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1.10 CANTIDADES EN POR UNIDAD 23
.-. Se usan las ecuaciones (1.37), (1.39) y (1.40) para calcular P, Q y IS 1 en redes trifásicas balanceadas ya que, generalmente, se conocen el voltaje línea a línea, la corriente de línea y el factor de potencia cos O,. Cuando se habla de un sistema trifásico se suponen, a menos que se indique otra cosa, condiciones balanceadas; y se entenderá que los términos voltaje, co- rriente y potencia se refieren, a menos que se identifiquen de otra forma, al voltaje línea a línea, la corriente de línea y la potencia trifásica total, respectivamente.
Si la carga está conectada en A, el voltaje a través de cada impedancia es el voltaje línea a línea, y la magnitud de la corriente que la atraviesa es la de la corriente de línea dividida entre la 6, o,
IILI 151 = iVLi y lIpl = - (1.41) \/3 La potencia total trifásica es
y al sustituir los valores de IVp 1 e IIp 1 de la ecuación (1.41), en esta ecuación, se obtiene
P = fiIvLI I Z ~ I C O S e, (1.43)
que es idéntica a la ecuación (1.37). Se deduce que las ecuaciones (1.39) y (1.40) son tam- bién válidas sin importar si una carga en particular está conectada en A o en Y.
CANTIDA DES EN POR UNIDAD
Las líneas de transmisión de potencia se operan a niveles en los que el kilovolt (kv) es la unidad más conveniente para expresar sus voltajes. Debido a que se transmite una gran cantidad de potencia, los términos comunes son los kilowatts o megawatts y los kilovoltamperes o megavoltamperes. Sin embargo, estas cantidades, al igual que los amperes y los ohms, se expresan frecuentemente en por ciento o en por unidad de un valor base o de referencia especificado para cada una. Por ejemplo, si se selecciona una base de voltaje de 120 kv, los voltajes de 108, 120 y 126 k v equivaldrán a 0.90, 1.00 y 1.05 en por unidad o a 90, 100 y 105%, respectivamente. El valor en por unidad de cualquier cantidad se define como la relación de la cantidad a su base y se expresa como un decimal. La relación en por ciento es 100 veces el valor en por unidad. Ambos métodos de cálculo, porcentual y en por unidad, son más simples y más informativos que los volts, los amperes y los ohms reales. El método en por unidad tiene una ventaja sobre el porcentual: el producto de dos cantidades expresadas en por unidad se expresa tambiCn en por unidad, mientras que el producto de dos cantidades dadas en por ciento se debe dividir entre 100 para obtener el resultado en por ciento.
El voltaje, la corriente, los kilovoltamperes y la impedancia están relacionados de tal manera que la selección de los valores base para cualquiera dos de ellos determina la base de los dos restantes. Si se especifican los valores base de corriente y de voltaje, se pueden determinar las bases de impedancia y de kilovoltamperes. La impedancia base es aquella que tiene una caída de voltaje igual a la del voltaje base, cuando la corriente que fluye a travCs de
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