Current density in the unscreened three-phase high-current busduct

Transcription

1 Compute Applicatios i Electical Egieeig Vol. 4 Cuet esity i the usceee thee-phase high-cuet busuct Tomasz Szczegieliak Zygmut Piątek Daiusz usiak Częstochowa Uivesity o Techology 4- Częstochowa ul. Bzeźicka 6a zygmut.piatek@iteia.pl aiuszkusiak@wp.pl szczegieliakt@iteia.pl Desig o the high-cuet busucts o high cuets a voltages causes ecessity pecise escibig o electomagetic yamic a themal eects. owlege o the elatios betwee electoyamics a tuctioal paametes is ecessay i the optimizatio tuctio pocess o the high-cuet busucts. omatio about istibutio electomagetic iel is a base ito aalysis o electoyamics a themal eects i the high-cuet busucts. The pape pesets aalytical calculatios o the cuet esity i the thee-phase high-cuet busuct which phase couctos ae place i vetex o a squae. to accout wee take ski a poximity eect. The electomagetic iel pouce by high-cuet busucts ae usually calculate umeically with the use o a compute. Howeve the aalytical calculatio o the electomagetic iel is peeable because it esults i a mathematical expessio o showig its epeeces o vaious paametes o the lie aagemet. EYWODS: aalytical metho high-cuet busuct cuet esity. touctio Busba systems ae toay wiely employe i the iustial eviomet o electical eegy istibutio. The mai avatages o these evices ae like to thei moulaity that eables ast a easy istallatio plat moiicatio a maiteace [-9]. Seveal mauactues i the maket popose busba systems om ew to thousa ampees. Thei esig seems to be quite easy a o a log time thaks to the expeimetal kowlege ieet types a size have bee esige usig scala ules. The bus ucts usually ist o alumium o coppe busbas [-9]. A typical shiele thee-phase high-cuet busuct is epicte i Figue. The esig o the busucts use o high cuets a voltages equies the pecise aalysis o electomagetic yamic a themal eects. owlege o the elatios betwee electoyamics a tuctioal paametes is ecessay i the optimizatio tuctio pocess o the high-cuet busucts [-9]. 57

2 T. Szczegieliak Z. Piątek D. usiak / Cuet esity i the usceee Fig.. 45 kv GL Caio Noth [9] Electomagetic iel epes o value o cuets a o the lage ssectioal imesios o the phase coucto eve at iustial equecy ski a poximity eect Fig. shoul be take ito accout [-8]. x z X e e H w y e μ γ 4 Fig.. Ey cuets iuce i the scee by the magetic iel o the eighboig phase coucto 58

3 T. Szczegieliak Z. Piątek D. usiak / Cuet esity i the usceee. Cuet esity The most popula solutio o the high-cuet busucts ae symmetical o lat [-8]. this pape the aalytical calculatios o the cuet esity i the high-cuet busuct which phase couctos ae place i vetex o a squae will be pesete Fig.. y y μ H γ x XZ H y H Xz XY x μ μ x γ γ Fig.. Thee-phase high-cuet busuct which phase couctos ae place i vetex o a squae Let us ie the electomagetic iel i a thee-pole high-cuet busuct pesete i the ig.. Usig the Laplace s a Helmoltz s equatios we ca etemie the electomagetic iel i the couctos. The total cuet esity i the ist coucto is a sum o cuets iuce by each coucto that is to say z z whee 59

4 T. Szczegieliak Z. Piątek D. usiak / Cuet esity i the usceee 6 a ] exp[ a 4 Fo the positive sequece o cuets i.e. ] exp[ a ] exp[ 5 the total cuet esity i ist coucto has the ollowig om A 6 whee exp exp A 6a The total cuet esity i the seco coucto is escibe by z z 7 i which cuet esity ae escibe by Eq. i which cuet shoul be eplace with but cuet esity - B 8 whee 4 - exp exp B 8a Fo the thi coucto the total cuet esity is z z 9 i which cuet esity ae escibe by Eq. i which cuet shoul be eplace with a cuet esity

