Available online at ScienceDirect. Energy Procedia 50 (2014 ) 64 70
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1 Avill onl SccDirc Enrgy Procdi 5 (214 ) 64 7 T nrnionl Confrnc on Tcnologis nd Mrils for Rnwl Enrgy, Environmn nd Susiliy, TMREES14 nducd Ligng Disurncs Ovrd Sildd Cls Modlg y Currn Gnrors Mosf. Boumi, Djml. Ld Lorory of Elcricl Engrg Consn Dprmn of Elcricl Engrg culy of Scc nd Tcnology nivrsiy Consn1, musp_oumi@yoo.fr, Algri Lorory of Elcricl Engrg Consn Dprmn of Elcricl Engrg culy of Scc nd Tcnology nivrsiy Consn1, djml_ld@yoo.fr, Algri Asrc n is work w sudy couplg of ligng wv wi ovrd sildd cls. Tis sudy llows us o dduc currns nd volgs ducd cross nds of cl dircly. n our work, w propos o rprsn lcromgnic ciion disriud long cl locd nod (nd or juncion) gnror. Tis pproc will ld us o rduc nlysis of couplg of n ojc illumd y ligng wv prolm of n cid simulnously y svrl gnrors disposd on ll nods of cl. Currns nd volgs ducd on ll nods of cl sll dducd y simpl rsoluion of sysm of lr quions. 214 Elsvir Ld. Tis is n opn ccss ricl undr CC BY-NC-ND licns 214 T Auors. Pulisd y Elsvir Ld. Slcion (p://crivcommons.org/licnss/y-nc-nd/3./). nd pr-rviw undr rsponsiiliy of Euro-Mdirrnn nsiu for Susl Dvlopmn (EMSD). Slcion nd pr-rviw undr rsponsiiliy of Euro-Mdirrnn nsiu for Susl Dvlopmn (EMSD) Kywords: ligng; lcromgnic fild; lcromgnic couplg; sildd cl; volg ducd; currn sourc. 1. nroducion T nducd volgs y ligng srik on n ovrd l or lcommunicions cl cn cus dmg, s wll s lcronic powr nwork moniorg nd conrol nworks nd rnspor. n ddiion, cus of ir grr likliood of occurrnc, dirc ligng srik is mor imporn cus rownous dirc rds. Tis work ims o crcri volg nd currn surgs ducd y ligng wv on ls nd ovrd cls fr lcromgnic couplg. n is work w r couplg wn lcromgnic fild of ligng wic prssions r givn y [1] nd sildd cl nd usg Tylor modl [2], w driv sysm of lr quions, wic rsoluion llows us o dduc lcricl vrils ducd c nod of cl. 2. ormlism of couplg vi rnsfr impdnc Considr sildd cl, comprisg n prlll nr conducors, locd ig ov ground, s sown igur 1. T wir is illumd y n rnl lcromgnic fild. [1] Elsvir Ld. Tis is n opn ccss ricl undr CC BY-NC-ND licns (p://crivcommons.org/licnss/y-nc-nd/3./). Slcion nd pr-rviw undr rsponsiiliy of Euro-Mdirrnn nsiu for Susl Dvlopmn (EMSD) doi:1.116/j.gypro
2 Mosf. Boumi nd Djml. Ld / Enrgy Procdi 5 ( 214 ) E H Sildg rnl conducors y ig.. 1 Configurg sildd muliconducor cl Ernl sysm Equions coupld o rnl circui cn wrin: d d Y Z wr: Z, Y r impdnc nd dminc pr uni lng own rnl l; (), r rspcivly volg nd currn ovr sild; - j By(, )d E (,) (2) -Y E(, )d (3) T soluion nd is givn y followg quion [3]: (1) ( ) (), ( ) T ( ) (4) ( ) () ( ) T, Wr ol forcd funcions r: T, ( ) 11, ( ). E (, ) d E (, ) d 11, ( ). E (, ) d (5), ( ) 21, ( ). E (, ) d 21, ( ). E (, ) d (6) T igur 2 sows quivln digrm of rnl l cid y n rnl fild wic is rprsnd y wo currn gnrors.
