Yao Wenjun, He Zhenghao, Deng Heming

(1HubeiKeyLaboratoryofIntelligentWirelessCommunications,CollegeofElectronicsandInformationEngineering，South-CentralUniversityforNationalities,Wuhan430074,China;2CollegeofElectricalandElectronicEngineering,HuazhongUniversityofScienceandTechnology,Wuhan430074,China)

直流電壓下兩相體放電路徑預(yù)測

?

PredictionoftheDischargePathsofTwo-PhaseMixturesunderDCVoltage

Yao Wenjun1, He Zhenghao2, Deng Heming2

(1HubeiKeyLaboratoryofIntelligentWirelessCommunications,CollegeofElectronicsandInformationEngineering，South-CentralUniversityforNationalities,Wuhan430074,China;2CollegeofElectricalandElectronicEngineering,HuazhongUniversityofScienceandTechnology,Wuhan430074,China)

AbstractThepredictionoftheDischargePathsofTwo-phaseMixturesunderDCVoltagehasbeeninvestigatedbytheexperiment.Fromtheexperimentalresultstheprobabilityofselectingtheairorthetwo-phasemixturesisgovernedbythelocaldistortedelectricfield,whichishighlycorrelatedwiththemacroparticlesizes.Inordertoexplainthephenomena,anewstochasticmodelhasbeenputup.Onthebasisofthestreamertheoryandprobabilityandstatisticstheory,thepaperusesthestrengthofanelectricfieldfromthePoisson'sequationasthecriterionofthestreamerdevelopment.ThebreakdowntimeofthestreamerdevelopmentmeetsWeibulldistributionandthedistortedfieldvaluedecidesthedirectionforthestreamerdevelopmentintheTPMDspace.ThedevelopmentoftheDCdischargepathcanbeaffectedbythelocalelectricfield.Theobjectivefunction(optimalpath)correspondstotheenergyfunctionoftheHopfieldneuralnetwork.Thecomparisonofthesimulationwiththeexperimentshowsthatthestochasticmodelhasgivenagoodapproximation.

Keywordsprediction;dischargepath;two-phasemixture;electricfielddistortion;imulation

直流電壓下兩相體放電路徑預(yù)測

Thedischargeinlongairgapsisahotissueinthestudyontheoutdoorinsulationofpowersystem.Atthesametimeitisalsoafoundationofthemechanismoflightningdischargeandtheresearchonthelightningprotection.Intheaboveresearchthedispersionandrandomnessofdischargepathsarethetypicalcharacteristicsofthedischargeinlongairgaps.Thelightningstrikeandlightningshieldingfailurearealsocloselyrelatedtotherandomnessofdischargepaths.Sotheinvestigationoftherandomnessofdischargepathsisakeyissue.

Thesparkpathsinthepoint/planeandpoint/two-rodairgapshavebeenpredictedbyMacAlpineetalbasedontheexperimentaldata[1-4].Theyfoundthatthedevelopmentofsparkpathsinairisbysuccessivestepsandinadirectionsuggestedbyanangularprobabilitydistributionwhichisrelatedtothefieldatthetipofthepropagatingleader.Inthe[5]AgorisD.P.usedanewstochasticmodelforthesimulationoflightningandbreakdowninlongairgaps.Thecomparisonofthesimulationwiththeexperimentalresultsshowsthatthestochasticmodelhasgivenagoodapproximationinthecaseoflargedistancesbetweentheactiveelectrodeandtheground.Thefractaltheoryhasalsobeenappliedtothesimulationoftheprocessofinceptionandpropagationinthelightningdischarges.Xudiscoveredthatafractalcoefficientη=2candeliveracrediblemodeloflightningstrikes,andprovedtheconsistencyofthestrikingprobabilityandshieldingeffectbetweensimulationresultsandobservations[6].

