Potencia en Generadores Sincronos

8/17/2019 Potencia en Generadores Sincronos

1/19

ME III 10.- POTENCIA EN MAQUINAS SINCRONAS

MAQUINAS SINCRONAS HUBER MURILLO MANARIQUE PAGE 1

Cuando la máquna !"#a #$a%a&ando !n 'a()o *a '!lo(dad (on"#an#!+ la #!n",n d!l !"#a#o$d!!nd! d!l lu&o ma/n#(o /!n!$ado o$ lo" olo" d! !(#a(,n d!%do a la $!"!n(a d! la(o$$!n#! qu! ($(ula o$ lo" a$$ollam!n#o" d! la a$madu$a *(amo+. E"#o "! d!%! a qu! !l !"#a#o$no !" $!(o$$do o$ nn/una (o$$!n#! *IL 2 0+3 o$ #an#o la $!a((,n d! la a$madu$a !" nula 3(u4o!!(#o !" al#!$a$ !l lu&o #o#al.

5 * 5ol#o" +5n

6ona d! "a#u$a(,n

Cu$'a d! 'a()o.

R!(#a d!l !n#$!7!$$o

I nomnal

I*Am!$o"+

8/. N9 1.- Ca$a(#!$)"#(a" d! 'a()o

La $!la(,n !n#$! la #!n",n /!n!$ada * 5 !n 'ol#o" + 4 la (o$$!n#! d! !(#a(,n * I !n Am!$o"+ "! l! d!nomna (a$a(#!$)"#(a d! 'a()o3 dond! od!mo" o%"!$'a$ !l !"#ado d! "a#u$a(,n d!l/!n!$ado$ ")n($ono "om!#do a "#a $u!%a.

2.- COMPORTAMIENTO DE UN GENERADOR SINCRONO BAJO CARGA

En (a$/a la (o$$!n#! qu! a#$a'!"an lo" (ondu(#o$!" d!l !"#a#o$ ($!a un (amo ma/n#(o3

(au"ando al#!$a(on!" !n la n#!n"dad 4 d"#$%u(,n d!l (amo ma/n#(o $n(al3o%#!nndo"! (omo $!"ul#ado una d"#o$",n d!l (amo $!"ul#an#!.E"#a al#!$a(,n d!!nd! d!:- La (o$$!n#! d! la (a$/a. - 8a(#o$ d! o#!n(a d! la (a$/a.En "!/uda $!"!n#a$!mo" !l (omo$#am!n#o d!l al#!$nado$ (uando !" "om!#do a d'!$"a"(a$/a":

2.1.- Carga puramente resst!a.- S !l al#!$nado$ alm!n#a un ($(u#o u$am!n#! $!""#'o3 la(o$$!n#! d! (a$/a ($!a un (amo ma/n#(o $oo.El da/$ama *a+ mu!"#$a la al#!$a(,n d!l lu&o $n(al !n 'a()o 0o !n $!la(,n al lu&o d!$!a((,n d!l !"#a#o$ 4;o a$madu$a 0$.


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MAQUINAS SINCRONAS HUBER MURILLO MANARIQUE PAGE <

El (amo ma/n#(o ndu(do $odu(do o$ lo" do" olo" * al#!$nado$ %ola$ + d!"a"ado =09*!n a#$a>o+3 !n $!la(,n a lo" olo" $n(al!" 4 "#o" !&!$(!n "o%$! lo" olo" ndu(do" unau!$>a (on#$a$a al mo'm!n#o3 /a"#ándo"! o#!n(a m!(án(a a$a man#!n!$ al $o#o$ /$ando.

$

o

* a + * % +

8/. N9 < .- Como$#am!n#o d!l lu&o $n(al !n 'a()o * o + $!"!(#o al lu&o $odu(do o$ la

$!a((,n d!l ($(u#o !"#a#,$(o 4;o a$madu$a * $ +. Cuando la (a$/a !" $!""#'a

La al#!$a(,n d! o !" !qu!?a3 no $odu(!ndo una 'a$a(,n mu4 /$and! !n $!la(,n al lu&o

$!"ul#an#! * +. @!%do a la (a)da d! #!n",n !n lo" a$$ollam!n#o" d! la a$madu$a "!$á n!(!"a$oaum!n#a$ la (o$$!n#! d! !(#a(,n a$a man#!n!$ la #!n",n nomnal.

