110kv變電站電氣一次部分設(shè)計(jì)外文翻譯

杭州電子科技大學(xué)信息工程學(xué)院畢業(yè)設(shè)計(jì)（論文）外文文獻(xiàn)翻譯110kv變電站電氣一次部分設(shè)計(jì)翻譯題目人體暴露在變電站電場的評(píng)估系自動(dòng)控制系專業(yè)電氣工程與自動(dòng)化姓名班級(jí)學(xué)號(hào)指導(dǎo)教師

人體暴露在變電站電廠的評(píng)估摘要：本文研究人體暴露在變電站產(chǎn)生的極低頻率電場的。這個(gè)問題有兩個(gè)方便，即，它需要計(jì)算變電站的電場和在人體內(nèi)的感應(yīng)電流密度。利用源元法（SEM）解標(biāo)量積分方程評(píng)估變電站產(chǎn)生的極低頻率電場。利用分解域的直接邊界元方法（BEM-DM）解拉普拉斯連續(xù)方程就能知道暴露在這么一個(gè)極低頻率的電場的感應(yīng)電流密度。這里呈現(xiàn)了電場和內(nèi)部電流密度的說明計(jì)算結(jié)果。介紹一個(gè)暴露在變電站電廠中的人體產(chǎn)生一個(gè)極低頻率的電場，這一研究開始于一個(gè)日益增長的公眾關(guān)注的顧慮，它可能會(huì)引起健康問題。由許多的爭議關(guān)于可能極低頻率的電場和人類的白血病或者一種特定的腫瘤（比如神經(jīng)組織腫瘤）存在一定的聯(lián)系。忽略在極低頻率場下的位移電流，將電場和磁場分開來考慮。就電場而言暴露在感應(yīng)電流下的人體有一個(gè)軸向特性，而暴露在磁場中的內(nèi)部電流來自于閉環(huán)。本文運(yùn)用了邊界元法分析處理了人體暴露在變電站產(chǎn)生的極低頻率電場的評(píng)估報(bào)告。求解標(biāo)量積分方程通過源整合程序具有模擬電荷法（CSM）即我們熟知的源元法（SEM）評(píng)估了電場的空間分布。這個(gè)方法已經(jīng)運(yùn)用在了變電站環(huán)境中的電場的計(jì)算和建立金屬保護(hù)區(qū)模型，它可以看成是一個(gè)變相的間接源元法。內(nèi)部電流密度是被ICNIRP基本條例推薦下作為評(píng)估極低頻率暴露的一個(gè)主要因素。許多人體內(nèi)的感應(yīng)電流密度引起了極低頻率暴露已經(jīng)被那些運(yùn)用分析法或者數(shù)值法的研究人員報(bào)告研究過了。本文采用了有效的邊界元域分解法（BEM-DM），計(jì)劃，比有線差分法有更精確地近似值和比有線元素法更加簡便的計(jì)算。這個(gè)方程式是基于半靜止?fàn)顟B(tài)的近似值和等式的連續(xù)性。連續(xù)性方程簡化為拉普拉斯方程的變量勢，就是通過邊界元數(shù)值處理，提供結(jié)果系統(tǒng)而分散的極高邊際化。知道了沿著人體的標(biāo)量勢，人體內(nèi)的感應(yīng)電流密度也就確定下來了。理論背景2.1電場評(píng)估標(biāo)量勢在任意一點(diǎn)P（X,Z），引起了一個(gè)攜帶著線性電荷密度的導(dǎo)體部件，如圖1所示，有下列式給出給出【4】：上式中，pL表示該行的電荷密度。2L代表導(dǎo)線長度，R表示導(dǎo)線上的點(diǎn)于任意點(diǎn)P之間的距離。圖1:直導(dǎo)線幾何圖形如果電勢，沿著直線是已知的，這個(gè)完整的方程式寫成上式a表示半徑。經(jīng)執(zhí)行了離散化變電站獲得一個(gè)未知電荷沿著每一部分的系統(tǒng)方程。因此這個(gè)積分方程【2】轉(zhuǎn)化成一個(gè)相應(yīng)的矩陣方程【5】：這里的表示邊界元電位，表示麥克斯維爾系數(shù)，倒置的麥克斯維爾系數(shù)矩陣獲得未知的電荷。麥克斯維爾系數(shù)的細(xì)節(jié)在【5】中可以發(fā)現(xiàn)。在矩陣電場坐標(biāo)中，在任意點(diǎn)（X,Y,Z）,由第i個(gè)邊界域元素，圖2給出了【5】：這里代表第i部分的電荷，表示第i部分的長度。和：合場的矢量由每一個(gè)邊界元素組成。圖2：由第i部分產(chǎn)生的電場向量坐標(biāo)2.2內(nèi)部電流的計(jì)算按照真實(shí)的人體模型為基礎(chǔ)，圖3是基于半靜態(tài)近似值和相關(guān)的拉普拉斯變異的連續(xù)方程。圖3：真實(shí)的人體模型半靜態(tài)的近似值可以被利用是因?yàn)槿梭w模型的尺寸大小與影響電場的波長小很多。由于時(shí)諧，暴露在極低頻率下的連續(xù)方程是以拉普拉斯方程形式【13】，【14】：這里和表示相應(yīng)的介電常數(shù)和導(dǎo)電介質(zhì)常數(shù)，表示工作頻率。在極低頻率的范圍內(nèi)，所有的部件表現(xiàn)為良好的導(dǎo)體，而周圍的空氣是無損耗的電介質(zhì)。因此，周圍的空氣可以用標(biāo)準(zhǔn)的拉普拉斯方程表示：解拉普拉斯方程：在體內(nèi)，感應(yīng)電流密度，能夠用不同的歐姆定律獲得：這里表示電流密度，體積電荷密度。2.3空氣-人體界面條件要完全確定所考慮的問題，拉普拉斯方程必須伴隨邊界條件規(guī)定在不連續(xù)的物料特性傳導(dǎo)和導(dǎo)電介質(zhì)下。用標(biāo)量勢的形式表達(dá)電場，總所周知的條件對(duì)于電場的切向分量在兩個(gè)分界面附近可以表示為【14】：這里表示對(duì)應(yīng)的單位向量，而和分別表示空氣中的電勢和在人體中的電勢。