UNIVERSIDADE FEDERAL DO RIO GRANDE DO SUL ESCOLA DE ENGENHARIA DEPART DEPARTAMENTO AMENTO DE D E ENGENHARIA ENGEN HARIA ELÉTRICA ELÉTRI CA
CAÁ MARCINIAK FONSECA
PROJETO DE DIPLOMAÇÃO
DIMENSIONAMENTO DE BARRAMENTOS EM SUBESTAÇÕES
Porto Alegre 2009
UNIVERSIDADE FEDERAL DO RIO GRANDE DO SUL ESCOLA DE ENGENHARIA DEPART DEPARTAMENTO AMENTO DE D E ENGENHARIA ENGEN HARIA ELÉTRICA ELÉTRI CA
DIMENSIONAMENTO DE BARRAMENTOS EM SUBESTAÇÕES
Projet Projetoo de D!lo" D!lo"#$% #$%oo #!re&e #!re&e't# 't#do do #o De! De!#rt #rt#"e #"e'to 'to de E'ge'(#r# El)tr*# d# U'+er&d#de Feder#l do Ro Gr#'de do S,lS,l- *o"o *o"o !#rt !#rtee do& do& re., re.,& &t to& o& !#r# !#r# Gr#d Gr#d,# ,#$% $%oo e" E'ge'(#r# El)tr*#/
ORIENTADOR L,1 T#r#j Lo,rero
Porto Alegre 2009
UNIVERSIDADE FEDERAL DO RIO GRANDE DO SUL ESCOLA DE ENGENHARIA DEPART DEPARTAMENTO AMENTO DE D E ENGENHARIA ENGEN HARIA ELÉTRICA ELÉTRI CA
CA3 MARCINIA4 FONSECA
DIMENSIONAMENTO DE BARRAMENTOS EM SUBESTAÇÕES
E&te !rojeto 5o j,lg#do #de.,#do !#r# 5#1er j,& #o& *r)dto& d# D&*!l'# de 6Projeto de D!lo"#$%o7- do De!#rt#"e'to de E'ge'(#r# El)tr*# e #!ro+#do e" &,# 5or"# 5'#l !elo Ore't#dor e !el# 8#'*# E#"'#dor#/
Ore't#dor :::::::::::::::::::::: :::::::::::::::::::::::::::::::::: :::::::::::::: :: Pro5/ L,1 T#r#j do& Re& Lo,rero- UFRGS Do,tor !el# U'+er&d#de Feder#l do Ro Gr#'de do S,l ; Porto Alegre- 8r#&l 8#'*# E#"'#dor# Pro5/ Dr/ L,1 T#r#j do& Re& Lo,rero- UFRGS Do,tor !el# U'+er&d#de Feder#l do Ro Gr#'de do S,l ; Porto Alegre- 8r#&l Pro5/ Dr/ Ro
e& de Frere Gr#d,#do !el# U'+er&d#de Feder#l do Ro Gr#'de do S,l ; Porto Alegre- 8r#&l
Porto Alegre- De1e"
DEDICATÓRIA Ded*o e&te tr#<#l(o #o& "e,& #+?&- ee"!lo& de e&t,do e ded*#$%o/ 3 "'(# e&!o&# !el# !#*@'*# e #!oo d,r#'te o !rojeto/
AGRADECIMENTOS "'(# #+? El= M#r*'#B !elo #ltr,&"o '# l,t# !el# ed,*#$%o 'o 8r#&l e !elo '*e't+o <,&*# de *o'(e*"e'to/ Ao "e, #+ Ig'*o M#r*'#B !elo ee"!lo de r#*o'#ld#de e #"or # *@'*#- o .,e "e #j,do, # e&*ol(er # e'ge'(#r#/ A "'(# e&!o&# Mr*# !elo #"or- #"1#de- #!oo e !or #*redt#r '# re#l1#$%o de&te &o'(o/ A "'(# "%e- r"%o& e re&t#'te d# 5#"l# !elo *#r'(o e '*e't+o #o lo'go de&&e& #'o& de *,r&o- "e&"o e&t#'do lo'ge/ Ao& *oleg#& de !re5et,r#- e" e&!e*#l # M#r# Co'*e$%o Go,l#rt- !el# *o"!ree'&%o e #!oo 'e&&# et#!# 5'#l/ Ao& *oleg#& de e'ge'(#r# el)tr*# !elo &e, #,lo '#& t#re5#& de&e'+ol+d#& d,r#'te o *,r&o e #!oo '# <,&*# !or <e& de Frere !el# o!ort,'d#de de #!re'd1#do e #,lo 'o *o"e$o do tr#<#l(o/ Ao !ro5e&&or L,1 T#r#j do& Re& Lo,rero !el# ore't#$%o 'o tr#<#l(o/ U'+er&d#de Feder#l do Ro Gr#'de do S,l !or o5ere*er ," e'&'o !
RESUMO E&te tr#<#l(o +&# *o'*et,#r <#rr#"e'to& e" &,e& e #!re&e't#r ,"# &&te"t*# !#r# e&*ol(# e d"e'&o'#"e'to de&&e& *o'd,tore&/ P#r# #t'gr e&&e oe&/ Co"o # d&!o'<ld#de de <e& e *o'&der#$>e& 5'#& # re&!eto do& ")todo& e'*o'tr#do&- rotero de d"e'&o'#"e'to e !#r"etro& *l"t*o& #dot#do& 'o 8r#&l
Palavras-!av"s# E$%"$!ar&a El'(r&a) S&s("*as +" P,($&a) S./"s(a01"s) Barra*"$(,s) A*2a&+a+") D&*"$s&,$a*"$(,) C,$+.(,r"s)
ABSTRACT T(& !#!er #"& to *o'*e!t,#l1e <,&e& ' &,<&t#to'& #'d !re&e't # &=&te"#t* 5or &ele*t'g #'d &1'g t(e&e *o'd,*tor&/ To #*(e+e t(& go#l- t(e "o&t ,&ed "et(od& o5 &1'g o5 *o'd,*tor& #& &t,ded/ T(#t &1'g & & d+ded #**ord'g to t(e *rter# ele*tr*#l- t(er"#l- "e*(#'*#l #'d *oro'#/ T(& do*,"e't & t(e re&,lt o5 re&e#r*( o' <,&e& #'d &,<&t#to'&/ A& t(e #+#l#<lt= o5 &!e*5* t(eoret*#l <
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Sumário
6 INTRODUÇÃO))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))66 6)6 M,(&va07,)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))66 6)8 A2r"s"$(a07, +, Pr,/l"*a " O/9"(&v,s))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))68 6): Or%a$&5a07, +, Tra/al!,)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))68 8 BARRAMENTOS))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))6; 8)6 Barra*"$(,s C,$+.(,r"s E* S./"s(a01"s))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))6; 8)8 Barra*"$(,s R<%&+,s " Fl"= 8)8)6 Barra*"$(,s R<%&+,s)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))6? 8)8)8 Barra*"$(,s Fl"= :)6 Cr&('r&, El'(r&, Ca2a&+a+" +" C,$+.07, +" C,rr"$(" "* R"%&*" P"r*a$"$("*"$(" 8> :)6)6 M'(,+, IEEE))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))8? J/K/K/K 8#l#'$o T)r"*o///////////////////////////////////////////////////////////////////////////////////////////////////////2 J/K/K/2 Tr#'&"&&%o de *#lor !or *o'+e*$%o////////////////////////////////////////////////////////////////////////29 J/K/K/2/K Co'+e*$%o 5or$#d#////////////////////////////////////////////////////////////////////////////////////////////29 J/K/K/2/2 Co'+e*$%o '#t,r#l/////////////////////////////////////////////////////////////////////////////////////////////JK J/K/K/J Perd#& !or r#d#$%o///////////////////////////////////////////////////////////////////////////////////////////////////J2 J/K/K/ A.,e*"e'to &ol#r////////////////////////////////////////////////////////////////////////////////////////////////////JJ J/K/K/ Re&&t@'*# El)tr*# do *o'd,tor///////////////////////////////////////////////////////////////////////////////J :)6)8 M'(,+, CIGR))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))));6 J/K/2/K Tr#'&5er@'*# de *#lor !or *o'+e*$%o///////////////////////////////////////////////////////////////////////J J/K/2/K/K Re&5r#"e'to !or *o'+e*$%o 5or$#d# /////////////////////////////////////////////////////////////// J/K/2/K/2 Re&5r#"e'to !or *o'+e*$%o '#t,r#l///////////////////////////////////////////////////////////////// J/K/2/K/J Re&5r#"e'to !or *o'+e*$%o # <##& +elo*d#de& de +e'to//////////////////////////// J/K/2/2 Re&5r#"e'to !or r#d#$%o//////////////////////////////////////////////////////////////////////////////////////// J/K/2/J A.,e*"e'to !or r#d#$%o &ol#r/////////////////////////////////////////////////////////////////////////////// J/K/2/ A.,e*"e'to !or e5eto jo,le////////////////////////////////////////////////////////////////////////////////////0 J/K/2/ Re&&t@'*# el)tr*# do *o'd,tor///////////////////////////////////////////////////////////////////////////////K J/K/2/ D&tr<,$%o r#d#l de te"!er#t,r#////////////////////////////////////////////////////////////////////////////2 :)8 Cr&('r&, T'r*&, Ca2a&+a+" +" C,$+.07, +" C,rr"$(" "* R"%&*" +" C.r(,-C&r.&(,: :): Cr&('r&, M"$&, D&*"$s&,$a*"$(, .a$(, a Es,r0,s " &/ra01"s)))))))))))))))))))))))))))))))>8 :):)6 D&*"$s&,$a*"$(, *"$&, a, .r(,-&r.&(,))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))>8 ))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))>> :):)8 D&*"$s&,$a*"$(, "s(H(&, +,s /arra*"$(,s)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))>? :):):) D&*"$s&,$a*"$(, "s(H(&, +,s /arra*"$(,s))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))? :); D&*"$s&,$a*"$(, S,/ E"&(, C,r,$a))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))?: ; METODOLOGIA DE DIMENSIONAMENTO))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))?> ;)6 R,("&r, +" D&*"$s&,$a*"$(,))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))?> ;)8 D&"r"$0as E$(r" M'(,+,s IEEE " CIGR 2ara CHl.l, +a Ca2a&+a+" +" C,$+.07, +" C,rr"$(" "* C,$+.(,r"s A'r",s))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))?@ ;): C,$+&01"s Cl&*a(,l%&as $, Bras&l)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))8 ;); P"r&l N,r*al*"$(" Es,l!&+, 2ara Barra*"$(,s R<%&+,s))))))))))))))))))))))))))))))))))))))))))))))))))) ;) O Us, +" Pr,%ra*as C,*2.(a&,$a&s))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) CONCLUSÕES E SUGESTÕES DE TRABALOS FUTUROS)))))))))))))))))))))))))))))))))))))))))))? > REFERNCIAS)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))@
LISTA DE ILUSTRAÇÕES Fg/ 2/K ; Per5& de <#rr#"e'to& "#& e'*o'tr#do& 'o "er*#do/////////////////////////////////////////////////////////K Fg/ 2/2 ; C#
LISTA DE ABREIATURAS
ANEEL Ag@'*# N#*o'#l de E'erg# El)tr*# ONS O!er#dor N#*o'#l do S&te"# A8NT A&&o*#$%o 8r#&ler# de Nor"#& T)*'*#& A8AL A&&o*#$%o 8r#&ler# do Al,"'o N8R Nor"# 8r#&ler# UFRGS U'+er&d#de Feder#l do Ro Gr#'de do S,l IEEE I'&tt,te o5 Ele*tr*#l #'d Ele*tro'*& E'g'eer& IACS I'ter'#to'#l A''e#led Co!!er St#'d#rd& IEC I'ter'#to'#l Ele*trote*('*#l Co""&&o' ASTM A"er*#' So*et= 5or Te&t'g #'d M#ter#l& ALCAN Al,"'," Co"!#'= o5 C#'#d# AT Alt# Te'&%o MT M)d# Te'&%o SE S,
