Derivative Method Based Orientation Detection of Substation Grounding Grid

15 Pages·2017·1.68 MB·English

energies
Article
Derivative Method Based Orientation Detection of
Substation Grounding Grid
AamirQamar 1,2 ID,MuhammadUmair1,FanYang2,∗,MuhammadUzair1 ID
andZeeshanKaleem 1 ID
1 DepartmentofElectricalEngineering,COMSATSUniversity,WahCampus,Wah Cantt47040,Pakistan;
[e-mail](A.Q.);[e-mail](M.Umair);[e-mail](M.Uzair);
[e-mail](Z.K.)
2 StateKeyLaboratoryofPowerTransmissionEquipment&SystemSecurityandNewTechnology,
ChongqingUniversity,Chongqing400044,China
* Correspondence:[e-mail];Tel.:[phone]
(cid:1)(cid:2)(cid:3)(cid:1)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:1)
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)
Received:19April2018;Accepted:15May2018;Published:18July2018
Abstract: The grounding grid is a key part of substation protection, which provides safety to
personnel and equipment under normal as well as fault conditions. Currently, the topology of
a grounding grid is determined by assuming that its orientation is parallel to the plane of earth.
However,inpracticalscenarios,theassumedorientationmaynotcoincidewiththeactualorientation
ofthegroundinggrid. Hence,currentlyemployedmethodsfortopologydetectionfailstoproduce
thedesiredresults. Therefore, accuratedetectionofgroundinggridorientationismandatoryfor
measuringitstopologyaccurately. Inthispaper,weproposeaderivativemethodfororientation
detectionofgroundinggridinhighvoltagesubstations. Theproposedmethodisapplicabletoboth
equally and unequally spaced grounding grids. Furthermore, our method can also determine
the orientation of grounding grid in the challenging case when a diagonal branch is present
inthemesh. Theproposedmethodisbasedonthefactthatthedistributionofmagneticfluxdensity
isperpendiculartothesurfaceoftheearthwhenacurrentisinjectedintothegridthroughavertical
conductor. Takingthethirdorderderivativeofthemagneticfluxdensity,themainpeakcoinciding
withthepositionofundergroundconductoris accuratelyobtained. Thus,themainpeakdescribes
theorientationofburiedconductorofgroundinggrid. SimulationsareperformedusingComsol
Multiphysics 5.0 to demonstrate the accuracy of the proposed method. Our results demonstrate
thattheproposedmethodcalculatetheorientationofgroundinggridwithhighaccuracy. Wealso
investigatetheeffectofvaryingcriticalparametersofourmethod.
Keywords: groundinggrid;magneticfluxdensity;orientation
1. Introduction
Thegroundinggridprovidesalowimpedancepathfromelectricalequipmenttoearth,ensuring
protectionfromhighlighteningandshortcircuitcurrentunderfaultconditions[1,2]. Thegrounding
grid also maintains step and touch voltages within limit, ensuring the safety of personnel inside
thepremisesundernormalandfaultconditions.Atypicalgroundinggridcomprisesofbareconductors
buried0.3mto0.5m(12into18in)belowthe earth’ssurfaceandspacedequallyorunequallyfrom
3mto7m(10ftto20ft)apart. Thesebareconductorsareplacedingridormeshpatternandare
securelybondedtogetheratcrossconnections. Verticalconductorsareinstalledatmajorequipment
pointsandstructuressuchaslightningarrestersandpowertransformersetc. Theseverticalconductors
aretheonlyaccesspointstothegroundinggrid. Theburiedmeshofbareconductorsisspreadover
theentireareaoftheswitch-yardandoftenafewmetersbeyondthefence[3]. Verticalgrounding
Energies2018,11,1873;doi:10.3390/en11071873 www.mdpi.com/journal/energies
Energies2018,11,1873 2of15
conductorsarealsoconnectedtogroundinggrid,penetratingdeeperintothelowerresistivitysoil.
Theseverticalgroundingconductorseffectivelydissipatefaultcurrentsintotheearth,wheneveratwo
layerormultilayersoilisencountered[3].
The buried bare conductors are subjected to corrosion under decomposing nature of earth.