2.2.- Carga puramente n"u#t!a.- En !"#! (a"o la (o$$!n#! d! (a$/a !"#a d!"a"ada =09 enatras$ !n $!la(,n a la #!n",n 4 !l (amo d! $!a((,n d! a$madu$a !"#a$á (on"!(u!n-#!m!n#!!n la m"ma d$!((,n d!l (amo $n(al 4 !n ola$dad ou!"#a.

El !!(#o d! la (a$/a ndu(#'a !" d!"ma/n!#>an#! '!$ lo" !"qu!ma" * a + 4 * % +.La" (a$/a" ndu(#'a" alma(!nan !n!$/)a qu! !$#!n!(! al ndu(#o$ !n#on(!" lo d!'u!l'!#o#alm!n#! al /!n!$ado$ no !&!$(!ndo nn/n (on&u/ado $!nan#! !n !l ndu(do.La" (a$/a" ndu(#'a" alma(!nan !n!$/)a qu! !$#!n!(! al ndu(#o$ !n#on(!" lo d!'u!l'!#o#alm!n#! al /!n!$ado$ no !&!$(!ndo nn/n (on&u/ado $!nan#! !n !l ndu(do.En !"#! (a"o "olo "! $odu($á un /a"#o d! !n!$/)a m!(án(a a$a (om!n"a$ la" $dda".@!%do a !"#! !!(#o d!"ma/n!#>an#! "!$á n!(!"a$o un /$an aum!n#o d! (o$$!n#! d! !(#a(,na$a man#!n!$ la #!n",n nomnal.

o $E!(#o d!"ma/n!#>an#!

* a + * % +

* a +

8/. N9 B .- Como$#am!n#o d!l lu&o $n(al !n 'a()o * o + $!"!(#o al lu&o $odu(do o$ la

$!a((,n d!l ($(u#o !"#a#,$(o 4;o a$madu$a * $ +. Cuando la (a$/a !" ndu(#'a.


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MAQUINAS SINCRONAS HUBER MURILLO MANARIQUE PAGE

2.%.- Cargas puramente #apa#t!as.- La (o$$!n#! d!l !"#a#o$ a$a una (a$/a (aa(#'a

* a + * % +

O $E!(#o ma/n!#>an#!

8/. N9 D .- Como$#am!n#o d!l lu&o $n(al !n 'a()o * o + $!"!(#o al lu&o $odu(do o$ la

$!a((,n d!l ($(u#o !"#a#,$(o 4;o a$madu$a * $ +. Cuando la (a$/a !" (aa(#'a.

Cuando la (a$/a (aa(#'a !"#a d!"a"ada !n =09 en a"e&ant$ (on $!la(,n a la #!n",n !l(amo d! $!a((,n d! a$madu$a (on"!(u!n#!m!n#! "! !n(on#$a$á !n la m"ma d$!((,n d!l(amo $n(al 4 (on la m"ma ola$dad '!$ lo" !"qu!ma" * a + 4 * % +.El (amo ndu(do !n !"#! (a"o #!n! un !!(#o ma/n!#>an#!.La" (a$/a" (aa(#'a" alma(!nan !n!$/)a !n "u (amo !l(#$(o 4 la d!'u!l'!n #o#alm!n#! al/!n!$ado$3 no !&!$(!ndo (omo !n !l (a"o an#!$o$ nn/n (on&u/ado $!nan#! "o%$! !lndu(do. @!%do al !!(#o ma/n!#>an#! "!$á n!(!"a$o $!du($ la (o$$!n#! d! !(#a(,n a$aman#!n!$ la #!n",n nomnal.

2.'.- Cargas nterme"as.- En la $a(#(a no" !n(on#$amo" (on (a$/a" qu! $!"!n#and!"a"a&!" n#!$m!do" !n#$! #o#alm!n#! ndu(#'a3 (aa(#'a 4 $!""#'a.En !"#! (a"o !l (amo ndu(do u!d! "!$ d!"(omu!"#o !n do" (amo": Un #$an"'!$"al 4 !lo#$o d!"ma/n!#>an#! *ndu(#'o+ , ma/n!#>an#! *(aa(#'o+.

