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Giuliano Bozzo Moncada sistem
- 1. Giuliano Bozzo Moncada Giulianno Bozzo Moncada Giuliano David Bozzo Moncada Giulianno Bozzo Moncada Giuliano-Bozzo-Moncada Giulianno-Bozzo-Moncada Giuliano-David-Bozzo-Moncada Giulianno-Bozzo-Moncada DATOS DEL SISTEMA Giuliano Bozzo Moncada Usted es un ingeniero contratado por la empresa INGPAC para analizar el estado de su sistema eléctrico. Los datos que se le entregaron son los siguientes: Máquinas Generadoras Sincrónicas. Barra Potencia generación MW Tensión Nominal kV Potencia Nominal MVA Potencia reactiva máx MVAR Generador 1 1 60 12 100 50 Generador 4 4 50 15 50 100 Transformadores Barra Reactancia % Tensión Nominal kV Potencia Nominal MVA Potencia reactiva máx MVAR Transformador 1 1-2 30 12/110 100 50 Transformador 4 3-4 50 15/110 50 100 Líneas Reactancia Ω/kM Largo Km Capacidad Máxima MVA Línea 2-3 0,5 50 15 Línea 3-5 0,8 100 20 Línea 2-5 0,3 120 50 Cargas
- 2. Potencia Activa MW Potencia Reactiva MVAR Carga 2 10 5 Carga 3 50 20 Carga 4 50 40 Carga 5 40 10 1. Debe determinar la matriz de admitancia del sistema 10% 2. Determinar las tensiones de todas las barras por el método Gauss- Seidel en las 3 primeras iteraciones, considere los valores iniciales como los unitarios. 30% 3. Determine las potencia activas y reactivas de cada una de las líneas(Inicio y término) 20% Usando el Software PowerWorld 4. Con que nivel de potencia activa en la barra 3 se llega a tener 100% de la línea 2-3 5% 5. Con que nivel de potencia reactiva en la barra 2 se llega a tener 100% de la línea 2-3 5% 6. Con que nivel de potencia activa en la barra 3 se genera el Blackaut. 5% 7. Con que nivel de potencia activa en la barra 5 el generado 1 llega a su nivel máximo de generación reactiva. 5% 8. Informe 20% DESARROLLO DIAGRAMA UNILINEAL INICIAL
- 3. • Determinamos las Zonas para poder llevar el sistema a por unidad (pu). Determinar zonas: Impedancia de las líneas: Para calcular las impedancias de la línea tenemos que multiplicar por el kilometraje que se encuentra la línea con respecto a las barras Impedancia de los transformadores: JKmZ Km 20661,0 121 25 25505,032 = Ω Ω ⇒Ω=•= Ω − JKmZ Km 66115,0 121 80 801008,053 = Ω Ω ⇒Ω=•= Ω − JKmZ Km 29752,0 121 36 361203,052 = Ω Ω ⇒Ω=•= Ω − VbI = 12 [Kv] Ω== 44,1 100 122 ZbI VbII = 110 [Kv] Ω== 121 100 1102 ZbII VbIII = 15 [Kv] Ω== 25,2 100 152 ZbIII ( ) ZbI Sn Vb Xt 2 100 % ∗ =