Theaboveinvestigationonthepredictionofthedischargepathsisonlyintheair.Howabouttheinvestigationinthetwo-phasemixtureThetwo-phasemixture(TPM)isamixtureofgasandmacroparticlesofhighconcentration[7-9],suchasdust,aerosolandrain,etc. (Toavoidconfusion,thetermmacroparticlesisusedtorepresenttheseparticles.)Itisofsignificantinterestinmanytechnicalapplicationsandnaturalphenomena,suchastheformationofthunderstorms,themacroparticle-contaminatedinsulatedsystem,flashoverinrainyweatherandsandstorm,dustplasmaandlightingshieldingfailureinrain,mistorsandstorm.Thesephenomenaarerelativetotwo-phasemixturedischarges(TPMDs).Grigor,evA.I.reportedthatthecoacervationofm-sizedraindropsisincreasingundertheperiodicvariationofenvironmentalelectricalfieldunderlightningdischarge,andthecoacervationiscloselyrelevanttothechargeabilityofraindrops[10].Somestudieshavereportedthatasignificantincreaseintheflashovervoltageisproducedbysupplyingthetetrachloroethylenemistintothegas[11].Liquiddropletsarelikelytostronglymodifytheclassicaldevelopmentoffilamentarydischargeinanon-uniformfieldgeometry[12].

ThepredictionofthedischargepathsofTPMsisoneofthemostimportantscientificquestions.Yetfewpeoplehaveinvestigatedtheproblem.InthispapertheselectionofthedischargepathinTPMsisemployedasthestudyobject.ThepercentagesofthedischargesinTPMSorairaremadecomparativeanalysesfromtheexperimentandsimulation,whichrevealthatthesizesofTPMmacroparticlesdecidethepredictionofthedischargepathsofTPMs.

1Experimental

1.1Experimentalarrangement

Fig.1　Schematic of the experimental setup圖1　實(shí)驗(yàn)裝置圖

ThesketchoftheexperimentalequipmentisshowninFig.1.Theexperimentalarrangementandmethodsisthesameasthepaper[9].TPMsandairaresimultaneouslyjettedintoeachhalfofthedischargechamberataboutthesameflowvelocity,whichcanpreventtheparticlesfromdeposingontheelectrodes.Theexperimentalprocedureisasfollows:

1)Adjustthelocationoftherodandlocalizingelectrode:AddthevoltagetothecriticalbreakdownandputdownthelargernumericalvaluesasU1.Theadjustedtimesisabove50times.Whenthepercentagesoftheselectionoftwolocalizingelectrodesareequal(50±5%),theadjustmentoftheelectrodesiscompleted.

2)JetairandTPMscontinuouslyatthesameflowvelocity:Jettheairintotheleftdischargechamber.AtthesametimejettheTPMsintotherightdischargechamberandaddthevoltagetothecriticalbreakdownandputdownthelargernumericalvaluesasU2.Writedownthebreakdowntimesfromtherodtotheleftortherightlocalizingelectrodeandgettheirdischargetimes.

3)Exchangejetorientation:ExchangethejetorientationofairandTPM.Thenrepeat2).

4)Reducetheinfluenceofthetwolocalizingelectrodes:ExchangejetorientationofairandTPMafterwerepeattheexperiment10times,repeat2)and3).Intheexperimentaltherepeatedfrequencyshouldsurpass100times.

5)TheeffectsofmacroparticlesizesonTPMDs:Whenwecomparethepercentageofthedischargeselectionfromtherodtotheleftlocalizingelectrodewiththerightone,theeffectsofmacroparticlesizesonTPMDarepresent.

1.2Propertiesoftheexperimentalmaterials

3kindsofsolidmaterialsandatobaccoareusedtoproduceparticlesinairasgas-solidTPMs.Waterisusedtoproducedropletssuspendedinairasgas-liquidTPMs,whichformatwatermistwiththreedropletsizes.Total7kindsofdifferentdielectricmaterialshavebeenusedtodemonstratetheeffectsofmacroparticlesizesonTPMDsinthispaper.TheirmaterialpropertiesfortheexperimentareshowninTab. 1.IntheTab. 1εristherelativedielectricconstant.

Tab.1　PropertiesofExperimentalMaterials

2Results

2.1Photographofthepredictiononthe

dischargepath

Fig.2　 Photograph of the discharge path of the macroparticleswith different diameters圖2　不同粒徑顆粒的放電路徑圖片

Theexperimentalmaterialsare7kindsofdielectricmacroparticleswithdifferentaveragediameters.ThedischargepathinTPMsisshowninFig. 2.Thegapsbetweentherodandtheplaneelectrodeappliedinourworkare40cm, 44cmand48cm,respectively.Theresultsofthreegapsindicatetheeffectsarequitesimilar.Fig. 2istaken40cmandabout200kVasanexample.Whend<0.01mm,U-mist(d =0.0066mm),underpositiveornegativeDCvoltage,thepercentageissmallerthan50%andthedischargepathselectstheairbutTPM.ThephotographisshowninFig. 2a;Whend>0.1mm,thequartzsand(d=0.12mm)underpositiveornegativeDCvoltage,thepercentageishigherthan50%andthedischargepathselectstheTPMbutair.ThephotographisshowninFig. 2b;When0.01mm

Fig.3　Effect of the macroparticle diameters on the probabilityof selecting the TPM圖3　兩相體顆粒粒徑大小對放電路徑的影響

2.2Processofthepredictiononthedischargepath

TheN-mist(d=0.040mm)wasusedtotheexperiment.TheprocessofthedischargepathisshowninFig.4.