I * Am!$o" +

Ca$/a" ndu(#'a"I nom.

Ca$/a" $!""#'a"

Ca$/a" (aa(#'a"

5 nomnal 5 * 5ol#o" +

8/. N9 .- 5a$a(,n d! la (o$$!n#! d! !(#a(,n a$a man#!n!$ la #!n",n d! a$madu$a(on"#an#! * 5 !n %o$n!" + .

Solam!n#! !l (amo #$an"'!$"al $odu(! "u !!(#o $!nan#! (on"um!ndo o#!n(a m!(án(ad! la máquna a((onan#!. El !!(#o ma/n!#>an#! , d!"ma/n!#>an#! d!%!$á (om!n"a$"!al#!$ando la (o$$!n#! d! !(#a(,n.


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MAQUINAS SINCRONAS HUBER MURILLO MANARIQUE PAGE D

%.- POTENCIA EN (AS MA)UINAS SINCRONAS

Pa$a d!#!$mna$ la o#!n(a d! una máquna ")n($ona "! u#l>a la "/u!n#! !$!",n:

m 2 Nm!$o d! a"!". U 2 T!n",n d! a"! d!l !"#a#o$.

I! 2 Co$$!n#! d! a"! d!l !"#a#o$. 2 An/ulo o$mado o$ U ! I!La o#!n(a !l(#$(a d!"a$$ollada !n la máquna d! olo" "al!n#!" #am%n u!d! "!$!$!"ada !n un(,n d!l án/ulo d! (a$/a qu! "u$/! !n#$! lo" a"o$!" U *#!n",n d! a"! + 4Eo * u!$>a !l!(#$omo#$> ndu(da + d!#!$mnado o$ la o"(,n d!l án/ulo d!l $o#o$ !n$!la(,n al lu&o /$an#! d!l !"#a#o$. E"#! !!(#o "! $odu(! (uando !"#! (o$$!n#! ($(ulan#! *a%"o$%da o$ la (a$/a + !n lo" a$$ollam!n#o" d!l !"#a#o$3 d!%do a qu! "! ($!a un (amoma/n#(o qu! !"#á !n oo"(,n al (amo $n(al.

*$rmas #$nstru#t!as "e& r$t$r .- La o$ma d! (on"#$u((,n d!l $o#o$ !" mu4 mo$#an#! 4aqu! $odu(! (a$a(#!$)"#(a" qu! d!n!n "u un(onam!n#o #al!" (omo:- Im!dan(a !"#a#o$ $o#o$.- Im!dan(a $o#o$ !"#a#o$.- La 'a$a%ldad d!l !n#$!7!$$o "!/n "u o"(,n.

* An/ulo d! d!"a"a&! +

d * E&! d$!(#o +

Camo $n(ald! olo" "al!n#!"

q * !&! (uad$a#u$a +

8/. N9 F.- Como$#am!n#o d! la $!a((,n d! la a$madu$a (on $!"!(#o a lo" !&!" d 4 q.

a.- Ro#o$ d! olo" l"o" * $!dondo , (l)nd$(o +.- E" !l qu! (uml! la" (a$a(#!$)"#(a" qu! a(on#nua(,n "! d!#allan '!$ /. N9 * a +.

N


5/19



ROTOR

a+ Polo" l>o" %+ Polo" "al!n#!"8/. N9 .- Cla"(a(,n d! lo" $o#o$!" "!/n "u o$ma (on"#$u(#'a d!l $o#o$

- A$$ollam!n#o" d! (amo "#uado" !n la" $anu$a" aal!" * a lo la$/o d!l $o#o$ +.- S! u"an !n máquna" qu! un(onan !n al#a" '!lo(dad!" a((onada" o$ #u$%na" d! 'ao$

* #u$%o al#!$nado$!"3 !#(. +.- El dám!#$o d!l $o#o$ !" $!la#'am!n#! !qu!?o * a$o. =00 mm. +.- S! u#l>an !n $o#o$!" a$a máquna" ")n($ona" d! < , D olo" * al#a" '!lo(dad!" +.- T!n! "u !n#$!7!$$o (on"#an#!.

