SIMULACIÓN DE SISTEMAS DE POTENCIA
Autor: Ing. Fernando Román Aríspe
COCHABAMBA – BOLIVIA BOLIVIA 2014
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ÍNDICE GENERAL Capítulo 1 ........................................................................................................ ................................................ .................................................................................... ............................ 1 NOCIONES BÁSICAS DE SISTEMAS DE POTENCIA ......................................................... 1 INTRODUCCIÓN .................................................. ........................................................................................................ ................................................................. ........... 1 REPRESENTACIÓN DEL SISTEMA DE POTENCIA ........................................................ 2 Diagrama unifilar ................................................ ...................................................................................................... ................................................................. ........... 2 Modelado del sistema de potencia ................................................. ....................................................................................... ...................................... 3 ELEMENTOS DEL SISTEMA DE POTENCIA ................................................................... ................................................. .................. 3 Líneas de d e Transmisión Tr ansmisión .................................................. ........................................................................................................ ........................................................ 4 Circuito equivalente de una u na línea de transmisión trans misión ........................................................ .......................................................... 6 Capacidad térmica de los conductores (Ampacidad) ...................................................... ................ ...................................... 7 Cálculos de los parámetros eléctricos con el Programa Pro grama LTSIM ..................................... .................................... . 7 Potencia natural de una línea de transmisión................................................................... 9 El Transformador de potencia ........................................................................................... .............................................. ............................................. 10 Circuito equivalente del transformador ......................................................................... ......................................................... ................ 10 Generador Síncrono ...................................................... ........................................................................................................... ..................................................... 11 Diagrama de capacidad del d el generador ................................................. ........................................................................... .......................... 12 Calculo del diagrama de capacidad del generador con el programa GENSIM ............. 13 EJERCICIOS RESUELTOS ....................................................................... ............... .................................................................................. .......................... 14 EJERCICIOS PROPUESTOS .................................................. ............................................................................................... ............................................. 21 Capítulo 2 SIMULACIÓN DE FLUJOS DE POTENCIA ............................................... ........................................................ ......... 24 FORMULACIÓN BÁSICA DE FLUJOS DE POTENCIA ................................................. ............. .................................... 24 CARACTERÍSTICAS DEL PROGRAMA DE FLUJOS DE POTENCIA POTENC IA.......................... 28 Modo de edición y ejecución del programa de flujos de potencia .................................... 28 CONTROL DE LAS CONDICIONES DE OPERACIÓN DEL SEP .................................. 35 Control de Potencia Reactiva y el Voltaje ......................................................... ......................................................................... ................ 35 MODELO DE CARGA DEPENDIENTE DEL VOLTAJE ................................................. 39
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FORMULACIÓN BÁSICA DE FLUJO DE POTENCIA ÓPTIMO (FPO) ........................ 52 DESPACHO ECONÓMICO .................................................... ................................................................................................. ............................................. 54 Características de las unidades Térmicas .......................................................................... .............................. ............................................ 54 Coordinación hidrotérmica ................................................................................................ 55 Unit Commitment ......................................................... .............................................................................................................. ..................................................... 55 Reserva Rotante .................................................. ........................................................................................................ ............................................................... ......... 55 CALCULO DEL DESPACHO ECONÓMICO CON EL E L PROGRAMA POWERWORLD 56 Modos de edición y ejecución ........................................................................................... ....................................................... .................................... 56 DETERMINACIÓN DEL COSTO MARGINAL DEL SISTEMA ..................................... ........... .......................... 57 DETERMINACIÓN DE LOS INGRESOS Y RETIROS VALORIZADOS VA LORIZADOS ....................... 57 ANÁLISIS DE SEGURIDAD (N-1) DEL SEP – SIMULACIÓN SIMULACIÓN DE CONTINGENCIAS ...................................................................................................................................... ................................................................................ ............................................................... ......... 58 Análisis de contingencias (N-1) ........................................................................................ ........................................... ............................................. 58 Criterio N-1 ....................................................................................................................... 59 Simulación de contingencias ............................................................................................. ...................................................................................... ....... 59 EJERCICIOS RESUELTOS ....................................................................... ............... .................................................................................. .......................... 61 EJERCICIOS PROPUESTOS .................................................. ............................................................................................... ............................................. 71 Capítulo 4 CÁLCULO DE CORTOCIRCUITOS .................................................................... ................................ .................................... 75 FORMULACIÓN BÁSICA DE CORTOCIRCUITO .......................................................... ...................... .................................... 75 REDES DE SECUENCIA DE LOS COMPONENTES DEL SEP ....................................... 77 Redes de secuencia del generador síncrono síncr ono ...................................................................... ...................................................... ................ 77 Redes de secuencia de los transformadores transf ormadores ....................................................... ....................................................................... ................ 79 Red de secuencia de d e Líneas de transmisión....................................................... transmisión ....................................................................... ................ 80 FALLAS SIMÉTRICAS: CÁLCULO DE CORTOCIRCUITO TRIFÁSICO ..................... 80 FALLAS ASIMÉTRICAS: CALCULO DE CORTOCIRCUITO MONOFÁSICO, BIFASICO Y BIFÁSICO A TIERRA T IERRA .................................................................................. .............................................. .................................... 81 Falla Simple de d e Línea a Tierra (Monofásico) .................................................... .................................................................... ................ 81 Falla de Línea a Línea (Bifásico) ...................................................................................... ......................................... ............................................. 82
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EJERCICIOS RESUELTOS ....................................................................... ............... .................................................................................. .......................... 89 EJERCICIOS PROPUESTOS .................................................. ............................................................................................... ............................................. 98 Capítulo 5 ESTABILIDAD DE SISTEMAS S ISTEMAS DE POTENCIA ............................................... 103 FORMULACIÓN BÁSICA DE LA ESTABILIDAD EN SISTEMAS S ISTEMAS DE POTENCIA .. 103 CARACTERÍSTICAS DEL PROGRAMA DE ESTABILIDAD ...................................... .............. ........................ 105 MODOS DE EDICIÓN ED ICIÓN Y EJECUCIÓN DEL PROGRAMA P ROGRAMA DE ESTABILIDAD ESTABI LIDAD ...... 105 ANÁLISIS DE ESTABILIDAD TRANSITORIA DE UN SEP ........................................ ................ ........................ 110 Modelo de la maquina síncrona para par a estudios de estabilidad .......................................... 110 Eventos Para la Simulación de la Estabilidad Transitoria Transitor ia ............................................... 112 ANÁLISIS DE ESTABILIDAD DE VOLTAJE DE UN SEP ........................................... 112 ANÁLISIS DE ESTABILIDAD DE FRECUENCIA DE UN SEP .................................... 116 Control de potencia Activa y la frecuencia ..................................................................... ........................... .......................................... 116 Control Primario de frecuencia............................................. frec uencia........................................................................................ ........................................... 118 Gobernador de Velocidad V elocidad ..................................................... ................................................................................................ ........................................... 119 EJERCICIOS RESUELTOS ....................................................................... ............... ................................................................................ ........................ 119 EJERCICIOS PROPUESTOS .................................................. ............................................................................................. ........................................... 127 Anexo A : CALCULO DE AMPACIDAD DE LÍNEAS AÉREAS DE TRANSMISIÓN .... 130 Anexo B : PARÁMETROS DE SECUENCIA CERO C ERO ........................................................... 136 B.1
Impedancia serie de secuencia cero .................................................. .......................................................................... ........................ 136
B2.
Capacitancia de secuencia cero ............................................... ................................................................................. .................................. 137
ANEXO C: DIAGRAMA DE BLOQUES DE LOS GENERADORES, EXCITATRICES Y GOBERNADORES EMPLEADOS EMP LEADOS EN POWERWORLD .................................................... 139 C.1 Modelo de Maquinas síncronas ................................................. ................................................................................... .................................. 139 C.2
Diagrama de bloques de los modelos mo delos de excitación ................................................. ................................. ................ 140
C.3
Diagrama de bloques de los modelos de Gobernadores Gober nadores ........................................... 141
Bibliografia ....................................................... ................................................................................................................ ....................................................................... .............. 143
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Nociones Básicas de Sistemas de Potencia
CAPÍTULO 1 NOCIONES BÁSICAS DE SISTEMAS DE POTENCIA INTRODUCCIÓN Un sistema Eléctrico de Potencia (SEP) es una red formada por unidades generadoras, líneas de transmisión, transformadores de potencia, cargas y equipos asociados, conectados eléctricamente o mecánicamente a la red.
Figura 1.1 Elementos de un sistema eléctrico de potencia
De acuerdo a su función, los elementos del SEP pueden ser agrupados a grupados de la siguiente manera: Grupo1: -
Elementos de Producción. – Generadores Generadores y sus máquinas primarias. Elementos de Conversión. – Transformadores, Transformadores, rectificadores, inversores. Transmisión y distribución. – Líneas Líneas de transmisión y redes. Consumidores de energía eléctrica.
Grupo 2: Los elementos de control regulan o modifican el estado de operación del sistema. -
Excitación de la maquina síncrona. Reguladores de velocidad Capacitores shunt y compensadores Transformadores con LTC, etc.
