Universidad de Costa Rica Facultad de Ingeniería Escuela de Ingeniería Eléctrica
IE – 0502 0502 Proyecto Eléctrico
Simulación de los lazos de control automático y manual del regulador de tensión automático (AVR) de un generador hidroeléctrico.
Por: Oscar Méndez García
Ciudad Universitaria Rodrigo Facio Julio del 2012
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Simulación de los lazos de control automático y manual del regulador de tensión automático (AVR) de un generador hidroeléctrico. Por: Oscar Méndez García
Sometido a la Escuela de Ingeniería Eléctrica de la Facultad de Ingeniería de la Universidad de Costa Rica como requisito parcial para optar por el grado de:
BACHILLER EN INGENIERÍA ELÉCTRICA
Aprobado por el Tribunal:
____________________________ _____ _________________________________ M. Sc. Gonzalo Mora Jiménez Profesor Guía
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DEDICATORIA
En primer lugar quiero dedicar este trabajo a Dios y a mis padres los cuales son el pilar de mi vida y el motivo por po r el cual cu al estoy acá, a cá, día a día son so n los que me ayudan a seguir adelante, por lo cual siempre los admiro. También dedicarles este esfuerzo a mis abuelos que con sus oraciones han pedido por mi superación en los estudios y la cual día a día me fortalece; a mis hermanas por su apoyo y confianza a lo largo de nuestras vidas. Muy importante hacer una mención a las personas con las cuales comparto mi diario vivir y a lo largo de este tiempo hemos desarrollado un sentimiento de hermandad, cada uno aporto a su modo algo para el desarrollo de este proyecto y de mi vida universitaria, a mis compas Andrés, Josimar, Javier, Mapi, Fabricio, Christian, Danilo, Keilyn, Edgardo, Jean Carlos, Charlie, gracias gallada por siempre haberme brindado una mano cuando lo necesite. Y a todas aquellas amistades que han depositado su confianza y apoyo en mí, gracias, su buena vibra me ayuda a superarme todos los días.
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RECONOCIMIENTOS
En primer lugar al profesor M.Sc. Gonzalo Mora por haber estado dispuesto a servirme de profesor guía, además por su tiempo y disponibilidad para atender mis dudas y apoyarme. También un reconocimiento a los Ingenieros Jonathan Rodríguez y Donald Siles por su colaboración y disponibilidad para servirme de lectores y aclarar cada una de las dudas que tuve con respecto al trabajo, además por todo el apoyo que me brindaron cuando realice la práctica profesional al lado de ellos, sinceramente aprendí mucho el tiempo que estuve ahí. Un reconocimiento muy especial a todo el personal del Centro de Servicio Técnico Huetar (CSTH), subestación Cóncavas del ICE, por la mano y el apoyo que me brindaron en el momento que estuve realizando la práctica profesional, aprendí de todos un poco. Y para finalizar un reconocimiento a mi compañero y amigo Andrés Alpízar por toda la ayuda y tiempo que me brindo en este proyecto, de verdad hubiera sido muy complicado sin esa ayuda.
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ÍNDICE GENERAL 1.
CAPÍTULO 1: INTRODUCCIÓN.................................. ................................................... ..................... .... 1
1.1
Objetivos ................................. .................................................. .................................. .................................. .............................. ............. 3
1.1.1 Objetivo general ....................................................... .......................................................................................................... ................................................... 3 1.1.2
Objetivos específicos ................................................................................................ 3
1.2
Metodología .................................. ................................................... .................................. .................................. ........................ ....... 4
2
CAPÍTULO 2: DESARROLLO TEÓRICO ................................ ....................................... ....... 5
2.1
Generación de energía eléctrica. ................................................ .......................................................... .......... 5
2.1.1 Tipos de energías utilizadas en Costa Rica. .................................................... ................................................................... ............... 6 2.1.2 Planta Hidroeléctrica Cachi. .......................................................................................... ...................................... .................................................... 7
2.2
Sistema de control de tensión.................................. .................................................. .............................. ............. 9
2.2.1 Sistema de excitación. ...................................................... ............................................................................................... ......................................... 13
2.3
Control en voltaje de generación. ................................. .................................................. ...................... ..... 14
2.4
Excitatriz................................. ................................................. .................................. .................................. ............................ ........... 16
2.4.1 Excitatriz rotativa. ................................................... ..................................................................................................... .................................................. 16 2.4.2 Excitatriz estática. ................................................... ..................................................................................................... .................................................. 17 2.4.3 Sistema de excitación ex citación IEEET1. .......................................................................... ...................... .......................................................... ...... 18
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2.4.4 Sistema de excitación ex citación tipo ESST4B. ........................................................................ ................................ ........................................ 20
2.5
Regulador de tensión. ........................................... ............................................................ ............................... .............. 23
2.5.1 Modelado del regulador regulado r de tensión. ...................................................... ............................................................................. ....................... 25
2.6
Generador. ................................. .................................................. .................................. .................................. ......................... ........ 26
2.6.1 Modelado del generador. ............................................................................................. ........................................... .................................................. 28
2.7
Rectificador. ................................. .................................................. .................................. .................................. ...................... ..... 29
2.8
Sistemas de control automáticos................................... ................................................... ...................... ..... 30
2.8.1 Sistema de control de lazo abierto [9]. ..................................................................... 30 2.8.2 Sistema de control de lazo cerrado [9]. ........................................................ ..................................................................... ............. 31 2.8.2.1
Lazo de control como c omo servomecanismo. ser vomecanismo. ....................................................... ........................................................... .... 32
2.8.2.2
Lazo de control como regulador [9]. ............................................................ .... ............................................................ .... 33
2.8.2.3
Respuesta al escalón es calón en un u n sistema realimentado [9]. ...................................... 34
2.8.3 Error permanente. ..................................................................... ............... ...................................................................................... ................................ 35 2.8.4 Control Proporcional Integral (PI) [9]. [9 ]. ..................................................................... 35 2.8.5 Identificación de los modelos, modelo de primer orden más tiempo muerto POMTM [9]. .......................................................................................................... ..................................................... .................................................................... ............... 38 2.8.6 Aplicaciones de control para p ara el diseño de controladores. controlad ores. ........................................ 39 2.8.6.1
Método de sintonización de d e Rovira [9]. ........................................................ ............................................................ .... 39
2.8.6.2
Drolac...................................................... ......................................................................................................... .......................................................... ...... 40
2.9
Estabilidad en los sistemas de potencia. ................
