults

    showtheannoyingacousticnoisehasbeentranslatedintosomeenjoyablesoundlikeafallorw

    aterflowingwhen

    thisnovelmethodisapplied.

    Keywords:inverter;SPWM;harmonic;timesequence;chaos

    CLCnumber:TM464Documentcode:AArticleID:1005-9113(2007)01-0059-05

    ACdriving,UninterruptedPowerSupply(UPS) andactivefilterhavebeenextensivelyusedinmanyen

    gineeringfields.Largenumbersofhighspeedcon

    pletelycontrolledswitcheshavebeenworkedout.Asa result.PWMtechniquehasbecomethekerneltechnol

    ogyoftheinverters.

    Ingenera1.theoutputvoltageofSPWMinverter hasalargeamountofharmonicatthecarrierfrequency andthefrequencieswhichtimeofit.Theseharmonic currentinmotormaycausepulsatingtorque.The torqueintheairgapbetweenstatorandrotormaylead tostator'svibrationsandproducenoises.Whencarrier frequencyislower.thenoiseisacoustic.Itwiildo harmtothehearing.Ontheotherhand.thelowfre

    quencyoftheharmoniccurrentcanalsolcadtotheme

    chanicalvibrationsofmotor.anditreducesthestability ofsystemandthelifetime.

    Thesenoisescanbeeliminatedwhentheswitching frequencyorthecarrierfrequencyisraisedover l5kHz.However.softswitches(suchasZVSor ZCS)PWMorhighspeedswitcheshavetobeusedto

decreasetheswitchinglOSS.Boththecostandthediffi

    cuhiesofthetechnologywillberaisedsignificantly.If theharmonicdistributeoverawidercontinuousspec

    trum,theaveragepowerofthekthharmoniccouldbe reducedeffectively.Asaresult.thoughthetotal strengthofnoisemaynotbechanged,itsintensity wouldhavebeenreducedremarkably.

    Received2o040303

    Chaoticsignalhasbroadspectrum[.Inthelimit

    edtimeperiodsitstrackneveroverlapeachotherand itstravelformisextremelycomplex.Justbecauseofit weapplychaostoSPWMtechnologytochangethedis

    tributionoftheharmonic.Thenovelapproachproposed inthepaperwillbeillustratedbytheexampleofsingle

    phaseinverterwhosecarrierfrequencyisfulltriangle wave.Theprincipleofapplyingchaoticsignaltocon

    trolthespectrumoftheoutputvoltageisexplainedand analyzedtheoretically.Simulationsandexperiments withDSPdemonstratethevaliditiesoftheproposed method.TheresultsshowthatapplyingchaostoSPWM inverterhasfavorableeffectonthecontrolofnoiseand meehania1vibrati0n.

    1ChaoticTime-sequenceandItsApplicationsin SPWM

    1.1ChaoticTime-sequence

    Onedimensionallogisticmapisasimple,yettyp

    ica1.exampleofchaoticsystem.Thetimesequence

    canbeshownas

    +

    :

I(,p):px(1),(=0,1,2,3,).(1)

    When0<p?1.thedynamicalbehaviorofthe discretedynamicalsystemisverysimple.However,

    when3?P44.itbecomesverycomplex.Aninfinite sequenceofbifurcationgeneratedbyperioddoublingis ?

    59?

    JournaofHarbinInstituteofTechnolo toEq.(3)

    (k):L(k)

    

    (N

    e

    

    w

    

    Series),_Vo1.14,No.1,2007

    (3)

    whereL(k)isshowninEq.(2).

    Thus,accordingtoregularsamplingmethod,the

    samplingpointsinthenovelmethodare, fyfj=一?L(0)T,

    1:+L(k1)T,

    l:1,

    N1. 2,3,……

    andineachswitchingperiod,

=(1Msinto):,

    (1+Msinto)=.

    whereto

    istheswitchofftime,tistheswitchon time.BothareshowninFig.5.

    Fig.5Switchmotioninolleswitchingperiod SettheDCbusvoltageoftheinvertertobeE.andthe outputoftheinverter"is:

    r?=E,if+??++,

    J":E,if?z<+,

    lM=E,if++<z?+(),L

    :0,1,2,3,,N1.

    TheFouriertransformoftheoutputvoltageisana

    lyzedasEq.(4),

    )=fj:?N-I(fEe-J~'dF(touedt+)=f":ff…,+

    f()ed+f()d,】:

    l04ttz

    Fig.6SpectrumwhenapplyingconventionalSPWMtech. nique

    f/xl04Hz

    Fig.7SpectrumwhenapplyingthenovelSPWMtechnique DefineHF=,whereUisthemaximumvir

    )

    tualvalueoftheharmonicexceptthefundamentalcon

    ponent,Ufisthevirtualvalueofthefundamentalcon

    ponentoftheoutputvoltage.Accordingto(4),HF= 1.03whenapplyingtheconventionalSPWMtech. nique.However,whenapplyingthenovelSPWMtech

    nique.HF=0.17.Itindicatesthatthemagnitudeof theharmonichasbeenreducedeffectively.

2costo(++)2costo(+)+3simulatioIlS

    COStoCOSto(

    )2sinto(

    L(k)T)].