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Nociones Básicas de Sistemas de Potencia
Sistema de Excitación
AVR (Regulador Automatico de Voltaje)
Sensor de Voltaje V
Devanado de Campo
Va
Vapor TURBINA
Vb
Generador
PV
VC
Mecanismo de control de las válvulas
F
GOBERNADOR
Sensor de Frecuencia
Figura 1.2 Sistema de excitación y gobernador de la turbina del generador
El estudio de los sistemas de potencia obliga a una representación fiel de las características de los elementos que conforman al sistema de potencia, para realizar la simulación del comportamiento del sistema en forma global, aspecto, que permitirá estudiar en condiciones normales o anormales al sistema de potencia.
REPRESENTACIÓN DEL SISTEMA DE POTENCIA Uno de los aspectos más importantes a considerar en el estudio de los sistemas eléctricos de potencia, es su representación, la cual sin duda es el punto de partida de los análisis y estudios posteriores. La representación repres entación de un sistema sis tema de potencia en forma más sencilla consiste consist e de un diagrama, en el cual se coloca toda la información de los elementos y estructuras que constituyen el sistema de potencia. La forma y composición de la representación del sistema de potencia depende en forma directa del análisis que se pretenda llevar a cabo; de ahí, que sean posibles elaborar dos tipos de diagramas, uno en el cual se realice una representación general del sistema pero informativa (Diagrama unifilar), y otra exhaustiva y particular a cada uno de los elementos que conforman el sistema de potencia con sus valores (Diagrama de Impedancia).
Diagrama unifilar Un diagrama unifilar es la representación del sistema trifásico que se obtiene al reemplazar los diferentes elementos del sistema en el equivalente por fase por simples símbolos utilizados y normalizados. Los objetivos de un diagrama unifilar son a) Permitir una representación del sistema en forma más simple y b) Mostrar los datos más importantes o características del sistema en forma concisa. La cantidad de información y los elementos que son representados en el diagrama unifilar
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Nociones Básicas de Sistemas de Potencia
Estudio de Coordinación de Protecciones, donde es transcendental la ubicación y características de los interruptores, relés, y transformadores de medida. En los estudios de Estabilidad en Régimen Transitorio, se hace necesaria la constante de inercia de las máquinas máqu inas y las constantes de tiempo de los reguladores, información que no es e s necesaria en los estudios de cortocircuito. Barra 1
Barra 5
Barra 3
Barra 1
G1
Barra 5
Barra 3
G1 Carga 1
T1
Carga 1
T1
Barra 4
Barra 4
T2 (a)
T2 (b)
Barra 2
Barra 2
G2
G2
Figura 1.3 Diagrama Unifilar, (a) Norma IEC (b) Norma ANSI
La estandarización o normalización para los elementos del sistema de potencia, trae como consecuencia que pueda existir representaciones distintas para los mismos elementos, dependiendo del país o de la empresa en que se realice el estudio.
Modelado del sistema de potencia El análisis de un sistema de potencia requiere modelar el sistema cuantitativamente. El modelo de un elemento, es una abstracción de una situación real que permite poder simular el comportamiento del elemento cuantitativamente, sin llegar a un análisis físico real de la situación. Para ese propósito, es necesario considerar todos los elementos que lo constituyen con sus respectivos modelos equivalentes, de manera de poder simular el comportamiento de cada elemento y en forma integral del sistema de potencia; el tipo de modelo y su exactitud va a depender de la naturaleza del estudio y la exactitud que se requiera. Los elementos pasivos en los sistemas de potencia son las líneas de transmisión,
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Nociones Básicas de Sistemas de Potencia
Líneas de Transmisión Los elementos de mayor extensión dentro de los sistemas de potencia son las líneas de transmisión, y por tal motivo es importante conocer su modelo equivalente, para simular su comportamiento en cualquier situación dentro del sistema de potencia.
Resistencia eléctrica La resistencia de un conductor es la causa principal de la pérdida de potencia en las líneas de transmisión y depende del material del cual está hecho ( ). ). La resistencia de corriente directa (cd) del conductor está dada por:
·
(1.1)
Donde se aprecia que a mayor sección transversal S o Área del conductor, menor la resistencia R, y a mayor longitud del conductor L mayor la resistencia. Otro factor que modifica el valor de la resistencia eléctrica es la variación de la temperatura inicial. La ecuación (1.2) permite calcular la resistencia a cualquier temperatura:
1
(1.2)
Donde R es la resistencia a una temperatura temperatur a final, R0 es la resistencia a una temperatura inicial y es es el coeficiente de variación de la resistencia con la temperatura del material. La resistencia con corriente alterna Rac es mayor que con corriente continua Rdc, por el efecto pelicular. La concentración de la corriente cor riente en la parte periférica de la sección del conductor, hace que aumente la resistencia. La resistencia en corriente alterna se calcula mediante las siguientes ecuaciones.
0. 5 ·· ·· ··· ··· · ≈ 11 ≈ 0.25
(1.3) Para x ≤ 1
(1.4)
Para x > 1
(1.5)
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Nociones Básicas de Sistemas de Potencia
Figura 1.4 Distribución de corriente en un conductor [
Reactancia inductiva de la línea de transmisión La reactancia inductiva es un parámetro eléctrico que se presenta únicamente en corriente alterna. En líneas de alta tensión, la reactancia inductiva es mayor que la resistencia de 3 a 10 veces más, por esta razón r azón influyen en la caída de tensión y en la capacidad de transmisión que tendrá la línea [2, 3, 8].
·2·· · l n · · RMG · ·RMG · ·……· H
(1.6) (1.7)
DMG: Distancia Media Geométrica [m] (entre fases):
(1.8)
RMGH: Radio Medio Geométrico [m] (haz de conductores):
(1.9)
Para un solo conductor por fase
Susceptancia capacitiva
La susceptancia capacitiva es un parámetro eléctrico importante que se halla en porción directa a la capacitancia de la línea. Tanto mayor sea la capacitancia mayor será la susceptancia capacitiva y por tanto, mayor será el aporte de energía reactiva inyectada por la
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Nociones Básicas de Sistemas de Potencia
Se puede estimar la potencia reactiva inyectada por la propia línea al sistema de potencia utilizando la siguiente expresión:
′ ′· ·
(1.13) (1.14)
Figura 1.5 Capacitancia entre conductores y tierra [
Circuito equivalente de una línea de transmisión El circuito nominal es la representación gráfica de los parámetros eléctricos de la línea de transmisión. La clasificación de las líneas de transmisión se realiza según su longitud. Las líneas de 80 a 240 km de longitud son consideradas líneas medias, y en su modelo equivalente se representa: la resistencia e inductancias en serie, la capacitancia en derivación dividida en dos partes iguales y colocadas en ambos extremos de la línea, bajo el concepto de parámetros concentrados (Figura 1.6). 1.6). Las líneas de longitud superior a 240 km, o líneas largas, lar gas, el cálculo del modelo equivalente debe ser más preciso debido a que los fenómenos f enómenos asociados con estas son muy complejos, por lo cual se consideran todos los parámetros de manera distribuida. Las líneas aéreas de longitud menor a 80 kilómetros, son consideradas cortas, y su modelo equivalente consiste solo de la resistencia e inductancias en serie, porque, la susceptancia
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Nociones Básicas de Sistemas de Potencia
Z' = R 1 + jX1
Y' = B1 2 2
Y' 2
Figura 1.6 Representación del circuito nominal
Capacidad térmica de los conductores (Ampacidad) La ampacidad de un conductor es la capacidad de transportar corriente eléctrica bajo condiciones atmosféricas y temperaturas de trabajo específicas, y está definida como la corriente eléctrica máxima que puede llevar en forma confiable una línea área de transmisión. La temperatura del conductor afecta la flecha entre torres, si la temperatura es elevada, puede sobrepasar el límite elástico del conductor en tal forma fo rma que no pueda contraerse contrae rse a su longitud original cuando se enfrié. El método utilizado para el cálculo de la ampacidad se basa en la norma IEEE Std 738-1993 que relaciona la temperatura y corriente del conductor considerando factores ambientales y meteorológicos. Ver Anexo Anexo A.
Cálculos de los parámetros eléctricos con el Programa LTSIM El programa LTSIM fue desarrollado para calcular los parámetros eléctricos de la línea de transmisión aérea, y guardar los resultados en Excel. La Figura 1.7 muestra la ventana principal del programa para el cálculo de d e los parámetros de secuencia positiva de la línea. Además tiene las siguientes funciones incorporadas:
Ampacidad, calcula la corriente máxima que puede transportar una línea área de transmisión (ver Figura Figura 1.8) Circuito Equivalente, calcula los parámetros eléctricos según la longitud de la línea (ver Figura Figura 1.9)
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Nociones Básicas de Sistemas de Potencia
Figura 1.7 Cálculo parámetros de secuencia positiva
Figura 1.8 Cálculo Ampacidad de la línea
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Nociones Básicas de Sistemas de Potencia
Potencia natural de una línea de transmisión La potencia natural o potencia característica (P C C ) es el nivel de carga para la cual se encuentra un balance entre la potencia reactiva consumida por la inductancia serie ( I I 2 X 1) y la potencia reactiva generada por la admitancia “shunt” (V 2 ·Bc), de la propia línea. En otras palabras el reactivo producido por la línea es igual al consumido por la misma línea. Para niveles de carga menores a su potencia natural, la línea suministra potencia reactiva al sistema provocando problemas de sobretensiones y para niveles de carga mayor a su potencia natural la línea consume potencia reactiva del sistema comportándose como inductor, provocando problemas de caídas de tensión. La potencia natural Pc también se la conoce como carga de la impedancia característica (Surge Impedance Loading) SIL y puede expresar en función del cuadrado de la tensión y la impedancia característica.
