The Analysis and Calculation of DC Earth Electrode Electric Field Coupling with Thermal based on Shell Theory

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1 Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v Articl h Aalysis ad alculatio of D Earth Elctrod Elctric Fild ouplig with hrmal basd o Shll hory Jigli Li, Liyig Guo, Pg Hu, Yuabo Li, Yu Zhag ad Pgwi H ollg of Elctrical Egirig, Zhgzhou Uivrsity, Zhgzhou 45, Ha Provic, hia; lijigli@zzu.du.c Xiyag Elctric ompay, Stat Grid Ha Elctric Powr ompay, Xiyag 464, hia; guoliyigyur@6.com Hz Elctric ompay, Stat Grid Shadog Elctric Powr ompay, Hz 74, hia; liyuabo654@6.com orrspodc: lijigli@zzu.du.c; l.: Abstract: Durig HVD arth rtur opratio systms, a high magitud currt will b ijctd ito soil through arth lctrod, th pottial o th surfac would chag widly ad produc ufavorabl ffcts o th A systms aroud. his papr prsts a ffctiv fiit lmt mthod FEM couplig lctric fild with thrmal fild to valuat th lctrical fild iducd by th ijctd D currt. Firstly, ow to th charactristic of FEM, this mthod ca cosidr arbitrary soil ad arth lctrod structur. Scodly, by sttig th lctrical ad thrmal paramtrs of soil as a fuctio of tmpratur at th sam tim, th dyamic couplig procss of lctric fild ad thrmal fild is simulatd accuratly. hirdly, to dal with th sigular poit i FEM subdivisio ad th hug computatio i traditioal thr-dimsioal FEM, th FEM couplig -D arth lctrod with -D soil basd o "shll" thory is itroducd. Fially, basd o th suggstd mthod, th ffct of abormal rsistac rgio ARR ar D arth lctrod o lctric fild distributio is aalyzd. Kywords: D arth lctrod; lctro-thrmal couplig; abormal rsistac rgio ARR; shll thory, fiit lmt mthod. troductio Wh th high voltag dirct currt HVD trasmissio systm is workig udr moo-polar groud rtur mod, a high magitud currt will b ijctd ito soil through th arth lctrod. h ijctd currt will caus th tmpratur ris of both arth lctrod ad soil, D bias of trasformr i arby A substatios, D corrosio o th udrgroud mtals pipli ad A arth lctrod arby [-4]. h D lctric fild is iflucd by th soil structur, ijctd currt ad arth lctrod structur. So it is importat to calculat th D arth lctrod lctric fild accuratly ad aalyz th ifluc of soil structur ad arth lctrod o D lctrical fild udr-groud. At prst, th rsarchs o th D arth lctrod maily focus o thr aspcts: th D arth lctrod tmpratur ris procss ad th soil paramtrs iflucs o th tmpratur ris procss [5-8]; th trasformr D bias ad udrgroud mtal D corrosio basd o circuit simulatio softwar[9-]; arth lctrod lctric fild distributio law at complx soil structur[-]. th rsarchs about D arth lctrod lctric fild calculatio, Rf [] prsts th modlig of D arth lctrod lctric lctrical fild udr complx tctoic, which taks D arth pol as poit sourc, thus rducig th amout of calculatio, but this modlig is ot suitabl for th aalysis of lctrical fild ad thrmal fild ar th arth lctrod accuratly. Rfs [5-8] stablish -D fiit lmt D arth pol modlig cosidrig coupl of lctric fild