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6 INTRODUÇÃO
6)6 MOTIAÇÃO S,e& &%o '&t#l#$>e& el)tr*#& de #lt# !ot@'*# .,e 5,'*o'#" *o"o !o'to de *o'trole e tr#'&5er@'*# e" ," &&te"# de tr#'&"&&%o el)tr*#- dre*o'#'do e *o'trol#'do 5l,o e'erg)t*otr#'&5or"#'do o& '+e& de te'&%o e 5,'*o'#'do *o"o !o'to& de e'treg# !#r# *o'&,"dore& 'd,&tr#&/ O de&e'+ol+"e'to &o*oQe*o'"*o .,e o 8r#&l +e" &o5re'do 'o& lt"o& #'o&- 5#1 *o" .,e &ej# 'e*e&&r# ,"# "#or o5ert# de e'erg# 'o !#&/ I&&o &? &er !o&&+el *o" '+e&t"e'to& e" ger#$%o e tr#'&"&&%o/ Co'&e.,e'te"e'te- 'o+#& &,e& &%o t#"<)" '*l,d#& 'e&&e !ro*e&&o '# "edd# .,e &%o !#rte 'tegr#'te do &&te"# e'erg)t*o- 'o #,lo #o *o'trole e d&tr<,$%o d# e'erg# #o& *e'tro& *o'&,"dore&/ Ne&te *e'ro- o !rojeto de &,e& ) de gr#'de rele+'*#/ E o d"e'&o'#"e'to de *o'd,tore& ) ," 5#tor "!ort#'te #o !rojeto/ O *orreto d"e'&o'#"e'to do& *o'd,tore&- #l)" de o<+#"e'te &er +t#l !#r# # &eg,r#'$# d#& '&t#l#$>e&- e.,!#"e'to& e o!er#dore&- t#"<)" te" '5l,@'*# 'o *,&to 5'#l do !rojeto- tor'#'do #&&" de gr#'de +#lor e 'tere&&e !#r# # +#<ld#de do !rojeto/ O d"e'&o'#"e'to de <#rr#"e'to& *o'd,tore& !#r# &,e& ) ," !ro*ed"e'to tr#<#l(o&o- #l)" &er de ,"# *ert# *o"!led#de/ É ," !ro*e&&o .,e "!l*# # ee*,$%o de ',"ero&o& *l*,lo& e # *o'&,lt# de +ro& .,#dro& e t#
K2 #!re&e't# #& !r'*!#& *#r#*ter&t*#& do& *o'd,tore& ,tl1#do& e" &,e&- e& 'o 8r#&l t#"<)" ) ," 5#tor de "ot+#$%o- !o& 5#1Q&e 'e*e&&r# "#or do*,"e't#$%o e" l'g,# !ort,g,e&#/
6)8 APRESENTAÇÃO DO PROBLEMA E OBJETIOS O tr#<#l(o oe& # 5" de e"<#&#r # !ro!o&t# de &&te"t*# !#r# o d"e'&o'#"e'to/ N# "e"?r# de&*rt+# re5ere'te #o !rojeto de ,"# &,
6): ORGANIAÇÃO DO TRABALO P#r# #l*#'$#r todo& o& o
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8 BARRAMENTOS
8)6 BARRAMENTOS CONDUTORES EM SUBESTAÇÕES A e'erg# el)tr*# ) tr#'&!ort#d# e" Alt# Te'&%o AT #t) & &,e& #tr#+)& de l'(#& #)re#& de *o'd,tore& ',&- &e'do # &,# lg#$%o 5et# dret#"e'te #tr#+)& de ," !?rt*o de re*e!$%o !re&e'te '# &,e& el)tr*#& 'd,&tr#&- 'o .,#l &e '*l,e" #& &,e&*o'*et,#Q&e o& <#rr#"e'to& *o"o &e'do ," gr,!o de *o'd,tore& el)tr*o&- 'or"#l"e'te '& !'t#do& o, '%o- e+e't,#l"e'te e'*#!&,l#do&- de&t'#do& # !er"tr o tr#'&!orte de #lt#& *orre'te& e'tre do& !o'to&- o, # !ro!or*o'#r ,"# d&tr<,$%o de *orre'te& *o" +#r#& #l"e't#$>e& e
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8)8 BARRAMENTOS R GIDOS E FLEEIS O& "et#& "#& ,&#do& *o"o *o'd,tore& e" *#e& do& 5o& 'd+d,#&/ O *oe&- e"e& el)tr*#&/ U" o,tro !ro
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8)8)8 BARRAMENTOS FLEEIS E" <#rr#"e'to& 5le+e& &%o ,&#do& 'or"#l"e'te *#
AAC All Al,"'," Co'd,*tor todo& o& *o'd,tore& de #l,"'o 5g/ 2/2/ Te" ,"# #lt# rel#$%o !e&oQ*o'd,t+d#de/ Utl1# 5o& de #l,"'o do t!o KJ0QHK9 e !o&&, ,"# *o'd,t+d#de de K-2Z IACS I'ter'#to'#l A''e#led Co!!er St#'d#rd&- # "#& #lt# e'tre todo& o& *o'd,tore& ,tl1#do& e" l'(#& #)re#&/ De+do # &&o- ) re*o"e'd#do 29 !#r# o ,&o e" re#& ,r<#'#& *o" l"t#$>e& de e&!#$o o'de +%o& *,rto& e #lt# *o'd,t+d#de &%o 'e*e&&ro&/ É o *#e&/
F&%) 8)8 Ca/, AAC
●
ACSR Al,"'," Co'd,*tor- Stell Re'5or*ed *o'd,tore& de #l,"'o *o" #l"# de #$o CAA/ De+do # &,# #lt# re&&t@'*# "e*'*#- te" "#& #lt# #"!#*d#de !#r# # "e&"o &e$%o de *o'd,tor "edd# e" re# de &e$%o tr#'&+er&#l de #l,"'o- o #$o ) de&*o'&der#do/ Po&&, 5o& de #l,"'o do t!o KJ0QHK9 '# !er5er# e 5o& de #$o 'o '*leo/ É re*o"e'd#do !#r# o ,&o e" l'(#& de tr#'&"&&%o e" re#& r,r#& o'de o& +%o& &%o "#ore&/ O #$o 5#1 *o" .,e o *o'd,tor 5.,e "#& !e&#do- te'do 'or"#l"e'te de KK # KZ do !e&o do *o'd,tor 2/ V#lore& t!*o& !#r# # !ro!or$%o e'tre 5o& de #l,"'o e #$o &%o KXK- X- 2X e XK9 "#& !ode" o*orrer +#r#$>e& # 5" de &e o
20 De+do !re&e'$# do '*leo de #$ol'(#&
de&e'(#d#&
*o" ACSR
&e
de5or"#" "e'o& do .,e #& .,e ,&#" o,tro& *o'd,tore&- !rod,1'do "e'o& 5le*(# !#r# ,"# "e&"# d#d# te'&%o 'o& *#e& &,jet#& # gr#'de& r#j#d#& de +e'to/ O *#
●
AAAC All Al,"'," Allo= Co'd,*tor todo& o& *o'd,tore& de lg# de #l,"'o/ É 5eto de 5o& de #l,"'o do t!o 20KQTK/ Te" #lt# re&&t@'*# "e*'*# e #"!#*d#de &e"el(#'te #o& do& !r"ero&/ E" *o"!#r#$%o *o" ," *#
2K ●
ACAR Al,"'," Co'd,*tor- Allo= Re'5or*ed *o'd,tor de #l,"'o- re5or$#do *o" 5o& de lg# de #l,"'o/ Co'&&te de ,"# "&t,r# de 5o& de #l,"'o 20KQTK e KJ0Q HK9 de "e&"o d"etro/ De+do # tere" o "e&"o d"etro- o& 5o& !ode" &er 'ter*#"<+e& *o" o oe& de 5o& do *#
F&%) 8); Ca/, ACAR
A& &,e&- e" ger#l !o&&,e" +%o& *,rto&- o .,e red,1 # 'e*e&&d#de de *#e& '# *o'&tr,$%o do *o'd,tor *o" o oe&/ E&&#& "od5*#$>e& !ode" &er 5et#& # 5" de &e #,"e't#r o '+el t)r"*o do *o'd,tor "#'te'do o "e&"o d"etro-
22 #,"e'to do #,toQ#"orte*"e'to do *o'd,tor #j,d#'do '# d"',$%o d#& +e& e?l*#& e #t) "e&"o #,"e'to '# tr#$%o "e*'*# d# l'(# !rod,1'do d"',$%o '# 5le*(#/ A& "od5*#$>e& !ode" +r '# 5or"# de #lter#$>e& do 5or"#to do& 5o&- ",d#'$# do& gr#,& de t@"!er# do #l,"'o do& 5o&- ,tl1#$%o de dre'te& t!o& de re+e&t"e'to !#r# !rote$%o *orro&%o do '*leo de #$o e" *#e& !ode" &er ,&#d#& &e!#r#d#"e'te o, e" *o"<'#$%o #t'g'doQ&e #&&" #& !ro!red#de& de&ej#d#& e ot"1#'do # !er5or"#'*e/ O& *#
2J
F&%) 8) Ca/, TQ = a/, s(a$+ar+
O& *#e& t!*#& de o!er#$%o- o ACSS <#&*#"e'te !er"te .,e tod# # *#rg# "e*'*# &ej# *#rreg#d# !elo '*leo de #$o/ O *#e& *l"t*#& de&5#+or+e&/ E&&e& *#e& o'de #lt#& *orre'te& &%o re.,erd#& e" &t,#$>e& de e"erg@'*#/ E&te" #'d# o& *#e& *#,&#d#& !elo +e'to/ O *#
2 5or"#d# ,"# 5g,r# rot#t+# *o" o& do& *o'd,tore& 'o &e'tdo #'tQ(orro/ No& *#e& *#,&#d#& !elo +e'to e *o'&e.,e'te 5#dg# do "#ter#l &%o t#"<)" red,1d#& de+do # +#r#$%o do !er5l #o lo'go do *o"!r"e'to do *o'd,tor/ Co"o re&,lt#do- o& *o'd,tore& VR !ode" &er '&t#l#do& e" lo*#& o'de (#j# #lt#& *#rg#& de te'&%o &e'do "e'or # 'e*e&&d#de de #"orte*edore&/ A 5g 2/ "o&tr# # geo"etr# do *#
F&%) 8)> Ca/, R
E&te" #'d# o,tr#& 'o+#& te*'olog#& ,&#d#& e" *#
2
F&%) 8)? Ca/, OAL ACSR
F&%) 8) Ca/, SDC
F&%) 8)@ Ca/, LNC
A& 'or"#&
Utl1#$%o !ode &er de&t'#do # tr#'&!orte de e'erg# el)tr*# e'tre do& !o'to& o, # d&tr<,$%o de e'erg#- &ej# e" &,e& #
●
A"<e'te !ode- !or ee"!lo- &er ,&#do '#& 1o'#& *o&ter#& o'de ( !ro
●
Corre'te # *orre'te 'o"'#l e de *,rtoQ*r*,to .,e !oder &er *o'd,1d# &%o o& !r'*!#& 'd*e& !#r# # e&*ol(# d# 5or"# d#& <#rr#& e !#r# o d"e'&o'#"e'to do <#rr#"e'to/
2
: DIMENSIONAMENTO DE BARRAMENTOS
:)6 CRITRIO ELTRICO CAPACIDADE DE CONDUÇÃO DE CORRENTE EM R EGIME PERMANENTEMENTE O d"e'&o'#"e'to d# *#!#*d#de de *o'd,$%o de *orre'te e" reg"e !er"#'e'te*(#"#d# t#"<)" de #"!#*d#de- ) *#l*,l#do le+#'do e" *o'&der#$%o !ro!red#de& .,"*#& do& ele"e'to& .,e *o"!>e" o &&te"#/ O *l*,lo ,tl1# *o"o !#r"etro& o& +#lore& de *o'd,t+d#de !er"&&+d#de- e"&&+d#de e *#lor e&!e*5*o do "et#l .,e *o"!>e o *o'd,tor e t#"<)" !ro!red#de& 5&*#&- *o"o o d"etro- geo"etr# e *o"!r"e'to do *o'd,tor/ Al)" d&&o*o'd$>e& *l"t*#& &%o 5,'d#"e't#& !#r# o d"e'&o'#"e'to ,"# +e1 .,e 5#1e" !#rte d# e.,#$%o de <#l#'$o t)r"*o do *o'd,tor/ A 5g,r# J/K #!re&e't# # +#r#$%o de *#!#*d#de de *o'd,$%o de *orre'te do *o'd,tor e" 5,'$%o do &e, d"etro !#r# d5ere'te& *o'd$>e& de *o'&er+#$%o do *o'd,tor/
2
F&%) :)6 R"la07, "$(r" , D&*"(r, " a Ca2a&+a+" +" C,$+.07, +" C,rr"$(" +, C,$(.+,r
:)6)6 MTODO IEEE O ")todo #!re&e't#do !elo IEEE 2 *o'&&te e" deter"'#r- #tr#+)& do& 5#tore& *t#do&- #& !erd#& e g#'(o& de *#lor 'o *o'd,tor/ De !o&&e de&&e& d#do&- j,'t#"e'te *o" o +#lor d# re&&t@'*# el)tr*# do *o'd,tor- deter"'#Q&e # *orre'te .,e !oder 5l,r '," deter"'#do *o'd,tor # ,"# deter"'#d# te"!er#t,r#/ A *orre'te *#l*,l#d# ) e't%o *o"!#r#d# *o" # *orre'te d#d# !#r# # !ot@'*# 5or'e*d#/
2
:)6)6)6 BALANÇO TRMICO E" *o'd$>e& de e.,l
q c q r = q s I ∙ R T c
J/K
o, I =
qc q r − q s R T c
J/2
O'de q c ) # .,#'td#de de *#lor d&&!#d# !or *o'+e*$%o e" X"W q r
) # .,#'td#de de *#lor d&&!#d# !or r#d#$%oW
I ) +#lor e5*#1 d# *orre'te e" #"!ere&W R T c
) # re&&te'*# el)tr*# e" *orre'te #lter'#d# e" o("&X" *o"o &e'do 5,'$%o d#
te"!er#t,r# do *o'd,torW q s
) # .,#'td#de de *#lor re*e<d# !or #.,e*"e'to &ol#r/
No *#&o de '%o (#+er e.,l
dT c dt
=q s I 2 ∙ R T c
J/J
O'de mC p T c
) *#!#*d#de de *#lor tot#l do *o'd,torW
) # te"!er#t,r# do *o'd,tor e" YC/
U" *o'd,tor &o< *o'd$>e& tr#'&t?r#& de *#rg# !ode &er *l#&&5*#do *o"o ," &&te"# de 5l,o de *#lor *o" re&&t@'*# t)r"*# 'ter'# de&!re1+el/ A re&&t@'*# t)r"*# e'tre # &,!er5*e do &&te"# e o #r #o &e, redor ) ",to "#or do .,e # re&&t@'*# t)r"*# 'ter'# do &&te"# de 5or"# .,e e&t# #*#<# !or de5'r o !ro*e&&o de tr#'&5er@'*# de *#lor J/