42
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2.9.1 Respuesta al escalón. es calón. ................................................................................................ ....................................................... ......................................... 42 2.9.2 Estabilidad con diagrama de Bode. .................................................... ........................................................................... ....................... 42
3.
CAPÍTULO 3: SINTONIZACIÓN DEL SISTEMA DE
REGULACIÓN AUTOMÁTICO......................... .......................................... ................................... ...................... .....45 3.1
Sintonización mediante Rate-Feedback [6]. ..................... ...................................... ................. 46
3.1.1 Pasos para la sintonización mediante Rate-Feedback. .............................................. 47 3.1.2 Modelado del sistema de excitación IEEET1 mediante Rate-Feedback. Rate- Feedback. ................. 50 3.1.3 Sintonización del d el conjunto excitador IEEET1.................................................... ......................................................... ...... 52
3.2
Sintonización mediante método planta controlador. ....................... 62
3.2.1 Pasos para la identificación y sintonización mediante el programa Drolac del software Matlab. ................................................................................................................... ................................................................. .................................................. 63 3.2.2 Modelado del sistema de excitación ESST4B mediante planta-controlador. ...........64 3.2.3 Sintonización del d el conjunto excitador ESST4B. .................................................. ........................................................ ...... 65
3.3
Sintonización mediante filtro de adelanto-atraso. ............................ ............................ 78
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4.1.1 Sistema de excitación ex citación IEEET1, unidades 1 y 2. ....................................................... ....................... ................................ 86 4.1.2 Sistema de excitación IEEET1, unidad 3. .................................................... ................................................................. ............. 87 4.1.3 Sistema de excitación ex citación ESST4B, unidades 1 y 2. ...................................................... ............. ......................................... 88 4.1.4 Sistema de excitación ESST4B, unidad 3. ................................................... ................................................................ ............. 89 4.1.5 Sistema de excitación ex citación IEEET1, unidades 1 y 2. ....................................................... ................................ ....................... 90 4.1.6 Sistema de excitación IEEET1, unidad 3. .................................................... ................................................................. ............. 90
4.2
Estabilidad mediante mediante diagrama de bode. ..................................... .......................................... ..... 91
4.2.1 Sistema de excitación ex citación IEEET1, unidades 1 y 2. ....................................................... ....................... ................................ 92 4.2.2 Sistema de excitación IEEET1, unidad 3. .................................................... ................................................................. ............. 94 4.2.3 Sistema de excitación ex citación ESST4B, unidades 1 y 2. ...................................................... ............. ......................................... 95 4.2.4 Sistema de excitación ESST4B, unidad 3. ................................................... ................................................................ ............. 97 4.2.5 Sistema de excitación ex citación IEEET1, unidades 1 y 2. ....................................................... ....................... ................................ 99 4.2.6 Sistema de excitación IEEET1, unidad 3. .................................................... ............................................................... ........... 100
5.
