MANUAL BÁSICO DE IMPLEMENTACIÓN DE LA HERRAMIENTA DE SIMULACIÓN “POWER SYSTEM ANALYSIS TOOLBOX

MANUAL BÁSICO DE IMPLEMENTACIÓN DE LA HERRAMIENTA DE SIMULACIÓN “POWER SYSTEM ANALYSIS TOOLBOX” ,

PSAT

JORGE HERNÁN HOLGUÍN ARBOLEDA JULIAN OCAMPO ZULUAGA

UNIVERSIDAD UNIVERSIDAD NACIONAL DE COLOMBIA FACULTAD DE INGENIERIA Y ARQUITECTURA INGENIERÍA ELÉCTRICA MANIZALES, ABRIL 2010

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MANUAL BÁSICO DE IMPLEMENTACIÓN DE LA HERRAMIENTA DE SIMULACIÓN “POWER SYSTEM ANALYSIS TOOLBOX” ,

PSAT

JORGE HERNÁN HOLGUÍN ARBOLEDA Cod: 0205025 JULIAN OCAMPO ZULUAGA Cod: 0205032

Monografía en Ingeniería Eléctrica E léctrica

Director de Trabajo de Grado CESAR ARANGO LEMOINE Ingeniero Electricista

UNIVERSIDAD UNIVERSIDAD NACIONAL DE COLOMBIA FACULTAD DE INGENIERIA Y ARQUITECTURA INGENIERÍA ELÉCTRICA MANIZALES, ABRIL 2010

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TABLA DE CONTENIDO LISTA DE FIGURAS ............................................................................... ................................................................................................ ................. I LISTA DE TABLAS.................................................... ................................................................................ .............................................. .................. II RESUMEN ........................................................ .................................................................................... ..................................................... ......................... III INTRODUCCIÓN ...................................................... .................................................................................. ............................................. ................. IV 1. QUE ES PSAT .......................................................................... .................................................................................................... .......................... 1 2. CARACTERÍSTICAS CAR ACTERÍSTICAS DEL DE L PSAT P SAT ................................................................. ........................................................................ ....... 3 2.1 Rutinas disponibles en PSAT ................................................... ......................................................................... ...................... 3 2.2 Modelos disponibles en PSAT ....................................................................... ....................................................................... 3 2.3 Herramientas adicionales ..................................................... ............................................................................... .......................... 3 2.3.1 GUI principal ..................................................... ................................................................................. ....................................... ........... 4 2.3.2 Conversión Conve rsión de Formato de Datos ...................................... ............................................................ ...................... 5 2.3.3 Modelos Definidos por el Usuario ............................. ......................................................... ............................... ... 6 2.3.4 Librerías Simulink S imulink ......................................................................... .................................................................................... ........... 7 2.3.5 Uso de Líneas de Comando ............................................................. .................................................................... ....... 9 3. MODELOS MODEL OS Y RUTINAS DE PSAT ........................................................... .................................................................... ......... 10 3.1 Modelo de Sistema de potencia po tencia ................................................... ................................................................... ................ 11 3.2 Flujo de Potencia .................................................................... ........................................................................................ .................... 12 3.3 Análisis de Bifurcación – Flujo de Potencia Continuo (CPF) ........................ 13 3.4 Flujo Óptimo de Potencia (OPF) .................................................. .................................................................. ................ 14 3.4.1Modelo OPF Estándar ....................................................................... ............................................................................ ..... 14 3.5 Estabilidad E stabilidad de Pequeña Señal (SSS)...................................................... ........................................................... ..... 15