2 Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v of ad thrmal fild. h rsult of this mthod is vry accurat, at th sam tim hug ukow quatity will b gratd; v thr xists th problm of split sigularity, wh th larg domai is cosidrig. So it is sstial to stablish th modlig of D groudig dvic both cosidrig larg domai ad calculatio accuracy. O th othr had, rsarch about th ffct of soil structur o D arth lctrod maily focus o simpl soil structur, such as lvl ad vrtical layrd soil [-] or moutais ad rivrs [], but thr ar vry littl rsarchs about soils with massiv txtur. h aim of this papr is to prst a mthod for D arth lctrod lctric fild cosidrig both groudig dvic structur ad larg disprs currt domai. Du to th hug gap, somtims up to 6, btw larg disprs currt domai ad vry small sctio siz of groudig coductor, th computatio will b a sharp ris i traditioal thr-dimsioal fiit lmt mthod, ad somtims thr will b sigular poit o itrfac of groudig coductor ad soil i th procss of FEM gomtry subdivisio. o solv th abov problm, this papr itroducs th "shll" thory [Error! Rfrc sourc ot foud.-6] ito FEM mthod, which taks lctrod coductor as -D surfac i gomtric modl, as -D coductor with virtual thickss i FEM quatio. Bcaus of cosidrig coductio of groudig coductor, th "shll" FEM mthod ca calculat HVD groudig dvic charactristic accuratly, at th sam tim, th FEM computatio i groudig coductor ad soil adjact domai hav a dcli attribut to th -D gomtric modl of groudig coductor. h high amplitud currt which rachs svral thousad amps flows through D arth lctrod chroically. Bcaus of th covrsio of lctric rgy ito hat, th tmpratur of soil aroud arth lctrod will rais, ad th, th lctrical ad thrmal paramtrs of soil chagig corrspodigly [5-8]. ordr to simulat th actual workig coditio of D arth lctrod accuratly, this papr st th lctrical ad thrmal paramtrs of soil as fuctio of tmpratur i th corrspodig soil lmt ad tim. Fially, basd o th wid applicability of FEM to ay complx soil structur, this papr aalyzs th ifluc of ARR ar D groudig o lctric fild distributio. Hop that coclusio of this papr ca provid rfrc for actual D groudig dsig.. umrical modl of arth lctrod systm basd o shll thory his sctio may b dividd by subhadigs. t should provid a cocis ad prcis dscriptio of th xprimtal rsults, thir itrprtatio as wll as th xprimtal coclusios that ca b draw. urrt flowig procss of D arth lctrod is couplig procss btw lctric fild ad thrmal fild. hy ar satisfid with th costat lctric fild thory, Joul hatig law ad th basic pricipls of hat trasfr. W calculat lctric fild ad thrmal fild by FEM rspctivly, ad th coupl thm... Fiit lmt modl of lctric fild Laplac's quatio of costat lctric fild is usd to dscrib D arth pol lctric fild gratd i th flowig procss. ϕ = ϕ is th scalar pottial. Formula satisfis th followig boudary coditios: th ifiit distat plac, O th arth surfac, ϕ = Whr, is th ormal uit vctor; γ is th coductivity. r γ ϕ =

3 Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v of h cotiuity coditios of pottial ad currt dsity ar satisfid at th arth grid ad th soil cotiuum itrfac ad th itrfac of diffrt soil i complx soil. this papr, w us four-od ttrahdral uit to discrt solutio domai, ad us Galrki wightd rsidual mthod ad itrpolatio mthod to dal with th govrig quatios. Fially, th fiit lmt quatio of tim t is obtaid, K{ ϕ} P = 4 h total stiffss matrix K is rlatd to th soil lctrical coductivity; P is th quatity that is rlatd to th ijctio currt... Fiit lmt modl of thrmal fild Accordig to th Joul hatig law ad hat trasfr pricipl, th trasit hat coductio quatio of soil is as: k Q v = 5 t Whr, k rprst th thrmal coductivity of soil, W/m ; is th tmpratur of ach poit i th soil, ; v is volumtric hat capacity, J/m ; Q rprsts hat sourc dsity, adq = ρj, W/m, ad it is dtrmid by th lctric currt dsity paramtr calculatd by th lctric fild. Formula 5 satisfis th followig boudary coditios: th ifiit distat plac, O th arth surfac, = 6 k = h 7 Whr, h ad rprst th groud hat trasfr cofficit ad ambit tmpratur. Galrki wightd rsidual mthod ad itrpolatio mthod ar usd to dal with th govrig quatios. Fially, th fiit lmt quatio of tim t is obtaid, { } F = 8 t h matrix,, F, rspctivly, is rlatd to th thrmal coductivity of k, spcific hat capacity v ad hat sourc dsity Q... h itroductio of thi shlls thory Du to th hug gap, somtims up to 6, btw larg disprs currt domai ad vry small sctio siz of groudig coductor, th computatio will b a sharp ris i traditioal thr-dimsioal fiit lmt mthod, ad somtims thr will b sigular poit o itrfac of groudig coductor ad soil i th procss of FEM gomtry subdivisio. hrfor, this papr itroducs thi shlls thory to solv th abov problm. h shll thory is origially usd to study mchaical proprtis such as th dformatio ad itral forc distributio of thi shll. As show i Figur a, it is rig pol with a virtual thickss d. Ad th triagular lmt is usd to divid arth coductor surfac, as show i figur b.