3 66 Mosf. Boumi nd Djml. Ld / Enrgy Procdi 5 ( 214 ) 64 7 Ousid sildg () s1, () ( ) s2, ground = ig.. 2 Equivln modl of rnl l cid y n rnl fild. Tis qudrupol rprsnion, figur 2, w cn wri: ( ) ( ) () ( ) (7) ( s1, s2, ) Comprg wo sysms (4) nd (7), w dduc prssions of wo currn gnrors [1]: 1 s1, ( 11, ( ). E (, ) d E (, ) d 11, ( ). E (, ) d) ( ) s2, 12, ( ). E 21, 22, 12, ( ) ( ( ) 11, ( ). E (, ) d 21, (, ) d E (, ) d ( ). E (, ) d 11, ( ). E (, ) d T oundry condiions ) Z () (1) ( (8) (9) ( ) Z ( ) (11) nrnl sysm Equions coupld o rnl circui my wrin: d d ) ) Z Y ) ) ( ( Z ( ) ( ( Wr: Y Ar rspcivly squr of ordr n impdnc nd dminc mrics lr own rnl l; Z,, r compl vcors of ordr n volgs (ol) nd ol currn long nr conducor. () is disriuion of currn long cl sild. Z is lr rnsfr impdnc givn y [6]. (12)
4 4 Mosf. Boumi nd Djml. Ld / Enrgy Procdi 5 ( 214 ) dv Z (13) d Wi:, V r currn nd rnl volg rspcivly; Disriuions of currn () nd volg () r clculd nlyiclly s follows [1]: () ( ) ( ) (14) d () ( ) Anlogously, nd from rlionsip (12) mnnr, rnl circui cn sn s muliconducor rnsmission l cid y fild qul o Z () wic cn convnionlly rprsnd y four-pol crcrid y followg rlionsips: Wr: () ( ) () ( ) T, ( ) (15) ( ) T, ( ) ( ) ( ). Z T, 11, ( ) d (16) ( ) ( ). Z T, 21, ( ) d (17) Now if w wn o rprsn cimn of rnl l wi currn gnrors nds of c nr conducor, w v: n is rprsnion, w cn wri: ( ) ( ) nrnl conducors nsid sildg [ ()] () ( s1, [ s1, ] () [ s2, ] = ig. 3. Equivln modl of rnl l. [ ( )] ( ) (18) s2, ) Comprg wo sysms (15) nd (18) w dduc prssions of currn gnrors: 1 s 1, 12, ( ) 11, ( ). Z ( ) d (19) 1 ( ) ( ) ( ). Z s2, 22, T oundry condiions r wrin: 12, 11, ( ) d (2)
5 68 Mosf. Boumi nd Djml. Ld / Enrgy Procdi 5 ( 214 ) 64 7 ( ) Z () ( ) Z ( ) (21) T currn gnrors y modlg rspons of nwork of sildd cls illumd y n lcromgnic wv r dvlopd wo sgs. T firs sp volvs rg rnl sysm (consisg of silds) dircly cid y lcromgnic wv, nd scond sp for nr sysm cid roug rnsfr impdnc. is rfor o solv wo disc lr yp [A] [X] = [B] sysms. T modology rms sm consruc is compriss mri [A] nd vcor [B] c sp. 3. Rsuls nd discussions W considr n ril cl 1km long ig of 1m ov ground fi conduciviy s =.1S / m nd illumd y rdid y ligng cnnl of 7.5km lcromgnic wv, po impc is considrd symmricl o nds nd disnc of 5m from cl, usg MTL modl [4] for rurn rc wr dcy r = 2km wi ypicl vlu of v = m / s, wi currn s of cnnl is sum of wo funcions Hidlrs [5] for currn s of cnnl wi d Tl 1. Tl 1. Ligng prmrs. 1 (ka) 11 (s) 21 (s) n 1 2 (ka) 12 (s) 22 (s) n (22) Currn(K A) Tim(s) ig. 4. () currn s of cnnl,() currn s of cnnl [7].. T rsul w o for currn s of cnnl is confirmd y civd y Nucci l. [7]. As firs vlidion, w considr cs of sildd cl s wo lyrs (cor sild) nd r lyrs (cor, scrn nd sildg). E Z c A B sildg scrn soul B Z c 5m 5m impc 1m ground ig. 5: Gomry conidéré.