Fig.4　Process on the selection of the discharge path of the N-mist圖4　噴射水霧的放電路徑選擇過程

TheFig.4a-4frepresentsthesixdifferentimportantstages.TheFig.4ashowsthatthewaterwassprayedtothedischargeroomandwasgeneratedthespaceofTPM.TheFig.4band4cshowsthecoronadischargeunderDCvoltage.Theblue-purplehaloneartherodelectrodegetsstrongerwiththedischarge.TheFig.4dto4fshowsthebreakdowninthegapsbetweentherodandtheplaneelectrode.Thedischargepath

selectstheairandtheshapesofthepathsaremoreandmorecomplex.

2.3Effectofthesprayangleonthepredictionofdischargepath

TheU-mist(d=0.0066mm)andN-mist(d=0.040mm)aretwokindsofmacroparticleswiththedifferentdiameter.TheirsprayangleisdifferentandtheprobabilityofselectingtheTPMisalsodifferent.Fig. 5showstheeffectofthesprayangleonthepredictionofdischargepath.UnderthesameDCvoltagepolaritytheTPMsareinjectedtothedischargechamberatthesameangle.TheeffectoftheU-mistonthedischargepathismoreremarkablethantheN-mist.Astheangleisfromthefronttothebackunderthepositivevoltage,thepercentageofthedischargepathinselectingtheU-mistisabout40%higherthanthatoftheN-mist.Simultaneouslythepercentagehaschangedverylittleasthevoltagerisesandunderthenegativevoltagethepercentagedecreasesasthevoltagerises.Intheexperimentthemistisrepelledbytherodelectrodeandrepulsedtotheplaneelectrode.Theappearanceismoreobviousasthevoltagerises.

Fig.5　Effect of the spray angle on the prediction of discharge path圖5　噴射角度對放電路徑的影響

2.4Effectofthemacroparticlediameteronthepredictionofdischargepath

TheFig. 6showsthephotographofthedischargepathonthequartzsandswiththedifferentdiameters.Thediameteroffinesandis0.15mmandthediameterofcoarsesandis0.80mm.Inthefigurethepositivevoltageis120kVandthenegativevoltageis240kVforthepureairanddusttwo-phasemixture.Fromthepicturetheobviousdischargepathscanbeseenandthebreakdownvoltageisdifferentunderthepositiveandnegativevoltage.Underthepositivevoltagethebreakdownislowerandthewidthsofthedischargepathsarefiner.Underthenegativevoltagethebreakdownvoltageishigherandthewidthsandbrightnessofthedischargepathsarebigger.Atthesamethewidthofdusttwo-phasemixtureisslightlywiderthanthatofpureair.Thewidthofcoarsesandtwo-phasemixtureisslightlywiderthanthatoffinesand.Thereasonisthatthedustmacroparticlesdistorteelectricalfieldandthedistributionofelectricfieldismorenon-uniform.Theionizationbetweenthecoarsesandmacroparticlesisstrongerthanthatofthefinesandmacroparticles.

(Left: positive voltage, Right: negative voltage )Fig.6　Photograph of the discharge path on different quartz sands under the different voltage polarity圖6　不同石英砂在不同電壓極性下的放電路徑圖片

3Discussion

Becausetherearemanynon-uniformdielectricinthedischargespace,TPMDsmusthavesomenewmechanismbesidesthatofgasdischarge.Themechanismincludes: 1)theinteractionsbetweenthemacroparticlesandtheelectricalfield,theelectronsandionsorthephotoionization; 2)thesurfacetrapsofthemacroparticlescapturetheelectronsandions; 3)thesemacroparticlesinTPMsdistorttheelectrostaticfield,interactwithions,electronsorphotonsandarechargedbydiffusion.Sothepredictionofthedischargepathsoftwo-phasemixtureisprimarilydeterminedbythedistortedelectricalfield.Thenewstochasticmodelisbasedontheselectionofpositivedischargepath.ThedevelopmentoftheDCdischargepathcanbeaffectedbythelocalelectricfield.