This phenomena effects conductivity of the grounding grid and with the passage of time, it may
resultinabrokengrid[4]. Inefficientorbrokengroundinggridrepresentsacriticalfaultandhidden
dangertoequipment,lifeandsmoothoperationofpowergrid.
Electromagnetic field methods [5–7], electric circuit analysis [4,8,9], electrochemical
methods[10,11] and optimization techniques [12,13] have been extensively used for corrosion and
breakpointdiagnosis. However,inthecaseofunknowngroundinggridstopologyandorientationare
thosetwodistinctiveparametersthatmustbeevaluatedbeforeapplyinganyfaultdiagnosistechnique.
Thetopologyofagroundinggridisdefinedastheformationtakenbytheinterconnectionsofgrounding
gridconductorswhereasorientationisthelocationofgroundinggridwithreferencetotheplaneofearth.
Configuration drawings providing topology and orientation references are often lost and
mishandled. Excavationisnotusedtodeterminegroundinggridtopologyandorientationbecauseit
notonlyrequirespoweroutagebuthasalsoproveditselfaspoortimeandcosteffectivesolution.
A method for topology detection is developed in [14] based on the concept of regret.
This method cannot detect the complete topology of grounding grid when a broken branch
isencountered. Moreover,thismethodrequiresorientationofgroundinggridbeforeitcanbeapplied
for topology detection. Reference [15] measures the grounding grid configuration by employing
transientelectromagneticmethod(TEM).Secondarymagneticfieldsduetoinducededdycurrents
inthegroundinggridarerecorded. Groundingconductorslieunderpointsofminimummagnetic
fieldintensity. Theflawin[15]isthattheorientationofgroundinggridispresumedtobeparallel
to the plane of the earth which in real scenarios is unknown. In [16], line derivative is used to
configurethetopologyofgroundinggrid. Thelocationofpeaksobtainedbytakingthederivative
of magnetic flux density represents the position of ground branches. It can be seen in Figure 1a,
where the grounding grid is located parallel to the substation boundary such that the location of
each ground branch is a function of either x or y. Therefore, line derivative l and l is used to
x y
determinethelocationofgroundbrancheslyingalongx-axisandy-axis,respectively. Although[16]
works well with the assumption that grounding grid is located parallel to the plane of the earth
(substationboundary)butamajorflawarisesincircumstanceswheregroundinggridisnotlying
paralleltotheplaneoftheearthasshowninFigure1b. Here,locationandthusthemagneticflux
densityofgroundbranchesisdescribedasafunctionofbothxandy. Hence,[16]willnotbeableto
detectgroundinggridtopologyusinglinederivativeapproachasshowninFigure1b. Furthermore,in
lightoftheabovediscussion,[16]willalsofailbytakingthediagonalbranchintoaccount.
y
Substation
Wall
x
(a)
Figure1.Cont.
Energies2018,11,1873 3of15
y
Substation
Wall
x
(b)
Figure1.Dependingonsubstationdesignrequirements,groundinggridcanbelocatedatany
anglewithreferencetosubstationboundary. (a)Orientationofgroundinggridisassumed
paralleltothesubstationboundary. Forinstance,thelocationofgroundbranchesbelowl
x
areafunctionofxandsimilarlythelocationofgroundbranchesbelowl areafunctionof
y
y. Therefore,linederivativetechniquecanbeusedtodeterminegroundinggridtopology.
(b)Groundinggridislocatedatananglewiththesubstationboundary. Here,locationof
brancheswithrespecttoxy-planareafunctionofbothxandy. Ontheotherhand,l isonly
x
afunctionofxandsimilarlyl isafunctionofythuslinederivativesl andl willproduce
y x y
incorrectresults.
Theorientationofgroundinggridhasfirstdeterminedby[17]usingcircularderivativeandthen
appliedlineandcirclederivativetomeasurethecompletetopology. Inordertogeneratesatisfactory
resultsfromtheapproachusedin[17],groundinggridmustbeequallyspacedasshowninFigure2a.
