Computr Applicatios i Elctrical Egirig Vol. 3 5 Aalysis of th powr losss i th thr-phas high-currt busucts Tomasz Szczgiliak, Zygmut Piątk, Dariusz Kusiak Częstochowa Uivrsity of Tchology 4- Częstochowa, ul. Brzźicka 6a, -mail: zygmut.piatk@itria.pl, ariuszkusiak@wp.pl, szczgiliakt@itria.pl This papr prsts a aalytical mtho for trmiig th powr losss i th thr-phas gas-isulat trasmissio li (i.., high-currt busuct) of circular crosssctio gomtry. Th mathmatical mol taks ito accout th ski ffct a th proximity ffcts, as wll as th complt lctromagtic couplig btw phas couctors a closurs (i.., scrs). Apart from aalytical calculatio, computr simulatios for high-currt busuct systm powr losss wr also prform with th ai of th commrcial FEMM softwar, usig two-imsioal fiit lmts. KEYWORDS: high-currt busuct, powr losss, lctromagtic fil. Itrouctio Followig th vlopmt of thrmal a hyrolctric powr statios, at th bgiig of th 3s, high-currt trasmissio lis with scr busucts coctig big grators with uit trasformrs bga to b istall. Du to th cssity of trasmittig powr bcomig highr a highr, a to th viromtal protctio rquirmts, th lgth of th li was to b a fw kilomtrs [-]. It is stimat that util ow th lgth of th xistig lis of that typ has ot surpass km. Th gas most oft us for isulatio is SF 6 (sulphur hxafluori) whos prssur valus rag from.9 to.5 MPa (at C). Rctly, SF 6 has b rplac with th 95% mixtur of itrog N a 5% of SF 6 of.3 MPa prssur, or with a 9% mixtur of itrog N a % of SF 6 of.94 MPa prssur, as wll as with a 8% mixtur of itrog N a % of SF 6 of.7 MPa prssur corrspoig to th.4 MPa prssur i th cas wh pur SF 6 is us [8-]. Th cotmporary solutios cosist of trasmissio lis isulat with air at atmosphric prssur, with uty-rat voltag valus rachig up to 36 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, 3.5 ka for uclar plats with powr valu of 3 MW [8-]. Toay high-currt busucts ar appli i may projcts arou th worl wh high-powr trasmissio of high
T. Szczgiliak, Z. Piątk, D. Kusiak / Aalysis of th powr losss i... rliability a maximum availability is rquir. Th sizs of w projcts ar costatly icrasig: from som hur mtrs to svral kilomtrs [8-]. Th most popular shil thr-phas high-currt busucts ar pict i Figur a. Fig.. Thr-pol high-currts busuct [] Fig.. Sigl-pol high-currts busuct [] Powr losss p o valu of currts, a for th larg cross-sctioal imsios of th phas couctor, v at iustrial frqucy, ski, xtral (Fig. 3) a itral (Fig. 4) proximity ffct shoul b tak ito accout [-7].. Powr losss Th lctromagtic fil a th powr losss prouc by high-currt busucts ar usually calculat umrically with th us of a computr [9,]. Howvr, th aalytical calculatio of ths paramtrs is prfrabl, bcaus it rsults i a mathmatical xprssio for showig its pcs o various paramtrs of th li arragmt [-8].
T. Szczgiliak, Z. Piątk, D. Kusiak / Aalysis of th powr losss i... 3 μ μ μ L L L 3 R R R 3 R 4 Fig. 3. Sigl-pol thr-phas high-currt busuct Usig th Laplac s a Hlmoltz s quatios w ca trmi th lctromagtic fil i th couctors a th scrs for sigl a thr-pol high currt busucts [, ]. I th cas of thr-phas sigl-pol high-currt busuct show i Figur 3 th powr losss i th phas couctors is [7] Γ l I a P L () 4 R b b I tur, powr losss i th outr scrs ( a 3 ) ar th sam a ca b writ ow as follows: Ps 3 P P 3 () whr P 3 P Γ l I a (a) 4 π γ R 4 Γ l I R4 a A R4 b b (b) i which A j 3 (c) Powr losss i th mil scr ( ) ar Ps P P (3) i which a P Γ l I R4 a B R4 b b (3a) 3
T. Szczgiliak, Z. Piątk, D. Kusiak / Aalysis of th powr losss i... j 3 B (3b) y X μ γ r X3 r I 3 3 r X Θ γ r X I J γ R x R I γ R 4 R 3 Fig. 4. Thr-pol thr-phas high-currt busuct For th thr-pol high-currt busuct (pict i th Figur 4) th powr losss of th phas couctors ar th sam a ca b writ ow as follows [3]: PL 3 PL P 3 (4) whr Γ l I R a D Θ R b b P3 (4a) a D xp- j cosθ xp j cosθ (4b) 3 3 3 Powr losss i th scr of th thr-pol high-currt busuct (prst i th figur 4) ar xprss by formula [3] Γ I R4 9 a π R3 R3 l Ps (5) Paramtrs a, a, a, a, a, b, b, b,, ar xprss by Bssl s fuctios a prst i th paprs [-7], but th complx propagatio costat of lctromagtic wav i th couctor quals π Γ j μ μ xp[j ] k j k j k (6) 4 with th attuatio costat 4