- 4. ( ) ( ) JMvA Kv Xt 3,0 44,1 100 12 100 3,0 1 2 = Ω ∗ = ( ) ( ) JMvA Kv Xt 1 25,2 50 15 100 5,0 4 2 = Ω ∗ = Característica de las barras Matriz de admitancia: −∠∠∠ −∠∠ ∠∠−∠∠ ∠∠−∠∠ ∠−∠ 908736,40905125,1903611,30 090190100 905125,190190353,79084,40 903611,309084,490532,1190333,3 00090333,390333,3 Matriz de Admitancia con Programa POWER WORLD Barra Pc Qc Pg Qg V φ 1 0 0 ? ? 1 0 Referencia 2 0,1 0,05 0 0 ? ? Carga 3 0,5 0,2 0 0 ? ? Carga 4 0,5 0,4 0,5 ? 1 ? Generador 5 0,4 0,1 0 0 ? ? carga
- 5. METODO GAUSS - SEIDEL: ( ) ( ) ∑= ∗∗∗ ∗ −−− = n j iji xyxyx xxxx x YV YYV JQcPcJQgPg V 1 0 * 1 ´ ( ) ( ) ( )25 0 523 0 321 0 1 2222 * 2 22221 2 1 YVYVYV YYV JQcPcJQgPg V ∗+∗+∗∗− ∗ −−− = ( ) ( ) ( )903611,3019084,40190333,301 90532,11 1 90532,1101 05,01,0001 2 ∠∗∠+∠∗∠+∠∗∠∗ −∠ − −∠∗∠ −−− = JJ V °−∠= 4989,09958,01 2V ( ) ( ) ( )34 0 435 1 532 1 2 3333 * 3 33331 3 1 YVYVYV YYV JQcPcJQgPg V ∗+∗+∗∗− ∗ −−− = ( ) ( ) ( )90101905125,1019084,44989,09958,0 90353,7 1 90353,701 2,05,0001 3 ∠∗∠+∠∗∠+∠∗−∠∗ −∠ − −∠∗∠ −−− = JJ V 3456,4972739,01 3 −∠=V ( ) ( ) ( )53 0 352 1 2 5555 * 5 55551 5 1 YVYV YYV JQcPcJQgPg V ∗+∗∗− ∗ −−− = ( ) ( ) ( )905125,13456,4972739,0903611,34989,09958,0 908736,4 1 908736,401 1,04,0001 5 ∠∗−∠+∠∗−∠∗ −∠ − −∠∗∠ −−− = JJ V °−∠= 54252,6973571,01 5V
- 6. ( )* 44 * 44 * 43 * 344 1 4 Im YVVYVVgQQ cg ∗∗+∗∗+= ( )90101019013456,4972739,001Im4,01 4 ∠∗∠∗∠+−∠∗∠∗∠+= gQg JQg ˆ4301,01 4 = 4.max 1 4 gg QQ < ( ) ( ) ( )43 1 3 4444 * 4 44441 4 1 YV YYV JQcPcJQgPg V ∗∗− ∗ −−− = ( ) ( ) ( )9013456,4972739,0 901 1 90101 4,05,04301,05,01 4 ∠∗−∠∗ −∠ − −∠∗∠ −−− = JJ V °−∠= 21520,4002,11 4V PRIMERA ITERACIÓN GAUSS-SAIDEL ( )∑= ∗∗∗∗∗+= n j iJJiiJJicigi SenYVVQQ 1 σδδ
- 7. Segunda Iteración: ( ) ( ) ( )25 1 523 1 321 0 1 2222 *1 2 22222 2 1 YVYVYV YYV JQcPcJQgPg V ∗+∗+∗∗− ∗ −−− = ( ) ( ) ( 97357,09084,43456,4972739,090333,301 90532,11 1 90532,114989,09958,0 05,01,0002 2 +∠∗−∠+∠∗∠∗ −∠ − −∠∗∠ −−− = JJ V °−∠= 2257,49762,02 2V ( ) ( ) ( )34 1 435 2 532 2 2 3333 *1 3 33332 3 1 YVYVYV YYV JQcPcJQgPg V ∗+∗+∗∗− ∗ −−− = ( ) ( ) ( )901215,400,1905125,154252,6973571,09084,42257,49762,0 90353,7 1 90353,73456,4972739,0 2,05,0002 3 ∠∗−∠+∠∗−∠+∠∗−∠∗ −∠ − −∠∗∠ −−− = JJ V
