{"id":2110,"date":"2005-04-14T20:20:32","date_gmt":"2005-04-15T03:20:32","guid":{"rendered":"https:\/\/brainfiller.com\/?p=2110"},"modified":"2025-11-19T09:40:24","modified_gmt":"2025-11-19T16:40:24","slug":"x-r-ratio","status":"publish","type":"post","link":"https:\/\/brainfiller.com\/es\/electrical-safety-codes-and-standards\/x-r-ratio\/","title":{"rendered":"Relaci\u00f3n X\/R"},"content":{"rendered":"
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\"Short<\/a>Antecedentes de X\/R<\/strong><\/h2>

Los c\u00e1lculos de cortocircuito son en realidad una versi\u00f3n elaborada de la Ley de Ohm. Uno de los componentes clave en el proceso de c\u00e1lculo es determinar la impedancia total del circuito desde la fuente de suministro, pasando por el sistema de transmisi\u00f3n, los transformadores y los conductores, hasta el punto en cuesti\u00f3n, como un panel o una centralita. Las impedancias de los distintos elementos del circuito tienen resistencia y reactancia y, a menudo, se las denomina \u201cimpedancia compleja\u201d o \u201cnotaci\u00f3n polar\u201d. Un valor de impedancia compleja se puede representar gr\u00e1ficamente trazando la resistencia a lo largo del eje horizontal y la reactancia a lo largo del eje vertical. La magnitud total de la impedancia es la hipotenusa del tri\u00e1ngulo resultante. La relaci\u00f3n X\/R es la cantidad de reactancia X dividida por la cantidad de resistencia R, que tambi\u00e9n es la tangente de un \u00e1ngulo creado por la reactancia y la resistencia en un circuito.<\/p>

Al calcular corrientes de cortocircuito, normalmente hay muchas impedancias que deben sumarse. El mes pasado, determinamos c\u00f3mo calcular la impedancia de fuente equivalente y agregarla a la impedancia de un transformador. Lo mantuve simple al sumar solo las magnitudes, es decir, agregamos 5,75% del transformador y 0,97% de la fuente e ignoramos los \u00e1ngulos y los componentes X y R individuales. Sin embargo, cada una de estas impedancias tiene una cantidad espec\u00edfica de reactancia y resistencia y una relaci\u00f3n X\/R (incluso cuando se calcula como un valor porcentual). El problema con sumar solo las magnitudes de las impedancias es que la impedancia total ser\u00e1 artificialmente alta, lo que dar\u00e1 lugar a una corriente de cortocircuito calculada m\u00e1s baja (e incorrecta). Esto tiene el potencial de crear una condici\u00f3n peligrosa si un c\u00e1lculo de cortocircuito incorrecto conduce a una aplicaci\u00f3n incorrecta de la protecci\u00f3n contra sobrecorriente. Los diagramas a continuaci\u00f3n ilustran una comparaci\u00f3n de la suma de impedancias que incluye la magnitud y el \u00e1ngulo frente a la suma de las magnitudes \u00fanicamente.<\/p>

Fuente de datos X\/R<\/strong><\/h2>

Tomemos el siguiente ejemplo en el que queremos sumar la impedancia de la fuente de 0,97% y una relaci\u00f3n X\/R de 15 a la impedancia del transformador de 5,75% y una relaci\u00f3n X\/R de 7. Antes de comenzar, \u00bfde d\u00f3nde provienen estas relaciones X\/R? Muy a menudo, las relaciones X\/R son dif\u00edciles de obtener. La relaci\u00f3n X\/R del transformador generalmente no est\u00e1 disponible a menos que tenga buenos datos de prueba obtenidos cuando el transformador se construy\u00f3 y prob\u00f3 originalmente. En ausencia de datos de prueba reales, una buena fuente de datos X\/R "razonables" es la norma IEEE Std. 242 - IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems. Este libro contiene una tabla de relaciones X\/R sugeridas basadas en el tama\u00f1o y voltaje en kVA del transformador. Los valores se basan en ANSI C57, que es la norma predominante para transformadores. Seg\u00fan la norma IEEE Std. 242, un transformador de 1500 kVA con una tensi\u00f3n secundaria < 600 voltios y una tensi\u00f3n primaria de hasta 15.000 voltios, la relaci\u00f3n X\/R sugerida es 7,0. Esto significa que hay 7 veces m\u00e1s reactancia que resistencia en la impedancia del transformador.<\/p>