+.- R$t$r "e p$&$s sa&entes .- E" u#l>ado !n #odo #o d! /!n!$ado$!"3 #!n!ndo la""/u!n#!" (a$a(#!$)"#(a" $n(al!" '!$ /. N9 * % +:- P$!"!n#a$ un !n#$!7!$$o 'a$a%l! qu! d!!nd! d! "u o"(,n $!"!(#o al !"#a#o$.- S! u"a !n '!lo(dad!" %a&a" * D olo" +.

- Son u#l>ada" !n máquna" a((onada" o$ #u$%na" 7d$ául(a". * 7d$o/!n!$ado$!" +.La" máquna" d! olo" "al!n#!" #!n!n una d$!((,n d! ma/n!#>a(,n $!!$!n#!d!#!$mnada o$ la" !an"on!" ola$!". La $!lu(#an(a !" a$!(a%l!m!n#! m!no$ !n !l !&!d$!(#o * ola$ + qu! !n !l d! (uad$a#u$a * n!u#$o +. En la "/u!n#! /u$a u!d!n '!$"! lo"lu&o" lon/#udnal!" 4 #$an"'!$"al!" !n !l !n#$!7!$$o d! una máquna ")n($ona.

E&! d$!(#o E&! (uad$a#u$a

8lu&o" lon/#udnal!" 8lu&o" #$an"'!$"al!"

8/. N9 .- 8lu&o" !n una máquna d! olo" "al!n#!".

'.- M,)UINA SNCRONA DE PO(OS SA(IENTES

ESTATOR

ROTOR

ESTATOR

ESTATOR ESTATOR

ROTOR

N S N S


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MAQUINAS SINCRONAS HUBER MURILLO MANARIQUE PAGE F

Pa$a !"#uda$ !l !!(#o d! lo" olo" "al!n#!" "! u!d! d!"(omon!$ la (o$$!n#! !"#a#,$(a *I! +3 !n am%o" da/$ama"3 4 #!n!ndo (omo $!!$!n(a la #!n",n ndu(da * E + "! /$a(an lo"lu&o" d! (amo 4 d! la $!a((,n d! la a$madu$a a$a o$ma$ !l lu&o $!"ul#an#! qu! "! 7a$á$!"!n#! !n !l !n#$!7!$$o d! la máquna d! olo" "al!n#!".@ond!:

2 8lu&o $n(al $odu(do o$ !l (amo *ndu(#o$+.

! 2 8lu&o d!%do a la $!a((,n d! la a$madu$a *!"#a#o$ , ndu(do+.

2 8lu&o $!"ul#an#! !"#!n#! !n !l !n#$!7!$$o.I! 2 Co$$!n#! !"#a#,$(a3 #$a%a&ando (on (a$/a.Iq 2 Comon!n#! d! la (o$$!n#! !"#a#,$(a3 !n !&! (uad$a#u$a.Id 2 Comon!n#! d! la (o$$!n#! !"#a#,$(a3 !n !&! d$!(#o.I! 2 Co$$!n#! !"#a#,$(a3 #$a%a&ando (on (a$/a.E 2 T!n",n ndu(da n#!$na *u!$>a !l!(#$omo#$>+3 o$ a"! d!l /!n!$ado$.

2 An/ulo !n#$! la #!n",n !n #!$mnal!" *5+ 4 la (o$$!n#! !"#a#,$(a *I!+.

2 An/ulo !n#$! la #!n",n !n #!$mnal!" *5+ 4 la #!n",n ndu(da *E+.Jq 2 Comon!n#! d! la $!a(#an(a ")n($ona !n !&! (uad$a#u$a.Jd 2 Comon!n#! d! la $!a(#an(a ")n($ona !n !&! d$!(#o.

Iq E

5 Iq.JqI!.R

Id I! IdJd

q

Iq Ed ! @a/$ama a"o$al a$omado.

Id I!

@a/$ama d! 8M !n olo" "al!n#!"

8/. N9 =.- @a/$ama" a"o$al!" d! la" máquna" ")n($ona" d! olo" "al!n#!".

