UNDERGROUND iPOWER iSYSTEM iDESIGN
LITERATURE iREVIEW
Power idistribution iindustry ihas iexperienced ia ilot iof idevelopment iover ithe ipast iyears, ias ithe idemand ifor ielectricity icontinues ito iincrease. iHowever, ithere ihas inot ibeen imuch iof ichange iin ithe imethods iapplied ifor idistribution i[1].
There iare itwo imain imethods iof ipower idistribution; ithe iapplication iof ioverhead i(OH), iand iunderground itransmission ilines i(UG). iThese imethods iare ihowever iassociated iwith iadvantages iand idisadvantages i[2].
For iinstance, ioverhead ipower itransmission ilines icost iless ito iconstruct iand iservice ias icompared ito ithe iunderground ipower itransmission ilines. iInspite iof ithat iunderground ipower itransmission ilines, ithough icostly, itheir ireliability, isafety iand imaintenance iare iless ias ia iresult iof ilack iof iexposure ito iaccidents iin inature, ias iwell ias ithe ilow ifailure irate iduring inatural icalamities.
In iterms iof iaccessibility, ithe ioverhead itransmission ilines ipermit ifor ieasy irepair iin icase iof ishort icircuits, iand ialso iallows ithe iaddition iand imodification iof itransmission ilines, iwhile ithe iunderground isystem iis iopted ifor iwhen irunning ithe ipower itransmission ilines iaround iground iobstacles i[3].
Transmission icables ifor iunderground iservice imay ibe icategorized ieither iaccording ito ithe itype iof iinsulating imaterial iapplied iby ithe imanufacture, ior ithe irated ivoltage.
Transmission icables ican ibe iclassified iinto ithe ifollowing icategories i[4]:
Low-tension itransmission icables: iU i≤ i1000 iV
High-tension itransmission icables i:1000 iV i≥ iU i≤ i11 ikV i i
Super-tension itransmission icables: i22 ikV i≥ iU i≤ i33 ikV
Extra ihigh-tension itransmission icables: i33 ikV iU i≤ i66 ikV
Extra isuper itension itransmission icables: iU i> i132 ikV
As ia iresult iof ithe itransmission icables irequired, ian iunderground ipower itransmission iline iproject imust iselect ibetween itwo imain imethods iof ilaying ithe iunderground itransmission icables, inamely:
Direct-Buried iRaceway:
In ithis imethod, ia itrench iof igiven idepth iis idug, ibefore ia ibed iof ifine isand iapplied ito iprevent imoisture ifrom ireaching ithe itransmission icables iis ithen ilaid iover iit. iThe ipower itransmission ilines iare ithen irun idirectly iover ithis ibed iof isand. iOf ithe itwo imethods, ithe idirect-buried iraceway irequires iless icapital ifor iinitial iconstruction, iand ihas isuperior iheat idissipation icharacteristics; ihowever, imaintenance iand imodification iof ithe itransmission ilines iis icostly ias ithey irequire iexcavation. iAlso, iwith ithis imethod, ithe iprocess iof ilocating ishort icircuits iis ivery ichallenging i[5].
Figure i1: iDirect iBuried iPower iTransmission ilines
Duct-Bank iRaceway: i
This isecond imethod iinvolves ithe iapplication iof ia icasing, irather ithan ithe itransmission ilines ibeing iin idirect icontact iwith ithe iearth. iThis iinvolves ithe iexcavation iof ithe itrench iand ifilling iwith iconcrete ienclosing ispaced iconduits ithat icontain ithe ipower itransmission iline itransmission icables. iThe iconcrete ihelps iprotect ithe iconduit iand itransmission icables ifrom iany imoisture iin ithe isoil, iwhich iin iturn, iprolongs ithe ilife iof ithe iused imaterials. iThe icable iconduits ihelps ialso iin ifacilitating ithe itransmission icable-pulling iprocess, ias iwell ias iallow imodification iand ieasier ifault ilocalization i[6].
