UNIVERSIDAD DE LA SERENA – DPTO. DE INGENIERIA MECANICA
PARAMETROS DE UN TRANSFORMAD TRANSFORMADOR OR Informe N°2 Máqun!" E#$%&r%!"
Esteban Munizaga Eduardo Sepúlveda Agustín Sepúlveda
E# "'uen&e (o%umen&o e"&á refer(o ! (o" &)o" (e )rue*!" o en"!+o" en %r%u&o", que "erán (e u&#(!( )!r! #! (e&ermn!%-n (e&ermn!%-n (e #!" %!r!%&er"&%!" + )!ráme&ro" que e"&án )re"en&e" )re"en&e" en #o" %on"&&u+en&e" (e un &r!n"form!(or. &r!n"form!(or.
INTRODUCCIN P!r! (e&ermn!r #o" )!ráme&ro" (e un &r!n"form!(or monofá"%o (e (o" (e/!n!(o" "e re%urre ! (o" m$&o(o" %om)#emen&!ro" en&re ", e"&o" m$&o(o" %on""&en en un! )rue*! (e /!%o 0o %r%u&o !*er&o1 + un! )rue*! (e Cor&o%r%u&o. Don(e %!(! )rue*! %on""&! en re!#!r ("&n&!" me(%one" (e %orren&e + /o#&!3e )!r! e# )o"&eror %á#%u#o (e #!" )er((!" + f!%&or (e )o&en%!. L! 4n!#(!( (e #o" )!ráme&ro" e" que "on #! %!#/e )!r! (e4nr (o" %on%e)&o" re#e/!n&e" %u!n(o no" refermo" ! #! %!#(!( (e# &r!n"form!(or %on e# que e"&!mo" &r!*!3!n(o. T!#e" %on%e)&o" "on e# f!%&or (e re'u#!%-n + #! e4%en%! o ren(men&o. E"&o" )un&o" "on #!" )rn%)!#e" %!r!%&er"&%!" (e un Tr!n"form!(or en fun%on!men&o, + que )erm&en form!r un *uen %r&ero !# momen&o (e #! "e#e%%on!r !#'uno0"1.
L!" )rue*!" (e %r%u&o !*er&o o en"!+o en /!%o e" !que# en"!+o en que no %r%u#! %orren&e )or e"&!r no %omun%!(o )or un %on(u%&or e#$%&r%o + %on""&e )rn%)!#men&e en m!n&ener #!" &ermn!#e" (e un! *o*n! en %r%u&o !*er&o men&r!" "e m)one un! &en"-n ! &r!/$" (e #!" &ermn!#e" (e# em*o*n!(o o)ue"&o. Se /erá #! "!&ur!%-n (e# %r%u&o m!'n$&%o + #!" )$r((!" que o%urren en e# n5%#eo. L!" )rue*!" (e en"!+o (e %or&o%r%u&o %on""&en en %one%&!r #!" &ermn!#e" (e un! *o*n! en %or&o%r%u&o men&r!" "e !)#%! un! &en"-n re(u%(! ! &r!/$" (e #!" &ermn!#e" (e #! o&r! *o*n! *!3o )rue*!. Se )ro(u%en )$r((!" (e )o&en%!6 un! )!r&e (e $"&!" "e )ro(u%en +! en /!%o + "e m!n&enen %on"&!n&e" e n/!r!*#e" en %!r'!.
MARCO TERICO •
Prue*! (e V!%o7
Con""&e en !)#%!r un! &en"-n nomn!# en %u!#quer! (e #o" (e/!n!(o" (e# &r!n"form!(or, %on e# o&ro (e/!n!(o !*er&o, "e #e !)#%! !# #!(o )rm!ro /o#&!3e + fre%uen%! nomn!#, re'"&rán(o"e #!" #e%&ur!" (e #! )o&en%! (e en&r!(! en /!%o + #! %orren&e en /!%o. E" o*/o que #o" 5n%o" )!ráme&ro" que &enen que "er %on"(er!(o" en #! )rue*! (e /!%- "on Rm + 38m, #! m)e(!n%! (e (")er"-n, R 9 :389, no !fe%&! ! #o"
(!&o" (e )rue*!. U"u!#men&e, #! &en"-n nomn!# "e !)#%! !# (e/!n!(o (e *!3! &en"-n.
