EE60 - Clase 7 - Estabilidad Transitoria - Aplicación Del PEBS en El SEIN (Manfred Bedriñana)
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Estabilidad Transitoria - Aplicación Del PEBS en El SEIN...
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UNIVERSIDAD NACIONAL DE INGENIERÍA Facultad de Ingeniería Eléctrica, Electrónica y Telecomunicaciones
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Tema
Análisis de la Estabilidad Transitoria Electromecánica mediante el Método de la Función de Energía Transitoria – Aplicación al Sistema Interconectado Nacional Peruano Presentado por
Manfred Fritz Manfred Fritz Bedriñana Bedriñana Aronés Aronés
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
- Tópicos 1. Introducción. 2. Estabilidad Transitoria Sistemas de Potencia.
de
3. Método Directo basado en la Función de Energía.
4. Implementación y Resultados. 5. Conclusiones.
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
1. Introducción
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
1. Introducción
1.1 Antecedentes ❖
El ingeniero de planeamiento necesita estudiar la estabilidad del sistema para un conjunto de disturbios seleccionados desde el peor, tal como la falla trifásica a tierra (cuya probabilidad de ocurrencia es pequeña), hasta las fallas monofásicas (las cuales constituyen cerca del 70% de los disturbios). Existe Existen n actual actualmen mente te una buena buena produc producció ción n de program programas as profes profesion ionale ales, s, los cual cuales es simu simula lan n el comp compor orta tami mien ento to del del sist sistem emaa en el tiem tiempo po frent frentee a tale taless disturbios. ✓ Hay literalmente miles de variables que pueden ser monitoreados inclusive en grandes sistemas. ✓
❖
El inge ingeni nier ero o de plan planea eami mien ento to requ requie iere re ve verr si la fall fallaa fue fue elim elimin inad adaa apropiadamente verificando verificando que el sistema no pierda el sincronismo. ✓
Un sistema permanece en sincronismo para un cierta falla si las variables del sistem sistemaa perman permanece ecen n a valore valoress de estado estado estaci estaciona onario rio cuando cuando t →
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
1. Introducción
1.1 Antecedentes ❖
En la operación actual, el sistema afronta condiciones y parámetros que pueden ser muy diferentes a los asumidos en la etapa de planeamiento. planeamiento. Para garantizar la seguridad del sistema de potencia frente a posibles condiciones condiciones anorma anormales les (conti (continge ngenci ncias) as),, el operad operador or debe debe simula simularr las contin contingen gencia ciass por adelantado, evaluar los resultados, y tomar alguna acción de control necesaria. ✓ Este proceso es llamado de “Evaluación de la Seguridad Dinámica (ESD)” ✓ Una técnica similar existe alrededor de la evaluación de seguridad estática, los centros de control modernos tienen software llevando en cuenta estas funciones. ✓
❖
Muy poco progreso ha sido hecho hecho en la ESD y el control preventivo. La razón es simplemente porque para conducir una simulación transitoria en el tiempo, para contingencia simple, este análisis compromete mucho tiempo de procesamiento. ✓ Incluso considerando generadores con modelos simplificados, el operador tiene que observar detenidamente los diagramas generados para el ángulo del rotor y la ve velo loci cida dad d de dive divers rsas as máqu máquin inas as para para toma tomarr una una deci decisi sión ón acer acerca ca de la estabilidad del sistema. ✓
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
1. Introducción
1.1 Antecedentes ❖
Los Los méto método doss dire direct ctos os se cara caract cter eriz izan an por por to toma marr un cami camino no dire direct cto o de decisión de estabilidad/inestabilidad por medio de la computación de un número simple tal como un índice de estabilidad transitoria (IET). El IET puede indicar cualitativamente si el sistema es estable o no y, si es estable, medir cuantitativamente el margen de estabilidad. ✓ En el método directo basado en las funciones de energía, comúnmente el IET es definido como la energía crítica del sistema. ✓
❖
De acuerdo con el estado del arte, las funciones de energía transitoria presentan diversas ventajas de orden práctico en la determinación del IET para el análisis eficiente y directo de la estabilidad transitoria de sistemas de potencia. ✓
Este Este métod método o dire direct cto o (bas (basad ado o en func funcio ione ness de ener energí gíaa tran transi sito tori ria) a) pose poseee actual actualmen mente te fundam fundament entos os teó teóric ricos os bien bien susten sustentad tados, os, pero pero alguno algunoss aspect aspectos os
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
1. Introducción
1.1 Antecedentes ❖
Dentro de las técnicas actuales relacionadas con el método directo basado en funciones de energía transitoria tenemos: Método de la Superficie Frontera de Energía Potencial (PEBS: Potential Energy Boundary Surface) propuesto por Kakimoto. ✓ Método del UEP de Control. Aquí existen tres principales variantes: El ✓
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
1. Introducción
1.2 Objetivos ❖
Se presenta y desarrolla una metodología de análisis de la estabilidad trans transit itor oria ia del del SEIN SEIN (Sis (Siste tema ma Eléct Eléctri rico co Inte Interc rcon onec ecta tado do Naci Nacion onal al)) medi median ante te el méto método do dire direct cto o basa basado do en la func funció ión n de ener nergía gía transitoria transitoria.. Se utilizan utilizan los conceptos conceptos mas recientes recientes involucra involucrados dos con este método.