- 8. °−∠= 91042,8954017,02 3V ( ) ( ) ( )53 1 352 2 2 5555 *1 5 55552 5 1 YVYV YYV JQcPcJQgPg V ∗+∗∗− ∗ −−− = ( ) ( ) ( 91042,8954017,0903611,32257,49762,0 908736,4 1 908736,454252,6973571,0 1,04,0002 5 ∗−∠+∠∗−∠∗ −∠ − −∠∗∠ −−− = JJ V °−∠= 7271,10949969,02 5V ( )* 44 *1 4 1 4 * 43 *2 3 1 44 2 4 Im YVVYVVgQQ cg ∗∗+∗∗+= ( )9012152,4002,12152,4002,190191041,8954017,02152,4002,1Im4,02 4 ∠∗∠∗−∠+−∠∗∠∗−∠+= gQg JQg ˆ4513,02 4 = 4.max 2 4 gg QQ < ( ) ( ) ( )43 2 3 4444 *1 4 44442 4 1 YV YYV JQcPcJQgPg V ∗∗− ∗ −−− = ( ) ( ) ( )90191042,8954017,0 901 1 9012152,4002,1 4,05,04513,05,02 4 ∠∗−∠∗ −∠ − −∠∗∠ −−− = JJ V °−∠= 6715,8005,12 4V SEGUNDA ITERACIÓN GAUSS-SAIDEL
- 9. Tercera Iteración: ( ) ( ) ( )25 2 523 2 321 0 1 2222 *2 2 22223 2 1 YVYVYV YYV JQcPcJQgPg V ∗+∗+∗∗− ∗ −−− = ( ) ( ) ( 949,09084,491042,8954017,090333,301 90532,11 1 90532,112257,4984,0 05,02,0003 2 +∠∗−∠+∠∗∠∗ −∠ − −∠∗−∠ −−− = JJ V °−∠= 3419,7960728,03 2V ( ) ( ) ( )34 1 435 2 532 2 2 3333 *1 3 33332 3 1 YVYVYV YYV JQcPcJQgPg V ∗+∗+∗∗− ∗ −−− = ( ) ( ) ( )9016715,8005,1905125,17271,10949969,09084,43419,7960728,0 90353,7 1 90353,791042,8954017,0 2,05,0002 3 ∠∗−∠+∠∗−∠+∠∗−∠∗ −∠ − −∠∗∠ −−− = JJ V
- 10. °−∠= 5548,129375,02 3V ( ) ( ) ( )53 2 352 3 2 5555 *2 5 55553 5 1 YVYV YYV JQcPcJQgPg V ∗+∗∗− ∗ −−− = ( ) ( ) ( 554,129375,0903611,33419,7960728,0 908736,4 1 908736,47271,10949969,0 1,04,0003 5 −∠+∠∗−∠∗ −∠ − −∠∗−∠ −−− = JJ V °−∠= 2047,1493233,03 5V ( )* 44 *2 4 2 4 * 43 *3 3 2 44 3 4 Im YVVYVVgQQ cg ∗∗+∗∗+= ( )9016715,800,16715,8005,19015548,129375,086715005,1Im30,03 4 ∠∗∠∗−∠+−∠∗∠∗−−∠+= gQg JQg ˆ470001,03 4 = 4.max 3 4 gg QQ < ( ) ( ) ( )43 3 3 4444 *2 4 44443 4 1 YV YYV JQcPcJQgPg V ∗∗− ∗ −−− = ( ) ( ) ( )9015548,129375,0 901 1 9016715,8005,1 4,05,0470001,05,03 4 ∠∗−∠∗ −∠ − −∠∗∠ −−− = JJ V °−∠= 2864,12007,13 4V TERCERA ITERACIÓN GAUSS-SAIDEL
- 11. ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∗ = − − − − − − − − − − 5 4 3 2 1 5 4 3 2 1 5 5 4 5 3 5 2 5 1 5 5 5 4 5 3 5 2 5 1 5 5 4 4 4 3 4 2 4 1 4 5 4 4 4 3 4 2 4 1 4 5 3 4 3 3 3 2 3 1 3 5 3 4 3 3 3 2 3 1 3 5 2 4 2 3 2 2 2 1 2 5 2 4 2 3 2 2 2 1 2 5 1 4 1 3 1 2 1 1 1 5 1 4 1 3 1 2 1 1 1 5 5 4 5 3 5 2 5 1 5 5 5 4 5 3 5 2 5 1 5 5 4 4 4 3 4 2 4 1 4 5 4 4 4 3 4 2 4 1 4 5 3 4 3 3 3 2 3 1 3 5 3 4 3 3 3 2 3 1 3 5 2 4 2 3 2 2 2 1 2 5 2 4 2 3 2 2 2 1 2 5 1 4 1 3 1 2 1 1 1 5 1 4 1 3 1 2 1 1 1 5 4 3 2 1 5 4 3 2 1 δ δ δ δ δ δδδδ δδδδδ δδδδδ δδδδδ δδδδδ δδδδδ δδδδδ δδδδδ δδδδδ δδδδδ V V V V V d dQ d dQ d dQ d dQ dv dQ dv dQ dv dQ dv dQ dv dQ dv dQ d dQ d dQ d dQ d dQ d dQ dv dQ dv dQ dv dQ dv dQ dv dQ d