Transmission Line Parameters - unioviedo.es

1 13 TransmissionLineParametersManuel Reta-Herna ndezUniversidad Auto .. Capacity(Ampacity).. Inductive of a Solid,Round, Dueto InternalMagnetic of a Two-Wire of a of TransposedThree-PhaseTransmission and of a a Single-PhaseLinewith Two of of Dueto Earth s is one of the majorcomponents of an majorfunctionis to transport electricenergy, with minimallosses,fromthe power sources to the loadcenters,usuallyseparatedby longdistances. The designof a transmissionline dependson fourelectricalparameters:1. Seriesresistance2. Seriesinductance3. Shuntcapacitance4. ShuntconductanceThe seriesresistancerelies basicallyon the physicalcompositionof the conductorat a seriesinductance and shuntcapacitance are producedby the presenceof magneticand electricfieldsaround the conductors,and dependon shuntconductanceis due toleakagecurrentsflowing acrossinsulatorsand air.

2 As leakagecurrentis considerablysmallcompared tonominalcurrent,it is usuallyneglected,and therefore, shuntconductanceis normallynot consideredforthe transmissionline evaluated,the line parametersare usedto modelthe transmissionline and to the Parameters (equivalentcircuitmodel)repres entingthe linedependsuponthe lengthof the line . 2006by Taylor& FrancisGroup, transmissionline is definedas a short-lengthline if its lengthis less than80 km (50 miles).In thiscase,the shutcapacitance effectis negligibleandonlythe resistance andinductive conditions,the line can be representedby the equivalentcircuit of asingle phasewith resistanceR, and inductivereactanceXLin series(seriesimpedance), as showninFig.

3 The transmissionline has a lengthbetween80 km (50 miles)and 240 km (150miles),the lineis considereda medium-lengthlineandits single-phaseequivalentcircuitcan be representedin anominalpcircuit configuration[1]. The shuntcapacitance of the line is dividedintotwo equalparts,eachplaced at the sendingand receivingendsof the the equivalentcircuit for andmedium-lengthtransmissionlinesuse , if the line is largerthan240 km, the modelmustconsiderparametersuniformlydist ributedalongthe seriesimpedanceandshuntcapacitance are foundby solving thecorrespondingdifferentialequations,wh ere voltagesand currents are describedas a functionof distanceand equivalentcircuitfor a calculationof the three basictransmissionline parametersis presentedin the following sections[1 7].

4 AC resistance of a conductor in a transmissionline is basedon the calculationof its DC DC currentis flowingalonga roundcylindricalconductor, the current is uniformlydistributedoverits cross-sectionareaand its DC resistanceis evaluatedbyRDC rlAV (13:1)wherer conductorresistivity at a given temperature(V-m)l conductorlength(m)A conductorcross-section area (m2) circuit of a short-lengthtransmissi on a h g lZtan h (g l/2)2Yg lg a zl equivalenttotalseriesimpedance(V),Y yl equivalenttotalshuntadmittance(S),z seriesimpedanceper unitlength(V=m),y shuntadmittanceper unitlength(S=m),g ffiffiffiffiffiffiffiffiZYp propagationconstant. 2006by Taylor & FrancisGroup, AC current is flowing, ratherthanDC current,the conductoreffectiveresistanceis higher due tofrequencyor the AC voltageproducesa secondeffecton the conductorresistancedueto thenonuniformdistributionof the known as frequencyincreases,the currenttendsto go towardthe surfaceof the conductorand the current densitydecreasesat the center.

5 Skineffectreducesthe effective cross-sectionarea usedby the current, and thus,the effectiveresistance , although in smallamount,a furtherresistance increaseoccurs whenothercurrent-carrying conductorsare presentin the immediatevicinity. A skin correctionfactork, obtainedbydifferentialequationsand Besselfunctions,is consideredto reevaluatethe AC resistance. For 60 Hz, RACk(13:2)Othervariationsin resistance are resistivity of any conductivematerialvarieslinearlyover an operatingtemperature,and therefore,the resistance of any conductorsuffersthe temperaturerises,the conductorresistance increaseslinearly, over normaloperatingtemperatures, accordingto the following equation:R2 R1T t2T t1 (13:3)whereR2 resistanceat second temperaturet2R1 resistanceat initialtemperaturet1T temperaturecoefficientfor the particularmaterial(8C)Resistivity (r) andtemperaturecoefficient(T) constantsdependuponthe resistivity and temperaturecoefficientsof sometypicalconductor materials[3].