4 Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v 4 of a b Figur. Schmatic diagram of groud coductor modl a -D arth coductor b Subdivisio graph of -D arth coductor w us four-od ttrahdral uit to discrt solutio domai, ad yild th followig Galrki rsidual quatios of a lmt: S dγ ϕ ds = 9 i Whr, S rprsts th surfac itgral uit itrval; d is th thickss of th shll quivalt uit; γ is th coductivity of th arth coductor. A scalar pottial is xpadd by odal basis fuctios as: j x, y ϕ j j= ϕ = Substitutio of ito 9 yilds fiit lmt quatio of lmt, i ϕj γ S i j j= R = [ d ]ds = i =,, ombiig formula ad formula 4, th fiit lmt quatios of th whol solutio domai ar obtaid: K { ϕ} P = h sam as th fiit lmt quatio of th currt fild is drivd, quatio 5 is tratd by th Galrki wightd rsidual mthod ad th itrpolatio mthod, j= d j S j= S k ds d ρ J i S j di v j ds = t j i ds ombiig formula 4 ad formula 8, th fiit lmt quatios of th whol solutio domai ar obtaid: { } F = 4 t From th abov drivatio, i th drawig of gomtric modl ad procss of FEM gomtry subdivisio, th lctrod coductor is quivalt to -D surfac, which ca gratly simplify th msh gratio procss ad rduc computatio, spcially i larg solutio ara. FEM quatio ad, th virtual thickss d is clvrly itroducd, so th calculatd rsults ar quivalt to th volum fractio of th thr prism lmt with a triagl bottom ad a thickss d. h abov mthod ca ot oly rflct diffusr fuctio of arth coductor to sur calculatio accuracy, but also solv th problm of hug computatio i larg solutio ara. additio, du to th cotradictio btw limitd computatioal rsourcs of fiit lmt mthod ad th ifiit flowig spac, this papr itroducs th spac coordiat trasformatio i th ifiit soil rgio far away from th groudig grid to simplify calculatio [7].

5 5 of.4. ouplig procss of lctric ad thrmal filds Accordig to [6], th lctrical ad thrmal paramtrs of soil show obvious dyamic tmpratur charactristics with tmpratur, which ar xprssd by fuctio ρ, ad k. h algorithm ca dirctly rflct th actual workig mchaism of D arth lctrod by couplig of lctric fild ad thrmal fild, ad provid thortical basis for practical groud dsig. Bcaus th fiit lmt quatio of tmpratur fild cotais th tmpratur to th tim partial diffrtial, w uss th tim domai diffrc mthod [5] to dal with it. h followig is th couplig procss of lctric fild ad thrmal fild: wh t = t, firstly, soil coductivity ρ =ρ iitial valu, th lctric fild calculatio matrix of tim t: { } = ϕ K P 5 K idicats that th rsistivity i this matrix is st to th rsistivity i iitial tim. Scodly, th hat sourc dsity Q at t tim is dtrmid by currt dsity J calculatd by th last stp, J Q ρ =.h spcific hat capacity is iitial valu; th thrmal coductivity is k iitial valu; Ad th mthod of tim domai diffrc is usd to dal with th trasit tmpratur fild. calculatio matrix of thrmal fild: {} } { F F = 6 F idicats that th hat sourc dsity i this matrix is st to fuctio of currt dsity i t tim. wh t = t, th lctrical coductivity wr dtrmid by tmpratur i t tim, { } = ϕ K P 7 h hat sourc dsity Q at t tim is dtrmid by currt dsity J calculatd by th last stp, J Q ρ =.h spcific hat capacity is ; th thrmal coductivity is k, {} } { K K F F K = 8 Summig up th abov calculatio procss, th calculatio matrix of lctric fild ad thrmal fild is obtaid by aalogy, { } = ϕ K P 9 {} } { = F F his mthod ca accuratly simulat th tim variatio of soil lctrical ad thrmal paramtrs, ad raliz th dyamic couplig procss btw lctric fild ad thrmal fild.. Vrificatio Accordig to [8], D arth lctrod, a sigl rig with radius of 55 m, was placd ito th layrd soil, ad th burid dpth is.5m. Bsids th paramtrs of soil ar show i abl. h rsistivity, volumtric hat capacity ad dsity of th cok, soil ad pol ar show i abl. Accordig to [5], th fittig formula of ρ, ad k chagig with tmpratur, ar show as formula, ad. Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v