29
:)6)6)8 TRANSMISSÃO DE CALOR POR CONECÇÃO Seg,'do e'&#o& 5eto& e" l#e& *l"t*#& *o'&er+#t+#& !#r# o +er%o de 0- "X& # K-2 "X& !#r# +elo*d#de do +e'to e te"!er#t,r# #"<e'te 'o +er%o de J0YC # YC &%o *o","e'te ,&#d#& !#r# o& *l*,lo&/
:)6)6)8)6 C ONECÇÃO FORÇADA A rel#$%o 5,'d#"e't#l !#r# tr#'&"&&%o de *#lor !or *o'+e*$%o de <#rr#"e'to& (or1o't#& .,#'do o '"ero de Re='old& e&t+er e'tre 0-K e K000- o, &ej# +e'to& 5r#*o& ) d#d# !or
[
D f V w q c = K-0K 0-0J2 μ f
] 0-2
κ f / K θ T c – T a
J/
[,#'do o '"ero de Re='old& e&t+er e'tre K000 e K000- o, &ej# +e'to& 5orte&- # e!re&&%o )
[
D f V w q c = 0-0KK9 μ f
0-
k f K θ T c – T a
]
O'de D
) o d"etro do *o'd,tor e" ""W
V w ) # +elo*d#de de +e'toW T a ) # te"!er#t,r# #"<e'teW κ f
) # *o'd,t+d#de t)r"*# do #r '# te"!er#t,r# T5W
ρ f ) de'&d#de do #rW μ f ) # +&*o&d#de #<&ol,t# do #rW K θ
) o 5#tor de dre$%o do +e'to/
J/
J0 O '"ero de Re='old& ) d#do !or R e = D.ρf.Vwμf
J/
O 5#tor de dre$%o do +e'to !ode &er *#l*,l#do !or K θ =K-K9M – *o& Φ 0-K9M*o& 2\ 0-JPL sen 2\
J/
o'de Φ ) o 'g,lo e'tre # dre$%o do +e'to e o eo do *o'd,tor/ Ee"!lo& de +#lore& ger#do& # !#rtr de&&# de5'$%o Φ
K θ
90Y Y J0Y 20Y 0Y
K 0- 0- 0-J9 0-J
O& +#lore& de +&*o&d#de- de'&d#de e *o'd,t+d#de t)r"*# do #r !ode" &er o
J/
e d# ele+#$%o do *o'd,tor #*"# do '+el do "#r e - d#d# e" "/ V&*o&d#de do #r K-×K0− T f 2J K- μ f = T f JJ-
J/9
De'&d#de do #r K-29J−K-2×K0− e -J9×K0−9 2e ρ f = K0-00JT f
J/K0
Co'd,t+d#de t)r"*# do #r κ f =2-2 ×K0− 2 -×K0− T f − -0×K0−9 T f 2
J/KK
JK O .,#dro 2 # &eg,r #!re&e't# +#lore& t!*o& de +&*o&d#de- de'&d#de do #r e *o'd,t+d#de e"!er#t,r# V&*o&d#de T f!"m
YC K0 20 J0 0 0 0 0 0 90 K00
d'"*#
t)r"*# do #r
J
r k# / m
r
P# / & 0-0000K 0-0000KK 0-0000K 0-0000K9K 0-0000K9 0-0000200 0-000020 0-0000209 0-00002KJ 0-00002K
Co'd,t+d#de
De'&d#de do Ar
0" K-2 K-20 K-K K-K2 K-09J K-00 K-029 K-000 0-92 0-9
K000" K-K0 K-0 K-0JJ K-000 0-99 0-90 0-9K2 0- 0-2 0-J9
k f
2000" 0-9 0-9 0-9KJ 0- 0- 0-JK 0-0 0-J 0-2 0-K
000" 0- 0-JK 0-0 0- 0-J 0-J 0-2 0-0 0-90 0-
X"/YC 0-020 0-02 0-02 0-02 0-020 0-02 0-029 0-0J02 0-0J09 0-0JK
V#lore& 'ter"edro& !ode" &er o
:)6)6)8)8 CONECÇÃO NATURAL Co" +elo*d#de do +e'to .,#l # 1ero- o*orre # *o'+e*$%o '#t,r#l/ N# +erd#de',"er*#"e'te o +#lor d# *o'+e*$%o '#t,r#l ) #!ro"#d#"e'te g,#l # d# *o'+e*$%o 5or$#d# !#r# +#lore& de +elo*d#de do +e'to de 0-9 "X& e dre$%o do +e'to de 1ero gr#,&/ A e.,#$%o !#r# o *l*,lo d# !erd# de *#lor !or *o'+e*$%o '#t,r#l ) d#d# !or q cn= 0-020 f 0- D0- T c – T a K-2 É re*o"e'd#do o ,&o do "#or +#lor e'tre o& do& +#lore& de
J/K2
q c !#r# ," d#do d"etro
do *o'd,tor/ Re*o"e'd#Q&e t#"<)" ,&#r o "#or +#lor e'tre # *o'+e*$%o '#t,r#l e 5or$#d# !#r# o *#&o de +e'to& ",to 5r#*o& 2/ A 5g,r# J/2 "o&tr# # rel#$%o e'tre # +elo*d#de do +e'to e" "l(#&X(or# e # *orre'te #lter'#d# e" #"!]re&/
J2
F&%) :)8 R"la07, "$(r" a v"l,&+a+" +, v"$(, " a ,rr"$(" al("r$a+a $, ,$+.(,r $%nte& '()*+ . *, T(TT-*+ . D.. C/rrent0Carr1!n# Capac!t1 %f 2C)R 345
:)6)6): PERDAS POR RADIAÇÃO A !erd# !or r#d#$%o de ," *o'd,tor ) d#d# !or q r =6728 K c − K a O'de σ ) # *o'&t#'te de Ste5#'Q8olt1"#'-
J/KJ ε
) # e"&&+d#de- 2 8 = 9D / K2 ) # re# do
*l'dro *r*,'&*rto e K ) # te"!er#t,r# e" gr#,& 4el+'/ S,<&tt,'do # *o'&t#'te- *o'+erte'do # re# e" ter"o& do d"etro do *o'd,tor e *o'+erte'do # te"!er#t,r# !#r# gr#,& Cel&,& *(eg#"o&
JJ T c 2J T a 2J − ] q r =0-0K D7 [ K00 K00
J/K
A e"&&+d#de do *o'd,tor de #l,"'o 'o+o ) #!ro"#d#"e'te g,#l # 0-2/ ," *o'd,tor e&*,re*do !elo& #'o& !ode *(eg#r # 0-9 o, "#&/ Nor"#l"e'te ) ,tl1#do ," +#lor ")do de 0- /
:)6)6); AUECIMENTO SOLAR A& *o'd$>e& d# &,!er5*e do *o'd,tor deter"'#r%o # .,#'td#de de e'erg# &ol#r .,e e&&e *o'd,tor #<&or+er/ Cor!o& 'egro& te" K00Z de #<&or$%o- e'.,#'to .,e *or!o&
J/K
O'de : ^ *oe5*e'te de #<&or$%o &ol#rW
; se ^ 5l,o tot#l de *#lor rr#d#do !elo &ol e !elo *), *orrgdo X*"2W θ
^ 'g,lo e5et+o de '*d@'*# do& r#o& &ol#re& gr#,&/
Se'do θ =#r**o& [ *o& c ∙ *o& < c− < " ]
O'de c
^ #ltt,de do &ol e" gr#,&W
< c
^ #1",te do &ol e" gr#,&W
< "
^ #1",te d# l'(# e" gr#,&/
J/K
J O<&er+#$%o o +#lor de : +#r# de 0-2J !#r# *o'd,tore& 'o+o& # 0-9 !#r# *o'd,tore& e&*,re*do& *o" o te"!o/ Utl1#Q&e 'or"#l"e'te o +#lor 'ter"edro de 0-/ O& +#lore& d# #ltt,de e do& #1",te& !ode" &er *#l*,l#do& # !#rtr de e.,#$>e& e'*o'tr#d#& '#& re5er@'*#& 2/ O +#lor d# #ltt,de do &ol ) e!re&&o !or c =arcsen [ *o& "at *o& = *o& > sen "at sen = ]
J/K
O'de > ) o 'g,lo d# (or# do d#/ Utl1#'doQ&e ," d# de K2 (or#& e ,"# tr#jet?r# &ol#r de K0Y- !ode"o& #!ro"#r _ !or ?%ra d%d!a −K2 ⋅KNY / Por ee"!lo- #& KK( tere"o& > ^ QKY e #& K( tere"o& > ^ Y/ ) # '*l'#$%o &ol#r .,e ) d#d# !or
= =2J-J sen
[
2 @ J0 J
]
J/K
O'de @ ) o d# do #'o/ @ +#r# de K !#r# KY de j#'ero # J !#r# JK de de1e"
J/K9
O'de A ) ,"# +#r+el do #1",te &ol#r d#d# !or J/20
A = sen > sen "at *o& > − *o& "at t#' =
C ^ *o'&t#'te de #1",te &ol#r .,e ) d#d# e" 5,'$%o do 'g,lo d# (or# do d# e d# +#r+el ` e +#le a'g,lo d# (or# do d# _ QK0c > 0 0c > K0
C gr#,& &e A b 0 0 K0
J O +#lor do 5l,o tot#l de *#lor ; s re*e<do !el# &,!er5*e #o '+el do "#r ) de!e'de'te d# #ltt,de do &ol e d# *l#rd#de d# #t"o&5er#/ E&&e +#lor !ode &er o
J
M
N
P
J/2K
; s= 2 B c C c D c * c $ c c
O& *oe5*e'te& de J/2K e&t%o #!re&e't#do& 'o .,#dro
2 B C D * $
A(*,s"ra l&*2a Q2-2J9K J-0 QK-9220 J-92K K0Q2 QJ-KKK K0Q K-9JK K0Q Q-00 K0Q9
A(*,s"ra &$+.s(r&al J-K2K K-2KK0 -KJ K0QK QJ-K K0Q2 - K0Q Q-J K0Q K-J2J K0Q
O .,#dro 2 # &eg,r "o&tr# +#lore& d# #ltt,de do &ol e d# .,#'td#de de *#lor re*e<d# !or r#d#$%o *#l*,l#do& # !#rtr de&&e ")todo c gr#,& K0 K 20 2 J0 J 0 0 0 0 0 90
; s X" At"o&5er# l"!# 2J JJ J 9J 0 29 9KJ 9K 99 K000 K020 K0J0 K00
At"o&5er# 'd,&tr#l KJ 20 J2 22 02 K K9 2 9 2 K 09 JJ 9
J A .,#'td#de de *#lor re*e<d# !or ,"# &,!er5*e !l#'# !er!e'd*,l#r #o& r#o& do &ol e lo*#l1#d# 5or# d# #t"o&5er# d# terr# ) de #!ro"#d#"e'te KJ2 X"/ E'tret#'to- !#rte de&&# e'erg# ) #<&or+d# !el# #t"o&5er# #'te& de #t'gr # terr#/ Po'to& "#& #lto& re*e
J/22
O 5#tor de *orre$%o ) de5'do *o"o 2
J/2J
K s%"ar = 2 B e C e
O'de 2 ^ K B ^ K-KfK0Q C ^ QK-K0fK0Q e
) # ele+#$%o #*"# do '+el do "#r e" "etro&
O .,#dro #<#o 2 5or'e*e #lg,'& +#lore& !#r# o 5#tor de *orre$%o Ele+#$%o #*"# do '+el do "#r e 0 K000 2000 000
F#tor de *orre$%o de ele+#$%o K s%"ar K-00 K-K0 K-K9 K-2
J
:)6)6) R ESISTNCIA ELTRICA DO CONDUTOR De&g'#Q&e !or re&&t@'*# el)tr*# # "#or o, "e'or d5*,ld#de # !#&&#ge" de el)tro'& o5ere*d# !or ," *o'd,tor !er*orrdo !or ,"# *orre'te el)tr*#/ Teor*#"e'te # *orre'te el)tr*# *o'&&te 'o de&lo*#"e'to de el)tro'& de ," !ote'*#l !#r# o,tro #tr#+)& do *o'd,tor/ E&t#& !#rt*,l#& #o &e de&lo*#re" !elo *o'd,tor *olde" *o" o& '*leo& do& to"o& do "#ter#l *o'd,tor *#,&#'do #&&" re&&t@'*# # !#&&#ge" de&&e& el)tro'&/ E&te r#*o*'o e!l*# !or .,e r#1%o o& *o'd,tore& #!re&e't#" re&&t@'*#& d&t't#&- d#d#& #& &,#& d5ere'te& *o'&tt,$>e& #t?"*#&/ A re&&t@'*# el)tr*# do *o'd,tor +#r# *o" # 5re.,@'*#- de'&d#de ")d# de *orre'te e te"!er#t,r#/ P#r# 0 H1 AC- # ,"# te"!er#t,r# de 2 YC e de YC- o 2"/m!n/m *"ectr!ca" C%nd/ct%r and%%k 5or'e*e e&&e& +#lore& *#l*,l#do& de re&&t@'*# el)tr*# !#r# o& *o'd,tore& de #l,"'o "#& ,&#do&/ E&te& +#lore& *#l*,l#do& '*l,e" o e5eto !el*,l#r .,e ) ," 5e'"e'o .,e o*orre e" *orre'te #lter'#d#/ A& *#rg#& el)tr*#& e" "o+"e'to te'de" # &e *o'*e'tr#r !el# !er5er# do *o'd,tor- de#'do #&&" # !#rte "#& 'ter'# *o" ,"# de'&d#de de *orre'te "e'or/ "edd# .,e e&&# 5re.,@'*# ) #,"e't#d#- e&te e5eto ) "#& &g'5*#t+o- #o !o'to de '%o !#&&#r "#& *#rg#& !elo *e'tro do *o'd,tor- #!e'#& '# reg%o !er5)r*#- d# o 'o"e e5eto !el*,l#r/ E&&e& +#lore&5or'e*do& !#r# todo& o& !r'*!#& t!o& de *o'd,tore&- '%o '*l,e" # *orre$%o de+do #o e5eto "#g')t*o 'o *e'tro do *o'd,tor de!e'de'te d# de'&d#de de *orre'te/ E&&e e5eto ) "#& &g'5*#t+o e" *o'd,tore& *o" #l"# de #$o *o" '"ero "!#r de *#"#d#& de #l,"'o/ Co'd,tore& *o" #l"# de #$o de ,"# '*# *#"#d# te" &,# re&&t@'*# #,"e't#d# de 20Z de+do #o e5eto !el*,l#r/ O #,"e'to de re&&t@'*# e" *o'd,tore& *o" J *#"#d#& ) #!ro"#d#"e'te JZ e" rel#$%o #o& *o'd,tore& *o" *o" *#"#d# '*#/ P#r# *o'd,tore& *o" #l"# de #$o de+eQ&e ter ," e&t,do de e'ge'(#r# e&!e*5*o !#r# deter"'#$%o de &,# re&&t@'*#/ De "#'er# #!ro"#d#- !odeQ&e deter"'#r .,#l.,er +#lor de re&&t@'*# el)tr*# de ," *o'd,tor !or 'ter!ol#$%o l'e#r- &#