Dónde:
(1.17)
U R: Tensión nominal de la línea [kV] Z C C: Impedancia característica de la línea []
Q [Mvar]
(1.18)
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Nociones Básicas de Sistemas de Potencia
El Transformador de potencia El transformador de potencia, es el elemento del sistema de potencia, que se encarga de modificar los niveles de tensión y corriente, adaptándolos a los requerimientos del sistema.
Circuito equivalente del transformador El circuito equivalente del transformador considera los efectos de los devanados, las dispersiones de flujo y las corrientes de excitación. Puede adoptar muy distintas y variadas formas, de acuerdo a los requerimientos de la situación a simular; pasando desde donde el artificio matemático del transformador ideal es utilizado hasta el modelo exacto. En las Figura las Figura 1.13 se muestra el circuito equivalente del transformador monofásico, donde se considera la corriente de magnetización I m y la corriente de pérdidas en el núcleo del transformador I C C. En las mayoría de las aplicaciones de los sistemas de potencia se ignoran I m y IC, por ser muy pequeñas comparadas con la corriente nominal, entonces una forma aproximada de presentar a los transformadores de potencia es suprimir la susceptancia de magnetización Bm y la conductancia GC de de la Figura la Figura 1.13a, 1.13a, dando lugar a un representación simple del transformador, en la que las resistencia y reactancia de los devanados están referidos a un solo nivel de voltaje.
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Nociones Básicas de Sistemas de Potencia
%
(1.20)
El valor de U k k también también suele ser llamado voltaje de cortocircuito ya que es útil para calcular la corriente que atraviesa el transformador en caso de sufrir cortocircuito con voltaje nominal aplicado al primario. En la práctica para obtener el circuito equivalente de un transformador se realiza la prueba de cortocircuito y de vacío.
Prueba de cortocircuito En la prueba de cortocircuito las terminales del secundario del transformador se cortocircuitan y los del primario se conectan a una fuente adecuada de voltaje. El voltaje del primario se ajusta hasta que la corriente de los devanados cortocircuitados sea igual a su valor ) la tensión nominal. Los datos registrados en la bobina energizada son la potencia la (P CC CC (V k k ) y la corriente (I k k ) . Entonces tenemos:
Prueba en vació
(1.21) (1.22)
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Nociones Básicas de Sistemas de Potencia
al generador pueden ser típicamente, turbina hidroeléctrica y/o turbina térmica (gas, vapor, biomasa, geotérmica). El estudio en régimen permanente de un generador sincrónico es más simple con ayuda de su circuito equivalente y diagrama vectorial. XS Ia Eaf R a XS Ia
Eaf
Van
Ia
Van
R aIa
Figura 1.14 Circuito equivalente y diagrama vectorial del Generador
La ecuación de tensión para un generador sincrónico de rotor cilíndrico es:
·
(1.26)
Para la simulación de flujos de potencia es necesaria la curva de capacidad del generador síncrono, para definir los límites de entrega de potencia activa y reactiva al sistema, para tal objetivo se deben obtener los parámetros eléctricos del generador.
Diagrama de capacidad del generador
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Calculo del diagrama de capacidad del generador con el programa GENSIM El programa GENSIM fue desarrollado para calcular calcul ar y graficar el diagrama de capacidad del d el generador, y guardar los datos en Excel. En la Figura la Figura 1.16 se muestra la ventana principal, los datos que se deben ingresar son la potencia nominal aparente (S N ) en [MVA], el factor de potencia y la relación de cortocircuito (SCR) en [p.u].
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EJERCICIOS RESUELTOS Ejemplo1.1: Líneas de transmisión La línea aérea de transmisión eléctrica AB en 115 [kV] (AB-115) está compuesta por los conductores cuyas características se muestran en la Tabla la Tabla 0.1 y son sujetadas por torres de disposición horizontal cuya figura y dimensiones se muestra en la Figura la Figura 1.17. a. Si la línea está compuesta de conductores IBIS 397,0 ACSR. Hallar los parámetros eléctricos en p.u. de secuencia positiva, para una longitud de 100 [km] y una frecuencia de 50 [Hz]. b. Determine la potencia reactiva que la línea entrega en vacío y la potencia natural de la línea. c. Encontrar la ampacidad del conductor y su capacidad de transporte de energía, bajo las siguientes condiciones
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Nociones Básicas de Sistemas de Potencia
TIPO
DIAMETRO [PULGADAS] [mm]
5/16''
7,937
Área [mm2]
Peso [kg/km]
Carga de [kg]
Resistencia [ /km]
42,14
335
5080
2,485
Tabla 0.1 Características de los conductores y el cable de guarda
Para los métodos hallar los parámetros eléctricos, eléctrico s, la potencia natural y la energía reactiva r eactiva en vacio de la línea, cuál de los casos es la mejor opción.
Solución: a. Introduciendo los datos de la línea AB al programa LTSIM, este nos muestran los valores calculados de la resistencia, reactancia y susceptancia de secuencia positiva en [/km] y [p.u./km].
0,0,1045408 45408 Ω/km Ω /km ; 01099 01099p.p.u./kmkm
−siem/km 0,0,0403251 29903251Ω/km 299 Ω/kmp.p.u./;kmkm 2,0,603×10 m/km 003484 003484p.p.u./kmkm
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Nociones Básicas de Sistemas de Potencia
A
C
B
6m
6m 4.86
6 CG2
CG1
2.8 A
33
B
C
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Nociones Básicas de Sistemas de Potencia
c. La opción de Ampacidad del programa LTSIM se debe colocar las condiciones de la línea AB, latitud de la línea debe estar en grados 17,533 y el 10 de junio es el día 162 del año. Los resultados se muestran a continuación
8,722 1,999 3,90 4,96×10− 8,8,721,993,90
La pérdida por convección forzada
Pérdidas por radiación térmica se utiliza Ganancia de calor por radiación solar
La resistencia de R en valores de [/pies] será
El valor de la corriente admisible del conductor IBIS será:
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Nociones Básicas de Sistemas de Potencia
Solución método2: Un conductor RAIL por fase a una tensión de 230[kV] Del programa LTSIM se obtiene los siguientes resultados
0,0,0000119 6286 6286 Ω/km Ω /km ; 062 Ω/km Ω /km ; km 0,4062 2, 8 0×10−siems/km 00119 p.p.u./kmkm; 0,000768 00768 p.p.u./kmkm; 0,001482 01482p.p.u./kmkm
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Nociones Básicas de Sistemas de Potencia
El generador de una unidad termoeléctrica tiene las siguientes características técnicas; frecuencia de 50 [Hz], potencia de 29 [MVA], factor de potencia en atraso de 0,85, voltaje nominal 10,5 [kV], reactancia síncrona saturada de 2,35 [p.u.], resistencia de armadura despreciable. Calcule la relación de corto circuito (SCR).
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Nociones Básicas de Sistemas de Potencia
Q(Mvar) 30
25
Límite de calentamiento del Rotor
20
Pn
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Nociones Básicas de Sistemas de Potencia
EJERCICIOS PROPUESTOS 1.- Una línea eléctrica en 115 kV usa conductores de fase IBIS 397,0 MCM con estructuras metálicas cuyas dimensiones se muestran en la Figura la Figura 1.21. a. Hallar los parámetros eléctricos en p.u. de secuencia positiva línea de transmisión para
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Nociones Básicas de Sistemas de Potencia
2.- En una línea de transmisión eléctrica en 115 [kV] se usa conductores de fase IBIS 397,0 ACSR, torres metálicas triangulares con las dimensiones que se muestran en la Figura la Figura 1.22. a. Hallar los parámetros eléctricos en p.u. de secuencia positiva línea de transmisión para una longitud de 105 [km], frecuencia de 50 [Hz].
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Cálculo de Flujo de Potencia Óptimo
Para la remuneración por energía a las diferentes unidades generadoras del sistema, se toma el concepto de Inyección Valorizada, que es igual al producto del precio de nodo y la energía inyectada (P Gi i). G )
Dónde:
· $
(3.8)
IV i: Inyección Valorizada en la barra i[$/h] P Gi Gi: Potencia que entrega el generador i al sistema [MW]
Utilidad de la unidad generadora La utilidad de las unidades generadoras es la diferencia entre la inyección valorizada y el costo de operación de la unidad generadora, la unidad que margina tiene una utilidad igual a cero.
Dónde:
$
(3.9)
F Gi Gi: es la función costo de operación del generador i F [$/h]
Retiro Valorizado RV Los pagos de los consumidores por concepto de compra de energía, se calcularan para cada periodo y bloque horario, donde los retiros retiros de energía de cada barra se calculan con el precio de nodo de la barra por el retiro de la energía de la barra.
Dónde:
· $
(3.10)
P CARGAi CARGAi: Es la potencia de la demanda en una barra i [MW]
ANÁLISIS DE SEGURIDAD (N-1) DEL SEP – SIMULACIÓN SIMULACIÓN DE CONTINGENCIAS La seguridad de un SEP es la capacidad de permanecer en estado normal, ante perturbaciones imprevistas, pero probables de ocurrir, asegurando el suministro de energía a los centros de consumo, y manteniendo la calidad de servicio. Se considera que el sistema se encuentra en estado normal cuando la demanda es satisfecha y las magnitudes eléctricas (voltaje y frecuencia) están dentro de sus límites.