6 Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v 6 of 6.5,,44 ρ = , 44, c = k = ,,55 6, 55,9.4,, , 55,9 W st th A currt for D arth lctrod. abl lists th calculatd rsults which iclud calculatio rsults obtaid by th mthod of this papr, by tratioal rcogizd Groudig alculatio Softwar DEGS ad by actual masurmt i [7]. h compariso rsult shows that th algorithm is ffctiv. abl. h soil aroud th groudig lvl stratificatio paramtr Soil layrs Rsistivity Ω m hickss m ρ fiit abl. Paramtrs of calculatd modl paramtrs soil cok pol dsity/kg m Rsistivity/Ω m ab volumtric hat capacity c 8 45 /J Kg K - thrmal coductivity /W m K - k abl. Rsults of comparig mod ompariso Rsistac/Ω Maximum tmpratur ris aftr d / MEA.5 Almost uchagd DEGS. FEM h ifluc aalysis of arr o th dc arth lctrod systm ordr to aalyz th iflucs of ARR s positio o D arth pol, w stablish a sigl rig arth lctrod modl udr a uiform soil coditio. h modl s rig diamtr is m, ad th iitial soil rsistivity is 8 Ω m. Usig a m 6 m 7 m rctagular block to simulat th ARR, th rsistivity of th low rsistivity-arr ad th high rsistivity-arr ar sttd 5 Ω m ad 5 Ω m, rspctivly. Fially, w aalyz th ifluc of high ad low rsistivity-arr at diffrt horizotal positios ad diffrt dpth o lctric fild distributio.

7 Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v 7 of 4.. h iflucs of ARR s horizotal positio o arth lctrod systm th vrtical dirctio, h uppr surfac of ARR is flat with th arth surfac. th horizotal dirctio, ARR i th ctr of arth lctrod ad 5m m 45m 6m 75m 9m away from it i x axis ar calculatd ad modld sparatly,umbrd from modl to modl 8. Ad modl is th cas of o ARRamly uiform soil. Surfac pottial distributio -D graph ad surfac pottial distributio curv a li which gos through th ctr of th circl arth lctrod ad is prpdicular to th log dg of th ARR of modl -8 udr soil structur with low rsistivity-arr5 Ω m ar sparatly listd i Figur a ad b. Figur shows th currt dsity distributio of modl -8. oclusios from figur a ar that, compard with that udr uiform soil coditios, th surfac pottial udr soil structur with low rsistivity-arr sigificatly rducs; f th positio of low rsistivity-arr is diffrt, dgr of surfac pottial amplitud rductio also is diffrt; Wh a part of th arth coductor is i low rsistivity-arr, rductio of surfac pottial is most obvious; Ad th mor a part of th arth coductor that is locatd i low rsistivity-arr is, th mor surfac pottial drops. For xampl, compard with that udr uiform soil coditio, th surfac pottial of modl 5 was dcrasd by.75%. As show i Figur b, th followig laws ca b obtaid: ompard with th uiform soil, th chagig trd of th pottial o th low rsistivity-arr is mor modrat; Wh th low rsistivity-arr is locatd i th rig of rig arth polamly modl to, th surfac pottial distributio curv is basically cosistt with that of modl ad oly flls by lss tha %, bsids, th pottial o low rsistivity-arr raiss. Bcaus th low soil rsistivity rgio has th ability to attract currt, ad th lowr th rsistivity is, th strogr th ability to attract currt is[]; Ad from Figur, bcaus th low rsistivity ara has th ability to attract currt, th currt dsity of ARR modl to is icrasd, so th pottial o ARR is icrasd. ompard with modl, Wh a part of th arth coductor is i low rsistivity-arramly modl 4 to 6, surfac pottial amplitud of modl 4 to 6 is sigificatly dcrasd ad flls by about %, bsids, th pottial o low rsistivity-arr raiss; h raso is that, th mor ARR is clos to th arth coductor, th mor currt it ca attract is, as show i figur. hrfor, th mor currt flows through th rgio with lowr rsistivity, which lads to th ovrall pottial dcrasig ad th pottial o ARR risig. Wh ARR is outsid th rig ad far away from th arth polmodl 7 to 8, th surfac pottial distributio curv is basically cosistt with that of modl ad oly flls by about %, ad th chagig trd of th pottial o ARR is mor modrat; W combi Figur to aalyz th raso. From it, th phomo of th low rsistivity-arr attractig currt modl 7-8 is still obvious; Howvr, compard with that of modl 4 to 6, th currt it attracts is lss, so low rsistivity-arr of modl 7 to 8 has littl ffct o th flowig capacity of th D arth lctrod. Which lads to th chag of th surfac pottial distributio of modl 7 to 8 is ot obvious, ad is almost coicidt with that udr uiform soil coditio a

