POWER LOSSES IN THE THREE-PHASE GAS-INSULATED LINE

Transcription

1 OZNAN UNVE STY OF TE CHNOLOGY ACADE MC JOUNALS No 89 Elctrical Egirig 7 DO.8/j Tomasz SZCZEGELNA Dariusz USA Zygmut ĄTE OWE LOSSES N THE THEE-HASE GAS-NSULATED LNE This papr prsts a aalytical mtho for trmiig th powr losss i th thr phas gas isulat li i.., high-currt usuct of circular cross sctio gomtry which phas couctors ar plac i vrtx of a squar. Th mathmatical mol taks ito accout th ski ffct a th proximity ffcts, as wll as th complt lctromagtic couplig tw phas couctors a closurs i.., scrs. Th powr losss prouc y high-currt usucts ar usually calculat umrically with th us of a computr. Howvr, th aalytical calculatio of th powr losss is prfral, caus it rsults i a mathmatical xprssio for showig its pcs o various paramtrs of th li arragmt. Morovr, kowlg of th rlatios tw lctroyamics a costructioal paramtrs is cssary i th optimizatio costructio procss of th high-currt usucts. EYWODS: high-currt usuct, lctromagtic fil, powr losss. NTODUCTON Followig th vlopmt of thrmal a hyrolctric powr statios, at th giig of th s, high-currt trasmissio lis with scr usucts coctig ig grators with uit trasformrs ga to istall. Du to th cssity of trasmittig powr comig highr a highr, a to th viromtal protctio rquirmts, th lgth of th li was to a fw kilomtrs [ 9]. t is stimat that util ow th lgth of th xistig lis of that typ has ot surpass km. GLs us for high powr trasmissio hav scri svral tims,.g. i fs. [, 5, 6, 8, 9, ]. Th gas most oft us for isulatio is SF 6 sulphur hxafluori whos prssur valus rag from.9 to.5 Ma at C. ctly, SF 6 has rplac with th 95% mixtur of itrog N a 5% of SF 6 of. Ma prssur, or with a 9% mixtur of itrog N a % of SF 6 of.9 Ma prssur, as wll as with a 8% Częstochowa Uivrsity of Tchology.

2 9 Tomasz Szczgiliak, Dariusz usiak, Zygmut iątk mixtur of itrog N a % of SF 6 of.7 Ma prssur corrspoig to th. Ma prssur i th cas wh pur SF 6 is us [,,,, 5, 8, 9]. Th cotmporary solutios cosist of trasmissio lis isulat with air at atmosphric prssur, with uty-rat voltag valus rachig up to 6 kv a uty rat currt valus rachig up to: ka for hyrolctric powr plats, ka for thrmal a uclar plats whos uty rat powr valus rach up to 9 MW,.5 ka for uclar plats with powr valu of MW [,,, 5, 8, 9]. Toay high currt usucts ar appli i may projcts arou th worl wh high powr trasmissio of high rliaility a maximum availaility is rquir. Th sizs of w projcts ar costatly icrasig: from som hur mtrs to svral kilomtrs [,,, 5, 9]. Th costructio a assmlig mthos of GL laorat rctly mak it possil to uil trasmissio lis ovr th grou a i urgrou tuls or irctly i th grou. Urgrou GL, ig larg powr trasmissio lis, ar most commoly uilt i aras with s hous-wllig whr rquirmts cocrig safty a viromtal protctio ar vry strict. Th sig of th usucts us for high currts a voltags rquirs th prcis aalysis of lctromagtic, yamic a thrmal ffcts. owlg of th rlatios tw lctroyamics a costructioal paramtrs is cssary i th optimizatio costructio procss of th high-currt usucts [ 9]. owr losss p o valu of currts, a for th larg cross-sctioal imsios of th phas couctor, v at iustrial frqucy, ski, xtral Fig. a itral Fig. proximity ffct shoul tak ito accout [, 9]. J J Fig.. Ey currts iuc i th scr y th magtic fil of th ow currt of th phas couctor Th most popular solutio of th high currt usucts ar symmtrical or flat [, 9]. this papr th aalytical calculatios of th powr losss i th high currt usuct which phas couctors ar plac i vrtx of a squar will prst Fig..