Análisis de contingencias (N-1) Una contingencia es el estado en que un elemento del SEP ha salido fuera de servicio (por
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Cálculo de Flujo de Potencia Óptimo
contingencias necesitan ser analizadas para tomar acciones correctivas y evitar la violación de límites y en el peor de los casos que provoquen una desconexión en cascada llegando a un apagón. Las contingencias pueden ser simples donde un solo elemento falla o complejas donde las fallas son más de un elemento. Ya que los sistemas son diseñados de la manera más confiable posible, es difícil y poco probable que ocurran contingencias con tingencias complejas.
Criterio N-1 Un sistema cumple con el criterio N-1 (al desconectarse un solo elemento) sigue en condiciones aceptables de funcionamiento. Los resultados de un análisis de contingencias permiten determinar los elementos débiles que posee el sistema. La aplicación del criterio N1 consiste en la simulación de una pérdida de un componente de la red (línea de transmisión, transformador, o un generador).
Simulación de contingencias El principal problema de la metodología a usarse para realizar un análisis de contingencias es la velocidad de la solución. Es difícil realizar una selección de las “salidas más creíbles”,
si se desea estudiar cada caso, cada solución nos llevaría segundos y si tenemos cientos de casos por estudiar, esto podría resultar horas completas para tener los reportes. repor tes. Por tal motivo es necesario el uso de programas especializados para realizar la simulación de contingencias. El programa PowerWorld permite simular las contingencias de un caso de estudio, manualmente o automáticamente, para ambos casos el simulador debe estar en modo RUN. La simulación de contingencias manualmente se realiza sobre el diagrama unifilar, abriendo y cerrando los interruptores de las líneas, uno por uno y fijarnos los voltajes de las barras y los flujos de potencia de las líneas y transformadores. Para un SEP grande que tiene cientos de barras, líneas, generadores, etc. el tiempo del análisis puede durar horas. Para la simulación de contingencias automáticamente, seleccionamos Contingency Analysis dentro del menú Options/Tools, el módulo de análisis de contingencias inicialmente está vacío, para insertar todo tipo de contingencias de forma automática, presionamos Auto la Figura 3.6 ahí se puede seleccionar Insert. Se visualiza el cuadro de dialogo mostrado en la Figura las contingencias de Línea, Transformador, Línea-transformador y generador. La simulación de la apertura de una línea es más compleja que la interrupción de servicio de un generador, pues el corte de una línea causa un cambio en la configuración del sistema. Para ello, en el cuadro de dialogo mostrada en la Figura la Figura 3.6, se 3.6, se selecciona la apertura de una rama (Single transmission line) y se pulsa Insert Contingencies. De esta manera se insertan automáticamente las contingencias correspondientes a la pérdida de cada una de las ramas del sistema.
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Cálculo de Flujo de Potencia Óptimo
Figura 3.6 Ventana de inserción automática de contingencias
Antes de realizar el análisis automático de contingencias puede ser necesario configurar las opciones del algoritmo y los límites de los parámetros a monitorizar. monitorizar . Estas opciones están en la pestaña Options, tal como se muestra en la Figura la Figura 3.7.
Figura 3.7 Pestaña de opciones de configuración de análisis de contingencias
Para un análisis completo de las contingencias se utiliza los flujos de potencia AC (Full Power Flow) porque muestra los flujos de potencia por las líneas y voltajes en las barras después de la contingencia. Para un análisis de contingencias con tingencias solo para los flujos de Potencia P otencia Activa por los elementos de transmisión utilizamos la opción flujos de potencia DC (Linearized Lossless DC). En la opción Limit Monitoring se establece los rangos mínimos y máximos de los voltajes en las barras para el estado normal y las sobrecargas de las líneas y transformadores.
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Cálculo de Flujo de Potencia Óptimo
Figura 3.8 Resultados del Análisis de Contingencias
EJERCICIOS RESUELTOS Ejemplo 3.1: Despacho económico en un sistema hidrotérmico Actividades
Construya el diagrama unifilar de la Figura la Figura 3.9, con 3.9, con la información necesaria de cada elemento del sistema eléctrico de potencia (SEP). Las centrales hidroeléctricas generan en los bloques bajo y medio del periodo seco un 40% de su capacidad. Determine la generación térmica necesaria para satisfacer la demanda de las 4:00 A.M. (60 MW) que se halla en el bloque horario bajo, con una reserva del 7% para las unidades térmicas. Ejecute el programa de flujos de potencia con despacho económico habilitado y analice los resultados de las barras, las conexiones y el balance global del sistema. Que acciones de control requiere realizar para cumplir las condiciones operativas. Determine cuál es la posición óptima de los taps, para los transformadores de generación y carga. Una vez optimizado el flujo de potencia, determine el costo medio de la unidad marginal, los costos de operación de cada unidad, costo de d e operación total del sistema, la inyección valorizada de los generadores, utilidad de los generadores y el retiro valorizado de las cargas.
Datos para el despacho económico TRAMO Línea1 A-B115 Línea2 B-C115 Línea3 C-D115 Línea4 E-D115
TENSION [kV] 115 115 115 115
R1 [p.u.]
X1 [p.u.]
B1 [p.u.]
0,0237 0,0478 0,0066 0,0308
0,1535 0,1414 0,0195 0,1995
0,01852 0,01513 0,00209 0,02408
CAPACIDAD [MW] 125 78 78 125
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Cálculo de Flujo de Potencia Óptimo
Gen A1 A2 A3 B1 B2 C1-C3 D1-D4
Un [kV] 11 11 11 10 10 11 10 GenTerm A1 A2 A3 B1 B2
TRANSFORMADORES AT1-AT3 115/11kV BT1 115/10 kV BT2 115/10 kV CT1-CT3 115/11 kV CT4 115/25 kV DT1-DT2 115/10 kV DT3 115/10 kV ET1 115/25 kV ET2 230/115 kV FT1 115/11kV
Sn [MVA] 20 22 24 29 32 15 23
COS 0,85 0,85 0,85 0,85 0,85 0,85 0,85
XSAT[p.u.] 2,10 2,00 1,90 1,95 1,95 1,65 1,50
PMAX[MW] 16,5 18,0 20,0 23,0 26,0 12,0 19,0
a [$/hr]
b [$/MW·hr]
c [$/MW²·hr]
200 180 140 120 140
7,00 6,30 6,80 1,50 2,00
0,008 0,009 0,007 0,008 0,006
U1/U2
SN [MVA]
R1[p.u.]
X1[p.u.]
115/11 115/10 115/10 115/11 115/25 115/10 115/10 115/25 230/115 230/11
29,0 35,0 37,0 15,0 16,0 45,0 12,5 25,0 100,0 75,0
0,00350 0,00693 0,00583 0,00570 0,0 0,00660 0,00780 0,00970 0,00146 0,00620
0,1320 0,1000 0,1316 0,0681 0,1611 0,1611 0,1060 0,0927 0,1149 0,0871 0,1560
Nota: Datos de los Transformadores Transformadores en base propia propia
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Cálculo de Flujo de Potencia Óptimo
B1
B2
B2-010
B1-010 BT1
BT2
B3-115
C4-115 Línea 2
Línea 1 A3-011
AT3
C1-011 C1
C5-025
A4-115
CT1
CT4
CT2
C2-011
8 MW 2,6 Mvar
A3 A2-011
C2
CT3
AT2
C3-011 C3
2 A1-011
Línea 3 AT1
A1 D3-115 Línea 5
D1-010 DT1
Línea 4
D1
E1-115
D2 ET1
ET2
15 MW 4,9 Mvar
E2-025
E3-230
D2-010 D4-010
10 MW 3,3 Mvar
DT2
Línea 6 7 MW 2,3 Mvar
F1-230
D4
DT3
FT1
25 MW 8.2 Mvar
F2-011 35 MW 11.5 Mvar
Figura 3.9 Diagrama unifilar para el Ejemplo 4.1 Hora 0:00:00 1:00:00 2:00:00 3:00:00
MW 102 90,32 80,6 71,3
Factor 1,02 0,90 0,81 0,71
Hora 12:00:00 13:00:00 14:00:00 15:00:00
MW 116,33 110,09 113,50 118,32
D3
Factor 1,16 1,10 1,14 1,18
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Cálculo de Flujo de Potencia Óptimo
MW 140 120 100 80 60 40 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : : : : : : : : : : : : : 0 1 2 3 4 5 6 7 8 9 0 1 2 1 1 1
0 0 : 3 1
0 0 0 0 0 0 0 0 : : : : 4 5 6 7 1 1 1 1
0 0 : 8 1
0 0 : 9 1
0 0 : 0 2
0 0 : 1 2
0 0 : 2 2
0 0 : 3 2
Curva de la carga Solución: Se debe efectuar el análisis según el bloque horario, tomando en cuenta la demanda y la reserva rotante. Hallamos la Generación Total para cubrir la demanda del periodo de las 4:00 A.M. más las pérdidas del sistema.
; 602% ; 61,2
Coordinación hidrotérmica
Debemos definir que parte de la demanda será cubierta por generación hidráulica y por generación térmica
Generación hidráulica: La Generación hidráulica en el periodo seco es la siguiente: Bloque Bajo
Central C (MWh) 0
Central D (MWh) 0
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Cálculo de Flujo de Potencia Óptimo
Total C y D
18 MW
Los generadores hidráulicos no deben tener habilitado la función Available for AGC y Enforce MW Limits.