Incontrast,thetopologyofgroundinggridisbasedonsubstationequipmentlayoutandtherefore
itmaynotnecessarilybeequallyspacedgridasdepictedinFigure2b. Topologyofgroundinggrid
mayvarywithtime,dependingonthechangesingridstationlayout. Modificationsingroundinggrid
includesadditionalverticalconductors,varyingspacebetweenadjacentbranchesandvaryinglengths
ororientationofgroundbranches[15].
Themethodby[17]doesnottakeintoaccountthechallengingcaseofadiagonalbranchpresent
in an unequally spaced grid. The presence of a diagonal branch in an equally spaced square grid
willreducetheangulardisplacementbetweengroundbranchesfrom90◦ to45◦. Thus,thespacing
betweengroundbranchdistinguishingpeakswillalsoreduce. Inconditionswhereadiagonalbranch
is connected to vertical conductor and side to side ratio of grounding grid is changed from 1:1.
Theangulardisplacementbetweenanormalandadiagonalbranchreducesbelow45◦andbecomesso
smallthatthederivativepeakswilloverlapwitheachother. Theseoverlappingswillproducefake
peaksandasaconsequence,[17]willnotbeabletodistinguishbetweenrealandfakepeaksdescribing
theorientationofgroundbranches.
Contributions: Inthispaper,weproposetheelectromagneticandderivativemethodtomeasure
theorientationofgroundinggrid. Weconsidertheworstconditionsofunequallyspacedgrounding
gridhaving7×3mmeshdimensionsandadiagonalbranch.Insuchcircumstances,theanglebetween
anormalbranchandadiagonalbranchreachesitsminimumvaluei.e.,23.19◦. Employing[17]insuch
conditionswillproducefakepeakshowninSection2duetooverlappingofpeakscorresponding
to normal and diagonal branch. This overlapping occurs due to large peak width in 1st order
derivative. Therefore, our proposed method uses 3rd order derivative on circle which reduces
the peak width by increasing the slope of tangent to the curve thereby nullifying the effects due
to overlapping. Therefore, peaks corresponding to orientation of ground branches are clearly
distinguished. Moreover, we also investigate the influence of circle radius for derivative. Due to
Energies2018,11,1873 4of15
theinverserelationbetweenpeakwidthandcircleradius,increaseincircleradiuscanfurthernullify
theeffectsofoverlapping.
Therestofthepaperisorganizedasfollows: Section2mainlyelaboratestheproblemregarding
theorientationofgroundinggridwithdiagonalbranchinunequallyspacedconfiguration. Section3
proposesaneffectivesolutiontotheproblemhighlightedinSection2. Section4consistsofsimulations
anddiscussionsrequiredfortheauthenticationofproposedsolution. Thissectionalsoinvestigates
theeffectofchangingtheradiusofcircleforderivative. Section5concludestheresultsandfindingsof
simulationanddiscussions.
A
A
A
(a)
A
B
(b)
Figure2.Basedonsubstationequipmentlayout,groundinggridcanbeconfiguredasequally
spaced or unequally spaced. (a) Equally spaced grounding grid configuration have all
the branches of equal length. (b) Unequally spaced grounding grid have branches of
unequallengths.
Energies2018,11,1873 5of15
2. OrientationDetectionofGroundingGrid
Thegroundinggridiscomprisedofseveralgroundingconductorsconnectedtogetherintheform
ofgridspanningovertheentireareaofsubstation. Determiningtheorientationofgroundinggrid
usingelectromagneticmethodrepresentsaninverseproblem. Inthisproblem,injectedcurrentIand
(cid:126)
magneticfluxdensityBareknownwhereasorientationofgroundinggridistobedetermined.
In order to solve this problem, [17] takes 1st order derivative of magnetic flux density on
acirclecenteringtheverticalconductor. CurrentIisinjectedthroughverticalconductorintoequally
spaced grounding grid and position of peaks in 1st order derivative represents the orientation of
thegroundinggridasshowninFigure3. Theangulardisplacementbetweenadjacentbranchesis90◦
andpositionofeachpeakisclearlydistinguishingtheorientationofcorrespondinggroundbranch.
