110kv变电站电气一次部分设计外文翻译

杭州电子科技大学信息工程学院毕业设计（论文）外文文献翻译110kv变电站电气一次部分设计翻译题目人体暴露在变电站电场的评估系自动控制系专业电气工程与自动化姓名班级学号指导教师

人体暴露在变电站电厂的评估摘要：本文研究人体暴露在变电站产生的极低频率电场的。这个问题有两个方便，即，它需要计算变电站的电场和在人体内的感应电流密度。利用源元法（SEM）解标量积分方程评估变电站产生的极低频率电场。利用分解域的直接边界元方法（BEM-DM）解拉普拉斯连续方程就能知道暴露在这么一个极低频率的电场的感应电流密度。这里呈现了电场和内部电流密度的说明计算结果。介绍一个暴露在变电站电厂中的人体产生一个极低频率的电场，这一研究开始于一个日益增长的公众关注的顾虑，它可能会引起健康问题。由许多的争议关于可能极低频率的电场和人类的白血病或者一种特定的肿瘤（比如神经组织肿瘤）存在一定的联系。忽略在极低频率场下的位移电流，将电场和磁场分开来考虑。就电场而言暴露在感应电流下的人体有一个轴向特性，而暴露在磁场中的内部电流来自于闭环。本文运用了边界元法分析处理了人体暴露在变电站产生的极低频率电场的评估报告。求解标量积分方程通过源整合程序具有模拟电荷法（CSM）即我们熟知的源元法（SEM）评估了电场的空间分布。这个方法已经运用在了变电站环境中的电场的计算和建立金属保护区模型，它可以看成是一个变相的间接源元法。内部电流密度是被ICNIRP基本条例推荐下作为评估极低频率暴露的一个主要因素。许多人体内的感应电流密度引起了极低频率暴露已经被那些运用分析法或者数值法的研究人员报告研究过了。本文采用了有效的边界元域分解法（BEM-DM），计划，比有线差分法有更精确地近似值和比有线元素法更加简便的计算。这个方程式是基于半静止状态的近似值和等式的连续性。连续性方程简化为拉普拉斯方程的变量势，就是通过边界元数值处理，提供结果系统而分散的极高边际化。知道了沿着人体的标量势，人体内的感应电流密度也就确定下来了。理论背景2.1电场评估标量势在任意一点P（X,Z），引起了一个携带着线性电荷密度的导体部件，如图1所示，有下列式给出给出【4】：上式中，pL表示该行的电荷密度。2L代表导线长度，R表示导线上的点于任意点P之间的距离。图1:直导线几何图形如果电势，沿着直线是已知的，这个完整的方程式写成上式a表示半径。经执行了离散化变电站获得一个未知电荷沿着每一部分的系统方程。因此这个积分方程【2】转化成一个相应的矩阵方程【5】：这里的表示边界元电位，表示麦克斯维尔系数，倒置的麦克斯维尔系数矩阵获得未知的电荷。麦克斯维尔系数的细节在【5】中可以发现。在矩阵电场坐标中，在任意点（X,Y,Z）,由第i个边界域元素，图2给出了【5】：这里代表第i部分的电荷，表示第i部分的长度。和：合场的矢量由每一个边界元素组成。图2：由第i部分产生的电场向量坐标2.2内部电流的计算按照真实的人体模型为基础，图3是基于半静态近似值和相关的拉普拉斯变异的连续方程。图3：真实的人体模型半静态的近似值可以被利用是因为人体模型的尺寸大小与影响电场的波长小很多。由于时谐，暴露在极低频率下的连续方程是以拉普拉斯方程形式【13】，【14】：这里和表示相应的介电常数和导电介质常数，表示工作频率。在极低频率的范围内，所有的部件表现为良好的导体，而周围的空气是无损耗的电介质。因此，周围的空气可以用标准的拉普拉斯方程表示：解拉普拉斯方程：在体内，感应电流密度，能够用不同的欧姆定律获得：这里表示电流密度，体积电荷密度。2.3空气-人体界面条件要完全确定所考虑的问题，拉普拉斯方程必须伴随边界条件规定在不连续的物料特性传导和导电介质下。用标量势的形式表达电场，总所周知的条件对于电场的切向分量在两个分界面附近可以表示为【14】：这里表示对应的单位向量，而和分别表示空气中的电势和在人体中的电势。