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
2. Estabilidad Transitoria de Sistemas de Potencia
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2. Estabilidad Transitoria Transitoria
Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
2.1 Definición Estabilidad de Sistemas de Potencia • Definición clásica: ❖
Es el térm érmino ino apl aplicad icado o a sist sistem emas as de pot potenci encia a de cor corrien riente te eléc eléctr triica alternada, denotando una condición en la cual varias maquinas síncronas del sistema permanecen en sincronismo o o en paso con con las otras. “
✓
”
“
”
Powerr Sy Syst stem em St Stab abil ilit ity, y, Vo Vol. l.I: I: El Elem emen ents ts of St Stab abil ilit ity y [15 [15]] E. W Ki Kimb mbar ark, k, Powe
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
2. Estabilidad Transitoria Transitoria
2.2 Tipos de Estabilidad en Sistemas de Potencia Estabilidad de Sistemas de Potencia
Estabilidad del Ángulo del Rotor
Estabilidad de Frecuencia
Estabilidad de Tensión
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
2. Estabilidad Transitoria Transitoria
2.3 Estabilidad Angular de Sistemas de Potencia
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
2. Estabilidad Transitoria Transitoria
2.3 Estabilidad Angular de Sistemas de Potencia
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
2. Estabilidad Transitoria Transitoria
2.3 Estabilidad Angular de Sistemas de Potencia
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
2. Estabilidad Transitoria Transitoria
2.4 Formulación Matemática de la Estabilidad Transitoria Transitoria
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
2. Estabilidad Transitoria Transitoria
2.5 Métodos para Análisis de la Estabilidad Transitoria
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3. Método Directo de la FET
Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
3.2 Formulación de la Función de Energía Transitoria • Ecu Ecuaci aciones de Oscil cilació ción en el COI 2
M i
d i 2
dt
(
)
cos ij − = P i − C ij sin ij + Dij cos j =1 j i
❖
n
f i (θ) i
Donde
=
1,..., m
m
m
P i = P mi − E i Gij ; P COI = P i − 2 2
i =1
m
cos ij Dij cos
i =1 j = i +1
• Func Funció ión n de Ener Energí gíaa ~) = 1 V (θ, ω 2
=
1
m
~2 M i
i
i =1 m
m
s
i =1
~2 M i i
i
− f i (θ )d i i
m −1
m
− P i ( i −
s i
m
)−
s C ij (cos ij − cos ij )
M i M T
P COI
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
3.3 Técnicas para Calcular la V
3. Método Directo de la FET
CR
• Méto étodo del UEP de menor ener nergía ❖
❖
Busc Buscam amo os UEPs UEPs (Pun (Punto toss de Equi Equili lib brio Ines Inesttable ables) s) del del sis sistema tema y elegi legimo moss el de menor enor ener energ gía, ía, esa esa ener energí gíaa es Vcr. cr. Requ Requie iere re much mucho o trab trabaj ajo o comp comput utac acio iona nal, l, es difí difíci cill enco encont ntra rarr todo todoss los los UEPs UEPs [23] 3] A. H. Abi biaad an and d K. Naga gapp ppan an,, Tr Tra ansie nsient nt Sta Stab bi lilitty R egi gio on of Mult M ultii mach chii ne ✓ [2 Power Systems, IEEE Trans ns.. Pow ower er App ppaar. an and d Sys yste tem ms, PAS-85 85,, vo voll 2, pp pp..16 1699178, 17 8, Feb 19 1966 66..