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3.6 Simulaciones en el Dominio del Tiempo ...................................... ...................................................... ................ 16 4. PRIMEROS PASOS ................................. ............................................................. ........................................................ .............................. 18 4.1 Descarga ............................................. ......................................................................... ........................................................ .............................. 18 4.2 Requerimientos ........................................................... ....................................................................................... ................................. ..... 18 4.3 Instalación ........................................................ .................................................................................... ............................................ ................ 19 4.4 Ejecutando PSAT ....................................................... ................................................................................... ................................. ..... 19 4.5 Cargando Datos ........................................... ....................................................................... ................................................ .................... 20 4.6 Corriendo el Programa .................................................... ................................................................................ .............................. 21 4.7 Visualización Visualizaci ón de Resultados R esultados ........................................................ ........................................................................ ................ 21 4.8 Guardando Resultados ................................................................ ................................................................................ ................ 22 4.9 Configuraciones ............................................................................. ........................................................................................... .............. 22 4.10 Diseño Dis eño de la Red de Potencia Po tencia .................................................... .................................................................... ................ 23 4.11 Herramientas............................. Herramientas......................................................... ........................................................ ..................................... ......... 23 4.12 Interfaces ....................................................... ................................................................................... ............................................ ................ 23 5. EJEMPLOS EN EL PSAT..................................................... ................................................................................. .............................. 25 5.1 Ejemplo de Flujo de Potencia ...................................................... ...................................................................... ................ 25 5.2 Ejemplo Prediseñado de Flujo de d e Potencia ................................................. ................................................. 37 5.3 Importando un Archivo desde PowerWorld .................................................. .................................................. 46 5.4 Ejemplo de Flujo de Potencia Continuo ....................................... ....................................................... ................ 49 5.5 Ejemplo de Flujo Óptimo de Potencia ..................................................... .......................................................... ..... 54 6.CONCLUSIONES.................................................................. .............................................................................................. .............................. 57 REFERENCIAS BIBLIOGRAFICAS .............................................. ...................................................................... ........................ 59 ANEXOS ........................................................... ....................................................................................... .................................................... ........................ 60

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LISTA DE FIGURAS Pág. Figura 1.1 Países del mundo donde dond e el PSAT es utilizado…………………………...2 Figura 2.1 Interfaz Gráfica del PSAT (GUI principal)…………………………………5 Figura 2.2 Interfaz Gráfica del DFC…………………………………………………….6 DFC…………………………………………………….6 Figura 2.3 Librería Simulink del PSAT………………………………………………….8 Figura 2.4 Interfaz de resultados de Simulink en PSAT…………………………….. PS AT……………………………...8 .8 Figura 4.1 Presentación del PSAT en el prompt de Matlab………………………...19 PSAT………………………………………………...20 ………...20 Figura 4.2 Interfaz principal del PSAT……………………………………… Figura 5.1 Diagrama unifilar para el ejemplo 5.1…………………………………….25 Figura 5.2 Librería de barras y conectores de Simulink S imulink del PSAT………………...26 Figura 5.3 Ventana CAD para edición de las redes…………………………………27 Figura 5.4 Ventana donde se modifican los parámetros de las barras……………28 Figura 5.5 Librería que contiene los bloques de sistemas sis temas de potencia…………...29 1-2……………………………………………….. 30 Figura 5.6 Parámetros de la línea 1-2……………………………………………….. Figura 5.7 Parámetros de la carga de la barra 1……………………………… 1…………………………………….30 …….30 Figura 5.8 Parámetros del generador PV…………………………………………….31 Figura 5.9 Diseño final para el ejemplo de la figura 5.1…………………………….32 Figura 5.10Reporte 5.10Reporte estático donde se muestran datos de tensión, angulo y potencias programadas…………………………………… programadas…………………………………………………………………3 ……………………………333 Figura 5.11 Resultados gráficos de magnitud de tensión, ángulo y potencias…..34 Figura 5.12 Ventana o interfaz donde se cargan los ejemplos prediseñados……37 Figura 5.13 Lista de ejemplos prediseñados con la extensión .mdl……………….38 Figura 5.14 Ejemplo prediseñado del libro del Kundur……………………………..39 Figura 5.15 Vista previa del sistema del 11 barras para el ejemplo 5.2…………..40 Figura 5.16 Interfaz que incluye la gráfica de convergencia……………………….41 Figura 5.17 Reporte Estático para el ejemplo 5.2…………………………………...41