D-n(e7
ℑ=
Xm V
R%7 re""&en%! (e )er((! G%7 %on(u%&!n%! ;o%7 !(m&!n%!
•
Prue*! (e %or&o%r%u&o7
Se re!#! ! /o#&!3e re(u%(o, =!"&! que %r%u#e un! %orren&e nomn!# )or e# %r%u&o. En e"&e %!"o no "e &om! #! r!m! (e m!'ne&!%-n, e"&o e" (e*(o ! que "o#o "e requere un )eque>o /o#&!3e )!r! o*&ener #!" %orren&e" nomn!#e" en #o" em*o*n!(o" (e*(o ! que (%=! m)e(!n%!" "on #m&!(!" )or #! m)e(!n%! (e (")er"-n (e #o" em*o*n!(o", )or #o &!n&o #! (en"(!( (e ?u3o en e# n5%#eo "erá )eque>! en #! )rue*! (e %or&o%r%u&o, #!" )$r((!" en e# n5%#eo + #! %orren&e (e m!'ne&!%-n "erá &o(!/! má" )eque>!. L! &en"-n re(u%(! V%%, ##!m!(! fre%uen&emen&e &en"-n (e m)e(!n%!, "e "o#u%on! )!r! que #! %orren&e (e %or&o%r%u&o I%% no o%!"one (!>o en #o" enro##!men&o". Se e"%o'e u"u!#men&e I%% %omo #! %orren&e (e )#en! %!r'! 0nomn!#1. U"u!#men&e e"&! )rue*! "e =!%e )or e# #!(o (e A.T. 0)!r! que #! %orren&e "e! má" )eque>!1. E"&! )rue*! "r/e )!r! (e&ermn!r #o" /!#ore" (e R 9, 89, R2 + 82. Se re!#! =!%en(o %r%u#!r #! %orren&e nomn!# )or uno (e #o" (e/!n!(o", e"&!n(o e# o&ro en %or&o%r%u&o. Norm!#men&e "e %or&o%r%u&o e# (e/!n!(o (e <.T. + "e m(en e# /o#&!3e + #! )o&en%! en e# (e/!n!(o (e A.T., !# %u!# "e #e !)#%! un! *!3! &en"-n.
L! )o&en%! (e# %or&o%r%u&o e" #! )$r((! &o&!# en e# %o*re (e# &r!n"form!(or. De*(o !# efe%&o )e%u#!r (e #!" )$r((!" )or ="&$re"", !(emá" P%% )ue(e "er m!+or que #!" )er((!" -=m%!" en e# %o*re. D-n(e7
@eq, 8eq + Req "on %ono%(!" )or m)e(!n%! equ/!#en&e, re!%&!n%! equ/!#en&e + re""&en%! equ/!#en&e, re")e%&/!men&e. Lue'o "e &enen #o" "'uen&e" "u)ue"&o"7 S V9 V2, )o(emo" (e%r que7
•
F!%&or (e Re'u#!%-n7
L! re'u#!%-n (e /o#&!3e e" un! me((! (e #! /!r!%-n (e &en"-n (e "!#(! (e un &r!n"form!(or, %u!n(o #! %orren&e (e %!r'! %on un f!%&or
(e )o&en%! %on"&!n&e /!r! (e %ero ! un /!#or nomn!#. L! %!r'! e"&á %one%&!(! !# #!(o "e%un(!ro + #! fuen&e (e /o#&!3e !# #!(o )rm!ro. Su)on'!mo" que e# &r!n"form!(or e"&á en&re'!n(o ! #! %!r'! un! %orren&e nomn!# ! un /o#&!3e nomn!# + %on un f!%&or (e )o&en%! e")e%4%o. L! fuen&e (e /o#&!3e e" !3u"&!(! )!r! o*&ener /o#&!3e %on"&!n&e ! e"&e /!#or + #! %!r'! e" (e"%one%&!(! (e# &r!n"form!(or, e# /o#&!3e (e "!#(! (e# &r!n"form!(or %!m*!rá6 #! (feren%! en&re #o" /!#ore" (e# /o#&!3e (e "!#(! %u!n(o e"&á "n %!r'!, + e# nomn!# ! )#en! %!r'!, eB)re"!(! %omo un! fr!%%-n (e# /!#or nomn!#, e" (e4n(! %omo #! re'u#!%-n (e# /o#&!3e nomn!# (e# &r!n"form!(or ! un f!%&or (e )o&en%! e")e%4%o. L! "'uen&e e%u!%-n re)re"en&! e# f!%&or (e re'u#!%-n en )or%en&!3e.