dQ d dQ d dQ d dQ d dQ dv dQ dv dQ dv dQ dv dQ dv dQ d dQ d dQ d dQ d dQ d dQ dv dQ dv dQ dv dQ dv dQ dv dQ d dQ d dQ d dQ d dQ d dQ dv dQ dv dQ dv dQ dv dQ dv dQ d dp d dp d dp d dp d dp dv dp dv dp dv dp dv dp dv dp d dp d dp d dp d dp d dp dv dp dv dp dv dp dv dp dv dp d dp d dp d dp d dp d dp dv dp dv dp dv dp dv dp dv dp d dp d dp d dp d dp d dp dv dp dv dp dv dp dv dp dv dp d dp d dp d dp d dp d dp dv dp dv dp dv dp dv dp dv dp Q Q Q Q Q P P P P P Todas las iteraciones realizadas con el programa son iguales a las calculadas para llegar a un valor mas exapto por el método gauss se necesita seguir iterando hasta que ya no varié mas. Método de Newton Raphon MATRIZ JACOBIANA
- 12. DESPEJAMOS LA MATRIZ ( )iJJiiJJ n J iCigi CosYVVPPP σδδ −−∗∗∗++−= ∑=1 ( ) ( ) ( )23322332211221 0 12222222222 σδδσδδσ −−∗∗∗+−−∗∗∗+−∗∗∗++−= CosYVVCosYVVCosYVVPPP Cg ( )25522552 σδδ −−∗∗∗+ CosYVV ( ) ( ) ( )900084,4119000333,3119053,11111,002 −−∗∗∗+−−∗∗∗+∗∗∗++−= CosCosCosP ( )9000336,311 −−∗∗∗+ Cos 1,02 =P
- 13. ( ) ( ) ( )3553355332233223333333333 σδδσδδσ −−∗∗∗+−−∗∗∗+−∗∗∗++−= CosYVVCosYVVCosYVVPPP Cg ( )34433443 σδδ −−∗∗∗+ CosYVV ( ) ( ) ( )90005125,111900084,411903353,7115,003 −−∗∗∗+−−∗∗∗+∗∗∗++−= CosCosCosP ( )9000111 −−∗∗∗+ Cos 5,03 =P ( ) ( )43344334444444444 σδδσ −−∗∗∗+−∗∗∗++−= CosYVVCosYVVPPP Cg ( ) ( )9000111901115,05,04 −−∗∗∗+∗∗∗++−= CosCosP 04 =P ( ) ( ) ( )5335533552255225555555555 σδδσδδσ −−∗∗∗+−−∗∗∗+−∗∗∗++−= CosYVVCosYVVCosYVVPPP Cg ( ) ( ) ( )90005125,111900036,311908736,4114,005 −−∗∗∗+−−∗∗∗+∗∗∗++−= CosCosCosP 4,05 =P ( )iJJiiJJ n J iCigi SenYVVQQQ σδδ −−∗∗∗++−= ∑=1 ( ) ( ) ( )2112211223322332222222222 σδδσδδσ −−∗∗∗+−−∗∗∗+−∗∗∗++−= SenYVVSenYVVSenYVVQQQ Cg
- 14. ( )25522552 σδδ −−∗∗∗+ SenYVV ( ) ( ) ( )9000333,311900084,41190532,111105,002 −−∗∗∗+−−∗∗∗+∗∗∗++−= SenSenSenQ ( )90003611,311 −−∗∗∗ Sen 0479,02 =Q ( ) ( ) ( )3443344332233223333333333 σδδσδδσ −−∗∗∗+−−∗∗∗+−∗∗∗++−= SenYVVSenYVVSenYVVQQQ Cg ( )35533553 σδδ −−∗∗∗+ SenYVV ( ) ( ) ( )9000111900084,41190353,7112,003 −−∗∗∗+−−∗∗∗+∗∗∗++−= SenSenSenQ ( )90005125,111 −−∗∗∗ Sen 2005,03 =Q ( ) ( ) ( )5335533552255225555555555 σδδσδδσ −−∗∗∗+−−∗∗∗+−∗∗∗++−= SenYVVSenYVVSenYVVQQQ Cg ( ) ( ) ( )90005125,11190003611,311908736,4111,005 −−∗∗∗+−−∗∗∗+∗∗∗++−= SenSenSenQ 1,05 =Q ( ) ( ) ( ) ( )25522552332233211221 0 122222 2 2 2 σδδσδδσδδσ −−∗∗+−−∗∗+−−∗+−∗∗∗= CosYVCosYVCosYVCosYV d d V P ( ) ( ) ( ) ( )90003611,31900084,419000333,3190532,1112 2 2 −−∗∗+−−∗∗+−−∗+∗∗∗= CosCosCosCos d d V P 0 2 2 = V P d d ( )2332232 3 2 σδδ −−∗∗= CosYV d d V P ( )900084,41 3 2 −−∗∗= Cos d d V P 0 3 2 = V P d d ( )2552252 5 2 σδδ −−∗∗= CosYV d d V P ( )90003611,31 5 2 −−∗∗= Cos d d V P 0 5 2 = V P d d