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LISTA DE TABLAS Pág. Tabla 2.1 Disponibilidad de herramientas en Matlab y GNU/Octave……………….4 Tabla 5.1 Datos de línea para el sistema sis tema de 4 barras, ej. 5.1………………………25 Tabla 5.2 Datos de Barra del sistema de 4 barras, ej. 5.1………………………….26 Tabla 5.3 Datos de la Red para el ejemplo 5.1……………………………… 5.1……………………………………....35 ……....35 Tabla 5.4 Resultados Estadísticos para el ejemplo 5.1……………………………..35 Tabla 5.5 Resultados de flujo de potencia para el ejemplo 5.1………………….....35 ejem plo 5.1………………………………......35 5.1………………………………......35 Tabla 5.6 Flujos en las líneas para el ejemplo Tabla 5.7 Generación Total para el ejemplo 5.1……………………………………..36 Tabla 5.8 Carga Total para el ejemplo 5.1……………………………………………36 Tabla 5.9 Pérdidas Totales para el ejemplo 5.1……………………………………...36 Tabla 5.10 Resumen de N-1 Contingencias………………………………………….53 Contingencias………………………………………….53 5.5………………………………………55 Tabla 5.11 Datos de la red para el ejemplo 5.5………………………………………55 Tabla 5.12 Resultados estadísticos para el ejemplo 5.5…………………………. 5.5…………………………....55 ...55 Tabla 5.13 Potencia ofertada ejemplo 5.5…………………………………………….55 5.5…………………………………………….55 Tabla 5.14 Potencia Demandada ejemplo 5.5……………………………………….55 5.5……………………………………….55 Tabla 5.15 Datos Totales ejemplo 5.5………………………………………………...55 5.5………………………………………………...55 Tabla A1 Datos de las barras para el sistema Manizales…………………………..60 Tabla A2 Datos de las líneas para el sistema Manizales…………………………...61 Tabla A3 Datos de los transformadores para el sistema Manizales……………….62

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RESUMEN En este trabajo se presenta el software PSAT (Power System Analysis Toolbox ), el cual se constituye como una herramienta útil para el análisis de sistemas de potencia. El objetivo del documento es brindar una amplia perspectiva de las capacidades de PSAT. En primer lugar se hace una breve descripción del programa clasificándolo dentro de una de las diferentes clases de paquetes de simulación; además se enumeran las diversas rutinas que puede ejecutar PSAT, así como las interfaces que tiene para resolver problemas conjuntamente con otros programas. Posteriormente, se explican y describen herramientas importantes del programa como la interfaz gráfica principal, la conversión de formato de datos, modelos definidos por el usuario, las librerías simulink y línea de comandos. c omandos. En el documento también se explican brevemente los métodos matemáticos utilizados por PSAT para resolver cada una de sus rutinas, las cuales son Flujo de Potencia, Flujo de Potencia Continuo, Flujo Óptimo de Potencia, Estabilidad de Pequeña señal y Simulaciones en el Dominio del Tiempo. Procediendo secuencialmente, se explica paso a paso todo el proceso necesario para descargar el instalador de PSAT e instalar, ejecutar, cargar los datos, correr el software, visualizar y guardar los resultados que entrega e ntrega el programa. Por último, se realizan ejemplos ejecutando diferentes rutinas de PSAT, entre estos se destaca la simulación del sistema de potencia de la ciudad de Manizales