3.1Calculationofdistortedelectricalfield

Tocomputetheelectricalfieldinthedischargespacethetwo-phasemacroparticlesareprocessedwithidealmethods.Supposethat(1)Themacroparticlesaresphereswiththesamephysicalproperties; (2)Theyareevenlydistributedandhavesamesizesinthedischargespace; (3)Thespacingbetweenthespheresisverylargeandhasnocharge.Thecalculationmethodsisthesameasthepaper[5].Thedischargeroomistakingplaceinatwo-dimensionalsquareareawithameshoflatticepointsupto200×200points.Eightpermissibledirection(includingdiagonals)ofstreamerpropagationareallowed.Thedistancebetweentwopointsofthelatticeisequaltoh,or1.41hfordiagonals.Therod-planeconfigurationisusedforthesimulation.Theupperelectrodeisarodwhosetopishemisphericandatpotentialφ=V0,whereV0istheappliedvoltage.Thelowerelectrodeisaplanewhosepotentialisatgroundpotentialφ=0.Thetwolocalizingelectrodesareplacedontheplane,whichisatpotentialφ=0too.Theselectionofthedischargepathcanbeobservedbythelocalizingelectrode.Therearevariouschargeinthestreamerchannel.Theirpotentialdistributionmeetsthepoissonequation.

(1)

Whereρisthechargeddensityinthestreamerchannel,Thechannelincludestheelectron,positiveandnegativeionsandpolarizationandchargedmacroparticles.Ifthereisnochargeinthestreamerchannel,thepotentialdistributionmeetstheLaplaceequation.

2φ=0.

(2)

TheelectricfieldcanbecalculatedbysolvingtheLaplaceequationwithboundariesontheelectrodesanddischargespace.InthecalculationthecurrentcontinuityequationandOhm'slawneedtobeused.

(3)

WhereJisthecurrentdensityandσistheelectricalconductivityofthestreamerchannel.Whenthestreamerspropagatefromtheanodetowardsthecathode,thekstepcanbediscretizedintothefollowingformula.

ρk+1=ρk+ts(σφk+1).

(4)

Wheretsisthetimestep.Theformula(4)isplugintotheformula(1)togetthefollowingformula.

(5)

Thepotentialdistributionatthek+1stepcanbesolvedbythesuccessiveover-relaxationiterationmethod.Sotheelectricalfieldinthedischargespacecanbederivedfromtheformula(6).TheheavylineinFigure7showsthepossiblepathinthestreamerpropagation.

E=-φ.

(6)

Fig.7　Schematic of possible new bounds of positivestreamer in the stochastic model圖7　正流注在方形網(wǎng)格空間發(fā)展的示意圖

3.2Initiationofthepositivestreamer

Underthepositivevoltageoftherodelectrode,thereisastrongelectricfieldareaneartherodelectrode,wherethecollisioncoefficientαisgreaterthantheattachmentη,αandηarethefunctionoftheelectricfieldintensityE.Bytheactionoftheelectricfieldthefreeelectronsintheareaaremovedalongthedirectiontotherodelectrodeandformtheinitialelectronavalanche.Whentheheadelectronsintheinitialelectronavalanchegettotherodelectrode,thepositiveionsstayneartheelectrodeandformthespacecharges.Thespacechargesstrengthenthespaceelectricfieldfromtherodtoplaneelectrode.Themarcoparticlesbetweentherodandtheplaneelectrodearepolarizedandcharged.Themacroparticlesurfacecanextractthephotoelectronsandcontributetocollisionionization,whichenhancesthesecondaryelectronavalanche.Atthesametimethemacroparticlecanobstructandcapturetheelectronsandabsorbthephotons,whichweakenthesecondaryelectronavalanche.Thesefactorsaffectthepropagationoftheelectronavalancheandhaveacompetitioneffect.Theeffectwillaffectthetransitionfromtheelectronavalanchetothestreameranddecidethedischargepath.

