B id irectional Ind irect Coupled F in ite Elem en tm ethod for Estimating Am pac ity of Power Cable

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1 42 2 o l. 42 N o. 2 V Jou rnal of N an jin U n iversity of A eronau tics & A stronau tics A p r (1.,, ; 2., ) : 3D,,, 2,, 2, 2, 90 C,,, : ; ; ; ; : TM : A : (2010) B id irectional Ind irect Coupled F in ite Elem en tm ethod for Estimatin Am pac ity of Power Cable W an S h ishan 1, L iu Z ey uan 1, D u Y ap in 2, W an X in hua 2 (1. Co llee of A utom ation Enineerin, N anjin U niversity of A eronautics & A stronautics, N anjin, , Ch ina; 2. D epartm ent of Buildin Services Enineerin, the Hon Kon Po lytechnic U niversity, Hon Kon, Ch ina) Abstract: A 32D fin ite elem en t harmon ic field model of m u lti2conducto r pow er cab les p laced on a perfo2 rated m etal tray is estab lished. Pow er lo ss den sities of all m etallic elem en ts w ith the sk in effect are ob2 tained. By tak in the pow er den sities as a load, the direct therm al2flu id coup led model of the cab le sys2 tem is set up and temperatu re rises are calcu lated. T herefo re, the m anetic field and the therm al2flu id field indirect coup led so lu tion fo r the cab le system is ach ieved. Becau se the conducto r resistivity is af2 fected by its temperatu re, the coup led model of the cab le system becom es a b i2indirect coup led model be2 tw een the m anetic field and the therm al2flu id field. U sin an iterative p rocedu re, the ampacity of the cab le system can be so lved w ith a h ih temperatu re 90 C. U sin the examp les of a non2armo red cab le w ith the sinle cu rren t and an armo red cab le w ith the mode of th ree2parallel cab le, the to tal pow er lo ss2 es, the ho ttest po in t temperatu re of conducto rs and the cu rren t distribu tion s are calcu lated and tested by the indirect coup led m ethod. indirect coup led model is valid and accu rate. p roperties of pow er cab le system ṡ T he m atch of calcu lated and tested resu lts illu strates that the b idirectional A nd it can be u sed fo r analyzin m anetic and therm al Key words: pow er cab le; indirect coup led2field; fin ite elem en t m ethod (FEM ) ; pow er lo sses; tempera2 tu re rises,, [122 ] (XPL E) : ; : :,,, , E2m ail: w ansh ishan@nuaa. edu. cn

2 C,,, [324 ], [526 ],, [7 ],,,,,,, ;,, [ 8210 ],, ;,, 2D, [11213 ],,, [14 ], AN SYS [15217 ] [18 ] [19220 ], 3D, 3D,, 2 3D, 2,,, , 2, XL PE PV C 1 2,, 1,, 112,, A V (D eree of freedom, DO F ), XL PE, PV C,, A DO F 3D, 1,, 12 ( 3 ) ; ( 3) , A DO F, L ap lace 2 A = 0 (1), Po isson 2 A = - ΛJ T (2) J T, I S ()

3 2, : 135 J T ds = I S (3) S () I S= 0J T, J T = J S + J e = J S + E Θ (4) : J S ; J e ; Θ, T Θ(T ) = Θ20 [ 1 + Α20 (T - 20) ] (5) : Θ20 20 C ; Α20 20 C ; E V E = - (jξa + V ) (6) (2 6), Po isson 2 A - jξλa Θ= - ΛJ S + ΛV Θ [J S - (jξa + V ) Θ] ds = I S S (7) 3, 3 S 3 S 6 A = 0, ;,,,, V = 0; V, A,, 0, FEM,, (1) J e P e (4 6), J e = - (jξa + V ) Θ (8) p e = ΘJ 2 e (9) FEM, p e, P e = P e, i = (p e, iv i) (10) V i (10),, (2) P 2 R ac (10), P dc, P 2 = P dc + P e (11) P e f, P 2 f, P 2 = P 2 (f ), R ac, R ac (f ) = P 2I 2 S = R dc + P ei 2 S (12), P e I 2 S, I S, (3), ( ) I S, W m = B H dv 2 = V V B 2 dv (2Λ) (13), W m = W m, i = (4) [B 2 i V i(2λ) ] (14) L ac = 2W m I 2 S (15), ;,,,,, 123, 3 1, ( 4) S 1 S 3, V = 0, S 5 S 7, V = C (), I S; S 4, S 8, 4 (123 ) DO F, S 1 I 1 = J T ds (16) S 1 S 1, z J z, FEM S 1 N

4 , 8 2,, 8 N, (16) I 1 = N J z, i ( 8 i) (17) S 1 S 2, S 3, I 2, I 3 (9, 10) ; (11), XL PE PV C, T L ap lace 2 T = 0 (18) (), Po isson : Κ ; p V Κ 2 T + p V = 0 (19), p V p dc p e;,, p e 11312, DO F (20 22) v v = 0 (20) (v ) v = f - p Θ+ Γ 2 v (21) : Θ ; Γ ; p ; f,, y ( + y ) Θc (v T ) = Κ 2 T + p V (22) c 11313,,,, Q = [ΡΕT 4 i S i ] (23) i : Ρ Stefan ; Ε, ; T i ( ) ; S i T 0,, 3 S 3 S 6, q = h T (24) : q ; h, h = - Κ T 5T 5n surface (25) DO F, (), 0;, ,,, (19, 22),,, (19, 22), 90 C40 C, 50 C, Θ, (7) DO F,,, Tn (, ), 2, Tn+ 1, m axtn+ 1 - Tn (26), Tn+ 1,, 1 2 C, m axtn+ 1- Tn >, Tn Tn+ 1,,2 : (1) T 0, (2) T (0) i = T 0 ( i= 1 N ) (3) T (5) (4) :,, (5) ;