• Méto Método do de la Supe Superf rfiicie cie Fron Fronte tera ra de Ener Energí gíaa Pote Potenc ncia iall (PEB (PEBS) S) ❖
El Vcr es la componente de energía potencial máxima a lo largo de la traye trayecto ctori riaa de falla falla ✓
Tra rans nsie ient nt st stab abil ilit ityy an anal alys ysis is of mu mult ltim imac achi hine ne powe po werr sys syste tems ms by Lya yapu puno novv s di dirrec ectt me meth thod od, Proc. of the 20th IEEE Conf. on [5] N. Kakimoto and Hayashi, ´
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
3.3 Métodos para Calcular la V
3. Método Directo de la FET
CR
• Método del UEP de Control o BCU ❖ ❖
El Vcr es la energía total en el UEP de control. El UEP de control es determinado mediante el cruce de la trayectoria de la falla lla en el PEBS y luego es usado el sistem tema gradie adien nte para desliza izarnos hast asta el prim primer er UEP UEP enco encont ntra rado do.. ✓
Foun unda dati tion onss of Di Dire rect ct Me Meth thod odss [6] H. D. Chiang, F. F. Wu, and P. P. Varaiya, Fo for Power Systems Transient Stability Analysis, IEEE Trans. Circuits Syst Sy stem ems, s, CA CASS-34, 34, pp pp.16 .1600-173 173,, Fe Feb b 198 1987. 7.
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
3.4 Método PEBS • Regió egión n del PEBS ❖
Referencia
GENERADOR 1
GENERADOR 2
P m1 = 249 MW H 1
BARRA 1
P m 2 = 421 MW
= 10 s
H 2
x'd 1 = j 0.088
BARRA 2
Carga 1 150 MW 45 MVAr
Carga 2 100 MW 30 MVAr
BARRA 3 (Slack) GENERADOR 3 Carga 3 1240 MW 250 MVAr
P m 3 H 3
= 820 MW = 60 60 s
x' d 3 = j 0.015
= 15 s
x' d 2 = j 0.050
Tray Trayeector ctoria ia Crít Crític icaa del Sistema falla y post-falla
3. Método Directo de la FET
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
3. Método Directo de la FET
3.4 Método PEBS Algoritmo para Algoritmo para cálculo de Tiempo Crítico 1. Calcular el SEP post-falla θ , resolviendo (ver Anexo B) s
f i (θ)
2.
0,
i
=
1,..., m
Calcular la trayectoria de falla dado por (3.23). M i
~ d i
dt
d i dt
3.
=
=
~
=
i ,
f i F (θ) i
=
0
t t d
1,2,..., m
Supervisar f T (θ) θ y V (θ) en cada paso de tiempo. Los parámetros en f (θ) y V (θ ) pertenecen a la configuración post-falla. ˆ
PE
PE
4.
T Dentro del pozo potencial f (θ) θ 0. Continuar los pasos 2 y 3 hasta que ~ * ). Esta es una buena estimación de V . Este es el cruce del PEBS(t * , θ* ,ω ˆ
cr
max
V PE
.(θ)
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
3. Método Directo de la FET
3.4 Método PEBS Observaciones ❖
Traye rayect ctor oria ia de Fall Fallaa Sost Sosten enid idaa en el PEBS Trayectoria de Falla Sostenida Sostenida
❖
Dos tipo tiposs de fall fallas as dist distin inta tass
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía (UNI-FIEE)
4. Implementación y
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.1 Implementación de la Metodología ETAPA INICIAL: REPARACIÓN DE DATOS PREPARACIÓN DATOS DE SISTEMAS DE POTENCIA PARA ANÁLISIS DE ESTABILIDAD TRANSITORIA (ARCHIVOS TEXTO)
DATOS ESTÁTICOS: FORMATOS CDF Y PTI PSS/E-26
SISTEMA ATHAY3 3 GENERADORES 3 BARRAS
SISTEMA WSCC3 3 GENERADORES 9 BARRAS
DATOS DINÁMICOS: FORMATO EPRI
SISTEMA IEEE17 17 GENERADORES 162 BARRAS
SISTEMA SEIN50 50 GENERADORES 460 BARRAS
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.1 Implementación de la Metodología ANÁLISIS 1: ESTABILIDAD TRANSITORIA MEDIANTE SIMULACIÓN EN EL DOMINIO DEL TIEMPO
a) Sistema EDO
i i
1 =
M i
=
i
−
s
MÓDULO 3A: SIMULACIÓN NUMÉRICA – PERIODO EN FALLA CALCULA CONDICIONES INICIALES Y REDUCE RED A NODOS INTERNOS . UTILIZA MÉTODO R UNGE UNGE K UTTA UTTA 4TO ORDEN Y TRAPECIO IMPLÍCITO . •
( P i
−
(
P ei 1 ,..., m
)
−
(
Di i
−
s
))
i
=
1,..., m
•
CONDICIONES FINALES
donde la potencia eléctrica es:
• •
MÓDULOS Y ÁNGULOS TENSIONES. ACTIVA Y REACTIVA DE SALIDA DE LOS GENERADORES .