- 15. ( ) ( ) ( )2552255223322332211221 0 12 2 2 σδδσδδσδδ δ −−∗∗∗−−−∗∗∗−−−∗∗∗−= SenYVVSenYVVSenYVV d dP ( ) ( ) ( )90003611,311900084,4119000333,311 2 2 −−∗∗∗−−−∗∗∗−−−∗∗∗−= SenSenSen d dP δ 5341,11 2 2 = δd dP ( )900084,411 3 2 −−∗∗∗= Sen d dP δ 84,4 3 2 −= δd dP ( )24422442 4 2 σδδ δ −−∗∗∗= SenYVV d dP ( )900053,1111 4 2 −−∗∗∗= Sen d dP δ 0 3 2 = δd dP ( )25522552 5 2 σδδ δ −−∗∗∗= SenYVV d dP ( )90003611,311 5 2 −−∗∗∗= Sen d dP δ 3611,3 3 2 −= δd dP ( ) ( ) ( ) ( )35533553443344332332233333 3 3 2 σδδσδδσδδσ −−∗∗+−−∗∗+−−∗+−∗∗∗= CosYVCosYVCosYVCosYV d d V P ( ) ( ) ( ) ( )90005125,11900011900084,4190353,712 3 3 −−∗∗+−−∗∗+−−∗+∗∗∗= CosCosCosCos d d V P 0 3 3 = V P d d ( )3223323 2 3 σδδ −−∗∗= CosYV d d V P ( )900084,41 2 3 −−∗∗= Cos d d V P 0 2 3 = V P d d ( )3553353 5 3 σδδ −−∗∗= CosYV d d V P ( )90005125,11 5 3 −−∗∗= Cos d d V P 0 5 3 = V P d d ( )23322332 3 2 σδδ δ −−∗∗∗= SenYVV d dP
- 16. ( )32233223 2 3 σδδ δ −−∗∗∗= SenYVV d dP ( )900084,411 2 3 −−∗∗∗= Sen d dP δ 84,4 3 2 −= δd dP ( ) ( ) ( )355335533443344332233223 3 3 σδδσδδσδδ δ −−∗∗∗−−−∗∗∗−−−∗∗∗−= SenYVVSenYVVSenYVV d dP ( ) ( ) ( )90005125,1119000111900084,411 3 3 −−∗∗∗−−−∗∗∗−−−∗∗∗−= SenSenSen d dP δ 3525,7 3 3 = δd dP ( )34433443 4 3 σδδ δ −−∗∗∗= SenYVV d dP ( )9000111 4 3 −−∗∗∗= Sen d dP δ 1 4 3 −= δd dP ( )35533553 5 3 σδδ δ −−∗∗∗= SenYVV d dP ( )90005125,111 5 3 −−∗∗∗= Sen d dP δ 5125,1 4 3 −= δd dP ( )4334434 3 4 σδδ −−∗∗= CosYV d d V P ( )900011 3 4 −−∗∗= Cos d d V P 0 3 4 = V P d d ( )43344334 3 4 σδδ δ −−∗∗∗= SenYVV d dP ( )9000111 3 4 −−∗∗∗= Sen d dP δ 1 4 3 −= δd dP ( )43344334 4 4 σδδ δ −−∗∗∗−= SenYVV d dP ( )9000111 4 4 −−∗∗∗−= Sen d dP δ 1 4 4 = δd dP ( )90003611,31 2 5 −−∗∗= Cos d d V P 0 2 5 = V P d d ( )5225525 2 5 σδδ −−∗∗= CosYV d d V P
- 17. ( )5335335 3 5 σδδ −−∗∗= CosYV d d V P ( )90005125,11 3 5 −−∗∗= Cos d d V P 0 3 5 = V P d d ( ) ( ) ( )5335533522552255555 5 5 2 σδδσδδσ −−∗∗+−−∗+−∗∗∗= CosYVCosYVCosYV d d V P ( ) ( ) ( )90005125,1190003611,31908736,412 5 5 −−∗∗+−−∗∗+∗∗∗= CosCosCos d d V P 0 5 5 = V P d d ( )52255225 2 5 σδδ δ −−∗∗∗= SenYVV d dP ( )90003611,311 2 5 −−∗∗∗= Sen d dP δ 