+Copper for Busbars Prefaces 1. Design Considerations 2. Copper for Busbar Purposes 3. Current-carrying Capacity of Busbars 4. Alternating Current Effects in Busbars . Effect of Busbar Arrange!ents on "ating #. $%ort-Circuit Effects &. 'ointing of Copper Busbars (. )ec%anical $trengt% "e*uire!ent "e*uire!ents s . Busbar ,!pedance 1. Appendices Bibliograp%y COPPER DEVELOPMENT ASSOCATION Publication 22, June 1996 Re!inte" Janua!# 2$$1 %it& 'o(e a(en"(ent'
Prefaces Preface to 1(4 Edition T&i' C)D)A) ublication &a' lon* been accete" a' t&e 'tan"a!" !e+e!ence %o! on bu'ba! "e'i*n) T&i' !e-i'e" an" u"ate" e"ition inco!o!ate' i nco!o!ate' !ecent !o*!e'' in t&e tec&nolo*# o+ bu'ba! "e'i*n a' !e+lecte" in ne% 'tan"a!"' an" en*inee!in* !actice') All "ata "ata an" +o!(ulae +o!(ulae &a-e &a-e been been (et!icate" (et!icate" an" t&e t&e (et&o" (et&o" o+ !e'ent !e'entation ation +acilitate +acilitate' ' t&e u'e o+ o+ calculato!' o! co(ute!') T&e (an# -a!iable' t o be con'i"e!e" a!e clea!l# e.laine" an" 'ecial attention &a' been *i-en to "ete!(inin* t&e (o't econo(ic loa"in*' in o!"e! to (a.i(i'e cu!!ent ca!!#in* caacit# +o! (ini(u( in'tallation co't' an" !unnin* lo''e') T&e!e i', t&e!e+o!e, a u'e+ul co(a!i'on o+ t&e elect!ical an" (ec&anical !oe!tie' o+ &i*& con"ucti-it# coe! an" alu(iniu() E.t!a attention &a' been *i-en to !eco((en"e" /ointin* tec&ni0ue', bot& b# bolti n* an" %el"in*) I(!o-e(ent' &a-e al'o been (a"e (a"e to t&e 'ection "ealin* %it& %it & 'in e++ect') T&e in+o!(ation i n+o!(ation on i(e"ance &a' been e.an"e" 'o t&at o%e! +acto! -a!iati on' can no% be +u!t&e! !e"icte") T&e table' o+ !atin*' an" !oe!tie' &a-e been e.an"e" a' &a-e t&e e.a(le' o+ t#ical calculation') T&e !e+e!ence' &a-e been u"ate" to inclu"e !ecent ublication') CDA %i'&e' to acno%le"*e t&e con'i"e!able &el *i-en in t&e !e-i'ion o+ t&i' te.t b# M! M oot&(an, C&ie+ En*inee!, u'ba! 3nit, al+ou! eatt# Po%e! Con't!uction Lt" an" b# M! 4 Je++e!ie', C&ie+ Metallu!*i't, T&o(a' olton 5 Son' Lt") al'o +o! (an# &el+ul co((ent' (a"e on t&e te.t b# M! Ca!# 7Si(le. 8 )E) Lt", M! A Jac'on 7AMICA, M! J C Po%e! 7!iti'& Elect!ic Reai!' Lt", M! E 4!i*&t 7Otte!(ill S%itc&*ea! Lt" an" (e(be!' o+ t&e !iti'& Non8:e!!ou' Non8:e!!ou' Metal' :e"e!ation ;i*& Con"ucti-it# Coe! !ou) Preface to 1# Edition
1. Design Considerations
Prefaces Preface to 1(4 Edition T&i' C)D)A) ublication &a' lon* been accete" a' t&e 'tan"a!" !e+e!ence %o! on bu'ba! "e'i*n) T&i' !e-i'e" an" u"ate" e"ition inco!o!ate' i nco!o!ate' !ecent !o*!e'' in t&e tec&nolo*# o+ bu'ba! "e'i*n a' !e+lecte" in ne% 'tan"a!"' an" en*inee!in* !actice') All "ata "ata an" +o!(ulae +o!(ulae &a-e &a-e been been (et!icate" (et!icate" an" t&e t&e (et&o" (et&o" o+ !e'ent !e'entation ation +acilitate +acilitate' ' t&e u'e o+ o+ calculato!' o! co(ute!') T&e (an# -a!iable' t o be con'i"e!e" a!e clea!l# e.laine" an" 'ecial attention &a' been *i-en to "ete!(inin* t&e (o't econo(ic loa"in*' in o!"e! to (a.i(i'e cu!!ent ca!!#in* caacit# +o! (ini(u( in'tallation co't' an" !unnin* lo''e') T&e!e i', t&e!e+o!e, a u'e+ul co(a!i'on o+ t&e elect!ical an" (ec&anical !oe!tie' o+ &i*& con"ucti-it# coe! an" alu(iniu() E.t!a attention &a' been *i-en to !eco((en"e" /ointin* tec&ni0ue', bot& b# bolti n* an" %el"in*) I(!o-e(ent' &a-e al'o been (a"e (a"e to t&e 'ection "ealin* %it& %it & 'in e++ect') T&e in+o!(ation i n+o!(ation on i(e"ance &a' been e.an"e" 'o t&at o%e! +acto! -a!iati on' can no% be +u!t&e! !e"icte") T&e table' o+ !atin*' an" !oe!tie' &a-e been e.an"e" a' &a-e t&e e.a(le' o+ t#ical calculation') T&e !e+e!ence' &a-e been u"ate" to inclu"e !ecent ublication') CDA %i'&e' to acno%le"*e t&e con'i"e!able &el *i-en in t&e !e-i'ion o+ t&i' te.t b# M! M oot&(an, C&ie+ En*inee!, u'ba! 3nit, al+ou! eatt# Po%e! Con't!uction Lt" an" b# M! 4 Je++e!ie', C&ie+ Metallu!*i't, T&o(a' olton 5 Son' Lt") al'o +o! (an# &el+ul co((ent' (a"e on t&e te.t b# M! Ca!# 7Si(le. 8 )E) Lt", M! A Jac'on 7AMICA, M! J C Po%e! 7!iti'& Elect!ic Reai!' Lt", M! E 4!i*&t 7Otte!(ill S%itc&*ea! Lt" an" (e(be!' o+ t&e !iti'& Non8:e!!ou' Non8:e!!ou' Metal' :e"e!ation ;i*& Con"ucti-it# Coe! !ou) Preface to 1# Edition
1. Design Considerations
,ntroduction ypes of Busbar C%oice of Busbar )aterial
,ntroduction T&e %o!" bu'ba!, "e!i-e" +!o( t&e Latin %o!" o(nibu' 7<+o! all<, *i-e' t&e i"ea o+ a uni-e!'al '#'te( o+ con-e#ance) In t&e elect!ical 'en'e, t&e te!( bu' i' u'e" to "e'c!ibe a /unction o+ ci!cuit', u'uall# in t&e +o!( o+ a '(all nu(be! o+ inut' an" (an# outut') <u'ba!< "e'c!ibe' t&e +o!( t&e bu' '#'te( u'uall# tae', a ba! o! ba!' o+ con"uctin* (ate!ial) In an# elect!ical ci!cuit 'o(e elect!ical ene!*# i' lo't a' &eat %&ic&, i+ not et %it&in 'a+e li(it', (a# i(ai! t&e e!+o!(ance o+ t&e '#'te() T&i' ene!*# lo'', %&ic& al'o !e!e'ent' a +inancial lo'' o-e! a e!io" o+ ti(e, i' !oo!tional to t&e e++ecti-e !e'i'tance o+ t&e con"ucto! an" t&e '0ua!e o+ t&e cu!!ent +lo%in* t&!ou*& it) A l o% !e'i'tance t&e!e+o!e (ean' a lo% lo''= a +acto! o+ inc!ea'in* i(o!tance a' t&e (a*nitu"e o+ t&e t &e cu!!ent inc!ea'e') T&e caacitie' o+ (o"e!n8"a# elect!ical lant an" (ac&ine!# a!e 'uc& t&at t&e t &e o%e! &an"le" b# t&ei! cont!ol '#'te(' *i-e' !i'e t o -e!# la!*e +o!ce') u'ba!', lie all t&e ot&e! e0ui(ent in t&e '#'te(, &a-e to be able to %it&'tan" t&e'e +o!ce' %it&out "a(a*e) It i' e''ential t&at t&e (ate!ial' u'e" in t&ei! con't!uction '&oul" &a-e t&e be't o''ible (ec&anical !oe!tie' an" a!e "e'i*ne" to oe!ate %it&in t&e te(e!atu!e li(it' lai" "o%n in S 1>9, S EN 6$?@981199?, 6$?@981199?, o! ot&e! national o! inte!national 'tan"a!"') A con"ucto con"ucto!! (ate!ial (ate!ial '&oul" '&oul" t&e!e+o! t&e!e+o!e e &a-e &a-e t&e +ollo% +ollo%in* in* !oe !oe!tie' !tie' i+ it i' to be be !o"uce !o"uce" " e++icientl# an" &a-e lo% !unnin* co't' +!o( t&e oint o+ -ie% o+ ene!*# con'u(tion an" (aintenance a Lo% elect!ical an" t&e!(al !e'i'tance b ;i*& (ec&anical 't!en*t& in ten'ion, t en'ion, co(!e''ion an" '&ea! c ;i*& !e'i'tance to +ati*ue +ailu!e " Lo% elect!ical !e'i'tance o+ 'u!+ace +il(' e Ea'e o+ +ab!ication + ;i*& !e'i'tance to co!!o'ion * Co(etiti-e +i!'t co't an" &i*& e-entual !eco-e!# -alue T&i' co(bination o+ !oe!tie' i' (et be't b# coe!) Alu(iniu( i' t &e (ain alte!nati-e (ate!ial, but a co(a!i'on o+ t&e !oe!tie' o+ t&e t%o (etal' '&o%' t&at in nea!l# all !e'ect' coe! i' t&e 'ue!io! (ate!ial)
ypes of Busbar u'ba!' can be 'ub8"i-i"e" into t&e +ollo%in* cate*o!ie', %it& in"i-i"ual bu'ba! '#'te(' in (an# ca'e' bein* con't!ucte" +!o( 'e-e!al "i++e!ent t#e' a Ai! a Ai! in'ulate in'ulate" " %it& oen &a'e &a'e con"ucto con"ucto!' !'
b Ai! in'ulate" %it& 'e*!e*atin* ba!!ie!' bet%een con"ucto!' o+ "i++e!ent &a'e') c Totall# enclo'e" but &a-in* t&e con't!uction a' t&o'e +o! 7a an" 7b " Ai! in'ulate" %&e!e eac& &a'e i' +ull# i'olate" +!o( it' a"/acent &a'e7' b# an ea!t&e" enclo'u!e) T&e'e a!e u'uall# calle"
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C%oice of Busbar )aterial At t&e !e'ent ti(e t&e onl# t%o co((e!ciall# a-ailable (ate!ial' 'uitable +o! con"ucto! u!o'e' a!e coe! an" alu(iniu() T&e table belo% *i-e' a co(a!i'on o+ 'o(e o+ t&ei! !oe!tie') It can be 'een t&at +o! con"ucti-it# an" 't!en*t&, &i *& con"ucti-it# coe! i' 'ue!io! to alu(iniu() T&e onl# "i'a"-anta*e o+ coe! i' it' "en'it#= +o! a *i-en cu!!ent an" te(e!atu!e !i'e, an alu(iniu( con"ucto! %oul" be li*&te!, e-en t&ou*& it' c!o''8'ection %oul" be la!*e!) In enclo'e" '#'te(' &o%e-e!, 'ace con'i"e!ation' a!e o+ *!eate! i(o!tance t&an %ei*&t) E-en in oen8ai! '#'te(' t&e %ei*&t o+ t&e bu'ba!', %&ic& a!e 'uo!te" at inte!-al', i' not nece''a!il# t&e "eci'i-e +acto!) able 2 ypical relatie properties of copper and alu!iniu! CopperC4A5
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T&e elect!o(a*netic 't!e''e' 'et u in t&e ba! a!e u'uall# (o!e 'e-e!e t&an t&e 't!e'' i nt!o"uce" b# it' %ei*&t) In a!ticula!, &ea-# cu!!ent8ca!!#in* e0ui(ent nece''itate' t&e u'e o+ la!*e 'ie con"ucto!', an" 'ace con'i"e!ation' (a# be i(o!tant) It '&oul" be !eali'e" t&at t&e u'e o+
coe! at &i*&e! oe!atin* te(e!atu!e' t&an %oul" be e!(i''ible +o! alu(iniu( allo%' '(alle! an" li*&te! coe! 'ection' to be u'e" t&an %oul" be !e0ui!e" at lo%e! te(e!atu!e') T&e abilit# o+ coe! to ab'o!b t&e &ea-# elect!o(a*netic an" t&e!(al 't!e''e' *ene!ate" b# o-e!loa" con"ition' al'o *i-e' a con'i"e!able +acto! o+ 'a+et#) Ot&e! +acto!', 'uc& a' t&e co't o+ +!e0uent 'uo!t' +o! t&e !elati-el# li( alu(iniu(, an" t&e *!eate! co't o+ in'ulation o+ t&e la!*e! 'u!+ace a!ea, (u't be con'i"e!e" %&en e-aluatin* t&e (ate!ial') :!o( ubli'&e" c!ee "ata, it can be 'een t&at &i*& con"ucti-it# alu(iniu( e.&ibit' e-i"ence o+ 'i*ni+icant c!ee at a(bient te(e!atu!e i+ &ea-il# 't!e''e") At t&e 'a(e 't!e'', a 'i(ila! !ate o+ c!ee i' onl# '&o%n b# &i*& con"ucti-it# coe! at a te(e!atu!e o+ 1>$HC, %&ic& i' abo-e t&e u'ual oe!atin* te(e!atu!e o+ bu'ba!') able 3 Co!parison of creep and fatigue properties of %ig% conductiity copper and alu!iniu! a5 Creep properties )aterial
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I+ (uc& &i*&e! 't!e''e' o! te(e!atu!e' a!e to be allo%e" +o!, coe! containin* '(all a(ount' 7about $)1G o+ 'il-e! can be u'e" 'ucce''+ull#) T&e c!ee !e'i'tance an" 'o+tenin* !e'i'tance o+ coe!8'il-e! allo#' inc!ea'e %it& inc!ea'in* 'il-e! content) In t&e con"ition' in %&ic& &i*& con"ucti-it# alu(iniu( an" coe! a!e u'e", eit&e! anneale" 7o! a'8%el"e" o! &al+8&a!", t&e +ati*ue 't!en*t& o+ coe! i' a!o.i(atel# "ouble t&at o+ alu(iniu() T&i' *i-e' a u'e+ul !e'e!-e o+ 't!en*t& a*ain't +ailu!e initiate" b# (ec&anical o! t&e!(al c#clin*) T&e *!eate! &a!"ne'' o+ coe! co(a!e" %it& alu(iniu( *i-e' i t bette! !e'i'tance to (ec&anical "a(a*e bot& "u!in* e!ection an" in 'e!-ice) It i' al'o le'' liel# to "e-elo !oble(' in cla(e" /oint' "ue to col" (etal +lo% un"e! t&e !olon*e" alication o+ a &i*& contact !e''u!e) It' &i*&e!
(o"ulu' o+ ela'ticit# *i-e' it *!eate! bea( 'ti++ne'' co(a!e" %it& an alu(iniu( con"ucto! o+ t&e 'a(e "i(en'ion') T&e te(e!atu!e -a!iation' encounte!e" un"e! 'e!-ice con"ition' !e0ui!e a ce!tain a(ount o+ +le.ibilit# to be allo%e" +o! in t&e "e'i*n) T&e lo%e! coe++icient o+ linea! e.an'ion o+ coe! !e"uce' t&e "e*!ee o+ +le.ibilit# !e0ui!e") ecau'e coe! i' le'' !one to t&e +o!(ation o+ &i*& !e'i'tance 'u!+ace o.i"e +i l(' t&an alu(iniu(, *oo" 0ualit# (ec&anical /oint' a!e ea'ie! to !o"uce in coe! con"ucto!') 4el"e" /oint' a!e al'o !ea"il# (a"e) S%itc& contact' an" 'i(ila! a!t' a!e nea!l# al%a#' !o"uce" +!o( coe! o! a coe! allo#) T&e u'e o+ coe! +o! t&e bu'ba!' to %&ic& t&e'e a!t' a!e connecte" t&e!e+o!e a-oi"' contact' bet%een "i''i(ila! (etal' an" t&e in&e!ent /ointin* an" co!!o'ion !oble(' a''ociate" %it& t&e() T&e &i*&e! (eltin* oint an" t&e!(al con"ucti-it# o+ coe! !e"uce t&e o''ibilit# o+ "a(a*e !e'ultin* +!o( &ot 'ot' o! acci"ental +la'&o-e!' in 'e!-ice) I+ a!cin* occu!', coe! bu'ba!' a!e le'' liel# to 'uo!t t&e a!c t&an alu(iniu() Table ? '&o%' t&at coe! can 'el+8e.tin*ui'& a!c' ac!o'' '(alle! 'ea!ation', an" at &i*&e! bu'ba! cu!!ent') T&i' 'el+8e.tin*ui'&in* be&a-iou! i' !elate" to t&e (uc& la!*e! &eat inut !e0ui!e" to -ao!i'e coe! t&an alu(iniu() able 4 $elf-e;tinguis%ing arcs in copper and alu!iniu! busbars Copper
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@22$
Coe! libe!ate' con'i"e!abl# le'' &eat "u!in* o.i"ation t &an alu(iniu( an" i' t&e!e+o!e (uc& le'' liel# to 'u'tain co(bu'tion in t&e ca'e o+ acci"ental i*nition b# an a!c) T&e la!*e a(ount' o+ &eat libe!ate" b# t&e o.i"ation o+ alu(iniu( in t&i' e-ent a!e 'u++icient to -ao!i'e (o!e (etal t&an %a' o!i*inall# o.i"i'e") T&i' -ao!i'e" alu(iniu( can it'el+ !ai"l# o.i"i'e, t&u' 'u'tainin* t&e !eaction) T&e e.ce'' &eat *ene!ate" in t&i' %a# &eat' nea!b# (ate!ial', inclu"in* t&e bu'ba! it'el+, t&e ai! an" an# 'uo!tin* +i.tu!e') A' t&e bu'ba! an" ai! te(e!atu!e' !i'e, t&e !ate' o+ t&e -ao!i'ation an" o.i"ation inc!ea'e, 'o accele!atin* t&e %&ole !oce'') A' t&e ai! te(e!atu!e i' inc!ea'e", t&e ai! e.an"' an" !oel' &ot o.i"e a!ticle') T&e bu'ba! (a# !eac& it' (eltin* oint, +u!t&e! inc!ea'in* t&e !ate o+ o.i"ation an" !o-i"in* &ot li0ui" to be !oelle", %&ile ot&e! (ate!ial' 'uc& a' %oo" anel' (a# be !ai'e" to t&ei! i*nition te(e!atu!e') T&e'e "an*e!' a!e ob-iate" b# t&e u'e o+ coe! bu'ba!') :inall#, coe! i' an econo(ical con"ucto! (ate!ial) It *i-e' lon* an" !eliable 'e!-ice at (ini(u( (aintenance co't', an" %&en an in'tallation i' e-entuall# !elace" t&e coe! %ill &a-e a &i*& !eco-e!# -alue) ecau'e o+ it' (an# a"-anta*e', coe! i' 'till u'e" %o!l"%i"e a' an elect!ical con"ucto! (ate!ial "e'ite atte(t' at 'ub'titution)
2.Copper for Busbar Purposes
ypes of
Properties of roug%t
In (o't count!ie', coe!' o+ "i++e!ent t#e' +o! 'eci+ic alication' &a-e been *i-en 'ea!ate i"entitie') In t&e 3nite" in*"o( t&i' tae' t&e +o!( o+ an allo# "e'i*nation nu(be! %&ic& i' u'e" in all !iti'& Stan"a!"' !ele-ant to coe! an" it' allo#') Coe! +o! elect!ical u!o'e' i' co-e!e" b# t&e +ollo%in* !iti'& Stan"a!"' S 1?@2 19F 7't!i %it& "!a%n o! !olle" e"*e' S 1?@@ 19$ 7Ro" an" ba! S 1?@? 19F> 7Co((utato! ba!' S 19 196 7;i*& con"ucti-it# tube' S ?1$9 19$ 7%i!e +o! *ene!al elect!ical u!o'e' an" +o! in'ulate" an" +le.ible co!"' S ?6$F 19$ 7Rolle" '&eet, 't!i an" +oil 7Coie' o+ t&e'e a!e obtainable +!o( t&e SI Sale' O++ice) @9F C&i'%ic ;i*& Roa", Lon"on 4S? ?AL) To b!in* t&e 3 in line %it& cu!!ent Eu!oean !e0ui!e(ent' S EN 'tan"a!"' a!e bein* int!o"uce") T&e Eu!oean Stan"a!"' !ele-ant to elect!ical alication' a!e e.ecte" to 'ue!'e"e t&e !iti'& Stan"a!"' in "ue cou!'e) T&e cu!!ent 'tan"a!"' (o't !ele-ant to bu'ba! alication' a!e S 1?@2, S 1?@@ an" S 19 %&ic& 'eci+# t&at t&e en" !o"uct' '&all be (anu+actu!e" +!o( coe! co(l#in* %it& t&e +ollo%in* !e0ui!e(ent' Cu8ETP Elect!ol#tic tou*& itc& &i*& con"ucti-it# coe! C4$$?A 7+o!(e!l# C1$1 Cu8:R;C :i!e8!e+ine" tou*& itc& &i*& con"ucti-it# coe! C4$$>A 7+o!(e!l# C1$2 Cu8O: O.#*en8+!ee &i*& con"ucti-it# coe! C4$$FA 7+o!(e!l# C1$@ Eu!oean Stan"a!"' EN196 an" EN19F &a-e !elace" S 6$119F1) Table > '&o%' t&e Eu!oean (ate!ial "e'i*nation' alon* %it& Inte!national Stan"a!"' O!*ani'ation 7ISO an" ol" !iti'& Stan"a!" "e'i*nation') able E9= B$ and ,$> designations for refinery s%apes and /roug%t coppers Designation
Description
,$> cast and /roug%t
European Designation
0or!er 6? Designations
Elect!ol#tic tou*& itc& &i*&8 con"ucti-it# coe!