8 Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v 8 of b Figur. surfac pottial distributio at diffrt horizotal positio of low rsistivity-arr a Surfac pottial distributio -D graph b surfac pottial distributio curv Figur. currt dsity distributio at diffrt horizotal positio of low rsistivity-arr Surfac pottial distributio -D graph ad surfac pottial distributio curv a li which gos through th ctr of th circl arth lctrod ad is prpdicular to th log dg of th ARR of modl -8 udr soil structur with high rsistivity-arr5 Ω m ar sparatly listd i Figur 4a ad b. Figur 5 shows th currt dsity distributio of modl to 8. oclusios from figur 4 a ar that, compard with that udr uiform soil coditio, th surfac pottial udr soil structur with high rsistivity-arr sigificatly rducs; f th positio of high rsistivity-arr is diffrt, dgr of surfac pottial amplitud ris also is diffrt; Wh a part of th groudig coductor is i high rsistivity-arr, icrasig of surfac pottial is most obvious; Ad th mor a part of th arth coductor that is locatd i ARR is,th mor surfac pottial riss. For xampl, compard with that udr uiform soil coditio, th surfac pottial of modl 5 was icrasd by 9.46%. As show i Figur 4 b, it is th surfac pottial distributio curv of modl to 8. h followig laws ca b obtaid: ompard with uiform soil, th chagig trd of pottial o

9 Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v 9 of th high rsistivity-arr is mor stp; Wh th high rsistivity-arr is locatd isid th rig of rig groudig polamly modl to, th surfac pottial distributio curv is basically cosistt with that of modl ad oly riss by lss tha %, bsids, th pottial o high rsistivity-arr drops. Bcaus th high soil rsistivity rgio has th ability to rjct currt, ad th highr th rsistivity is, th strogr th ability to rjct currt is[]. So th currt dsity of ARR modl to is dcrasd, ad th pottial o ARR gos dow. ompard with modl, wh a part of th arth coductor is i high rsistivity-arramly modl 4 to 6, surfac pottial amplitud of modl 4 to 6 is sigificatly icrasd ad riss by about %, bsids, th pottial abov high rsistivity-arr flls. W combi Figur 4 to aalyz th raso. From it, th rjctio of high rsistivity-arr to th currt is obvious, which lads to diffus capacity of arth coductor locatd isid th ARR wakig. t ca b quivalt to th ffctiv flowig lgth of th arth coductor bcoms shortr, so th whol surfac pottial is sigificatly icrasd; Bsids, th rjctio of high rsistivity-arr to th currt lads to th dcrasig of th currt dsity, so th surfac pottial o high rsistivity-arr drops. Wh ARR is outsid th rig ad far away from th arth polmodl 7 to 8, th surfac pottial distributio curv is basically cosistt with that of modl ad oly flls by about 6%, ad th chagig trd of th pottial o ARR is mor modrat; h raso is that, high rsistivity-arr is farthr from th arth coductor, so th rjctio of th currt is wakd. Which lads to th ffct of high rsistivity-arr o th whol lctric pottial distributio is small. a b Figur 4. surfac pottial distributio at diffrt horizotal positio of high rsistivity-arr a Surfac pottial distributio -D graph b surfac pottial distributio curv