Figura 3.10 Menú de los generadores (hidráulicos)
Generación térmica: La generación térmica debe cubrir la demanda restante
, , , donde , 61,2 26 24,8
La demanda de la carga se encuentra en el bloque horario bajo entonces la Reserva Rotante de la generación térmica es del 10 %. Gen Termico
a [$/hr]
A1 A2 A3
200 180 140
b [$/MW·hr] c [$/MW²·hr] 7,00 6,30 6,80
0,008 0,009 0,007
Pmin [MW] 9,9 11,1 12,3
Pmax [MW]con reserva 15,35 17,21 19,07
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Cálculo de Flujo de Potencia Óptimo
Figura 3.11 Menú de los generadores (térmicos)
Unit Commitment Para elegir los generadores térmicos que van a entrar en funcionamiento para cubrir la demanda, utilizando el simulador PowerWorld , ingresamos al menú Case Information/ Generators Fuel Cost, donde en la columna Min MW colocamos cero a todos los generadores térmicos, y hacemos correr el programa. Los generadores A1, A2 y A3 no inyectan potencia activa al sistema, su salida es cero, entonces estas unidades deben ser desconectadas, porque son muy caros. Los generadores térmicos que quedan en funcionamiento son B1 y B2.
Calculo del Despacho Económico Luego de definir los generadores térmicos con el Unit Commitment, se escoge la unidad marginal en la barra slack , que es la unidad con mayor costo medio. En nuestro caso es la unidad generadora B2. Se debe añadir la información de los límites de potencia po tencia mínima de las unidades térmicas, en
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Cálculo de Flujo de Potencia Óptimo
10 13 13 14 14
C3-011 D1-010 D1-010 D2-010 D2-010
Open Closed Open Closed Open
NO NO NO NO NO
0 7,4 0 7,4 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
11,61 16,4 16,45 16,4 16,45
Hydro Hydro Hydro Hydro Hydro
0 0 0 0 0
0 0 0 0 0
Tabla 3.3 Tabla para el e l Despacho Económico ejemplo 4.1
Para concluir con el despacho económico, debemos verificar que se cumplen las condiciones operativas del sistema: los voltajes de las barras estén dentro de su rango, las líneas y transformadores no estén sobrecargadas, y que los generadores estén trabajando dentro de su curva de capacidad. Por tener una demanda baja no se tienen problemas de sobrecarga en las líneas y transformadores, pero los voltajes de las barras de carga están fuera de su rango, por tal motivo se tuvo que mover los taps de los transformadores, tal como se muestra en la Tabla la Tabla 3.4. Trans BT1 BT2 CT1 CT2 CT4 DT1
Status Closed Closed Closed Closed Closed Closed
Tap 1,01 1,01 1,01 1,01 0,99375 1,01
TIPO Generación Generación Generación Generación Carga Generación
Trans DT2 DT3 ET1 ET2 FT1
Status Closed Closed Closed Closed Closed
Tap 1,01 0,99375 0,975 1,0125 0,9875
TIPO Generación Carga Carga Interconexión Carga
Tabla 3.4 Posición de los taps de los transformadores
En la Tabla la Tabla 3.5 se muestra el balance global del sistema, donde dond e se aprecia que se tiene perdida negativa de energía reactiva, esto es debido a que las líneas por están debajo de su potencia natural introducen energía reactiva al sistema. Demanda Generación Perdidas
MW 60,00 60,83 0,83
Mvar 19,70 13,10 -6,60
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Cálculo de Flujo de Potencia Óptimo
Figura 3.12 Simulación del Despacho Económico del ejemplo 4.1
Determinar los ingresos valorizados de los generadores y retiros valorizados de las cargas Para hallar los ingresos y retiros valorizados necesitamos el costo medio de la unidad
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Cálculo de Flujo de Potencia Óptimo
Hallamos el precio de nodo utilizando la ecuación (4.7); la inyección valorizada utilizando la ecuación (4.8) y la utilidad de los generadores con la ecuación (4.9).
9,916·1,09,916 ·ℎ$ $ 9,916·0,99859,901$ ·ℎ 9,916·17,93177,79 ℎ$ 9,901·18,09179,11 ℎ$ 177,79177,790 ℎ$ 179,11149,7629,35ℎ
Gen MW
Min MW
Max MW
IC
Lamb
Cost Medio
Factor de Nodo
Precio de Nodo
IV [$/h]
0 A1-011 0 A2-011 0 A3-011 18,09 B1-010 B2-010 17,93 5 C1-011
0 0 0 15 16,5 0
15,34 17,21 19,07 23,3 25,58 11,6
0 0 0 1,79 2,22 0
0 0 0 1,79 2,22 0
0 0 0 8,279 9,916 0
1,0213 1,0213 1,0213 0,9985 1,0000 1,0122
10,127 10,127 10,127 9,901 9,916 10,037
0,000 0,000 0,000 179,108 177,790 50,186
Name
Costo Operación [$/h] 0 0 0 149,76 177,79 0
Utilidad [$/h] 0,000 0,000 0,000 29,348 0,000 50,186
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Cálculo de Flujo de Potencia Óptimo
10,0383·4.848,184 ℎ$
Ejemplo 4.2: Análisis de Contingencias
Analizar el comportamiento en régimen permanente del ejemplo 4.1 trabajando en condiciones de emergencia (pérdidas de líneas). Utilizar la opción de análisis de contingencias de PowerWorld para hallar la contingencia más severa. Cuáles son las faltas que presentan la contingencia más severa. Que acciones de control requiere realizar para cumplir las condiciones operativas después de la contingencia.
Solución: Para simular las contingencias en PowerWorld , podemos hacerlo manualmente o automáticamente, para ambos casos el simulador debe estar en modo RUN. El sistema por tener una demanda baja de potencia, no presenta muchos problemas, a contingencias N-1 las más severas son la pérdida de la línea AB-115 (Línea 1) y ED-115 (Línea 4) presenta cada una, siete faltas. Numero
Label (Rotulo)
Procesar
1 2 3
L_00004A4-115-00007B3-115C1 L_00017E1-115-00015D3-115C1 L_00004A4-115-00017E1-115C1
YES YES YES
Solved Viola. YES YES YES
7 7 3
Sobrecarga
Min Voltaje 0,925 0,928 0,938
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Cálculo de Flujo de Potencia Óptimo
En la la Tabla 3.12 se muestra los generadores los valores de la excitatriz y la cantidad de energía reactiva que introducen al sistema. Name B1-010 B2-010 C1-011 C2-011 D1-010 D2-010
Gen MW 19,18 17,97 5 5 7,4 7,4
Gen Mvar 0,29 0,65 3,06 2,64 6,74 6,74
Set Volt 1,025 1,025 1,020 1,020 1,020 1,020
AVR YES YES YES YES YES YES
Tabla 3.12 Posición de la excitatriz (Set Volt) de los generadores
EJERCICIOS PROPUESTOS la Figura 3.13, con 3.13, con la información necesaria de cada 1.- Construya el diagrama unifilar de la Figura elemento del sistema eléctrico de potencia (SEP). Las centrales hidroeléctricas generan en los bloques bajo y medio del periodo seco un 35% de la generación total. Determine la generación térmica necesaria para satisfacer la demanda de las 08:00. Considerando Consider ando una reserva rotante según el bloque horario para térmicas. Ejecute el programa de flujos de potencia con la opción de despacho económico habilitado y analice los resultados de las barras, las conexiones y el balance global del sistema. Que acciones de control requiere realizar para cumplir las condiciones operativas,
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Cálculo de Flujo de Potencia Óptimo
Generación A1 - A3 B1 - B4 C1 - C3 D1-D2 F1- F2
TRAMO Línea 1 AB-115 Línea 2 AE-115 Línea 3 BC-115 Línea 4 BE-115 Línea 5 CD-115 Línea 6 DE-115 Línea 7 EF-230 Línea 8 EH-230
Un [kV] 10 11 11 10 11
Sn [MVA] 70 30 15 19 22
Gen Term
a [$/hr]
A1 A2 A3 D1 D2 F1 F2
110,0 90,0 135,0 20,0 15,0 93,6 70,0
LONGITUD [km] 57 112 47 86 55 62,5 170 97
b [$/MW·hr] 1,40 1,60 2,10 8,50 6,50 9,50 10,60
TENSION [kV] 115 115 115 115 115 115 230 230
XSAT[p.u.] 2,25 1,85 1,73 2,11 1,64
COS 0,85 0,85 0,85 0,85 0,85
c [$/MW²·hr] 0,0085 0,0075 0,0068 0,0025 0,0050 0,0058 0,0020
PNOM[MW] 56 24 12,25 15,5 17
PMIN [MW] 33,6 33,6 33,6 9,3 9,3 10,2 10,2
R1 [p.u.]
X1 [p.u.]
B1 [p.u.]