Pa$a o!$a(,n !qul%$ada !n $/m!n !$man!n#! Io !" nula.- El "/n(ado )"(o d! la" (omon!n#!" !n !&! d$!(#o 4 (uad$a#u$a !" !l "/u!n#!:

E&! d$!(#o * Jd + E&! (uad$a#u$a * J q +

E&! d!l $o#o$ 4 (ondu(#o$!" a"o(ado" Al !"#a#o$.

E"a(o n#!$ola$ d!l $o#o$ 4 (ondu(#o$!"a"o(ado" d!l !"#a#o$.

R!lu(#an(a ma/n#(a m)nma * mn. +. R!lu(#an(a ma/n#(a máma * ma. +

8lu&o d! !nla(! mámo * 0ma. +. 8lu&o d! !nla(! m)nmo * 0m)n. +

Jd Jq En #u$%o al#!$nado$!". Jq K Jd En 7d$o al#!$nado$!".

REACTANCIAS EN LOS EES @IRECTO CUA@RATURA


7/19



- La máquna d! olo" "al!n#!" #!n! una d$!((,n $!!$!n(al d! ma/n!#>a(,nd!#!$mnada o$ la "al!n(a d! lo" olo" d!l (amo.

La !$m!an(a a lo la$/o d!l !&! ola$ , d$!(#o !" a$!(a%l!m!n#! ma4o$ qu! la !$m!an(aa lo la$/o d!l !&! n#!$ola$ , (uad$a#u$a.@! la #a%la an#!$o$ "! u!d! (on(lu$ qu! :- A ma4o$ $!lu(#an(a "! o%#!n! m!no$ lu&o.- A m!no$ ndu(#an(a m!no$ $!a(#an(a.

Jd Jq La $!a(#an(a !n !l !&! !" ma4o$ qu! !n (uad$a#u$a.

An&ss "e &a p$ten#a en m/unas s0n#r$nas "e p$&$s sa&entes.- Pa$a $!al>a$ !l!"#udo d! la" máquna" ")n($ona" d! olo" "al!n#!" !" n!(!"a$o (on#a$ (on un ($(u#o!qu'al!n#! * /.N9 10 4 11 + dond! n#!$'!n/an !l mod!lo 4 lo" a$ám!#$o" ma" mo$#an#!"(omo "on: La $!a(#an(a ")n($ona 3 (ono$mada o$ la $!a(#an(a d! la máquna ma" la

$!a(#an(a (o$$!"ond!n#! a la $!a((,n d! a$madu$a.- En la /. N9 10 4 11 od!mo" '"ual>a$ !l mod!lo ad!(uado *a+ 4 !l da/$ama a"o$al *%+

qu! no" 'an a !$m#$ $!al>a$ !l anál"" d! la máquna ")n($ona d! olo" "al!n#!". A")m"mo "! d!%!n #!n!$ la" "/u!n#!" (on"d!$a(on!" :

-I

J Ja RE 5 6 L

8/. N9 10.- C$(u#o !qu'al!n#! $!al o$ a"! d! una MRS d! olo" "al!n#!"

5 Co"I Iq E

J" R

5 "!n 5 R.Iq & Id.JdE 5

Id I R.Id & Jd.Id

8/. N9 11.- R!$!"!n#a(,n d!l mod!lo 4 da/$ama a"o$al d! una máquna ")n($ona d!olo" "al!n#!" .

- R KKK J" R 0 * mo#'o o$ !l (ual "! d!"$!(a R +.- La J" 2 Jd J q * Mu4 mo$#an#! +.- E (09 !" la la #!n",n ndu(da n#!$na d! $!!$!n(a d!l /!n!$ado$.

R 2 R!""#!n(a d! a$madu$a o$ a"!.J" 2 Ja J.Ja 2 R!a(#an(a o$ a"! d!%do a la $!a((,n d! la a$madu$a.J 2 R!a(#an(a n#!$na o$ a"! d! la a$madu$a.


8/19



2 An/ulo !n#$! 5 ! I.

2 An/ulo !n#$! E 4 5. Al(ando la 5L * $(7oo 5ol#/! La + !n la /. N9 11.

E 2 5 (o" R . Iq Jd . Id * 1 +

E 2 5 (o" R . I . (o" * + Jd . I . "!n * + * < +

5 "!n 2 Jq . I . (o" * + - R. I . "!n * + * B +

5 S!n 2 Jq . Iq - R. Id * D +

@! la" !(ua(on!" an#!$o$!" 4 #!n!ndo E 2 E 0 * T!n",n ndu(da d! $!!$!n(a +.