Como 'ener!#men&e, #! %orren&e (e eB%&!%-n "erá )eque>! %om)!r!(! %on #! %orren&e nomn!# (e un &r!n"form!(or (e n5%#eo (e =erro, #! r!m! en (er/!%-n %on""&e (e Rm + 8m )ue(e no %on"(er!r"e )!r! %á#%u#o" (e re'u#!%-n (e /o#&!3e. E"&e %r%u&o equ/!#en&e "m)#4%!(o refer(o !# #!(o "e%un(!ro. Como e# &r!n"form!(or e"&á en&re'!n(o #! %orren&e nomn!# I L2 ! un f!%&or (e )o&en%!, e# /o#&!3e (e %!r'! e" V 2. E# %orre")on(en&e /o#&!3e (e en&r!(! e" V 9 refer(o !# #!(o "e%un(!ro. Cu!n(o #! %!r'! "e remue/e, m!n&enen(o e# /o#&!3e (e en&r!(! %on"&!n&e en #o" &ermn!#e" (e %!r'!, e# f!%&or (e re'u#!%-n (e /o#&!3e, en )or%en&!3e, no %on"(er!n(o #! r!m! (e m!'ne&!%-n %omo "'ue en #! e%u!%-n.
D-n(e7
Lo" &$rmno" V2, IL2 "on #o" /!#ore" nomn!#e"
•
Ren(men&o7
Pue(e (e&ermn!r"e me(!n&e #! me((! "mu#&áne! (e #! "!#(! + #! en&r!(!. Su)-n'!"e que e# /o#&!3e (e #! "!#(! "e m!n&ene %on"&!n&e !# /!#or nomn!# + e# &r!n"form!(or e"&á en&re'!n(o ! #! %!r'! un! %orren&e IL2 0no e" ne%e"!r!men&e e# /!#or nomn!#1. L!" )$r((!" en e# &r!n"form!(or "on #o" que "e &enen en e# n5%#eo (e*(o ! #! ="&$re"", ! #!" %orren&e" )!rá"&!" + #!" -=m%!" en #!" re""&en%!" (e #o" (e/!n!(o". Por P% "e )re"en&!n #!" )$r((!" en e# n5%#eo6 %omo #!" )$r((!" en e# n5%#eo "on (e)en(en&e" (e #! (en"(!( (e ?u3o + #! fre%uen%! )ue(e %on"(er!r"e que P% )erm!ne%e %on"&!n&e en e# &em)o " e# /o#&!3e (e "!#(! + #! fre%uen%! "e m!n&enen %on"&!n&e" en e# &em)o. L!" )$r((!" -=m%!" en #o" enro##!men&o", e"&án en fun%-n (e #! %orren&e. A %u!#quer %orren&e I L2, #!" )$r((!" -=m%!" &o&!#e" en e# &r!n"form!(or "on I 2L2 Req26 e"&!" )$r((!" "on ##!m!(!" )$r((!" en e# %o*re. Por &!n&o #! eB)re"-n )!r! (e&ermn!r #! e4%en%! o ren(men&o "erá #! "'uen&e.
S IL2 e" #! %orren&e nomn!#, en&on%e" "e o*&ene #! e4%en%! nomn!# (e# &r!n"form!(or.
•
F!%&or (e Corre%%-n )or Tem)er!&ur!
L! &em)er!&ur! !m*en&e !#&! n?u+e (e"f!/or!*#emen&e en #! %on(u%%-n (e e#e%&r%(!( (e*(o ! que !umen&! #! re""&en%! e#$%&r%!. Por e# %on&r!ro, ! menor &em)er!&ur! "e %on(u%e me3or #! e#e%&r%(!(. De =e%=o =!+ un fen-meno que "e ##!m! "u)er%on(u%&/(!( que "e )re"en&! en !#'uno" m!&er!#e" ! &em)er!&ur!" )or (e*!3o (e #o" 'r!(o" e#/n. E"&e f!%&or )ue(e "er (e&ermn!(o me(!n&e &!*#!" )ero en e"&e %!"o re%urrremo" ! #! "'uen&e eB)re"-n7 Z 2=
234,5 + T 1 234,5 + T 2
∗ Z 1
D-n(e7 T9 e" #! &em)er!&ur! !m*en&e6 T2 e" #! &em)er!&ur! ! %orre'r6 @9 e" #! m)e(!n%! ! %orre'r6 @2 e" #! m)e(!n%! %orre'(!6 + 2, e" #! %on"&!n&e (e# %o*re.