CAPÍTULO 5: CONCLUSIONES Y RECOMENDACIONES RECOMENDACIONES .... 103
5.1
Conclusiones ................................. .................................................. .................................. .................................. .................... ... 103
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Apéndice 1 Códigos en MATLAB. ......................................... .......................................................... .................... ... 110
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ÍNDICE DE FIGURAS Figura 2.1 Porcentajes Porc entajes de la producción de energía en el país [2]. [2 ].......................................... 7 Figura 2.2 Planta Hidroeléctrica Cachí [5]. [ 5]. ............................................................................ 9 Figura 2.3 Controles del regulador de tensión y el gobernador de la turbina para un turbogenerador de vapor v apor [15]. ....................................................................... ................. ............................................................................. ....................... 11 Figura 2.4 Diagrama de bloques simplificado: Control de voltaje del generador [15]. [ 15]. ....... 16 Figura 2.5 Sistema de excitación tipo IEEET1 [7]. .............................................................. 19 Figura 2.6 Sistema de excitación tipo ESST4B [7]. ............................................................. ................................................ ............. 21 Figura 2.7 Regulador Regulado r de tensión tens ión acoplado al sistema de excitación ex citación [11]. ............................ 24 Figura 2.8 Sistema de generación de una central hidroeléctrica [3]. .................................... 27 Figura 2.9 Rectificador controlado de onda completa [4]. ................................................... 30 Figura 2.10 Esquema Esqu ema para el sistema de control de lazo abierto. ......................................... 31 Figura 2.11 Esquema Esqu ema para el sistema de control de lazo cerrado. ........................................ 31 Figura 2.12 Representación esquemática para servo control. ............................................... 33 Figura 2.13 Respuesta Respu esta para un sistema realimentado. .......................................................... 34 Figura 2.14 Diagrama Dia grama de bloques bloque s del controlador PI. .......................................................... 36
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Figura 3.3 Modelo IEEET1 con Rate-Feedback Rate- Feedback [11]. [11] . .................................................... .......................................................... ...... 52 Figura 3.4 Modelo en Simulink del IEEET1 sin ajuste para las unidades unidad es 1 y 2................... 53 Figura 3.5 Tensión en terminales de las unidades 1 y 2, para los valores iniciales del IEEET1. ......................................................................................................... ................................................... ............................................................................. ....................... 54 Figura 3.6 Modelo en Simulink del IEEET1 con ajuste para las unidades 1 y 2. ................ .......... ...... 56 Figura 3.7 Tensión en terminales cuando se realizó la sintonización por Rate-Feedback para las unidades 1 y 2. ............................................. .................................................................................................. .................................................................... ............... 57 Figura 3.8 Tensión Tens ión en terminales de la unidad 3, para los valores iniciales del d el IEEET1. .... 58 Figura 3.9 Modelo en Simulink del IEEET1 con ajuste para las unidad un idad 3. .......................... 61 Figura 3.10 Tensión en terminales de la unidad 3, para los valores finales f inales del IEEET1. .... 61 Figura 3.11 Sistema de realimentación o lazo cerrado para método planta-controlador. planta -controlador. ..... 62 Figura 3.12 Modelo ESAC8B para método planta-controlador. .......................................... .................................... ...... 65 Figura 3.13 Modelo en Simulink del ESST4B sin ajuste para las unidades u nidades 1 y 2. ............... 66 Figura 3.14 Salida de la planta para ESST4B para valores iniciales sin ajustar en unidades 1 y 2. ................................................................................................ ......................................... ............................................................................................... ........................................ 67 Figura 3.15 Introducción del valor va lor de la planta en el programa. .......................................... 68
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Figura 3.20 Selección Sele cción del método de sintonización del de l controlador. ................................... 71 Figura 3.21 Valores de los parámetros p arámetros del controlador. c ontrolador. ................................................. ....................................................... ...... 71 Figura 3.22 Modelo en Simulink del ESST4B con ajuste para las unidades u nidades 1 y 2. .............. 73 Figura 3.23 Salida de la l a planta para ESST4B ESST4 B para unidades 1 y 2 con ajuste. .................... .............. ...... 73 Figura 3.24 Modelo en Simulink del ESST4B sin ajuste para la unidad 3........................... 3........................... 75 Figura 3.25 Salida de la planta para ESST4B para valores iniciales sin ajustar en la unidad 3. .................................................................................................. ............................................ ............................................................................................... ......................................... 75 Figura 3.26 Modelo en Simulink del ESST4B con ajuste para la unidad 3. ........................ 77 Figura 3.27 Salida de la l a planta para ESST4B ESST4 B con valores finales en la unidad 3. ............... 78 Figura 3.28 Sistema de excitación con filtro adelanto atraso. .............................................. 79 Figura 3.29 Modelo en Simulink para excitador IEEET1 con filtro adelanto-atraso unidades