10 Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v of Figur 5. currt dsity distributio at diffrt horizotal positio of high rsistivity-arr Earthig rsistac is a importat idx i D groudig dsig, so it is cssary for us to aalyz th arthig rsistac at diffrt horizotal positio of ARR. Figur 6 shows th arthig rsistac of low ad high rsistivity-arr at diffrt horizotal positio. As ca b s from th figur, wh th positio of ARR is diffrt, arthig rsistac is also diffrt. Showig arthig rsistac is dcrasd udr low rsistivity-arr, whil that is icrasd udr high rsistivity-arr; Wh a part of th arth coductor is i ARR, th chagig of arthig rsistac is biggst. ompard with that udr uiform soil, th arthig rsistac udr th soil coditio with low rsistivity-arr is dcrasd by 4.56%, whil it is icrasd by.58% udr th soil coditio with high rsistivity-arr. hus, th ifluc of ARR o arthig rsistac ca ot b igord. Espcially, stp pottial ad arthig rsistac ar both icrasd i high rsistivity-arr. hrfor, th ifluc of th low or high rsistivity-arr o th arth lctrod systm should b valuatd i th actual arth lctrod dsig. Figur 6. arthig rsistac of diffrt surfac abormal rsistac positio 4.. h ifluc of ARR s vrtical dpth o arth lctrod systm Du to th larg rag, dirct currt flowig i soil, th ifluc of dp soil structur o th D arth lctrod ca ot b igord. So it is cssary to aalyz th ifluc of ARR s vrtical dpth o lctric fild distributio. th cas of ARR locatd at a distac from th groud surfac to m, m, 4 m, 6 m, 8 m, m ad 5 m, th calculatio rsults, that is surfac pottial distributio of low rsistivity-arr ad high rsistivity-arr, show i Figur 7 ad figur 8. From

11 Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v of figur 7, th followig laws ca b obtaid: Wh low rsistivity-arr is locatd i diffrt vrtical dpth, ifluc dgr of it o th surfac pottial is diffrt; Espcially, wh th low rsistivity-arr is locatd i th surfac, th ifluc o th surfac pottial distributio is gratst. Wh it is locatd at a distac from th groud surfac to m, 4 m, 6 m, 8 m, m ad 5 m, surfac pottial distributio is slightly lowr tha that udr uiform soil. h raso is that th ability of low rsistivity rgio to attract currt maks th currt mor asily flowig ito low rsistivity-arr i th dpths of soil, so surfac currt dsity ad th surfac pottial is dcrasd. From figur 8, th ifluc of high rsistivity-arr at diffrt vrtical dpths o surfac pottial is diffrt; Particularly, wh ARR is locatd o th surfac of th arth, th ifluc is gratst; Wh it is locatd blow th groud m, 4 m, 6 m, 8 m, m ad 5 m, th surfac pottial distributio is slightly highr tha that udr uiform soil. Ad phomo of pottial ris o ARR is mor obvious. h raso is that th ability of low rsistivity rgio rjctig currt maks th currt maily gathrig i th ara o ARR, so currt dsity o ARR icrass, ad th th pottial riss. Figur 7. Surfac pottial distributio of low rsistivity-arr at diffrt dpths Figur 8. Surfac pottial distributio of high rsistivity-arr at diffrt dpths Figur 9 shows th arthig rsistac at diffrt ARR s vrtical dpths. hat ca b obtaid: ompard with th coditio of high rsistivity-arr, arthig rsistac udr soil with low rsistivity-arr is low. Wh th vrtical dpth of ARR is 5 m, th gap btw thm still is 9.4%; With th icras of th ARR s dpth, th arthig rsistac of thm will vtually td to b

12 Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v of stabl; ompard with th.57 Ω of th uiform soil, th arthig rsistac of low rsistivity-arr at th 5m vrtical dpth, is rducd by.%, ad th high rsistivity-arr is icrasd by.6%. t ca b kow that, wh th vrtical dpth of ARR is dpr, th ifluc o groud rsistac ca rach about %; t is cssary to survy th dp soil gological coditio at practical arth lctrod dsig. 5. oclusios Figur 9. arthig rsistac of ARR at diffrt dpths his papr stablishs fiit lmt modl of th D arth lctrod osidrig massiv ARR basd o shll thory. Ad aalyzs th ifluc of ARR at diffrt horizotal positios ad diffrt dpth o lctric fild distributio. h followig ruls ar obtaid: h mor ARR is clos to th arth coductor, th biggr ifluc of ARR o Surfac pottial is; Bsids, wh ARR is clos to th arth coductor, thr is a crtai ifluc o th whol surfac lctric pottial distributio; Howvr, wh ARR is far away from th arth lctrod, oly part surfac pottial distributio is affctd. h mor low rsistivity-arr is clos to th groud coductor, th mor obvious arthig rsistac is dcrasd; O th cotrary, th mor high rsistivity-arr is clos to th groud coductor, th mor obvious groud rsistac is icrasd. summary, th ifluc of ARR at diffrt horizotal positios ad diffrt dpth o D arth lctrod paramtrs ca ot b igord. th actual dsig, a dtaild survy o gological coditios of th polar sit ar th D arth lctrod should b do. osidrig massiv ARR, aalyzs th ifluc of ARR ar D arth lctrod o lctric fild distributio. Hop that coclusio of this papr ca provid rfrc for actual D arth lctrod dsig. Ackowldgmts: h authors wish to thak atioal atural Scic Foudatio of hia Grat o. 575 for thir fiacial support. Author otributios: Jigli Li, Liyig Guo cocivd ad dsigd th simulatios; Liyig Guo ad Yuabo Li prformd th simulatios; all authors aalyzd th data; Jigli Li, Liyig Guo wrot th papr, whil othr authors offrd thir modificatio suggstios for th mauscript. oflicts of trst: h authors dclar o coflict of itrst. Rfrcs. H, J.L.; Zg, R. Groudig tchology of lctric powr systm. Scic Prss: Bijig, hıa, 7.. Liag, X.M.; Zhag, P; hag, Y. Rct Advacs i High-Voltag Dirct-urrt Powr rasmissio ad ts Dvlopig. Pottial pwr. sys. ch., 6, -9.