J R T s/per!%r − R T !nfer!%r ] T c −T !nfer!%r R T !nfer!%r R T c =[ T s/per!%r −T !nfer!%r
J/2
O& +#lore& de re&&t+d#de d# "#or# do& "et#& *o","e'te ,&#do& *o"o *o'd,tore& #,"e't#" ," !o,*o "#& r#!d#"e'te do .,e o "odelo l'e#r !ro!o&to !ort#'do o *l*,lo ) "#& *o'&er+#t+o/ Seg,'do o IEEE Std J 2 o ,&o de +#lore& t#
T !nfer!%r = 2 ℃ e T c
do *o'd,tor
.,e +# de 20 ℃ # 00 ℃ *o" erro& d# orde" de 'o ""o JZ e !ode'do &er de&*o'&der#do '# "#or !#rte do& *#&o&/ U" o,tro ")todo- "#& *o","e'te ,&#do- &,gere # ,tl1#$%o d# re&&t@'*# el)tr*# e" *orre'te *o't',#/ E&&# re&&t@'*# el)tr*# !#r# ,"# d#d# te"!er#t,r# !ode &er *#l*,l#d# #tr#+)& de R=
M 2
n d
K
J/2
O'de ρ ^ re&&t+d#de el)tr*# do #l,"'o- e" ,"# d#d# te"!er#t,r# 'or"#l"e'te- '# te"!er#t,r# de 20 YC- *o'5or"e # N8R 020 n ^ ',"ero de 5o& de #l,"'o d ^ d"etro do& 5o& de #l,"'o K ^ 5#tor de #*r)&*"o d# re&&t@'*# el)tr*# de+do # tor$%o do& 5o&/ Nor"#& 'ter'#*o'#& tr#1e" e&&e& +#lore& !#r# o& *#
J9 !er"te *#l*,l#r # re&&t@'*# e" O("XB"/ P#r# o *l*,lo d# re&&t@'*# e.,+#le'te RT # ,"# o,tr# te"!er#t,r#- ,tl1#Q&e # &eg,'te e.,#$%o RT = R 20 [ K20 T − 20 ]
J/2
Se'do- 20 o *oe5*e'te de te"!er#t,r# # 20YC do #l,"'o/ O .,#dro # &eg,r #!re&e't# +#lore& de
20 e de
20 !#r# o #l,"'o *o" +#r#&
*o'd,t+d#de&/ Co'd,t+d#de M'"#
20 Y C −K
20 mm 2 / km
K-0 K-J K- K- K- K-9 2-0 2-2 2-J 2- 2-
0-000J0 0-0000 0-000 0-0000 0-0000 0-000 0-0009J 0-00K0 0-00KK2 0-00KK9 0-00K2
2-2 2-K2 2-00 2-0J 2-9 2-J 2-0 2-K9 2- 2-J0 2-
O *l*,lo d# re&&t@'*# el)tr*# e" *orre'te #lter'#d#- le+# e" *o'&der#$%o o e5eto !el*,l#r e o e5eto de !ro"d#de / M#& *o"o o e5eto de !ro"d#de )- e" ger#l- ",to !e.,e'o 'o *#&o de *#
J/2
O'de o 5#tor de+do #o e5eto !el*,l#r ) d#do !or 1 ) =
A 2) 2
K92 0-L/ A )
J/2
0 e o 5#tor de+do #o e5eto de !ro"d#de #!ro"#d#"e'te 1ero !or d 2 K-K d 2 0-JK2 ] 1 = $ A × ×[ ) ) 0-2 $ A
J/29
&e'do A ) = A =
L/ / f.4E
−M
J/J0
RT
2 A $ A = K92−0- A 2
J/JK
d ^ d"etro do *o'd,tor e" !oleg#d#& ) ^ e&!#$#"e'to e'tre #& l'(#& A 5g,r# J/J "o&tr# # rel#$%o e'tre # re&&t@'*# el)tr*# do *o'd,tor e o &e, d"etro !#r# d5ere'te& te"!er#t,r#&/
K
F&%) :): R"la07, "$(r" r"s&s($&a " +&*"(r, +, ,$+.(,r $%nte& '()*+ . *, T(TT-*+ . D.. C/rrent0Carr1!n# Capac!t1 %f 2C)R 345
:)6)8 MTODO CIGR A&&" *o"o o ")todo !ro!o&to !elo IEEE- o ")todo do CIGRÉ SC22 G22QK2 t#"<)" !ro!>e" o d"e'do'#"e'to do *o'd,tor ,tl1#'do o <#l#'$o t)r"*o do *o'd,tor *o" o oe& de o!er#$%o- # ,"# te"!er#t,r# .,e '%o #t'j# # ""# 5le*(# #d"&&+el e t#"!o,*o #t'j# +#lore& !r?"o& # te"!er#t,r# de re*o1"e'to do #l,"'o o .,e #*#rret#r# !erd# '# 5or$# de tr#$%o do *o'd,tor o, #!e'#& d"',$%o d# +d# tl do *o'd,tor/ Co"o 'o ")todo #'teror- # te"!er#t,r# do *o'd,tor de!e'der d# *orre'te de *#rg#- d#&
2 *#r#*ter&t*#& el)tr*#& do *o'd,tor e do& !#r"etro& #t"o&5)r*o& t#& *o"o o +e'to e # r#d#$%o &ol#r/ A *o'd$%o de e&t#<ld#de t)r"*# ) d#d# .,#'do 'e'(,"# e'erg# t)r"*# ) #r"#1e'#d# 'o *o'd,tor- o, &ej#- todo o #.,e*"e'to !ro+o*#do 'o *o'd,tor ) d&&!#do '# #t"o&5er#/ De&&# 5or"# # e.,#$%o de e.,l
J/J2
O'de F ^ #.,e*"e'to !or e5eto o,leW G ^ #.,e*"e'to !or "#g'et1#$%oW . )
^ #.,e*"e'to !or r#d#$%o &ol#rW
!
^ #.,e*"e'to !or e5eto Coro'#W
. c
^ re&5r#"e'to !or *o'+e*$%oW
r
^ re&5r#"e'to !or r#d#$%oW
. w
^ re&5r#"e'to !or e+#!or#$%o/
O re&5r#"e'to !or e+#!or#$%o '%o #lter# &g'5*#'te"e'te o <#l#'$o t)r"*o do *o'd,tor/ A!e'#& &er# rele+#'te .,#'do o *o'd,tor e&t+e&&e "do o, "ol(#do e "e&"o #&&" e" ," *,rto e&!#$o de te"!o/ E&te ")todo- #&&" *o"o o #'teror *o'&der# .,e o& e5eto& rel#*o'#do& # e+#!or#$%o !ode" &er g'or#do&/ T#"<)" ) g'or#do o #.,e*"e'to !or e5eto Coro'# !or &er de orde" de gr#'de1# de&!re1+el e" *o"!#r#$%o *o" o& de"#& !#r"etro&/ O #.,e*"e'to !or e5eto Coro'# #!e'#& &er# &g'5*#'te *o" #lto& gr#de'te& de te'&%o '# &,!er5*e .,e &o"e'te &e #!re&e't#" d,r#'te !re*!t#$>e& e *o" #lt#& +elo*d#de& de +e'to o'de o*orre gr#'de *o'+e*$%o e e+#!or#$%o/ De+do #o 5#to de .,e ) 'e*e&&ro *#l*,l#r o ""o '+el de *orre'te <#&e#do e" +#lore& ")do& o, ""o& d#& *o'd$>e& "etereol?g*#& e&t+e&- '%o &er# o *#&o de '*l,r e&&e e5eto- de+do # &,# '#t,re1# e&!ord*#/
J O& e5eto& de "#g'et1#$%o re5ere"Q&e #o #.,e*"e'to do *o'd,tor de+do #o 5l,o "#g')t*o **l*o .,e *#,&# o #!#re*"e'to de *orre'te& !#r#&t#&- (&tere&e e +&*o&d#de "#g')t*# 9/ E&te 5e'"e'o o*orre &o"e'te e" *orre'te #lter'#d# e ) 'or"#l"e'te de&!re1#do !#r# *o'd,tore& de "et#l '%o 5erro&o/ Pode" &o"e'te &er &g'5*#t+o& !#r# *o'd,tore& *o" '*leo de #$o/ I&to o*orre !or.,e- e" *#e& !o&- '# "#or# do& *#&o&- *#
:)6)8)6 TRANSFERNCIA DE CALOR POR CONECÇÃO A &,!er5*e .,e'te do *o't,tor #.,e*e o #r #dj#*e'te e # de'&d#de do #r #.,e*do d"',/ E't%o o #r te'de # &,<r- 'o *#&o d# *o'+e*$%o '#t,r#l o'de # +elo*d#de do +e'to ) *o'&der#d# 1ero VH0 o, ) *#rreg#do !#r# lo'ge do *o'd,tor 'o *#&o d# *o'+e*$%o 5or$#d# V ≠0 / O #r 5ro 5l, &,<&tt,'do o #r .,e'te e #&&" re&5r#'do o *o'd,tor/ Alg,'& !#r"etro &%o te& !#r# o& *l*,lo& &,<&e.,e'te&/ S%o ele& ●
O '"ero de N,&&elt- d#do !or
@/ =? c
D f
O'de ?c
^ *oe5*e'te de tr#'5er@'*# de *#lor !or *o'+e*$%o e" X"4W
c ^ *o'd,t+d#de t)r"*# do #r d#d# e" X"4W D
^ d"etro eter'o do *o'd,tor/
J/JJ
●
O '"ero de Re='old& R e =
r V D
J/J
f
O'de V ^ +elo*d#de do +e'to e" "X&W
^ +&*o&d#de d'"*# e" "X&W
f
r ^ de'&d#de rel#t+# do #r- d#d# !or
r =/0 W
&e'do ^ de'&d#de do #r '# #ltt,de e" .,e&t%oW 0 ^ de'&d#de do #r #o '+el do "#rW ●
O '"ero de Gr#&(o5 DJ T s−T a # r = T f 2J f 2
J/J
O'de T s ^ te"!er#t,r# d# &,!er5*e do *o'd,torW ^ te"!er#t,r# #"<e'teW
T a ●
O '"ero de Pr#'dtl r =
c f
J/J
O'de c ^ *#lor e&!e*5*o do #r !re&&%o *o'&t#'te e" X Bg 4W ^ +&*o&d#de d'"*# do #r e" BgX"&/
E.,#$>e& e"!r*#& !ode" &er e"!reg#d#& !#r# o *l*,lo d#& +#r+e& #*"# / S%o el#& f
=K-J2× K0− 9-×K0− T f
J/J
f
=2-M2 × K0−2 O-2× K0−N T f
J/J
r
=0-K −2-×K0− T f
J/J9
#
=9-0 m / s2
J/0
T f
=0- T sT a
J/K
r
= e−K-KP×−M 1
J/2
o'de 1 ) # #lt,r# #*"# do '+el do "#r A tr#'&5er@'*# de *#lor !or *o'+e*$%o ) d#d# !or C = f T s−T a @/
J/J
O'de o '"ero de N,&&elt ) *#l*,l#do 'de!e'de'te"e'te !#r# o *#&o d# *o'+e*$%o &er 5or$#d# o, '#t,r#l/
:)6)8)6)6 R ESFRIAMENTO POR CONECÇÃO FORÇADA E" o!er#$%o 'or"#l- o'de # te"!er#t,r# d# !el*,l# 5l"e de #r &o
- o '"ero de N,&&elt !ode &er re!re&e't#do !or
@/ = BK R e n
J/
O'de BK e n &%o *o'&t#'te& .,e de!e'de" do '"ero de Re='old& e d# r,go&d#de R f d# &,!er5*e do *o'd,tor/ E&&# r,go&d#de !ode &er *#l*,l#d# de #*ordo *o" # e.,#$%o J/ R f =
d 2 D −d
J/
O'de d ) o d"etro d# *#"#d# "#& eter'# do *o'd,tor e D ) o d"etro tot#l/ F&%) :); R.%,s&+a+" +, a/,
Co'd,tore& l&o& #!re&e't#" re# 0 # Z "#or do .,e *o'd,tore& tr#'$#do&/ O #,"e'to*o'&der#'do o re&5r#"e'to !or *o'+e$%o 5or$#d#- e'tre *o'd,tore& l&o& e tr#'$#do& ) # *(#"#d# 5,'$%o r,go&d#de/
O .,#dro # &eg,r "o&tr# o& +#lore& de BK e n e" 5,'$%o do '"ero de Re='old& e d# r,go&d#de/ F## de
F## de Re
R,go&d#de 0-0 R f 0-K
BK
n
2- ×K0J
0-K
0-K
de
#t)
K02
R f 0-0
2-PN ×K0J
×K0
0-K
0-JJ
0-0 R f 0-K
2-PN ×K0J
×K0
0-0
0-00
A dre$%o do +e'to t#"<)" te" !#!el "!ort#'te 'o *l*,lo e5et+o do re&5r#"e'to !or *o'+e*$%o 5or$#d#/ O '"ero de N,&&elt +#r# *o" o &e'o do 'g,lo de '*d@'*# do +e'to e" rel#$%o #o eo do *o'd,tor *o"o "o&tr#do '# e.,#$%o J/ mK
@/ = @/90 [ 2K B 2 sen ]
J/
O'de 2K= 0-M2
- B 2=0-PL e mK=K-0L !#r# 0Y 2MY
2K= 0-2 - B 2=0-ML e mK= 0-90 !#r# 2MY 90Y [,#'do o +e'to &o!r# !#r#lelo #o *o'd,tor- o, &ej# 'g,lo '*d@'*# 0Y- 'ot#Q&e .,e o +#lor do '"ero de N,&&elt +#le 0-M2 @/90 / Co" +elo*d#de& de +e'do ",to <## V 0- "X& - '%o ( dre$%o !re5ere'*#l de +e'to e !#r# t#l *#&o ,tl1#Q&e ,"# *orre$%o <#&e#d# e" te&te& !#r# o '"ero de N,&&elt @/ c%r = 0-NN @/ 90
J/
:)6)8)6)8 R ESFRIAMENTO POR CONECÇÃO NATURAL P#r# o *l*,lo d# tr#'&5er@'*# de *#lor !or *o'+e*$%o '#t,r#l- o '"ero de N,&&elt de!e'de do !rod,to do& '"ero& de Gr#&(o5 e Pr#'dtl- *#l*,l#do& # !#rtr d#& e.,#$>e& J/J e J/J re&!e*t+#"e'te- t#"<)" *(#"#do de '"ero de R#=leg(/ @/ = 22 r ⋅ r m
2
J/
O& +#lore& d#& *o'&t#'te& 22 e m2 &%o de!e'de'te& do '"ero de R#=leg(/ O .,#dro # &eg,r "o&tr# o& +#lore& !#r# e&&#& *o'&t#'te& r ⋅ .r
22
m2
de
#t)
K02
K0M
0-0
0-K
K0M
K0P
0-0
0-20
:)6)8)6): R ESFRIAMENTO POR CONECÇÃO A BAIAS ELOCIDADES DE ENTO [,#'do o*orre e" ,"# reg%o- +elo*d#de& ",to <##&
de +e'to- o *l*,lo do