5 T. Szczegieliak Z. Piątek D. usiak / Cuet esity i the usceee whee C C exp- exp a 4 the above omulas a ae the moiie Bessel s uctios o oe - a + calculate o a [] a the complex popagatio tat o electomagetic wave i the coucto equals μ μ exp[ ] k k k 4 with the atteuatio tat μ k whee δ is the electical ski epth o the electomagetic wave peetatio ito the couctig eviomet is the agula equecy stas o the 7 - couctivity o coucto a μ 4 H m is the magetic pemeability o the vacuum. we itouce the paametes: k a the eeece cuet esity the the elative cuet esity i the ist coucto has a om k 4 the same way we ca calculate the elative cuet esity i the seco a thi coucto. Depeece o the elative cuet esities o paamete α o ieet values o the elative walls thickess β a o elative istace betwee couctos λ is pesete i the Fig. 4. A aalytical metho pesete i the pape ca be use oly o cicula high-cuet busucts. Cuet esity i the high-cuet busucts ca be etemie by speciie compute pogam o example FEMM Fig. 5. []. Howeve the aalytical calculatio o the electomagetic iel is peeable 6

6 T. Szczegieliak Z. Piątek D. usiak / Cuet esity i the usceee because it esults i a mathematical expessio o showig its epeeces o vaious paametes o the lie aagemet. a.9.8 b.9.8 c.9.8 Fig. 4. elative cuet esity: a i the thi coucto b i the ist coucto c i the seco coucto 6

7 T. Szczegieliak Z. Piątek D. usiak / Cuet esity i the usceee Fig. 5. Magitue o cuet esity i the high-cuet busuct which phase couctos ae place i vetex o a squae. Coclusios The pape pesets a aalytical metho o etemiig the cuet esity i the thee-phase high-cuet busuct o cicula s-sectio geomety. The mathematical moel takes ito accout the ski eect a the poximity eects. The cuet esity occus i the high-cuet busucts ae usually calculate umeically with the use o a compute. Howeve the aalytical calculatio o the electomagetic iel is peeable because it esults i a mathematical expessio o showig its epeeces o vaious paametes o the lie aagemet. Moeove kowlege o the elatios betwee electoyamics a tuctioal paametes is ecessay i the optimizatio tuctio pocess o the high-cuet busucts. Pesete i the igue system o tubula couctos is the most ote istalle whe symmetical o lat high-cuet busuct ca ot be use. This situatio appeas i the aow tuels shats cable ucts. eeeces [] Nawowski.: Toy wielkopąowe izolowae powietzem lub SF 6. Wy. Pol. Pozańskie Pozań 998. [] Piątek Z.: mpeaces o high-cuet busucts. Wy. Pol. Częst. Czestochowa 8. [] Szczegieliak T.: Staty mocy w ieekaowaych i ekaowaych uowych toach wielkopąowych Paca Doktoska Gliwice. 6

8 T. Szczegieliak Z. Piątek D. usiak / Cuet esity i the usceee [4] Piątek Z. Szczegieliak T. usiak D.: Staty mocy w płaskim uowym tóazowym toze wielkopąowym Wiaomości Elektotechicze s [5] Piątek Z. usiak D. Szczegieliak T.: Pole magetycze oziaływaia zwotego w wupzewoowym ieekaowaym toze wielkopąowym XV Coeece Compute Applicatios i Electical Egieeig Pozań ss. -4. [6] Piątek Z. Szczegieliak T. usiak D.: Wpływ zewętzego zawiska zbliżeia a staty mocy w tóazowym płaskim toze wielkopąowym XV Coeece Compute Applicatios i Electical Egieeig s 5-6 Pozań. [7] usiak D. Piątek Z. Szczegieliak T.: The Asymmety o the Magetic Fiel Distibutio i a Flat Ushiele -Phase High Cuet Busuct Acta Techica auiesis Vol.6 s [8] Szczegieliak T. Piątek Z. usiak D.: Aaliza gęstości pąów w ieosłoiętym tóazowym toze wielkopąowym Compute Applicatios i Electical Egieeig s Pozań 4. [9] och H.: Gas-sulate Tasmissio Lies oh Wiley&Sos Lt.. [] Mc Lachla N.W.: Fukce Bessela la iżyieów. PWN Waszawa 964. [] MEEE D.C.: Fiite Elemet Metho Magetics vesio 4. ap Mathematica Buil 64