5 2, : 137,, (9) (5) 2 (6) T (1) i, T (1) i T i= T (1) i - T (0) i (7) m ax T i: m ax ( T i),,,, (8) ; m ax ( T i) >, T (0) i = T (1) i, (3) (8),, (3) ( 9),, 2,, , 2, 1, PV C mm 20 C ΘCu, 20(8 m ) ΑCu(1 C - 1 ) ΛCu 1 ΚCu(W m - 1 K - 1 ) 398 ΛX 1 ΚX(W m - 1 K - 1 ) 0108 ΕX C Θtray, 20(8 m ) Λtray 200 Κtray(W m - 1 K - 1 ) 4913 Εtray 017 FEM AN SYS, So lid97, 2, F lu2 id142,, Hz 1, I S 50 H z, (, 3 B ),, 4 25 mm ( 3), 5%,,,, 50 H z,,,, 50 H z, 2D 3 I SA W W A (1) B (2) C (3) % : (1)A : ; (2)B: ; (3)C: , 10%,, 4 % R acm L acλh , DO F,, 5, 10%,, 2, 5 ( T0= 2416 C) I SA T C T C %

6 138 42, 90 C, FEM A Hz 50 H z, 7, 350 H z, A 350 H z, 350 H z, (1 ) 7713%, 115%, 2112%, 7 1,, Hz % P R acm L acλh C % A B C W C ,,,, 4 W 3, 8, 2,,, 4, 3D,,,, ;, 4,, XL PE PV C 2715 mm I S= 500 A, I 123= 500 A, I 4= A I 4 100%, % I 1 I 2 I ,, N o. 3, 3313% 2, ;,, 312,, W W,,,,, (1179 m m 8 ) ;, (6147 ΛH 5116 ΛH ) 313, 4 I S= 500 A, 10 10( T0= 2315 C) T C T C ,,,,,, %

7 2, : C A, A 4 2,,,, : (1) 2,,,, (2) 50 H z,, 2D ;,,, 3D (3) 50 H z,, : [ 1 ]. [M ]. :, [ 2 ] Petty K A. Pow er p lant electrical reference series, V o l 4 w ire and cable [M ]. Califo rnia; Palo A lto, [3 ] Ferkal K, Po loujadoff M. P roxim ity effect and eddy currency lo sses in insulated cables [J ]. on Pow er D elivery, 1996, 11 (3): IEEE T rans [4 ] V aucheret P, H artlein R A, B lack W Z. Ampacity deratin facto rs fo r cables in sho rt sem ent of con2 duit [J ]. IEEE T rans on Pow er D elivery, 2005, 20 (2): [5 ] A l2saud M S, E l2kady M A, F indlay R D. A novel finite elem ent op tim ization alo rithm w ith app lica2 tion to pow er cable therm al circuit desin [C ]P roc Pow er Enineerin Society General M eetin. T am 2 pa,u SA : IEEE, 2007: 128. [6 ] L i H J. E stim ation of therm al param eters and p redic2 tion of temperature rise in crane pow er cables [C ] P roc Generation, T ransm ission and D istribution. U K: IET, 2004, 151 (3): [7 ] E rtas K A. T herm al analysis fo r determ ination of current carryin capacity of PE and XL PE insulated pow er cables usin finite elem ent m ethod [C ]P roc M EL ECON D ubrovnik, C roatia: IEEE, 2004 (3): [ 8 ]. [D ]. :, [ 9 ]. [D ]. :, [ 10 ]. [D ] :, [11 ] Burnett Y, D u J. Current distribution in sinle2co re cables connected in parallel [ C ]P roc Generation, T ransm ission and D istribution. U K: IET, 2001, 148 (5): [ 12 ] D u Y, H uan Y Z. Current distribution in parallel sinle2co re cables on m etal tray [C ]P roc Industry A pp lication Conference. w O rleans, U SA : IEEE, 2007: [ 13 ] D u Y, Burnett J. Experim ental investiation into harm onic im pedance of low 2vo ltae cables [ C ] P roc Generation, T ransm ission and D istribution. U K: IET, 2000, 147 (6): [ 14 ]. [M ]. :, [15 ] Ho S L, L i Y, L in X, et al. Calculation of eddy cur2 rent, fluid, and therm al fields in an air insulated bus duct system [J ]. IEEE T rans on M a, 2007, 43 (4): [16 ]. [D ]. :, [17 ] Salinas E. Passive and active sh ieldin of pow er2fre2 quency m anetic fields from secondary substation com ponents [ C ]P roc Pow er CON Perth, A ustrilia: IEEE, 2000 (2): [ 18 ]. [D ]., : [ 19 ],,,. [J ]., 2003, 18 (2): [ 20 ]. [D ]. :, 20021