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Determinación de las curvas de cargabilidad para la central Hidroeléctrica San Carlos
Sebastian Cano Rendon
Tutores:
Clara Rosa Rojo Ceballos Carlos Alberto Serna Machado
Universidad Nacional de Colombia Facultad de Minas, Escuela de ingeniería Eléctrica Electr!nica "SA#EN S$A$ E$S$%$ Medellín, Colombia &'() (
Dedicatoria
A mis *adres+
Luis Ángel Cano Blandón y Aura Rendon Calle por darme la vida, ser un ejemplo y enseñarme los valores que hoy me constituyen como persona.
A mi hermano+
Luis elipe Cano Rendon por enseñarme a a!rir mi mente y no cerrarme a "nicas posi!ilidades.
A mi novia+
#uliana Restrepo $ri!e por ser el amor y el apoyo incondicional en los momentos m%s di&'ciles de este proceso y darme la &uer(a para terminarlo.
A mis tutores+
Carlos Al!erto )erna *achado por ser m%s que un tutor utor,, un amig amigo o y Clara lara Rosa osa Rojo Rojo Ce! Ce!allo alloss por por !rin !rinda darm rme e el apoy apoyo o y su disp dispos osic ició ión n de ense enseñan ñan(a (a siempre.
A mis com*aeros+
+racias a todos mis amigos por acompañarme a lo larg largo o de mi carr carrer era a y los los nuev nuevos os que que hice hice en ese ese proceso.
A -ios+
or todo-
&
Dedicatoria
A mis *adres+
Luis Ángel Cano Blandón y Aura Rendon Calle por darme la vida, ser un ejemplo y enseñarme los valores que hoy me constituyen como persona.
A mi hermano+
Luis elipe Cano Rendon por enseñarme a a!rir mi mente y no cerrarme a "nicas posi!ilidades.
A mi novia+
#uliana Restrepo $ri!e por ser el amor y el apoyo incondicional en los momentos m%s di&'ciles de este proceso y darme la &uer(a para terminarlo.
A mis tutores+
Carlos Al!erto )erna *achado por ser m%s que un tutor utor,, un amig amigo o y Clara lara Rosa osa Rojo Rojo Ce! Ce!allo alloss por por !rin !rinda darm rme e el apoy apoyo o y su disp dispos osic ició ión n de ense enseñan ñan(a (a siempre.
A mis com*aeros+
+racias a todos mis amigos por acompañarme a lo larg largo o de mi carr carrer era a y los los nuev nuevos os que que hice hice en ese ese proceso.
A -ios+
or todo-
&
Introducción
-ado el re.uerimiento com*rendido en el cuarto */rra0o de la */gina 1 del acuerdo C2N No$ 345 6Consejo Nacional de 2*eraci!n7 cita .ue+ 89os agentes generadores de *lantas des*achadas centralmente deben re*ortar al CN- la curva de carga con las restricciones de cada unidad la característica de cada uno de los limitadores en un *lano %:, *ara tensi!n nominal en bornes del generador;, se crea la necesidad de validar actualiare Mat9ab, en el cual se introducen los datos necesarios *ara reali
4
Tabla de contenido
-edicatoria$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$& "ntroducci!n$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$4 ?abla de contenido$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 1 ?abla de ilustraciones$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 3 Ca*ítulo ($ Estado del arte$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ (' Determinación de curvas de cargabilidad para maquinas sincrónicas. $$$$$$$$$$$$$$$$$$(( Ca*ítulo &$ Marco te!rico$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(5 1. aquina s!ncrona.$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(5 1.1
$enerador s!ncrono de polos lisos. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&'
%.
$enerador s!ncrono de polos salientes. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&4
&.
"stabilidad de la maquina s!ncrona. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&)
'. Determinación de par(metros para generadores utili)ados en la elaboración de la curva de cargabilidad *+ d , +q-.$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&) '.1
Curva de saturación o circuito abierto. ................................................25
'.#
!nea de entre/ierro ............................................................................26
'.%
Curva de cortocircuito. .......................................................................26
'.&
Reactancia s!ncrona de e0e directo + d..................................................27
'.'
Reactancia s!ncrona de e0e de cuadratura + q........................................27
Ca*ítulo 4$ -iseo de so0t>are *ara elaborar la curva de cargabilidad de una ma.uina sincr!nica$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$& 1. Curva de cargabilidad generador s!ncrono. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$& #. Curva de cargabilidad generador de polos lisos $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$& #.1 (ima corriente de armadura ................................................................28
%.
