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測

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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　實驗裝置圖

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 電子信息工程學院，智能無線通信湖北省重點實驗室，武漢 430074；2 華中科技大學 電氣與電子工程學院，武漢 430074)

摘要通過實驗研究了兩相體放電路徑的預測問題，結果表明：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。為了解釋實驗現象，利用傳統的流注理論和概論統計理論，以泊松方程求解的空間場強為流注發(fā)展的判據，并假設流注發(fā)展的擊穿時間滿足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)展問題的目標函數(即最短路徑)與連續(xù)性Hopfield神經網絡的能量函數相對應，將經過的節(jié)點順序(局部電場值的影響大小)與網絡的神經元狀態(tài)相對應，此時對應的節(jié)點發(fā)展順序就是待求的最佳路線。仿真和實驗結果比較顯示，基于該模型兩相體直流放電路徑選擇概率分布的計算結果與實驗所得規(guī)律一致。

關鍵詞預測；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

基金項目國家自然科學 項目(50237010)；中南民族大學中央高?；究蒲袠I(yè)務費專項(CZY11003)

中圖分類號TM85

文獻標識碼A

文章編號1672-4321(2016)02-0103-08