Cu8ETP
C4$$?A
C1$1
:i!e8 !e+ine" tou*& itc& &i*&8 con"ucti-it# coe!
Cu8:R;C
C4$$>A
C1$2
O.#*en8+!ee &i*&8con"ucti-it# coe!
Cu8O:
C4$$FA
C1$@
Coe! to be u'e" +o! elect!ical u!o'e' i' o+ &i*& u!it# becau'e i(u!itie' in coe!, to*et&e! %it& t&e c&an*e' in (ic!o8't!uctu!e !o"uce" b# %o!in*, (ate!iall# a++ect t&e (ec&anical an" elect!ical !oe!tie') T&e "e*!ee to %&ic& t&e elect!ical con"ucti-it# i' a++ecte" b# an i(u!it# "een"' la!*el# on t&e ele(ent !e'ent) :o! e.a(le, t&e !e'ence o+ onl# $)$?G &o'&o!u' !e"uce' t&e con"ucti-it# o+ &i*& con"ucti-it# coe! to a!oun" F$G IACS) 7T&e a!o.i(ate e++ect on con"ucti-it# o+ -a!iou' i(u!it# ele(ent' i' '&o%n in :i*u!e 1) T&e le-el o+ total i(u!itie', inclu"in* o.#*en, '&oul" t&e!e+o!e be le'' t&an $)1G an" coe! o+ t&i' t#e i' no%n a' &i*& con"ucti-it# 7;C coe!) Mic!o'coic an" anal#tical cont!ol' a!e alie" to en'u!e a con'i'tent !o"uct an" in t&e anneale" con"ition con"ucti-itie' o-e! 1$$G IACS a!e u'ual) T&i' +i*u!e co!!e'on"' to t&e 'tan"a!" !e'i'ti-it# o+ $)$12?1 µΩ( 'et 'o(e #ea!' a*o b# t&e Inte!national Elect!otec&nical Co((i''ion) 0igure 1 - Appro;i!ate effect of i!purity ele!ents on t%e electrical resistiity of copper
ypes of
G) et%een t&e'e li(it' t&e !e'ence o+ t&e o.#*en in t&i' +o!( &a' onl# a 'li*&t e++ect on t&e (ec&anical an" elect!ical !oe!tie' o+ t&e coe!) It can, &o%e-e!, *i-e !i 'e to o!o'it# an" inte!*!anula! c!ac' o! +i''u!e' i+ t&e coe! i' &eate" in a !e"ucin* at(o'&e!e, a' can &aen "u!in* %el"in* o! b!ain*) T&i' i' a !e'ult o+ t&e !eaction o+ t&e cu!ou' o.i"e a!ticle' %it&
&#"!o*en an" i' no%n a' <&#"!o*en e(b!ittle(ent<) P!o-i"e" a !e"ucin* at(o'&e!e i' a-oi"e", *oo" %el"' an" b!ae' can be !ea"il# ac&ie-e") 7See Jointin* o+ Coe! u'ba!') >;ygen-free %ig%-conductiity copper= C(A C135 In -ie% o+ t&e abo-e !e(a!', i+ %el"in* an" b!ain* oe!ation' un"e! !e"ucin* con"ition' a!e una-oi"able, it i' nece''a!# to u'e a "i++e!ent 7an" (o!e e.en'i-e *!a"e o+ &i*& con"ucti-it# coe! %&ic& i' 'eciall# !o"uce" +o! t&i' u!o'e) T&i' t#e o+ coe!, no%n a' G coe!) T&i' enable' a con"ucti-it# o+ 1$$G IACS to be 'eci+ie" e-en in t&e ab'ence o+ t&e 'ca-en*in* o.#*en) Effects of %ot and cold /or@ing on structures In t&e a'8ca't +o!(, ;C coe! i' a-ailable in %i!eba! an" billet +o!(, alt&ou*& t&e a"-ance(ent o+ (o"e!n ca'tin* tec&nolo*# i' lea"in* to a "ecline in %i!eba! !o"uction) T&e ca't '&ae i' &ot8 %o!e" b# !ollin* o! e.t!u'ion to !o"uce a +o!( 'uitable +o! +u!t&e! !oce''in* b# col" %o! into it' +inal %!ou*&t +o!(, eit&e! b# !ollin* o! "!a%in* t&!ou*& "ie') In t&e ca'e o+ tou*&8itc& ;C coe!, t&e a'8ca't 't!uctu!e i' coa!'e8*!aine" %it& o.#*en !e'ent a' coe!8cu!ou' o.i"e eutectic in t&e *!ain boun"a!ie') T&e &ot %o!in* oe!ation b!ea' u t&e coa!'e *!ain' an" "i'e!'e' t&e cu!ou' o.i"e to *i-e a uni+o!( "i't!ibution o+ o.i "e a!ticle' t&!ou*&out a ne% net%o! o+ +ine *!ain') In t&e ca'e o+ o.#*en8+!ee ;C coe!, t&e &ot %o!in* oe!ation b!ea' u t&e coa!'e *!ain' into a ne% net%o! o+ +ine *!ain')
3. Current-carrying Capacity of Busbars Design "e*uire!ents Calculation of Current-carrying Capacity )et%ods of
Design "e*uire!ents T&e cu!!ent8ca!!#in* caacit# o+ a bu'ba! i' u'uall# "ete!(ine" b# t &e (a.i(u( te(e!atu!e at %&ic& t&e ba! i' e!(itte" to oe!ate, a' "e+ine" b# national an" inte!national 'tan"a!"' 'uc& a' !iti'& Stan"a!" S 1>9, A(e!ican Stan"a!" ANSI C@)2$, etc) T&e'e 'tan"a!"' *i-e (a.i(u( te(e!atu!e !i'e' a' %ell a' (a.i(u( a(bient te(e!atu!e') S 1>9 'tiulate' a (a.i(u( te(e!atu!e !i'e o+ >$HC abo-e a 2? &ou! (ean a(bient te(e!atu!e o+ u to @>HC, an" a ea a(bient te(e!atu!e o+ ?$HC) ANSI C@)2$ alte!nati-el# e!(it' a te(e!atu!e !i'e o+ 6>HC abo-e a (a.i(u( a(bient o+ ?$HC, !o-i"e" t&at 'il-e!8late" 7o! accetable alte!nati-e bolte" te!(ination' a!e u'e") I+ not, a te(e!atu!e !i'e o+ @$HC i' allo%e") T&e'e ue! te(e!atu!e li(it' &a-e been c&o'en becau'e at &i *&e! (a.i(u( oe!atin* te(e!atu!e' t&e !ate o+ 'u!+ace o.i"ation in ai! o+ con"ucto! (ate!ial' inc!ea'e' !ai"l# an" (a# *i-e !i'e in t&e lon* te!( to e.ce''i-e local &eatin* at /oint' an" contact') T&i' te(e!atu!e li(it i' (uc& (o!e i(o!tant +o! alu(iniu( t&an coe! becau'e it o.i"i'e' -e!# (uc& (o!e !ea"il# t&an coe!) In !acti'e t&e'e li(itation' on te(e!atu!e !i'e (a# be !ela.e" +o! coe! bu'ba!' i+ 'uitable in'ulation (ate!ial' a!e u'e") A no(inal !i'e o+ 6$HC o! (o!e abo-e an a(bient o+ ?$HC i' allo%e" b# S EN 6$?@981199? !o-i"e" t&at 'uitable !ecaution' a!e taen) S EN 6$?@98 1199? 7e0ui-alent to IEC ?@9 'tate' t&at t&e te(e!atu!e !i'e o+ bu'ba!' an" con"ucto!' i' li(ite" b# t&e (ec&anical 't!en*t& o+ t&e bu'ba! (ate!ial, t&e e++ect on a"/acent e0ui(ent, t&e e!(i''ible te(e!atu!e !i'e o+ in'ulatin* (ate!ial' in contact %it& t&e ba!', an" t&e e++ect on aa!atu' connecte" to t&e bu'ba!') T&e !atin* o+ a bu'ba! (u't al'o tae account o+ t&e (ec&anical 't!e''e' 'et u "ue to e.an'ion, '&o!t8ci!cuit cu!!ent' an" a''ociate" i nte!8&a'e +o!ce') In 'o(e bu'ba! '#'te(' con'i"e!ation (u't al'o be *i-en to t&e caitali'e" co't o+ t&e &eat *ene!ate" b# t&e e++ecti-e o&(ic !e'i'tance an" cu!!ent 7I 2R %&ic& lea"' to an oti(i'e" "e'i*n u'in* el-in<' La% o+ Ma.i(u( Econo(#) T&i' la% 'tate' t&at
Calculation of Current-carrying Capacity A -e!# a!o.i(ate (et&o" o+ e'ti(atin* t&e cu!!ent ca!!#in* caacit# o+ a coe! bu'ba! i' to a''u(e a cu!!ent "en'it# o+ 2 A(( 2 712>$ Ain2 in 'till ai!) T&i' (et&o" '&oul" onl# be u'e" to e'ti(ate a liel# 'ie o+ bu'ba!, t&e +inal 'ie bein* c&o'en a+te! con'i"e!ation &a' been *i-en to t&e calculation (et&o"' an" e.e!i(ental !e'ult' *i-en in t&e +ollo%in* 'ection')
)et%ods of
7b Ra"iation 7c Con"uction In (o't ca'e' con-ection an" !a"iation &eat lo''e' "ete!(ine t&e cu!!ent8ca!!#in* caacit# o+ a bu'ba! '#'te() Con"uction can onl# be u'e" %&e!e a no%n a(ount o+ &eat can +lo% into a &eat 'in out'i"e t&e bu'ba! '#'te( o! %&e!e a"/acent a!t' o+ t&e '#'te( &a-e "i++e!in* coolin* caacitie') T&e !oo!tion o+ &eat lo'' b# con-ection an" !a"iation i' "een"ent on t&e con"ucto! 'ie %it& t&e o!tion att!ibutable to con-ection bein* inc!ea'e" +o! a '(all con"ucto! an" "ec!ea'e" +o! la!*e! con"ucto!') Conection T&e &eat "i''iate" e! unit a!ea b# con-ection "een"' on t&e '&ae an" 'ie o+ t&e con"ucto! an" it' te(e!atu!e !i'e) T&i' -alue i' u'uall# calculate" +o! 'till ai! con"ition' but can be inc!ea'e" *!eatl# i+ +o!ce" ai! coolin* i' e!(i''ible) 4&e!e out"oo! bu'ba! '#'te(' a!e conce!ne" calculation' '&oul" al%a#' be t!eate" a' in 'till ai! unle'' 'eci+ic in+o!(ation i' *i-en to t&e cont!a!#) T&e +ollo%in* +o!(ulae can be u'e" to e'ti(ate t&e con-ection &eat lo'' +!o( a bo"# in 4( 2
%&e!e θ K te(e!atu!e !i'e, HC L K &ei*&t o! %i"t& o+ ba!, (( " K "ia(ete! o+ tube, (( T&e "ia*!a(' belo% in"icate %&ic& +o!(ulae '&oul" be u'e" +o! -a!iou' con"ucto! *eo(et!ie'
It can be 'een %&en "ia*!a(' 7a an" 7b a!e co(a!e" an" a''u(in* a 'i (ila! c!o''8'ectional a!ea t&e &eat lo'' +!o( a!!an*e(ent 7b i' (uc& la!*e!, !o-i"e" t&e *a bet%een t&e la(ination' i' not le'' t&an t&e t&icne'' o+ eac& ba!) Conection %eat loss forced air cooling I+ t&e ai! -elocit# o-e! t&e bu'ba! 'u!+ace i' le'' t&an $)> (' t&e abo-e +o!(ulae +o! 4-, 4 & an" 4c al#) :o! &i*&e! ai! -elocitie' t&e +ollo%in* (a# be u'e"
%&e!e 4a K &eat lo't e! unit len*t& +!o( ba!, 4( - K ai! -elocit#, (' A K 'u!+ace a!ea e! unit len*t& o+ ba!, ( 2( "adiation T&e !ate at %&ic& &eat i' !a"iate" +!o( a bo"# i' !oo!tional to t&e "i++e!ence bet%een t&e +ou!t& o%e! o+ t&e te(e!atu!e' o+ t&e bo"# an" it' 'u!!oun"in*', an" i' !oo!tional to t&e !elati-e e(i''i-it# bet%een t&e bo"# an" it' 'u!!oun"in*')
T&e +ollo%in* table li't' t#ical ab'olute e(i''i-itie' ε +o! coe! bu'ba!' in -a!iou' con"ition') C&an*e' in e(i''i-it# *i-e !i'e to c&an*e' in cu!!ent !atin*', a' '&o%n in Table ) !i*&t (etal $)1 Pa!tiall# o.i"i'e" $)@$ ;ea-il# o.i"i'e" $)$ Dull non8(etallic aint $)9
able & Percentage increase in current rating /%en p%ase arrange!ent
is increased fro! .1 to . - t%ree-
P%ase centres= !!
9o. of bars in parallel
1
2
2
1
2@
2@
2>
2
1>
16
1F
@
1$
11
1?
?
9
9
12
>
6
9
T&e +i*u!e' *i-en in Table a!e a!o.i(ate -alue' alicable to F$ to 16$ (( %i"e bu'ba!' +o! a 1$>HC oe!atin* te(e!atu!e an" ?$HC a(bient) T&e !elati-e e(i''i-it# i' calculate" a' +ollo%'
%&e!e e K !elati-e e(i''i-it#
ε1 K ab'olute e(i''i-it# o+ bo"# 1 ε2 K ab'olute e(i''i-it# o+ bo"# 2 T&e !ate o+ &eat lo'' b# !a"iation +!o( a bo"# 74( 2 i' *i-en b#
%&e!e e K !elati-e e(i''i-it# T1 K ab'olute te(e!atu!e o+ bo"# 1, T2 K ab'olute te(e!atu!e o+ bo"# 2, 7i)e), a(bient te(e!atu!e o+ t&e 'u!!oun"in*' Ra"iation i' con'i"e!e" to t!a-el in 't!ai*&t line' an" lea-e t&e bo"# at !i*&t an*le' to it' 'u!+ace) T&e "ia*!a(' abo-e "e+ine t&e e++ecti-e 'u!+ace a!ea' +o! !a"iation +!o( con"ucto!' o+ co((on '&ae')
Ω((
%&e!e R+ K e++ecti-e a)c) !e'i'tance o+ con"ucto!,
Ω 7'ee abo-e
Appro;i!ate dc Current "atings for 0lat and "ound bars T&e +ollo%in* e0uation' can be u'e" to obtain t&e a!o.i(ate ")c) cu!!ent !atin* +o! 'in*le +lat an" !oun" coe! bu'ba!' ca!!#in* a "i!ect cu!!ent) T&e e0uation' a''u(e a natu!all# b!i*&t coe! +ini'& %&e!e e(i''i-it# i' $)1 an" %&e!e !atin*' can be i(!o-e" 'ub'tantiall# b# coatin* %it& a (att blac o! 'i(ila! 'u!+ace) T&e e0uation' a!e al'o a!o.i(atel# t!ue +o! a)c) cu!!ent !o-i"e" t&at t&e 'in e++ect an" !o.i(it# !atio' 'ta# clo'e to 1)$, a' i' t!ue +o! (an# lo% cu!!ent alication') Met&o"' o+ calculation +o! ot&e! con+i*u!ation' an" con"ition' can be +oun" in 'ub'e0uent 'ection') 7a :lat ba!' on e"*e
71 %&e!e I K cu!!ent, A A K c!o''8'ectional a!ea, ((2 K e!i(ete! o+ con"ucto!, ((
θ K te(e!atu!e "i++e!ence bet%een con"ucto! an" t&e a(bient ai!, HC α K !e'i'tance te(e!atu!e coe++icient o+ coe! at t &e a(bient te(e!atu!e, e! HC ρ K !e'i'ti-it# o+ coe! at t&e a(bient te(e!atu!e, µΩ c( 7b ;ollo% !oun" ba!'
72 7c Soli" !oun" ba!'
7@ I+ t&e te(e!atu!e !i'e o+ t&e con"ucto! i' >$HC abo-e an a(bient o+ ?$HC an" t&e !e'i'ti-it# o+ t&e coe! at 2$HC i' 1)2? µΩc(, t&en t&e abo-e +o!(ulae beco(e 7i :lat ba!'
7? 7ii ;ollo% !oun" ba!'
7> 7iii Soli" !oun" ba!'
76 :o! &i*& con"ucti-it# coe! tube' %&e!e "ia(ete! an" (a'' e! unit len*t& 7'ee Table 1? a!e no%n,
7 %&e!e ( K (a'' e! unit len*t& o+ tube, *( " K out'i"e "ia(ete! o+ tube, (( "e-rating for different current or te!perature rise conditions 4&e!e a bu'ba! '#'te( i' to be u'e" un"e! ne% cu!!ent o! te(e!atu!e !i'e con"ition', t&e +ollo%in* +o!(ula can be u'e" to +in" t&e co!!e'on"in* ne% te(e!atu!e !i'e o! cu!!ent
7F %&e!e I1 K cu!!ent 1, A I2 K cu!!ent 2, A
θ1 K te(e!atu!e !i'e +o! cu!!ent 1, HC θ2 K te(e!atu!e !i'e +o! cu!!ent 2, HC T1 K %o!in* te(e!atu!e +o! cu!!ent 1, HC T2 K %o!in* te(e!atu!e +o! cu!!ent 2, HC
α2$ K te(e!atu!e coe++icient o+ !e'i'tance at 2$HC 7 K $)$$@9@ I+ t&e %o!in* te(e!atu!e o+ t&e bu'ba! '#'te( i' t&e 'a(e in eac& ca'e 7i)e), T 1 K T2, +o! e.a(le %&en !e8!atin* +o! a c&an*e in a(bient te(e!atu!e in a &otte! cli(ate, t&i' +o!(ula beco(e'
a!inated bars 4&en a nu(be! o+ con"ucto!' a!e u'e" in a!allel, t&e total cu!!ent caacit# i' le'' t&an t&e !atin* +o! a 'in*le ba! ti(e' t&e nu(be! o+ ba!' u'e") T&i' i' "ue to t&e ob't!uction to con-ection an" !a"iation lo''e' +!o( t&e inne! con"ucto!') To +acilitate t&e (ain* o+ inte!lea-e" /oint', t&e 'acin* bet%een la(inate" ba!' i' o+ten (a"e e0ual to t&e ba! t&icne'') :o! 6)@ (( t&ic ba!' u to 1>$ (( %i"e, (ounte" on e"*e %it& 6)@ (( 'acin*' bet%een la(ination', t&e i'olate" ba! ")c) !atin* (a# be (ultilie" b# t&e +ollo%in* +acto!' to obtain t&e total !atin*) 9o. of la!inations )ultiplying factor
9o. of la!inations
)ultiplying factor
2
1)F
@
2)>
?
