Download - Maquinas Eléctricas Chapman
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CONTENIDO
Prefacio a la segunda edicion Prefacio a la primera edici6n
1 Introduccion a 10s principios de las rnaquinas
I - 1 Las maquioas electricas y los transformadores en la vida cotidiana 1-2 Nota sobre las unidades 1-3 Movimiento giratorio, Ley de Newton y relaciones de potencia 1-4 Campo magnktico 1-5 Ley de Faraday. Voltaje inducido por un campo magnktico variable en el tiempo 1-6 Produccicin de fuerza inducida sobre un conductor 1-7 Voltaje inducido sobre un conductor movil en un calnpo magnetic0 1-8 Resumen
2 Transformadores
Por que los transformadores son tan importantes en la vida rnoderna Tipos y construccion de transformadores El transformador ideal Teoria del funcionamiento de 10s transformadores monofasicos reales Circuj to equivalen te de un transformador Sistema de medicion por un~dad Regulaci6n de voltaje y la eficiencia del transformador Transformador con dertvaciones y reguladores de voltaje El autotransformador Transformadores tri fhsicos
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en su direcci6n en el circuit0 original, si el punteado de las bobinas de un Iado del transfor- mador esta a1 contrario del punteado de las bobinas del otro lado.
La solucion de circuitos que contengan transformadores ideales se ilustra con el ejemplo siguiente.
Ejemplo 2-1. Un sistema de potencia monofasico consta de un generador de 480-V 60-Hz que suministra una carga Z,,,, = 4 + j 3 fl a traves de una linea de transmision con una impedancia de Z,,,,, = 0.18 + j0.24 a. Conteste las siguientes preguntas sobre este sistema. a) Si el sistema es exactamente corno se acaba de describir iCu6l ser6 el voltaje sobre la
carga? (figura 2-6a), i,Cuales seran las perdidas en la linea de transmisibn? b) Supongase que un transformador elevador de 1 : 10 esta colocado en el extremo del generador
de la linea de transrnisidn y a un transformador reducidor de 10: 1 est6 colocado a1 extremo de carga de la linea (figura 2-6b). ~ C u a l sera el voltaje en la carga ahora?
Solucion - a) La figura 2-6a ilustra el sistema de potencia sin transformadores. Aqui IG = Ilinea -
I,,,,,. La corriente de la linea en este sistema esta dada por
FIGURA 2-6 El sistema de fuerza del ejemplo 2-1, a) sin transformadores y b) con transformadores en 10s extremos de la linea de trasmision.
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TRANSFORMADORES
- - 480 LO" 4.18 + j3 .24
Por esto, el voltaje de la carga es
y las perdidas en la linea son
b) La figura 2-6b rnuestra el sisterna de potencia con 10s transformadores. Para analizar este sistema es necesario convertirlo en un nivel de voltaje comun. Esto se hace en dos pasos:
1. Eliminar el trasformador T, trasladando la carga a1 nivel de voltaje de la linea de trasrnisi6n.
2. Elirninar el trasformador T, trasladando 10s elementos y la carga equivalente a1 voltaje de la linea de trasmision a1 lado de la fuente de alirnentaci6n.
El valor de la irnpedancia reflejada de la carga, en el voltaje del sisterna de trasmisibn, es
La irnpedancia total a1 nivel de la linea de trasmisi6n es entonces
El circuit0 equivalente se muestra en Ia figura 2-7a.
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1- I I circuito equivalente
circuito equivalente
b) FIGURA 2-7 a) Sistema con la carga referida a1 nivel de voltaje del sistema de transmisi6n. b) Sistema con la carga y la lilrea dc tlas11lisi611 refelidas a1 l l i v c l Jr vultaje deI generador.
La impedancia total a1 nivel de la linea de trasmisian (z;~,,,, + z;,,,,) se refleja ahora a travCs de TI a1 nivel de voltaje de la fuente
Obs6wcse quc zLarga = 4 + j 3 y Zlirea = 0.0018 + j 0,0024 a. El circuito equivalente resultante se muestra en la Figura 2-76. La corriente del generador es
Conociendo la corriente I,, podemos ahora devolvernns y encnntrar I,i,,,, e I,,,~,,. Devnlvikn- donos a travks de T I , encontramos
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TRANSFORMADORES
= h(Y5.94 L - 3b.88" A)
= 9.594 L -36.88" A
Regresando a traves de T2, nos da
Ahora nos es posible contestar las preguntas hechas originalmente. El voltaje de la carga es
y las perdidas en la linea son
- Pp*rdids - (llinea)2 Rlinea
= (9.594 A)2(0. 18 Q)
= 16.7 W
N6tese que elevando el voltaje de la trasmision del sistema de potencia se reducen las pkrdidas de trasmision en un factor cercano a 90. TambiCn la caida de voltaje en la carga es mucho menor en el sistema con trasformadores que en el sistema sin trasformadores. Este simple ejemplo nos ilustra graficamente las ventajas de usar lineas de trasmision de mayores voltajes, asi como la extraordinaria importancia de 10s trasformadores en 10s sistemas de potencia modernos.