A"um!ndo qu! R KKK J" R 2 0

E 2 E 0 2 5 (o" Jd . Id

Id 2 * E - 5 (o" + ; Jd 3 Iq 2 5 "!n ; Jq * +

P!$o I 2 Id &Iq

I 2 * E - 5(o" + ; Jd & 5"!n ; Jq * F +

A .- (a p$ten#a nterna genera"a p$r &a MRS es

S 2 E . I

S 2 E *E - 5(o" + ; Jd &E . 5"!n ; Jq * +

S 3 E 4 - 5 . E #$s 6 7 8" - 9 E . 5 sen 7 8/ * +

S P : 9 )

- B ;< - - ;< 0 ;< B ;< <

8/. N9 1


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MAQUINAS SINCRONAS HUBER MURILLO MANARIQUE PAGE =

- B ;< - - ;< 0 ;< B ;< <

8/. N9 1B.- Cu$'a d! la o#!n(a $!a(#'a !n máquna" ")n($ona" d! olo" "al!n#!"

B.- (a p$ten#a genera"a en +$rnes p$r &a MRS es

S 2 5 . I

5 2 5"!n & 5(o" ! I 2 Id - & q

S 2 * 5"!n & 5(o" + * Id - & q +

S 2 5 . "!n . Id & 5 . (o" . Id - & 5 . "!n . Iq 5 . (o" . Iq

S 5 . sen . I" : 5 . #$s . I/ : 9 3 5 . #$s . I" - 5 . sen . I/ 6

S P : 9 )

P 2 5 . "!n * E - 5 (o" + ; Jd 5 . (o" . 5 . "!n ; Jq

P 2 5. E . "!n ; Jd - 5 . (o" S!n ; Jd 5 . "!n . (o" + ; Jq

P 2 5. E . "!n ; Jd 5 . (o" S!n 1 ; Jq - 1; Jd

< "!n . (o" 2 "!n < "!n . (o" 2 * 1 ; < + "!n <

P 3 5. E 7 8" 6. sen : 3 5 4 7 2 6 Sen 2 ; 3 8" 8/ 6 7 8/ . 8" <

@!!nd! d! 5 @!%do a la d!$!n(a d! la $!lu(#an(a

4 la !(#a(,n !n /. No d!!nd! d! la !(#a(,nd! la máquna d! la máquna.

Cuando Jd Jq * En#on(!" Jd - Jq 2 Jd +. Lu!/o la nu!'a !(ua(,n !":

P 3 5. E 7 8" 6. sen : 3 5 4 7 2 . 8/ 6 Sen 2

Lu!/o " anal>amo" la" 'a$a(on!" d!l án/ulo #!n!mo":

S 2 0 P 2 0 S 2 =09 Pma 2 5 . E ; Jd


10/19



P máma

Po#!n(aa(#'a

o ;D ;< B ;DG$ado" !l!(#$(o".

8/. N9 1D.- Cu$'a d! la o#!n(a a(#'a !n máquna" ")n($ona" d! olo" "al!n#!"

U#l>ando un $o/$ama (omu#a(onal a$a o%#!n!$ la P #o#al d! la" máquna". Ad!má" 7a(!$ lo" da/$ama" a"o$al!" a$a (a$/a" u$am!n#! ndu(#'a" 4;o (aa(#'a".

Q 2 * 5 . (o" . Id - 5 . "!n . Iq +

Q 2 5 . (o" * E - 5 (o" + ; Jd 5 . "!n . 5 . "!n ; Jq

Q 2 5 . E . (o" ; Jd - 5 . (o" ; Jd 5 . "!n ; Jq

Q 2 5 . E . (o" ; Jd - 5 * (o" ; Jd "!n ; Jq +

) 5 . E . #$s 7 8" - 5 4 3 8/ . #$s4 : 8" . sen4 6 7 8/ . 8"

@!!nd! d! la !(- @!!nd! d! la "al!n(a d!l ($(u#o ndu(#o$#a(on d! la máquna.