@)2
>
@)9
6
?)?
F
>)>
1$
6)>
4. Alternating Current Effects in Busbars $@in Effect Pro;i!ity Effect Condition for )ini!u! oss Penetration Dept%
$@in Effect T&e aa!ent !e'i'tance o+ a con"ucto! i' al%a#' &i*&e! +o! a)c) t&an +o! ")c) T&e alte!natin* (a*netic +lu. c!eate" b# an alte!natin* cu!!ent inte!act' %it& t &e con"ucto!, *ene!atin* a bac e)()+) %&ic& ten"' to !e"uce t&e cu!!ent in t&e con"ucto!) T&e cent!e o!tion' o+ t&e con"ucto! a!e a++ecte" b# t&e *!eate't nu(be! o+ line' o+ +o!ce, t&e nu(be! o+ line lina*e' "ec!ea'in* a' t&e e"*e' a!e a!oac&e") T&e elect!o(oti-e +o!ce !o"uce" in t&i' %a# b# 'el+8in"uctance -a!ie' bot& in (a*nitu"e an" &a'e t&!ou*& t&e c!o''8'ection o+ t&e con"ucto!, bein* la!*e! in t&e cent!e an" '(alle! to%a!"' t&e out'i"e) T&e cu!!ent t&e!e+o!e ten"' to c!o%" into t&o'e a!t' o+ t&e con"ucto! in %&ic& t&e oo'in* e)()+) i' a (ini(u(= t&at i', into t&e 'in o+ a ci!cula! con"ucto! o! t&e e"*e' o+ a +lat 't!i , !o"ucin* %&at i' no%n a' <'in< o!
%&e!e R+ K a)c) !e'i'tance o+ con"ucto! Ro K ")c) !e'i'tance o+ con"ucto! S K 'in e++ect !atio T&e (a*nitu"e an" i(o!tance o+ t&e e++ect inc!ea'e' %it& t&e +!e0uenc#, an" t&e 'ie, '&ae an" t&icne'' o+ con"ucto!, but i' in"een"ent o+ t&e (a*nitu"e o+ t&e cu!!ent +lo%in*) It '&oul" be note" t&at a' t&e con"ucto! te(e!atu!e inc!ea'e' t&e 'in e++ect "ec!ea'e' *i-in* !i'e to a lo%e! t&an e.ecte" a)c) !e'i'tance at ele-ate" te(e!atu!e') T&i' e++ect i' (o!e (a!e" +o! a coe! con"ucto! t&an an alu(iniu( con"ucto! o+ e0ual c!o''8'ectional a!ea becau'e o+ it' lo%e! !e'i'ti-it#) T&e "i++e!ence i' a!ticula!l# noticeable in la!*e bu'ba! 'ection') Copper rods T&e 'in e++ect !atio o+ 'oli" coe! !o"' can be calculate" +!o( t&e +o!(ulae "e!i-e" b# Ma.%ell, Ra#lei*& an" ot&e!' 7Bulletin of the Bureau of Standards, 1912
%&e!e S K Sin e++ect !atio
" K "ia(ete! o+ !o", (( + K +!e0uenc#, ;
ρ K !e'i'ti-it#, µΩ c( µ K e!(eabilit# o+ coe! 7K1 :o! ;C coe! at 2$HC, ρ K 1)2? µΩ c(, &ence
%&e!e A K c!o''8'ectional a!ea o+ t&e con"ucto!, ((2 0igure 4 $@in effect in
Copper tubes
Sin e++ect in tubula! coe! con"ucto!' i' a +unction o+ t&e t&icne'' o+ t&e %all o+ t&e tube an" t&e !atio o+ t&at t&icne'' to t&e tube "ia(ete!, an" +o! a *i-en c!o'' 'ectional a!ea it can be !e"uce" b# inc!ea'in* t&e tube "ia(ete! an" !e"ucin* t&e %all t&icne'') :i*u!e >, :i*u!e 6, an" :i*u!e , %&ic& &a-e been "!a%n +!o( +o!(ulae "e!i-e" b# D%i*&t 71922 an" A!nol" 719@6, can be u'e" to +in" t&e -alue o+ 'in e++ect +o! -a!iou' con"ucto! 'ection') In t&e ca'e o+ tube' 7:i*u!e >, it can be 'een t&at to obtain lo% 'in e++ect !atio -alue' it i' "e'i!able to en'u!e, %&e!e o''ible, lo% -alue' o+ t" an" √7+!) :o! a *i-en c!o''8'ectional a!ea t&e 'in e++ect !atio +o! a t&in coe! tube i' a!eciabl# lo%e! t&an t&at +o! an# ot&e! +o!( o+ con"ucto!) Coe! tube', t&e!e+o!e, &a-e a (a.i(u( e++icienc# a' con"ucto!' o+ alte!natin* cu!!ent', a!ticula!l# t&o'e o+ &i*& (a*nitu"e o! &i*& +!e0uenc#) T&e e++ect o+ %all t&icne'' on 'in e++ect +o! a 1$$ (( "ia(ete! tube ca!!#in* a >$; alte!natin* cu!!ent i' clea!l# '&o%n in :i*u!e >)
0igure "esistance of
0igure # $@in effect for rods and tubes
0lat copper bars T&e 'in e++ect in +lat coe! ba!' i' a +unction o+ it' t&icne'' an" %i"t&) 4it& t&e la!*e! 'ie' o+ con"ucto!, +o! a *i-en c!o''8'ectional a!ea o+ coe!, t&e 'in e+ +ect in a t&in ba! o! 't!i i' u'uall# le'' t&an in a ci!cula! coe! !o" but *!eate! t&an in a t&in tube) It i' "een"ent on t&e !atio o+ t&e %i"t& to t&e t&icne'' o+ t&e ba! an" inc!ea'e' a' t&e t&icne'' o+ t&e ba! inc!ea'e') A t&in coe! 't!i, t&e!e+o!e, i' (o!e e++icient t&an a t&ic one a' an alte!natin* cu!!ent con"ucto!) :i*u!e can be u'e" to +in" t&e 'in e++ect -alue +o! +lat ba!') 0igure & $@in effect for rectangular conductors
$*uare copper tubes T&e 'in e++ect !atio +o! '0ua!e coe! tube' can be obtaine" +!o( :i*u!e F) 0igure ( $@in effect ratio for %ollo/ s*uare conductors
Pro;i!ity Effect n t&e +o!e*oin* con'i"e!ation o+ 'in e++ect i t &a' been a''u(e" t&at t&e con"ucto! i' i'olate" an" at 'uc& a "i'tance +!o( t&e !etu!n con"ucto! t&at t &e e++ect o+ t&e cu!!ent in it can be ne*lecte") 4&en con"ucto!' a!e clo'e to*et&e!, a!ticula!l# in lo% -olta*e e0ui(ent, a +u!t&e! "i'to!tion o+ cu!!ent "en'it# !e'ult' +!o( t&e inte!action o+ t&e (a*netic +iel"' o+ ot&e! con"ucto!') In t&e 'a(e %a# a' an e)()+) (a# be in"uce" in a con"ucto! b# it' o%n (a*netic +lu., 'o (a# t&e (a*netic +lu. o+ one con"ucto! !o"uce an e)()+) in an# ot&e! con"ucto! 'u++icientl# nea! +o! t&e e++ect to be 'i*ni+icant) I+ t%o 'uc& con"ucto!' ca!!# cu!!ent' in oo'ite "i!ection', t&ei! elect!o8(a*netic +iel"' a!e oo'e" to one anot&e! an" ten" to +o!ce one anot&e! aa!t) T&i' !e'ult' in a "ec!ea'e o+ +lu.
lina*e' a!oun" t&e a"/acent a!t' o+ t&e con"ucto!' an" an inc!ea'e in t&e (o!e !e(ote a!t', %&ic& lea"' to a concent!ation o+ cu!!ent in t&e a"/acent a!t' %&e!e t&e oo'in* e)()+) i' a (ini(u() I+ t&e cu!!ent' in t&e con"ucto!' a!e in t &e 'a(e "i!ection t&e action i' !e-e!'e" an" t&e# ten" to c!o%" into t&e (o!e !e(ote a!t' o+ t&e con"ucto!') T&i' e++ect, no%n a' t&e <!o.i(it# e++ect< 7o! <'&ae e++ect<, ten"' u'uall# to inc!ea'e t&e aa!ent a)c) !e'i'tance) In 'o(e ca'e', &o%e-e!, !o.i(it# e++ect (a# ten" to neut!ali'e t&e 'in e++ect an" !o"uce a bette! "i't!ibution o+ cu!!ent a' in t&e ca'e o+ 't!i con"ucto!' a!!an*e" %it& t&ei! +lat 'i"e' to%a!"' one anot&e!) I+ t&e con"ucto!' a!e a!!an*e" e"*e%i'e to one anot&e! t&e !o.i(it# e++ect inc!ea'e') In (o't ca'e' t&e !o.i(it# e++ect al'o ten"' to inc!ea'e t&e 't!e''e' 'et u un"e! '&o!t8ci!cuit con"ition' an" t&i' (a# t&e!e+o!e &a-e to be taen into account) T&e cu!!ent' in -a!iou' a!t' o+ a con"ucto! 'ub/ecte" to 'in an" !o.i(it# e++ect' (a# -a!# con'i"e!abl# in &a'e, an" t&e !e'ultin* ci!culatin* cu!!ent *i-e !i'e to a""itional lo''e' %&ic& can be (ini(i'e" onl# b# t&e c&oice o+ 'uitable t#e' o+ con"ucto! an" b# t&ei! ca!e+ul a!!an*e(ent) T&e (a*nitu"e o+ t&e !o.i(it# e++ect "een"', a(on*'t ot&e! t&in*', on t&e +!e0uenc# o+ t&e cu!!ent an" t&e 'acin* an" a!!an*e(ent o+ t&e con"ucto!') T&e *!a&' in :i*u!e 1? 7Section 6 can be u'e" to obtain -alue' o+ !o.i(it# e++ect +o! -a!iou' con"ucto! con+i*u!ation' at >$ o! 6$ ;) Met&o"' o+ calculation +o! ot&e! +!e0uencie' a!e a-ailable 7D%i*&t 19?6) T&e unbalancin* o+ cu!!ent "ue to t&e !o.i(it# e++ect can be !e"uce" b# 'acin* t&e con"ucto!' o+ "i++e!ent &a'e' a' +a! aa!t a' o''ible an" 'o(eti(e' b# (o"i+#in* t&ei! '&ae in acco!"ance %it& t &e 'acin* a"ote") In t&e ca'e o+ la(inate" ba!' a !e"uction (a# be obtaine" b# t!an'o'in* t&e la(ination' at +!e0uent inte!-al' o! b# e(lo#in* cu!!ent balance!' u'in* in"uctance') P!o.i(it# e++ect (a# be co(letel# o-e!co(e b# a"otin* a concent!ic a!!an*e(ent o+ con"ucto!' %it& one in'i"e t&e ot&e! a' i' u'e" +o! i'olate" &a'e bu'ba! '#'te(') T&e (a*netic +iel" !oun" bu'ba! con"ucto!' (a# be con'i"e!abl# (o"i+ie" an" t&e cu!!ent "i'to!tion inc!ea'e" b# t&e !e'ence o+ (a*netic (ate!ial' an" onl# (etal' 'uc& a' coe! o! coe! allo#' '&oul" be u'e" +o! a!t' liel# to co(e %it&in t&e (a*netic +iel" o+ t&e ba!')
Condition for )ini!u! oss ot& 'in an" !o.i(it# e++ect' a!e "ue to ci!culatin* o!
Penetration Dept% In t&e ca'e o+ 'ecial con"ucto! a!!an*e(ent', o! %&e!e &i*& +!e0uencie' a!e e(lo#e", t&e alte!natin* cu!!ent !e'i'tance (a# be calculate" u'in* t&e ea!lie! 'ection') It i' o+ten nece''a!# to no% t&e "et& o+ enet!ation o+ t&e cu!!ent into a con"ucto!, t&at i' t&e "et& at %&ic& t&e cu!!ent "en'it# &a' been !e"uce" to 1e, o! $)@6F o+ it' -alue at t&e con"ucto! 'u!+ace) T&i' can be calculate" u'in* t&e +ollo%in* +o!(ula %&en it' !e'i'ti-it# an" t&e +!e0uenc# a!e no%n) "et& o+ enet!ation
%&e!e " K "et& o+ enet!ation, ((
ρ K !e'i'ti-it# o+ coe!, µΩ c( + K +!e0uenc#, ;
. Effect of Busbar Arrange!ents on "ating a!inated copper bars
C%annel and angle bars
,nter-leaing of conductors
Co!parison of conductor arrange!ents
ransposition of conductors
Enclosed copper conductors
Co!pound insulated conductors
ubular bars
Plastic insulated conductors
Concentric conductors
,solated p%ase busbars
T&e e++icienc# o+ all t#e' o+ &ea-# cu!!ent bu'ba!' "een"' uon ca!e+ul "e'i*n, t&e (o't i(o!tant +acto!' bein* a T&e !o-i'ion o+ a (a.i(u( 'u!+ace a!ea +o! t&e "i''iation o+ &eat) b An a!!an*e(ent o+ ba!' %&ic& cau'e a (ini(u( o+ inte!+e!ence %it& t&e natu!al (o-e(ent' o+ ai! cu!!ent') c An a!o.i(atel# uni+o!( cu!!ent "en'it# in all a!t' o+ t&e con"ucto!') T&i' i' no!(all# obtaine" b# &a-in* a' (uc& coe! a' o''ible e0ui"i'tant +!o( t&e (a*netic cent!e o+ t&e bu'ba!) " Lo% 'in e++ect an" !o.i(it# e++ect +o! a)c) bu'ba! '#'te(') To (eet t&e'e !e0ui!e(ent' t&e!e a!e (an# "i++e!ent a!!an*e(ent' o+ coe! bu'ba!' u'in* la(ination', a' %ell a' coe! e.t!u'ion' o+ -a!iou' c!o''8'ection') 0igure Busbar arrange!ents
a!inated copper bars To obtain t&e be't an" (o't e++icient !atin* +o! !ectan*ula! 't!i coe! con"ucto!' t&e# '&oul" be (ounte" %&ene-e! o''ible %it& t&ei! (a/o! c!o''8'ectional a.e' -e!tical 'o *i-in* (a.i(u( coolin* 'u!+ace') La(ination' o+ 6 o! 6)@ (( t&icne'', o+ -a!#in* %i"t&' an" %it& 6 o! 6)@ (( 'acin*' a!e !obabl# t&e (o't co((on an" a!e 'ati'+acto!# in (o't a)c) lo% cu!!ent ca'e' an" +o! all ")c) '#'te(') It i' not o''ible to *i-e an# *ene!all# alicable +acto!' +o! calculatin* t&e ")c) !atin* o+ la(inate" ba!', 'ince t&i' "een"' uon t&e 'ie an" !oo!tion' o+ t&e la(ination' an" on t&ei! a!!an*e(ent) A *ui"e to t&e e.ecte" !elati-e !atin*' a!e *i-en in Table F belo% +o! a >$ ; '#'te() T&e !atin*' +o! 'in*le ba!' can be e'ti(ate" u'in* t&e (et&o"' *i-en in Section @ an" Section ?) able ( )ultiplying factors for la!inated bars
Table 1@ 7Aen"i. 2 *i-e' a)c) !atin*' +o! -a!iou' con+i*u!ation' o+ la(inate" ba!' ba'e" on te't (ea'u!e(ent')
:o! all no!(al li*&t an" (e"iu( cu!!ent u!o'e' an a!!an*e(ent 'uc& a' t&at in :i*u!e 9a i' enti!el# 'ati'+acto!#, but +o! a)c) cu!!ent' in e.ce'' o+ @$$$ A %&e!e la!*e nu(be!' o+ la(ination' %oul" be !e0ui!e" it i' nece''a!# to !ea!!an*e t&e la(ination' to *i-e bette! utili 'ation o+ t&e coe! ba!') T&e e++ect o+ u'in* a la!*e nu(be! o+ la(ination' (ounte" 'i"e b# 'i"e i' '&o%n in :i*u!e 1$ +o! a)c) cu!!ent') T&e cu!!ent "i't!ibution i' in"een"ent o+ t&e total cu!!ent (a*nitu"e) 0igure 1 Alternating current distribution in a bar /it% ten la!inations
T&i' cu!-e '&o%' t&at "ue to 'in e++ect t&e!e i' a con'i"e!able -a!iation in t&e cu!!ent ca!!ie" b# eac& la(ination, t&e oute! la(ination' ca!!#in* a!o.i(atel# +ou! ti(e' t&e cu!!ent in t&o'e at t&e cent!e) T&e t%o cent!e la(ination' to*et&e! ca!!# onl# about one8tent& o+ t&e total cu!!ent) T&e cu!!ent' in t&e "i++e!ent la(ination' (a# al'o -a!# a!eciabl# in &a'e, %it& t&e !e'ult t&at t&ei! nu(e!ical 'u( (a# be *!eate! t&an t&ei! -ecto!ial 'u(, %&ic& i' e0ual to t&e line cu!!ent) T&e'e ci!culatin* cu!!ent' *i-e !i'e to a""itional lo''e' an" lo%e! e++i cienc# o+ t&e '#'te() It '&oul" al'o be note" t&at t&e cu!-e i' non8'#((et!ical "ue to t&e !o.i(it# e++ect o+ an a"/acent &a'e) :o! t&e'e !ea'on' it i' !eco((en"e" t&at alte!nate a!!an*e(ent', 'uc& a' t&o'e "i'cu''e" in t&e +ollo%in* 'ection', a!e u'e" +o! &ea-# cu!!ent a)c) '-'te(')
,nter-leaing of conductors 4&e!e lon* lo%8-olta*e a)c) ba!' a!e ca!!#in* &ea-# cu!!ent', a!ticula!l# at a lo% o%e! +acto!, in"ucti-e -olt "!o (a# beco(e a 'e!iou' !oble( %it& la(inate" ba!' a!!an*e" a' i n :i*u!e 9a) T&e -olta*e "!o +o! an# *i-en 'ie o+ con"ucto! i' !oo!tional to t&e cu!!ent an" t&e len*t& o+ t&e ba!', an" inc!ea'e' a' t&e 'ea!ation bet%een con"ucto!' o+ "i++e!ent &a'e' inc!ea'e') In t&e ca'e o+ la(inate" ba!' t&e in"ucti-e -olt "!o can be !e"uce" b# 'littin* u t&e ba!' into an e0ui-alent nu(be! o+ '(alle! ci!cuit' in a!allel, %it& t&e con"ucto!' o+ "i++e!ent &a'e' inte!lea-e" a' '&o%n in :i*u!e 9b) T&i' !e"uce' t&e a-e!a*e 'acin* bet%een con"ucto!' o+ "i++e!ent &a'e' an" 'o !e"uce' t&e in"ucti-e -olt "!o)
ransposition of conductors
T&e unbalance" cu!!ent "i't!ibution in a la(inate" ba! ca!!#in* a)c) cu!!ent "ue to 'in an" !o.i(it# e++ect' (a# be counte!acte" b# t!an'o'in* la(ination' o! *!ou' o+ la(ination' at inte!-al') Tain*' an" ot&e! connection' (ae t!an'o'ition "i++icult, but it can be %o!t&%&ile %&e!e lon* 'ection' o+ ba!' a!e +!ee +!o( tain*') T&e a!!an*e(ent i' a' '&o%n in :i*u!e 9e)
ubular bars A tubula! coe! con"ucto! i' t&e (o't e++icient o''ible a' !e*a!"' 'in e++ect, a' t&e (a.i(u( a(ount o+ (ate!ial i' locate" at a uni+o!( "i'tance +!o( t&e (a*netic cent!e o+ t&e con"ucto!) T&e 'in e++ect !e"uce' a' t&e "ia(ete! inc!ea'e' +o! a con'tant %all t&icne'', %it& -alue' clo'e to unit# o''ible %&en t&e !atio o+ out'i"e "ia(ete! to %all t&icne'' e.cee"' about 2$) T&e natu!al coolin* i' not a' *oo" a' t&at +o! a la(inate" coe! ba! '#'te( o+ t&e 'a(e c!o''8 'ectional a!ea, but %&en t&e !o.i(it# e++ect' a!e taen into account t&e one8iece tube en'u!e' t&at t&e %&ole tube attain' an e-en te(e!atu!e 8 a con"ition !a!el# obtaine" %it& l a(inate" ba! '#'te(') Tubula! coe! con"ucto!' al'o len" t&e('el-e' to alte!nati-e (et&o"' o+ coolin* b#, +o! e.a(le, +o!ce" ai! o! li0ui" coolin* %&e!e &eat can be !e(o-e" +!o( t&e inte!nal 'u!+ace o+ t&e tube') Cu!!ent !atin*' o+ 'e-e!al ti(e' t&e natu!al ai! coole" -alue a!e o''ible u'in* +o!ce" coolin* %it& t&e la!*e't inc!ea'e' %&en li0ui" coolin* i' e(lo#e") A tubula! ba! al'o occuie' le'' 'ace t&an t&e (o!e u'ual coe! la(inate" ba! an" &a' a +u!t&e! a"-anta*e t&at it' 't!en*t& an" !i*i"it# a!e *!eate! an" uni+o!( in all "e+lection lane') T&e'e a"-anta*e' a!e, &o%e-e!, 'o(e%&at !e"uce" b# t&e "i++icult# o+ (ain* /oint' an" connection' %&ic& a!e (o!e "i++icult t&an t&o'e +o! la(inate" ba!') T&e'e !oble(' &a-e no% been !e"uce" b# t&e int!o"uction o+ coe! %el"in* an" e.ot&e!(ic coe! +o!(in* (et&o"') Coe! tube' a!e a!ticula!l# 'uitable +o! &i*& cu!!ent alication', 'uc& a' a!c +u!nace', %&e!e +o!ce" li0ui" coolin* can be u'e" to *!eat a"-anta*e) T&e tube can al'o be u'e" in i'olate" &a'e bu'ba! '#'te(' "ue to t&e ea'e %it& %&ic& it can be 'uo!te" b# in'ulato!')