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Figura 4.3 Respuestas Respu estas del sistema de excitación ESST4B para las unidades 1 y 2. ............. 88 Figura 4.4 Respuestas del sistema de excitación ESST4B para la unidad 3. ....................... 89 Figura 4.5 Respuestas del sistema de excitación IEEET1 para las unidades 1 y 2. ............. ....... ...... 90 Figura 4.6 Respuestas del sistema de excitación IEEET1 para las unidades 1 y 2. ............. ....... ...... 91 Figura 4.7 Diagrama Dia grama de bode para IEEET1 sin sintonizar en las unidades 1 y 2. ................ 92 Figura 4.8 Diagrama Dia grama de bode para IEEET1 sintonizado en las unidades 1 y 2. ................... 93 Figura 4.9 Diagrama Dia grama de bode para IEEET1 sin s in sintonizar en la unidad 3............................ 94 Figura 4.10 Diagrama Dia grama de bode bod e para IEEET1 sintonizado en la unidad 3. ............................ 95 Figura 4.11 Diagrama Dia grama de bode bod e para ESST4B ESS T4B sin sintonizar en las unidades 1 y 2. ............. 96 Figura 4.12 Diagrama Dia grama de bode bod e para ESST4B ESS T4B sintonizado en las unidades 1 y 2. ................ 97 Figura 4.13 Diagrama Dia grama de bode bod e para ESST4B ESS T4B sin sintonizar en la unidad 3. ........................ 98
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ÍNDICE DE TABLAS Tabla 2.1 Datos de la Planta Hidroeléctrica Cachí. ................................................ ............................................................... ............... 9 Tabla 2.2 Rango Ran go de valores para los parámetros pa rámetros del excitador IEEET1 [8]. [ 8]. ........................ 20 Tabla 2.3 Parámetros del excitador ESST4B [8]. [8] . ................................................... ................................................................ ............. 22 Tabla 2.4 Constantes para la sintonización sintoniz ación por el método de Rovira Rovir a [9]. ............................ 40 Tabla 3.1 Parámetros Parám etros de ajuste ajus te inicial para el IEEET1 para par a las unidades 1 y 2. .................. 53 Tabla 3.2 Parámetros de d e ajuste final para el IEEET1 para las unidades unidad es 1 y 2. .................... 56 Tabla 3.3 Parámetros de d e ajuste inicial para el IEEET1 para la unidades 3. ......................... 58 Tabla 3.4 Parámetros Parám etros de ajuste ajus te final para el IEEET1 para las unidad 3. .............................. 60 Tabla 3.5 Parámetros Parám etros de ajuste ajus te inicial para ESST4B ESS T4B para las unidades 1 y 2. ..................... 66 Tabla 3.6 Parámetros de d e ajuste final para ESST4B para las unidades unidad es 1 y 2. ....................... 72
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NOMENCLATURA ∆V: Diferencia de tensión. ∆u: Cambio en el escalón. ∆y: Cambio en la salida. ωm: Velocidad del rotor. ωmg: Frecuencia de cruce de ganancia. ωmf : Frecuencia de cruce de fase.
AVR : Regulador de tensión automático. d (s): Perturbación. e (s): Señal de error.
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IT: Corriente en terminales de la maquina sincrónica. K A: Ganancia del regulador de tensión. K C: Ganancia proporcional del regulador de tensión. K Cx Cx: Factor de rectificación de carga proporcional a la reactancia de conmutación. K E: Ganancia del excitador K G: Ganancia de la realimentación del lazo interno de regulación de campo. K i: Ganancia integral del regulador de tensión. K IM IM: Ganancia integral del regulador de tensión. K IR IR : Ganancia integral del regulador de tensión. K Ix Ix: Coeficiente de ganancia del circuito de potencial. K F: Ganancia del Rate-Feedback.
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MF: Margen de fase. MG: Margen de ganancia. Myd(s): Función de transferencia de control regulatorio. Myr(s): Función de transferencia de servo control. pe: Potencia eléctrica. pref : Potencia de referencia.
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THETAP: Angulo del fasor del coeficiente de ganancia del circuito potencial. t75: Tiempo al 75%. t25: Tiempo al 25%. u (s): Señal de control. VB: Tensión disponible en la excitatriz. VOEL: Salida del limitador de sobre-excitación.
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RESUMEN El principal objetivo de este trabajo es simular los lazos de control de un regulador de tensión automático (AVR). Se realizó un estudio sobre sistemas de control de tensión y sistemas de control automático. Para la simulación de los lazos de control del AVR se buscaron modelos teóricos de sistemas de excitación en este caso se trabajaron los modelos IEET1 y el ESST4B.
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1. CAPÍTULO 1: Introducción En los sistemas eléctricos de potencia se presentan frecuentemente perturbaciones tales como cambios en la carga y generación, estas variaciones provocan desbalances que generan oscilaciones de frecuencia de diferente magnitud; con esto se forman múltiples problemas en la transmisión de potencia. Estas oscilaciones que se producen deben de ser suprimidas o amortiguadas por los elementos de control del sistema.
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amplificada y aplicada a la etapa del controlador de potencia del campo del generador. El desempeño de un regulador de tensión eficaz va de la mano con su velocidad de respuesta después de una variación de la carga, evitando así un cambio drástico en la tensión de salida. Además debe poder llevar con exactitud la tensión nuevamente a su valor nominal y ser sensible a los pequeños cambios de la carga. Desarrollar un método para la sintonización de los AVR mediante simulación es la
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1.1
Objetivos
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1.2
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2
CAPÍTULO 2: Desarrollo teórico
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La demanda de energía eléctrica de una ciudad, región o país tiene una variación a lo largo del día, esta variación es función de muchos factores, entre los que destacan: tipos
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medio de producción se convierte en el de mayor porcentaje e importante para el país, en el siguiente grafico se mostrara el porcentaje según cada tipo de energía que se genera en el
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2. La estabilidad relativa dice que tan estable es el sistema, logrando establecer el riesgo que tiene el sistema de volverse inestable cuando se dé un cambio en sus parámetros. 3. La robustez hace referencia a la inestabilidad del sistema ante la variación de los parámetros de la plante, en este caso los márgenes de ganancia y fase se utilizan como índices de robustez. 4. Se pretende que un sistema establea sea lo suficientemente estable para cuando se presente una variación de los parámetros del modelo de la planta, el sistema no se vuelva inestable. Esto plantea un sistema con los márgenes de ganancia y faso lo suficientemente grandes, para no llegar a la inestabilidad ante la variación de los parámetros, entonces el sistema poseerá estabilidad relativa y será robusto cuando: MF > 30°
(2.24)
MG > 6 dB
(2.25)
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Figura 2.17 Diagrama de Bode.
