42 2 o l. 42 N o. 2 V 2010 4 Jou rnal of N an jin U n iversity of A eronau tics & A stronau tics A p r. 2010 1 1 2 2 (1.,, 210016; 2., ) : 3D,,, 2,, 2, 2, 90 C,,, : ; ; ; ; : TM 726. 4: A : 100522615 (2010) 0220133207 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, 210016, 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) : 2009207210; : 2009210220 :,,, 1967 8, E2m ail: w ansh ishan@nuaa. edu. cn
134 42 90 C,,, [324 ], [526 ],, [7 ],,,,,,, ;,, [ 8210 ],, ;,, 2D, [11213 ],,, [14 ], AN SYS [15217 ] [18 ] [19220 ], 3D, 3D,, 2 3D, 2,,, 1 111 1, 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) 3 11211, A DO F, L ap lace 2 A = 0 (1), Po isson 2 A = - ΛJ T (2) J T, I S ()
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 11212 (7) 3, 3 S 3 S 6 A = 0, ;,,,, V = 0; V, A,, 0, FEM,, 11213 (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
136 42 8 1, 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), 113 2 11311 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 11314 T 0,, 3 S 3 S 6, q = h T (24) : q ; h, h = - Κ T 5T 5n surface (25) DO F, (), 0;, 0 114 2 2 2,,, (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) ;
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,, 3 2 211 1, 2, 1, 2 1 2418 PV C 3315 8 00010 2 mm 20 C ΘCu, 20(8 m ) 212 10-8 212 ΑCu(1 C - 1 ) 3193 10-3 ΛCu 1 ΚCu(W m - 1 K - 1 ) 398 ΛX 1 ΚX(W m - 1 K - 1 ) 0108 ΕX 0185 20 C Θtray, 20(8 m ) 1133 10-7 Λtray 200 Κtray(W m - 1 K - 1 ) 4913 Εtray 017 FEM AN SYS, So lid97, 2, F lu2 id142,, 213 50 Hz 1, I S 50 H z, (, 3 B ),, 4 25 mm 21311 ( 3), 5%,,,, 50 H z,,,, 50 H z, 2D 3 I SA W W A (1) B (2) C (3) % 43216 17612 219 019 18010 18317-2101 46018 20010 313 110 20413 20911-2130 48011 21716 316 111 22213 23114-3193 50113 23614 319 112 24115 25218-4147 : (1)A : ; (2)B: ; (3)C: 21312 4, 10%,, 4 % R acm 8 01962 01993-311 L acλh 6159 7127-914 21313 2, DO F,, 5, 10%,, 2, 5 ( T0= 2416 C) I SA T C T C 43216 3619 3710 1213 1214-018 46018 3911 3813 1415 1317 518 48011 4014 4010 1518 1514 216 50113 4117 4112 1711 1616 310 %
138 42, 90 C, FEM 1 280 A 214 350 Hz 50 H z, 7, 350 H z, 197140 A 350 H z, 350 H z, (1 ) 7713%, 115%, 2112%, 7 1,, 6 7 6 350 Hz % P 2 8113 8615-610 R acm 8 2109 2115-218 L acλh 6108 6136-414 C 810 713 916 7 % A B C W C 7713 115 2112 8113 810 6515 114 3311 10115 813,,,, 4 W 3, 8, 2,,, 4, 3D,,,, ;, 4,, 8 311 1610 XL PE 2113 2415 PV C 2715 mm 10 00010 I S= 500 A, I 123= 500 A, I 4= - 500 A I 4 100%, 3 9 9 % I 1 I 2 I 3 22125 20174 25179 26110 57101 59130 20121 17140 23125 25142 62189 64145,, N o. 3, 3313% 2, ;,, 312,, 44813 W 56014 W,,,,, (1179 m 8 2124 m 8 ) ;, (6147 ΛH 5116 ΛH ) 313, 4 I S= 500 A, 10 10( T0= 2315 C) T C T C 6112 5718 3717 3413 919 6718 6518 4413 4213 417,,,,,, %
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