#.#
!mite de m(ima potencia activa *de turbina- ......................................29
#.%
!mite de corriente m(ima en el rotor .................................................30
#.&
!mite de estabilidad teórico , pr(ctico ................................................31
#.'
!mite de potencia m!nima. ..................................................................32
Curva de cargabilidad generador de polos salientes $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$44 %.1
(ima corriente de armadura............................................................33
%.#
!mite de m(ima potencia activa *de turbina- ......................................33
%.%
!mite de corriente m(ima en el rotor .................................................34
%.&
!mite de estabilidad teórico , pr(ctico ................................................34
1
&.
%.'
!mite de potencia m!nima. ..................................................................35
%.2
!mite de corriente m!nima de ecitación. ............................................35
3alidación de resultados. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$43 &.1
aquina s!ncrona de la central /idroeléctrica Hunico. ..........................36
&.# aquina s!ncrona de polos lisos de Tesis Determinación teórica , eperimental de la capacidad de potencia reactiva de generadores s!ncronos. 38 &.% aquina s!ncrona de polos salientes de Tesis Determinación teórica , eperimental de la capacidad de potencia reactiva de generadores s!ncronos. 39 '.
anual de 4suario. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1(
Ca*ítulo 1$ Calculo de *ar/metros curvas de cargabilidad *ara las m/.uinas de la central =idroeléctrica San Carlos$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$11 1. Calculo de par(metros.$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$11 #. Caculo curvas de cargabilidad central Hidroeléctrica San Carlos. $$$$$$$$$$$$$$$$$$)5 #.1
Curva de cargabilidad seg5n datos del 6abricante en p.u. , valores reales.
60
%.
#.#
Curva de cargabilidad unidad 1 en p.u. , valores reales. .......................62
#.%
Curva de cargabilidad unidad # en p.u. , valores reales. .......................64
#.&
Curva de cargabilidad unidad % en p.u. , valores reales. .......................66
#.'
Curva de cargabilidad unidad & en p.u. , valores reales. .......................68
#.2
Curva de cargabilidad unidad ' en p.u. , valores reales. .......................70
#.7
Curva de cargabilidad unidad 2 en p.u. , valores reales. .......................72
#.8
Curva de cargabilidad unidad 7 en p.u. , valores reales. .......................74
#.9
Curva de cargabilidad unidad 8 en p.u. , valores reales. .......................76
n(lisis de resultados. $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$B5
Conclusiones$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ ' Re0erencias$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$& Ane@o ($ "n0orme de la central$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1 1. Con6ormación de la central $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1 #. "lementos principales de la central San Carlos $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1 #.1.
Trans6ormadores de puesta a tierra ................................................100
%.1#.
T5neles de cables , 6uniculares.....................................................100
Ane@o &$ Curvas de cargabilidad con E@cel$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$ ('(
3
Tabla de ilustraciones
"lustraci!n ( -iagrama 0undamental de un generador síncrono$ Fuente+ 6S<>ander, (5117 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(( "lustraci!n & Método *ara determinar limite *ractico de estabilidad$ Fuente+ 6S<>ander, (5117$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(& "lustraci!n 4$ #r/0ico de la curva de carga basado en el diagrama 0asorial$ Fuente+ 6S<>ander, (5117$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ (& "lustraci!n 1$ Curva de cargabilidad tí*ica en un generador síncrono$ Fuente 6Nilsson Mercurio, (5517$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ (4 "lustraci!n )$ Curvas de cargabilidad *ara generadores de di0erentes turbinas$ Fuente 6Elsamah, #oDaraju, Faried, &'('7$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(1 "lustraci!n 3$ Curva de Cargabilidad$ Fuente+ 6A, &'((7$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$() "lustraci!n B$ Curva de cargabilidad$ Fuente+ 6A, &''7$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$() "lustraci!n $ Curva de cargabilidad generador síncrono de *olos salientes$ Fuente+ 6A, &'((7$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(3 "lustraci!n 5$ entana *rinci*al del *rograma *ara gra0icar cartas de 2*eraci!n$ Fuente+ 6arrera Naranjo, &'(47$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(B "lustraci!n ('$ Estator generador central San Carlos$ Fuente 6"SA#EN, &'(17$$$$$$$$$$$$$$$$$(5 "lustraci!n (($ Ma.uina síncrona de *olos salientes *olos lisos$ Fuente 69alou@, &''(7$&' "lustraci!n (&$Circuito e.uivalente *or 0ase .ue muestra la 0em inducida en el devanado de armadura debida a la reacci!n de armadura$ Fuente 6#uru =i