re&5r#"e'to !or *o'+e*$%o !ode &er <#&e#do e" ,"# "&t,r# de #"e& de re&5r#"e'to !or *o'+e*$%o #!re&e't#do& e e't%o ,&#r o "#or +#lor e'*o'tr#do ●
.,e '%o ( dre$%o !re5ere'*#l do +e'to- ," 'g,lo de Y ) #&&,"do e # *o'+e*$%o 5or$#d# ) *#l*,l#d# *o'5or"e e.,#$>e& J/J e J//
●
O &eg,'do +#lor de . C ) *#l*,l#do ,&#'do #& e.,#$>e& J/J e J//
●
O re&5r#"e'to !or *o'+e*$%o '#t,r#l ) *#l*,l#do ,&#'do # e.,#$%o J//
O "#or +#lor de'tre o& tr@& *#l*,l#do& de+e &er o e&*ol(do/
:)6)8)8 R ESFRIAMENTO POR RADIAÇÃO A tr#'&5er@'*# de *#lor !or r#d#$%o ) 'or"#l"e'te !e.,e'# e" rel#$%o #o re&5r#"e'to tot#l- e&!e*#l"e'te .,#'do o*orre *o'+e*$%o 5or$#d#/ A e.,#$%o J/9 ) # &,gerd# !#r# e&&e *l*,lo r = D B [ T s 2J − T a 2J ]
J/9
O'de ) # e"&&+d#de e de!e'de d#& *o'd$>e& d# &,!er5*e do *o'd,tor +#r#'do de
0-2J !#r# *o'd,tore& 'o+o& # 0-9 !#r# *o'd,tore& e&*,re*do& *o" o te"!o e
B ) # *o'&t#'te
de Ste5#'Q8olt1"#''/ A&&" *o"o 'o ")todo IEEE- t#"<)" ) &,gerdo o ,&o do +#lor 0- !#r# e"&&+d#de/
:)6)8): AUECIMENTO POR RADIAÇÃO SOLAR O *l*,lo d# r#d#$%o &ol#r 'o *o'd,tor !ode &er 5eto ,tl1#'do # e.,#$%o J/0 *o'(e*e'doQ&e o +#lor d# 'te'&d#de dret# e d5,&# d# r#d#$%o &ol#r e de"#& !#r"etro& do *o'd,tor e do lo*#l/ P#r# d5,&%o &otr?!*# d# r#d#$%o e" ," *o'd,tor (or1o't#l- o *#lor tot#l re*e<do !or ,'d#de de *o"!r"e'to do *o'd,tor ) d#do !or
. ) = ) D [ I D sen $ sen s B ] 2
J/0
O'de I D ^ r#d#$%o &ol#r dret#W ) ^ #<&or+d#de d# &,!er5*e do *o'd,torW ^ 'g,lo e'tre o 5ee &ol#r e o eo do *o'd,torW $
^ re5let+d#de o, #l
) ^ #ltt,de do &olW I d
^ r#d#$%o &ol#r d5,&#W
< ^ 'g,lo d# (or# do &olW @ h
^ d# do #'o/
E&&#& gr#'de1#& &%o *#l*,l#d#& !or K2L0 sen ) I D = sen ) 0-JKM
B = I d
2
K $
I d = NO0−0-MO I D sen ) K-2
J/K J/2 J/J
9 =#r**o& [*o& s *o& ) −C ]
J/
) = arcsen [ sen sen ) *o& *o& ) *o& < ]
J/
) =arcsen [
*o& ) sen< *o& )
) = 2J-M sen [ JP0Y
J/
]
2LM @ h JPN
]
J/
O'de ) ^ #1",te do &olW C ^ #1",te do *o'd,torW
^ l#tt,deW ) ^ '*l'#$%o do &ol/
O +#lor do 'g,lo d# (or# do &ol #,"e't# K gr#,& # *#d# (or# *o"e$#'do e" 1ero & K2(/ E&te *l*,lo e&t t#"<)" de&*rto '# &e$%o J/K/K// A 'te'&d#de d# r#d#$%o &ol#r dret# I D +#r# de #*ordo *o" # "#&&# de #r #tr#+e&&#d# !elo& r#o&/ Por &&o- # #ltt,de do &ol ) ) *o'&der#d# 'o *l*,lo/ A 'te'&d#de I D #,"e'to de # KJZ do '+el do "#r # ,"# #ltt,de de K000"- &e'do .,e o +#lor "#& #lto o*orre 'o +er%o e de KJ # 22Z # ,"# #ltt,de de 2000"/ O +#lor do #le&/ N# !rt*#- o ")todo ,&#do ) *o'&der#r # r#d#$%o &ol#r glo<#l/ E&te ")todo *o'&&te e" ,tl1#r # e.,#$%o &"!l5*#d# # &eg,r . ) = s )D
J/
0 O'de ) ) # r#d#$%o &ol#r glo<#l e D e D ) ) o d"etro do *o'd,tor/
:)6)8); AUECIMENTO POR EFEITO POR EFEITO JOULE A tr#'&5er@'*# tr#'&5er@'*# de *#lor !or e5eto o,le ) o #.,e*"e'to do *o'd,tor de+do # re&&t@'*# do *o'd,tor/ *o'd,tor/ E&t# tr#'&5er@'*# ) d#d# !or 2
. F F =k J J I R dc [ K T a − 20 ]
J/9
O'de I ^ *orre'te e5et+#W Rdc ^ re&&t@'*# e" *orre'te *o't',# # 20YCW ^ *oe5*e'te de te"!er#t,r# # 20YC +er .,#dro '# !g'# J9W T a
^ ) # te"!er#t,r# ")d# do *o'd,torW
k J ^ 5#tor de *orre$%o !#r# #,"e'to d# re&&t@'*# !or e5eto !el*,l#r/ !el*,l#r/ P#r# o 5#tor de *orre$%o ) &,gerdo o ,&o de ," +#lor ")do de K-0K2J/ A re&&t@'*# re&&t@'*# e" *orre'te #lter'#d# !ode &er *#l*,l#d# *o"o # &eg,r Rac = k J R dc
J/0
E&te ")todo ) ,&#do !#r# o *l*,lo do #.,e*"e'to !or e5eto o,le e" *o'd,tore& .,e ,tl1#" "#ter#& '%o 5erro&o& #!e'#&- o, &ej#- *#
K te"!er#t,r# de+do # &&o/ Por 5" # e.,#$%o J/9 ) ,&#d#/ O do*,"e'to CIGRÉ G K2Q22 re5ereQ&e # *o"!ort#"e'to t)r"*o de l'(#& #)re#& de "#'e "#'er r## ger# ger#l/ l/ De De&t &t## 5or" 5or"## de+e de+eQ& Q&ee #d#! #d#!t# t#rr # re& re&&t &t@' @'* *## el)t el)tr* r*## !#r# !#r# o *#&o *#&o de l'( l'(#& #& de tr#'&"&&%o .,e ,tl1#" *#e&- o& *#
:)6)8) R ESISTNCIA ESISTNCIA ELTRICA DO CONDUTOR A re&&t@' re&&t@'*# *# el)tr*# el)tr*# Rdc e" CC do *o'd,tor !ode &er *#l*,l#d# de #*ordo *o" # e.,#$%o K K = Rdc R s
na
∑ R" K
J/K
a
O'de # *o'd,t'*# do '*leo de #$o- &e (o,+er- ) d#d# !or
[
n d s2 P1 s = K∑ R s M s K K s
K
s
]
J/2
&e'do
K s = K d s
d s " s
J/J
^ d"etro do 5o de #$o
s ^ re&&t+d#de do #$o # 20YCW s d s
^ '"ero d# *#"#d#W ^ d"etro ")do d# *#"#d#W
" s ^ *o"!r"e'to d# *#"#d#W n s ^ '"ero de *#"#d#& de 5o& de #$o/ E o'de # *o'd,t'*# de *#d# *#"#d# de "#ter#l '%o 5erro& #l,"'o o, *o
J/
2 &e'do
K a= K
d a
2
J/
" a
d a ^ d"etro do 5oW a ^ re&&t+d#de do "#ter#l # 20YCW
d a ^ d"etro ")do d# *#"#d#W n a
^ '"ero de 5o& '# *#"#d#W
" a
^ *o"!r"e'to d# *#"#d#W
na
^ '"ero de *#"#d#&/
:)6)8)> DISTRIBUIÇÃO RADIAL DE TEMPERATURA A d&tr<,$%o r#d#l de te"!er#t,r# 'o 'teror do *o'd,tor ) "!ort#'te !o& # re&&t@'*# el)tr*# de!e'de d# te"!er#t,r# ")d# T a do *o'd,tor e t#"<)" !or.,e # 5le*(# de!e'de do te"!er#t,r# T c do '*leo do *o'd,tor/ A&&,"'do &er !e.,e'o o *#lor ger#do 'o '*leo do *o'd,tor e # ger#$%o de *#lor 'o 'teror do *o'd,tor &er ,'5or"e- !odeQ&e ,&#r # e.,#$%o &"!l5*#d#
[
]
T K D22 D − 2 T c −T s= l' 2 2 D − D22 D2 O'de T
^ g#'(o tot#l de *#lor !or ,'d#de de *o"!r"e'toW
D ^ d"etro eter'o do *o'd,torW
D 2 ^ d"etro 'ter'o do *o'd,tor*o'd,tor- o, &ej#- d"etro do '*leo de #$oW T s ^ te"!er#t,r# '# &,!er5*eW T c ^ te"!er#t,r# do '*leoW ^ *o'd,t+d#de r#d#l t)r"*# e5et+#/
J/
J O +#lor ")do d# *o'd,t+d#de r#d#l t)r"*# e5et+# ) o
T M
J/
:)8 CRITRIO TRMICO CAPACIDADE DE CONDUÇÃO DE CORRENTE EM R EGIME DE CURTO-CIRCUITO E&te *#!t,lo #e& '# o*orr@'*# de 5#l(#&/ Alg,'& #,tore& de'o""#" e&&e t!o de d"e'&o'#"e'to *o"o *rt)ro t)r"*o- !o& tr#t#Q &e d# deter"'#$%o d# &e$%o ""# do *o'd,tor !#r# .,e .,#'do (#j# ," *,rtoQ*r*,to '# l'(#'%o o*orr# o re*o1"e'to do <#rr#"e'to &o< o e5eto de ," #.,e*"e'to e*e&&+o K/ M#& *o'+)" e&*l#re*er .,e e&te *rt)ro !ode &er e'te'ddo t#"<)" *o"o el)tr*o- d5e'*#'doQ&e do &,<*#!t,lo #'teror #!e'#& !elo 5#to de .,e e&te ) o d"e'&o'#"e'to e" &t,#$%o de '%o e&t#<ld#de e #.,ele e" &t,#$%o de e&t#<ld#de 2 J / F#l#Q&e e" *rt)ro t)r"*o # 5" de d5ere'*#r do *rt)ro "e*'*o .,e e'+ol+e o *l*,lo d# re&&t@'*# "e*'*# #o *,rtoQ*r*,to !r'*!#l"e'te e" *#e& *l"t*#&/ No e't#'do- !#r# o& *l*,lo& #., !re&e'te&- #d"teQ&e .,e o& !#r"etro& *l"t*o& !er"#'e*e" *o'&t#'te& e .,#l.,er ",d#'$# '# *orre'te el)tr*# ) l"t#d# # ," !,l&o .,e +# de ,"# *orre'te '*#l I ! #t) ,"# *orre'te 5'#l I f / A 5g J/ l,&tr# o .,e #*o'te*e *o" ," *o'd,tor .,#'do o*orre ," !,l&o de *orre'te/ A 5g,r# re!re&e't# ,"# &t,#$%o e" .,e o !#&&o de *orre'te ) "#'tdo !elo te"!o &,5*e'te !#r# o &&te"# #t'gr ," 'o+o e&t#do de e.,l
&o
F&%) :) Pass, +" ,rr"$(" $%nte& I*** )td LMN 3O5 3O5
Seg,'do o IEEE 2- # *,r+# de te"!er#t,r# *orre&!o'de'te #o degr#, de *orre'te !ode &er e'*o'tr#d# re+ol+e'doQ&e # e.,#$%o J/K !#r# *#d# 'ter+#do de te"!o/ M#& !#r# &&o o ,&o de ," !rogr#"# *o"!,t#*o'#l &er# #*o'&el(+el- &e'do .,#'to "e'or o 'ter+#lo to"#do- "el(or # !re*&%o 'o& re&,lt#do&/ O ")todo de&*re+e #'d# ,"# &ol,$%o "#',#l ,&#'do ,"# l'e#r1#$%o d# e.,#$%o de re&5r#"e'to !or r#d#$%o e./ J/K/ A e.,#$%o e.,#$%o 5'#l ) d#d# !or −t /
T c t =T ! T f −T ! K −e
J/
Se'do .,e # *o'&t#'te de te"!o ) d#d# !or =
T f −T ! mC p
R T c × I f 2 − I !2
J/9
O'de #& +#r+e& ,tl1#d#& j e&t%o de&*rt#& '# &e$%o J/K e # re&&t@'*# el)tr*# do *o'd,tor ) ,tl1#d# !#r# # te"!er#t,r# ")d# T !−T f / 2 / O CIGRÉ t#"<)" #!re&e't# ," ")todo !#r# # deter"'#$%o d# *,r+#/ O det#l(#"e'to
de&te #&&,'to e&t #l)" do o
F&%) :)> D&a%ra*a "s."*H(&, +, .r(,-&r.&(, $%nte& )C@*ID*R *-*CTRIC. *-*CTRIC. Ca"c/"at!%n %f s?%rt0c!rc s?%rt0c!rc/!t /!t c/rrents 34E5 34E5
É 'tere&&#'te #o e&t,do d#& *orre'te& de *,rtoQ*r*,to- de*o"!or e&&e d#gr#"# e" &,#& *o"!o'e'te& #lter'#d# !er?d*# e *o't',# #!er?d*# #"orte*d#- *o"o "o&tr# # 5g,r# J//
F&%) :)? D",*2,s&07, +a ,rr"$(" +" .r(,-&r.&(, $%nte& *T0MPPE$ *T0MPPE$ 3445 3445
A e&*ol(# do +#lor do te"!o de *,rtoQ*r*,to ) ," 5#tor rele+#'te !#r# o& *l*,lo& d# &e$%o do <#rr#"e'to/ Se'do #&&"- ," do& d#do& do !roe& d# &,e& e&&#& .,e r%o et'g,r o *,rtoQ*r*,to- o!t#'doQ&e !or #&&,"r o te"!o de 5#l(# *o"o &e'do g,#l #o te"!o de #t,#$%o d#& !rote$>e&/ E" '&t#l#$>e& "#ore& e de "#or "!ort'*# !odeQ&e ter- *o" !re*&%o- o te"!o tot#l de te"!or1#$%o do& rel)& e de 'terr,!$%o do& d&j,'tore& e&te'te&/ e" &,e& de ")d# te'&%o- o te"!o de 5#l(# 'or"#l"e'te +#r# de # K2 **lo&- &to )- de 0-KJ # 0-20 &eg,'do& e" 0H1/ [,#'do '%o ) 5#*l # deter"'#$%o de&&e +#lor- !or 5#lt# de '5or"#$>e& t)*'*#& do& 0-N s K2. e.,!#"e'to&- *o&t,"#Q&e e&t"#r o +#lor de t =0-N s K2.