ReferringtoFigure3b,firstpeakcorrespondsto0rad,secondpeakcorrespondsto1.57radandso
on. Inthisway,orientationofgroundinggridisaccuratelydeterminedwhichisparallelintheplane
ofearth. Furthermore,introducingadiagonalbranchinthegroundinggridofFigure3aasshown
inFigure4a. Theangulardisplacementbetweenadjacentbrancheshasreducedto45◦. Theresult
obtainedinFigure4bissatisfactoryshowingthepeakcorrespondingtodiagonalbranch. Thispeak
is located at 0.78 rad (45◦). However, in the simulation results shown in Figures 3b and 4b, it
isobservedthattheinter-influence-sphere(peakwidth)spacehasreducedconsiderably. Thisshows
that if a grounding grid with unequal spacing is encountered the angular displacement between
adjacentbrancheswillfurtherreduce. Thisisthecasewheretheapproachusedby[17]willfailthat
isthepossibilityofgroundinggridbranchestobeunequallyspacedplusdiagonalbranch.Thisscenario
is depicted in Figure 5a. The effect of reduction in inter influence sphere (peak width) space will
becomemoreprominent,therebyincreasingdifficultiesindistinguishinggroundinggridbranches.
y
x
A rc C xulF citengaM fo evitavireD etulosbA)dar/T( |'zB| ytisneD
A Angle (rad)
(a) (b)
Figure3.(a)3×3mequallyspacedsquaregroundinggridconfiguration. Cisthecirclewith
radiusequaltor onwhichwetakethederivative. (b)1storderderivativeofmagneticflux
c
densityonC.Peakat0radcorrespondstobranchpositionat0◦,peakat1.57radcorresponds
tobranchpositionat90◦,peakat3.14radcorrespondstobranchpositionat180◦ andpeakat
4.71radcorrespondstobranchpositionat270◦. FromthelocationofpeaksinFigure3b,it
isdeterminedthatgroundinggridislyingparallelintheplaneofearthasshowninFigure3a.
Figure 5a illustrates the above problem of unequally spaced grounding grid with a diagonal
branch. Theangulardisplacementbetweengroundbrancheswillreducebelow45◦ andaminimum
angulardisplacementof23.19◦ isencounteredina7×3mmesh. Oursimulationresultsofa7×3m
groundinggridmeshwithadiagonalbranchareshowninFigure5b. Applyingthetechniquein[17]
results in overlapping of side peaks of a normal and a diagonal branch. As a result another peak
appears,whichdepictsthepresenceofanadditionalgroundbranchbetweennormalanddiagonal
branch. Themethodin[17]failsbecausethereisnobranchpresentbetweendiagonalbranchand
Energies2018,11,1873 6of15
normal branch as shown in Figure 5a. Therefore, [17] cannot be applied to solve the problem of
orientationdetectionundersuchcircumstances.
Inthispaper,3rdorderderivativeisusedtopreciselymeasuretheorientationofgroundinggrid
undercircumstancesforwhich[17]fails. Thereasonwhy3rdorderderivativeisusedisthereduction
inpeakwidth(mainpeakwidthplussidepeakswidth). Themainpeakwidthisthewidthbetween
zerovaluepointsofthemainpeakwheresidepeakwidthisthewidthbetweenzerovaluepointsof
thesidepeak. Thisreductioninpeakwidthisunderstoodbyanalyzingthatthederivativeissimply
theslopeoftheoriginalsignal,meansthirdorderderivativeistheslopeofsecondorderderivative
function. Therefore, higher odd derivatives increase the slope of tangent to the curve resulting
insharpeningofpeak(highresolution)withhighpeakamplitudeandlowpeakwidth[18,19].
y
x
rc
45°
A
C
A
(a)
x
u
lF
c
ite
ng)d
aa
M fo er/T( |'z
vB
ita| y
viretisn
De
eD
tu
lo
s
b
A
Angle (rad)
(b)
Figure 4. (a) Equally spaced grounding grid having diagonal branch. The angular
displacementbetweenanormalbranchandadiagonalbranchis45◦. (b)1storderderivative
ofmagneticfluxdensityonC.Interinfluencesphere(peakwidth)spacebetweenpeakat
0rad,correspondingtobranchpositionat0◦,andpeakat0.78rad,correspondingtobranch
positionat45◦,hasreducedconsiderably.