Cuando Jd Jq * Lu!/o Jq . (o" Jd . "!n 2 Jd . "!n +Lu!/o la nu!'a !(ua(,n !":

) 3 5. E 7 8" 6. #$s - 3 5 4 7 8/ 6 Sen4

Lu!/o " anal>amo" la" 'a$a(on!" d!l án/ulo #!n!mo":

S 2 0 Q 2 Qma S 2 =09 Q 2 - 5 ; Jq

Ha/a un $o/$ama (omu#a(onal o%#!n!$ la Q #o#al d! la" máquna". Ad!má" 7a(!$ lo" da/$ama" a"o$al!" a$a (a$/a" u$am!n#! ndu(#'a" 4;o (aa(#'a".

V²sen2

Xd . X


11/19



'a$ Q máma

- ;< - ;D o ;D ;<G$ado" !l!(#$(o".

8/. N9 1.- Cu$'a d! la o#!n(a $!a(#'a !n máquna" ")n($ona" d! olo" "al!n#!"

Pr$+&ema .- Un /!n!$ado$ d! olo" "al!n#!" d! 1


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MAQUINAS SINCRONAS HUBER MURILLO MANARIQUE PAGE 1<

Pd !" la o#!n(a qu! d!!nd! d! la #!n",n d! la $!d 4 d! la !(#a(,n d!l (amo.Pq !" la o#!n(a d!%do a la d!$!n(a !n la $!lu(#an(a d!l !n#$!7!$$o a la (ual no d!!nd!la !(#a(,n d! la máquna.

=.- M,)UINA SNCRONA DE PO(OS (I>OS

Pa$a $!al>a$ !l !"#udo d! la" máquna" ")n($ona" !" n!(!"a$o (on#a$ (on un ($(u#o!qu'al!n#! * /.N9 1D + dond! n#!$'!n/an lo" a$ám!#$o" ma" mo$#an#!" (omo "on: La$!a(#an(a ")n($ona 3 (ono$mada o$ la $!a(#an(a d! la máquna ma" la $!a(#an(a(o$$!"ond!n#! a la $!a((,n d! a$madu$a. En ""#!ma" d! o#!n(a "! u#l>an mod!lo" d!l($(u#o !qu'al!n#! qu! $!$!"!n#! la" (a$a(#!$)"#(a" !#!$na" d!l /!n!$ado$ (on una!a(##ud "u(!n#!.En la /. N9 1D od!mo" '"ual>a$ !l mod!lo ad!(uado *a+ 4 !l da/$ama a"o$al *%+ qu! no"'an a !$m#$ $!al>a$ !l anál"" d! la máquna ")n($ona. A") m"mo "! d!%!n #!n!$ la"

"/u!n#!" (on"d!$a(on!" :

- R KKK J" R 0 * mo#'o o$ !l (ual "! d!"$!(a R +.

- !" !l án/ulo d! m!dan(a !n#$! J" 4 R . * 6 L +.

- 2 a$(. #an/. * J" ; R + =09.

- La J" Jd J q * Mu4 mo$#an#! +.5 L 09 !" la la #!n",n d! $!!$!n(a !n lo" #!$mnal!" d!l /!n!$ado$. S!ndo:

8 2 8MM $odu(da o$ la (o$$!n#! d! (amo I.8a 2 8MM $odu(da o$ la (o$$!n#! d! a$madu$a I *!"#a#o$ , ndu(do +.8 2 8MM $!"ul#an#! !n !l !n#$!7!$$o.J" 2 Ja J. 2 JdR 2 R!""#an(a d! a"! d! lo" a$$ollam!n#o".

2 An/ulo !n#$! 5 ! I.

2 An/ulo !n#$! E 4 5.-

Jd 2 J"I * % + @a/$ama a"o$al E

Ja J R 8a I.Ja

E E# 5 8 8 E#

5 I.J

* a + C$(u#o !qu'al!n#! I.RI

8/. N9 1F.- R!$!"!n#a(,n d!l ($(u#o !qu'al!n#! 4 da/$ama a"o$al o$ a"! d! la"máquna" ")n($ona" d! olo" l>o".An&ss "e &a p$ten#a "e &as m/unas s0n#r$nas "e p$&$s &?$s.- Pa$a 7a(!$ lad!du((,n ma#!má#(a d! la" !(ua(on!" d! o#!n(a d! la" máquna" d! olo" l>o"u#l>a$!mo" !l mod!lo 4 da/$ama '!(#o$al d! la /. N9 1D.