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3. CAPÍTULO 3: Sintonización del sistema de regulación automático. Se centrara la atención en el funcionamiento del lazo de control como servomecanismo; ya que se desea seguir en este caso un valor de referencia en la tensión y luego estudiar la dinámica del sistema cuando este valor de entrada varía. El procedimiento de sintonización de pequeña señal aquí sugerido, está basado en la respuesta al impulso del generador a circuito abierto. Se lleva a voltaje nominal la unidad y después se le aplica un pequeño escalón en la referencia; luego se graban las tensiones de campo y terminales. Si la respuesta del lazo de regulación de tensión no es la adecuada sea esto porque la respuesta se muestre muy lenta o demasiado oscilatoria, entonces se vuelve a sintonizar los parámetros hasta que la respuesta tenga el desempeño deseado.
Figura 3.1. Lazo de control de tensión simple [11]. En la figura anterior se presenta un lazo de regulación de tensión muy simplificado para una unidad que está en vacío. EL regulador automático de voltaje es representado repres entado con
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una ganancia y una constante de tiempo (K A y TA), el generador es representado con la constante de tiempo transitoria de circuito abierto T’do. Para obtener los parámetros adecuados se desarrollaran tres métodos mediante la predicción de la respuesta que se obtiene de la definición de unos parámetros de ajuste en términos de otros.
3.1 Sintonización mediante Rate-Feedback [6]. El método de sintonización de Rate-Feedback analiza la respuesta en frecuencia del sistema en lazo cerrado, dando acá énfasis a la influencia que tienen las ganancias. Se define un modelo del sistema de excitador-generador, tal como se muestra en la figura siguiente y a partir de él se obtendrá una relación de parámetros que para realizar la sintonización.
Figura 3.2 Sistema de excitación con Rate-Feedback [11].
Sobre el ajuste de la ganancia del sistema, se menciona que ésta debe ser un compromiso entre el margen de fase obtenido y la velocidad de respuesta del regulador de
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tensión. Se debe tener el cuidado de mantener la estabilidad del lazo de regulación de voltaje, así como la estabilidad del lazo interno.
3.1.1 Pasos para la sintonización mediante Rate-Feedback. El procedimiento de ajuste a realizar cuando la respuesta ante un impulso, en la condiciones de circuito abierto, sea muy poco amortiguada o inestable, es el siguiente. 1. Comparar K A , T A , T E , T do con los datos típicos. La relación un valor mayor a 200, donde valores de
T A
y
T E
K E está
K A K E
debe tener
entre un valor cercano a 0 o a 1. Los
dependerán de las características del regulador de
tensión y del excitador. El valor de T do dependerá de las características del generador. Estos parámetros se establecen como exactos, por lo tanto se procede a establecer
T F y K F .
2. Se asume en un principio que la frecuencia de cruce del lazo interno ocurrirá exactamente en
1 T A
, interpretando esto de la siguiente manera.
log
K A K E
log
T F K F
log
1 T A
log
K E T E
Por lo tanto despejando la relación que se tiene para siguiente:
K A ,
(3.1) se obtendrá lo
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K A
T E T F T A K F
(3.2)
3. Ante lo mencionado en el punto anterior, se establece un intervalo adecuado para los posibles valores de la frecuencia frecuen cia de cruce por cero del lazo externo. extern o. 1 1 log log5 T F 5T A T A T F
log
(3.3)
4. Una vez definido el intervalo adecuado, se establecerá un punto donde se espera que pueda ocurrir el cruce de frecuencia del lazo externo, dicho punto 1
será preferiblemente el punto medio entre los logaritmos de
1 T F
log
C
T A
1 1 log T A T F log C
y
1 T F
, o sea:
log
2
1
T F K F
T F
1 T A 5
1 2,236T A
(3.4)
(3.5)
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T F K F
K F
5. El valor que se tiene para
K A se
C T do
5 5T A T do
11,18T A2
T do
(3.7)
(3.8)
compara con el que se ha asumido en el
punto 2: 5.1.Si
K A
está cerca de
T E T F T A K F
, con los valores de
T F
y
K F que
se
escogieron en el punto 3 y en el punto 4, entonces es admitido utilizar estos parámetros para realizar la sintonización con valores cualesquiera de estos, pero que incidan en una misma relación para
5.2.Si el valor del parámetro
K A es
mucho mayor que
T F K F T E T F
T A K F
, entonces se
puede utilizar lo que se planteó en el punto anterior, pero si aun con esto la respuesta es muy oscilatoria, entonces se buscara un valor de T T
K A
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5.3.Si el valor del parámetro K es más bajo que A
0,7T E T F T A K F
, se tendrá que el
segundo punto de cruce, ocurrirá en valores inferiores a
1 T A
. Por lo tanto
se escogerá este segundo punto de intersección, el cual puede ser escogido a una frecuencia de: 2 C
2,236 K A T do T E
(3.9)
Para obtener los valores de T y K se calculara de la siguiente forma: F
F
T F
5
(3.10)
2 C
K F
11,18 2 T do 2C
(3.11)
Entonces estos valores serán aptos para la sintonización, mientras se mantenga la relación constante entre utilizándose un valor de
T F mayor
T F K F
mencionada en el punto 5.1 y
al calculado.