6 BundleConductorEffectThereare two types of transmissionline conductors:overheadand ,madeof naked metalandsuspendedon insulators,are preferredover undergroundconductorsbecauseof the lowercostandeasymaintenance. Also, overheadtransmissionlinesuse aluminumconductors,becauseof the lowercostand lighterweight compared to copper conductors,althoughmore cross-sectionarea is neededto c onductthe sameamountof current. Thereare differenttypesof commercially availablealuminumconductors:aluminum-con ductor-steel-reinforced (ACSR),aluminum-conductor-alloy-reinforc ed (ACAR),all-aluminum-conductor(AAC), andall-aluminum-alloy-conductor(AAAC). and TemperatureCoefficientof SomeConductorsMaterialResistivity at 208C(V-m)Temperature Coefficient(8C) 10 10 10 10 2006by Taylor& FrancisGroup, one of the mostusedconductorsin consistsof alternatelayersofstrandedconductors,spir aledin oppositedirectionsto holdthe strandstogether, surroundinga core exampleof aluminumand purposeof introducinga steelcore insidethe strandedaluminumconductorsis to obtaina highstrength-to-weight ratio.

7 A strandedconductor offersmoreflexibility and easierto manufacture thanasolidlargeconductor. However, the totalresistanceis increasedbecausethe outsidestrandsare largerthanthe insidestrandson accountof the spiraling[8]. The resistance of eachwoundconductor at anylayer, per unitlength,is basedon its totallengthas follows:Rcond rAffiffiffiffiffiffiffiffiffiffiffiffiff iffiffiffiffiffiffiffiffiffiffi1 p1p 2sV=m (13:4)whereRcond resistanceof woundconductor(V)ffiffiffiffiffiffiffiff iffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffi1 p1p 2s lengthof woundconductor(m)pcond lturn2rlayer relativepitchof woundconductorlturn lengthof one turnof the spiral(m)2rlayer diameterof the layer (m)The parallelcombination ofnconductors,with samediameterper layer, gives the resistance per layeras follows:Rlayer 1 Pni 11 RiV=m (13.)

8 5)Similarly, the totalresistance of the strandedconductoris evaluatedby the parallelcombinationofresistances per high-voltagetransmissionlines,there may be more thanone conductorper phase(bundleconfig-uration)to increasethe current capability and to reduce corona surfacepotentialgradientof a conductor exceeds the dielectricstrengthof the surroundingair(30 kV=cm duringfair weather),producingionizationin the area closeto the conductor, with consequentcorona losses,audiblenoise,and radiointerference. As coronaeffectis a functionof conductordiameter, line configuration,and conductorsurfacecondition,thenmeteorolog icalconditionsplay a key role inits lossesunderrain or snow, for instance,are muchhigher thanin dry , however, can be reducedby increasing the totalconductorsurface.

9 Although coronalossesrely on meteorologicalconditions,theirevaluation takes intoaccountthe conductancebetweencon-ductorsand betweenconductorsand increasingthe numberof conductorsper phase,thetotalcross-sectionarea increases,the current capacity increases,and the totalAC resistancedecreasesproportionallyto the numberof conductorsper be appliedto anyAluminum Strands2 Layers, 30 ConductorsSteel Strands7 strandedsteelcore (ACSR). 2006by Taylor & FrancisGroup, are always usedat 345 kV and above maintainthe distance betweenbundleconductorsalongthe line ,spacers madeof steelor aluminumbarsare (Ampacity)In overheadtransmissionlines,the current-carrying capacity is determinedmostlyby the conductorresistance and the heatdissipatedfromits surface[8].

10 The heatgeneratedin a conductor (Joule s effect)is dissipatedfrom its surfaceareaby convection and radiationgivenbyI2R S(wc wr)W (13:6)whereR conductor resistance (V)I conductor current-carrying (A)S conductorsurfacearea (sq. in.)wc convectionheatloss (W=sq. in.)wr radiationheatloss (W=sq. in.)Heat dissipationby convectionis definedaswc 0:0128ffiffiffiffiffipvpT0:123airffiffif fiffiffiffiffiffiffiffidcondpDtW (13:7)wherep atmosphericpressure (atm)v wind velocity (ft=s)dcond conductordiameter(in.)Tair air temperature(kelvin)Dt Tc Tair temperaturerise of the conductor(8C)Heat dissipationby radiationis obtainedfromStefan Boltzmannlaw and is definedaswr 36:8 ETc1000 4 Tair1000 4"#W=sq:in: (13:8)wherewr radiationheatloss (W=sq.)