"lustraci!n &$ Curva de cargabilidad generador *olos salientes$ Fuente elaboraci!n *ro*ia $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$45 "lustraci!n &5$ "nter0a< gr/0ica *rograma GCurvasG$ Fuente+ Elaboraci!n %ro*ia$$$$$$$$$$$$$$$1' "lustraci!n 4'$ %artes del so0t>are$ Fuente+ Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1( "lustraci!n 4($ alores de límite de tem*eratura en cabe
"lustraci!n )5$ Curva de cargabilidad unidad ) valores reales$ Fuente+ elaboraci!n *ro*ia con *rograma 8Curvas;$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$B' "lustraci!n 3'$ Curva de cargabilidad unidad 3 en *$u$ Fuente+ elaboraci!n *ro*ia con *rograma 8Curvas;$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ B( "lustraci!n 3($ Curva de cargabilidad unidad 3 valores reales$ Fuente+ elaboraci!n *ro*ia con *rograma 8Curvas;$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$B& "lustraci!n 3&$ Curva de cargabilidad unidad B en *$u$ Fuente+ elaboraci!n *ro*ia con *rograma 8Curvas;$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ B4 "lustraci!n 34$ Curva de cargabilidad unidad B valores reales$ Fuente+ elaboraci!n *ro*ia con *rograma 8Curvas;$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$B1 "lustraci!n 31$ Curva de cargabilidad unidad en *$u$ Fuente+ elaboraci!n *ro*ia con *rograma 8Curvas;$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ B) "lustraci!n 3)$ Curva de cargabilidad unidad valores reales$ Fuente+ elaboraci!n *ro*ia con *rograma 8Curvas;$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$B3 "lustraci!n 33$ 2rgani>>$scielo$org$coIimgIrevistasIeiaIn(1In(1a'0ig($gi0$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1 "lustraci!n 3$?orres de ca*taci!n$ Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$) "lustraci!n 35$ /lvula es0érica$ Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$3 "lustraci!n B'$ Canjilones de turbina e inectores$ Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$B "lustraci!n B($ Sistema de regulador de velocidad$ Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$$$$$$$$$B "lustraci!n B&$ ?urbina *elton Central =idroeléctrica San Carlos$ Fuente+ Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ "lustraci!n B4$ -evanado de armadura ma.uina San Carlos$ Fuente+ 6"SA#EN, &'(17$$$$5' "lustraci!n B1$ Rotor ma.uina San Carlos$ Fuente+ 6"SA#EN, &'(17$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$5( "lustraci!n B)$ "nterru*tores mono*olares de ma.uina San Carlos$ Fuente+ elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$5& "lustraci!n B3$ ?rans0ormador de *otencia San Carlos$ Fuente+ Elaboraci!n *ro*ia$$$$$$$$$54 "lustraci!n BB$ Cables de *otencia San Carlos$ Fuente+ Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$54 "lustraci!n B$ Subestaci!n *rinci*al San Carlos$ Fuente+ Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$51 "lustraci!n B5$ anco de baterías San Carlos$ Fuente+ Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$$$5) "lustraci!n '$ Com*resores de aire San Carlos$ Fuente+ Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$53 "lustraci!n ($ "ntercambiador de calor San Carlos$ Fuente+Elaboraci!n *ro*ia$$$$$$$$$$$$$$$5B "lustraci!n &$ -uctos de conducci!n de aire *ara cabinas de trans0ormaci!n$ Fuente Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$5B "lustraci!n 4$ omba de aceite cojinete in0erior$ Fuente+ Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$5 "lustraci!n 1$ *arte su*erior de ma.uina San Carlos$ Fuente+ Elaboraci!n *ro*ia$$$$$$$$$$55 "lustraci!n )$ ?Hnel de cables 0unicular San Carlos$ Fuente+ Elaboraci!n *ro*ia$$$$$$$$$$55 "lustraci!n 3$"nicio *rograma curvas de cargabilidad con E@cel$ Fuente elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$('( "lustraci!n B$ "nter0a< *ara c/lculo de curva de cargabilidad con E@cel de ma.uina con *olos salientes$ Fuete elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$('&
5
"lustraci!n $"nter0a< *ara c/lculo de curva de cargabilidad con E@cel de ma.uina con *olos lisos$ Fuete elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$('4 "lustraci!n 5$ Ejem*lo curva de cargabilidad$ Fuente+ Elaboraci!n *ro*ia$$$$$$$$$$$$$$$$$$$$$('1