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I t 2 = t k
J/0
O'de 2 ^ &e$%o "'"# do *o'd,torW I t ^ *orre'te t)r"*#W k ^ 5#tor rel#t+o & !ro!red#de& t)r"*#& do *o'd,torW t ^ te"!o de *,rtoQ*r*,to/
A *(#"#d# *orre'te t)r"*# I t ) o +#lor ")do e5*#1 d# *orre'te de *,rtoQ*r*,to e" *,rto te"!o/ E&&# *orre'te t#"<)" !ode &er 'ter!ret#d# *o"o o +#lor *o'&t#'te d# *orre'te .,e- 'o !erodo .,e +# do #!#re*"e'to do *,rtoQ*r*,to #t) # &,# 'terr,!$%o- !rod,1r# o "e&"o .,#'td#de de *#lor 'o *o'd,tor .,e # *orre'te re#l de *,rtoQ*r*,to/ E&&# *orre'te !ode &er e!re&&# !or KJ I t = I k mn
J/K
Se'do I k ^ +#lor RMS d# *o"!o'e'te &")tr*# d# *orre'te de *,rtoQ*r*,to/ m e n &%o 5#tore& #d"e'&o'#& .,e .,#'t5*#" o e5eto t)r"*o d# *orre'te de *,rtoQ *r*,to/ O 5#tor m tr#d,1 o e5eto d# *o"!o'e'te *o't',# d# *orre'te de *,rtoQ*r*,to e do &e, #"orte*"e'to/ O 5#tor n re!re&e't# o e5eto d# *o"!o'e'te #lter'#d# d# *orre'te de *,rtoQ*r*,to e &e, #"orte*"e'to/ O& +#lore& &%o retr#do& d# 5g,r# # &eg,r/
F&%) :) Fa(,r"s m " n $%nte& I*C QENQP 34M5
P#r# # o
.,e ) *(#"#do o 5#tor de #"!lt,de/
E&&e 5#tor re!re&e't# o de*r)&*"o d# *o"!o'e'te *o't',# d# *orre'te de *,rtoQ*r*,to/ N# 5g,r#T k ) o te"!o de *,rtoQ*r*,to/ O 5#tor !ode &er e!re&&o !or =e −twR / A sen 0 sen wt −0
O'de 0 =
2
J/2
e wt = - e't%o !ode t#"<)" &er *#l*,l#do e" 5,'$%o d# rel#$%o
9 e'tre # re&&t@'*# e # re#t'*# d# l'(# R / A . A 5g,r# J/9 "o&tr# e&&# rel#$%o/
F&%) :)@ Fa(,r +" ass&*"(r&a $%nte& I*C QENQP 34M5
Co"o ger#l"e'te '%o &e *o'(e*e R / A - to"#Q&e =K- *o"o !or (!?te&e e 'e&te *#&o R / A =0-0OK / P#r# o +#lor de n ) 'e*e&&ro o *o'(e*"e'to de I 88 cc / I p .,e ) t#"<)" ," !#r"etro d# rede #'logo # "#& .,e !or &,# +e1- .,#'t5*# o de*r)&*"o d# *orre'te #lter'#d# de *,rtoQ *r*,to/ O !#r"etro I 8cc8 ) o +#lor '*#l e" #"!lt,de d# *o"!o'e'te &")tr*# d# *orre'te de *,rtoQ*r*,to/ É o +#lor .,e &e deter"'# do *l*,lo de *,rtoQ*r*,to #tr#+)& d# *orre'te 'o"'#l de o!er#$%o e # "!ed'*# 'o tr#jeto/ O !#r"etro I p ) o +#lor e5*#1 d# *orre'te !er"#'e'te de *,rtoQ*r*,to/ Co'&der#Q&e- !#r# o +#lor de n- .,e # *o'&t#'te de te"!o do *r*,to &e tor'# ",to gr#'de e e't%o I 88 cc= I p - !ort#'to- # r#1%o I 88 cc / I p =K e n =K / Seg,'do # 'or"# 'ter'#*o'#l IEC 0QK KJ- o& +#lore& ""o& re*o"e'd#do& !#r# # te"!er#t,r# do *o'd,tor d,r#'te ," *,rtoQ*r*,to !#r# *#
0 T!o de <#rr#"e'to Per5& ',& o, !'t#do& '%o &,jeto& # tr#$%o !r)+# 8#rr#& de &,e& *o'tt,d#& !or *#
M#ter#l Co
Te"!er#t,r# ""# 200 YC K0 YC
Co
K0 YC KJ0 YC
O 5#tor k e&t rel#*o'#do & !ro!red#de& do *o'd,tor e te"!er#t,r#& 5'#l e '*#l e !ode &er e!re&&o !or
k = M/KMM
c ⋅l' [ K T cc−T ! ]
J/J
O'de c ^ *#lor e&!e*5*o do "#ter#l do *o'd,torW ^ !e&o e&!e*5*o do "#ter#l do *o'd,torW ^ *oe5*e'te t)r"*o de re&&t@'*# do "#ter#l # 0YCW ^ re&&t+d#de do "#ter#l do *o'd,torW
T ! ^ te"!er#t,r# do *o'd,tor #'te& do *,rtoQ*r*,toW T cc
^ te"!er#t,r# ""# #d"td# !#r# o *o'd,tor/
Se'do #&&"- o *oe5*e'te k !ode &er t#
T !
0 0 0 0 90 K0
V#lore& de k 8#rr#& de *o
8#rr#& de #l,"'o
T cc = 200 C
T cc =KO0 C
T cc =KL0 C
T cc =KJ0 C
K-09 KJ- K2-J K2-2K KK- K0-J
K2- K2-20 KK-K K0-2 K0-K2 9-02
-J -20 - -J -9K Q
-02 -K -9 -K -0 Q
K P#r# o& +#lore& do .,#dro 5or#" ,tl1#do&
=K-OO0K×K0−P ⋅cm !#r# o *o
=J-0OLL × K0−P ⋅cm !#r# o #l,"'o/ A"<#& #& re&&t+d#de # 20 YC/
Alg,'& #,tore& ,tl1#" #d#!t#$>e& de&t#& e.,#$>e&/ Seg,'do # re5er@'*# ,"# red,$%o '# e.,#$%o !ode &er ,&#d#- 5#1e'doQ&e ,&o de +#lore& !#dr>e& de " e '/ De&&# 5or"# !odeQ&e ,tl1#r dret#"e'te o +#lor d# *orre'te de *,rtoQ*r*,to 'o *l*,lo/ Ne&te *#&o- # re# "'"# do& *o'd,tore& 5le+e& #)reo& !#r# .,e #& *orre'te& de *,rtoQ *r*,to !re+&t#& '%o !ro+o.,e" ,"# ele+#$%o de te"!er#t,r# &,!eror # #d"td# !ode &er e!re&&# !el# e.,#$%o J//
2 =
K000 I cc
PP-KKJ
K T cc c log t K T !
J/
O'de 2 ^ re# "'"# do& *o'd,tore& e" 5,'$%o do *,rtoQ*r*,to e" !olW I cc
^ *orre'te de *,rtoQ*r*,to e" A/
A re5er@'*# K- #!re&e't# # "e&"# e.,#$%o de ,"# "#'er# "#& !rt*#- j '*or!or#'do #& *o'&t#'te& do& "#ter#& '# 5?r",l# e t#"<)" o& 5#tore& m e n/ A *orre'te de *,rtoQ*r*,to e" 4A ""# !er"td# !#r# ,"# d#d# &e$%o de *o'd,tor d,r#'te ," *erto te"!o &er
K 2 K T I cc= K log 2 cc K 2 T ! t
J/
O'de K K
^ 0-J !#r# *o'd,tore& de *o
K 2
^ 2J-2 !#r# *o'd,tore& de *o
A lg# B0DPE)S da 2-C2@ te" t#"<)" ,"# e.,#$%o &e"el(#'te !#r# e&te *l*,lo M
I cc=
2-KL×K0 2
t
log
T cc 2NL T ! 2NL
J/
2
:): CRITRIO MECNICO DIMENSIONAMENTO UANTO A ESFORÇOS E IBRAÇÕES O d"e'&o'#"e'to do& <#rr#"e'to& &o< o *rt)ro "e*'*o ) &,e& e #o& o!er#dore& .,e !or +e't,r# e&t+ere" !r?"o& #o& e.,!#"e'to&/ [,#'to #o d"e'&o'#"e'to "e*'*o e&tt*o- e'te'deQ&e !el#& 5or$#& re&,lt#'te& d#& de5or"#$>e& de+d#& #o !e&o do <#rr#"e'to/ Ne&te &e$%o- *l*,lo& de "o"e'to 5letor !#ro *#&o do& <#rr#"e'to& rgdo& e de tr#$%o e 5le*(# 'o& *#e& !r'*!#& !#r# +e& !r?!r#& e 5or$#d#& 'o& *o'd,tore& e <#rr#&/
:):)6 DIMENSIONAMENTO MECNICO AO CURTO-CIRCUITO P#r# o e&t,do d#& 5or$#& &,rgd#& e" !re&e'$# de ," *,rtoQ*r*,to ) 'e*e&&ro o *o'(e*"e'to d# *orre'te ""# .,e o *o'd,tor ter .,e &,!ort#r e" *#&o de 5#l(#/ O, &ej#- e&te ) o +#lor ""o '&t#'t'eo d# *orre'te de *,rtoQ*r*,to e o*orre '# &,# 5#&e '*#l/ O *l*,lo de&&e +#lor !ode &er 5eto #tr#+)& d# e!re&&%o I max= 2 I 8cc8
J/
O'de I max ^ *orre'te ""# o, *orre'te de *(o.,eW ^ 5#tor #d"e'&o'#l .,e re!re&e't# o de*r)&*"o d# *orre'te *o't',# d# *orre'te de
*,rtoQ*r*,toW I 88 cc ^ *orre'te de *,rto '*#l
J A& +#r+e& e I 8cc8 j 5or#" d&*,tdo& '# &e$%o J/2/ P#rt'doQ&e do e.,#*o'#"e'to d# '5l,@'*# do *#"!o "#g')t*o .,e ," *o'd,tor !er*orrdo !or *orre'te !ro+o*#d# e" o,tro *o'd,tor- #!l*#'do # d# le de 8ot e S#+#rt .,e d o +#lor d# de'&d#de d5ere'*#l de *#"!o "#g')t*o e" ," ele"e'to de *orre'te *(eg#Q&e # e.,#$%o d# 5or$# ele"e't#r d $ K2 e'tre do& *o'd,tore&/ = d $
0 I K I 2 × [ dx K dx 2r ] r J
J/
A!l*#'doQ&e *l*,lo +etor#l e 'tegr#'doQ&e # e!re&&%o #o lo'go do *o"!r"e'to " do <#rr#"e'to *(eg#Q&e # e!re&&%o ger#l !#r# # 5or$# ger#d# e" do& *o'd,tore& !#r#lelo& !er*orrdo& !or *orre'te K2KJK 2 0 a 2− a " $ e = × I K I 2× 2 a
J/9
O'de $ e ^ 5or$# eletro"#g')t*#W I K e I 2 ^ *orre'te& 'o& *o'd,tore&W " ^ *o"!r"e'to do& *o'd,tore& a ^ e&!#$#"e'to e'tre o& *o'd,tore&
A !#rtr de&&# e!re&&%o 'ot#Q&e .,e ●
# 5or$# e&t 'o !l#'o do& *o'd,tore&W
●
.,#'do #& *orre'te& &%o de "e&"o &e'tdo- # 5or$# ) de #tr#$%o
●
.,#'do #& *orre'te& &%o de &e'tdo& o!o&to&- # 5or$# ) de re!,l&%o
Co'&der#'do o *#&o o'de #& 5or$#& &%o 'o "e&"o &e'tdo e de #"!lt,de ""#&,<&tt,'do
% !or
−O
M × K0
−2
@ ⋅ 2
e # d&t'*# e'tre o& *o'd,tore& ",to !e.,e'# e"
rel#$%o #o *o"!r"e'to d# l'(# " ! a *(eg#Q&e # e.,#$%o $ e =2 ×K0− I 2cc
" a
J/0
PodeQ&e #'d# 5#1erQ&e *o'dder#$>e& .,#'to #o t!o de *,rtoQ*r*,to- de&e'+ol+e'doQ&e e.,#$>e& "#& !re*&#& !#r# o& *,rto e'tre d,#& 5#&e& 5#&e&- e'tre #& tr@& 5#&e&- e'tre # 5#&e e 'e,tro'&t#l#$>e& "o'o5&*#&- tr5&*#&- *orre'te *o't',# e #&&" !or d#'te/ PodeQ&e ded,1r K2K*o" <#&e e" d+er&#& re5er@'*#&- #& e.,#$>e& der+#d#& de J/9 !#r# *#d# *#&o *(eg#'do #& e!re&&>e& # &eg,r/ P#r# &&te"#& "o'o5&*o&- ,tl1#'do #& "e&"#& *o'&der#$>e& .,#'to #o 5#tor de #&&"etr# g,#l # K-- *(eg#Q&e # " 2a 2 −a $ e K "=−K2-9×K0 I a −
2 cc
J/K