3611,3 2 5 −= δd dP ( )53355335 3 5 σδδ δ −−∗∗∗= SenYVV d dP ( )90005125,111 3 5 −−∗∗∗= Sen d dP δ 5125,1 3 5 −= δd dP ( ) ( )5335533552255225 5 5 σδδσδδ δ −−∗∗∗−−−∗∗∗−= SenYVVSenYVV d dP ( ) ( )90005125,11190003611,311 5 5 −−∗∗∗−−−∗∗∗−= SenSen d dP δ 8736,4 5 5 = δd dP ( ) ( ) ( ) ( )25522552332233211221122222 2 2 2 σδδσδδσδδσ −−∗∗+−−∗∗+−−∗∗+−∗∗∗= SenYVSenYVSenYVSenYV d d V Q ( ) ( ) ( ) ( )90003611,31900084,419000333,3190532,1112 2 2 −−∗∗+−−∗∗+−−∗∗+∗∗∗= SenSenSenSen d d V Q 5299,11 2 2 = V Q d d ( )2332232 3 2 σδδ −−∗∗= SenYV d d V Q ( )900084,41 3 2 −−∗∗= Sen d d V Q 84,4 3 2 −= V Q d d ( )2552252 5 2 σδδ −−∗∗= SenYV d d V Q ( )90003611,31 5 2 −−∗∗= Sen d d V Q 3611,3 5 2 −= V Q d d
- 18. ( ) ( ) ( )255225522332233221122112 2 2 σδδσδδσδδ δ −−∗∗∗+−−∗∗∗+−−∗∗∗= CosYVVCosYVVCosYVV d dQ ( ) ( ) ( )90003611,311900084,4119000333,311 2 2 −−∗∗∗+−−∗∗∗+−−∗∗∗= CosCosCos d dQ δ 0 2 2 = δd dQ ( )23322332 3 2 σδδ δ −−∗∗∗−= CosYVV d dQ ( )900084,411 3 2 −−∗∗∗−= Cos d dQ δ 0 3 2 = δd dQ ( )25522552 5 2 σδδ δ −−∗∗∗−= CosYVV d dQ ( )90003611,311 5 2 −−∗∗∗−= Cos d dQ δ 0 5 2 = δd dQ ( )3223323 2 3 σδδ −−∗∗= SenYV d d V Q ( )900084,41 2 3 −−∗∗= Sen d d V Q 84,4 2 3 −= V Q d d ( ) ( ) ( ) ( )35533553443344322332233333 3 3 2 σδδσδδσδδσ −−∗∗+−−∗∗+−−∗∗+−∗∗∗= SenYVSenYVSenYVSenYV d d V Q ( ) ( ) ( ) ( )90005125,11900011900084,4190353,712 3 3 −−∗∗+−−∗∗+−−∗∗+∗∗∗= SenSenSenSen d d V Q 3535,7 3 3 = V Q d d ( )3553353 5 3 σδδ −−∗∗= SenYV d d V Q ( )90005125,11 5 3 −−∗∗= Sen d d V Q 5125,1 5 3 −= V Q d d ( )32233223 2 3 σδδ δ −−∗∗∗−= CosYVV d dQ ( )900084,411 2 3 −−∗∗∗−= Cos d dQ δ 0 2 3 = δd dQ ( ) ( ) ( )355335533443344332233223 3 3 σδδσδδσδδ δ −−∗∗∗+−−∗∗∗+−−∗∗∗= CosYVVCosYVVCosYVV d dQ
- 19. ( ) ( ) ( )90005125,1119000111900084,411 3 3 −−∗∗∗+−−∗∗∗+−−∗∗∗= CosCosCos d dQ δ 0 3 3 = δd dQ ( )34433443 4 3 σδδ δ −−∗∗∗−= CosYVV d dQ ( )9000111 4 3 −−∗∗∗−= Cos d dQ δ 0 4 3 = δd dQ ( )35533553 5 3 σδδ δ −−∗∗∗−= CosYVV d dQ ( )90005125,111 5 3 −−∗∗∗−= Cos d dQ δ 0 5 3 = δd dQ ( )5225525 2 5 σδδ −−∗∗= senYV d d V Q ( )90003611,31 2 5 −−∗∗= sen d d V Q 3611,3 2 5 −= V Q d d ( )5335535 3 5 σδδ −−∗∗= senYV d d V Q ( )90005125,11 3 5 −−∗∗= sen d d V Q 5125,1 3 5 −= V Q d d ( ) ( ) ( )5335533522552255555 5 5 2 σδδσδδσ −−∗∗+−−∗∗+−∗∗∗= SenYVSenYVSenYV d d V Q ( ) ( ) ( )90005125,11190003611,31908736,412 5 5 −−∗∗+−−∗∗+∗∗∗= SenSenSen d d V Q 8736,4 5 5 = V Q d d ( )52255225 2 5 σδδ δ −−∗∗∗−= CosYVV d dQ ( )90003611,311 2 5 −−∗∗∗−= Cos d dQ δ 0 2 5 = δd dQ ( )53355335 3 5 σδδ δ −−∗∗∗−= CosYVV d dQ ( )90005125,111 2 5 −−∗∗∗−= Cos d dQ δ 0 2 5 = δd dQ ( ) ( )5335533552255225 5 5 σδδσδδ δ −−∗∗∗+−−∗∗∗= CosYVVCosYVV d dQ ( ) ( )90005125,11190003611,311 5 5 −−∗∗∗+−−∗∗∗= CosCos d dQ δ 0 5 5 = δd dQ