0,0626 0,0530 0,0516 0,0408 0,0311 0,0686 0,0020 0,0115
0,1784 0,3298 0,1527 0,2638 0,1580 0,1898 0,1329 0,0761
0,02066 0,04330 0,01635 0,03187 0,02175 0,02332 0,24620 0,14021
CAPACIDAD [MW] 78 120 78 120 120 78 160 160
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Cálculo de Flujo de Potencia Óptimo
69/25 IT1 69/25 kV 69/25 JT1 69/25 kV Nota: Datos de los Transformadores Transformadores en base propia
Hora 0:00:00 1:00:00 2:00:00 3:00:00 4:00:00 5:00:00 6:00:00 7:00:00 8:00:00 9:00:00 10:00:00 11:00:00
MW 199,9 177,5 154,7 126,0 98,8 9 8,8 101,7 137,5 177,6 190,0 214,9 222,9 227,7
Factor 1,05 0,93 0,81 0,66 0,52 0,54 0,72 0,93 1,00 1,13 1,17 1,20
37 37
Hora 12:00:00 13:00:00 14:00:00 15:00:00 16:00:00 17:00:00 18:00:00 19:00:00 20:00:00 21:00:00 22:00:00 23:00:00
0,0153 0,0052
MW 228,6 216,4 223,1 232,6 233,9 232,2 246,3 282,0 284,5 277,1 258,6 213,9
Factor 1,20 1,14 1,17 1,22 1,23 1,22 1,30 1,48 1,50 1,46 1,36 1,13
0,1048 0,1670
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Cálculo de Flujo de Potencia Óptimo A 3
A 2
A 1
A
A 1
1
3
1 -0
0 A
A 2
-0
-0 1
0
T
A
0 T
3
T
A
2
A 1
4 -1 1 5
A T 4 A 5 -0
L
B 4
2
ín 5
1 M M
5 .7 .7 0 ar
B 1
B
B 2
1 -0
W
-0 1
B
1
3 1 5
3
ín
L
B 4
9
B -1
T
.5
1 B T
B
3
1 1
2
í
B 2
4
T
L
B 3
1
6 v
ea
-0 7
.8
7
1 0
3
ea
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Cálculo de Cortocircuitos
CAPÍTULO 4 CÁLCULO DE CORTOCIRCUITOS Los Cortocircuitos ocurren en los sistemas de potencia cuando falla el aislamiento del equipo, debido a descargas atmosféricas o maniobras de interruptores o a otras causas. caus as. Las corrientes de cortocircuito pueden ser mucho mayores a las corrientes de operación normal, tal que si se mantienen, pueden causar daños irreparables en los equipos (devanados y barras colectoras, etc.). Por lo tanto, es necesario eliminar rápidamente la sección fallada mediante los sistemas de protección adecuados. Por lo señalado, es necesario calcular las corrientes de cortocircuito, para dimensionar y seleccionar interruptores, ajustar y coordinar los diferentes dispositivos de protección del
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Cálculo de Cortocircuitos
En este texto solo se utilizara las componentes de secuencia de la fase f ase a, (V a1 a1 , V a2 a2 y V a0 a0 ). Para simplificar se elimina el subíndice a y se denota estos tres componentes como (V 1 , V 2 y V 0 ). La relación que existe entre los voltajes de las fases y los valores equivalentes en el dominio de la secuencia se define por las ecuaciones (4.1) y (4.5).
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Cálculo de Cortocircuitos
Comparando las ecuaciones (4.12) y (4.15), se tiene que la corriente de neutro es igual a tres veces la corriente de secuencia cero.
3·
(4.16)
En un sistema balanceado conectado en Υ, las corrientes de línea no tienen componentes de secuencia cero, puesto que la corriente de neutro es cero. También, en cualquier sistema trifásico sin trayectoria neutra, como un sistema conectado en ∆ o un sistema de tres hilos conectado en Υ con neutro no aterrizado, las corrientes de línea no tienen componente de secuencia cero.
REDES DE SECUENCIA DE LOS COMPONENTES DEL SEP Las corrientes de cortocircuito pueden ser calculadas a partir de las redes de secuencia las mismas que se utilizaran e interconectaran dependiendo del tipo de falla, una vez interconectado los esquemas se procede a determinar el equivalente de Thevenin para luego
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Cálculo de Cortocircuitos
Los diagramas de secuencia del generador conectado en estrella y aterrizado se muestra la Figura 4.4. Icc
E0
PERIODO SUB TRANSITORIO
PERIODO TRANSITORIO
PERIODO ESTABLE
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Cálculo de Cortocircuitos
Redes de secuencia de los transformadores En los transformadores la impedancia de secuencia positiva suelen tener un valor similar o igual al valor de la secuencia negativa, además el transformador no tiene la capacidad de generar voltajes ni corrientes entonces el diagrama de secuencia es el mismo para secuencia positiva como negativa. También cabe aclarar que los diagramas d iagramas para par a secuencia s ecuencia positiva y
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Cálculo de Cortocircuitos
Red de secuencia de Líneas de transmisión Las redes de secuencia positiva de las líneas de transmisión fueron estudiadas en el Capítulo 2 de este texto, por lo que únicamente se mencionara que la reactancia que presenta la línea ante corrientes de secuencia positiva es la misma que presenta para corrientes negativas. La impedancia de secuencia cero de una línea de transmisión depende de su estructura (cable
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Cálculo de Cortocircuitos
Z1
Vc Vb
Ic I b
+ -
Vf
I1 V1
F
Z2
I2
+ -
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Cálculo de Cortocircuitos
Z1
Vc
Ic
+ -
Vf
V1 Z2
Vb
Ib
I1 + -
I2 +
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Estabilidad de Sistemas de Potencia
En las fracciones de segundo posteriores a los que se produce la desconexión, la carga sigue demandando la misma potencia que en el instante anterior. Por su parte, las turbinas de las unidades generadoras son incapaces de d e entregar el déficit de potencia, debido a las constantes cons tantes de tiempo asociadas a la producción de energía. En consecuencia, este déficit es compensado mediante extracción de energía cinética almacenada en los rotores de las máquinas, iniciándose así un descenso en la frecuencia del sistema (Figura 5.18, punto 5.18, punto A). Luego de uno o dos segundos, la caída de frecuencia es detectada por los “reguladores de velocidad” o gobernadores de las unidades generadoras. Frente a ella, éstos efectúan una acción proporcional directamente sobre las válvulas de las turbinas, aumentando la potencia activa inyectada al sistema este proceso se conoce como regulación Primaria. Mientras tanto, la potencia consumida por algunas cargas disminuye en forma aproximadamente proporcional a la caída de frecuencia, por lo que esta última durará hasta que la superposición de los dos efectos mencionados logre igualar generación y consumo, deteniendo la caída de frecuencia (Figura 5.18, punto 5.18, punto B). En los segundos siguientes, debido a las constantes de tiempo de las turbinas, la inyección de potencia superará a la carga, produciéndose una pequeña recuperación de la frecuencia hasta llegar a una nueva condición de equilibrio (Figura 5.18, punto 5.18, punto C). En este punto, la frecuencia f recuencia del sistema presenta un error que se mantendrá en el tiempo (Figura 5.18, 5.18, punto D), característico de una acción de control proporcional.
Control Primario de frecuencia Corresponde a una acción de control proporcional de cada unidad, debido a sus reguladores de velocidad. Permite acotar las desviaciones de frecuencia, frente a perturbaciones en el equilibrio generación/carga, en un tiempo de respuesta de pocos segundos. El inverso del llamado “estatismo” o droop “R” es la constante de proporcionalidad que caracteriza a esta acción. Permite ajustar la variación en la potencia mecánica entregada por una turbina, respecto de variaciones en la velocidad angular del rotor de la unidad (o lo que es proporcional, la frecuencia de la tensión). Dada una consigna, la unidad genera gener a la potencia indicada, a la frecuencia nominal, permitiendo variaciones en torno a ese punto frente a desviaciones en la frecuencia del sistema.
|||||| %
(5.5)
La regulación primaria por sí sola no es capaz de corregir la desviación sufrida por la frecuencia, en otras palabras con ella sola la frecuencia no retornaría a su valor nominal, se necesita para ello un control secundario gracias al cual se restablece la frecuencia del sistema a su valor nominal, reajustando las características de los gobernadores y en sistemas interconectados restablece los flujos pactados por los enlaces del mismo con otros sistemas.
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Estabilidad de Sistemas de Potencia
Para simular el comportamiento de la frecuencia después de una perturbación (pérdida de generación o pérdida de carga) es necesario incluir el efecto de los gobernadores de los generadores. En esta sección se hará un repaso al sistema de control primario (gobernador), que utilizan los programas de simulación de estabilidad.
Gobernador de Velocidad El gobernador de velocidad controla el torque o la potencia de entrada en el eje de la máquina sincrónica. Los cambios de velocidad ω o carga en la máquina, originan variaciones en el torque mecánico T m. La magnitud de dichas variaciones depende del cambio de velocidad, del tipo de gobernador usado y de la fuente de energía. Las ecuaciones que describen matemáticamente el comportamiento de estos dispositivos se deducen a partir de los diagramas de bloques de los modelos de gobernadores. gobernador es. A continuación se muestran un modelo de gobernador con su respetivo diagrama de bloque que utilizan los simuladores de estabilidad.
Gobernador para hidroturbinas Este tipo representa a los gobernadores usados en las plantas hidroeléctricas y su función principal, es actuar sobre el mecanismo que controla el caudal del agua, logrando así, un control del par entregado a los generadores. En la Figura la Figura 5.19 se aprecia la representación en diagrama de bloques del modelo del gobernador para hidroturbinas y en él se identifican sus variables de estado.