Concentric conductors T&i' a!!an*e(ent i' not %i"el# u'e" "ue to "i++icultie' o+ 'uo!t but &a' t&e a"-anta*e o+ t&e oti(u( co(bination o+ lo% !eactance an" e""# cu!!ent lo''e' an" i' %ell 'uite" to +u!nace an" %el" 'et alication') It '&oul" be note" t&at t&e i'olate" &a'e bu'ba! '#'te(' a!e o+ t&i' t#e
%it& t&e cu!!ent in t&e e.te!nal enclo'u!e bein* al(o't e0ual to t&at in t&e con"ucto! %&en t&e continuou'l# bon"e" t&!ee8&a'e enclo'u!e '#'te( i' u'e")
C%annel and angle bars Alte!nati-e a!!an*e(ent' to +lat o! tubula! coe! ba!' a!e t&e c&annel an" an*le ba!' %&ic& can &a-e a"-anta*e') T&e (o't i(o!tant o+ t&e'e '&ae' a!e '&o%n in t&e "ia*!a(' belo%) T&e'e a!e ea'il# 'uo!te" an" *i-e *!eat !i*i"it# an" 't!en*t& %&ile t&e (ain* o+ /oint' an" connection' !e'ent' no 'e!iou' "i++icult#) T&e e!(i''ible alte!natin* cu!!ent "en'it# in +!ee ai! +o! a *i-en te(e!atu!e !i'e i' u'uall# *!eate! in t&e ca'e o+ t%o an*le8'&ae" con"ucto!' 7"ia*!a( 7a t&an in an# ot&e! a!!an*e(ent o+ con"ucto! (ate!ial)
:o! lo% -olta*e &ea-# cu!!ent 'in*le8&a'e ba!' %it& na!!o% &a'e cent!e', 'in*le coe! c&annel' %it& t&e %eb' o+ t&e <*o< an" 7Aen"i. 2) T&e !atin*' *i-en a!e t&e (a.i(u( cu!!ent !atin*' %&ic& "o not tae t&e co't o+ lo''e' into account an" &ence a!e not oti(i'e")
Co!parison of conductor arrange!ents T&e e.tent to %&ic& t&e a)c) cu!!ent !atin* +o! a *i-en te(e!atu!e !i'e o+ a con"ucto! containin* a *i-en c!o''8'ectional a!ea o+ coe! "een"' on t &e c!o''8'ection '&ae) T&e a!o.i(ate !elati-e a)c) !atin*' +o! a t#ical c!o''8'ectional a!ea o+ 1$ $$$ ((2 a!e '&o%n in :i*u!e 11) :o! c!o''8'ectional a!ea' *!eate! t&an 1$ $$$ ((2 t&e +acto!' a!e *!eate! t&an t&o'e '&o%n, an" a!e '(alle! +o! '(alle! c!o''8'ection') In t&e ca'e o+ "ouble8c&annel bu'ba!', t&e !atio o+ %eb8to8 +lan*e len*t&' an" al'o t&e %eb t&icne'' &a-e a con'i"e!able e++ect on t&e cu!!ent ca!!#in* caacit#) 0igure 11 Co!paratie a.c. ratings of arious conductor arrange!ents eac% %aing a cross sectional area of 1= !! 2 of
Enclosed copper conductors In (an# ca'e' bu'ba!' a!e 'u!!oun"e" b# enclo'u!e', no!(all# (etallic, %&ic& !e"uce t&e bu'ba! &eat "i''iation "ue to !e"uction in coolin* ai! +lo% an" !a"iation lo''e' an" t&e!e+o!e *i-e cu!!ent !atin*' %&ic& (a# be con'i"e!abl# le'' t&an t&o'e +o! +!ee ai ! e.o'u!e) Ventilate" enclo'u!e', &o%e-e!, !o-i"e (ec&anical !otection an" 'o(e coolin* ai! +lo% %it& t&e lea't !e"uction in cu!!ent !atin*) T&e !e"uction in !atin* +o! a *i-en te(e!atu!e !i'e %ill -a!# con'i"e!abl# %it& t&e t#e an" 'ie o+ ba! an" enclo'u!e) T&e *!eate't "ec!ea'e in cu!!ent !atin* occu!' %it& ba!' %&ic& "een" (ainl# on +!ee ai! ci!culation an" le'' on uni+o!( cu!!ent "i't!ibution 'uc& a' t&e (o"i+ie" &ollo% '0ua!e a!!an*e(ent 7:i*u!e 9") In t&e'e ca'e' t&e !atin* (a# be !e"uce" to bet%een 6$ an" 6>G %&en t&e con"ucto!' a!e enclo'e" in non8(a*netic (etal enclo'u!e') In t&e ca'e o+ tubula! con"ucto!' o! t&o'e o+ clo'el# *!oue" +lat la(ination', %&ic& a!e no!(all# not 'o %ell coole" b# ai! ci!culation, t&e !atin*' (a# be !e"uce" to about >G o+ +!ee ai! !atin*' +o! no!(al te(e!atu!e !i'e') 4&e!e t&e bu'ba! '#'te( i' enclo'e" in t&ic (a*netic enclo'u!e', 'uc& a' i n (etal8cla" '%itc&*ea!, t&e !e"uction i' a!o.i(atel# a +u!t&e! 1>G) T&e e++ect o+ t&in '&eet8'teel enclo'u!e' i' 'o(e%&at le'') T&e'e a""itional !e"uction' a!e "ue to t&e &eat *ene!ate" b# t&e alte!natin* (a*netic +iel"' t&!ou*& &#'te!e'i' an" e""# cu!!ent lo''e') e'i"e' t&e "e!atin* cau'e" b# enclo'u!e con"ition', ot&e! li(itation' on (a.i(u( %o!in* te(e!atu!e a!e o+ten !e'ent, 'uc& a' %&en t&e out'i"e o+ enclo'u!e' '&oul" not e.cee" a *i-en 'a+et# -alue) T&e'e "e!atin*' a!e a++ecte" b# t&e elect!ical clea!ance' in-ol-e" an" t&e "e*!ee o+ -entilati on in t&e enclo'u!e) T&e abo-e +i*u!e' an" t&e cu!-e' '&o%n in :i*u!e 12 '&oul" onl# be taen a' a !ou*& *ui"e to t&e !e0ui!e" "e!atin*= an accu!ate +i*u!e can onl# be obtaine" b# te'tin*) All a!t' 'uc& a' con"ucto! an" '%itc& +ittin*', enclo'u!e' an" inte!&a'e ba!!ie!' (a# be 'ub/ect to a!eciable te(e!atu!e !i'e "ue to ci!culatin* an" e""# cu!!ent lo''e' %&en clo'e to t&e &ea-# cu!!ent ba!' an" connection') T&e'e lo''e' can be !e"uce" to a (ini(u( b# (ain* t&e'e a!t' +!o( &i*& con"ucti-it# non8(a*netic (ate!ial 'uc& a' coe! o! coe! allo#) 0igure 12 Co!parison of appro;i!ate current ratings for busbars in different enclosures
Co!pound insulated conductors T&e cu!!ent !atin* o+ coe! i((e!'e" in oil o! co(oun" "een" uon a nu(be! o+ +acto!' %&ic& (a# -a!# %i"el# %it& "e'i*n, an" can no!(all# onl# be con+i!(e" b# ca!!#in* out t e(e!atu!e !i'e te't' on t&e co(lete a''e(bl#) T&e !atin*' o+ enclo'e" ba!' a!e nea!l# al%a#' (uc& lo%e! t&an t&e +!ee ai! !atin*') T&e te(e!atu!e !i'e i' "een"ent on t&e !ate at %&ic& &eat i' con"ucte" t&!ou*& t&e in'ulatin* (e"ia an" "i''iate" +!o( t&e out'i"e ca'in* b# !a"iation an" con-ection) T&e!e i' nea!l# al%a#' a clo'e! &a'e 'acin* bet%een con"ucto!' *i-in* &i*& !o.i(it# e++ect' an" &i*&e! &eat lo''e' in t&e (a*netic oute! ca'in*' an" 'o *i-in* !i'e to &i*&e! te(e!atu!e !i'e') P!o.i(it# e++ect i' o+ten (o!e i(o!tant +o! in'ulate" ba!' t&an t&o'e in ai!) La(inate" ba!' &a-e +e%e! a"-anta*e' %&en i((e!'e" in oil o! co(oun" an" ci!cula! coe! con"ucto!' eit&e! 'oli" o! &ollo% t&ou*& a!e o+ten !e+e!!e" a!ticula!l# +o! &i*&8-olta*e *ea! an" &i*& cu!!ent *ene!ato!', t!an'+o!(e!', etc), %&e!e (o!e e++ecti-e coolin* 'uc& a' %ate! coolin* can be e(lo#e" to i(!o-e con"ucto! (ate!ial utili'ation an" &ence !e"uce t&e o-e!all 'ie o+ lant)
Plastic insulated conductors T&e!e i' a %i"enin* u'e o+ la'tic continuou' in'ulation a' t&e !i(a!# in'ulation +o! lo% cu!!ent an" -olta*e bu'ba!') T&i' in'ulation i' u'uall# o+ t&e '&!in8on P)V)C) t#e t&ou*& %!a8on tae i' 'o(eti(e' u'e") T&i' (et&o" i' u'e" +o! -olta*e' u to about 1> V, t&ou*& (uc& &i*&e! le-el' can be attaine" %&en 'eciali'e" in'ulation '#'te(' 'uc& a' eo.# !e'in o! 'i (ila! ba'e" tae' an" o%"e!' a!e e(lo#e") T&e'e '#'te(' a!e a!ticula!l# u'e+ul %&e!e &i*& ato(ic !a"iation
le-el', o! &i*& te(e!atu!e' 7u to 1@$HC a!e encounte!e", alt&ou*& account (u't be taen o+ t&e o''ibilit# o+ &alo*en *a''in* +!o( P)V)C) in'ulation' at te(e!atu!e' a!oun" 1$$HC) Mo"i+ie" P)V)C) (ate!ial' %it& i(!o-e" &i*&8te(e!atu!e e!+o!(ance a!e a-ailable)
,solated p%ase busbars 'olate" &a'e bu'ba!' con'i't o+ a (etallic enclo'e" con"ucto! %&e!e eac& in"i-i"ual &a'e o! ole i' 'u!!oun"e" b# a 'ea!atel# ea!t&e" '&eat& %&ic& i' connecte" at it' en"' b# a +ull '&o!t8 ci!cuit cu!!ent !ate" ba!) T&e '&eat& i' inten"e" !i(a!il# to !e-ent inte!&a'e '&o!t8ci!cuit cu!!ent' "e-eloin*) T&e# &a-e t&e +u!t&e! a"-anta*e t&at t&e &i*& (a*netic +iel"' c!eate" b# t&e con"ucto! cu!!ent a!e al(o't co(letel# cancelle" b# an e0ual an" oo'ite cu!!ent in"uce" in t&e enclo'u!e o! '&eat& %it& !e"uction' o+ 9>G o! bette! in t &e e.te!nal (a*netic +iel" bein* o''ible) An i(o!tant !e'ult i' t&at t&e lieli&oo" o+ 'teel%o! o-e!&eatin* %&en a"/acent to t&e bu'ba! '#'te( i' con'i"e!abl# !e"uce" e.cet %&e!e t&e '&eat& '&o!t8ci!cuit ba!' a!e locate") T&i' cu!!ent +lo%in* in t&e enclo'u!e (ae' t&e (et&o" o+ e'ti(atin* t&e e!+o!(ance o+ t&e bu'ba! '#'te( (uc& (o!e co(licate" an" can onl# be !e'ol-e" b# obtainin* a &eat balance bet%een con"ucto! an" enclo'u!e u'in* an inte!acti-e calculation (et&o") T&e'e bu'ba!' a!e u'e" no!(all# +o! oe!atin* -olta*e' o+ bet%een 11 V an" @6 V t&ou*& e0ui(ent u'in* (uc& lo%e! -olta*e' an" &i*&e! -olta*e' a!e i nc!ea'in*l# c&an*in* to t&i' '#'te() E.a(le' o+ 'uc& e0ui(ent a!e e.cite! connection', '%itc&*ea! inte!connection', *ene!ato! to t!an'+o!(e! connection', &i*& -olta*e '%it c&*ea! u'in* S: 6 7'ul&u! &e.a+luo!i"e *a' in'ulation 7t&i' *a' &a-in* an in'ulation le-el (an# ti(e' bette! t&an ai!) T&e cu!!ent +lo%in* in t&e con"ucto! !an*e' +!o( a' little a' 1$$$ A to in e.ce'' o+ ?$ A) To obtain t&e &i*&e! cu!!ent' +o!ce" coolin* i' u'e", t&e (o't co((onl# u'e" coolin* (e"ia bein* ai! an" %ate! t&ou*& ot&e! coolin* *a'e' o! li0ui"' can be u'e") T&e u'e o+ t&e'e coolin* '#'te(' u'uall# c!eate' (uc& inc!ea'e" &eat lo''e' an" 'o t&ei! u'e (u't be /u'ti+ie" b# bene+it' in ot&e! a!ea', e)*), !e"uce" ci-il co't', !e"uce" &#'ical 'ie %&e!e 'ace i' at a !e(iu( o! !e"uction in 'ie to enable no!(al (anu+actu!in* (et&o"' be u'e" bot& +o! t&e ba'ic bu'ba! (ate!ial an" al'o t&e co(lete bu'ba! '#'te() Anot&e! +acto! %&ic& in+luence' t&e (et&o" c&o'en +o! +o!ce" coolin* i' t&e natu!all# coole" !atin* o+ t&e bu'ba! '#'te( an" al'o it' abilit# to 'u'tain o-e!loa" con"ition') T&e bu'ba!' a!e u'uall# (anu+actu!e" in 'in*le8&a'e unit' o+ t!an'o!table len*t& an" con'i't o+ a cent!al con"ucto! u'uall# tubula! o+ !oun", '0ua!e o! c&annel c!o''8'ection, 'uo!te" b# o!celain o! eo.# !e'in in'ulato!') T&e in'ulato!' a!e locate" b# t&e e.te!nal (etallic '&eat& t &!ou*& %&ic& t&e# a!e no!(all# !e(o-e" +o! 'e!-icin*)
#. $%ort-Circuit Effects $%ort-Circuit
$%ort-Circuit J* an" at @$$HC it i' about ?1$ J* ) S&o!t8ci!cuit &eatin* c&a!acte!i'tic' a!e not ea'# to calculate accu!atel# becau'e o+ co(le. a)c) an" ")c) cu!!ent e++ect', but +o! (o't u!o'e' t&e +o!(ulae belo% %ill no!(all# *i-e 'u++icientl# accu!ate !e'ult'
%&e!e t K (a.i(u( '&o!t8ci!cuit ti(e, ' A K con"ucto! c!o''8'ection a!ea, ((2 I K con"ucto! cu!!ent, A
θ K con"ucto! te(e!atu!e !i'e, I+ θ K @$$HC, t&en
T&e -alue o+ t obtaine" +!o( t&e abo-e e0uation '&oul" al%a#' be *!eate! t&an t&e !e0ui!e" '&o!t ci!cuit %it&'tan" ti(e %&ic& i' u'uall# 1 to ? 'econ"') T&e te(e!atu!e !i'e e! 'econ" "ue to a cu!!ent I i' *i-en b# t &e +ollo%in* a!o.i(ate +o!(ula
7IA '&oul" be le'' t&an $)2> +o! !ea'onable accu!ac#) T&e (a.i(u( '&o!t8ci!cuit te(e!atu!e i' -e!# o+ten c&o'en to be @$$HC +o! ea!t& ba! '#'te(' but t&e ue! li(it +o! t&e &a'e' i' no!(all# lo%e! an" i' "een"ent on t&e (ec&anical !oe!tie' !e0ui!e" an" 'u!+ace +ini'& o+ t&e coe! (ate!ial)
%&e!e θ K te(e!atu!e !i'e, HC
θ(a. K (a.i(u( te(e!atu!e !i'e, HC e K e.onential con'tant 7K2)1F t K ti(e, '
τ K ti(e con'tant, ' T&e ti(e con'tant can be +oun" u'in* t&e +ollo%in* +o!(ula
%&e!e % K !ate o+ *ene!ation o+ &eat at tK$, 4
( K (a'', * c K 'eci+ic &eat, J* T&e ti(e con'tant *i-e' t&e ti(e taen to !eac& $)6@6 o+ t&e (a.i(u( te(e!atu!e !i'e,
θ (a.)