P#r# &&te"#& tr5&*o&- o *o'd,tor do "eo ) o "#& egdo/ A e!re&&%o 5*# 2 a 2− a " $ e J "=−KK-22×K0 I a −
2 cc
J/2
P#r# '&t#l#$>e& de *orre'te *o't',#- o +#lor d# *orre'te '%o #d"te d5ere'$# e'tre #"!lt,de e e5*#1 e # !#rtr d# e.,#$%o J/9 *(eg#Q&e # " 2 a 2− a $ e cc= ×K0 I a −
2 cc
J/J
De !o&&e do +#lor d# 5or$# eer*d# !el# *orre'te de *,rtoQ*r*,to 'o <#rr#"e'to- !odeQ&e e&t#
$ e⋅" L
J/
P#r# +g# e'g#&t#d# G =
$ e⋅" KP
J/
A *o'd$%o de d"e'&o'#"e'to ) 5et# de "#'er# # .,e # &ol*t#$%o de 5le%o org'#d# d#& 5or$#& de&e'+ol+d#& !elo *,rtoQ*r*,to- '%o ,ltr#!#&&e" # ""# de5or"#$%o !er"td#/ E&&# *o'd$%o &e e&t#
d#d# !or G S
J/
O'de S ^ "?d,lo de re&&t@'*#W ^ l"te de e&*o#"e'toW
O l"te de e&*o"e'to *o'&&te '# te'&%o e" .,e o "#ter#l *o"e$# # de5or"#rQ&e !l#&t*#"e'te e .,e !#r# o #l,"'o ) de 0-2Z do *o"!r"e'to org'#l "eddo &eg,'do # A8AL/ M#& d+er&#& 'or"#& #dot#" o +#lor de 0-Z do *o"!r"e'to/ E&te& +#lore& &%o 5or'e*do& 'o& *#tlogo& de 5#e& *o"o # ALCAN- A8AL- ASTM- et*/ O .,#dro # &eg,r #!re&e't# e&&e& +#lore& V#lore& de 0-Z
T!o de <#rr#"e'to 8#rr#& *(#t#& T,
Al,"'o
Co
K2-N× K0
J
2K ×K0
K2-N× K0
J
22-N ×K0
J J
O "?d,lo de re&&t@'*# ) de5'do # !#rtr d# geo"etr# do <#rr#"e'to- *o'5or"e 5g,r#
T!o de <#rr#"e'to
Verg#l(%o
T,
Per5l U
Geo"etr#
M?d,lo de Re&&t@'*#
S =
S =
DJ J2
D − d
J2D
? 2 a 2 #< 2 S = K2 2#
Mo"e'to de I')r*#
F =
F =
D
D− d
BeJ2 ?J aeKJ F = J Se'do a 2d 2 e 2= 2 a d e K= − e 2
8#rr# *(#t#
a 2 S = P
aJ F = K2
F&%) :)6 M+.l, +" R"s&s($&a " M,*"$(, +" I$'r&a $%nte& G)C. Res!stnc!a d%s Gater!a!s VME. 34N5
Se # *o'd$%o J/ '%o 5or &#t&5et#- ) 'e*e&&ro e&*ol(er o,tro <#rr#"e'to e re5#1er o& *l*,lo&/
:):)8 DIMENSIONAMENTO ESTÁTICO DOS BARRAMENTOS Ne&te t!o de d"e'&o'#"e'to e'*o'tr#"Q&e t#"<)" o& *l*,lo& !#r# o& e&5or$o& re#l1#do& !el#& <#rr#& de+do& #o &e, !r?!ro !e&o/ No *#&o de <#rr#"e'to& rgdo&- de+do ,tl1#$%o de +%o& rel#t+#"e'te *,rto&- # 5le%o re5ere'te #o !r?!ro !e&o '%o !re*&#- '# "#or# d#& +e1e& &er +er5*#do/ P#r# <#rr#"e'to& 5le+e&- o !roe& "e*'*#& e 5le*(#& !#r# deter"'#d#& *o'd$>e& e !ort#'to '%o ) e&!e*5*#"e'te ," d"e'&o'#"e'to de <#rr#"e'to/ E&te *l*,lo ) '*l,do *o"o ," *o"!le"e'to #o *#!t,lo #'teror- ,"# +e1 .,e ,tl1#Q&e do& +#lore& de *,rtoQ *r*,to l deter"'#do& e ) !#rte "!ort#'te !#r# # "o't#ge" d# l'(# #)re# '# &,
J/
2 ^ re# d# &e$%o tr#'&+er&#l do *o'd,torW
adm ^ l"te de re&&t@'*# "e*'*# # tr#$%o/
O l"te de re&&t@'*# tr#$%o !ode &er e'*o'tr#do 'o& *#tlogo& de *o'd,tore& e t#"<)" e&t !#dro'1#do !el# ASTM/ A *,r+# !l#'# ger#d# !or ," *o'd,tor &,&!e'&o &o< o e5eto d# gr#+d#de ) # 5,'$%o "#te"t*# *(#"#d# *#te'r#/ E'tret#'do- (&tor*#"e'te- !or &"!l*d#de- *o'&der#Q&e # !#r
F&%) :)66 Ca("$Hr&a $%nte& CU"c/"% mecn!c% para ca%s – n%tas a/"a d!sc!p"!na *@ EWWLE 3OE5
O !rojeto de ,"# &,
J/
Ne&t# e.,#$%o- o !#r"etro C ) *o'(e*do *o"o 6!#r"etro d# *#te'r#7 e +#le C =
T 0 p
J/9
O'de T 0 ) # tr#$%o (or1o't#l e p ) o !e&o do *#e& '*#& !#r# .,e 'o "o"e'to do *,rtoQ*r*,to *o'd$>e& 5'#& # te'&%o ""# '%o &ej# ,ltr#!#&&#d#- *o" te"!er#t,r# e *#rg# 5'#l/ O de&e'+ol+"e'to d#& e.,#$>e& d# *#te'r#- le+#'do e" *o'&der#$%o o e5eto d# +#r#$%o d# te"!er#t,r# 'o *o"!r"e'to do& *o'd,tore&- le+# # *o'(e*d# eq/aYZ% da m/danYa de estad%
9 .,e ) d#d# !or K22022
[
]
*2 p f 2 " 2 *2 p0 " 2 *2 # f −# 0−T f = T T 2 2 2T 0 J 0
2 0
J/90
O'de " ^ *o"!r"e'to do +%oW * ^ "?d,lo de el#&t*d#de do *o'd,torW 2 ^ re# d# &e$%o tr#'&+er&#l do *o'd,torW
^ *oe5*e'te de dl#t#$%o l'e#r do "et#l do *o'd,torW
O& !#r"etro& '*#& &%o T 0 ^ te'&%o '*#l 'o *#
p 0 ^ *#rg# '*#l 'o *o'd,tor !or ,'d#de de *o"!r"e'toW O& !#r"etro& 5'#& &%o # f ^ te"!er#t,r# 5'#l ""# #d"td#W p f = p0 q
.,e ) # *#rg# 5'#l &,<"etd# #o *o'd,torW
q ^ 5or$# de *,rtoQ*r*,to q d&tr<,d# #o lo'go do *o"!r"e'to.
O'de q =
$ e "
e o +#lor de $ e !ode &er e'*o'tr#do #tr#+)& d#& e.,#$>e& J/K- J/2 e J/J/
P#r# e'*o'tr#r o +#lor de
T 0 '# e.,#$%o J/90- re*o"e'd#Q&e o ,&o de 5err#"e't#&
*o"!,t#*o'#&- e+t#'do #&&"- o ,&o de ")todo& ',")r*o&- o .,e &er# ",to d&!e'do&o/ De !o&&e do +#lor d# tr#$%o- !odeQ&e e'*o'tr#r o !#r"etro C d# *#te'r# '# e.,#$%o J/9 e e't%o # 5le*(# 1 'o +%o/ A 5le*(# ) ,"# '5or"#$%o etr#"#"e'te "!ort#'te- ,"# +e1 .,e '%o de+e ,ltr#!#&&#r o l"te de &eg,r#'$# #d"tdo !#r# # '&t#l#$%o/ A 5le*(# ) # d&t'*# 1 '# 5g,r# J/KK*o"!ree'de'do o "#or *o"!r"e'to '# +ert*#l e'tre o *#
0
[ ]
?8 − K K 1 =C *o&( 2C
8 2C&'(
?8 2C
2
J/9K
O'de ?8 ) # !roje$%o (or1o't#l do +%o e 8 ) # !roje$%o +ert*#l do +%o/ [,#'do '%o ( de&'+el e'tre o& !o'to& de #!oo- 8 &er 1ero e ?8 &er # d&t'*# e'tre o& !o'to&/ A e.,#$%o J/ tor'#Q&e
[ ]
1 =C *o&(
? 8 −K 2C
J/92
:):):) DIMENSIONAMENTO ESTÁTICO DOS BARRAMENTOS E&te *rt)ro de d"e'&o'#"e'to- 5,'d#"e't#Q&e e" +er5*#r &e o <#rr#"e'to e&*ol(do '%o #!re&e't# ,"# 5re.,@'*# !r?!r# de re&&o''*# !r?"# 5re.,@'*# d# rede 0 H1 'o 8r#&l/ U" *o'd,tor- .,#'do #!o#do e" do& !o'to& rel#t+#"e'te #5#&t#do&- e&t &e"!re &,jeto # o&*l#$>e& e +e& *#,&#d#& !or +ro& 5#tore&/ E&&e& 5#tore& !ode" &er de orge" eletrod'"*# e t#"<)" de+do #o +e'to/ E'.,#'to e" reg"e !er"#'e'te- o& e&5or$o& eletrod'"*o& .,e #t,#" &oe& !oder%o *re&*er #*"# do& l"te& de e&t#<ld#de do &&te"#/ Co'+)" !ort#'to g#r#'tr .,e t#l '%o #*o'te*e/ A 5re.,@'*# !r?!r# de ," <#rr#"e'to rgdo ) d#d# !el# e.,#$%o ger#l K2 f p =
$2K 2
2 "
*F m
O'de " ^ *o"!r"e'to do <#rr#"e'toW * ^ "?d,lo de el#&t*d#deW F ^ "o"e'to de ')r*#W
J/9J
K m
^ "#&&# d# <#rr# BgX*"W
$K ^ *o'&t#'te
O "o"e'to de ')r*# F !ode &er *#l*,l#do de #*ordo *o" #& e.,#$>e& !re&e'te& '# 5g,r# J/K0/ O +#lor d# *o'&t#'te $K !ode &er retr#do do .,#dro # &eg,r K2 T!o de <#rr#
V#lor de $K $K= -J0
$K=
$K=J-92O
C,r+#& <#&e#d#& '# e.,#$%o J/9J &%o "o&tr#d#& '# 5g,r# J/K2 &er+'do *o"o ," g,# !#r# e+t#r *o"!r"e'to& *rt*o& de <#rr#&/
2
F&%) :)68 C,*2r&*"$(,s Cr<(&,s s"%.$+, a r".$&a 2r2r&a $%nte& B/s C%nd/ct%r )?apes and 2pp"!cat!%ns
E" &e tr#t#'do de <#rr#"e'to& 5le+e&- # 5re.,@'*# !r?!r# ) d#d# !or K2 f p =
K T 2 " m
J/9
O'de " ^ *o"!r"e'to do +%oW T
^ tr#$%o 'o *#
m
^ "#&&# do *#
O +#lor re&,lt#'te do *l*,lo de
f p
de+e e&t#r &,5*e'te"e'te #5#&t#do do +#lor d#
5re.,@'*# el)tr*# d# rede e de &e,& "lt!lo&/ Utl1#Q&e K0Z de #5#&t#"e'to do +#lor d# 5re.,@'*# d# rede e 20Z de #5#&t#"e'to !#r# o do
J Se'do #&&"- o& +#lore& # &e e+t#r &%o [ f − 0-K f , f 0-K f ]%[ 25 −0-2 f ⋅2 f , 2 f 0- f ]
J/9
O'de f ) # 5re.,@'*# el)tr*# d# rede/ P#r# # rede el)tr*#
H1 e e'tre K00 e K0 H1/
:); DIMENSIONAMENTO SOB EFEITO CORONA O e5eto *oro'# ) ," 5e'"e'o .,e #!#re*e '# &,!er5*e do& *o'd,tore& de ,"# l'(# #)re# de #lt# te'&%o .,#'do o +#lor do gr#de'te de !ote'*#l e&te'te 'e&&e *o'd,tor e*ede o +#lor do gr#de'te *rt*o d&r,!t+o do #r- ger#'do de&*#rg#& el)tr*#& 'o& g#&e& !re&e'te& #o redor do <#rr#"e'to/ E" ger#l- #t'ge l'(#& *o" te'&%o #*"# de KK0BV 2/ Nor"#l"e'te '%o ) ," 5#tor *o'&der#do e" <#rr#"e'to& rgdo& #<#o de&t# te'&%o/ De&*#rg#& el)tr*#& e" g#&e& &%o ger#l"e'te '*#d#& !or ," *#"!o el)tr*o .,e #*eler# el)tro'& l+re& 'ele e&te'te&/ [,#'do e&&e& el)tro'& #d.,re" e'erg# &,5*e'te do *#"!o el)tr*o !ode" !rod,1r 'o+o& el)tro'& !or *(o.,e *o" o,tro& to"o&/ É o *(#"#do !ro*e&&o de o'1#$%o !or "!#*to/ D,r#'te # &,# #*eler#$%o 'o *#"!o el)tr*o- *#d# el)tro' l+re *olde *o" to"o& de og@'o- 'trog@'o e o,tro& g#&e& !re&e'te&- !erde'do- 'e&&# *ol&%o- !#rte de &,# e'erg# *')t*#/ O*#&o'#l"e'te ," el)tro' !ode #t'gr ," to"o *o" 5or$# &,5*e'te- de 5or"# # e*tQlo/ Ne&&#& *o'd$>e&- o to"o #t'gdo !#&&# # ," e&t#do de e'erg# "#& ele+#do/ O e&t#do or<t#l de ," o, "#& el)tro'& ",d# e o el)tro' .,e *old, *o" o to"o !erde !#rte de &,# e'erg#- !#r# *r#r e&&e e&t#do/ Po&teror"e'te- o to"o #t'gdo !ode re+erter #o &e, e&t#do '*#l- le& eletro"#g')t*#&/ O e5eto *oro'# ) *#r#*ter1#do !r"er#"e'te !or e5eto& +&,#&- .,#'do #& !e.,e'#& de&*#rg#& 5or"#" ,"# e&!)*e de *oro# #o redor do *o'd,tor/ De!o& !roe& "e*'*#& e re#$>e& .,"*#&/ E&&#& re#$>e& o*orre" 'o