POTENCIA
DATOS DINÁMICOS DE GENERADORES (MODELO CLÁSICO )
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.1 Implementación de la Metodología ANÁLISIS 3: ESTABILIDAD TRANSITORIA MEDIANTE MÉTODOS DIRECTOS BASADOS EN FET
• •
MÓDULOS Y ÁNGULOS TENSIONES. POTENCIA ACTIVA Y REACTIVA DE SALIDA DE LOS GENERADORES.
MÓDULO 3C: SIMULACIÓN NUMÉRICA – PERIODO FALLA SOSTENIDA CALCULA CONDICIONES INICIALES Y REDUCE RED A NODOS INTERNOS. UNGE K UTTA UTTA 4TO UTILIZA MÉTODO R UNGE ORDEN Y TRAPECIO IMPLÍCITO . •
c) Margen de Energía Transitoria MET = V cr − PEBS − V cl PEBS
( )
= V cr − PEBS − V θ PEBS
cl
•
DATOS DINÁMICOS DE GENERADORES (MODELO CLÁSICO)
RAYECTORIA DE ÁNGULOS TRAYECTORIA Y VELOCIDADES
V cr − PEBS : Es la energía energía crítica aproximada
obtenida por el método PEBS, en p.u.
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.2 Resultados en Sistemas de Prueba
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4.2 Resultados en Sistemas de Prueba Prueba
4. Implementación y Resultados
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4.2 Resultados en Sistemas de Prueba Prueba
4. Implementación y Resultados
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4.2 Resultados en Sistemas de Prueba Prueba
4. Implementación y Resultados
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4.2 Resultados en Sistemas de Prueba Prueba
4. Implementación y Resultados
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.2 Resultados en Sistemas de Prueba Prueba 4.2.2 Sist istema WSCC3 SCC3
c) Fu Func ncio ione ness de En Ener ergí gíaa Tra rans nsit itor oria ia Tiempo de Eliminación Eliminaci ón
t cl 2
=
0.17 s.
y D'i
=
0 p.u.
Carga C
BARRA 2
BARRA 7
BARRA 9
BARRA 3
SISTEMA WSCC3 (3 generadores, 9 barras) Evento 1: cc-3 cc-3 en la Barra 7, en t = 0 s Evento 2: Eliminación de cc-3 cc-3 con salida de línea: Barra 5 - Barra 7, en t = 0.17 s
BARRA 8 GENERADOR 2
cc – 3 3ø
GENERADOR 3
V
KE
1.2
V
PE
V BARRA 5
Carga A
1
BARRA 6 Carga B
BARRA 4
] . u . p [ a i r o t i s n a r T a i g r e n E
0.8
0.6
0.4
V
= 0.908
CR
TOTAL
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.2 Resultados en Sistemas de Prueba Prueba 4.2.2 Sist istema WSCC3 SCC3
c) Fu Func ncio ione ness de En Ener ergí gíaa Tra rans nsit itor oria ia Tiempo de Eliminación Eliminaci ón
t cl 1
=
0.16 s.
y D'i
=
1 p.u.