3 owr losss i th thr-phas gas-isulat li 9 x z Xr,Θ r Θ J H w y J μ γ Fig.. Ey currts iuc i th scr y th magtic fil of th ighorig phas couctor μ L L L μ μ Fig.. Thr-phas high-currt usuct which phas couctors ar plac i vrtx of a squar rst i th figur systm of tuular couctors is th most oft istall wh symmtrical or flat high-currt usuct ca ot us. This situatio appars i th arrow tuls, shafts, cal ucts Fig..

4 9 Tomasz Szczgiliak, Dariusz usiak, Zygmut iątk Fig.. High currt usuct i th powr plat. prouc y prmissio of Holuct Lt []. ELECTOMAGNETC FELD Lt us cosir th lctromagtic fil i a thr-pol high-currt usuct prst i th Fig.. Usig th Laplac s a Hlmoltz s quatios w ca trmi th lctromagtic fil i th couctors a th scrs [, 9]. Th total currt sity i th first scr is a sum of currts iuc y ach couctor, that is to say J r, Θ J r, Θ J r, Θ J r, Θ J r, Θ J r, Θ For th positiv squc of currts, i.. xp[ j π] a xp[j π ] th currt sity J r, Θ is fi y Eq. i which J r r c r j r whr c whras currt sity J r, Θ ca xprss as follows a c J r, Θ J r, Θ J r, Θ D f r

5 owr losss i th thr-phas gas-isulat li 9 whr π D xp- j π cosθ xp j π cosθ a a r r f r Th currt sity i th sco scr ar fi y Eq. rspctivly, i which currt shoul rplac with a costat D with costat π G xpj π cosθ xp- j π cosθ 5 Formulas for scr ar otai i th sam way y rplacig a D, rspctivly, with a π π M xp- j π cosθ xp j π cosθ 6 th aov formulas, r, r, r, r, r, r, r, r, r a r ar th moifi Bssl s fuctios of orr,,, a +, calculat for r a r [], a th complx propagatio costat of lctromagtic wav i th scr quals π j μ μ xp[j ] k j k j k 7 with th attuatio costat μ k 8 whr δ is th lctrical ski pth of th lctromagtic wav ptratio ito th couctig viromt, is th agular frqucy, stas for th 7 - couctivity of th scr, a μ H m is th magtic prmaility of th vacuum. si th phas couctors r of th high currt usuct th currt sity quals [, 9] r r J r 9

6 9 Tomasz Szczgiliak, Dariusz usiak, Zygmut iątk Th complx propagatio costat i th couctors is is th couctivity of th phas couctor.. OWE LOSSES j μ, a owr losss i th thr-phas gas-isulat lis ca trmi with oytig thorm. But if w us oytig thorm, w ca ot isolat th ral part as a activ powr a th imagiary part as a ractiv powr. t is har o accout of th complx propagatio costat a complx moifi Bssl s fuctios. Thrfor, th activ powr powr losss will calculat from Joul-Lz law [,, 9]: V J r J r V owr losss i th couctors of th sigl pol high currt trasmissio li prst i th figur ar xprss y formula: l a C i which a j - j j a j c tur, powr losss i th outr scrs a ar th sam a ca writ ow as follows: whr l a π γ

7 owr losss i th thr-phas gas-isulat li 95 i which j j c j j c j j c c j j a a c c a a l whr j j - j a a c owr losss i th first scr ar 5 whr a l 6