#r !rod,1'do o1'o e ?do de 'trog@'o/ O& !roe& lo*#l1#d#& e" reg>e& ,r<#'#& 5orte"e'te !o+o#d#&- o'de o& e5eto& +&,#& !ode" *#,&#r "edo #o& "or#dore&/ Al)" d&&o- o tr#'&tor'o *#,&#do !el# r#do 'ter5er@'*#& !ode" &er '#*et+el !#r# # !o!,l#$%o/ U"# &)re de *o'd$>e& *o'trol#" # te'&%o d&r,!t+#- t#& *o"o # !re&&%o do #r- # !re&e'$# do +#!or dig,#- o t!o de te'&%o #!l*#d# e # 5otoo'1#$#o '*de'te/ A d+erg@'*# do *#"!o eer*e '5l,@'*# #d*o'#l- e .,#l.,er &#l@'*# tr#'&5or"#Q&e e" 5o'te !,'t,#l de de&*#rg#&/ E" &,e&- e5eto& de&#gr#d+e& !ode" &er org'#do& 'o& *#'to& ++o& d#& <#rr#&- *o'e*tore&ro&*#& de !#r#5,&o&- et*/ A te'&%o *rt*# d&r,!t+# !ode &er e!re&&# !or K222 a V 0 =2K-K m 0 r l' r
J/9
O'de V 0
^ te'&%o d&r,!t+# do #r e" BVW
^ 5#tor de de'&d#de do #rW m0
^ 5#tor de rreg,l#rd#de e'tre 0 e KW
r ^ r#o do *o'd,tor e" *"W a ^ e&!#$#"e'to e'tre do& *o'd,tore& e" *"W O +#lor do 5#tor de de'&d#de do #r !ode &er *#l*,l#do d# &eg,'te 5or"# =
J-92KK p 2OJ T
J/9
O'de T ) # te"!er#t,r# e" YC e p ) # !re&&%o #t"o&5)r*# e" *e't"etro& de "er*ro/ O 5#tor de rreg,l#rd#de do #r de!e'der do *o'd,tor e d#& *o'd$>e& *l"t*#&- *o'5or"e .,#dro 2
Fa(,r +" &rr"%.lar&+a+" m 0 =K
C,$+&07, L&o 'o+o- *l'dr*o
0/9J m 00-9L
E'+el(e*do- *l'dr*o
0/ m00-90
E'+el(e*do- *#
0/0 m0 0-
E'+el(e*do- *#
O<+#"e'te- !#r# o !rojeto *o'+)" ,tl1#r o !or *#&o- m0 =0-L / Co" <#&e '# e.,#$%o J/9- o d"e'&o'#"e'to do *o'd,tor de+e &er +er5*#do !#r# .,e # te'&%o 'o"'#l do <#rr#"e'to '%o ,ltr#!#&&e # te'&%o de d&r,!t,r#- o, &ej# e
( n 2K-K m0 r
a r
J/9
Pode &e #'d# *o'&der#r- #lter'#t+#"e'te e.,#$%o J/9- # te'&%o *rt*# +&,#l de *oro'#d#d# !or 22
[
V =2K-K m0 r K
]
0-J a l' r r
J/99
; METODOLOGIA DE DIMENSIONAMENTO
;)6 R OTEIRO DE DIMENSIONAMENTO Ao lo'go de&te !rojeto- de&*re+e"Q&e et#!#& de d"e'&o'#"e'to de <#rr#"e'to& *o'd,tore& e" &,e& "#& &e" e5et,#r ," rotero !ro!r#"e'te dto/ PodeQ&e orde'#r o& !#&&o& !#r# ," e& *l"t*#& do lo*#l/ O d"e'&o'#"e'to t)r"*o t#"<)" !ode &er *o'&der#do *o"o ," do& deter"'#'te& d# *#!#*d#de de *o'd,$%o de *orre'te/ Ne&te *#&o- e5et,#Q&e o& *l*,lo& d# &e$%o do *o'd,tor&,!o'do ,"# te"!er#t,r# ""# #d"td# e ,"# *orre'te ""# de &o
"e*'*o& e&t%o !re&e'te& '# &e$%o J/J/ Ne&te *#&o *o'&der#Q&e o e&5or$o tot#l # .,e o <#rr#"e'to e&t &,<"etdo- o, &ej#- o e&5or$o do !r?!ro !e&o #*re&*do do e&5or$o *#,&#do !or ,"# !o&&+el *orre'te de *,rtoQ*r*,to/ Por 5" '# e&*#l# de !rord#de&- e&t o d"e'&o'#"e'to *o" rel#$%o & +e&/ Ne&te *rt)ro- de+eQ&e te't#r e+t#r .,e # 5re.,@'*# !r?!r# do <#rr#"e'to e&tej# e" re&&o''*# *o" # 5re.,@'*# d# rede- !o& #o o*orrer ," *,rtoQ*r*,to- &er%o ger#d#& 5or$#& eletro"#g')t*#& !,l&#'te& 'o& *o'd,tore& e &to ro"!er# o& "e&"o&/ Ne&te *rt)ro- !odeQ&e t#"<)" e5et,#r *l*,lo& # 5" de e+t#r t#"<)" # #$%o do +e'to "#& &to ) ," *erto e#gero 'o d"e'&o'#"e'to de <#rr#"e'to& e" &,e&- +&to .,e !#r# ," *o'd,tor *(eg#r # e'tr#r e" re&&o''*# de+do #o +e'to ) 'e*e&&r# ,"# *o"<'#$%o de e5eto&/ Al)" d&&o- o& *o'd,tore& de &,
r%cess% Dad%s de entrada
Es,l!a +, T&2,
Es,l!a +a F,r*a
+" Barra*"$(,
" +, *a("r&al
- C,rr"$(" $,*&$al
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;); PERFIL NORMALMENTE ESCOLIDO PARA BARRAMENTOS R GIDOS O& <#rr#"e'to& t,<,l#re& &%o .,#&e .,e &e"!re # "el(or e&*ol(# e'tre o& <#rr#"e'to& rgdo& de &,e&/ I&to &e de+e !or.,e !#r# ,"# "e&"# &e$%o de "et#l *o'd,tor *oe&- # *orre'te !#&&# !el# !er5er# do& *o'd,tore& de+do #o e5eto !el*,l#r- &to )- o 'teror d# &e$%o 5*# ',tl1#do/ Co"o *o'&e.,@'*# d&&o- &%o "#& <#r#to& .,e o& "#*$o& o, e" *(#!# !#r# ,"# "e&"# *#!#*d#de de *o'd,$%o de *orre'te/ O,tro 5#tor ) o de .,e !o&&,e" "#or re&t@'*# "e*'*# do .,e ,"# &e$%o ret#'g,l#r "#or "o"e'to de ')r*#- !#r# o *#&o de ," e&5or$o de tr#$%o e" ," *,rtoQ*r*,to '# l'(#+e'to- et*/
;) O USO DE PROGRAMAS COMPUTACIONAIS O *l*,lo de <#rr#"e'to& e" &,e& ) tr#<#l(o&o e ",t#& +e1e& *o"!leo- eg'do *l*,lo& ter#t+o&/ Por &&o- *#d# +e1 "#&- o de&e'+ol+"e'to de #!l*#$>e& *o"!,t#*o'#& &e tor'# "!ort#'te !#r# 5#*lt#r e&&e& *l*,lo&/ O,tro 5#tor .,e +# # 5#+or do ,&o de 5err#"e't#& de '5or"t*# ) o ,&o de ",t#&
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CONCLUSÕES E SUGESTÕES DE TRABALOS FUTUROS
O d"e'&o'#"e'to de <#rr#"e'to& ) ,"# et#!# "!ort#'te 'o !rojeto de ,"# &,e& e do& o!er#dore&/ T#"<)" te" rele+'*# o 5#to de <#rr#"e'to& "#l d"e'&o'#do& ele+#re" o *,&to do !rojeto/ N%o ( '#& 'or"#& e&/ De&t# 5or"#- o ")todo ,tl1#do 'o *l*,lo do& <#rr#"e'to& 5*# # *rt)ro do e'ge'(ero re&!o'&+el !elo !rojeto e 'or"#l"e'te re*#e" e" 'or"#& 'ter'#*o'#& o, !#dr>e& 'ter'o& d#& !r?!r#& e"!re&#&/ E&te" #lg,"#& re*o"e'd#$>e& 'ter'#*o'#&- &e'do # !r'*!#l del#& o I*** )td QEP – /!de f%r Des!#n %f )/stat!%n R!#!d0B/s )tr/ct J/ O,tr#& <e&- o d"e'&o'#"e'to el)tr*o te'de # &er "#& '5l,e'te e" &e tr#t#'do de <#rr#"e'to& 5le+e&- !o& 'or"#l"e'te- o *rt)ro de #"!#*d#de r deter"'#r # &e$%o do *o'd,tor .,e &er #!e'#& *o'5r"#d# 'o& *l*,lo& "e*'*o&/ e" <#rr#"e'to& rgdo&# te'd@'*# ) e" rel#$%o #o d"e'&o'#"e'to "e*'*o- o, &ej#- +# de regr# o <#rr#"e'to e&t &,!erd"e'&o'#do 'o .,e d1 re&!eto # *#!#*d#de de *o'd,$%o de *orre'te/ N# !rt*#- o d"e'&o'#"e'to !or e5eto *oro'# '%o !re*&# &er +er5*#do/ Ele #!e'#& e&t#r !re&e'te '# "e"?r# de *l*,lo .,#'do #& e&!e*5*#$>e& do !rojeto #&&" o egre"/
A !r'*!#l &,ge&t%o de *o't',d#de de&te tr#<#l(o ) # *o'5e*$%o de ," &o5t#re .,e #,to"#t1e o& *l*,lo& #!re&e't#do& 'e&te tr#<#l(o/ Co"o j 5o d&*,tdo #'teror"e'te- o &o5t#re '%o &,<&tt, 'e" el"'# # 'e*e&&d#de de #!re&e't#$%o do& *l*,lo& "#& 5#*lt# o ,&o de t#e& t#"<)" ) ," te"# .,e !oder# re*ee& de <#rr#"e'to& '%o *o!l#'#re& 'o& *o'j,'to& de "#'oe& e *o'e>e& de <#rr#"e'to& &e*,'dro& 'o& <#rr#"e'to& !r'*!#& e t#"<)" *o'&der#$>e& &oe& do& *o'd,tore& "#& !odeQ&e t#"<)" '*l,r o& *l*,lo& d#& *ol,'#& de &ol#dore& d# &,e& de *o't',d#de de&te& !rojeto/ A re&!eto d# *#!#*d#de de *o'd,$%o de *orre'te- *orr.,er#"e'te *#Q&e 'o terre'o d# #"!#*d#de e&t#t&t*#/ E&t# ) ,"# .,e&t%o .,e +e" &e'do *#d# +e1 "#& d&*,td# !el#& #,tord#de& do r#"o e'erg)t*o e&/ O& e5eto& de rdo 'ter5er@'*# !ode" &er <#&t#'te
9 #!ro5,'d#do& *o" e.,#*o'#"e'to& e "odel#ge" eletro"#g')t*#/ O e5eto *oro'# t#"<)" ) re&!o'&+el !or !erd#& de e'erg# '#& l'(#& de tr#'&"&&%o- tr#1e'do "!#*to& e*o'"*o&/ Perd#& e&&#& .,e '%o &%o t%o &e'td#& e" &e tr#t#'do de <#rr#"e'to& '# "#or !#rte d#& &,e&/ T#l+e1 #!e'#& e" &e tr#t#'do de &,e& de gr#'de !orte/ E&te" ")todo& e d&!o&t+o& J2 !#r# red,$%o do e5eto *oro'# .,e !ode" t#"<)" &er det#l(#do&/
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