对于感应电流密度的法向量的交界条件表示成标量势，接近身体与空气表面可表示成：这里的表示表面电荷密度，表示相应组织的电导率，表示在人体表面的标量势。最后，对于交界面的电通量密度的法向量以标量势表示，在人体和空气表面可表示为：这里的表示接近人体的空气的电势。2.3有区域分解的边界元法的要点有区域分解的边界元方法手段处理了人体模型【13】，【14】。利用标量函数的格林定律，下面的积分表达式【10】，可以用子域获得这里表示三位基本解拉普拉斯方程，表示衍生的法向量边界，表示以CANCHY形式出现的几何图形。带着元素的离散化方程【15】，结果可以表示成下列表达式：这里i表示原点，表示第j个边界元素的。目前实施的边界元法是基于等参二次插值函数方法，确定了三角元素。电势或者正常导数在任何的第j边界元点可写成的对应值的线性组合，在配置节点n和插值函数fn：这里表示从坐标生成的来自计算正方形区域的三角形单元。结合式子【16】，【17】，下面的等式系统对于每一个子域可以获得：这里的H和G是矩阵定义为：这里的n表示配置节点内的第j个观察元素。从每个单独的系统结合而成的方程。计算样本一个计算的样本是有关110/10kv变电站GIS类型在克罗地亚的斯普利特。改变电站如图4。这个50赫兹的电场被计算在高1米的地方，由于在这个变电站没有真正的对于公众暴露的可能，而一个专业的暴露是严格限制在这段时间内的，计算包括了变电站外面的栅栏。要强调的是，接地设备（电源线），保护套件（GIS总线），或者金属外壳（变压器，开关设备）可以忽略其影响，也就是，金属外壳接地，因为它产生了可以忽略不计的电场。所以，重要的要被变电站所考虑的内在的电场源是架空线路和无保护的导体。计算值的范围在图4中已经标出。尤其是，在区域3，4是评估电场暴露的重要地区，这不在本次计算考虑的范围。这个立体电场分布在有高价值数据获得的区域2。在图5中，由于不缺乏无保护的导体和它们离变电站栅栏距离非常远，所以在电场源始架空线，这个我们从图5中可以清楚地看到。它的最大电场强度时Emax=380/70V/m，值得一提的是，最大值点位于架空线路得正下方。最后的2个数值是有关于真实的人体模型暴露于该区域场。在这个例子中，一个接地的人体被假设成坐落于附近的变电站，数值6显示了一个高2米，0.6米半径的圆柱体区域，真实的感应电动势，基于人体暴露在380V/m电场强度的变电站中。图像6还显示了感应电流密度沿图4：变电站布局躯干和头部。图5：在2号区域电场的分布图6a：整体区域图6b：内部标量势在图5中显示了整个电场，这个案例研究了包括三个方案。第一个方案是人体暴露在380V/m场强的电场中，这是由下列的边界条件获得的：En=0在圆柱体的侧表面，=760V应用于圆柱体的上表面。在第二个方案中，电场的垂直分量为0，但是别的分量为380V/m，这些条件是由=0对应于圆柱体的上表面，而圆柱体的侧表面En=380V/m。在第三个方案中，电场的垂直和别的分量都等于380V/m，边界条件为顶面p=760V/m，侧表面为380V/m。在这三个案例中，圆柱体的地面均保持接地，=0。图7中的结果显示，轴向电流密度在对头部和躯干显示了不同的情况，它显示了高度的顶峰相当于高度的腰部和颈部，别的部件的电流密度在这些案例中可以被忽略不计。图7：沿着头部和躯干的感应电流密度最大的密度电流显示大约是0.4mA/㎡，获得的数值结果分别对对应外部电场和电流密度，远远低于ICNRP的范围。总结在本文中，人体暴露于极低频率下的变电站产生电场的分析运用于解剖的基础和真实的人体模型。这个问题包括2个部分，发电厂的电场计算和内部电流密度。发电厂产生的电场的计算利用源元法表现一个差异的间接源元法。在人体内的感应电流密度是通过区域分解的源元法解拉普拉斯方程获得的。高效的边界源元法比时域差分法更精确，比FEM的计算量更少。

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