Electro!agnetic $tresses 4&en a con"ucto! ca!!ie' a cu!!ent it c!eate' a (a*netic +iel" %&ic& inte!act' %it& an# ot&e! (a*netic +iel" !e'ent to !o"uce a +o!ce) 4&en t&e cu!!ent' +lo%in* in t%o a"/acent con"ucto!' a!e in t&e 'a(e "i!ection t&e +o!ce i' one o+ att!action, an" %&en t&e cu!!ent' a!e in oo'ite "i!ection' a !eul'i-e +o!ce i' !o"uce") In (o't bu'ba! '#'te(' t&e cu!!ent8ca!!#in* con"ucto!' a!e u'uall# 't!ai*&t an" a!allel to one anot&e!) T&e +o!ce !o"uce" b# t&e t%o con"ucto!' i' !oo!tional to t&e !o"uct' o+ t&ei! cu!!ent') No!(all# in (o't bu'ba! '#'te(' t&e +o!ce' a!e -e!# ' (all an" can be ne*lecte", but un"e! '&o!t8ci!cuit con"ition', t&e# beco(e la!*e an" (u't be taen into account to*et&e! %it& t&e con"ucto! (ate!ial +ib!e 't!e''e' %&en "e'i*nin* t&e con"ucto! in'ulato! an" it' a''ociate" 'uo!t' to en'u!e a"e0uate 'a+et# +acto!') T&e +acto!' to be taen into account (a# be 'u((a!i'e" a' +ollo%' a 't!e''e' "ue to "i!ect late!al att!acti-e an" !eul'i-e +o!ce') b Vib!ational 't!e''e') c Lon*itu"inal 't!e''e' !e'ultin* +!o( late!al "e+lection) " T%i'tin* (o(ent' "ue to late!al "e+lection) In (o't ca'e' t&e +o!ce' "ue to '&o!t8ci!cuit' a!e alie" -e!# 'u""enl#) Di!ect cu!!ent' *i-e !i'e to uni"i!ectional +o!ce' %&ile alte!natin* cu!!ent' !o"uce -ib!ational +o!ce') )a;i!u! stresses 4&en a bu'ba! '#'te( i' !unnin* no!(all# t&e inte!&a'e +o!ce' a!e no!(all# -e!# '(all %it& t&e 'tatic %ei*&t o+ t&e bu'ba!' bein* t&e "o(inant co(onent) 3n"e! '&o!t8ci!cuit con"ition' t&i' i' -e!# o+ten not t&e ca'e a' t&e cu!!ent !i'e' to a ea o+ 'o(e t&i!t# ti(e' it' no!(al -alue, +allin* a+te! a +e% c#cle' to ten ti(e' it' initial -alue) T&e'e &i*& t!an'ito!# cu!!ent' c!eate la!*e (ec&anical +o!ce' not onl# in t&e bu'ba!' t&e('el-e' but al'o in t&ei! 'uo!tin* '#'te() T&i' (ean' t&at t&e 'uo!t in'ulato!' an" t&ei! a''ociate" 'teel%o! (u't be "e'i*ne" to %it&'tan" t&e'e &i*& loa"' a' %ell a' t&ei! no!(al 't!uctu!al !e0ui!e(ent' 'uc& a' %in", ice, 'ei'(ic an" 'tatic loa"') T&e ea o! +ull# a'#((et!ical '&o!t ci!cuit cu!!ent i' "een"ent on t&e o%e! +acto! 7co' φ o+ t&e bu'ba! '#'te( an" it' a''ociate" connecte" elect!ical lant) T&e -alue i ' obtaine" b# (ultil#in* t&e !)()') '#((et!ical cu!!ent b# t&e a!o!iate +acto! *i-en in alance" t&!ee8&a'e '&o!t8ci!cuit 't!e''e') I+ t&e o%e! +acto! o+ t&e '#'te( i' not no%n t&en a +acto! o+ 2)>> %ill no!(all# be clo'e to t&e actual '#'te( -alue e'eciall# %&e!e *ene!ation i' conce!ne") Note t&at t&e t&eo!etical (a.i(u( +o! t&i' +acto! i' 2√2 o! 2)F2F %&e!e co' φ K $) T&e'e ea -alue' !e"uce e.onentiall# an" a+te! a!o.i(atel# 1$ c#cle' t&e +acto! +all' to 1)$, i)e), t&e '#((et!ical !)()') '&o!t ci!cuit cu!!ent) T&e ea +o!ce' t&e!e+o!e no!(all# occu! in t&e +i!'t t %o c#cle' 7$)$? ' a' '&o%n in :i*u!e 1@)
In t&e ca'e o+ a co(letel# a'#((et!ical cu!!ent %a-e, t&e +o!ce' %ill be alie" %it& a +!e0uenc# e0ual to t&at o+ t&e 'ul# +!e0uenc# an" %it& a "ouble +!e0uenc# a' t&e %a-e beco(e' '#((et!ical) T&e!e+o!e in t&e ca'e o+ a >$ ; 'ul# t&e'e +o!ce' &a-e +!e0uencie' o+ >$ o! 1$$ ;) T&e (a.i(u( 't!e''e' to %&ic& a bu' 't!uctu!e i' liel# to be 'ub/ecte" %oul" occu! "u!in* a '&o!t8ci!cuit on a 'in*le8&a'e bu'ba! '#'te( in %&ic& t&e line '&o!t8ci!cuit cu!!ent' a!e "i'lace" b# 1F$H) In a t&!ee8&a'e '#'te( a '&o!t8ci!cuit bet%een t%o &a'e' i' al(o't i"entical to t&e 'in*le8&a'e ca'e an" alt&ou*& t&e &a'e cu!!ent' a!e no!(all# "i'lace" b# 12$H, un"e! '&o!t8ci!cuit con"ition' t&e &a'e cu!!ent' o+ t&e t%o &a'e' a!e al(o't 1F$H out o+ &a'e) T&e e++ect o+ t&e t&i!" &a'e can be ne*lecte") In a balance" t&!ee8&a'e '&o!t8ci!cuit, t&e !e'ultant +o!ce' on an# one o+ t&e t&!ee &a'e' i' le'' t&an in t&e 'in*le8&a'e ca'e an" i' "een"ent on t&e !elati-e &#'ical o'ition' o+ t&e t&!ee &a'e') In t&e ca'e o+ a 'in*le8&a'e '&o!t8ci!cuit, t&e +o!ce' !o"uce" a!e uni"i!ectional an" a!e t&e!e+o!e (o!e 'e-e!e t&an t&o'e "ue to a t&!ee8&a'e '&o!t8ci!cuit, %&ic& alte!nate in "i!ection) T&e '&o!t8ci!cuit +o!ce' &a-e to be ab'o!be" +i!'t b# t&e con"ucto!) T&e con"ucto! t&e!e+o!e (u't &a-e an a"e0uate !oo+ 't!en*t& to ca!!# t&e'e +o!ce' %it&out e!(anent "i'to!tion) Coe! 'ati'+ie' t&i' !e0ui!e(ent a' it &a' &i*& 't!en*t& co(a!e" %it& ot&e! con"ucto! (ate!ial' 7Table 2) ecau'e o+ t&e &i*& 't!en*t& o+ coe!, t &e in'ulato!' can be (o!e %i"el# 'ace" t&an i' o''ible %it& lo%e!8't!en*t& (ate!ial') 0igure 13 $%ort-circuit current /aefor!
$ingle p%ase s%ort circuit stresses
T&e elect!o(a*netic +o!ce "e-eloe" bet%een t%o 't!ai*&t a!allel con"ucto!' o+ ci!cula! c!o''8 'ection eac& ca!!#in* t&e 'a(e cu!!ent i' calculate" +!o( t&e +ollo%in* + o!(ula
%&e!e :(a. K +o!ce on con"ucto!, N( I K cu!!ent in bot& &a'e', A ' K &a'e 'acin*, (( T&e -alue o+ I i' no!(all# taen in t&e +ull# a'#((et!ical con"ition a' 2)>> ti(e' t&e !)()') '#((et!ical -alue o! 1)F ti(e' t&e ea !)()') -alue o+ t&e '&o!t8ci!cuit cu!!ent a' "i'cu''e" abo-e) It i' o''ible, in ce!tain ci!cu('tance', +o! t&e +o!ce' to be *!eate! t&an t&i' "ue to t&e e++ect o+ an i(ul'e in t&e ca'e o+ a -e!# !i*i" con"ucto!, o! "ue to !e'onance in t&e ca'e o+ ba!' liable to (ec&anical -ib!ation) It i' t&e!e+o!e u'ual to allo% a 'a+et# +acto! o+ 2)> in 'uc& ca'e') Balanced t%ree-p%ase s%ort-circuit stresses A t&!ee8&a'e '#'te( &a' it' no!(al cu!!ent' "i'lace" b# 12$H an" %&en a balance" t&!ee8 &a'e '&o!t8ci!cuit occu!' t&e "i'lace(ent i' (aintaine") A' %it& all balance" t&!ee8&a'e cu!!ent', t&e in'tantaneou' cu!!ent in one &a'e i' balance" b# t&e cu!!ent' in t&e ot&e! t%o &a'e') T&e "i!ection' o+ t&e cu!!ent' a!e con'tantl# c&an*in* an" 'o t&e!e+o!e a!e t&e +o!ce') T&e (a.i(u( +o!ce' a!e "een"ent on t&e oint in t&e c#cle at %&ic& t&e +ault o! '&o!t8ci!cuit occu!') T&e (a.i(u( +o!ce aea!in* on an# &a'e !e'ultin* +!o( a +ull# o++'et a'#((et!ical ea cu!!ent i' *i-en b#
79
T&e con"ition %&en t&e (a.i(u( +o!ce aea!' on t &e out'i"e &a'e' 7Re" o! lue i' *i-en b#
71$ T&e con"ition %&en t&e (a.i(u( +o!ce i' on t&e cent!e &a'e 7ello% i' *i-en b#
711 %&e!e :(a. K (a.i(u( +o!ce on con"ucto!, N( I K ea a'#((et!ical cu!!ent, A ' K con"ucto! 'acin*, (( T&e ea cu!!ent I attaine" "u!in* t&e '&o!t8ci!cuit -a!ie' %it & t&e o%e! +acto! o+ t&e ci!cuit Po/er factor
,= ; ,!(' sy!!etrical5
$
2)F2F
$)$
2)>>
$)2
2)2
$)2>
2)1
$)@
2
$)>
1)
$)
1)>
1)$
1)?1?
Correction for end effect It &a' been a''u(e" 'o +a! t&at t&e con"ucto!' a!e o+ in+inite len*t&) T&i' a''u(tion "oe' not *ene!all# lea" to *!eat e!!o!' in t&e calculate" '&o!t8ci!cuit +o!ce') T&i' i' not t!ue, &o%e-e!, at t&e en"' o+ ba!' %&e!e t&e!e i' a *!eat c&an*e in +lu. co(a!e" %it& t&e uni+o!( (a*netic +iel" o-e! (o't o+ t&e lon* 't!ai*&t con"ucto!) 4&e!e t&e con"ucto! i' !elati-el# '&o!t t&i' e++ect can be con'i"e!able, t&e no!(al +o!(ulae *i-in* o-e!e'ti(ate' +o! t &e +o!ce') To o-e!co(e t&i' !oble( t&e !ece"in* +o!(ulae can be !e%!itten in t&e +ollo%in* +o!(
%&e!e :tot K total +o!ce on t&e con"ucto!, N L K len*t& o+ con"ucto!, ( c K con'tant +!o( !ele-ant !e-iou' +o!(ula T&e +ollo%in* 'ub'titution (a# t&en be (a"e
T&e +o!(ula %ill t&en be o+ t&e +o!(
712 I+
i' -e!# la!*e t&en
i' al(o't e0ual to
an" t&e!e+o!e t&e (o"i+ie" +o!(ula beco(e' al(o't i"entical %it& t&e 'tan"a!" +o!(ula) In (an# ca'e', t&e +ollo%in* +o!(ula i' 'u++icientl# accu!ate
71@ %&e!e :tot i' a*ain t&e total +o!ce alon* t&e con"ucto! in Ne%ton') :o!(ulae 9 to 11 (a# be u'e" %&e!e
i' *!eate! t&an 2$) :o! -alue' bet%een 2$ an" ?, i' *!eate! t&an 2$) :o! -alue' bet%een 2$ an" ?, e0uation 1@ abo-e '&oul" be u'e") :o! -alue' le'' t&an ?, e0uation 12 '&oul" be u'e")
Pro;i!ity factor 0igure 14 - Pro;i!ity factor for rectangular copper conductor
T&e +o!(ulae in t&e !e-iou' 'ection u'e" +o! calculatin* '&o!t8ci!cuit +o!ce' "o not tae into account t&e e++ect o+ con"ucto!' %&ic& a!e not !oun" a' t&e# 't!ictl# onl# al# to !oun" con"ucto!') To o-e!co(e t&i' %&en con'i"e!in* !ectan*ula! con"ucto!', a !o.i(it# +acto! i' int!o"uce" into t&e o!"ina!# +o!ce +o!(ulae, it' -alue bein* +oun" u'in* t&e cu!-e' in :i*u!e 1?) E.cet in ca'e' %&e!e t&e con"ucto!' a!e -e!# '(all o! a!e 'ace" a con'i"e!able "i'tance aa!t t&e co!!ecte" *ene!al +o!(ula +o! +o!ce e! unit len*t& beco(e'
T&e -alue o+
i' +i!'t calculate" t&en i' !ea" +!o( t&e cu!-e +o! t&e a!o!iate
!atio) :!o( t&e cu!-e' it can be 'een t&at t&e e++ect o+ con"ucto! '&ae "ec!ea'e' !ai"l# %it& inc!ea'in* 'acin* an" i' a (a.i(u( +o! 't!i con"ucto!' o+ '(all t&ic ne'') It i' al(o't unit# +o! '0ua!e con"ucto!' an" i' unit# +o! a ci!cula! con"ucto!) Alte!nati-el#, t&e !o.i(it# +acto! can be calculate" u'in* t&e +ollo%in* +o!(ula, +!o( %&ic& t&e cu!-e' in :i*u!e 1? %e!e "!a%n 7D%i*&t 191) 7See :i*u!e 1? +o! e.lanation o+ '#(bol')
T&i' +o!(ula *i-e' t&e inte!(e"iate cu!-e' o+ :i*u!e 1?, +o! 'a, b$, a$ Fibrational stresses
St!e''e' %ill be in"uce" in a con"ucto! b# natu!al o! +o!ce" -ib!ation' t&e a(litu"e o+ %&ic& "ete!(ine' t&e -alue o+ t&e 't!e'', %&ic& can be calculate" +!o( t&e +o!(ulae *i-en in Section F) T&e con"ucto! '&oul" be "e'i*ne" to &a-e a natu!al +!e0uenc# %&ic& i' not %it&in @$G o+ t&e -ib!ation' in"uce" b# t&e (a*netic +iel"' !e'ultin* +!o( t&e cu!!ent' +lo%in* in a"/acent con"ucto!') T&i' t#e o+ -ib!ation no!(all# occu!' "u!in* continuou' !unnin* an" "oe' not occu! %&en '&o!t8ci!cuit cu!!ent' a!e +lo%in*) T&e 't!e''e' !e'ultin* +!o( t&e '&o!t8ci!cuit +o!ce' a!e calculate" u'in* t&e bea( t&eo!# +o!(ulae +o! 'i(l# 'uo!te" bea(' +o! a 'in*le cantile-e! to (ulti'an a!!an*e(ent', t&e alie" +o!ce' bein* "e!i-e" +!o( t&e !e-iou' 'ection') T&e !e'ultin* "e+lection' enable t&e con"ucto! 't!e'' to be calculate" an" 'o "ete!(ine i+ it i' liel# to e!(anentl# "a(a*e t&e con"ucto! becau'e it &a' e.cee"e" t&e !oo+ 't!e'' o+ t&e con"ucto! (ate!ial) )et%ods of reducing conductor stresses In ca'e' %&e!e t&e!e i' a lieli&oo" o+ -ib!ation at no!(al cu!!ent' o! %&en 'ub/ecte" to '&o!t8 ci!cuit +o!ce' cau'in* "a(a*e to t&e con"ucto!, t&e +ollo%in* can &e u'e" to !e"uce o! eli(inate t&e e++ect a Re"uce t&e 'an bet%een in'ulato! 'uo!t') T&i' (et&o" can be u'e" to !e"uce t&e e++ect' o+ bot& continuou' -ib!ation an" t&at "ue to '&o!t8 ci!cuit +o!ce') b Inc!ea'e t&e 'an bet%een in'ulato! 'uo!t') T&i' (et&o" can onl# be u'e" to !e"uce t&e e++ect' o+ -ib!ation !e'ultin* +!o( a continuou' cu!!ent) It %ill inc!ea'e t&e 't!e''e' "ue to a '&o!t8ci!cuit cu!!ent) c Inc!ea'e o! "ec!ea'e t&e +le.ibilit# o+ t&e con"ucto! 'uo!t') T&i' (et&o" %ill !e"uce t&e e++ect' o+ -ib!ation "ue to continuou' cu!!ent but &a' -e!# litt le e++ect on t&at "ue to '&o!t8ci!cuit +o!ce') " Inc!ea'e t&e con"ucto! +le.ibilit#) T&i' can onl# be u'e" to !e"uce t&e e++ect' o+ -ib!ation "ue to a continuou' cu!!ent) T&e '&o!t8 ci!cuit e++ect i' inc!ea'e") e Dec!ea'e t&e con"ucto! +le.ibilit#) T&i' (et&o" %ill !e"uce t&e e++ect' o+ -ib!ation "ue to eit&e! a continuou' cu!!ent o! a '&o!t8 ci!cuit) It %ill be note" t&at in ca!!#in* out t&e -a!iou' 'u**e'tion' abo-e, c&an*e' can onl# be (a"e %it&in t&e o-e!all "e'i*n !e0ui!e(ent' o+ t&e bu'ba! '#'te()
Corona Disc%arge 4it& -e!# &i*& -olta*e ai!8in'ulate" bu'ba!', a!ticula!l# o+ t&e t #e u'uall# in'talle" out o+ "oo!', it i' nece''a!# to en'u!e t&at %it& t&e 'acin* a"ote" bet%een con"ucto!' o+ "i++e!ent &a'e', o! bet%een con"ucto!' an" ea!t&, t&e elect!o(a*netic 't!e'' in t&e ai! 'u!!oun"in* t&e con"ucto!' i' lo% enou*& not to cau'e a co!ona "i'c&a!*e) Co!ona "i'c&a!*e i' to be a-oi"e" %&e!e o''ible a' it c!eate' ioni'e" *a' %&ic& can lea" to a la!*e !e"uction in t&e ai! in'ulation 'u!!oun"in* t&e con"ucto! an" 'o can cau'e +la'&8o-e!) S&oul" +la'&8o-e! occu!, t&i' %ill i n (an# ca'e' lea" to a
'&o!t8ci!cuit bet%een eit&e! a"/acent &a'e' o! ole' o! t&e nea!e't ea!t& oint o! lane) T&i' %il l cau'e con'i"e!able bu!nin* o+ t&e con"ucto!' an" a''ociate" e0ui(ent to*et&e! %it & (ec&anical "a(a*e) Co!ona "i'c&a!*e can al'o cau'e !a"io inte!+e!ence %&ic& (a# be unaccetable) To a-oi" t&e'e con"ition' t&e bu'ba! '#'te( '&oul" be +!ee +!o( '&a! e"*e' o! '(all !a"ii on t&e con"ucto! '#'te() I+ t&i' i' not o''ible t&en a""itional e0ui(ent %ill &a-e to be inco!o!ate" in t&e "e'i*n 'uc& a' co!ona !in*' an" 't!e'' !elie-in* cone' (ounte" in t&e a!ea' o+ &i*& elect!ic 't!e'') T&e '(alle't !a"ii !e0ui!e" +o! !e-ention o+ co!ona can be calculate" +!o( t&e +o!(ula
%&e!e E K !)()') -olta*e to neut!al, V ! K con"ucto! !a"iu', (( " K "i'tance bet%een con"ucto! cent!e', ((
δ K ai! "en'it# +acto! ( K con"ucto! 'u!+ace con"ition +acto! T&e -alue' +o! t&e +acto!' ( an" " a!e a' +ollo%' ( K 1 +o! a oli'&e" con"ucto! 'u!+ace, $)9F to $)9@ +o! !ou*&ene" o! %eat&e!e" 'u!+ace', an" $)F to $)F$ +o! 't!an"e" con"ucto!') " K 1 at 1 ba! ba!o(et!ic !e''u!e an" 2>HC) At ot&e! !e''u!e' an" te(e!atu!e' t&e -alue i' +oun" a' +ollo%'
%&e!e b K ba!o(et!ic !e''u!e, ba! T K te(e!atu!e, HC At location' abo-e 'ea le-el t&e no!(al !e''u!e i' !e"uce" b# a!o.i(atel# $)12 ba! e! 1$$$ ( o+ altitu"e) T&e -olta*e E- at %&ic& t&e co!ona "i'c&a!*e no!(all# beco(e' -i'ible i' 'o(e%&at &i*&e! t&an *i-en b# t&e abo-e +o!(ula an" can be "ete!(ine" a' +ollo%'
In ba" %eat&e! con"ition' t&e "i'c&a!*e (a# aea! at a -olta*e lo%e! t&an t&at in"icate" b# t&e +o!(ulae an" it i' t&e!e+o!e a"-i'able to (ae an allo%ance o+ about 2$G a' a 'a+et# +acto!)