- 20. − − − − − − − ∗ −− −− −− −− − −−− −− = ∆ ∆ ∆ ∆ ∆ ∆ ∆ − 1,0 2005,0 0479,0 4,0 0 5,0 1,0 00008736,45125,13611,3 00005125,13535,784,4 00003611,384,45299,11 8736,405125,113611,3000 0110000 5125,113525,784,4000 3611,3084,45341,11000 1 5 4 3 2 5 3 2 δ δ δ δ V V V °−→−=∆ °−→−=∆ °−→−=∆ °−→−=∆ →−=∆ →−=∆ →−=∆ 5,2341,0 9,2240,0 9,2240,0 19,1730003,0 897219,0102781,0 902086,0097914,0 924781,0075219,0 5 4 3 2 5 3 2 δ δ δ δ V V V ( ) ( )4334433444444444 σδδσ −−∗∗∗+−∗∗∗+= SenYVVSenYVVQQG C ( ) ( )909,229,221902086,0190114,04 −+−∗∗∗+∗∗∗+= SenSenQG 487535,04 =QG El QG4 es menor que el Qmax. Del generador por lo cual se cumple que la barra 4 es de generación PRIMERA ITERACIÓN CON PROGRAMA
- 21. SEGUNDA ITERACIÓN ( ) ( ) ( )23322332211221 0 12222222222 σδδσδδσ −−∗∗∗+−−∗∗∗+−∗∗∗++−= CosYVVCosYVVCosYVVPPP Cg ( )25522552 σδδ −−∗∗∗+ CosYVV ( )905,2319,17336,38972,09248,0 −+−∗∗∗+ Cos 10499,02 −=P ( ) ( ) ( )3553355332233223333333333 σδδσδδσ −−∗∗∗+−−∗∗∗+−∗∗∗++−= CosYVVCosYVVCosYVVPPP Cg ( )34433443 σδδ −−∗∗∗+ CosYVV ( )909,229,22119021,0 −+−∗∗∗+ Cos ( ) ( ) ( )909,2219,1784,49021,09248,090019,17333,319248,09053,119248,09248,01,002 −+−∗∗∗+−−−∗∗∗+∗∗∗++−= CosCosCosP ( ) ( ) ( )905,239,225125,18972,09021,09019,179,2284,49248,09021,090353,79021,09021,05,003 −+−∗∗∗+−+−∗∗∗+∗∗∗++−= CosCosCosP
- 22. 111082,03 =P ( ) ( )43344334444444444 σδδσ −−∗∗∗+−∗∗∗++−= CosYVVCosYVVPPP Cg ( ) ( )909,229,221902,0190115,05,04 −+−∗∗∗+∗∗∗++−= CosCosP 04 =P ( ) ( ) ( )5335533552255225555555555 σδδσδδσ −−∗∗∗+−−∗∗∗+−∗∗∗++−= CosYVVCosYVVCosYVVPPP Cg 072224,05 =P ( )iJJiiJJ n J iCigi SenYVVQQQ σδδ −−∗∗∗++−= ∑=1 ( ) ( ) ( )2112211223322332222222222 σδδσδδσ −−∗∗∗+−−∗∗∗+−∗∗∗++−= SenYVVSenYVVSenYVVQQQ Cg ( )25522552 σδδ −−∗∗∗+ SenYVV ( ) ( ) 33,319248,0909,2219,1784,4902,09248,090532,119248,09248,005,002 ∗∗+−+−∗∗∗+∗∗∗++−= SenSenQ ( )905,2319,173611,38972,09248,0 −+−∗∗∗+ Sen ( ) ( ) ( )909,225,235125,1902,08972,09019,175,2336,39248,08972,0908736,48972,08972,04,005 −+−∗∗∗+−+−∗∗∗+∗∗∗++−= CosCosCosP