Figura 5.19 Diagrama de bloques del gobernador de la Turbina
EJERCICIOS RESUELTOS Ejemplo 5.1 Estabilidad Transitoria, estabilidad de frecuencia Actividades
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Estabilidad de Sistemas de Potencia
a) Ejecute el programa de flujos de potencia, ingrese al módulo de estabilidad transitoria e ingrese los siguientes eventos: b) Ingresar los eventos para una falla trifásica cerca de la barra B2-230, la falla se despeja a los 5 ciclos (0.083 seg) con la apertura de los interruptores en los extremos de la línea 2. Utilizar el modelo clásico para los generadores (sin mecanismos de control). c) Analizar los ángulos de los rotores, la frecuencia, la potencia mecánica, la potencia eléctrica activa [MW], la potencia eléctrica Reactiva [Mvar], los voltajes en las terminales de los generadores, determinar si el sistema es estable. d) Ingresar los eventos para la pérdida de Generación (GenC) y la pérdida de Carga en la barra E1-230. Caso 1: Utilizar el modelo clásico para los generadores sin mecanismos de control Graficar el ángulo del rotor y la frecuencia hasta un tiempo de 40seg. Caso2: Utilizar el modelo clásico para los generadores con mecanismos de control, gobernador TVGO1, graficar la frecuencia hasta un tiempo de 40seg. e) En los dos casos analizar los ángulos de los rotores, la frecuencia, la potencia mecánica, la potencia eléctrica activa [MW], la potencia eléctrica Reactiva [Mvar], los voltajes en las terminales de los generadores, determinar si el sistema es estable. (Fuente: “Power System Control and Stability”, Anderson & Found) B1-018
C2-230
D1-230
B2-230 Linea 3
C1-014
Linea 4 5
GenB
a 2
BT2
e ni e L ni L
100 MW 35 Mvar
F1-230 125 MW 50 Mvar
CT3
a
Linea 1
Linea 6
A2-230 AT1 A1-016
slack
GenA a) Cortocircuito Trifásico
E1-230 90 MW 30 Mvar
GenC
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Estabilidad de Sistemas de Potencia
B1-018
C2-230
D1-230
B2-230 Linea 3
C1-014
B1-018
C2-230
D1-230
B2-230
Linea 4
Linea 3 5
GenB
5 a
2 e
BT2
CT3
a ni e L
e ni e
Linea 1
Linea 6
A2-230
100 MW 35 Mvar
F1-230
90 MW 30 Mvar
125 MW 50 Mvar
Linea 1
E1-230
Linea 6
A2-230
AT1
90 MW 30 Mvar
AT1
A1-016
slack
GenC
L L
E1-230
CT3
a in
100 MW 35 Mvar
F1-230 125 MW 50 Mvar
a 2
BT2
GenB
GenC
L in
C1-014
Linea 4
A1-016
slack
GenA
GenA
b) Perdida de Generación
c) Perdida de Carga
Figura 5.20 Diagrama unifilar para el Ejemplo 6.1 [ ¡Error! No se encuentra el origen de la r eferencia.]
Datos del sistema eléctrico TRANSFOR.
U1/U2 230/16,5 230/18 230/13,8
AT1 230/16,5kV BT2 230/18 kV CT2 230/13,8 kV
TENSION [kV] 230 230 230 230 230 230
TRAMO Línea1 AF-230 Línea2 BF-230 Línea3 BD-230 Línea4 CD-230 Línea5 CE-230 Línea6 AE-230
SN [MVA] 500 250 150
R1[p.u.] 0 0 0
X1[p.u.] 0,0576 0,0625 0,0586
R1 [p.u.]
X1 [p.u.]
B1 [p.u.]
0,0100 0,0320 0,0085 0,0119 0,0390 0,0170
0,0850 0,1610 0,0720 0,1008 0,1700 0,0920
0,176 0,306 0,149 0,209 0,358 0,0158
CAPACIDAD [MVA] 200 200 200 200 200 200
Nota: los datos de las líneas y los transformadores transformadores esta en base del sistema sistema 100MVA
Modelo clásico del generador
GENA GENB GENC
S[MVA]
V[KV]
500 250 130
11 11 10
SET POINT 1,025 1,025 1,025
H [seg]
X’d[p.u.]
23,64 6,4 3,01
0,0608 0,1198 0,1813
Modelo del gobernador TGOV1 R
VMAX[p.u.]
Vmin[p.u.]
T1
T2
T3
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Estabilidad de Sistemas de Potencia
Solución: Antes de iniciar el estudio de estabilidad es necesario preparar los datos del sistema mediante un estudio de flujos de potencia, para asegurar que las condiciones iníciales de operación para el análisis de estabilidad sean iguales a las del ejemplo de Anderson & Found. En la Tabla 5.3 se muestra un reporte del estudio de flujos de potencia. Barras
Volt [p.u.]
Angulo [Deg]
A1-016 B1-018 C1-014 A2-230 F1-230 E1-230 B2-230 D1-230 C2-230
1,040 1,025 1,025 1,026 0,996 1,013 1,026 1,016 1,032
0 9,28 4,66 -2,22 -3,99 -3,69 3,72 0,73 1,97
Gen [MW] 71,64 163 85
Gen [Mvar] 27,03 6,64 -10,91
Carga [MW]
Carga [Mvar]
125 90
50 30
100
35
Tabla 5.3 Resultados del flujo de potencia del Ejemplo 6.1
a) Análisis del comportamiento del SEP ante una Falla trifásica Cuando el circuito esta en modo Run se debe ingresar al módulo de estabilidad transitoria f alla trifásica en la barra B2Add-Ons, Transient Stability, se debe añadir el evento de una falla 230, la falla es despejada a los 5 ciclos (0,083 seg) con la apertura de la Línea 2. El tiempo de simulación será de 2 segundos después de ocurrida la falla, este tiempo es suficiente para determinar si un sistema es estable o no. Primero se obtienen las gráficas de los ángulos de los generadores conectados a las barras B1-018 y C1-014, tomado como ángulo del generador A1-016 como ángulo de referencia. La Figura La Figura 5.21 es el resultado de la simulación.
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Estabilidad de Sistemas de Potencia
Figura 5.21 Grafica de diferencia de ángulo Vs tiempo (generador de referencia A1-016)
De la Figura la Figura 5.21 se observa que el ángulo máximo es de 85º y este valor se obtiene a los 0,43 segundos después de iniciado la falla, también se nota que la segunda oscilación no es mayor que la primera por tal motivo el sistema es estable por que el sistema tiende a reducir las oscilaciones.
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Estabilidad de Sistemas de Potencia
sistema es estable ya que la tendencia de la separación sep aración angular se mantiene, es decir no tiende aumentar. En la Figura la Figura 5.23 se muestran cuatro graficas adicionales, que son de frecuencia, potencia eléctrica activa, potencia eléctrica reactiva y el voltaje. En ellas se ve como son afectadas las magnitudes eléctricas después de la falla.
Frecuencia de los tres generadores [Hz]
Potencia eléctrica reactiva [Mvar]
Potencia eléctrica activa [MW]
Voltaje en [p.u.]
Figura 5.23 Graficas de la frecuencia, Potencias eléctricas y Voltaje
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Estabilidad de Sistemas de Potencia
Ángulos de los rotores de los generadores
Frecuencia de los generadores
Figura 5.24 Pérdida de generación sin mecanismos de control
La simulación de la pérdida de generación con mecanismos de control o reguladores se muestra en la Figura la Figura 5.25, en 5.25, en ella se ve que el sistema se desacelera y la frecuencia frecue ncia disminuye, pero después de algunos segundos la frecuencia empieza a incrementarse y estabilizarse en un nuevo valor, esto es debido a que los gobernadores de las unidades generadoras ordenan a los controles de la turbina inyectar más agua, gas o vapor, aumentando la potencia mecánica tal como se muestra en la figura.
Frecuencia de los generadores
Potencia mecánica de los generadores
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Estabilidad de Sistemas de Potencia
Frecuencia de los generadores
Potencia mecánica de los generadores
Figura 5.26 Pérdida de carga sin mecanismo de control
En la Figura la Figura 5.27 se ve la simulación para la pérdida de carga con mecanismo de control en ellos se aprecia que el sistema se acelera y la frecuencia se incrementa, pero después de algunos segundos se estabiliza en un nuevo valor, debido a la acción de los gobernadores, que ordenan a la turbina disminuir la entrada de agua, gas o vapor, reduciendo la potencia mecánica tal como se muestra en la Figura la Figura 5.27.
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Estabilidad de Sistemas de Potencia
simular diferentes disturbios simultáneos para diversos tiempos, sin restricciones en cuanto al número y secuencia de estos, y poder observar en forma gráfica el comportamiento del sistema ante estos.
EJERCICIOS PROPUESTOS 1. Con el sistema del ejemplo 6.1, ingresar los eventos para una falla trifásica cerca de la barra B2-230, la falla se despeja a los 5 ciclos (0.083 seg) con la apertura de los interruptores en los extremos de la línea 2. Simular los siguientes casos. f) Caso 1: Utilizar el modelo GENRU con el excitador IEEET1. g) Caso 2: Utilizar el modelo GENRU con el excitador IEEET1 y el gobernador TGOV1. En todos los casos analizar los ángulos de los rotores, la frecuencia, la potencia eléctrica activa [MW], la potencia eléctrica Reactiva [Mvar], los voltajes en las terminales de los generadores, determinar en todos los casos si el sistema es estable. Simular un despeje a los 10 ciclos. Simular la pérdida de generación (Gen C) y la pérdida de carga y graficar la frecuencia y potencia mecánica
Modelo GENRU del generador Datos
GEN A
GEN B
GEN C
S[MVA]
250
200
130
V[KV] SET POINT FP
10
11
10
1,04
1,025
1,025
1
0,85
0,85
TIPO
Hidra
vapor
vapor
H[seg]
23,64
6,4
30,1
Xd[p.u.]