&. 'ointing of Copper Busbars Busbar 'ointing )et%ods 'oint "esistance Bolting Arrange!ents Cla!ps elded 'oints
Busbar 'ointing )et%ods It i' nece''a!# t&at a con"ucto! /oint '&all be (ec&anicall# 't!on* an" &a-e a !elati-el# lo% !e'i'tance %&ic& (u't !e(ain 'ub'tantiall# con'tant t&!ou*&out t&e li+e o+ t&e /oint) E++icient /oint' in coe! bu'ba! con"ucto!' can be (a"e -e!# 'i(l# b# boltin*, cla(in*, !i-etin*, 'ol"e!in* o! %el"in*, t&e +i!'t t%o bein* u'e" e.ten'i-el#, t&ou*& coe! %el"in* i' no% (o!e *ene!all# a-ailable t&!ou*& i(!o-e(ent' in %el"in* tec&nolo*#) elded Goints in coe! bu'ba!' &a-e t&e a"-anta*e t&at t&e cu!!ent ca!!#in* caacit# i' uni(ai!e", a' t&e /oint i' e++ecti-el# a continuou' coe! con"ucto!) Bolted Goints a!e co(act, !eliable an" -e!'atile but &a-e t&e "i'a"-anta*e t&at t&e# nece''itate t&e "!illin* o! unc&in* o+ &ole' t&!ou*& t&e con"ucto!' %it& t&e bolt &ole' cau'in* 'o(e "i'to!tion o+ t&e line' o+ cu!!ent +lo%) T&i' /oint t#e al'o &a' a 'o(e%&at (o!e une-en contact !e''u!e t&an one u'in* cla( late') Cla!ped Goints a!e ea'# to (ae %it& t&e +ull c!o''8'ection bein* uni(ai!e") T&e e.t!a (a'' at t&e /oint an" &ence coolin* a!ea &el' to *i-e a coole! !unnin* /oint an" %it & a %ell8"e'i*ne" cla(, *i-e' a -e!# e-en contact !e''u!e) T&e +u!t&e! a""e" a"-anta*e i' t&at o+ ea'# e!ection "u!in* in'tallation) A "i'a"-anta*e i' t&e (uc& &i*&e! co't' o+ t&e cla(' an" a''ociate" +i.in*') "ieted Goints a!e e++icient i+ %ell (a"e, but &a-e t&e "i'a"-anta*e t&at t&e# cannot ea'il# be un"one o! ti*&tene" in 'e!-ice an" t&at t&e# a!e not 'o con-enient to (ae +!o( an in'tallation oint o+ -ie%) $oldered or braed Goints a!e !a!el# u'e" +o! bu'ba!' unle'' t&e# a!e !ein+o!ce" %it& bolt' o! cla(' 'ince &eatin* un"e! '&o!t8ci!cuit con"ition' can (ae t&e( bot& (ec&anicall# an" elect!icall# un'oun")
'oint "esistance T&e !e'i'tance o+ a /oint i' a++ecte" (ainl# b# t%o +acto!' a St!ea(line e++ect o! '!ea"in* !e'i'tance R ', t&e "i-e!'ion o+ t&e cu!!ent +lo% t&!ou*& a /oint) b T&e contact !e'i'tance o! inte!+ace !e'i'tance o+ t &e /oint R /) T&e total /oint !e'i'tance R / K R' Ri)
T&e abo-e i' 'eci+icall# +o! a ")c) cu!!ent) 4&e!e a)c) cu!!ent' a!e +lo%in*, t &e c&an*e' in !e'i'tance "ue to 'in an" !o.i(it# e++ect' in t&e /oint one (u't al'o be taen into account) e+o!e con'i"e!in* t&e e++ect o+ t&e abo-e +acto!' on t&e e++icienc# o+ a /oint, it i' i(o!tant to !eali'e t&e natu!e o+ t&e t%o contact 'u!+ace') No (atte! &o% %ell a contact 'u!+ace i' oli'&e", t&e 'u!+ace i' !eall# (a"e u o+ a la!*e nu(be! o+ ea' an" t!ou*&' %&ic& a!e !ea"il# -i'ible un"e! a (ic!o'coe) 4&en t%o 'u!+ace' a!e b!ou*&t to*et&e! contact i' onl# (a"e at t&e ea', %&ic& a!e 'ub/ecte" to (uc& &i*&e! contact !e''u!e' t&an t&e a-e!a*e /oint contact !e''u!e, an" &ence "e+o!( "u!in* t&e /ointin* !oce'') T&e actual contact a!ea in t&e co(lete" /oint i' (uc& '(alle! t&an t&e total 'u!+ace a!ea o+ t&e /oi nt) It &a' been '&o%n t&at i n a t#ical bu'ba! /oint 'u!+ace t&e e++ecti-e contact a!ea i' con+ine" to t&e !e*ion in %&ic& t&e !e''u!e i' alie", i)e), nea! t&e bolt' in t&e ca'e o+ a lae" /oint) $trea!line effect T&e "i'to!tion o+ t&e line' o+ cu!!ent +lo% at an o-e!lain* /oint bet%een t%o con"ucto!' a++ect' t&e !e'i'tance o+ t&e /oint) T&i' e++ect (u't al'o occu! %&en t&e cu!!ent +lo%' +!o( ea to ea +!o( 'u!+ace to 'u!+ace t&ou*& t&e o-e!all e++ect i' t&at t&!ou*& t&e /oint) In t&e ca'e o+ an o-e!lain* /oint bet%een t%o + lat coe! ba!', t&e 't!ea(line e++ect i' "een"ent onl# on t&e !atio o+ t&e len*t& o+ t&e o-e!la to t&e t&icne'' o+ t&e ba!' an" not on t&e %i"t&, !o-i"e" t&at t&i' "i(en'ion i' t&e 'a(e +o! bot& ba!') It &a' been '&o%n bot& (at&e(aticall# an" e.e!i(entall# t&at e-en in a e!+ectl# (a"e o-e!lain* /oint bet%een t%o !elati-el# t&in +lat con"ucto!' &a-in* a uni+o!( contact !e'i'tance, t&e "i't!ibution o+ cu!!ent o-e! t&e contact a!ea i' not uni+o!() P!acticall# all o+ t&e cu!!ent +lo%in* ac!o'' t&e contact 'u!+ace' i' concent!ate" to%a!"' t&e e.t!e(itie' o+ t&e /oint an" t&e cu!!ent "en'it# at t&e en"' o+ t&e o-e!lain* con"ucto!' (a# be (an# ti(e' t&at at t&e cent!e o+ t&e /oint) It i' e-i"ent +!o( t&e abo-e t&at t&e e++icienc# o+ an o-e!lain* /oint "oe' not inc!ea'e a' t&e len*t& o+ t&e o-e!la inc!ea'e' an" t&at +!o( a u!el# elect!ical oint o+ -ie% no a"-anta*e i' to be *aine" b# e(lo#in* an un"ul# lon* o-e!la) T&e !elation bet%een t&e !e'i'tance "ue to 't!ea(line e++ect o+ an o-e!lain* /oint bet%een t%o +lat coe! con"ucto!' an" t&e !atio o+ t&e len*t& o+ t&e o-e!la to t&e t&icne'' i' '&o%n in :i*u!e 1>) It &a' al'o been +oun" t&at t&e "i'to!tion e++ect in a T8/oint i' about t&e 'a(e a' a 't!ai*&t /oint) T&e !e'i'tance !atio e in :i*u!e 1> i' t&e !atio o+ t&e !e'i'tance o+ a /oint "ue to 't!ea(line e++ect RS, to t&e !e'i'tance o+ an e0ual len*t& o+ 'in*le con"ucto! R b, i)e)
%&e!e a K b!ea"t& o+ ba!, (( b K t&icne'' o+ ba!, (( l K len*t& o+ o-e!la, ((
ρ K !e'i'ti-it# o+ t&e con"ucto!, µΩ (( :!o( t&e *!a& it can be 'een t&en t&at t&e e++ect +all' -e!# !ai"l# +o! !atio' u to t%o an" t&en -e!# (uc& (o!e 'lo%l# +o! -alue' u to 'e-en) T&i' (ean' t&at in (o't ca'e' t&e 't!ea(line e++ect &a' -e!# little e++ect a' t&e o-e!la i' o+ nece''it# (uc& *!eate! t&an 'e-en)
0igure 1 $trea!line effect in oerlapping Goints
Contact resistance T&e contact inte!+ace bet%een t&e t%o +ace' o+ a bu'ba! /oint con'i't' o+ a la!*e nu(be! o+ 'ea!ate oint contact', t&e a!ea o+ %&ic& inc!ea'e' a' (o!e !e''u!e i' alie" an" t&e ea' a!e c!u'&e") T&e!e a!e t%o (ain +acto!' %&ic& t&e!e+o!e a++ect t&e actual inte!+ace !e'i'tance o+ t&e 'u!+ace') a T&e con"ition o+ t&e 'u!+ace') b T&e total alie" !e''u!e) T&e t#e o+ coatin* alie" to t&e contact 'u!+ace' to !e-ent o! "ela# t&e on'et o+ o.i"ation %&en oe!atin* at ele-ate" te(e!atu!e' o! in a &o'tile en-i!on(ent i' al'o i(o!tant, a!ticula!l# in t &e lon* te!() Condition of contact surfaces T&e con"ition o+ t&e contact 'u!+ace' o+ a /oint &a' an i(o!tant bea!in* on it' e++icienc#) T&e 'u!+ace' o+ t&e coe! '&oul" be +lat an" clean but nee" not be oli'&e") Mac&inin* i' not u'uall# !e0ui!e") Pe!+ectl# +lat /oint +ace' a!e not nece''a!# 'ince -e!# *oo" !e'ult' can in (o't ca'e' be
obtaine" (e!el# b# en'u!in* t&at t&e /oint i' ti*&t an" clean) T&i' i' a!ticula!l# t&e ca'e %&e!e e.t!u"e" coe! ba!' a!e u'e") 4&e!e ca't coe! ba!' a!e u'e", &o%e-e!, (ac&inin* (a# be nece''a!# i+ t&e /oint' a!e to obtain a 'u++icientl# +lat contact 'u!+ace) O.i"e', 'ul&i"e' an" ot&e! 'u!+ace conta(inant' &a-e, o+ cou!'e, a &i*&e! !e'i'tance t&an t&e ba'e (etal) Coe!, lie all ot&e! co((on (etal', !ea"il# "e-elo' a -e!# t&in 'u!+ace o.i"e +il( e-en at o!"ina!# te(e!atu!e' %&en +!eel# e.o'e" to ai!, alt&ou*& alu(iniu( o.i"i'e' (uc& (o!e !ai"l#, an" it' o.i"e &a' a (uc& &i*&e! !e'i'ti-it#) T&e ne*ati-e te(e!atu!e coe++icient o+ !e'i'tance o+ coe! o.i"e (ean' t&at t&e /oint con"ucti-it# ten"' to inc!ea'e %it& te(e!atu!e) T&i' "oe' not, o+ cou!'e, (ean t&at a /oint can be (a"e %it&out cleanin* /u't !io! to /ointin* to en'u!e t&at t&e o.i"e la#e! i' t&in enou*& to be ea'il# b!oen a' t&e contact 'u!+ace ea' "e+o!( %&en t&e contact !e''u!e i' alie") Preparation of surfaces Contact 'u!+ace' '&oul" be +lattene" b# (ac&inin* i+ nece''a!# an" t&o!ou*&l# cleane") A *!oun" o! 'an"8!ou*&ene" 'u!+ace i' !e+e!able to a '(oot& one) It i' i(o!tant to !e-ent t&e !e8o.i"ation o+ t&e /oint in 'e!-ice an" it i' t&e!e+o!e !eco((en"e" t&at t&e contact +ace' '&oul" be co-e!e" %it& a t&in la#e! o+ et!oleu( /ell# i((e"iatel# a+te! cleanin* t&e contact 'u!+ace') T&e /oint 'u!+ace' '&oul" t&en be bolte" t o*et&e!, t&e e.ce'' et!oleu( /ell# bein* !e''e" out a' t&e contact !e''u!e i' alie") T&e !e(ainin* /ell# %ill &el to !otect t&e /oint +!o( "ete!io!ation) It '&oul" be note" t&at in ca'e' %&e!e /oint' &a-e to e!+o!( !eliabl# in &i*&e! t&an no!(al a(bient te(e!atu!e con"ition', it (a# be a"-i'able to u'e a &i*& (eltin* oint /ell# to !e-ent it +!o( +lo%in* out o+ t&e /oint, lea-in* it liable to attac b# o.i"ation an" t&e en-i!on(ent) T&e +ollo%in* 'ection' "e'c!ibe t&e u'e o+ coatin*' on con"ucto! contact 'u!+ace') It '&oul" be note" t&at !ecent te't' ca!!ie" out to in-e'ti*ate t&e e!+o!(ance o+ bolte" /oint' un"e! c#clic &eatin* %it& %i"e te(e!atu!e -a!iation' in"icate t&at /oint' %it&out coatin*' *i-e t&e (o't !eliable lon*8te!( e!+o!(ance 7Jac'on 19F2) T&e !ea'on +o! t&i' i' t&at (o't coatin*' a!e o+ 'o+t (ate!ial' %&ic& %&en 'ub/ecte" to continuou' !e''u!e' an" !ai'e" te(e!atu!e' ten" to +lo%) T&i' &a' t&e e++ect o+ !e"ucin* t&e nu(be! o+ &i*& !e''u!e contact oint' +o!(e" %&en t&e /oint i' ne%l# bolte" to*et&e!) inning. T&e tinnin* o+ t&e contact 'u!+ace' o+ a bolte" o! cla(e" /oint %it & u!e tin o! a lea"8tin allo# i' no!(all# unnece''a!#, alt&ou*& a"-anta*e' can be *aine" in ce!tain ci!cu('tance') I+ t&e /oint +ace' a!e -e!# !ou*&, tinnin* (a# !e'ult in 'o(e i(!o-e(ent in e++icienc#) In (o't ca'e', &o%e-e!, it' c&ie+ -i!tue lie' in t&e +act t&at it ten"' to !e-ent o.i"ation an" &ence 'ub'e0uent /oint "ete!io!ation) It (a# t&e!e+o!e be !eco((en"e" in ca'e' %&e!e t&e /oint' oe!ate at unu'uall# &i*& te(e!atu!e' o! cu!!ent "en'itie' o! %&en 'ub/ecte" to co!!o'i-e at(o'&e!e') :o! t&e be't !e'ult' t&e 'u!+ace' '&oul" be tinne" o! !e8tinne" i((e"iatel# !io! to t&e +inal /oint cla(in*) It '&oul" be note" t&at bot& t&e elect!ical con"ucti-it# an" t&e o.i"ation !otecti-e action "ec!ea'e a' t&e lea" content o+ t&e 'ol"e! i nc!ea'e') Lea" al'o &a' t&e e++ect o+ !e"ucin* t&e 'u!+ace &a!"ne'' o+ t&e coatin* an" a &i*& lea" content in t &e tinnin* (ate!ial '&oul" be a-oi"e" a' t&i' can cau'e t&e latin* to c!ee once t&e /oint i' bolte" to*et&e! !e'ultin* in !e(atu!e +ailu!e "ue to o-e!&eatin*) $iler or nic@el plating. T&i' t#e o+ latin* i' bein* u'e" inc!ea'in*l#, a!ticula!l# %&e!e e0ui(ent i' (anu+actu!e" to A(e!ican 'tan"a!"' %&ic& !e0ui!e late" /oint' +o! &i*& te(e!atu!e oe!ation) Nicel8latin* !o-i"e' a &a!"e! 'u!+ace t&an 'il-e! an" (a# t&e!e+o!e be !e+e!able) T&e'e latin*' a!e e.en'i-e to al# an" (u't be !otecte" !io! to t&e +inal /oi ntin* !oce'' a' t&e# a!e al%a#' -e!# t&in coatin*' an" can t&e!e+o!e be ea'il# "a(a*e") T&e!e i' al'o
'o(e "oubt a' to t&e 'tabilit# o+ t&e'e /oint' un"e! !olon*e" &i*& te(e!atu!e c#clin*) Ve!# &i*& contact !e'i'tance' can be "e-eloe" 'o(e ti(e a+te! /ointin*) It i' t&e!e+o!e 'u**e'te" t&at natu!al (etal /oint' a!e in (o't ca'e' !e+e!able) Effect of pressure on contact resistance It &a' been '&o%n abo-e t&at t&e contact !e'i'tance i' "een"ent (o!e on t&e total alie" !e''u!e t&an on t&e a!ea o+ contact) I+ t&e total alie" !e''u!e !e(ain' con'tant an" t&e contact a!ea i' -a!ie", a' i' t&e ca'e in a '%itc& bla"e (o-in* bet%een '!in* loa"e" contact', t&e total contact !e'i'tance !e(ain' !acticall# con'tant) T&i' can be e.!e''e" b# an e0uation o+ t&e +o!(