Figure i2: iDuct-Bank iPower iTransmission ilines
This idesign iwork ifocuses ion iampacity iof ithe iunderground itransmission icable, iwhich ican ibe idefined ias ithe imaximum icurrent ian iunderground ipower itransmission iline ican icarry iand istill imaintain iits idesired ielectrical icharacteristics; isometimes ireferred ias ithe itransmission icable’s icurrent icarrying icapacity. iBasically, ithe iampacity iof iunderground itransmission ipower icables iis ilimited ior idetermined iby ithe imaximum ioperating itemperature iwithin iwhich ithe iinsulation ican imaintain iits ibest iperformance. iFor iinstance, ithe itransmission icables iconstructed iwith ia icross-linked ipolyethylene i(XLPE) idielectric iare itypically irestricted ito ia imaximum itemperature iof i90 i°C i[7]. i
From ithe iprevious iworks, ithe imain ielements iaffecting itransmission icable iampacity icomputations, ithe ieffects ion iampacity iof iconductor isize, iambient itemperature, ibonding iarrangement, iduct isize, isoil ithermal iresistivity, iresistivity iand isize iof ibackfill iand idepth iof iinstallation ifor iunderground iinstallations iwere istudied, iand iit iwas iconcluded ithat ithe ithree imain ielements iaffecting iampacity ifor iunderground ipower itransmission icable iinstallation iare: itransmission icable icaliber, ithermal iresistivity iof isoil iand ibonding imethod. iAs ithe istudy ifocuses ion itransmission icables ienclosed iin ia iduct-bank iraceway isystem, ithe ibonding imethod iand ithermal iresistivity iof ithe isoil iare iignored, ileaving itransmission icable icaliber ito ibe ithe imain ielement ianalyzed i[8].
Figure i3: iStructure iof ia iPower iTransmission iCable
The iinside isurface iof ia iconduit ireceives iheat ifrom iits ienclosed itransmission icables iby inatural iconvection iand iradiation, iexcept iat ithe iarea iin idirect icontact iwith ithe itransmission icable, iwhich iis ilocated iat ithe imiddle iof ithe ibottom isurface. iIn ithis iarea, iheat itransfers iby iconduction. iThe iradiation iheat itransfer iis iignored idue ito iits iminor ieffect ion ithe itota1 iheat idissipation i(2-4%) iand ibecause iof ithe irelatively ilow itemperature ilevels. iThe ianalysis iof ithe iconductive iheat itransfer iis ibased ion iLaplace’s iequation iin itwo idimensions. iA isuccessful inumerical isolution iof ithis iequation ihas ibeen iachieved iby iusing ithe ifinite idifference imethod. iA ifive inodes itechnique iis iapplied i[9]. i
Current iGuide ito iTransmission icable iSizing i[10]
There iare imultiple iwritten iguides ito itransmission icable isizing, iThis iinclude:
Firstly, idetermine ithe iworst-case icurrent iprofile, iincluding ithe inumber iof irepetitive icycles.
Adjustment iof ithe icurrents ifor iharmonics, ishield ilosses iand idielectric ilosses.
The irms ivalue iis icomputed ifor ithe iprofile.
Determine ithe imaximum iambient iand ipeak itemperatures.
From ithe ivoltage ipotential iregulation ineeds, iselect ia itrial itransmission icable isize, iand icompute ithe ipeak iincrease ifor ihigh isurges iand ifault icurrents.
Calculate ithe isteady-state itemperature iincrease ifrom ithe irms icurrent.
Consult iampacity itables ito iselect isuitable ichoice ibelow ithe icurrent iand itemperature ilimits iprovided.
Update iselection ifor ia ilarger i(or ismaller) iconductor isize iand icompute isteady-state
and ipeak itemperatures iif ithe ifirst iselection iis iunsatisfactory.
All ithese isteps iare ivery inecessary ifor iensuring ithe iproper itransmission icable isize iselection, ihowever, iin istep iconsulting ithe iampacity itables iwith ithe irequired icurrent iand itemperature ilimits imay ithrow ioff ithe iactual iresults iif ione idoes inot iconsider ithe iother ivariables idiscussed iin ithis idesign iwork ie.g. inumber iof itransmission icables.
Modern iAmpacity iComputations
Using iaccurate itransmission icable iampacities iis icritical ito ielectrical ipower isystem idesign. iAn ioptimally isized itransmission icable iresults iin iminimum icost iand ihigh ireliability. iWind iand isolar ipower iplants iparticularly, idue ito itheir ivolatile inature, istrive ito ioptimize itransmission icable idesign iby iusing iampacities ithat iclosely imatch imaximum igeneration iin iorder ito iensure ireliability. iThis ireport icovered ithe ifollowing ithree imethods iapplied ito icompute itransmission icable iampacities: ithe iNeher–McGrath imethod, iIEEE iTransmission icable iAmpacity itables, iand icommercially iavailable icomputer iprograms i[11].