Thepositiveandnegativeions，thepolarizedandchargedmacroparticleswilldistorttheelectricalfieldafteronestreamerisdeveloped.Beforethespacesareeliminated,thenewstreamerisn’tformattedbecausethedensityanddistributionofnewoneareusuallyassociatedwiththeintensityoftheformerone.Theeliminatingtimeisdifferent.Therandomandirregularityofthedischargewillbeproduced.

3.3Coronadischargeinthepositivestreamer

initiation

Alargenumberofelectronavalanchesaregeneratedbytheactionofthedistortedelectricalfieldneartherodelectrode.Whenthepositiveionsrecombinewiththenegativeionsorelectrons,therayradiationswillbeproducedandthehalocomesout,whichformscoronadischarges.Ifalargenumberofpositivespacechargesaccumulatearoundtheanode,thediscontinuousstreamercoronawilltransformastableglowdischarge.Thereisanapproximateuniformfieldbetweenthepositivespacechargesandtheanode.Whenthedensityofthepositivespacechargesissmall,thepositiveionswillneutralizetheanode,whichcanclearthewayforanewstreamerappearing.Whenthedensityofthepositivespacechargesisverybigandthelocalfieldishighenough,thebreakdownwilloccurinthespacefromthepositiveionstotheanode.Theionizingradiationwillproducephotoelectron.Thephotoelectronattachesoneselftothemacroparticlesorthemoleculesandatomswhichformpositiveions.Thepositiveionsdrifttotheanodeandcompensatethelossforthepositiveparticlesinthespacecharges.Soasthepositiveionsexist,theglowdischargesexist.

3.4Probabilitymodelonthesuccessivepropagation

ofthepositivestreamer

Twoconditionsshouldbesatisfiedinordertohavethedevelopmentofthesuccessivestreamer.Firstly,theelectricfieldofthestreamerheadshouldbegreaterthanacriticalvalueinordertohaveionizationoftheairormarcoparticles.Secondly,asecondseedelectronshouldexistinthecollisionionizationareainordertostarttheformationofanavalanche.Thecriterionofthestreamergrowthhasbeenbasedmainlyonabovetwoassumptions.Ineverytimestepofthestreamergrowth,thelocalelectricfieldEishouldbecalculatedbetweenthepointsthatbelongtotheconductivestructureandthepointsaroundit.IfthelocalelectricfieldEiisgreaterthanathresholdvalueEth,thetimefortheformationofthenewstreamersegmentiscalculated.Thistimeisnecessaryforthestreamertopropagatefromonepointofthelatticetoanotherinacertaindirectionanditisnamedtheformationtime[5].Theformationtimeisarandomvariablehavinganarbitraryprobabilitydensityfunction,duetotherandomnatureofappearanceofsecondseedelectronsinthefrontofstreamertripsandthestatisticalfluctuationsoftheformationtimeofelectronavalanches.

Thedistortedextentofthelocalelectricfieldisonlycorrelatedwiththemacroparticlesizesandhaslittlerelationshipwiththedielectricconstantandthevolumefraction[9].ThedistortedelectricfieldneatthemacroparticleisshowninFig. 8.Theequationisasfollows:

(7)

Fig.8　The distorted electric field near the macroparticle圖8　 顆粒附近畸變電場

TheprobabilitydistributionoftheformationtimematchestheWeibulldistribution.Theformulaoftheformationtimeisasfollows:

ρ(ts)=γ(E)e-γ(E)t.

(8)

wheretsistheformationtime,whosevalueisdependedonthelocalelectricfieldEi.γ(E)istheprobabilityfunctionofthestreamerpropagation:

(9)

whereτisthetimestepofthecurrentiterationofthecomputerprogram.Itiscalculatedbytheformula

(10)

ThelocalelectricfieldEibetweentheadjacenttwopointscanbecalculatedbythetheformula

(11)

ThethresholdvalueEthcanbecalculatedbythetheformula[9],

(12)

whenthestreamerdevelopstothestepk,thepropagationdirectionfromonepointPtoanotherP′ischosenonthebasisoftheprobabilityfunctionp(ts)andtheformationtimets.

(13)

whereζisarandomnumberofuniformdistributionattheinterval(0, 1).Theshortesttsischosentothetimestep.

3.5Simulationresultsandcomparision

ThestochasticmodeisappliedtotheprobabilitydistributionofthehitpointunderthepositiveDCvoltage.Thelocalizingelectrodeisregardedasthestrikepoint.Theexperimentaltimesis100.Thehittedtimesoftheleftandrightelectrodeisrecordedandalsoincludesthesamehittedtimes.TheprobabilityofselectingtheairortheTPMsiscalculatedbytheformula(14).