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INTRODUCCIÓN

Las herramientas computacionales para el análisis de sistemas de potencia pueden ser divididas en dos tipos: Programas comerciales y programas destinados a la educación e investigación. Los primeros tienen la gran ventaja de ser computacionalmente eficientes y se pueden mencionar algunos como, por ejemplo: NEPLAN, PowerWorld y ATP. A pesar de su alta eficiencia los programas comerciales, para propósitos de educación e investigación, poseen la gran desventaja de ser de código cerrado, es decir, no existe la posibilidad de modificar sus rutinas y/o agregar nuevos modelos de dispositivos eléctricos, de modo que cuando se investiga dichos tipos de software no cuentan con la flexibilidad necesaria para simular y evaluar el impacto de nuevas tecnologías, en desarrollo, y aun no implementadas en los sistemas de potencia reales; reduciendo así su aplicabilidad en centros de enseñanza. Para propósitos académicos y de investigación es más importante la flexibilidad que la eficiencia, allí radica la importancia de contar con herramientas computacionales de código abierto dentro de los cuales se encuentra el software libre PSAT. En el presente documento se describen las características de PSAT mostrando las capacidades que tiene el software para correr flujos de potencia, flujos de potencia óptimos, análisis de estabilidad en pequeña señal, simulaciones en el dominio del tiempo así como sus herramientas para conversión de formatos, definir y/o modificar las rutinas y modelos existentes, la facilidad de trabajar mediante el

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1. QUE ES PSAT PSAT: Sus siglas en inglés corresponden a Power System Analysis Toolbox, que en español significa “Caja de Herramientas para el Análisis de Sistemas de Potencia”. PSAT es una herramienta de código abierto basada en MATLAB para análisis y control de sistemas de potencia. La versión de línea de comando del PSAT también es compatible con GNU Octave (homologo de MATLAB para Linux). Puede ser utilizado en gran variedad de sistemas de potencia: desde pequeñas redes para propósitos académicos hasta sistemas reales de tamaño medio. PSAT puede realizar flujos de potencia, flujos de potencia continuos, flujos óptimos de potencia, análisis de estabilidad de pequeña señal y simulaciones en el dominio del tiempo [1]. Mediante una interfaz gráfica de usuario (GUIs) y una librería basada en Simulink se pueden ejecutar todas las órdenes de forma sencilla. Este software puede ser utilizado con eficacia en la enseñanza debido a que su ambiente de trabajo resulta amigable para el usuario y su manejo se explica por sí solo; por tanto los estudiantes pueden enfocarse en la aprehensión de conceptos propios del análisis de sistemas de potencia mediante la interpretación de resultados obtenidos luego de ejecutar el flujo de potencia de una red cualquiera, pequeña o mediana.

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Por otra parte PSAT es un software que, por su característica de ser de código abierto, cobra relevancia en un ambiente investigativo ya que es posible modificar sus rutinas, en caso de que se pretendan desarrollar métodos alternativos para analizar sistemas de potencia, y además también se pueden modificar o implementar códigos correspondientes a modificaciones o invención de nuevos dispositivos para sistemas de potencia, según sea el caso. Esta característica hace de PSAT una herramienta computacional bastante usada, alrededor del mundo, para realizar investigaciones asociadas a tesis de maestría y doctorado. A continuación se muestra un mapamundi que permite reconocer los lugares del mundo donde PSAT está siendo utilizado.

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2. CARACTERÍSTICAS DEL PSAT 2.1 Rutinas disponibles en PSAT PSAT dispone de un amplio número de rutinas, como: •

Flujos de Potencia

•

Análisis de bifurcación (CPF-Flujo de Potencia Continuo)

•

Flujo Optimo de Potencia (OPF-Optimal Power Flow)

•

Análisis de Estabilidad de Pequeña Señal

•

Simulación en el Dominio del Tiempo

•

Unidades de Medición Fasorial

2.2 Modelos disponibles en PSAT PSAT posee un amplio número de modelos estáticos y dinámicos disponibles para realizar a fondo un análisis de sistemas sis temas de potencia. •

Información de flujos de potencia

•

Información de mercado

•

Interruptores

•

Medidores

•

Cargas

•

Máquinas

•

Controles

•

Transformadores regulantes FACTS:SVCs, TCSCs, SSSCs, UPFCs

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1. 2. 3. 4. 5.