對(duì)于感應(yīng)電流密度的法向量的交界條件表示成標(biāo)量勢，接近身體與空氣表面可表示成：這里的表示表面電荷密度，表示相應(yīng)組織的電導(dǎo)率，表示在人體表面的標(biāo)量勢。最后，對(duì)于交界面的電通量密度的法向量以標(biāo)量勢表示，在人體和空氣表面可表示為：這里的表示接近人體的空氣的電勢。2.3有區(qū)域分解的邊界元法的要點(diǎn)有區(qū)域分解的邊界元方法手段處理了人體模型【13】，【14】。利用標(biāo)量函數(shù)的格林定律，下面的積分表達(dá)式【10】，可以用子域獲得這里表示三位基本解拉普拉斯方程，表示衍生的法向量邊界，表示以CANCHY形式出現(xiàn)的幾何圖形。帶著元素的離散化方程【15】，結(jié)果可以表示成下列表達(dá)式：這里i表示原點(diǎn)，表示第j個(gè)邊界元素的。目前實(shí)施的邊界元法是基于等參二次插值函數(shù)方法，確定了三角元素。電勢或者正常導(dǎo)數(shù)在任何的第j邊界元點(diǎn)可寫成的對(duì)應(yīng)值的線性組合，在配置節(jié)點(diǎn)n和插值函數(shù)fn：這里表示從坐標(biāo)生成的來自計(jì)算正方形區(qū)域的三角形單元。結(jié)合式子【16】，【17】，下面的等式系統(tǒng)對(duì)于每一個(gè)子域可以獲得：這里的H和G是矩陣定義為：這里的n表示配置節(jié)點(diǎn)內(nèi)的第j個(gè)觀察元素。從每個(gè)單獨(dú)的系統(tǒng)結(jié)合而成的方程。計(jì)算樣本一個(gè)計(jì)算的樣本是有關(guān)110/10kv變電站GIS類型在克羅地亞的斯普利特。改變電站如圖4。這個(gè)50赫茲的電場被計(jì)算在高1米的地方，由于在這個(gè)變電站沒有真正的對(duì)于公眾暴露的可能，而一個(gè)專業(yè)的暴露是嚴(yán)格限制在這段時(shí)間內(nèi)的，計(jì)算包括了變電站外面的柵欄。要強(qiáng)調(diào)的是，接地設(shè)備（電源線），保護(hù)套件（GIS總線），或者金屬外殼（變壓器，開關(guān)設(shè)備）可以忽略其影響，也就是，金屬外殼接地，因?yàn)樗a(chǎn)生了可以忽略不計(jì)的電場。所以，重要的要被變電站所考慮的內(nèi)在的電場源是架空線路和無保護(hù)的導(dǎo)體。計(jì)算值的范圍在圖4中已經(jīng)標(biāo)出。尤其是，在區(qū)域3，4是評(píng)估電場暴露的重要地區(qū)，這不在本次計(jì)算考慮的范圍。這個(gè)立體電場分布在有高價(jià)值數(shù)據(jù)獲得的區(qū)域2。在圖5中，由于不缺乏無保護(hù)的導(dǎo)體和它們離變電站柵欄距離非常遠(yuǎn)，所以在電場源始架空線，這個(gè)我們從圖5中可以清楚地看到。它的最大電場強(qiáng)度時(shí)Emax=380/70V/m，值得一提的是，最大值點(diǎn)位于架空線路得正下方。最后的2個(gè)數(shù)值是有關(guān)于真實(shí)的人體模型暴露于該區(qū)域場。在這個(gè)例子中，一個(gè)接地的人體被假設(shè)成坐落于附近的變電站，數(shù)值6顯示了一個(gè)高2米，0.6米半徑的圓柱體區(qū)域，真實(shí)的感應(yīng)電動(dòng)勢，基于人體暴露在380V/m電場強(qiáng)度的變電站中。圖像6還顯示了感應(yīng)電流密度沿圖4：變電站布局軀干和頭部。圖5：在2號(hào)區(qū)域電場的分布圖6a：整體區(qū)域圖6b：內(nèi)部標(biāo)量勢在圖5中顯示了整個(gè)電場，這個(gè)案例研究了包括三個(gè)方案。第一個(gè)方案是人體暴露在380V/m場強(qiáng)的電場中，這是由下列的邊界條件獲得的：En=0在圓柱體的側(cè)表面，=760V應(yīng)用于圓柱體的上表面。在第二個(gè)方案中，電場的垂直分量為0，但是別的分量為380V/m，這些條件是由=0對(duì)應(yīng)于圓柱體的上表面，而圓柱體的側(cè)表面En=380V/m。在第三個(gè)方案中，電場的垂直和別的分量都等于380V/m，邊界條件為頂面p=760V/m，側(cè)表面為380V/m。在這三個(gè)案例中，圓柱體的地面均保持接地，=0。圖7中的結(jié)果顯示，軸向電流密度在對(duì)頭部和軀干顯示了不同的情況，它顯示了高度的頂峰相當(dāng)于高度的腰部和頸部，別的部件的電流密度在這些案例中可以被忽略不計(jì)。圖7：沿著頭部和軀干的感應(yīng)電流密度最大的密度電流顯示大約是0.4mA/㎡，獲得的數(shù)值結(jié)果分別對(duì)對(duì)應(yīng)外部電場和電流密度，遠(yuǎn)遠(yuǎn)低于ICNRP的范圍?？偨Y(jié)在本文中，人體暴露于極低頻率下的變電站產(chǎn)生電場的分析運(yùn)用于解剖的基礎(chǔ)和真實(shí)的人體模型。這個(gè)問題包括2個(gè)部分，發(fā)電廠的電場計(jì)算和內(nèi)部電流密度。發(fā)電廠產(chǎn)生的電場的計(jì)算利用源元法表現(xiàn)一個(gè)差異的間接源元法。在人體內(nèi)的感應(yīng)電流密度是通過區(qū)域分解的源元法解拉普拉斯方程獲得的。高效的邊界源元法比時(shí)域差分法更精確，比FEM的計(jì)算量更少。