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Cabe resaltar que se incluirá el generador en el sistema de excitación, ya que este de este depende en gran parte el método de sintonización por lo cual se incluirá un modelo para el generador tal y como se mostró en el capítulo capítu lo anterior. Entonces partiendo del modelo original que se tenía para el sistema de excitación IEEET1 que se presentó en la figura 2.5, entonces se omitirán las señales de entradas procedentes del filtro de regulación y las señales V S , condescendiendo que en la entrada sea aplicada únicamente la tensión de referencia V REF REF . El nuevo sistema excitador generador se adapta de manera conveniente, con tal de obtener un diagrama similar al que se planteó para desarrollar el método de Rate-Feedback (Figura 3.2). Una vez que se ha incorporado el generador al modelo y se realimenta la señal se le dará un valor nulo a la función de saturación
S E ,
V T ,
esto porque es una función no lineal,
entonces al proponer el valor nulo para esta función se hará desaparecer el lazo que se tiene en paralelo con K . E
En la figura que se mostrara a continuación se presentara el modelo una vez que se ha aproximado lo más cercano posible al modelo con Rate-Feedback; para este caso debido
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Figura 3.3 Modelo IEEET1 con Rate-Feedback [11]. 3.1.3 Sintonización del conjunto excitador IEEET1. En primer lugar antes de realizar la sintonización, se deben considerar valores iniciales para los parámetros, dichos valores se pueden obtener de las especificaciones del fabricante, estos rangos de valores se mencionan en el capítulo 2, entonces se seleccionaran según los rangos que se establecen para determinar un punto de partida para la sintonización, en este proyecto a la hora de hacer uso de la constante de tiempo del generador T do , se emplearan los valores que tiene la Planta Hidroeléctrica de Cachi, por lo
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Tabla 3.1 Parámetros de ajuste inicial para el IEEET1 para las unidades 1 y 2. Parámetros del sistema de excitación. Parámetro Valor K E 0,5 TE 0,5 TA 0,5 VRMIN -10 VRMAX 10 Parámetros de ajuste. Parámetro Valor K F 0,15 TF 1,5 K A 100 Parámetro del generador. Parámetro Valor T´do 5,85 Según con los parámetros que se establecieron en la tabla anterior se desarrollara el
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Entrada escalon Salida de la planta 1.05
1.045
1.04
1.035 ) u . p 1.03 ( d u t i l p m1.025 A
1.02
1.015
1.01
1.005
1 10
15
20
25
30 Tiempo(s)
35
40
45
Figura 3.5 Tensión en terminales de las unidades 1 y 2, para los valores iniciales del IEEET1. Como se puede apreciar posee en la figura 3 la gráfica de la tensión en terminales
50
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un valor de 150. Además el valor para la constante de tiempo del generador será en este caso tanto para la unidad 1 y la unidad 2 de T do 5,85 2. Verificación del valor de K . El valor de K según la relación planteada en A
el K A
procedimiento T E T F T A K F
A
de
0,5 1,5 0,5 0,15
Rate-Feedback
10
3. Valor adecuado para T . Entonces se tendrá que F
T F 5T A 5 0,5 2,5
4. Valor adecuando para K . F
K F
5 5T A2 T do
11,18T A2 T do
2
11,180,5 5,85
0,477778
corresponde
a
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Tabla 3.2 Parámetros de ajuste final para el IEEET1 para las unidades 1 y 2. Parámetros del sistema de excitación. Parámetro Valor K E 0,5 TE 0,5 TA 0,5 VRMIN -10 VRMAX 10 Parámetros de ajuste. Parámetro Valor K F 0,477778 TF 2,5 K A 150 Parámetro del generador. Parámetro Valor T´do 5,85
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1.06 Entrada escalon Salida de la planta
1.05
1.04
) u . p ( d u 1.03 t i l p m A
1.02
1.01
1
15
20
25
30 Tiempo(s)
35
40
45
50
Figura 3.7 Tensión en terminales cuando se realizó la sintonización por RateFeedback para las unidades 1 y 2. Ahora se procederá a utilizar el mismo modelo pero para la unidad 3 de la Planta
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Tabla 3.3 Parámetros de ajuste inicial para el IEEET1 para la unidades 3. Parámetros del sistema de excitación. Parámetro Valor K E 0,5 TE 0,5 TA 0,5 VRMIN -10 VRMAX 10 Parámetros de ajuste. Parámetro Valor K F 0,15
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Como se pudo apreciar la tensión en terminales para la unidad 3 al igual que en las unidades 1 y 2 poseen un sobrepaso superior al 5% por lo tanto es necesario realizar la sintonización para reducir este sobrepaso, los pasos a realizar serán los siguientes.