Cuenta con una interfaz interfaz gráfica de usuario amigable. Una librería Simulink muy útil para construir diagramas de red unifilares. Conversión de archivos de otros formatos. formatos. Editor de modelos definidos por el usuario. Versión en línea línea de comandos. Debido a la actual limitación de GNU/Octave no todas las herramientas están disponibles en esta plataforma. Función

Matlab GNU/Octave

Flujo de Potencia Continuo

Si

Si

Flujo Óptimo de Potencia

Si

Si

Análisis de Estabilidad de Pequeña Señal

Si

Si

Simulación en el Dominio del Tiempo

Si

Si

GUIs y librerías Simulink

Si

No

Conversión de Formatos

Si

Si

Modelos Definidos por el Usuario

Si

No

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para almacenar las configuraciones de los parámetros de las rutinas y datos para los modelos; logrando correr igualmente en la versión v ersión de líneas de comando.

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programas, tales como: IEEE CDF, CYME, MatPower, PST, EPRI WECC, SPP/E, PSAP, Eurostag, EPRI BPA, Tsinghua University, INPTC1(Enel), VST, Simpow, Neplan, DigSilent, PowerWorld, PET y GE. [2]

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El primer paso es ingresar en el GUI del UDM las variables y el sistema de ecuaciones diferenciales algebraicas que describen el nuevo modelo. PSAT compila automáticamente las ecuaciones, calcula las expresiones simbólicas de las matrices Jacobianas y expresa una función de Matlab para el nuevo componente. El usuario puede guardar el modelo y/o instalarlo en PSAT, el UDM también tiene un desinstalador del modelo, así, cuando el modelo es innecesario este puede ser desinstalado sin ningún problema. 2.3.4 Librerías Simulink PSAT proporciona un modelo grafico de librerías Simulink que permite al usuario dibujar los diagramas de red usando bloques pictóricos. La librería PMC (Physical Model Component) de PSAT proporciona un juego completo de bloques de Simulink para diseño de redes, las cuales son agrupadas como sigue: conexiones, flujos de potencia, OPF y CPF, fallos, medidores, cargas, maquinas, transformadores, FACTS, turbinas de viento y otros modelos. El PSAT está basado en Matlab y el entorno Simulink es usado solo como una

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Figura 2.3 Librería Simulink del PSAT. Se muestran las diferentes categorías para el diseño de redes. redes. 2.3.4.1 Mostrando resultados en modelos Simulink Después de resolver los flujos de potencia, hay algunas formas en las cuales los resultados pueden ser visualizados. El PMC permite mostrar resultados tales como la magnitud y ángulo de la tensión en la barra, y los valores de flujo de

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2.3.5 Uso de Líneas de Comando La versión de línea de comando de PSAT es una opción adecuada cuando se usan las rutinas disponibles, tales como flujos de potencia, dentro de las rutinas definidas por el usuario, así, este permite acostumbrarse a elaborar rutinas que no cuentan en el GUI de PSAT, PS AT, haciendo este flexible y adecuado para trabajar. Esta característica permite usar PSAT en las siguientes condiciones: •

•

•

Si no es posible visualizar o es demorado para visualizar el ambiente gráfico. Cuando el usuario necesite escribir scripts que incluyen el uso de rutinas PSAT dentro de programas. Cuando PSAT corre en GNU/Octave, el cual no proporciona el Simulink.