13 Prprits O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v of. Rao H.; Lı Y. Study o Four HVD Systms Sharig a ommo Groud Elctrod. High Vol. Eg. 5, 4, Zhao J.; H J.L. Aalysis o th commo groudig lctrodmod for UHVD ad HVD powr trasmissio systms. Elc. Pwr. 7, 4, Yua ao.; Luo L.; Yag Q.; Sıma W.X.; Wag J.D. Aalysis o th mpratur haractristic of Soil ad ts fluc oth irqu Groudig Elctrod Hatig. Proc. SEE.,, Zhag.; a X.R.; Huag Y.H. Aalysis o rasit mpratur Ris of UHVD ommo Groudig Elctrod. High Vol. Eg. 5, 4, Du H.Z.,W X.S. st ad Simulatio for Horizotal Groud Elctrod s mpratur Ris. High Vol. Eg., 9, Wag Y.; Lı X.P. st ad omputatio for Vrtical Groud Elctrod s rasit mpratur Ris. Proc. SEE.,, Wag X.X.; Rua L.;W X.S.; Qua Y.. haractristics Aalysis of D-bias urrts osidrig Dp-arth Rsistivity. High Vol. Eg. 5, 4, hı X.H.; Zhag Y.J. Protctiv Distac btw HVD Elctrod ad Udrgroud Mtal Pipli. Pwr. Sys. ch. 8,, -5.. Rua L.; Qua J..; Yag X.K. fluc of Dp Earth Rsistivity o Dirct urrt Distributio i A Powr Grid. High Vol. Eg. 4, 4, Fu Z.X.; a H.D.; Lıu H.F. Pottial umrical Simulatio ad Aalysis of flucig Factors oforoidal HVD Groudig Elctrod. Pwr. Sys. ch. 6, 4, Ma J.J. Groud Pottial Distributio of HVD Groud Elctrod osidrig ctoics.mastr's thsis, orth hia Elctric Powr Uivrsity, Bijig, hia,. 4. Li L. Shll vctor lmts basd umrical mthods for lctromagtic scttrig. PH.D. thsis, Uivrsity of Elctroic Scic ad tchology, hgdu, hia,. 5. E. Abius,F. Edlvik.hi Sht Modlig Usig Shll Elmts i th Fiit-Elmt im-domai Mthod. EEE ras. At. Propag., 6, 54, Li L.; Hu J.; Hu H.Q. Solvig Scattrig from oductig Body oatd by hi-layr Matrial by Hybrid Shll Vctor Elmt with Boudary tgral Mthod. tl. J At. Propag., pp: Li J.L.; Jiag J.D.; Li L.L. Simulatio ad Exprimt Study o Rsistac-Rducig Mchaism of Groudig Dvic With Spiculs. Pwr. sys. ch., 7, Zhag L.; Su L. Paramtric omputatio ad Masurmt of Jiagchg HVD Groudig Elctrod. Hubi lctric powr, 5, 9, by th authors. Lics Prprits, Basl, Switzrlad. his articl is a op accss articl distributd udr th trms ad coditios of th rativ ommos by Attributio -BY lics