0,146
0,8958
1,3125
X'd[p.u.]
0,0608
0,1198
0,1813
Xq[p.u.]
0,0969
0,8645
1,2578
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Estabilidad de Sistemas de Potencia
Modelo de excitador IEEET1 KA [p.u.]
TA [seg]
KE [p.u.]
TE [seg]
KF [p.u.]
TF VRMAX VRMIN SE(EFD1) [seg] [p.u.] [p.u.] [p.u.]
20
0,2
1
0,314
0,063
0,35
3,0
-3,0
0,3034
EFD1 [p.u.]
SE(EFD2) [p.u.]
EFD2 [p.u.]
2,8
1,2884
3,73
Modelo del gobernador TG0V1 GenA GenB GenC
R 0,05 0,05 0,05
VMAX[p.u.] 5 2,5 1
Vmin[p.u.] 0 0 0
T1 0,5 0,5 0,5
T2 3 3 3
T3 10 10 10
la Figura 5.28, con 5.28, con la información necesaria de cada 2. Construya el diagrama unifilar de la Figura elemento del SEP, los datos de las líneas y transformadores están en p.u. para una base de 100MVA. Determine los voltajes internos de los generadores A y C (Eaf ) antes de la falla. Determine los ángulos de los rotores de los generadores Ay C antes de la falla. Se presenta un cortocircuito solido trifásico en la línea AC-230 cerca de la barra A2230. La falla se elimina cuando se abren los interruptores en los extremos de la línea A2-230 y C2-230. Estos interruptores permanecen abiertos. Utilizar el módulo de estabilidad transitoria del programa PowerWorld, determinar d eterminar el tiempo crítico de liberación de la falla.
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Estabilidad de Sistemas de Potencia
TRAMO Línea1 AB-230 Línea2 AC-230 Línea3 BC-230 Línea4 BC-230
TENSION [kV] 230 230 230 230
TRANSFOR. AT1 230/10kV CT1 230/10 kV
U1/U2 230/10 230/10
R1 [p.u.]
X1 [p.u.]
B1 [p.u.]
0,007 0 ,007 0,018 0 ,018 0,008 0 ,008 0,008 0 ,008
0,040 0,110 0,047 0,047
0,082 0,226 0,098 0,098
SN [MVA] 450 300
R1[p.u.] 0 0
CAPACIDAD [MVA] 200 200 200 200 X1[p.u.] 0,022 0,040
Modelo clásico del generador S[MVA] P[MW] GEN A GEN C
400 250
350 185
V[kV]
H [seg]
10 10
11.2 8.0
SetPointVol [p.u] 1,03 1,02
X'd[p.u.] 0,067 0,1
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Anexos
ANEXO A : CALCULO DE AMPACIDAD DE LÍNEAS AÉREAS DE TRANSMISIÓN La norma IEEE Std 738 emplea una metodología basada en la ecuación fundamental del balance de calor que se define a continuación:
· ℃−℃ 25℃ ℃ ℃−℃ 25℃
(A.1) (A.2)
Por ser una norma norte americana se usa el sistema de unidades inglesas (US) donde: I : Capacidad de conducción o ampacidad del conductor [A] q R: Perdidas de calor por radiación [W/pie] qC : Perdidas de calor por convección [W/pie] qS : Ganancia de calor por radiación solar [W/pie] R: Resistencia del conductor [/pie] R75ºC : Resistencia del conductor a 75ºC (dato) [/pie] R25ºC : Resistencia del conductor a 25ºC (dato) [/pie] T C C: Temperatura máxima del conductor [ºC]
La temperatura en la superficie de un conductor depende de propiedades como: resistividad, diámetro, condiciones de la superficie (emisividad, absorción), condiciones climatológicas del ambiente (temperatura del aire, etc.) y la corriente eléctrica.
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Anexos
Las ecuaciones de calor recibido QS , el factor por corrección por altura k h y el coeficiente de absorción , se dan en las siguientes tablas. Qs [W/pie2] Atmosfera Atmosfera clara industrial 5 21,7 12,6 10 40,2 22,3 15 54,2 30,5 20 64,4 39,2 25 71,5 46,6 30 77,0 53,0 35 81,5 57,5 40 84,8 61,5 45 87,4 64,5 50 90,0 67,5 60 92,9 71,6 70 95,0 75,2 80 95,8 77,4 90 96,4 78,9 Fuente: IEEE std 738-1993. Art 2.5 Altitud solar Hc [ º ]
Tabla A.1 Calor total recibido por una superficie sobre el nivel del mar, debido a los rayos del sol
Ecuaciones para hallar QS:
Atmósfera limpia
3.924145.92762· 0.17856· 0.003223·
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Anexos
Estado de la superficie del conductor Pulido Sin Brillo Oxidado Oxidado y ligeramente sucio Muy oxidado Muy oxidado y sucio
Material Cobre Aluminio 0,15 0,08 0,24 0,23 0,50 0,35 0,60 0,50 0,75 0,70 0,88 - 0,93 0,88 - 0,94
Tabla A.3 Valores simultáneos para los coeficientes absorción y coeficiente emisividad ke
Angulo efectivo de incidencia de los rayos solares:
coscoscos·cos
(A.8)
La altitud HC y el azimut Z C del sol están en función de la localización de la línea de transmisión, el número de día del año y la hora del día. La altura del sol para el hemisferio sur se obtiene a partir de la ecuación Dónde:
sin sin ·sincos ·cos·cos
(A.9)
S S : Hora angular H C C: Altura del sol [º] S S: Declinación solar : Latitud [º]
La declinación solar S puede ser obtenida para cualquier día por la siguiente ecuación dada por Morgan:
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Anexos
La hora angular S es una medida con relación a la posición del sol cuando esta pasa por el meridiano local (medio día) así se tiene:
Dónde:
cos cos t t a n · t an an 15· − · ℎ12 − ℎ12
(A.11)
(A.12)
Hora: Hora del día de acuerdo al uso horario ts: Horas después del amanecer
Para determinar el valor del azimut del sol ZC se utiliza la siguiente ecuación
sin cos ·
Para el hemisferio sud ZC puede ser determinado como se indica a continuación: (a) S> 0 (invierno) S> 0 (mañana)
||
(A.13)
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La norma IEEE Std.738 propone dos ecuaciones para realizar el cálculo de las pérdidas de energía por convección forzada, es decir, en presencia del viento aquella que proporcione el resultado más alto será considerada para hallar el valor respectivo de las pérdidas:
. · · 1.010.371··· . · · 0.1695· · ·
Dónde:
(A.16) (A.17)
qC1 y qC2: Perdidas de calor por convección forzada [W/m] V : Velocidad del viento [pies/hora] f : Conductividad térmica del aire [W/pie-ºC] f : Viscosidad absoluta del aire [Lb/hora-pie]
Los coeficientes de la densidad ( f ), ), viscosidad ( f ) y conductividad ( f ) son tomados de la Tabla A.4.
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Anexos
Viscosidad absoluta del aire:
0.0415 415 1.1.2034·10− 1.1.1442·10− 1.9416·10− 0.0074 074 2.2.279·10− · 1.34·10− ·
(A.19)
Conductividad térmica del aire:
(A.20)
Donde:
T f : Temperatura media [ºC] H: Altitud sobre el nivel del mar [m] Una vez calculado los parámetros previos, es posible determinar la capacidad de corriente despejando la corriente de la ecuación de la ampacidad (A.1).
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ANEXO B : PARÁMETROS DE SECUENCIA CERO B.1 IMPEDANCIA SERIE DE SECUENCIA CERO Simple terna sin cables de guarda:
Donde:
· 3 4 ·· ·· 3·ln · 658.37·
Z 0S 0S : Impedancia de secuencia cero para una terna sin blindaje [/km] R0: Resistencia de secuencia cero [/km] X L0: Reactancia inductiva de secuencia cero [/km]
Anexos
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Anexos
Dcg12: Distancia entre los cables de guarda [m] Dcg1cg2
cg1
Cg
cg2
DCcg1
DAcg
DAcg1 DBcg1 DCcg
A
A
B
C
DBcg hcg
C
hcg1
B
a) Sim Simple ple te terna rna con con 1 C. C. Gu Guard arda
b) Sim Simple ple ter tern na con con 2 C. C. Gua Guard rdaa
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Anexos
ANEXO C: DIAGRAMA DE BLOQUES DE LOS GENERADORES, EXCITATRICES Y GOBERNADORES EMPLEADOS EN POWERWORLD C.1 MODELO DE MAQUINAS MAQUINAS SÍNCRONAS SÍNCRONAS
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Anexos
Figura 0.3 Generador de polos salientes sin devanados de amortiguación E fd
+
1 sT' sT'd0
-
+
-
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Anexos
Figura 0.5 Modelo del sistema de excitación de la IEEE tipo ST1 VREF
VS
EC 1 1 + sTR
2
+ -
+
+
VIMAX
1
3 1 + sTC
K A
1 + sTB
1 + sTA
VT VRMAX - K CIIFD
EFD
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Anexos
Gobernador TGOV1 Figura 0.8 Modelo de gobernador TGOV1con turbina a Gas VMAX P
+
P
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