%&e!e Ri K !e'i'tance o+ t&e contact K total contact !e''u!e n K e.onent bet%een $)? an" 1 C K a con'tant T&e *!eate! t&e alie" total !e''u!e t&e lo%e! %ill be t&e /oint !e'i'tance an" t&e!e+o!e +o! &i*& e++icienc# /oint' &i*& !e''u!e i' u'uall# nece''a!#) T&i' &a' t&e a"-anta*e t&at t&e &i*& !e''u!e &el' to !e-ent "ete!io!ation o+ t&e /oint) :i*u!e 16 '&o%' t&e e++ect o+ !e''u!e on /oint !e'i'tance) 0igure 1# %e effect of pressure on t%e contact resistance of a Goint bet/een t/o copper conductors
Joint !e'i'tance +all' !ai"l# %it & inc!ea'in* !e''u!e, but abo-e a !e''u!e o+ about 1> N(( 2 t&e!e i' little +u!t&e! i(!o-e(ent) Ce!tain !ecaution' (u't be ob'e!-e" to en'u!e t&at t&e contact !e''u!e i' not un"ul# &i*&, 'ince it i' i(o!tant t&at t&e !oo+ 't!e'' o+ t&e con"ucto! (ate!ial o! it' bolt' an" cla(' i' not e.cee"e")
A' a ba! &eat' u un"e! loa" t&e contact !e''u!e in a /oint (a"e %it& 'teel bolt' ten"' to inc!ea'e becau'e o+ t&e "i++e!ence in e.an'ion coe++icient' bet%een coe! an" t&e 'teel) It i' t&e!e+o!e e''ential t&at t&e initial contact !e''u!e i' et to a 'uc& a le-el t&at t&e contact !e''u!e i' not e.ce''i-e %&en at oe!atin* te(e!atu!e) I+ t&e ela'tic li(it o+ t&e ba! i' e.cee"e" t&e /oint %ill &a-e a !e"uce" contact !e''u!e %&en it !etu!n' to it' col" 'tate "ue to t&e /oint (ate!ial' &a-in* "e+o!(e" o! 't!etc&e") To a-oi" t&i', it i' &el+ul to u'e "i'c '!in* %a'&e!' %&o'e '!in* !atin* i' c&o'en to (aintain a 'ub'tantiall# con'tant contact !e''u!e un"e! col" an" &ot %o!in* con"ition') T&i' t#e o+ /oint "ete!io!ation i' -e!# (uc& (o!e liel# to &aen %it& 'o+t (ate!ial', 'uc& a' E1E alu(iniu(, %&e!e t&e (ate!ial ela'tic li(it i' lo% co(a!e" %it& t&at o+ &i*& con"ucti-it# coe!) 'oint efficiency T&e e++icienc# o+ a /oint (a# be (ea'u!e" in te!(' o+ t&e !atio o+ t&e !e'i'tance o+ t&e o!tion o+ t&e con"ucto! co(!i'in* t&e /oint an" t&at o+ an e0ual len*t& o+ 't!ai*&t con"ucto!) T&e !e'i'tance o+ a /oint, a' al!ea"# (entione", i' (a"e u o+ t%o a!t', one "ue to t&e "i'to!tion o+ line' o+ cu!!ent +lo% an" t&e ot&e! to contact !e'i'tance) T&e !e'i'tance "ue to t&e 't!ea(line e++ect at an o-e!la /oint i' *i-en b#
%&e!e +o! a *i-en /oint a, b an" l a!e t&e %i"t&, t&icne'' an" o-e!la len*t&, t&e'e all bein* con'tant, an" contact !e'i'tance o+ t&e /oint i'
%&e!e K contact !e'i'tance e! unit a!ea) T&e total /oint !e'i'tance i'
an" t&e e++icienc# o+ t&e /oint i'
T&e !e'i'tance o+ an e0ual len*t& o+ 't!ai*&t con"ucto! i' *i-en b#
T&e !e'i'tance !atio e i' obtaine" +!o( :i*u!e 1>) In (o't ca'e' it i' ina"-i'able to u'e contact !e''u!e' o+ le'' t&an N(( 2, 1$ N((2 bein* !e+e!!e") T&e contact !e''u!e c&o'en i' in+luence" b# t&e 'ie an" nu(be! o+ bolt' o! cla(', t&e latte! *i-in* a (o!e e-en contact !e''u!e) :o! t&e 'ae o+ '#((et!# t&e len*t& o+ o-e!la i' o+ten (a"e e0ual to t&e %i"t& o+ t&e ba!, t&ou*& %it& t&ic an" na!!o% ba!' t&e o-e!la can be inc!ea'e" to i(!o-e t&e o-e!all /oint e!+o!(ance) O%in* to t&e la!*e! 'u!+ace a!ea +!o( %&ic& &eat (a# be "i''iate", e++icient /oint' bet%een 'in*le coe! con"ucto!' u'uall# &a-e a lo%e! te(e!atu!e !i'e t&an t&e con"ucto!' t&e('el-e') It i' i(o!tant, in *ene!al, to en'u!e t&at all /oint' &a-e a !ea'onable (a!*in o+ 'a+et#) T&i' i' a!ticula!l# 'o %&e!e (ulti8con"ucto!' /oin at one /oint an"o! t&e con"ucto!' a!e no!(all# !unnin* clo'e to t&e 'eci+ie" (a.i(u( te(e!atu!e !i'e')
Bolting Arrange!ents In "eci"in* t&e nu(be!, 'ie an" "i't!ibution o+ bolt' !e0ui!e" to !o"uce t&e nece''a!# contact !e''u!e to *i-e &i*& /oint e++icienc#, bot& elect!ical an" (ec&anical con'i"e!ation' &a-e to be taen into account) T&e (et&o"' u'e" to "ete!(ine t&e'e !e0ui!e(ent' &a-e been *i-en in !e-iou' 'ection') A /oint no!(all# "ec!ea'e' in !e'i'tance %it& an inc!ea'e in t&e 'ie an" nu(be! o+ bolt' u'e") olt 'ie' u'uall# -a!# +!o( M6 to M2$ %it& bet%een +ou! an" 'i. bein* u'e" in eac& /oint %it& a !e+e!ence +o! +ou! bolt' in na!!o% con"ucto!' an" 'i. in la!*e con"ucto!') T&e to!0ue c&o'en +o! eac& bolt 'ie i' "een"ent on t&e bolt (ate!ial an" t&e (a.i(u( oe!atin* te(e!atu!e e.ecte") ecau'e o+ t&e 't!en*t& o+ coe!, "e+o!(ation o+ t&e con"ucto! un"e! t&e !e''u!e o+ t&e /oint i' not no!(all# a con'i"e!ation) Table 9 '&o%' t#ical boltin* a!!an*e(ent' +o! -a!iou' bu'ba! 'ie') T&e !eco((en"e" to!0ue 'ettin*' a!e alicable to &i*&8ten'ile 'teel 7F)F o! alu(iniu( b!one 7C4@$, +o!(e!l# C#1$? +a'tene!' %it& unlub!icate" t&!ea"' o+ no!(al 'u!+ace +ini'&) In t&e ca'e o+ 'tainle'' 'teel bolt', t&e'e to!0ue 'ettin*' (a# be u'e", but t&e t&!ea"' (u't be lub!icate" !io! to u'e) In a""ition to t&e !oo+ o! #iel" 't!e'' o+ t&e bolt (ate!ial an" t&e t&!ea" c&a!acte!i'tic', t&e co!!ect ti*&tenin* to!0ue "een"' on t&e "i++e!ential e.an'ion bet%een t&e bolt an" con"ucto! (ate!ial') al-ani'e" 'teel bolt' a!e no!(all# u'e" but b!a'' o! b!one bolt' &a-e been u'e" becau'e t&ei! coe++icient' o+ e.an'ion clo'el# (atc& t&e coe! con"ucto! an" &ence t&e contact !e''u!e "oe' not -a!# %i"el# %it& oe!atin* te(e!atu!e) Coe! allo# bolt' al'o &a-e t&e a"-anta*e t&at t&e o''ibilit# o+ "i''i(ila! (etal co!!o'ion i' a-oi"e") ecau'e t&e'e allo#' "o not &a-e an ea'il# "i'ce!nible #iel" 't!e'', &o%e-e!, ca!e &a' to be taen not to e.cee" t&e co!!ect ti*&tenin* to!0ue) ecau'e o+ t&ei! non8(a*netic !oe!tie', coe! allo#' (a# al'o be !e+e!!e" to (il" o! &i*&8 ten'ile 'teel %&e!e &i*& (a*netic +iel"' a!e e.ecte") Alte!nati-el#, a non8(a*netic 'tainle'' 'teel (a# be u'e") In (o't ca'e' &o%e-e!, &i*&8ten'ile 'teel i' u'e" +o! it' -e!# &i*& #iel" 't!e'') able ypical busbar bolting arrange!ents single face oerlap5 Bar /idt% !!
'oint oerlap !!
'oint area !!2
9u!ber of bolts
)etric bolt sie coarse t%read5
Bolt tor*ue 9!
as%er dia!eter !!
as%er t%ic@ness !!
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&i*&8ten'ile 'teel o! alu(iniu( b!one 7C4@$, +o!(e!l# C1$?
Cla!ps T&e c&oice o+ cla( (ate!ial an" (et&o" o+ (anu+actu!e "een"' on t&e a)c) o! ")c) cu!!ent !e0ui!e(ent', an" on t&e nu(be! o+ cla(' o+ a *i-en 'ie !e0ui!e") T&e (anu+actu!in* (et&o"' u'e" inclu"e (ac&inin* +!o( late, 'an" o! "ie ca'tin*, o! 'ta(in* +!o( late) In t&e ca'e o+ lo% cu!!ent a)c) 7le'' t&an @$$$ A an" ")c) '#'te(' t&e cla(' '&oul" be (a"e +!o( a &i*&8't!en*t& (ate!ial co(atible %it& t&e !e0ui!e" contact !e''u!e) T&e# can t&e!e+o!e be (a"e +!o( 'teel in ca't, +o!*e" o! 'ta(e" +o!() 4&e!e a)c) cu!!ent' in e.ce'' o+ @$$$ A a!e conce!ne", t&e c&oice o+ (ate!ial i' bet%een t&e lo% o! non8(a*netic 'teel' o! a b!a'' o! b!one) Steel cla(' a!e *ene!all# un'uitable becau'e o+ t&e &#'te!e'i' lo''e' in"uce" in t&e()
elded 'oints T&e ine!t *a' '&iel"e" a!c !oce''e', tun*'ten ine!t *a' 7TI an" (etal ine!t *a' 7MI a!e t&e !e+e!!e" %el"in* (et&o"' +o! &i*& con"ucti-it# coe!' an" a!e caable o+ !o"ucin* e.cellent bu'ba! /oint') T&e %el"in* "ata *i-en in Table 1$ a!e !o-i"e" a' a *ui"e to *oo" !actice, but t&e actual %el"in* con"ition' t&at %ill *i-e t&e be't !e'ult' +o! a a!ticula! /oint (u't be "ete!(ine" +!o( e.e!ience) Ce!tain &#'ical an" (etallu!*ical !oe!tie' o+ coe! (u't, &o%e-e!, be taen account o+ %&en %el"in*) T&e &i*& t&e!(al "i++u'i-it# o+ coe! 8 +ou! o! +i-e ti(e' t&at o+ (il" 'teel 8 oo'e' t&e +o!(ation o+ an a"e0uate %el" ool nece''a!# +o! *oo" +u'ion an" "eo.i"ation %&ic& can *i-e !i'e to lac o+ +u'ion "e+ect' an" o!o'it#) T&e !ai" &eat 'in e++ect, %&ic& i' a!ticula!l# !onounce" in t&ice! 'ection', (u't t&e!e+o!e be o-e!co(e) P!e&eatin* o+ t&e coe! be+o!e %el"in* i' nece''a!# +o! t&icne'' abo-e about @ (( a' in"icate" in Table 1$) A' e.laine" in Section 2, t&e tou*& itc& *!a"e' o+ coe!, C4$$?A an" C4$$>A 7+o!(e!l# C1$1 an" C1$2, contain a!ticle' o+ cu!ou' o.i"e %&ic& a!e no!(all# in a +o!( %&ic& &a' a (ini(al e++ect on elect!ical an" (ec&anical !oe!tie') P!olon*e" &eatin* o+ t&e coe! &o%e-e!, allo%' t&e o.i"e a!ticle' to "i++u'e to *!ain boun"a!ie' %&e!e t&e# can 'e!iou'l# a++ect t&e !oe!tie') T&i' "i++u'ion e++ect i' bot& ti(e an" te(e!atu!e "een"ent an" i' (ini(i'e" b# e!+o!(in* t&e %el"in* oe!ation a' 0uicl# a' o''ible an" b# !e't!ictin* t&e o-e!all &eatin* o+ t&e co(onent a' +a! a' o''ible con'i'tent %it& a"e0uate +u'ion an" a 'ati'+acto!# %el" !o+ile) T&i' con'i"e!ation ob-iou'l# "oe' not al# to o.#*en8+!ee coe!' %&ic& "o not contain t&e o.i"e a!ticle') able 1 elding data for
a5 "eco!!ended usage of B$ 21 filler alloys for , and ), /elding of %ig% conductiity copper. , Designation
),
rade Argon or
9itrogen
Argon or
9itrogen
C4$$?A
Elect!ol#tic tou*& itc& &i*& con"ucti-it#
C, C21
Not !eco((en"e"
C, CF, C21
Not !eco((en"e"
C4$$>A
:i!e8!e+ine" tou*& itc& &i*& con"ucti-it#
C, C21
Not !eco((en"e"
C, CF, C21
Not !eco((en"e"
C4$$FA
O.#*en8+!ee &i*& con"ucti-it#
C, C21
Not !eco((en"e"
C, C21
Not !eco((en"e"
b5 ypical operating data for , butt /elds in %ig% conductiity copper. 7Di!ect cu!!ent= elect!o"e ne*ati-e= a!*on an" &eliu( '&iel"in* $%ielding gas
Argon
%ic@ness !!5
Pre%eat te!perature 7C5
Electrode dia!eter !!5
0iller rod dia!eter !!5
as nole dia!eter !!5
eld current A5
as flo/ l:!in5
eld current A5
as flo/ l:!in5
1)>
None
1)682)?
1)6
9)>
F$81@$
?86
$89$
681$
@
None
2)?8@)2
1)6
9)>812
12$82?$
?86
1F$822$
681$
6
u to ?$$
@)28?)F
@)2
1281F
22$8@>$
68F
2$$82?$
1$81>
12
?$$86$$
?)F
@)28?)F
1281F
@@$8?2$
F81$
26$82F$
1$81>
12
>$$8$$
?)F
@)28?)F
1281F
?$$
F81$
2F$8@2$
1282$
Ma# be !e"uce" 'i*ni+icantl# in &eliu( '&iel"in* c5 ypical operating data for ), butt /elds i n %ig% conductiity copper. 71)6 (( "ia(ete! +ille! %i!e= a!*on '&iel"in* %ic@ness !!5
Pre%eat te!perature 7C5
elding current A5
Arc oltage F5
ire feed rate !:!in5
as flo/ rate l:!in5
6
None
2?$8@2$
2>82F
6)>8F)$
1$81>
12
u to >$$
@2$8@F$
268@$
>)>86)>
1$81>
1F
u to >$$
@?$8?$$
2F8@2
>)>86)>
1281
2?
u to $$
@?$8?2$
2F8@2
>)>86)>
1?82$
2?
u to $$
@?$8?6$
2F8@2
>)>86)>
1?82$
T&e!(al e.an'ion '&oul" be allo%e" +o! "u!in* %el"in* a' t&i' lea"' to t&e clo'in* o+ !oot *a' a' t&e te(e!atu!e o+ t&e (etal !i'e') T&e !oot *a' i n"icate" in Table 11 '&oul" t&e!e+o!e be allo%e") O.#8acet#lene an" o.#8!oane %el"in* (et&o"' can be u'e" %it& o.#*en8+!ee coe! but t &e# a!e not !eco((en"e" +o! %el"in* tou*& itc& coe!' a' t&e !e"ucin* at(o'&e!e !o"uce" in t&e +la(e can !eact %it& t&e cu!ou' o.i"e a!ticle' to !o"uce 'tea( in'i"e t&e (etal) T&i' *i-e' !i'e to o!o'it# an" i' no%n a' <&#"!o*en e(b!ittle(ent<) :u!t&e! "etail' o+ t&e +acto!' in-ol-e" in t&e %el"in* o+ coe! can be +oun" in t&e CDA ublication No 9F) able 11 "eco!!ended edge preparations for , and ), butt-/elds.