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3. MODELOS Y RUTINAS DE PSAT

Rutinas PSAT Como se ha dicho anteriormente, el PSAT PSA T tiene las siguientes rutinas disponibles: •

Flujos de Potencia

•

Análisis de Bifurcación

•

Flujo Óptimo de Potencia

•

Análisis de Estabilidad de Pequeña Señal

•

Simulaciones en el Dominio del Tiempo Unidades de Medición Fasorial

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3.1 Modelo de Sistema de potencia Los modelos de sistemas de potencia son formados por un sistema de ecuaciones algebraicas diferenciales:

Donde x  son las variables de estado, y  son las variables algebraicas, p  son las variables independientes, f  son ecuaciones diferenciales, y g  son ecuaciones algebraicas. PSAT hace uso de la ecuación (1) en todos los algoritmos

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Donde x c c  son las componentes de las variables de estado; y c c  las variables algebraicas tales como la tensión V y el ángulo Θ en las barras donde el elemento está conectado; y p c c  son variables independientes. Después, la ecuación diferencial f  de la ecuación (1) es construida concatenando f c  c  de cada uno de los componentes del sistema de potencia. Las ecuaciones presentadas en (3) simultáneamente con la matriz Jacobiana están definidas en una función el cual es usada para análisis estático y dinámico mediante de una estructura que contiene datos, parámetros y la topología de la red.

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flujo de potencia ya que típicamente se conocen los parámetros de entrada del modelo dinámico. El modelo de barra slack distribuida está basado en el concepto de centros generalizados de potencia y consiste en pérdidas de distribución entre todos los generadores. Las pérdidas por distribución entre los generadores es obtenida tras rescribir las potencias activas P G  sigue: G  de la barra slack y PV de los generadores como sigue: (5) Donde P  son las potencias activas de los generadores deseados, k  es una

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3.4 Flujo Óptimo de Potencia (OPF)

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Donde g  y y son definidos como en la ecuación (1), las variables de control p son P S  las potencias demandadas y ofertadas P D  D  y S,  mientras F  y h  son las restricciones de desigualdad, respectivamente. El objetivo es maximizar el beneficio social, así, la función funci ón objetivo F es definida

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De aquí, solo serán examinados los análisis dinámicos, pero seria de notar que la rutina para realizar análisis de sensibilidad QV es válida. La matriz jacobiana AC  de un sistema dinámico es definida tras linealizar la ecuación (5) en torno a un punto de operación.

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PSAT es capaz de introducir perturbaciones comunes por medio de funciones incrustadas. Estas funciones incrustadas son útiles para simular perturbaciones comunes para análisis transitorio tales como fallas y operaciones de interrupción. Las perturbaciones pueden ser obtenidas al cambiar los parámetros o valores de las variables después de completar c ompletar el flujo de potencia.

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4. PRIMEROS PASOS En esta sección se explica cómo descargar, instalar y correr PSAT. La estructura del toolbox y una breve descripción des cripción de sus principales características.

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5.5 Ejemplo de Flujo Óptimo de Potencia En este ejemplo se efectuará la rutina OPF en un caso de 6 barras proporcionado por PSAT. El ejemplo se encuentra en la carpeta Test  del directorio PSAT en la ventana de carga de archivos y tiene el nombre de d_006.mdl, d_006.mdl, la figura 5.30 muestra la red del sistema para este caso. Después de haber cargado el archivo dar clic en el botón OPF (ver figura 2.1), automáticamente se correrá la rutina. Para conocer resultados tales como potencias demandas y ofertadas o pérdidas u otros resultados después de la optimización, se procede a lo habitual, se ingresa a la static report  y luego se apertura el reporte detallado de resultados, aquellos resultados se pueden observar en las tablas 5.11 a 5.15.