“Ejemplo de tabla de factor de corrección de temperatura”
DESARRO!!O DE !A E"#ERIENCIA Ensa$o en va%ío o prueba de %ir%uito abierto
P!r! re!#!r e"&! )rue*! re!#%e #o" "'uen&e" )!"o"7
!1 EB%&e e# &r!n"form!(or )or e# (e/!n!(o (e A.T. + (e3e !*er&o e# (e/!n!(o (e <.T. *1 Tome %omo mnmo 9H #e%&ur!", )!r&en(o (e# 2H (e #! &en"-n nomn!# (e# (e/!n!(o eB%&!(o, =!"&! ##e'!r !# 99H (e# /!#or nomn!#. %1 Lo" /!#ore" o*&en(o" "e (e*en re'"&r!r en un! &!*#!.
#rueba o ensa$o en %orto %ir%uito P!r! efe%&u!r e"&! )rue*! re!#%e #o" "'uen&e" )!"o"7 !1 Pon'! en %or&o%r%u&o e# (e/!n!(o (e <.T. 0que (em!n(! m!+or %orren&e1. EB%&e e# &r!n"form!(or )or e# #!(o (e A.T. *1 Tome %omo mnmo (e #e%&ur!", )!r&en(o (e# 2H (e #! %orren&e nomn!# (e# (e/!n!(o, =!"&! ##e'!r !# 99H, em)e%e %on #!" %orren&e" má" !#&!", =!"&! ##e'!r ! #!" má" *!3!". %1 Re'"&r!r #o" /!#ore" o*&en(o" en un! &!*#! %omo #! que "e n(%! ! %on&nu!%-n.
E&uipos utilizados
Tr!n"form!(or (e &)o !%or!!(o
Mu#&&e"&er
FEM
Datos de pla%a Voltajes
De/!n!(o )rm!ro JVK 9H 2H 2H
Potencia Total
De/!n!(o "e%un(!ro JVK , , ,
S JVAK H, H, H,
Tabla de datos 'edidos $ %al%ulados( Lo" "'uen&e" %á#%u#o" fueron re!#!(o" en EB%e# me(!n&e #!" f-rmu#!" )er&nen&e" en e# m!r%o &e-r%o.
" $ + & . % / ,
" $ + & . %
Voltaje (V) V !ri#ario %&'& ,'. $+/', $-.'. $/*'+** +$ +&* +-.
PRUEBAS DE CIRCUITO ABIERTO Corriente (A) Pérdida (Watts) fd! I !ri#ario P !ri#ario Cos() &'&E*+ $ *'&,%% -'&*E*+ & *'-,/& ,'+E*+ *'$,/ $',E*$ / *'+.&& *'&/ $+ *'$%-* *'. $% *'$$% *'/++ *'$+*, $'&. &* *'*,-, '+ %/ *'*%+-
Potencia (VA) S !ri#ario +'-$$, -'*$&/ $$',$*&. &*'&/* ./'-, $+* $/$', &$+'/ $*%-'+
Rc (Ω1
PRUEBA DE CIRCUITO ABIERTO 0oc 0Ω91 1c 0Ω91 B# 0Ω91
2# 0Ω1
-&%+', +,/&'$ &&+&'* &*.-' +%$-'* +&-+', +*/$'.
'.%,E* -'.*&E* %'$./E* $'+&,E*& +'$*-E*& &'***E*& &',%+E*&
*'***$/.$ *'***&&-+ *'***&**, *'***&+.+ *'***&./& *'***+-* *'***/*
*'***& *'****'***.*'**$+* *'**+*% *'**+,% *'**&,
+&+,'$, +++%'., $-&%'*+ /&.'%/+' &&.'%& +-&'.&
/ ,
" $ + & . % / , $*
" $ + & . % / , $*
$%.&'& /*'+
Voltaje (3) V!ri#ario $+'$/ $*','+$ %',/ %'+. .'. -'%/ &'%+'+.