Carga C
BARRA 2
BARRA 7
BARRA 9
BARRA 3
SISTEMA WSCC3 (3 generadores, 9 barras) Evento 1: cc-3 cc-3 en la Barra 7, en t = 0 s Evento 2: Eliminación de cc-3 cc-3 con salida de línea: Barra 5 - Barra 7, en t = 0.16 s
BARRA 8 GENERADOR 2
cc – 3 3ø
GENERADOR 3
V
KE
1.2
V
PE
V
TOTAL
1 BARRA 5
Carga A
BARRA 6 Carga B
BARRA 4
] . u . p [ a i r o t i s n a r T a i g r e n E
0.8
0.6
0.4
V
= 0.908
CR
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.2 Resultados en Sistemas de Prueba Prueba 4.2.2 Sist istema WSCC3 SCC3
c) Fu Func ncio ione ness de En Ener ergí gíaa Tra rans nsit itor oria ia Tiempo de Eliminación Eliminaci ón
t cl 2
=
0.17 s.
y D'i
=
1 p.u.
Carga C
BARRA 2
BARRA 7
BARRA 9
BARRA 3
SISTEMA WSCC3 (3 generadores, 9 barras) Evento 1: cc-3 cc-3 en la Barra 7, en t = 0 s Evento 2: Eliminación de cc-3 con salida de línea: Barra 5 - Barra 7, en t = 0.17 s
BARRA 8 GENERADOR 2
cc – 3 3ø
GENERADOR 3
V
KE
1.2
V
PE
V BARRA 5
Carga A
1
BARRA 6 Carga B
BARRA 4
] . u . p [ a i r o t i s n a r T a i g r e n E
0.8
0.6
0.4
V
= 0.908
CR
TOTAL
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.2 Resultados en Sistemas de Prueba Prueba 4.2.2 Sist istema WSCC3 SCC3
d) Método Directo basado en FET Método PEBS
Carga C
BARRA 2
BARRA 7
BARRA 9
SISTEMA WSCC3 (3 generadores, 9 barras) Evento 1: cc-3 cc-3 en la Barra 7, en t = 0 s Evento 2: Eliminación de cc-3 cc-3 con salida de línea: Barra 5 - Barra 7
BARRA 3
BARRA 8 GENERADOR 2
cc – 3 3ø
V
GENERADOR 3
PE
2
BARRA 5
Carga A
BARRA 6 Carga B
BARRA 4
] . u . p [ a i r o t i s n a r T a i g r e n E
V
TOTAL
1.5 V
= 1.1472, t = 0.351 s.
CR-PEBS
1
0.5
ex
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.2 Resultados en Sistemas de Prueba Prueba 4.2.2 Sist istema WSCC3 SCC3
d) Método Directo basado en FET Método PEBS
Márgenes de Energía Transitoria
Identificación de Generador i # Barra 1 2 3
1 2 3
PEBS V (θ)
=
V (θ ) = =
MET = MET
t cl
0.16
=
cl
(rad)
t ex
0.17
=
cl
i
(deg) -12.86 39.35 17.34
(rad)
i
(deg)
-0.2430 0.7460 0.3230
0.819 p.u.
0.935 p.u.
0.328 p.u.
0.212 p.u.
icl t cl =
icl t cl =
0.819 p.u. 0.089 p.u.
0.35
=
ex
i
-0.2240 0.6870 0.3030
MET = MET
Exacto V (θ)
t cl
SISTEMA WSCC3 (3 generadores, 9 barras) Evento 1: cc-3 cc-3 en la Barra 7, en t = 0 s Evento 2: Eliminación de cc-3 cc-3 con salida de línea: Barra 5 - Barra 7
0.935 p.u. -0.027 p.u.
-13.93 42.74 18.50
(rad)
V
(deg)
-0.7370 2.4300 0.6230
PE
-42.23 139.22 35.67
2
V
TOTAL
1.147 p.u. iex t ex =
0.908 p.u.
] . u . p [ a i r o t i s n a r T a i g r e n E
1.5 V
= 1.1472, t = 0.351 s.