    +()

    +,]})

    )]j[2sinto(Yk++

    +sintoYksintofYk+

    (4)

    AccordingtoEq.(4),spectrumoftheoutput voltagecanbeworkedout.Calculatethespectrumof theoutputvoltagewhichfundamentalfrequencyisset t0be50Hz,E:220,M=0.8.N=2000.andthe

    fixedcarrierfrequencyfis6kHz.Fig.6showsthe conventionalspectrum.Fig.7showsthespectrumwhen usingthehovelapproach.Comparedwiththeconven

    tionalspectrum.theharmonicdistributionisinawider continuesrangewhenapplyingthenovelmethod. SimulatedbyMATLAB,whenthemodulatingfre

    quencyissettobe50Hz,E=220,M:0.8,N

    2000.andthefixedcarrier~equencyfis6kHz. Fig.8showstheoutputvoltageanditsspectrumofthe conventionaSPWMinverter,Fig.9showstheoutput voltageanditsspectrumwhenthecarrier~equencyva

    tiesaccordingtothechaoticlogistictimesequence.

    Theresultsofthesimulationshowthat,whenthecarri

    er~equencyvariesaccordingtosomechaotictime??se-- quence,theharmoniesclusterednearthefixedfre

    quenciescouldberestrainedeffectively.

Jo1~17~aZofHarbinInstituteofTechnolo(NewSeries),Vo1.14,No.1,2007

    OO.o05O.0lOO.Ol5o.020

    t/s

    (a)Outputvoltageoftheinverter O123456

    f/xl04Hz

    (b)Spectrumoftheoutputvoltage Fig.8SimulatewithconventionalSPWMtechnique

    150

    100

    50

    0

    

    50

    

    100

    

    150

    ?

    2oo

    t/s

    (a)Outputvuhageoftheinverter ?

    62?

    JTxl(PHz

    (b)Spectrumoftheoutputvoltage Fig.9Simulatewiththenovelmethod 4Experiments

    TheconventionalSPWMtechniqueandthenovel

    methodproposedinthepaperhavebeenimplemented

    usingaTMS320F240digitalsignalprocessor(DSP). Thefundamentalfrequencyissettobe50Hz.the modulationindex.M=0.8.theDCbusvoltageis 150V,theaverageswitchingfrequencyis6kHz,and itvariesaccordingtothelogisticchaoticmap,asis showninEq.(1),whereP=4,x0:0.85.Fig.10 showstheswitchingsignalanditsspectrumgivenby DSPwiththeconventionalandthenovelSPWMtech. nique.ItisseenfromFig.10thatthemagnitudeofthe harmonicsclusteredinsomefrequencieshavebeenre. duceddramaticallythoughthefumlamentalcomponent isstillunchanged.

    Theinverterissupplyinganinductionmotor.A microphoneistakenasatransducertomeasurethe loadnoise.Fig.11showsthenoisesignalanditsspec- trum.ItisseenfromFig.11thatthemagnitudeofthe individualharmonicsinsomefrequencyhasbeenre. strainedeffectivelyandtheharmonicdistributionis moreevenlywhenapplyingthenovelapproach.Com- paredwiththeconventionalSPWMtechnique.whenu. singthenovelmethod.thenoiseofthemotorisnoton. 1yreducedtoagreatextent.butalsosoundswelllikea fallorwaterflowing.

    ?

    '!'.:.

    ::::.?

    :一譬'L''.?1…?………一.l..::;{j!:::j

    i:}l氡蠹'?

    #

_'_I_.??--..-I_''__.

    i..:i蔓…..-...蠢誊…....莲耋一-l-r……'-'?''!.T -????a-l_2.?o-:--.O?晴AI1,?.?O

    :.?..sz.?.O?O??:

    (a)ConventionalSPWMtechnique ?

    I'??['''

    :?

    

    ,_-??-^-n;一??V-I-

    ^一一…?j.…一j?:-L】?^?i?.-??血一j... L:__000:l_2.oov:M?.oo^Chl,$48v=' ..I.O0l.SRH,2Vi~.v:o.00000?., (h)Thenovelmethodwhen

    Fig.10Switchingsignal

    applyingchaostoSPWMtechnique anditsspectrumgivenbyDSP ???加????加

    'l

JournafofHarbinInstituteofTechnolo

    tOD

    (NewSeries),Vo1.14,No.1,2007 Stop

    L

    Ch'220.OnIVM10.OrrisACh1 …一6510

    (a)ConventionalSPWMtechnique ,

越血啦矗

    {l{耶霹lllj}lrf

    i;i.'::I

    一…一一I

    Ch'220.OirJVM10.Om$^Ch12.OOV

    I.一一651000ms

    (b)ThenovelmethodwhenapplyingchaosIoSPWMtechnique Fig.11Thenoisesignaloftheinductionmotorandits spectrum

    5Conclusion

    AnovelapproachonSPWMtechniquehasbeen

    proposedandexaminedforDCAC【】()?rerconversionin

    thepaper.IntheconventionalSPWMinverter. the

    outputvoltagehaslargeharmonicatthecarrierfre

    quency.WhencarrierfrequencyiSlower.theharmon

    iCmayleadtoacousticnoiseandmechanicalvibration. Thenovelapproachproposedinthepaperpresentsa waytorestraintheharmonic.Boththeoryandsimula

    tionsconfirmthatwhenusingthenovelapproach. the

    harmonicdistributionoftheoutputvoltageiSevenlyin awiderrangewithlimitedamplitude.Thus.noises andmechanicalvibrationofmotorcouldberestrained effectively.Theexperimentalresultshaveprovedthe advantagesofthemethodeffectively.

    References:

    [1]LiawCM,LinYM,WuCH,ela1.Analysis.design. andimplementationofarandomfrequencyPWMinverter. IEEETransactionsonPowerElectronics,2O0o,l5(5):

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