13/19


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MAQUINAS SINCRONAS HUBER MURILLO MANARIQUE PAGE 1D

& * E ; Jd + "!n - * E ; Jd + (o" "!n - * 5 . E ; Jd + "!n V

S 2 3 5 . E 7 8" 6 sen 9 ; 3 E 4 7 8" 6 - 3 5 . E 7 8" 6 #$s <

S P : 9 )

P mámaPo#!n(aa(#'a

;D ;< B ;D

8/. N9 1.- Cu$'a d! la o#!n(a a(#'a !n máquna" ")n($ona" d! olo" l>o".

- - B ;D - ;< - ; D o ;D ;< B ;D

8/ N9 1=.- Cu$'a d! la o#!n(a $!a(#'a !n máquna" ")n($ona" d! olo" l>o".

B.- P$ten#a en +$rnes genera"a p$r &a m/una es 5 2 5 L 0

P máma

;D ;< B ;D

8/. N9 o".


15/19



S 2 E . I 2 P & Q

S 2 5 * E ; Jd + "!n & * E ; Jd + (o" - * 5 ; Jd + V

S 2 3 5 . E 7 8" 6 sen 9 ; 3 5 . E 7 8" 6 #$s - 3 5 4 7 8" 6 <

S P : 9 )

Q máma

- -B ;D - ;< - ;D o ;D ;< B ;D

8/ N9 o".

TareaI.- Ha/a un $o/$ama (omu#a(onal o%#!n!$ la P 4 Q #o#al!" d! la" máquna" ")n($ona"

d! olo" l>o" !n %o$n!" d! la máquna 4 !n la #!n",n ndu(da n#!$na.II.- Ad!má" 7a(!$ lo" da/$ama" a"o$al!" a$a (a$/a" u$am!n#! ndu(#'a" 4;o

(aa(#'a".III.- Pr$+&ema.- Un /!n!$ado$ d! olo" l>o" * (!n#$al San#a Ro"a + !"#a #$a%a&ando !n

(ond(on!" nomnal!" a un S 2 10 M'a.3 F0 H> 3 1B. ' 3 8P 2 0.Con Jd 2 11.a$ lo" (ál(ulo" !n %o$n!" d!l al#!$nado$ :

1.- La Pma 3 Qma 4 !l ma.


16/19


MAQUINAS SINCRONAS HUBER MURILLO MANARIQUE PAGE 1F

.- OPERACIN DE (A MRS CON REACTANCIA SNCRONA CONSTANTE

I.J"

E 5 E 5 5

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a + 8a(#o$ d! o#!n(a un#a$o. Ca$/a" u$am!n#! $!""#'a".

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* % + 8a(#o$ d! o#!n(a ndu(#'o * ( + 8a(#o$ d! (a$/a (aa(#'oa#$a"ado E 5 ad!lan#ado E K 5.

8/. N9


17/19



Pa$a un a(#o$ d! o#!n(a un#a$o 4 !n a#$a"o "! $!"!n#a "!m$! una (a)da d! #!n",n(uando "! n($!m!n#a la (a$/a /.N9 1 * a +.P!$o (uando "! #!n! !l a(#o$ d! o#!n(a !n ad!lan#o la $!/ula(,n !" (!$o 4 mu(7a" '!(!"(uando "! aum!n#an la (a$/a la $!/ula(,n $!"ul#a "!$ n!/a#'a /. N9 1 * % +.

8nalm!n#! od!mo" d!($ qu! un /!n!$ado$ !" "ea& (uando la R!/ula.* + 0.

ad!lan#o5 * + 0.0 ad!lan#o


18/19



@ond! E1 4 Em "on la" #!n",n!" d! la" a$m,n(a" undam!n#al 4 o$d!n m $!"!(#'am!n#!.

8/.N9


19/19


MAQUINAS SINCRONAS HUBER MURILLO MANARIQUEPAGE 1=

8/.N9

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