Figura 5.30 Ejemplo de 6 barras para OPF

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Buses:

6

Lines: Generators:

11 3

Loads:

3

Supplies:

3

Demands:

3

Tabla 5.11 Datos de la red para el ejemplo 5.5 Objective Function [$/h]:

-121,64724

Active Limits:

8

Number of Iterations:

10

Barrier Parameter:

8,1952E-11

Variable Mismatch:

1,7684E-06

Power Flow Equation Mismatch: Objective Function Mismatch:

1,6646E-07 4,641E-07

Tabla 5.12 Resultados estadísticos para el ejemplo 5.5 Bus

mu min

Ps min

Ps

Ps max

[MW]

[MW]

[MW]

mu max

Bus1

0,67964038

0,001 0,00100005

20 9,2571E-10

Bus2

2,6916E-09

0,001 24,9999996

25 0,18046735

Bus3

1,5915E-09

0,001 19,9999998

20 2,14549204

Tabla 5.13 Potencia ofertada ejemplo 5.5 Bus

mu min

Pd min [MW]

Pd [MW]

Pd max [MW]

mu max

Bus6

4,9626E-09

0,001 8,06930342

20 1,2924E-08

Bus5 Bus4

1,88E-09 1,1844E-09

0,001 9,99999989 0,001 24,9999999

10 0,5611841 25 2,17498093

Tabla 5.14 Potencia Demandada ejemplo 5.5 TOTAL LOSSES [MW]: BID LOSSES [MW]

11,807 1,932

TOTAL DEMAND [MW]:

43,0693032

TOTAL TRANSACTION LEVEL [MW]:

323,069303

IMO PAY [$/h]:

62,1225294

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En el reporte estático además de las anteriores se presentan variables adicionales como potencias reactivas, tensiones, flujo de potencia y flujos en líneas de transmisión.

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6.CONCLUSIONES

•

•

•

•

•

•

El uso de programas de simulación constituye una herramienta esencial para el estudio de flujos de potencia, ya que permiten visualizar los conceptos teóricos de forma más dinámica y cercana a un sistema de potencia real. Para el uso de simuladores de flujo de carga se requiere un entendimiento previo de los conceptos teóricos en sistemas de potencia, permitiendo al usuario obtener una mejor y correcta interpretación en el análisis de resultados. El gran tamaño y complejidad de los sistemas eléctricos de potencia actuales han obligado al ingeniero electricista hacer uso de programas de simulación, y hacer de estos la forma más adecuada y confiable de trabajar en estos campos. El PSAT se convierte en una opción factible para muchos usuarios, debido a que este paquete simulador es gratuito y además se basa en una herramienta de cálculo matemático muy poderosa como lo es el MATLAB. También cabe resaltar que el PSAT es de código abierto y esto lo hace tentativo para usuarios que quieran mejorar su estructura. Quizá el PSAT sea gráficamente algo sencillo e interfaz poco amigable y no se presentan tantas opciones en comparación de programas comerciales como el PowerWorld, pero este programa es matemáticamente muy confiable y presentan rutinas que muchos otros no presentan. Como en el caso de la interfaz PSAT-GAMS, algunos simuladores mejoran y/o complementan sus capacidades al trabajar conjuntamente

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•

•

Debido a su buen funcionamiento para propósitos académicos y de investigación, el software libre constituye una excelente opción, al momento de adquirir paquetes de análisis de sistemas de potencia, para las universidades. La opción de obtener resultados en formato Excel, que brinda PSAT, abre inmensas posibilidades para realizar operaciones sistemáticos, por ejemplo de tipo económico, con los resultados arrojados por las simulaciones. Sin duda, de este modo se pueden agilizar muchos los cálculos.

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REFERENCIAS BIBLIOGRAFICAS [1] Url: http://www.power.uwaterloo.ca/~fmilano/psat.htm. “Página Web del desarrollador del programa, Federico Milano” [2]

Luigi Vanfretti , “Introduction to PSAT: A toolbox for Computer Methods in  Electric Power Engineering ”, ”, Renssealer Institute, 2006 [3] Jhon J. Grainger, William D. Stevenson J. “Análisis de Sistemas Eléctricos de Potencia”. México: McGraw-Hill, 1994