R$5R+6 &'*.** &'$&/* &'**& &'*%/& &'*+/% +'/*-/ &'**%$ +'...% +'.,&$ +'**/
-',$&E*& $'.$E*+
*'***-.%$ *'**$$,*+
*'**-/, *'*$.&.
PRUEBAS DE CORTO CIRCUITO Corriente (A) Pérdida (Watts) fd! I!ri#ario P!ri#ario Cos(4) &'-% &, *'/,., &'* +, *',$+, +'., ++ *'///* +'&$% *',*.+'$$ *'/,., $',/ $$ *'/$/ $'%& , *',**$ $'. *'/*** $'$ &'*'/$/% *'% $ *'.&+$
PRUEBAS DE CORTO CIRCUITO R$7R+6 8sc $'-&** &'$$/ $'-.,* &'&%$'-+*+ &'+&/ $'-&,+ &'&,-% $'-$& &'&%.% $'*+, &'&&&& $'-*&. &'&$* $'&&&& &'&&&& $'&.. &'+/,$'*+* &'++/.
2$52+6 $'-*/% $'*& $'-% $'&&$',&+ $'%,,. $'-.* +'**** $'//// +'-*
%$$.,',* .$'$$
Potencia (3A) S!ri#ario &'/ &$'%% +'%% $/'%$-'.$ $&'*% $*'** %'-* '+/ $'-/
2$72+6 *'%- *'%*$% *'%/%+ *'%$./ *'%.. *'/,,/ *'%+/* $'**** *', $'+-*,
Corre%%i)n a *+ ,C "
Rc a %-9C
2# a %-9C
$ + & . % / , $*
-%',/$% &'$..& /'*/.$ '&*$, &,'+/%% &'*/+ &*'$++& +-'-$.& $+'$-/+
&*'*/.$ &+'+&-/ ++'+$ $+'*.*, .',/$+ '/%+. &'.%*$ +'-/. *',*$.
R$ : R+; a %-9C *'*++$ *'*++% *'*++ *'*+$/ *'*+$, *'*+*& *'*+$/ *'*$,& *'*$,*'*$/
2$ : 2+; a %-9C
8sc a %-9C
*'*$*, *'*$*+ *'*$$ *'*$*% *'*$*/ *'*$& *'*$**'*$*'*$&% *'*$/$
*'*, *'*,% *'*,*'*/. *'*/, *'*/+ *'*/& *'*/+ *'*%. *'*.%
Corrientes de e-%ita%i)n. p/rdida. $ 'agnetiza%i)n Pre/!men&e %on #o" (!&o" (e )#!%! (e o*&ene7 a=
V 1 nominal V 2 nominal
=
230 [ V ] 36.5 [ V ]
= 6.3014 '
V 2 =a∗V 2 =6.3014∗36.5 [ V ]= 230 [ V ]
I 2=
'
I 2 =
500 [ VA ] S = =13.6986 [ A ] V 2 36.5 [ V ]
I 2 13.6986 [ A ] = =2.1739 [ A ] a 6.3014
Con"(er!n(o un Co"01H, n(u%&/o "e o*&ene7 .° )or #o &!n&o, I2 2.9Q
∠.°
De&ermn!%-n (e /o#&!3e" en )#en! %!r'!7 E Plenacarga =V 2 + I 2 ( R 2 + X 2 j ) [ V ] '
'
'
'
I 1= I 2 + Ie [ A ]
Ie =
E pc Rc‖ Xm
= Ic + ℑ [ A ]
'
V 1 Plenacarga = E pc + I 1 ( R 1 + X 1 j ) [ V ]
V+; I6+ +&* +'$%&,*+.%
&.'/%
"
R+;
2+;
$ + & . % / , $*
$'-& $'-. $'-+ $'-& $'-$ $'* $'-* $'&& $'& $'*+
*'%*'%* *'%/ *'%$ *'% *'/, *'%+ $'** *', $'+-