Energies2018,11,1873 7of15
y
x
bd
3m 4-7[m] by
45° 36.86° 23.19°
3m bx
rc
4m
7m
C
(a)
x
u
lF
c
ite
ng)d
aa
M fo er/T( |'z
vB
ita| y
viretisn
De
eD
tu
lo
s
b
A
Angle (rad)
(b)
Figure5.(a)Variationinmeshdimensions: Reductioninangulardisplacementfrom45◦ to
23.19◦ betweenb andb ,whenlengthofbranchb isincreasedfrom3mto7m. Firstorder
x d x
derivativeofmagneticfluxdensityistakenoncircleCofradiusr . (b)1storderderivative
c
oncircleCformeshdimensions7×3m. Peakat0radcorrespondstoorientationofb ,peak
x
at0.4047radcorrespondstoorientationofb ,thethirdpeakisafakewhichappearsdueto
d
overlappingofsidepeaksofb andb .
x d
3. DerivativeMethodBasedAnalysisofCurrentCarryingBuriedConductor
Asinglecurrentcarryingconductorisanalysedherefordemonstrationoftheproposedmethod.
Figure 6a shows a conductor of finite length placed along x-axis carrying current I and buried at
adepthhbelowthesurfaceinamono-layersoilofpermeabilityµ.
AccordingtoAmpere’slaw,magneticfluxdensityatthesurfaceisgivenas:
µI
(cid:126)B = ϕ (1)
(cid:98)
2πR
FromFigure6a:
h= Rcosϕ (2)
s = Rsinϕ (3)
s =rsinθ (4)
Energies2018,11,1873 8of15
Puttingvaluesfrom(1–4)into(1),magneticfluxdensityinzdirectionisobtained:
(cid:18) (cid:19)
µI rsinθ
B(cid:126) = (5)
z 2π (h2+r2sin2θ)
(cid:126)
TakingthederivativeofmagneticfluxdensityB oncircleC:
z
(cid:48) µI (cid:18)rcosθ(h2−r2sin2θ)(cid:19)
B = (6)
z 2π (h2+r2sin2θ)2
(cid:48)
PlotofB hasonemainpeakandtwosidepeaksasshowninFigure6b. Themainpeakisat0rad
z
whichcoincidespreciselywithorientationofburiedconductor.
(a)
|'''z
fo evitavB| ,)dar/T
ireD( |'z
etulosbB| ytisne3dar/T)
AD(
d x
eu
zilamrolF citen
Ng
a
M
Angle (rad)
(b)
Figure 6. (a) Single current carrying conductor model: Conductor of finite length along
x-axis carrying current I and buried at a depth h below the surface in a mono-layer soil
of permeability µ, derivative of magnetic flux density is taken at the surface of earth on
thecircleC.(b)1stand3rdordercircularderivativeofmagneticfluxdensity: thepositionof
themainpeakisat0radwhichrepresentstheorientationofburiedconductor. Mainpeak
(cid:48)(cid:48)(cid:48) (cid:48) (cid:48)(cid:48)(cid:48)
width of B is considerably less than the main peak width of B and amplitude of B
z z z
(cid:48)
isgreaterthanB .
z
Thewidthofthepeakdefinesacrucialparameterindeterminingorientationofgroundinggrid
especiallyincasewhereitisunequallyspaced. Therefore,widthofthepeakshouldbereducedas
muchaspossible. UnderworstcaseconditionsasdiscussedearlierinSection2,3rdorderderivative
isusedtodetermineorientationofgroundinggrid. Bytaking3rdorderderivativeofB ,theslopeof
z
tangenttothecurveincreases,resultinginnarrowingofpeaksasshowninFigure6b.
Energies2018,11,1873 9of15
(cid:48)
ThemainpeakwidthofB canbedeterminedasfollows:
z
(cid:48) µI (cid:18)rcosθ(h2−r2sin2θ)(cid:19)
B = =0 (7)
z 2π (h2+r2sin2θ)2
FromEquation(7),wedeterminethatθ = ±sin−1(h/r)rad.