[4] Peter Sauer and M.A. Pai, “Power “Power System Dynamicd and Stability”. USA: USA: Prentice Hall, 1988 [5] C. A. Cañizares (editor), (editor), “Voltege Stability Assessment: Concepts, Practices and Tools”, IEEE/PES Power System Stability Subcommiteee, Aug.2002 [6] PSAT Quick Reference Manual versión 2.1.2 [7] P. Kundur, “Power system system stability and control”. USA: USA: McGraw-Hill, 1994

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ANEXOS

Barra

Nombre

1

Esm-ISA 220

2

Enea 220

KV

Tipo

220 Slack

Generación MW 150

Limites MVAR

MVAR Min Max 31 -99990 999900 50

-99990 999900

Carga MW 0 0

Voltaje V δ

MVAR 0 1.00 0.00 0

220

PV

90

3

Esmeralda 115 115

PV

112,1

11,85 -99990 999900 46,92

4

Peralonso 115 115

PV

4,17

-5,27

-99990 999900

0

0

-99990 999900

23

6,04

3,84

5

Marmato

33

PV

2,92

0

6

Esm-ISA 115

115

PQ

0

0

0

0

7

Enea 115

115

PQ

0

0

16,83

7,85

8 9

Peralonso Insula 115

33 115

PQ PQ

0 0

0 0

2,06 0

0,56 0

10

Insula

33

PQ

0

0

2,04

0,63

Manizales Manizale s 115 115

PQ

0

0

0

0

11 12

Manizales

33

PQ

0

0

4,07

0,84

13 14

Chipre Villamaria

33 33

PQ PQ

0 0

0 0

11,78 4,29

3,24 0,8

15

Chinchiná

33

PQ

0

0

10,66

4,87

16

Manuela

33

PQ

0

0

0,65

0,12

17

Enea

33

PQ

0

0

5,59

1,17

18

Alta Suiza

33

PQ

0

0

19,08

4,07

19 20

Herveo Industrial II

33 33

PQ PQ

0 0

0 0

2,72 15,09

0,44 5,14

21

Liofilizado Liofiliza do

33

PQ

0

0

9,2

2,97

22

Stepan-IBC Stepan-I BC

33

PQ

0

0

0,38

0,12

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Líneas Nodo A

Nodo B

R p.u

X p.u

B p.u

3 3

6 6

0,00141 0,00141

0,01066 0,01066

0.00000 0.00000

3

9

0,01728

0,04423

0,00536

3

11

0,03716

0,09508

0,01154

5

8

0,04052

0,08308

0,00009

7 7

4 11

0,01617 0,01349

0,04236 0,03536

0,0049 0,0041

9 11

11 4

0,01988 0,01513

0,05086 0,0397

0,00618 0,00458

12 12

5 5

0,04711 0,05206

0,11295 0,12646

0,0001 0,00012

12

14

0,05832

0,06626

0,00007

13

8

0,06321

0,13715

0,00014

13 15

12 10

0,06235 0,09298

0,1494 0,020168

0,00014 0,00021

15

12

0,23052

0,4887

0,00052

15 16

21 10

0,00805 0,13843

0,00645 0,35376

0,00001 0,0003

16 16

12 22

0,10992 0,0911

0,28093 0,19219

0,00024 0,00021

17

19

1,07901

1,26433

0,00119

18 18

5 8

0,08898 0,06693

0,21341 0,14116

0,0002 0,00015

18 18 18

17 17 20

0,1339 0,13391 0,04089

0,31064 0,31064 0,08093

0,00028 0,00028 0,0001

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Transformadores

Tap

Nodo A

Nodo B

R p.u

X p.u

Magnitud

δ

1 1

6 6

0 0

0,09 0,09

1 1

0° 0°

2

7

0

0,16

1

0°

4

8

0

0,12

1

0°

4

8

0

0,12

1

0°

7

17

0

0,094

1

0°

9

10

0

0,089

1

0°

11

12

0

0,09

1

0°

Tabla A3 Datos de los transformadores para el sistema Manizales