8 96 Tomasz Szczgiliak, Dariusz usiak, Zygmut iątk. NUMECAL EXAMLE Bas o th riv formula, th powr losss i th high currt trasmissio lis pict i figur wr calculat. Accorig to th otatio appli i figur, th followig gomtry of th usuct has slct: = mm, = mm, = 5 mm, = mm, = 6 mm. Both th phas couctors a th scr ar ma of alumiium, which has a lctric couctivity of γ = MS m. Th frqucy is 5 Hz. Currts i th phas couctors ar = A, xp[ j π] A, xp[j π ] A. Th lgth of th usuct systm is assum to l = mm. Th rsults of th calculatios ar show i Tal. Apart from aalytical calculatio, computr simulatios for high currt usuct systm powr losss wr also prform with th ai of th commrcial FEMM softwar [], usig two-imsioal fiit lmts. Figur 5 shows th computatioal fiit lmt msh for sigl-pol highcurrt trasmissio li. Fig. 5. Th fiit lmt msh us i FEMM computatios 5. CONCLUSONS A aalytical approach to th solutio of th powr losss i th thr-phas high-currt usuct has prst i this papr. Th propos mtho allows us to calculat th powr losss i a st tuular usars. Th

9 owr losss i th thr-phas gas-isulat li 97 mathmatical mol taks ito accout th ski ffct a th proximity ffcts, as wll as th complt lctromagtic couplig tw phas couctors a scrs. To vrify th aalytical formula w prform computatios y mas of th fiit lmt mtho. As tal shows, th powr losss calculat o th asis aalytical formula a powr losss trmi y FEMM softwar ar almost th sam spcially for phas couctors. gral, th rlativ rror os ot xc % for cosir usuct. t is otical that th aalytical calculat valus ar slightly smallr tha th comput os. Th icras valus proaly com from that i th aalytical mol, phas couctors ar cosir as a systm of paralll filamts. Tal. owr losss of th thr-phas gas-isulat li gio Aalytical FEMM calculatio computatios has L 7.7 W 7.7 W has L 7.7 W 7.9 W has L 7.7 W 7.5 W Scr.89 W 78. W Scr W 97.7 W Scr W.7 W A aalytical mtho prst i th papr ca us oly for circular high currt usucts. But umrical mtho ca us almost for all typs of usucts. th papr usig th Joul-Lz law th activ powr powr losss i th thr-phas high-currt usuct wr trmi. Usig th oytig thorm w ca trmi appart powr. O th asis of trmi activ a appart powr from oytig thorm w ca trmi th ractiv powr mitt i th phas couctors a scrs of th thr-phas high-currt usucts. But w shoul a that ractiv powr trmi from oytig thorm is coct with itral iuctacs of th scrs a phas couctors. EFEENCES [] Nawrowski.: Tory wilkoprąow izolowa powitrzm lu SF 6. Wy. ol. ozańskij, ozań 998. [] iątk Z.: mpacs of high currt usucts. Wy. ol. Częst., Czstochowa 8.

10 98 Tomasz Szczgiliak, Dariusz usiak, Zygmut iątk [] Bark., Nawrowski., Tomczwski A.: Trójfazow tory wilkoprąow złożo z przwoów rurowych w iywiualych osłoach. XV Symp. TZE, yzya 7, str.. [] CGE TB 8.: Gas sulat Trasmissio Lis GL, CGE, aris, Frac,. [5] CGE TB 5.: Applicatio of Log High Capacity Gas sulat Lis GL, CGE, aris, Frac, 8. [6] och, H.: Gas sulat Trasmissio Lis GL. Joh Wily & Sos,. [7] iątk, Z.; Slf a mutual impacs of a fiit lgth gas isulat trasmissio li GL. Elctric owr Systms sarch, 7, 77, 9. [8] Sarajcv,.; Numrical Aalysis of th magtic fil of High Currt Busuct a GL Systms. Ergis,, 96. [9] Szczgiliak, T. owr Losss of th Scr a Uscr Tuular High Currt Busuct. Doctoral, Silsia Uivrsity of Tchology, Gliwic. [] Holuct Lt. Thr phas usuct; ola Availal oli: [] Mc Lachla N.W.: Bssl fuctios for girs i olish..; WN, Warsaw 96. [] Mkr, D.C., Fiit Elmt Mtho Magtics, vrsio. apr, Mathmatica Buil, civ: 6.. 7, rvis: 5.. 7