P=TTPM/Ttotal.

(14)

Tab.2showsthecomparisonwiththesimulationfromtheexperimentforthequartzsand.TheFig.8showsthecomparisonofthepercentagesoftheselectionofthedischargepathinTPMsfor7kindsofdifferentmacroparticlesizes.Theobjectivefunction(optimalpath)correspondstotheenergyfunctionoftheHopfieldneuralnetwork.Thestatesoftheneuronsofthisnetworkwillcorrespondtothesequenceofnodeswhichisdeterminedbythevaluesofthelocalelectricfield.AccordingtothestabilitytheoryofcontinuousHopfieldneuralnetwork,whentheenergyfunctiontendstotheminimumvalueandthestatesoftheneuronsalsotendtoanequilibriumpoint,thesequenceofnodesistheoptimalpathforthedischargedevelopment.TheoptimalpathhasbeenshowninFig.9.

Fig.9　Comparison of the percentages of the selectionof the discharge path in TPMDs.圖9　兩相體放電路徑選擇百分比的比較

TimesHittheleftHittherightHitthetwosidesExperirment80155Simulation75178

4Conclusion

Inthiswork7kindsofTPMsareinvestigatedbythedischargeexperimentsunderDCvoltage.ThepercentagesofthedischargepathinTPMsarecomparedwiththoseinair.ThestochasticmodeisusedtosimulatethedispersionandrandomnessofthedischargepathsofTPMs.Theconclusionsareasfollows.

1)TheelectricfieldisdistortedandthedistortionalextentisdecidedbythemacroparticlesizeswhentheTPMsareaddedtothedischargespace.

2)TheprobabilityofselectingtheairortheTPMsisgovernedbythelocaldistortedelectricfield.

3)Theresultsfromthestochasticmodehaveagoodapproximationwiththatfromtheexperiment.

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姚文俊1，何正浩2，鄧鶴鳴2

(1 中南民族大學(xué) 電子信息工程學(xué)院，智能無線通信湖北省重點(diǎn)實(shí)驗(yàn)室，武漢 430074；2 華中科技大學(xué) 電氣與電子工程學(xué)院，武漢 430074)

摘要通過實(shí)驗(yàn)研究了兩相體放電路徑的預(yù)測問題，結(jié)果表明：放電路徑中選擇空氣或兩相體由被畸變的電場決定，而電場的畸變受兩相體顆粒粒徑大小的影響。為了解釋實(shí)驗(yàn)現(xiàn)象，利用傳統(tǒng)的流注理論和概論統(tǒng)計(jì)理論，以泊松方程求解的空間場強(qiáng)為流注發(fā)展的判據(jù)，并假設(shè)流注發(fā)展的擊穿時(shí)間滿足Weibull分布，將兩相體空間電場畸變后電場值的變化決定流注的發(fā)展方向，建立了正極性的放電路徑選擇的物理模型。將直流電壓下兩相體放電路徑發(fā)展問題的目標(biāo)函數(shù)(即最短路徑)與連續(xù)性Hopfield神經(jīng)網(wǎng)絡(luò)的能量函數(shù)相對應(yīng)，將經(jīng)過的節(jié)點(diǎn)順序(局部電場值的影響大小)與網(wǎng)絡(luò)的神經(jīng)元狀態(tài)相對應(yīng)，此時(shí)對應(yīng)的節(jié)點(diǎn)發(fā)展順序就是待求的最佳路線。仿真和實(shí)驗(yàn)結(jié)果比較顯示，基于該模型兩相體直流放電路徑選擇概率分布的計(jì)算結(jié)果與實(shí)驗(yàn)所得規(guī)律一致。

關(guān)鍵詞預(yù)測；放電路徑；兩相體；電磁畸變；仿真

收稿日期2015-12-16

作者簡介姚文俊(1970-)，男，副教授，博士，研究方向：兩相體放電，E-mail:yaowj@mail.scuec.edu.cn

基金項(xiàng)目國家自然科學(xué) 項(xiàng)目(50237010)；中南民族大學(xué)中央高?；究蒲袠I(yè)務(wù)費(fèi)專項(xiàng)(CZY11003)

中圖分類號TM85

文獻(xiàn)標(biāo)識碼A

文章編號1672-4321(2016)02-0103-08