CR-PEBS
1
0.5
ex
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.2 Resultados en Sistemas de Prueba 4.2. 4.2.3 3 Sist Sistem ema a IE IEEE EE17 17 17 Generadores, 162 Barras, 284 Ramos
a) Preparación de datos y Cálculo Cál culoss Pre Prelim limina inares res Flujo de Carga pre-falla Identificación
Total Pérdidas : Tensión eenn B Baarra
MW MVAr 162.96 -440.65 Generación (+ (+) Shunt (+)
Carga (-)
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.2 Resultados en Sistemas de Prueba Prueba 4.2. 4.2.3 3 Si Sist stem ema a IEEE IEEE17 17 17 Generadores, 162 Barras, 284 Ramos
a) Preparación de datos y Cálculo Cál culoss Pre Prelim limina inares res Condiciones Iniciales de Generadores Ident ififica ci ción d G d
T en ensión Int er er nnaa T ra ra ns nsit or or ia ia Mód l Á l
0
E i i
Potencia M á i P
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4. Implementación y Resultados
Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4.2 Resultados en Sistemas de Prueba Prueba 4.2. 4.2.3 3 Si Sist stem ema a IEEE IEEE17 17
b) Simulación en el Dominio del Tiemp Tiempo o Descripción de Casos Caso • Evento 1 en
t
=
0
: Cortocircuito trifásico en la línea 75-9 próximo a Barra Barra 75. - Barra Barra 75: 75: “FT.CL 3 345” - Barra Barra 9: 9: “94 3 345”
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.2 Resultados en Sistemas de Prueba 4.2. 4.2.3 3 Sist Sistem ema a IE IEEE EE17 17 Validación de Resultados Obtenidos SISTEMA IEEE17 (17 generadores, generadores, 162 barras) Evento 1: cc-3 cc-3 en la Barra 75, en t = 0 s Evento 2: Eliminación de cc-3 cc-3 con salida de línea: Barra 75 - Barra 9, en t = 0.354 s 200
b) Simulación en el Dominio del Tiemp Tiempo o
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.2 Resultados en Sistemas de Prueba Prueba 4.2. 4.2.3 3 Si Sist stem ema a IEEE IEEE17 17
b) Simulación en el Dominio del Tiemp Tiempo o Cálculo de Tiempo Crítico SISTEMA IEEE17 (17 generadores, 162 barras) Evento 1: cc-3 cc-3 en la Barra 75, en t = 0 s Evento 2: Eliminación de cc-3 cc-3 con salida de línea: Barra 75 - Barra 9 200 Gen # 1
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4.2 Resultados en Sistemas de Prueba Prueba
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4.2 Resultados en Sistemas de Prueba Prueba
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4.2 Resultados en Sistemas de Prueba Prueba
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4.3 Resultados en Sistema SEIN50
4. Implementación y Resultados
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4. Implementación y Resultados
4.3 Resultados en Sistema SEIN50 4.3. 4.3.4 4 Esta Estab bilid ilidad ad Tran Transi sittoria oria medi median ante te Mé Méttodo odo Dire Direct cto o basa asado en FET ** Caso 2 ** a) Mé Méttodo PE PEB BS SISTEMA SEIN50 (50 generadores, 460 barras) Evento 1: cc-3 cc-3 en la Barra 64, en t = 0 s Evento 2: Eliminación de cc-3 cc-3 con salida de línea: Barra 64 - Barra 65
0.25
V
PE
V
TOTAL
0.2 ] . u . p [ a i r o t i s n a r T a i g r e n E
0.15
0.1
V
= 0.1376, t = 0.108 s.
CR-PEBS
ex
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4. Implementación y Resultados
Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
4.3 Resultados en Sistema SEIN50 4.3. 4.3.4 4 Esta Estab bilid ilidad ad Tran Transi sittoria oria medi median ante te Mé Méttodo odo Dire Direct cto o basa asado en FET ** Caso 2 **
b) Márgenes de Energía
a) Mét éto odo PEB EBS S SISTEMA SEIN50 (50 generadores, 460 barras) Evento 1: cc-3 cc-3 en la Barra 64, en t = 0 s Evento 2: Eliminación de cc-3 con salida de línea: Barra 64 - Barra 65
0.25
V
PE
V
TOTAL
0.2 ] . u . p [ a i r o t i s n a r T a i g r e n
0.15
0.1
V
= 0.1376, t = 0.108 s.