La relaci\u00f3n X\/R de la fuente puede ser a\u00fan m\u00e1s dif\u00edcil de determinar. Muchas empresas de servicios p\u00fablicos pueden proporcionar corrientes de cortocircuito, impedancias y relaciones X\/R, lo que facilita el c\u00e1lculo. Sin embargo, muchas empresas de servicios p\u00fablicos solo pueden proporcionar la corriente de cortocircuito. El mes pasado, nuestro problema indicaba que la corriente de cortocircuito de la fuente (de la empresa de servicios p\u00fablicos) era de 6740 amperios a 13,2 kV y no se proporcion\u00f3 ninguna relaci\u00f3n X\/R. \u00bfC\u00f3mo debemos manejar la relaci\u00f3n X\/R de la fuente cuando no se proporciona? Una suposici\u00f3n muy com\u00fan es utilizar una relaci\u00f3n X\/R de entre 12 y 15. La tangente inversa (Tan-1) de 15 es 86,1859 grados, que son casi 90 grados. Esto generalmente se considera una suposici\u00f3n conservadora, ya que agregar una impedancia con un \u00e1ngulo pronunciado a una impedancia con un \u00e1ngulo poco profundo producir\u00e1 una impedancia general con una magnitud menor.<\/p>

Ejemplo de c\u00e1lculo<\/strong><\/h2>

En otro art\u00edculo calculamos una corriente de cortocircuito de 26.845 amperios. Este mes volveremos a analizar ese ejemplo e incluiremos los \u00e1ngulos X\/R. Los nuevos resultados de corriente de cortocircuito ser\u00e1n ligeramente superiores. Las f\u00f3rmulas principales para este ejemplo son:<\/p>

\u0398 = Arctan X\/R
X = Seno \u03b8 * Z
R = Cos \u03b8 * Z o X \/ (X\/R)
Fuente R y X
%Z = 0,97 y X\/R = 15
Tangente inversa 15,00 = 86,1859\u00b0
X = Pecado 86,1859 * 0,97% = 0,9978 * 0,97% = 0,9679%
R = cos 86,1859 * 0,97% = 0,0665 * 0,97% = 0,0645%<\/p>

Transformador R y X
%Z = 5,75 y X\/R = 7
Tangente inversa 7,00 = 81,8699\u00b0
X = Seno 81,8699*5,75 % = 0,9899 * 5,75 % = 5,6919%
R = cos 81,8699 * 5,75 % = 0,1414 * 5,75 % = 0,8131%<\/p>

Resistencia total R de la fuente y del transformador
Rtotal = 0,0645% + 0,8131%
Rtotal = 0,8776%<\/p>

Reactancia total X de la fuente y del transformador
Xtotal = 0,9679% + 5,6919%
Xtotal = 6.6598%<\/p>

Impedancia total Z de la fuente y del transformador<\/p>

Ztotal = ra\u00edz cuadrada ( Rtotal2 + Ztotal2)
Ztotal = ra\u00edz cuadrada (0,8776%2 + 6,6598%2)
Ztotal = 6,7174%<\/p>

En otro art\u00edculo solo agregamos las magnitudes de las impedancias y el resultado fue:
6.72% = 0.97% + 5.75%<\/p>

Si dividimos la impedancia en los componentes R y X, la impedancia correcta es 6,7174%. Esto es tan parecido al 6,72% original del mes pasado que podr\u00eda pensar que no vale la pena el esfuerzo adicional. En el caso en el que las relaciones X\/R dan \u00e1ngulos cercanos, hay poca diferencia entre los dos m\u00e9todos, como en nuestro caso, donde tenemos una X\/R de 15, que es 86,1859\u00b0, y 7, que es 81,8699\u00b0. Sin embargo, en la mayor\u00eda de los casos, suele haber una mayor diferencia en los \u00e1ngulos, como cuando se tienen en cuenta transformadores m\u00e1s peque\u00f1os y conductores de bajo voltaje.<\/p>

Con bastante frecuencia, la suma de una impedancia de un X\/R y un \u00e1ngulo altos con una impedancia de un X\/R y un \u00e1ngulo bajos puede generar un error grave y generar valores de cortocircuito calculados artificialmente bajos. Esta es una situaci\u00f3n potencialmente peligrosa, por lo que se debe tener en cuenta la relaci\u00f3n X\/R. La relaci\u00f3n X\/R tambi\u00e9n se utiliza para determinar cu\u00e1nta asimetr\u00eda hay en una forma de onda de cortocircuito, lo cual es importante para realizar pruebas de cortocircuito.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Background of X\/R Short circuit calculations are actually just an elaborate version of Ohm\u2019s Law. One of the key components in the calculation process is to determine the total impedance of the circuit from the utility\/source, through the transmission system,…<\/p>","protected":false},"author":2,"featured_media":12712,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"elementor_theme","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"footnotes":"","_tec_slr_enabled":"","_tec_slr_layout":""},"categories":[404,403,407,408],"tags":[],"class_list":["post-2110","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-electrical-power-system-design-and-analysis","category-electrical-safety-codes-and-standards","category-emerging-electrical-safety-technologies-and-trends","category-short-circuit-analysis-and-fault-current-calculations"],"acf":[],"yoast_head":"\nThe 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