(. )ec%anical $trengt% "e*uire!ents All bu'ba! '#'te(' &a-e to be "e'i*ne" to %it&'tan" t&e (ec&anical +o!ce' to %&ic& t&e# (a# be 'ub/ecte", %&et&e! t&e'e be "ue to t&ei! o%n %ei*&t, %in" an" ice loa"', o! '&o!t8ci!cuit +o!ce') T&i' +o!ce beco(e' (o!e one!ou' %it& inc!ea'in* -olta*e an" "ec!ea'in* cu!!ent "ue to !e'ecti-el# lon*e! in'ulato!' an" '(alle! con"ucto!') T&e con"ucto! it'el+ '&oul" &a-e 'u++icient (ate!ial 't!en*t& un"e! all oe!ational con"ition') It (u't be able to 'uo!t it'el+ %it&out un"ue "e+lection un"e! no!(al %o!in* con"ition', an" not 'u++e! e!(anent "a(a*e un"e! abno!(al con"ition') T&e +ollo%in* 'ection enable' t&e (ec&anical 't!en*t& !e0ui!e(ent o+ a con"ucto! to be calculate" u'in* t&e '&o!t8ci!cuit +o!ce' obtaine" +!o( t&e +o!(ulae *i-en !e-iou'l#) Deflection 9atural 0re*uency ind and ,ce oadings )a;i!u! Per!issible $tress %er!al E;pansion
Deflection T&e (a.i(u( "e+lection o+ a bea( ca!!#in* a uni+o!(l# "i't!ibute" loa" an" +!eel# 'uo!te" at eac& en" i' *i-en b# t&e +o!(ula
%&e!e ∆ K (a.i(u( "e+lection, (( %K %ei*&t e! unit len*t& o+ loa"e" bea(, N(( L K bea( len*t& bet%een 'uo!t', (( E K (o"ulu' o+ ela'ticit# 712? . 1$@N((2 I K (o(ent o+ ine!tia o+ bea( 'ection, (( I+ one en" o+ a bea( i' !i*i"l# +i.e" in a &o!iontal o'ition t&e "e+lection i' $)?1> ti(e' t&at *i-en b# t&e abo-e +o!(ula an" it +ollo%' t&at i+ a +!eel# 'uo!te" bea( i' al'o 'uo!te" at it' (i"8 oint t&en it' (a.i(u( "e+lection i' !e"uce" to $)$2> o+ it' +o!(e! -alue) I+ bot& en"' o+ a bea( a!e !i*i"l# +i.e" in a &o!iontal o'ition t&e "e+lection i' $)2 ti(e' t&at *i-en b# t&e abo-e +o!(ula) T&u' %it& a continuou' bea( +!eel# 'uo!te" at +ou! o! (o!e oint' t&e (a.i(u( "e+lection in t&e cent!e 'an' (a# be a''u(e" to be $)2 ti(e' t&at *i-en b# t&e +o!(ula, %&ile t&e "e+lection in t&e en" 'an' i' $)?1> ti(e') T&e "e+lection in t&e en" 'an', t&e!e+o!e, (a# be a''u(e" to be t%ice t&at in t&e cent!e 'an', a''u(in* e0ual 'an "i'tance')
)o!ents of inertia In t&e abo-e +o!(ula t&e (o(ent o+ ine!tia I +o! t&e 'ection o+ t&e bea( &a' to be calculate" about t&e neut!al a.i' %&ic& !un' a!allel to t &e bea( %&e!e t&e bea( &a' e!o ten'ile +o!ce') In (o't ca'e' t&i' i' t&e 'a(e a.i' o+ t&e cent!e o+ c!o''8'ection) :o! a !ectan*ula! 'ection o+ "et& D an" b!ea"t&
:o! a ci!cula! 'ection o+ "ia(ete! D
:o! a tubula! 'ection o+ inte!nal "ia(ete! " an" e.te!nal "ia(ete! D
It '&oul" be note" t&at t&e -alue o+ I +o! a *i-en c!o''8'ection i' "een"ent on t&e "i!ection in %&ic& eac& in"i-i"ual +o!ce i' alie") Mo(ent' o+ ine!tia +o! a !an*e o+ coe! !o"', ba!', 'ection' an" tube' a!e *i-en in Table' 12 16 7Aen"i. 2)
9atural 0re*uency T&e natu!al +!e0uenc# o+ a bea( 'i(l# 'uo!te" at it' en" i'
an" +o! a bea( %it& bot& en"' +i.e" &o!iontall# it i'
%&e!e + n K natu!al +!e0uenc#, ;
∆ K "e+lection, (( A' t&e "e+lection %it& +i.e" en"' i' $)2 ti(e' t&e -alue %it& +!eel# 'uo!te" en"' it +ollo%' t&at t&e natu!al +!e0uenc# i' inc!ea'e" b# 2)2> ti(e' b# en"8+i.in*= +i.in* one en" onl# inc!ea'e' t&e natu!al +!e0uenc# b# about >$G) 4&e!e e0ui(ent i' to be (ounte" out'i"e, natu!al +!e0uencie' o+ le'' t&an 2)> ; '&oul" be a-oi"e" to !e-ent -ib!ation "ue to %in" e""ie')
ind and ,ce oadings
In con'i"e!in* t&e loa"in* o+ a con"ucto! +o! out"oo! 'e!-ice not onl# (u't t &e %ei*&t o+ t&e con"ucto! it'el+ be taen into account but al'o t&e %ei*&t o+ a coatin* o+ ice %&ic& it (a# ca!!#, to*et&e! %it& t&e %in" !e''u!e on t&e ice loa"e" con"ucto!) T&e (a.i(u( t&icne'' o+ t&e ice an" t&e (a.i(u( %in" 'ee" a!e no!(all# 'eci+ie" b# t&e u!c&a'e! o+ t&e bu'ba!' but %&e!e t&e'e a!e not 'eci+ie" t&e# a!e u'uall# a-ailable +!o( national 'tan"a!"' bo"ie' %it&in t&e count!# %&e!e t&e e0ui(ent i' to be in'talle") T&e %in" an" ice loa"in* can be calculate" u'in* t&e +ollo%in* +o!(ulae 4in" loa"in* 4% K 7D2t . 1$> Ice loa"in*
%&e!e %% K %in" loa"in*, N( %i K ice loa"in*, N( K %in" !e''u!e, N((2 D K "ia(ete!, (( t K ice t&icne'', (( It i' a''u(e" t&at t&e %in" loa" i' at !i*&t an*le' to t&e -e!tical loa" o+ t&e con"ucto! %ei*&t, an" t&at it' ice loa" an" &ence t&e !e'ultant loa" on t&e con"ucto! &a' to be a""e" -e!ticall#) T&e !e'ultant loa" i' *i-en b#
%&e!e R K !e'ultant loa", N( % K con"ucto! %ei*&t e! unit len*t&, N( an" %&e!e R act' at an an*le θ H to t&e -e!tical *i-en b# t&e +o!(ula
T&e -e!tical 'a* o! "e+lection in t&e con"ucto! 'an i' *i-en b#
%&e!e ∆i i' t&e 'a* in (( in a lane incline" at an an*le
θ to t&e -e!tical)
)a;i!u! Per!issible $tress T&e (a.i(u( e!(i''ible 't!e'' in a con"ucto! i' t&e !e'ultant o+ it' o%n natu!al %ei*&t 7% an" t&e a""itional +o!ce' o+ %in" 7% % an" ice 7%i loa"in*' 7'ee abo-e an" t&e (a*netic +o!ce' !e'ultin* +!o( a '&o!t ci!cuit) It '&oul" be note" t&at t&e "i!ection o+ a '&o!t8ci!cuit +o!ce 74' "een"' on t&e o'ition o+ a"/acent &a'e' an" t&e "i!ection o+ t&e cu!!ent' in t&e() In a *ene!al ca'e t&e +ollo%in* (et&o" '&oul" be u'e" +o! calculatin* t&e !e'ultant +o!ce an" it' "i!ection
an"
T&e (a.i(u( 'in 't!e'' in t&e con"ucto! can t&en be calculate" u'in* t&e +ollo%i n* +o!(ula
%&e!e + K (a.i(u( 'in 't!e'', N((2 M K (a.i(u( ben"in* (o(ent, N (( B K 'ection (o"ulu', ((@
:o! a 'in*le bea( o+ len*t& L 7(( uni+o!(l# loa"e" an" +!eel# 'uo!te" at bot& en"' o! +!eel# 'uo!te" at one en" an" +i.e" at t&e ot&e!,
%&e!e 4 K loa", N(( L K 'an, (( :o! a ci!cula! 'ection o+ e.te!nal "ia(ete! D o! + o! a !ectan*ula! 'ection o+ "et& D,
%&e!e I K (o(ent o+ ine!tia, (( D K "ia(ete!, (( T&en t&e (a.i(u( 't!e''
T&e (a.i(u( e!(i''ible 't!e'' i' "een"ent on t&e con"ucto! (ate!ial, te(e!, etc), but (u't not e.cee" t&e (ate!ial !oo+ 't!e'' o! e!(anent "e+o!(ation %ill occu!) :o! a con"ucto! (anu+actu!e" +!o( &a!" "!a%n coe! t&e -alue i' a!o.i(atel# 2?> N(( 2) :o! a bea( %&ic& i' &o!iontall# +i.e" at bot& en"' t&e ben"in* (o(ent at t&e cent!e i' !e"uce" to one t&i!" an" t&at at i t' en"' to t%o8t&i!"' o+ t&o'e +o! a 'i(le 'uo!te" bea()
%er!al E;pansion I+ t&e c&an*e' in len*t& t&at occu! in a con"ucto! a' it e.an"' an" cont!act' %it& te(e!atu!e -a!iation' a!e not allo%e" +o!, un"ue +o!ce' %ill be 'et u in t&e con"ucto! 'uo!t '#'te( o! in t&e e0ui(ent to %&ic& t&e bu'ba! i' connecte") T&e coe++icient o+ linea! e.an'ion +o! coe! (a# be taen a' 1 . 1$ 6 HC 7+o! te(e!atu!e' +!o( a(bient u to 2$$HC co(a!e" %it& 2@ . 1$ 6 HC +o! alu(iniu() T&e lo%e! -alue +o! coe! i' o+ *!eat i(o!tance %&en allo%in* +o! t&e!(al e.an'ion un"e! bot& no!(al an" t!an'ito!# con"ition', a' u to 2>G le'' e.an'ion nee" be acco((o"ate" +o! a a!ticula! len*t& o+ bu'ba!) I+ a len*t& o+ coe! ba! %e!e to be et +!o( e.an"in* o! cont!actin*, a +o!ce o+ nea!l# 2 N e! ((2 o+ c!o''8'ectional a!ea %oul" be "e-eloe" +o! a t e(e!atu!e c&an*e o+ 1HC) In (o't ca'e' t&e 'uo!t' e.an" +a! le'' "ue to (uc& '(alle! te(e!atu!e c&an*e' an" lo%e! t&e!(al e.an'ion coe++icient') It i' t&e!e+o!e no!(al !actice to allo% +o! t&e +ull e.an'ion u'in* +le.ible con"ucto! connection' at 'uitable oint') ypes of e;pansion Goints
In t&e ca'e o+ '&o!t ba!' it i' u'uall# not nece''a!# to (ae an# 'ecial !o-i'ion to acco((o"ate e.an'ion) T&e!e %ill no!(all# be one o! t%o !ea'onabl# +le.ible ben"' caable o+ !elie-in* an# un"ue 't!e''e' %&ic& (a# be 'et u) 0igure 1& ypes of e;pansion Goints in copper conductors
To !elie-e inte!(e"iate 'uo!t' o+ 't!e'', cla(' %&ic& allo% t &e con"ucto! to (o-e +!eel# in t&e lon*itu"inal "i!ection '&oul" be !o-i"e") T&e'e cla(' (u't be "e'i*ne" an" a!!an*e" %it& ca!e to a-oi" t&e "an*e! o+ 't!e''e' buil"in* u at an# oint at %&ic& t&e ba! (a# beco(e %e"*e" o! !e-ente" +!o( (o-in* +!eel#) In t&e ca'e o+ lon* 't!ai*&t !un' it i' a"-i'able t&at e.an'ion /oint' '&oul" be int!o"uce") T&e /oint' (a# u'e la(inate" t&in coe! 't!i' o! lea-e' an" &a-e t&e 'a(e total cu!!ent !atin* a' t&e bu'ba! it'el+) A' an alte!nati-e to la(inate" +le.ible /oint', coe! b!ai" (a# be u'e") T&i' t#e o+ /oint i' u'uall# (o!e e.en'i-e to (anu+actu!e but &a' t&e a"-anta*e t&at it can acco((o"ate e.an'ion in (o!e t&an one "i!ection 7in (o't ca'e' t&!ee "i!ection' an" al'o ten"' to eli(inate -ib!ation +o!ce' bein* a''e" +!o( one iece o+ e0ui(ent to anot&e!) It i' i(o!tant t&at t&e +e!!ule into %&ic& t&e coe! b!ai" i' cla(e" i' o+ 'u++icient t&icne'' to en'u!e con'i'tent &i*& con"ucti-it# a+te! (anu+actu!e an" "u!in* it' 'e!-ice li+e) 4&e!e &i*& !e'i'tance' "e-elo in t&e /oint a+te! (anu+actu!e, o-e!&eatin* an" ulti(atel# b!ai" +ailu!e "ue to o.i"ation o+ t&e b!ai" (ate!ial (a# !e'ult
. Busbar ,!pedance FoltDrop ,nductance 0or!ulae Capacitance 0or!ulae eo!etric )ean Distance 0or!ulae T&e bu'ba! !eactance i' not no!(all# 'u++icientl# la!*e to a++ect t&e total !eactance o+ a o%e! '#'te( an" &ence i' not inclu"e" in t&e calculati on' %&en e'tabli'&in* t&e '&o!t8ci!cuit cu!!ent' an" !eacti-e -olt "!o' %it&in a o%e! '#'te() T&e e.cetion to t&i' i' %&en con'i"e!in* ce!tain &ea-# cu!!ent in"u't!ial alication' 'uc& a' +u!nace', %el"in* 'et', o! !oll &eatin* e0ui(ent +o! 'teel (ill') In t&e'e ca'e' t&e !eactance (a# be !e0ui!e" to be no%n +o! cont!ol u!o'e', o! to obtain bu'ba! a!!an*e(ent' to *i-e (ini(u( o! balance" !eactance) T&i' (a# be i(o!tant becau'e o+ it' e++ect on bot& -olt "!o an" o%e! +acto!, an" &ence on t&e *ene!atin* lant VA !e0ui!e(ent e! 4 o+ loa", o! on t&e ta!i++' a#able %&e!e t&e o%e! i' u!c&a'e" +!o( out'i"e) T&e bu'ba! i(e"ance i' (a"e u o+ t&!ee co(onent' !e'i'tance, in"uctance an" caacitance) T&e -alue' o+ t&e'e co(onent' a!e *i-en an o&(ic -alue %&ic& in t&e ca'e o+ in"uctance an" caacitance i' "een"ent on t&e +!e0uenc# o+ t&e '#'te() T&e# a!e "e+ine" a' +ollo%' Re'i'tance
%&e!e R+ K !e'i'tance at +!e0uenc# + 7;, Ro K ")c) !e'i'tance S K 'in e++ect !atio K !o.i(it# !atio In"uctance
%&e!e L K in"ucti-e !eactance,
Ω
+ K +!e0uenc#, ; L K in"uctance, ; Caacitance
%&e!e c K caaciti-e !eactance,
Ω
Ω
+ K +!e0uenc#, ; C K caacitance, : I(e"ance
%&e!e K L 8 C T&e -alue o+ C i' u'uall# -e!# (uc& '(alle! t&an L, an" L i' u'uall# (uc& la!*e! t&an R+ ) T&e -alue o+ i' taen to be o'iti-e %it& t&e 'i*n o+ L 8 C to in"icate %&et&e! t&e '#'te( &a' a o'iti-e o! ne*ati-e o%e! +acto!)
Folt Drop T&e -olt "!o in a bu'ba! '#'te( i' e'ti(ate" a' +ollo%' +!o( t&e u'ual +o!(ula V K I B %&e!e V K -olt "!o, V I K cu!!ent +lo%in* in t&e con"ucto!, A B K bu'ba! i(e"ance,
Ω
;o%e-e!, to +in" t&e (a*nitu"e o+ t&e loa" -olta*e V L a-ailable, t&e bu'ba! -olt "!o V (u't be 'ubt!acte" -ecto!iall# +!o( t&e 'ul# -olta*e V S
VS K 'ul# -olta*e, V
θL K an*le o+ loa", H
V K bu'ba! -olt "!o, V
φ K an*le o+ bu'ba!, H
VL K loa" -olta*e, V R K bu'ba! !e'i'tance, 4 I K cu!!ent, A K bu'ba! !eactance, 4
T&e aa!ent -olt "!o in t&e bu'ba! t!unin*, &a'e to neut!al, i' *i-en b#
Multil# b# √@ +o! &a'e to &a'e -olt "!o) T&e abo-e +o!(ula *i-e' a -e!# clo'e a!o.i(ation a' lon* a' t&e bu'ba! '#'te( -olt "!o !e(ain' '(all in co(a!i'on to t&e '#'te( -olta*e)
1. Appendices $u!!ary of )et%ods of Busbar "ating ables of Properties of
$u!!ary of )et%ods of Busbar "ating T&e +ollo%in* e.a(le' 'u((a!i'e t&e !atin* (et&o"' "etaile" in 'ection @ an" 'ection ? +o! t#ical ca'e') 3nle'' ot&e!%i'e 'tate", a te(e!atu!e !i'e o+ >$HC abo-e an a(bient o+ ?$HC an" a +!e0uenc# o+ >$ ; &a-e been a''u(e") T&e !atin*' (a# be inc!ea'e" b# blacenin* t&e bu'ba! 'u!+ace') 7'ee Ra"iation Case , d.c.= single rectangular-section bar on edge in still air Case ,, d.c.= single circular-section bar solid or %ollo/5 in still air Case ,,, d.c.= la!inated bars in still air Case ,F a.c.= single rectangular-section bar in still air Case F a.c.= single circular section bar= in still air Case F, a.c.= la!inated bars= in still air Case F,, Enclosed busbars Case F,,, Econo!ical use of busbar configurations
Case , d.c.= single rectangular-section bar on edge in still air
Al# Al# +o!(ula +o!(ula ? o! !ea" !ea" "i!ect "i!ect +!o( +!o( Table Table 12, 12, +o! 'tan"a!" 'tan"a!" 'ie') 'ie') E.a(le Coe! ba! l$$ (( . 6)@ (( 7A K 6@$ (( 2, K 212)6 (( I K )@ 76@$ $)> 7212)6$)@9 K 1>$ A 7o! !ea" "i!ect +!o( Table 12)
Case ,, d.c.= single circular-section bar solid or %ollo/5 in still air
Al# Al# +o!(ula +o!(ula 6 o! !ea" !ea" "i!ect "i!ect +!o( +!o( Table Table 16 16 +o! 'tan"a!" 'tan"a!" 'ie') 'ie') E.a(le >$ (( "ia(ete! coe! !o" I K F)6@ 7196? $)> 71>$)@6 K 2@6$ A 7o! !ea" "i!ect +!o( Table 16)
Case ,,, d.c.= la!inated bars in still air
a A a Al# l# +o!(ula +o!(ula ?, ?, o! !ea" !ea" "i!ect "i!ect +!o( +!o( Table Table 12 12 for one bar ) b Multil# b# a!o!iate +acto! +!o( 'ection @ E.a(le ? coe! ba!' 1$$ (( . 6)@ (( %it& 6)@ (( 'acin*) I K 1>$ A e! ba!) Multil#in* +acto! +o! ? ba!' K @)2$) ;ence I K @)2 . 1>$ K >$2$ A
Case ,F a.c.= single rectangular-section bar in still air
Di-i"e ")c) !atin* b# a!o!iate -alue o+
a' obtaine" +!o( :i*u!e E.a(le
Coe! ba! 1$$ (( . 6)@ (( 7ab K 1$$6)@ K 16 ")c) !atin* K 1>9 A 7Ca'e I) R+ R Ro K 1)12 +!o( :i*u!e
√1)12K 1)$>F ;ence I K 1>$1)$>F K 1?F$ A
Case F a.c.= single circular section bar= in still air
a Di-i"e ")c) !atin* b# a!o!iate -alue o+
a' obtaine" +!o( :i*u!e ? 7'oli" !o"' o! tube') E.a(le >$ (( "ia(ete! coe! !o") ")c) !atin* K 2@6$ A 7Ca'e II
;ence R+ R Ro K 1)61, +!o( :i*u!e ? ;ence
Case F, a.c.= la!inated bars= in still air
a Dete!(ine !atin* o+ one bar a' +o! Ca'e IV) b Multil# b# a!o!iate +acto!, Table F E.a(le ? coe! ba!' 1$$ (( . 6)@ (( %it& 6)@ (( 'acin*) ")c) !atin* e! ba! K 1>$ A 7a' Ca'e I a)c) !atin* e! ba! K 1?F$ A 7a' Ca'e IV) Multil#in* +acto! +o! ? ba!' K 2)@ ;ence I K 2)@ . 1?F$ K @?$?A
Case F,, Enclosed busbars
a Multil# 'till ai! !atin* b# a!o!iate con'tant 7'ee Enclo'e" coe! con"ucto!' i)e)) b# $)6 to $)6> +o! con"ucto! con+i*u!ation' la!*el# "een"ent on ai! ci!culation 7e)*), (o"i+ie" &ollo% '0ua!e a!!an*e(ent, a!!an*e(ent, :i*u!e 9c, o! b# $) +o! tubula! con"ucto!' o! clo'el# *!oue" +lat la(ination') b Multil# b# +u!t&e! $)F> i+ enclo'u!e o+ t&ic (a*netic (ate!ial) E.a(le ? coe! ba!' 1$$ (( . 6)@ (( a!!an*e" a' in :i*u!e 9c, to ca!!# a)c) ")c) !atin*, 'in*le ba! K 1>$ A 7a' in Ca'e I) a)c) !atin*, 'in*le ba! K 1?F$ A 7a' in Ca'e IV) Multil#in* +acto! +o! ? la(ination' 7Table F K 2)@ Multil#in* +acto! +o! con+i*u!ation o+ :i*u!e 9c, 7'ee :i*u!e 11 K 1)2F ;ence 'till ai! !atin* +o! t&i' con+i*u!ation K 1?F$ . 2)@ . 1)2F K ?@6$ A Multil#in* +acto! +o! non8(a*netic non8(a*netic enclo'u!e 7Enclo'e" coe! con"ucto!' K $)6$ ;ence enclo'e" !atin* K ?@6$ . $)6 K 261$ A Multil#in* +acto! +o! (a*netic enclo'u!e K $)F> ;ence !atin* in (a*netic enclo'u!e K261$ .$)F> K 222$ A Case F,,, Econo!ical use of busbar configurations
E.a(le T%o c&annel', eac& 1$$ (( &i*& . ?> (( +lan*e %i"t& . F)6 (( t&ic 7A K 1?@$ (( 2 e! c&annel) a)c) 6$ ;, @$HC !i'e on ?$HC a(bient in 'till ai!) :!o( Table 1>, !atin* ba'e" on >$HC !i'e on ?$HC a(bient) K >>>$ A 3'e !e8!atin* +o!(ula 7e0uation F to obtain !atin* +o! $HC %o!in* %o!i n* te(e!atu!e an" ?$HC a(bient) ;ence !atin* un"e! con"ition' 'eci+ie" K >>>$ . $)>6 K ?19> A E0ui-alent ?8ba! la(inate" con+i*u!ation +o! 'a(e c!o''8'ectional a!ea K 11F (( . 6)@ (( e! ba! 7A K ?@ (( 2, K 2?9 (() ;ence ")c), !atin* e! ba! +o! >$HC !i'e on ?$HC a(bient) K 1@$$ A 7+!o( e0uation ?, an" alication o+ a!o!iate con-e!'ion con'tant a' abo-e) ab K 11F6)@ K 1F) 7'ee :i*u!e K 1)$F 7+!o( :i*u!e +o! 6$ ;) ;ence a)c) !atin* e! ba! K 1@$$1)$F K 119$ A Multil#in* +acto! +o! ? la(ination' K 2)@ 7Table F ;ence a)c) !atin* +o! ? la(ination' K 119$ . 2)@ K 26$ A T&u' t&e "ouble c&annel a!!an*e(ent i' able to ca!!# (o!e cu!!ent t&an la(inate" ba!', in t&e !atio 1)>21 +o! t&i' c!o''8'ectional c!o''8'ecti onal a!ea) T&i' co!!e'on"' to t&e +acto! *i-en in :i*u!e 11) :o! la!*e! c!o''8'ectional a!ea' t&i' +acto! %oul" be 'till *!eate!, +o! '(alle! 'ection' t&e inc!ea'e %oul" be !at&e! le'' t&an t&i', t&e t &e e.act -alue "een"' on t&e !atio o+ %eb to +l an*e len*t&' o+ t&e c&annel u'e", an" on t&e t&icne'' o+ %eb an" c&annel= a !at&e! %i"e 'acin* bet%een *o an" !etu!n con"ucto!' i' al'o a''u(e" in Table 1>, in o!"e! to a!o.i(ate to t&e e0ui8in"uctance line con"ition 7'ee Con"ition +o! (ini(u( lo'')
ables of Properties of
Busbar $ie !!
Appro;. d.c. rating 71
Appro;. a.c. 72 rating 72 rating
)o!ent of inertia= ,
0lat !!4
)odulus of $ection= H
I$ectional area !!2
eig%t @g:!
Appro; d.c.resistanc e 27C :!
$till air 7@A 7@A
0ree air 7@A 7@A
$till air A
0ree air A
Edge/is e !!4
Edge/is e !!3
0lat !!3
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able 13. a.c. current ratings of la!inated bars 9u!ber and sie of bars
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