Procedimiento de sintonización del IEEET1 1. Se tiene que la relación
K A K E
100 0,5
200 , pero este valor debe de ser mayor
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Este valor encontrado de K se utilizara para calcular el nuevo valor de K
A
F
5. Se establece el nuevo valor de K
A
K A
T E T F T A K F
0,5 2,5 0,5 0,450081
5,5545
Ahora con los nuevos valores que se obtuvieron en la sintonización (Tabla 3.4) se procederá a variar los parámetros del sistema excitador-generador IEEET1 como se
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3.2 Sintonización mediante método planta controlador. El método de sintonización mediante método planta-controlador plantea su operación en definir un modelo de lazo cerrado (realimentado), donde se establecen los parámetros de la planta y del controlador para el sistema de excitación; dicho modelo presentara la siguiente forma, la cual es un clásico sistema s istema de realimentación sencillo.
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método se desarrollara dos veces, uno para el valor de las constantes de tiempo de las unidades 1 y 2 y el otro para el valor de la constante de tiempo de la unidad 3.
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cual desplegara una ventana donde se podrá seleccionar el método de sintonización que se desea.
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K Cx Cx=0 y VB=1. Además aplicando un poco de algebra de bloques se logra reducir el modelo hasta obtener el mostrado a continuación, este modelo implica que tanto la ganancia K IM
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Tabla 3.5 Parámetros de ajuste inicial para ESST4B para las unidades 1 y 2. Parámetros del sistema de excitación.
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Una vez que se ha realizado la simulación se llega a obtener la siguiente grafica en
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5. Capítulo 5: Conclusiones y Recomendaciones 5.1Conclusiones 5.1 Conclusiones
Los sistemas de control de tensión son de suma importancia ya que mantienen los niveles de tensión dentro de los límites aceptables.
En los sistemas de potencia se utilizan ampliamente los sistemas de control automático.
La principal función del sistema de control de excitación consiste en el control de tensión y en la mejora de la estabilidad del sistema eléctrico
Los sistemas de excitación además de proveer la corriente directa al devanado de campo, presenta funciones de control y protección, que influyen sobre el comportamiento del sistema eléctrico.
El regulador de tensión constituye el elemento que controla la salida de la excitatriz, registra la salida del generador, esta señal se conduce a un detector de error donde se compara con una señal que se tendrá de referencia.
El sistema de control de lazo cerrado es el cual la acción de control es dependiente de la salida o bien la salida tiene una influencia sobre la entrada, para esta acción es necesario que la entrada sea modificada en cada instante respecto a la salida, esto mediante la realimentación.
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Para estos sistemas se pretende que la respuesta tenga el comportamiento de servo control ya que se desea un buen seguimiento del valor de referencia en la tensión.
Es posible representar mediante funciones de transferencias teóricas al generador y al regulador de tensión.
Mediante la sintonización de controladores se puede corregir la respuesta al sistema en caso de presentarse inestabilidad.
El método de Rate-Feedback analiza la respuesta en frecuencia del sistema en lazo cerrado, dando énfasis a la influencia de las ganancias; brindando las pautas para encontrar los parámetros adecuados para el ajuste.
El método de sintonización planta-controlador, ofrece la posibilidad de escoger el método de sintonización que mejor se ajuste a las necesidades que se presenten.
El método de sintonización mediante filtro de adelanto-atraso logra minimizar el error en régimen permanente, sin comprometer el margen de fase de lazo abierto.
Mediante el diagrama de bode se puede analizar la estabilidad del sistema, según los criterios de estabilidad que se utilizan para este análisis.
Se pudo determinar el efecto que produce el controlador una vez que este se sintonizo contra la respuesta original del sistema planteado.
Mediante estos métodos de sintonización se ofrece una opción para el ajuste de controladores, en el cual se pude conocer el comportamiento que este tendrá el sistema ante el método elegido, siendo esta una mejor opción contra el método que
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comúnmente se aplica el de prueba y error, en el cual la respuesta se conocerá hasta que aplique directamente en la práctica, sin tener una respuesta previa.
5.2Recomendaciones 5.2 Recomendaciones
Es primer lugar lugar se debe de tener claro las las condiciones que se plantean para el sistema de control de tensión opere en un rango aceptable.
Es muy importante seleccionar el sistema de excitación que más se ajuste al sistema que se desea modelar.
Utilizar únicamente los valores para los parámetros según los datos y rangos que se brindan para cada sistema de excitación.
Según el método que se esté utilizando tener cuidado a la hora de realizar la sintonización y verificar paso a paso cada punto que se desarrolló para no incurrir en el error.
Tener presentes muy bien las técnicas de reducción o algebra de bloques para logran reducir el sistema de manera correcta.
A la hora de realizar la identificación del modelo utilizar un método de sintonización y un criterio de error que cumpla con las condiciones que se plantean para estabilidad o margen aceptable del sistema.
Preferiblemente desarrollar la sintonización mediante un programa que lleve a cabo este proceso, esto con la intensión de evitar error en algún calculo que se pase por
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alto, además con un programa que lo realice se logra una precisión aún mejor a la hora de obtener los datos.
Desarrollar alguno de los tres métodos según sea el caso que se presente, con el fin de evitar utilizar el método de prueba y error, muy comúnmente usado en la práctica.