T. Szczgiliak, Z. Piątk, D. Kusiak / Aalysis of th powr losss i... μ k (7) whr δ is th lctrical ski pth of th lctromagtic wav ptratio ito th couctig viromt, is th agular frqucy, stas for th couctivity of couctor, a μ prmability of th vacuum. Th complx propagatio costat i th scr is th couctivity of th scr. 7-4 H m 3. Numrical xampl is th magtic Γ j μ, a is Bas o th riv formula, th powr losss i th high-currt busuct pict i Figur 3 a 4 wr calculat. Calculatios wr ma for highcurrt busucts prouc by Holuct (for mols: EHON-/ a HOIO-4/). Accorig to th otatio appli i Figur 3, th followig gomtry of th busuct has b slct: R = 3 mm, R = 4 mm, R 3 = 3 mm, R 4 = 4 mm, = 64 mm. For th busuct pict i figur 4, th gomtrical paramtrs ar: R = 3 mm, R = 4 mm, R 3 = 3 mm, R 4 = 4 mm, = mm. Both th phas couctors a th scr ar ma of alumiium, which has a lctric couctivity of γ = 35 MS m. Th frqucy is 5 Hz. Th lgth of th busuct systm is assum to b l = m. Currts i th phas couctors ar I xp[ j ] A, I xp[ j π] A, I 3 xp[j π] A. Th 3 3 rsults of th calculatios ar show i Tabls a. Tabl. Powr losss of th thr-pol high-currt busuct pict i Figur 4 Mtho P (W) L L L 3 Scr Aalytical 53.447 53.447 53.447 64.9 FEMM 565.78 565.4 565.37 48.88 Apart from aalytical calculatio, computr simulatios for high-currt busuct 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 thr-pol highcurrt busuct. 5
T. Szczgiliak, Z. Piątk, D. Kusiak / Aalysis of th powr losss i... Tabl. Powr losss of th sigl-pol high-currt busuct pict i Figur 3 Mtho L L L 3 P (W) Scr Scr Scr 3 Aalytical 538.38 538.38 538.38 44.789 7.664 44.789 FEMM 546. 546.5 546.79 43.887.65 4.67 6 Fig. 5. Th fiit lmt msh us i FEMM computatios 4. Coclusios A aalytical approach to th solutio of th powr losss i th thr-phas high-currt busuct has b prst i this papr. Th propos mtho allows us to calculat th powr losss i a st tubular busbars. Th mathmatical mol taks ito accout th ski ffct a th proximity ffcts, as wll as th complt lctromagtic couplig btw phas couctors a scrs. To vrify th aalytical formula w prform computatios by mas of th fiit lmt mtho.
T. Szczgiliak, Z. Piątk, D. Kusiak / Aalysis of th powr losss i... As Tabls a show, th powr losss calculat o th basis aalytical formula a powr losss trmi by FEMM softwar ar iffrt both for sigl-pol a thr-pol high-currt busuct. Ths iffrcs coul b caus scarc of th fiit lmt msh us i FEMM computatios. A aalytical mtho prst i th papr ca b us oly for circular high-currt busucts. But umrical mtho ca b us almost for all typs of busucts. Rfrcs [] Nawrowski R.: Tory wilkoprąow izolowa powitrzm lub SF 6. Wy. Pol. Pozańskij, Pozań 998. [] Piątk Z.: Impacs of high-currt busucts. Wy. Pol. Częst., Czstochowa 8. [3] Szczgiliak T.: Straty mocy w ikraowaych i kraowaych rurowych torach wilkoprąowych, Praca Doktorska, Gliwic,. [4] Piątk Z., Szczgiliak T., Kusiak D.: Powr losss i th scrs of th symmtrical thr phas high currt busuct, Computr Applicatios i Elctrical Egirig. E. by Ryszar Nawrowski, Pozań. [5] Piątk Z., Szczgiliak T., Kusiak D.: Wpływ zwętrzgo zjawiska zbliżia a straty mocy w trójfazowym płaskim torz wilkoprąowym, XVI Cofrc Computr Applicatios i Elctrical Egirig, s 5-6 Pozań. [6] Piątk Z., Szczgiliak T., Kusiak D.: Straty mocy w kraach trójfazowgo jobiguowgo toru wilkoprąowgo, Elctrical Egirig, Iss.73, s.9-98, 3. [7] Szczgiliak T., Kusiak D., Jabłoński P., Piątk Z.: Powr losss i a thrphas sigl-pol gas-isulat trasmissio li (GIL), Itratioal Rviw of Elctrical Egirig (IREE), Octobr 3, Vol. 8, N. 5. [8] Koch, H.: Gas-Isulat Trasmissio Lis (GIL). Joh Wily & Sos,. [9] CIGRE TB 8.: Gas Isulat Trasmissio Lis (GIL, CIGRE, Paris, Frac, 3. [] CIGRE TB 35.: Applicatio of Log High Capacity Gas Isulat Lis (GIL), CIGRE, Paris, Frac, 8. [] Holuct Z. H. Lt. Polska.: Szyoprzwoy trójfazow okrągł. [Oli]. Availabl: http://www.holuct.com.pl/ix.php?mu=p [] Mkr, D.C., Fiit Elmt Mtho Magtics, vrsio 4. (apr, Mathmatica Buil), http://www.fmm.ifo. (Rciv: 4.. 5, rvis:.. 5) 7