2-4 T E O R ~ A DEL FUNCIONAMIENTO DE LOS TRASFORMADORES MONOFASICOS REALES
Los trasformadores ideales descritos en la seccion 2-3, nunca se pod& construir en realidad. Lo qut: pucde co~lstluirse son trasformadores reales; dos o mas bobinas de alambrc, fisicamcntc envueltas alrededor de un nucleo ferromagnktico. Las caracteristicas de un trasformador real se aproximan mucho a las de un trasformador ideal, pero s610 hasta un cierto grado. En esta secci6n estudiaremos el comportamiento de 10s trasformadores reales.
Para entender el funcionamiento de un trasformador real, refiramonos a la figura 2-8. Esta nos muestra un trasformador que consiste en dos bobinas de alambre enrrolladas
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74
El factor de potencia se da por
FP = cos tl = psc vsc Is,
y esta retardado. Asi el angulo de corriente es negativo, y eI angulo de impedancia 0 es positivo:
0 = cos- , PSC (2-50) vsc Is,
Entonces,
La impedancia serie Z,, es igual a
Es posible clelcrrriir~ar la i~r~yeclaricia suit: lolal, rcrerida a1 ladu y r i ~ ~ l a ~ i u , usalldu esta tecnica, pero no hay una manera facil de dividir la impedancia serie entre componentes primario y secundario. Afortunadamente, tal separaci6n no es necesaria para resolver proble- mas normales .
Estos mismos ensayos tambien pueden realizarse en el lado secundario deI transfor- mador, si se piensa que es mas conveniente hacerlos, bien por 10s niveles de voltaie o por cualquier otra raz6n. Si 10s ensayos se hacen en el lado secundario, 10s resultados, natural- mente, daran las impedancias del circuito equivalente referidas a1 lado secundario del trans- formador y no a1 primario.
Ejemplo 2-2. Se necesita deterrninar las impedancias del circuito equivalente de un transfor- mador de 20-kVA, 8,0001240 V, 60-Hz. Los ensayos de circuito abierto y de corto circuito se realizaron en el lado primario del transformador y se tomaron 10s siguientes datos:
- - - - - - - - - -
Ensayo de circuit0 abierto Ensayo de cortocircuito (En el primario) (En el primario)
Encuenrre la impedancia del circuito equivalente aproximado, referido a1 lado primdriu y dibuje el esquema de tal circuito.
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Solucion. El factor de potencia durante el ensayo de circuito abierto es
400 W = cos 0 =
(8,000 V)(0.214 A)
= 0.234 atrasado
La admitancia de excitaci6n se da por
Entonces ,
R,. = = 1 5 9 k O 0 .OW0063
"YM = I
0.0000261 = 38.4 kn
El factor de potcncia durantc el cnsayo dc corto circuito es
psc FP = cost) = - vsc 1sc
= cos 0 = 240 W
(489 V)(2.5 A)
= 0.196 atrasado
La impedancia serie se da por
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FIGURA 2-21 1 El circuit0 equivalente del ejemplo 2-2.
Entonces, las resistencias y reactancias equivalentes son
En la figura 2-21 se muestra el circuito equivalente simplificado resultante.
2-6 SISTEMA DE MEDICION POK-UNIDAD
Corno se ilustro en el ejemplo 2-1. relativamente simple. resolver circuitos que contengan transformadores puede llegar a ser una operacion absolutamente tediosa por la necesidad de trasladar a un solo nivel, todos 10s niveles de voltaje en 10s diferentes lados de 10s transfor- madores del sisterna. Solarnente hasta despues de que este paso se ha dado, se puede calcular el sistema para sus voltajes y corrientes.
Hay otro enfoque para resolver circuitos que contengan transformadores, que elirnina la riecesidad de una conversi6n explicita del nivel de voltaje de cada uno de 10s transtorma- dores del sistema. En su lugar , las conversiones requeridas se manejan automaticamente por el mCtodo en si, sin que el usuario tenga que preocuparse nunca por las transformaciones de irnpedancia. Puesto que tales transformaciones de impedancia pueden evitarse, 10s circuitos que contengan muchos transformadores pueden resolverse facilrnente, con menos probabili- dades de cometer un error. Este rnetodo de calculo se conoce como el vivt~rnn d e medici6n por-unidad (pu).
Hay todavia otra ventaja en el sistema por-unidad, que es absolutarnente importante para la maquinaria elkctrica y 10s transformadorcs. Como cl tamafio dc una mdquina o un transformador varia, sus irnpedancias internas varian arnpliarnente. Asi, una reactancia de circuito primario de 0.1 R, podria ser un nurnero enorrnemente alto para un transformador o extremadarnente bajo para otro; todo depende del voltaje del aparato y de su capacidad de potencia. Sin embargo, resulta que en un sistema por-unidad, relacionado con su capacidad de potencia, las impedancias de la maquina y el transformmador caen dentro de margenes bastante estrechos, para cada tipo y construction de aparato. Este hecho se convierte en un recurso rnuy util para verificar la solucion de 10s problemas.
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