CR-PEBS
ex
t cl
Identificación de Generador i # Barra
(rad)
1 2 3 4 5 6 7 8 9 10 41 42 43 44
-0.5180 0.3930 0.2030 -0.3190 -0.3180 -0.3260 0.5270 -0.2100 -0.4390 -0.2040 -0.1140 -0.0490 0.6950 0 1630
7 24 29 39 40 42 43 44 47 50 294 296 304 308
=
0.01
t cl
cl
=
0.03
t ex
cl
i
(deg) -29.70 22.51 11.63 -18.25 -18.23 -18.69 30.18 -12.01 -25.18 -11.68 -6.53 -2.79 39.85 9 34
(rad) -0 -0.5300 0.3920 0 .1960 -0 -0.3270 -0 -0.3270 -0 -0.3220 0.5400 -0 -0.2130 -0 -0.4510 -0 -0.1930 -0 -0.1230 -0 -0.0590 0.6870 0 1530
=
0.11 ex
i
i
(deg) -30.37 22.44 11.24 -18.75 -18.71 -18.43 30.95 -12.19 -25.83 -11.04 -7.03 -3.38 39.35 8 74
(rad)
(deg)
-0 -0.6850 0.3730 0.1060 -0 -0.4370 -0 -0.4350 -0 -0.2720 0.7130 -0 -0.2530 -0 -0.5960 -0 -0.0720 -0 -0.2360 -0 -0.1930 0.5740 0 0170
-39.27 21.34 6.10 -25.04 -24.91 -15.61 40.85 -14.49 -34.16 -4.11 -13.52 -11.05 32.88 0 97
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía (UNI-FIEE)
5. Conclusiones
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
5. Conclusiones
5.1 Conclusiones •
A partir de la aplicación de la metodología metodología en Sistemas de Prueba: Prueba: 1.
El método PEBS obtuvo un buen desempeño al predecir el tiempo crítico. ❖
2.
Este método permite calcular en forma aproximada la energía crítica. ❖ ❖
3.
Exist Existier ieron on casos casos donde donde la estima estimació ción n fue muy precis precisaa (sistem (sistemas as ATHAY3 THAY3 e IEEE17) en comparación a las técnicas de simulación numérica en el dominio del tiempo, hubo un caso (sistema WSCC3) donde el método se acerco con cierto grado de exactitud. exactitud. El cálculo de la energía energía crítica exacta exacta es aun un desafió hoy hoy en día. Teóricamente este valor valor se obtiene al evaluar la energía transitoria en el UEP de control, el cual está asociado a una falla particular.
La región de estabilidad estabilidad es una una superficie multidimensional multidimensional muy compleja. compleja. ❖
Valiéndose aliéndose de algunas algunas propiedad propiedades es del sistema dinámico, dinámico, el método método PEBS utiliza la superficie frontera de energía potencial y la trayectoria de falla sostenida para generar aproximaciones del UEP de control.
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Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
5. Conclusiones
5.1 Conclusiones •
A partir de la aplicación de la metodología metodología en el SEIN: 1.
Los Los tiem tiempo poss crít crític icos os calc calcul ulad ados os por por el méto método do PEBS PEBS estu estuvi vier eron on muy muy próximos próximos a los calculados por simulación en el dominio del tiempo. ❖
2.
3.
Los Los casos casos pres presen enta tado doss most mostra raro ron n los los prob proble lema mass de estr estrés és del del siste sistema ma y condiciones críticas de operación.
Los métodos métodos directos están están calificados calificados para superar superar problemas problemas de tiempo compu omputa taci cion onal al en el proc proces esam amie ient nto o y capac apacid idad ad de anál anális isis is de la estabilidad transitoria en la operación en tiempo ti empo real. Es impo import rtan ante te la apli aplica caci ción ón de esto estoss méto método doss en dist distin inta tass tare tareas as de planeamiento y operación: ❖ ❖
Auxilio a la operación operación del sistema Introduc Introducir ir concept conceptos os de energía energía que pueden abreviar y explica explicarr condicion condiciones es desfavorables desfavorables en el sistema
Los métodos métodos directos directos,, como el método PEBS, PEBS, se sitúan en una área que
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5. Conclusiones
Tesis - Estabilidad Transitoria Transitoria mediante el Método de la Funci ón de Energía
5.1 Conclusiones •
Como trabajos futuros se tiene lo siguiente: 1.
Desarr Desa rrol olla larr nuev nuevas as meto metodo dolo logí gías as que que actu actual alme ment ntee est están sien siendo do desarrolladas, como: método BCU, método shadowing, etc. ❖
Exist Existen en aplicaci aplicacion ones es de estos estos método métodoss en sistemas sistemas de prueba prueba y reales reales,, y actualmente están siendo integrados como herramientas para el auxilio en la operación.
Se está des
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