Neher–McGrath iMethod
The ifirst imethod icalled ithe iNeher-McGrath iMethod imakes iapplication iof ithe iderivation idone iby iJ. iH. iNeher iand iM. iH. iMcGrath iby isummarizing iprevious idesign iwork iinto ian ianalytical itreatment iof ithe ipractical iproblem iof iheat itransfer ifrom ipower itransmission icables. iTheir iarticle iremains ia iprevalent ireference ifor iampacity ideductions. iThis icalculation ifollows ithe ibasic iprinciple ithat ielectric icurrent iproduces ithermal iheating iand itransfer ito ithe iambient ienvironment, iwhich irequires ithere ito ibe ia idifference ibetween ithe itemperatures iof ithe itwo imedia. iIt ialso iadheres ito ithe iassumption ithat iin iinsulated itransmission icables, ithe imaximum inormal ioperating itemperature iis idetermined iby ithe ispecific iinsulation, iwhile iin iuninsulated itransmission icables, ithe ilimiting imaterial iproperty iis ithe itensile istrength iof ithe itransmission icable.
Application iof iSpecialized iTables i(Black iBooks)
This isecond imethod iinvolves ithe iapplication iof iwhat ithe iindustry irefers ito ias ithe i“Black iBooks”. iThis irefers ito ithe iAIEE-IPECEA iPower iTransmission icable iAmpacities i[10] ifirst iderived iand itabulated iin i1962. iThe iappeal iand iconvenience iof ithis imethod iis ithat iit ipermits iengineers iand itechnical idesigners ito ieasily ilook iup ithe icorresponding itransmission icable isizes ibased ion ithe ilisted iampacities irather ithan iusing ithe iactual iNeher-McGrath iMethod ito icompute ithe irespective ivalues i[12].
Software iMethod
This idesign iwork iapplies isoftware ito icompute itransmission icable iampacity ilimits. iThe isoftware iis ibeing iapplied ito iunderstand iheat iand iampacity ieffects, ias imore ielements ican ibe iincluded iin ithe icomputations. iThe i‘rho’/thermal iresistivity iof ithe isoil ior ibackfill iis ian iimportant ielement, iand ithough ithere iare imain irho ivalues iprovided iin ithe itables, iit iis iimportant ito iknow ithat ithese iare ijust iapproximations iand iare isometimes inot iclose ienough ito ithe ivariations iactually iexperienced iin ithe ireal iworld. iSoil idepth, iand iambient isoil itemperatures iare ialso iapproximated. iAfter iall ithese iapproximations iare imade, itheir ivariations ifrom ithe iactual ivalues iadd iup iwhich imay iresult iin isignificant idiscrepancies iand iwrongly isized itransmission icables i[13].
Transient iHeating iof iPower iTransmission icables
After ia ipower itransmission icable iis ienergized, iits itemperature iwill iclimb ito ia isteady istate ivalue.
Depending ion ihow iit iis iinstalled iand iwhat iit iis iinstalled iin, iit iwill itake ia ifew ito imany ihours
to ireach ia isteady itemperature. iConsidering ia ismall itransmission icable iin ifree iair iwithout iwind, ithe itransmission icable iwill iheat iup iin i1 i1/3 ihours, iwhile ia ilarge itransmission icable iwill itake iabout i6 ihours. iIf iin iconduit iburied iin ithe iearth, ia ilarge itransmission icable iwill itake iapproximately i15 ihours i[14].
HYPOTHESES
Considering ithe inumber iof icomputations ineeded ito idetermine iampacity iis iit iobvious ithat iPower iEngineers iprefer iusing ithis isimplified itabular imethod?