" $
Rc >> 2#
9,9H 2,22°
R+;5<2+; $'-&5*'%-j $'-.5*'%j $'-+5*'%/j $'-&5*'%$j $'-$5*'%j $'5*'/,j $'-5*'%+j $'&&5j $'&5*',j $'*+5$'+-j
Ie7E > Rc >> 2# ∠
H,92 ∠ 2,92°
I6+=( R+;5<2+;)
E
&'.&*'./j &'.+*'/$j &'.-*'.+j &'-/*'%-j &'-/*'%j &'&.*'-.j &'-*'.,j &'.$5*'**/j &'--*'$*,j &'&,5*'/j
+&&'.&*'./j +&&'.+*'/$j +&&'.-*'.+j +&&'-/*'%-j +&&'-/*'%j +&&'&.*'-.j +&&'-*'.,j +&&'.$5*'**/j +&&'--*'$*,j +&&'&,5*'/j
I$ 7I+;5Ic
$&'/$$$j*'*-/-
V$ sec?ndario car@a
22,QH ∠ ,QQ
H,9HQ ∠ ,2°
$&'/*&&j*'*%/-
22,QQ ,Q
∠
+
9,QH ∠ ,9°
H,9 ∠ 2,Q92Q°
$&'/--*j*'*%*-
2,92 ,Q
∠
&
9Q,H29∠ 2,229°
H,29 ∠ 9,HH°
H,2QH ∠ 9,9°
$&',%.+j*'*/-%
2, ∠ ,
-
,HHHH ∠ 9H,HQ°
H,Q9 ∠ 9H,9°
$'$/+/j*'*/./
2,2Q ∠ ,Q
%
, ∠ ,9° 29, ∠,Q°
/
9Q,99 ∠,H°
9,9
∠,Q°
$-'*%&&j*'$&%
2,H ,H
,
2,9Q ∠,299°
,Q
∠,9Q°
$%'%&j*'+/*
2Q,Q9 ∠ ,9
.
H,HH
∠,29°
$'&,+$j*'$**/
2,H2 ∠ ,Q9
H,Q2
∠,H°
$'.$,j*'$$&.
2, ∠ ,29Q
De&ermn!%-n (e /o#&!3e en /!%o7 '
Evacio =V 2 [ V ] I 1=+ Ie [ A ]
Ie =
E vacio Rc‖ Xm
= Ic +ℑ [ A ]
V 1 vacio= E vacio + I 1 ( R 1 + X 1 j ) [ V ]
" $
Rc >> 2#
9,9H ∠ 2,22°
Ie7E > Rc >> 2#
H,92 ∠ 2,22°
I$ 7I+;5Ic
H,92 ∠ 2,22°
V$ sec?ndario 3aco
2H, ∠ H,29
∠
+ & . % / ,
9,QH ∠ ,9° 9Q,H29∠ 2,229° H,29 ∠ 9,HH° ,HHHH ∠ 9H,HQ° , ∠ ,9° 29, ∠ ,Q° 9Q,99 ∠ ,H° 2,9Q ∠ ,299°
H,92Q ∠ ,9° H,9Q ∠ 2,229° H,2H ∠ 9,HH° H,2 ∠ 9H,HQ° H,QHH ∠ ,9° H,Q9 ∠ ,Q° 9,HH ∠ ,H° ,H9 ∠ ,299°
H,92Q ∠,9° H,9Q ∠2,229° H,2H ∠ 9,HH° H,2 ∠ 9H,HQ° H,QHH ∠ ,9° H,Q9 ∠ ,Q° 9,HH ∠ ,H° ,H9 ∠ ,299°
Regula%i)n de tensi)n $ e0%ien%ia V 1 ( 2
ario
%Reg =
carga )−V 1 ( 2
ario
V 1 ( 2
ario
'
vacio )
vacio )
'
∗100
Psalida V 2 ∗ I 2 ∗cos () V 2 V 1 ; φ I 2 ;φ1 I 1 ¿ = Pentrada V 1∗ I 1∗cos ( φ1 ) '
2
" $ + & . % / ,
CONC!USIN
Re@
9, 9, 9, 9, 9, 9, 9, 9, 9,
Eficiencia
92, 92, 92, 92, 92,2 92,H 99, 99, Q,
2H,2 ∠ H,9 2H,922 ∠ H,H2 2H,Q9 ∠ H,H2Q 29,9Q ∠ H,9H 22,9 ∠ H,HH 2,292 ∠ H,2Q 2,9 ∠ H,QHH 2,9 ∠ 2,H
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