(cid:48)(cid:48)(cid:48)
Inasimilarfashion,mainpeakwidthofB canbedeterminedasfollows:
z
(cid:48)(cid:48)(cid:48) µI r6sin6θ −sin4θ (6r6+23h2r4) sin2θ(36h2r4+23h4r2)−(6h4r2+h6)
B = ( + ) =0 (8)
z 2π (r2sin2θ+h2)4 (r2sin2θ+h2)4
√
FromEquation(8),wedeterminethatθ = ±sin−1( x),refertoappendixforthevalueofx.
Table1summarizestheeffectofincreasingtheorderofderivativeonthepeakwidth.
Table 1. Comparison of simulation results between 1st and 3rd order derivative. Keeping depth
constantat0.3mandradiusat2.9m.
SidePeak MainPeak MainPeakWidth SidePeakWidth
ShapeFunction
Width(Radian) Width(Radian) Difference(Radian) Difference(Radian)
(cid:48)
B 0.8274 0.206
z
0.122 0.6202
(cid:48)(cid:48)(cid:48)
B 0.2072 0.084
z
The width of main peaks and side peaks narrows to an extent that it will not overlap and
orientationofgroundinggridcanbeeasilydetermined.
4. SimulationsandDiscussions
Inthissection,anunequallyspacedgroundinggridofdimensions7×6misemployedformodel
study. It consists of seven nodes from node 1 to 7 and branches from b to b made up of copper
1 7
conductorsofradius0.02masshowninFigure7a. Adiagonalbranchb isalsoincludedinthemesh
d
configurationof7×3mwhereminimumangulardisplacementof23.19◦ betweendiagonalbranchb
d
andanormalbranchb is encountered. Adccurrentof25Aisinjectedfromnode1andreturnsat
1
node5,directionofarrowsrepresentsthedistributionofcurrentinthegrid. Thegridisburiedinsoil
atdepthof0.3mfromthesurfaceofearthinamono-layersoilasshowninFigure7b. Allsimulations
inthissectionarecarriedoutusingCOMSOLMultiphysics5.0,employingAC/DCmodule[20].
The magnetic flux density on the ground surface in z-direction is B . Employing derivative
z
method,1storderderivativeof B istakenonthecircleCasshowninFigure8a. Positionofpeaks
z
inthegradientofB representstheorientationofgridconductors. Thepeakpositioncorresponding
z
toorientationofb ,b andb areclearlydistinguishedat0rad,0.4047radand1.57radrespectively.
1 d 2
A situation of severe ambiguity arises in which a fake peak apparently represents the presence of
anotherbranchbetweenb andb asshowninFigure8a. However,incontrastthisbranchdoesnot
1 d
existinthegroundinggridofFigure7a. Thisisbecausesidepeakscorrespondingtob andb have
1 d
overlapped. Duetothisoverlappingofsidepeaks,anotherpeakappearsbetweenmainpeaksofb
1
andb . Inordertoresolvethisambiguity,3rdorderderivativeofB istakenwherepositionofpeaks
d z
representtheorientationofgroundinggridasshownintheFigure8b. Themainpeakandtheside
peakwidthisreducedtoanextentthattheeffectofoverlappingisnullifiedandpositionofindividual
peakscanbeclearlyidentified. Asaresult,positionofpeakscorrespondingtoorientationofb andb
1 d
areclearlydistinguishedat0radand0.4047radrespectively. Theorientationofgroundinggridisthus
accuratelydeterminedwhichisparallelintheplaneofearth.
Energies2018,11,1873 10of15
(a)
(b)
Figure7. (a)Simulationmodeltopview: Unequallyspacedgroundinggridhavingseven
nodesfromnode 1to7andbranchesfromb tob madeupofcopperconductorsofradius
1 7
0.02m. Adiagonalbranchb isalsoincludedinthemeshconfigurationof7×3mwhere
d
minimumangulardisplacementof23.19◦ betweendiagonalbranchb andanormalbranch
d
b is encountered. 25ADCcurrentflowsintonode1andreturnsatnode5withcurrent
1
distributionasshown. MagneticfluxdensityismeasuredalongthecircleCwhoseradius
is2.5m. (b)Simulationmodelsideview: Groundinggridisburiedatdepth0.3mbelow
theearthsurfaceinamonolayersoil.