AssessmentofHumanExposuretoPowerSubstationElectricFieldAbstract:Thepaperdealswithhumanexposuretoextremelylowfrequency(ELF)electricfieldsgeneratedbytransformersubstation.Theproblemistwofold,i.e.itrequiresthecalculationofpowersubstationelectricfieldandcurrentdensityinducedinsidethehumanbody.ELFelectricfieldgeneratedfromapowersubstationisassessedbysolvingtheScalarPotentialIntegralEquation(SPIE)usingtheSourceElementMethod(SEM),avariantoftheIndirectBoundaryElementMethod(IBEM).KnowingtheelectricfieldduetothesubstationthecurrentdensityinducedwithinthehumanbeingexposedtosuchfieldisobtainedbysolvingtheLaplaceequationvariantofthecontinuityequationusingthedirectBoundaryElementMethodwithdomaindecomposition(BEM-DM).Someillustrativecomputationalresultsforexternalelectricfieldandinternalcurrentdensityarepresented.INTRODUCTIONTheexposureofhumanstoextremelylowfrequency(ELF)fieldsgeneratedbytransformersubstationsinitiatedanincreasingpublicconcernregardingpossiblehealtheffects.Alotofcontroversyhasbeencausedduetothepossiblelinkbetweenthelowfrequencyfieldsandleukemia,orcertainformsoftumors(e.g.nervoustissuetumors)[1]-[3]inhumans.Neglectingthedisplacementcurrentsatextremelylowfrequenciestheelectricandmagneticfieldscanbeanalyzedseparately.Inthecaseoftheelectricfieldexposurethecurrentsinducedinthebodyhavetheaxialcharacter,whileinthemagneticfieldexposuretheinternalcurrentsformcloseloops.ThispaperdealswiththeassessmentofhumanexposuretoELFelectricfieldsgeneratedbypowersubstationsusingtheboundaryelementanalysis.ThespatialdistributionoftheelectricfieldisassessedbysolvingtheScalarPotentialIntegralEquation(SPIE)viathesourceintegrationprocedurefeaturingtheChargeSimulationMethod(CSM),alsoentitledastheSourceElementMethod(SEM)[4].Theapproachhasbeenalreadyutilizedfortheelectricfieldcomputationinthepowersubstationenvironment[5]-[7]aswellasforthemodelingofametallicpostprotectionzone[4],anditcanbereferredtoasavariantoftheIndirectBoundaryElementMethod(IBEM).TheinternalcurrentdensityisamainparameterfortheestimationoflowfrequencyexposureeffectsproposedbyICNIRPbasicrestrictions[8].ThecalculationofthecurrentdensityinducedinthehumanbodyduetoELFexposureshasalreadybeenreportedbysomeresearcherswhohaveusedeitheranalytical[1]-[2],ornumericaltechniques[9]-[12].ThispaperfeaturestheefficientBoundaryElementMethodwithdomaindecomposition(BEM-