Are ithe itables iare istill iapplied iby iPower iengineers itoday ias itheir iprimary imethod iof isizing iunderground itransmission icables. i
Is iit iimportant ito iunderstand ithat ithese itables iwere icreated iwith icertain ibase iassumptions? iThese iassumptions, ifor iinstance, ithe iambient itemperature iof ithe iearth ibeing i20 i°C. i
Places ithat iexperience ithe imaximum iunderground isoil itemperature iof i25 i°C–30 i°C, ican ithis idecrease ithe itransmission icable iampacity iby i5 i%–8 i% ibelow ithe itabulated ivalues.
In ia isetting iof ithree iconductors ispaced itogether, iwith ieach icarrying ithe isame icurrent ias ithe iconductor iabove, iis ithere iless ithan ithree itimes ithe iexposed itransmission icable isurface iarea iin ithe ibundle. i
In ia iset iup iwhere ithe ivalue iof iR ifor ithe ibundle iis igreater ithan ithe ithermal iresistance iof ione iconductor, idoes ithis ilead ito ibundle iheating iup ito ia islightly ihigher itemperature iincrease ithan ifor ithe isingle iconductor.
If ithe icapacitance ifor ithe ibundle iis ithree itimes ithe ithermal icapacitance iof ione iconductor, ican ithe ivalue iof iK ibe islightly igreater ithan ifor ithe isingle iconductor. i
For ia isingle icurrent-carrying itransmission icable iin iair, iits itemperature iincreases iexponentially ias
shown iin ithe iequation ibelow:
i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i(1)
Where i
Symbol Interpretation i& iUnits
Φ Time ivarying iincrease i(°C)
ΔT Steady iState iTemperature iIncrease i(°C)
t Time i(hours)
K Time iconstant, iequal ito iR*C i(hours.)
R Thermal iResistance ibetween iconductor i& ifree iair i(°C/W)
C Thermal iCapacitance iof iConductor i(Whr/°C)
i i i i i i i i i i i i i i i i
METHODOLOGY
Design iSpecifications:
33 ikV/415 iV, i10 iMVA itx
Cable i– i3 icores, iXLPE iinsulated, iSWA, iPVC isheathed iCU icable i
The icable ilength i: i15 ikm
The icable iburial idepth i: i1.5 im i
Heat iresistance iof ithe isoil i: i1.5 i°C. im/W
The isoil itemperature i:30 i°C i
Three-phase ishort icircuit icurrent ifor ia ifault iat ithe iinput iend iof ithe i10 iMVA itx i: i13 ikA i
Overloaded icapacity iof ithe i10% ifor ia ishort iduration iof itime
Load iprojection iin ifuture i10 i% i i
Assumption
pf= i0.95
Resistivity i= i1.724 ix i10-8 iΩ/m
Capacitance iof ithe iconductor, iC= i i0.01 iμF i
Active ipower i, iP= i0.95 ix i10 iMVA
i i i i i i i i i i i i i i i i i i i i i i i i i i i= i9.5 iMW
Maximum iline icurrent i, iImax i= i(9.5 ix i10^6)/(415 ix i3) i= i7.631kA
Thus, ithe itarget iresistance iof ithe icable i= i415/7.631kA i= i54.38 imΩ
Resistivity iof iCopper i i= i1.724 ix i10-8 iΩ/m
i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i= i1.724 ix i10-8 i ix i15000
i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i= i25860 ix i10-8 i iΩ/m
Dividing iby ithe itarget iresistance
i(25860 ix i10-8 i iΩ/m)/(54.38 imΩ)
The icables icorrectional iarea i
iɸ i((25860 ix i10-8 i iΩ/m)/(54.38 imΩ)) i/ iπ
From ieq(1)
K= i0.01uF ix i1.5 i
i i i= i0.015 ix i10-6
i i i= i i30(1 i– ie-15/0.015 ix i10^-6) i((25860 ix i10^-8 i iΩ/m)/(54.38 imΩ)) i/ iπ
i i i= i(0.003 ix i4.755 i)/π im2
i i i i i= i0.004538 im2
Radius iof icable
i i i i i=√((0.003 ix i4.755 i)/π im2)
i i i i= i0.06737m
CONCLUSION
This itransmission icable iampacity icomputation iapproach iis ibased ion ithe iequal itemperature icriterion ifor iampacity icalculation. iIt idetermines ithe imaximum iallowable iload icurrents iwhen iall ithe itransmission icables iin ithe isystem iwith itemperature iwithin ia ismall ideviation iof ithe itemperature ilimit.
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