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BIBLIOGRAFÍA 1. “ Siste Si stema ma elé el é ctr i co, fu f u entes ent es energé ener gé ti cas e h i stor i a de la electr el ectrii f i cación caci ón en Costa Co sta Rica ” ” . http://www.cientec.or.cr/ciencias/energia/articulo3.html
2. A pellidos, inicial del nombre del autor. “Generación eléctrica en Costa Rica”, Revista CIEMI, Costa Rica, N° 63, 2009. 3. “Magnetismo”.
http://acer.forestales.upm.es/basicas/udfisica/asignaturas/fisica/magnet/generador.ht ml
4. “CONVERTIDORES CA/CC - - RECTIFICADOR RECTIF ICADORES” ES” . http://tec.upc.es/el/TEMA3%20EP%20(v1).pdf
5. “Represa
Hidroeléctrica
Cachí”.
http://www.skyscrapercity.com/showthread.php?t=1110401
6. Koessler. R. “Techniques for tuning excitation system parameter ”. IEEE Transactions on Energy Conversion; Volumen 3, No. 4, 1988. 7. Siemens Energy, Inc. “PSS/E 32.0.5, MODEL LYBRARY” , 2010. 8. Power Technologies Inc, “PSS/E 30, VOLUME II: PROGRAM APPLICATION GUIDE”, 2010.
9. Alfaro, V.M. “Apuntes del curso IE -0431. Sistemas de control”, Universidad de Costa Rica.
10. Hernandez A. “Herramientas para el análisis del desempeño y la robustez de los
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11. Gatjens P. “Procedimiento para la sintonización de los dispositivos de ajuste de los reguladores automáticos de tensión de los sistemas de excitación: IEEET1, ESAC5A, ESAC8B y ESST4B”. Proyecto de graduación, Costa Rica, 2011.
12. Norma IEEE 421.2, “Guide for Identification, Testing, and Evaluation of the Dynamic Performance of Excitation Control Systems” , 1990.
13. Norma IEEE 421.5, “IEEE R ecommended ecommended Practice for Excitation Systems Models for owner System Stability Studies” , USA, 2005.
14. Norma IEEE 421.4, “IEEE Guide for the Preparation of Excitation System Specifications”, USA, 1990.
15. Duncan J/Sarma M. “Sistemas de Potencia. Análisis y Diseño.” 3era edición, THOMSON, 2004
16. “Estudio de los principales equipos de control y protección en una central hidroeléctrica”. http://dspace.ups.edu.ec/bitstream/123456789/283/2/Capitulo1_Diseno_de_automat izacion_de_protecciones_para_fase_I_de_central_hidroelectrica_Saucay.pdf
17. Cubillos F. “Sistemas de Excitación Estática de Generadores Sincrónicos”,
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19. Rodríguez J. “Actualización, implementación y puesta en marcha del sistema de control de excitación estática para la unidad No.1 de la Planta Hidroeléctrica Electriona”, Proyecto de graduación. Costa Rica, 2009. 20. Vargas L. “SISTEMAS DE EXCITACIÓN DE MAQUINAS SINCRONICAS”, apuntes curso EM-737 Fenómenos Dinámicos de redes de potencia. Universidad de Chile, 2010.
21. Alfaro V.M.” Sintonización de controladores PI y PID utilizando los criterios integrales IEA e ITAE”.
Revista Ingeniería, Costa Rica, No. 1 y 2. Volumen 13,
2003.
22. Alfaro V.M.” Métodos de sintonización de controladores PID que operan como servomecanismos”. Revista Ingeniería, Costa Rica, No. 1 y 2. Volumen 13, 2003.
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APÉNDICES Apéndice 1 Códigos en MATLAB. Identificación de modelos utilizando el método 123c de Alfaro. %Identificación de modelos utilizando el método 123c (programa principal) %Versión 2.6 @ 08.jun.2007 %Víctor M. Alfaro (c) 2004, 2006, 2007 %Departamento de Automática %Escuela de Ingeniería Eléctrica %Universidad de Costa Rica %San José, Costa Rica %
[email protected] % %La función fc_id123cv26 permite la identificación de modelos %de primer y segundo orden más tiempo muerto para una planta %a partir de su curva de reacción, utilizando el método 123c % [Alfaro, V. M. - "Identificación de modelos de orden reducido % a partir de la curva de reacción del proceso", % Ciencia y Tecnología (Costa Rica), Vol. 42 (2) ,2006] % clear s=tf('s' s=tf('s'); ); %-----------------------------------------------------%Proporcionar la función de transferencia de la planta %para la cual se quieren identificar los modelos % %DATO: gp - función de transferencia de la planta % %====================================================== gp=0.5/((0.75*s+0.6)*(0.3*s+1)*(5.85*s+1)); %gp.outputdelay=0.25; %======================================================
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Para generar grafica de bode. bode( )
Con esta función se genera el diagrama de bode de la función de transferencia que se desea modelar.
Reducción de bloques en MATLAB. Unidades 1 y 2. s=tf ('s'); A=(1/(0.5*s+1)) G=(1/(5.85*s+1)) Y=0.7 U=((0.9*s+5)/(1.63*s+3.5)) S=((U)/(1+(U*Y))) F=A*S*G
Unidad 3. s=tf ('s'); A=(1/(0.5*s+1)) G=(1/(6.21*s+1)) Y=0.7 U=((0.9*s+5)/(1.63*s+3.5)) S=((U)/(1+(U*Y))) F=A*S*G
Para utilizar el programa Drolac. drolac