6 Mosf. Boumi nd Djml. Ld / Enrgy Procdi 5 ( 214 ) Gomric nd pysicl d sildd cl usd r: : r s =.45mm ; r si = 1.475mm; s = 18 S / m ; rsi =1.8 ; r = ri =1 Scrn: r sc = 1.775mm; r sci = 2.475mm; sc = S / m; rsci = 1; r = ri = 1 Sildg: r s = 2.775mm; r si = 3.475mm; s =.33.18S / m; rsi = 1; r = ri = Sildg Sildg nducd volg(v) 25 nducd currn(a) Tim(s) Tim(s) ig. 6. () volgs ducd rmiy A, () ducd currn rmiy A.. 8 Scrn Sildg 1 Scrn Sildg nducd volg(v) 2 nducd currn(a) Tim(s) Tim(s) 6 ig. 7. () volgs ducd rmiy A, () ducd currn rmiy A Ponil difrnc(v) 2 Ponil difrnc(v) Tim(s) Tim(s) ig.8. () ponil diffrnc rmiy A for wo lyrs, () ponil diffrnc rmiy A for r lyrs.
7 7 Mosf. Boumi nd Djml. Ld / Enrgy Procdi 5 ( 214 ) 64 7 T rsuls w g, iglig currn vriion ovr souls ( nr lyr ) rspcivly for cl wi wo lyrs nd r lyrs, clrly sow cl wi conduciv scrn is r procd, ffc on currn soul of lr is muc lowr n of cl wi wo lyrs ( i wiou disply). Tis imporn osrvion is confirmd y nuion of lcromgnic wvs conducg mdi wi disnc. Anor rsul is lso vry imporn w g for currn on sild, sild currns r lmos sm, wic is consisn wi pproc of rnsfr impdnc [7] wic llows us o ssr couplg of lcromgnic wv wi rnl sysm (sild-ground ) is dpndn of rnl sysm ( soul - sildg). T wo rmrks: Rducion of currn on cl cor r lyrs. T non-dpndncy of currn on sild (ls lyr) of lyr numr of cl. Allow us o confirm vlidiy of our modl. 4. Conclusion Tis work is procssd for purpos of couplg ligng wv wi n ovrd cl. or clssic mod poss prolm ssocid wi cumrsom digil spil discriion nd clusion of lcricl condiions nds nd juncions nods. T formlism w propos ovrcoms spil discriion kg o ccoun lcromgnic ssul long c conducor nd lcricl condiions nds. T priculr rs of is formlism is i llows us o dduc gnrg volgs ducd cross nds of msd nwork dircly. Tis dvng mks i possil o n sudy ffc of disurnc on dirc lcricl dvics ms nwork. Tis formlism s cr dvng rms of compuion im viw. Rfrncs [1] M.A. mn, D. Knn Mc L nd E. Pilip Kridr, "T ls Pr, Elcr, 1995, (161) pp Elcromgnic rdiion from fi nnn". Amricn Journl Pysics, Vol.43/33,pp.33-38, Jnury [2] C. D. Tylor, R. S. Srwi, W. Jr. Hrrison, T Rspons of Trmd Two- WirTrnsmission L Ecid By Nonuniform Elcromgnic fild, EEE Trns. On Annns nd propgion vol.ap-13, pp , [3] A. Nucci, C. Mi,. Rcidi, M. no, On Clculions Proc. 19 nrnionl Confrnc on Ligng Procion, Gr, [4]. Hidlr, Anlyisc Blisrom-unkion ur LEMP- Brcnung, Ppr 1.9, pp , Munic, Spmr 16-2, [5] P. Dguqu, J Hml,"Compiilié Elcromgnéiqu, Bruis Prurions rdioélcriqus", Collcion Tcniqu Scifiqu ds Télécommunicions. Ediion Dunod, Pris199. [6] C.A. Nucci Ligng-nducd Ovr Volgs on Ovrd Powr Ls. Pr 1: Rurn- Srok Currn Modls wi Spcifid Cnnl- Bs Currn for Evluion of Rurn- Srok Elcromgnic ild, Cigré ppr prprd wi frmwork of sk orc of CGRE workg Group 33.1,1994.Elcr N 161, Augus 1995.
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