DM)[13],[14]scheme,moresophisticatedapproximationthanFiniteDifferencemethod(FDM)andalsocomputationallylessexpensivethanFiniteElementMethod(FEM).Theformulationisbasedonthequasi-staticapproximationandontheequationofcontinuity.ThecontinuityequationissimplifiedtotheLaplaceequationforthescalarpotentialwhichisnumericallyhandledviaBEM-DM[13],[14]providingtheresultingsystemofequationstobesparseandhighlybounded.Knowingthescalarpotentialalongthebody,theinducedcurrentdensityinsidethebodyisdetermined.THEORETICALBACKGROUNDElectricFieldAssessmentScalarpotentialatanarbitrarypointP(x,z)duetoaconductorsegmentcarryinglinearchargedensity,asshowninFigure1,isgivenby[4]:where:p,denotesthelinechargedensity,2Lstandsforthewirelength,RisthedistancebetweenapointonthestraightwireandanarbitrarypointP.Ifthepotentiale~alongthestraightwireisknown,theintegralequation(1)canbewrittenas:whereadenotesthewireradius.Havingperformedadiscretizationofthesubstationconductorsasystemofequationsforunknownchargesalongtheeachsegmentisobtained.Therefore,theintegralequation(2)transformsintoacorrespondingmatrixequation[5]:where:standfortheboundaryelementpotentials,denotetheboundaryelementcharges,andPI1,P12,.P,n,areMaxwellcoefficients.TheunknownchargesareobtainedbyinvertingtheMaxwellcoefficientmatrix(3).ThedetailsregardingtheMaxwellcoefficientscanbefoundin[5].Theelectricfieldcomponentsinrectangularcoordinatesatanarbitrarypoint(x,y,z),generatedbyani-thboundaryelement,Figure2,aregivenby[5]:where:qidenotesthechargeofi-thsegment,Listandsforthelengthofi-thsegment,andThetotalfieldcomponentsareassembledfromeachboundaryelement.TheInternalCurrentCalculationTheformulationoftherealisticthehumanbodymodel,Fig3,isbasedonthequasi-staticapproximationandtherelatedLaplaceequationvariantofthecontinuityequation.Thequasi-staticapproximationcanbeusedsincethedimensionsofthebodymodelarerathersmallcomparedtothewavelengthoftheimpressedfield.Forthecaseoftime-harmonicexposuresatextremelylowfrequenciestheequationofcontinuitytakestheformofLaplaceequation[13],[14]:where￡and6isthecorrespondingpermittivityandconductivityofthemedium,respectively,andistheoperatingfrequency.IntheELFrangeallorgansbehaveasgoodconductors,whilethesurroundingairisalosslessdielectricmedium.Thus,thesurroundingairisrepresentedbythestandardLaplaceequation:whilesolvingtheLaplaceequation:inthebodyregion,theinducedcurrentdensitycanbeobtainedfromthedifferentialformofOhm'sLaw:whereisthecurrentdensityandprepresentsthevolumechargedensity.Theair-bodyinterfaceconditionsTocompletelydefinetheconsideredproblemLaplaceequation(10)mustbeaccompaniedwithcertainboundaryconditionsprescribedatdiscontinuitiesinmaterialpropertiesofconductinganddielectricmedium,respectively.Expressingtheelectricfieldintermsofscalarpotentialthewell-knownconditionforthetangentialcomponentoftheelectricfieldinthevicinityofthetwo-mediainterfaceisgivenby[14]:wheredenotestheunitnormaltotheinterface,whilequantitiesandrepresentthepotentialintheair,andinthehumanbody,respectively.Theinterfaceconditionforthenormalcomponentoftheinducedcurrentdensity,expressedbythescalarpotential,nearthebody-airsurfaceisgivenby:wherep,isthesurfacechargedensity,isthecorrespondingtissueconductivity,andisthescalarpotentialatthebodysurface.Finally,theinterfaceconditionforthenormalcomponentoftheelectricfluxdensity,representedintermsofscalarpotential,attheair-bodysurfaceis:wheredenotesthepotentialintheairinthecloseproximityofthebody.OutlineoftheBoundaryElementMethodwithDomainDecompositionThehumanbodymodelishandledbymeansoftheBoundaryElementMethodwiththedomaindecomposition(BEM-DM)[13],[14]outlinedinthissection.UsingGreen'stheoremforscalarfunctions,thefollowingintegralrepresentationoftheequation(10)forasubdomainisobtained:WhereisthethreedimensionalfundamentalsolutionofLaplaceequation,isthederivativeinnormaldirectiontotheboundary,andisthegeometricallydependenttermbywhichtheCauchytypesingularityistakenintoaccount.Discretizationofeqn(15)withelementsresultsinthefollowingexpression:whereistandsforthesourcepointandrepresentsthej-thboundaryelementofThewhilenstandsforthecollocationnodesinsidethej-thobservationelement.TheindividualsystemofequationsarisingfromeachsubdomainistobeassembledpresentimplementationofBEMisbasedontheisoparametricapproachwithquadraticinterpolationfunctionsdefinedfortriangularelements.Thepotential,oritsnormalderivative,atanypointofthej-thboundaryelementcanbewrittenasalinearcombinationoftheircorrespondingvaluesatthecollocationnodesnandtheinterpolationfunctionswhereisthedimensionlesscoordinatespanningfromthecomputationalsquaredomaintothetriangularelement.Combiningequations(16)and(17)thefollowingsystemofequationsforeachsubdomainisobtained:whereHandGarematricesdefinedby:whilenstandsforthecollocationnodesinsidethej-thobservationelement.Theindividualsystemofequationsarisingfromeach.COMPUTATIONALEXAMPLEAcomputationalexampleisrelatedtothe110/10kV/kVtransmissionsubstationofGIS(Gas-InsulatedSubstation)typeinSplit,Croatia.Asimplifiedtwo-dimensionallayoutofthesubstationisshowninFig4.The50Hz-electricfieldiscalculatedatheightz=1maboveground.Asthereisnorealpossibilityofapublicexposurewithinthetransmissionsubstation,whileaprofessionalexposureisstrictlylimitedtoduration,thecalculationsareundertakenoutsidethefenceofthesubstation.Itistobeunderlinedthattheequipmentwithgroundedshields(powercables),sheaths(GISbuses),ormetalliccasings(transformers,switchgears)canbeneglectedduetotheshieldingeffect[15].Namely,themetallicenclosuresareconnectedtoground,thusproducingnegligibleelectricfield.Consequently,thesignificantelectricfieldsources,regardingthesubstationconsidered,areoverheadtransmissionlines,aswellastheunshieldedconductors.Thecalculationdomains,inwhichthehigherfieldvaluesareexpected,areassignedinFigure4(domains1to5).Inparticular,theareasassignedas3and4areimportantforthemagneticfieldexposureassessment,whichisnotwithinthescopeofthiswork.Thespatialelectricfielddistributionoverthedomain2,wherethehighestfieldvalueiscaptured,isshowninFigure5.Duetotheshortnessoftheunshieldedconductors,aswellastheirconsiderabledistancesfromthesubstationfence,themainelectricfieldsourcesaretheoverheadlines.Duetotheshortnessoftheunshieldedconductors,aswellastheirconsiderabledistancesfromthesubstationfence,themainelectricfieldsourcesaretheoverheadlines.ThisisclearlyvisibleinFig5wherethemaximalelectricfieldisEmax=38070V/m.Itisworthmentioningthatthemaximumpointislocatedjustbelowtheoverheadlineroute.Thelasttwofiguresarerelatedtotherealisticmodelofthehumanbodyexposedtothatfield.Inthisexample,agroundedhumanbodyisassumedtobelocatedinthevicinityofatransformersubstation.Figure6ashowstheintegrationdomain,consistingofacylinderof2minheightand0.6mdiameter,whileFigure6bshowsthescalarpotentialinducedintherealistic,anatomicallybasedmodelofthehumanbodyduetotheexposuretothe380V/melectricfieldgeneratedbythesubstation.Figure6showstheinducedcurrentdensityalongthetorsoandthehead.TheelectricfieldshowninFig5representsthetotalfield.Theexamplesstudiedincludethreescenarios:thefirstcaseconsidersthehumanbodyexposedtoaverticalfieldof380V/m.Thishasbeenachievedbyimposingthefollowingboundaryconditions:En=0inthelateralsurfaceofthecylinderandp=760Vappliedtothetopsurfaceofthecylinder.Inthesecondcase,theverticalcomponentoftheelectricfieldisnull,butthenormalcomponentisequalto380V/m.Theseconditionswereachievedbyimposingp=0tothetopsurfaceofthecylinder,andnormalelectricfieldEn=380V/mtothelateralsurfaceofthecylinder.Inthethirdcase,bothcomponents,theverticalandnormalonesareequalto380V/m.Theimposedboundaryconditionswerep=760V/mtothetopsurface,andEn=380V/mtothelateralsurface.Inthethreeexamplesthebottomsurfaceofthecylinderhasbeenkeptgrounded,=0.TheresultsareshowninFigure7,inwhichtheaxialcurrentdensityforthedifferentsituationsisshownalongthetorsoandhead.Itshowspeaksattheheightcorrespondingtothewaistandneck.Thenormalcomponentofthecurrentdensityisnegligableinthesecases.Currentdensitymaximumappearstobearound0.4mA/m.Theobtainednumericalresultsfortheexternalelectricfieldandcurrentdensity,respectively,stayfarbelowtheICNIRPlimitsEli,,=5kVImandJj,,l=2mAIm2,bothforgeneralpopulation.CONCLUSIONHumanexposuretoELFelectricfieldsgeneratedfrompowersubstationsisanalyzedinthispaperusingtheanatomicallybased,realisticmodelofhumanbeing.Theproblemistwofoldandinvolvesthecalculationofpowerstationelectricfieldandinternalcurrentdensity,respectively.TheelectricfieldgeneratedbythepowersubstationiscalculatedbytheSourceElementMethod(SEM)representingavariantofIndirectBoundaryElementMethod(IBEM).ThecurrentdensityinducedinsidethehumanbodyisobtainedbysolvingthecorrespondingLaplaceequationviatheBoundaryElementMethodwithDomainDecomposition.ThisefficientBEMprocedureisconsideredtobemoreaccuratethanFDTDandcomputationallylessexpensivethanFEM,asonlythedomainboundaryhastobediscretised.REFERENCES[1]King,R.W.P.,Sandler,S.S.,ElectricFieldsandCurrentsInducedinOrgansoftheHumanbodyWhenExposedtoELFandVLFElectromagneticFields,RadioSci.,Vol.31,pp.1153-1167,Sept.-Oct.1996.[2]King,R.W.P.,FieldsandCurrentsintheOrgansoftheHumanBodyWhenExposedtoPowerLinesandVLFTransmitters,IEEETrans.BiomedicalEng.,Vol.45,No4,pp.520-530,April1998.[3]D.Poljak:HumanExposuretoElectromagneticFieds,WITPres,Southampton-Boston,2003.[4]D.Poljak,C.A.Brebbia:BoundaryElementsforElectricalEngineers,WITPress,Southampton-Boston,2005.[5]J.E.T.Villas,F.C.Maia,D.Mukhedkar,V.S.DaCosta:ComputationofElectricFieldsUsingGroundGridPerformanceEquations,IEEETrans.onPowerDelivery,2(3),pp.709-716,July1987.[6]S.H.Myung,B.Y.Lee,J.K.Park:ThreeDimensionalElectricFieldAnalysisofSubstationUsi