- 23. 178871,02 =Q ( ) ( ) ( )3443344332233223333333333 σδδσδδσ −−∗∗∗+−−∗∗∗+−∗∗∗++−= SenYVVSenYVVSenYVVQQQ Cg ( )35533553 σδδ −−∗∗∗+ SenYVV ( ) ( ) ( 211902,09019,179,2284,49248,0902,090353,7902,0902,02,003 −∗∗∗+−+−∗∗∗+∗∗∗++−= SenSenSenQ ( )905,239,225125,18972,0902,0 −+−∗∗∗+ Sen 039122,03 =Q ( ) ( ) ( )5335533552255225555555555 σδδσδδσ −−∗∗∗+−−∗∗∗+−∗∗∗++−= SenYVVSenYVVSenYVVQQQ Cg ( ) ( ) 89,0905,175,233611,3924781,0897219,0908736,4897219,0897219,01,005 +−+−∗∗∗+∗∗∗++−= SenSenQ 02733,05 =Q ( ) ( ) ( ) ( )25522552332233211221 0 122222 2 2 2 σδδσδδσδδσ −−∗∗+−−∗∗+−−∗+−∗∗∗= CosYVCosYVCosYVCosYV d d V P ( ) ( ) ( ) 0909,2219,1784,4902086,090019,17333,3190532,11924781,02 2 2 +−+−∗∗+−−−∗+∗∗∗= CosCosCos d d V P 250605,0 2 2 −= V P d d ( )2332232 3 2 σδδ −−∗∗= CosYV d d V P ( )909,2219,1784,4924781,0 3 2 −+−∗∗= Cos d d V P 445327,0 3 2 = V P d d ( )2552252 5 2 σδδ −−∗∗= CosYV d d V P ( )905,2319,173611,3924781,0 5 2 −+−∗∗= Cos d d V P 341624,0 5 2 = V P d d ( ) ( ) ( )2552255223322332211221 0 12 2 2 σδδσδδσδδ δ −−∗∗∗−−−∗∗∗−−−∗∗∗−= SenYVVSenYVVSenYVV d dP ( ) ( ) 92478,0905,2319,1784,4902086,0924781,090019,17333,31924781,0 2 2 −−+−∗∗∗−−−−∗∗∗−= SenSen d dP δ
- 24. 73417,9 2 2 = δd dP ( )909,2219,1784,4902086,0924781,0 3 2 −+−∗∗∗= Sen d dP δ 01765,4 3 2 −= δd dP ( )24422442 4 2 σδδ δ −−∗∗∗= SenYVV d dP ( )905,2319,1701924781,0 4 2 −+−∗∗∗= Sen d dP δ 0 4 2 = δd dP ( )25522552 5 2 σδδ δ −−∗∗∗= SenYVV d dP ( )905,2319,173611,3897219,0924781,0 5 2 −+−∗∗∗= Sen d dP δ ( ) ( ) ( ) ( )35533553443344332332233333 3 3 2 σδδσδδσδδσ −−∗∗+−−∗∗+−−∗+−∗∗∗= CosYVCosYVCosYVCosYV d d V P ( ) ( ) ( ) 8972,0909,229,22119019,179,2284,492478,090353,7902086,02 3 3 +−+−∗∗+++−∗+∗∗∗= CosCosCos d d V P 433116,0 3 3 −= V P d d ( )3223323 2 3 σδδ −−∗∗= CosYV d d V P ( )9019,179,2284,4902086,0 2 3 −+−∗∗= Cos d d V P 434398,0 2 3 −= V P d d ( )23322332 3 2 σδδ δ −−∗∗∗= SenYVV d dP 77191,2 3 2 −= δd dP
- 25. ( )3553353 5 3 σδδ −−∗∗= CosYV d d V P ( )905,239,225125,1902086,0 5 3 −+−∗∗= Cos d d V P 014288,0 5 3 = V P d d ( )32233223 2 3 σδδ δ −−∗∗∗= SenYVV d dP ( )9019,179,2284,4924781,0902086,0 2 3 −+−∗∗∗= Sen d dP δ 01765,4 3 2 −= δd dP ( ) ( ) ( )355335533443344332233223 3 3 σδδσδδσδδ δ −−∗∗∗−−−∗∗∗−−−∗∗∗−= SenYVVSenYVVSenYVV d dP ( ) ( ) 902086,0909,229,2211902086,09019,179,2284,4924781,0902086,0 3 3 ∗−−+−∗∗∗−−+−∗∗∗−= SenSen d dP δ 14384,6 3 3 = δd dP ( )34433443 4 3 σδδ δ −−∗∗∗= SenYVV d dP ( )909,229,2211902086,0 4 3 −+−∗∗∗= Sen d dP δ 902086,0 4 3 −= δd dP ( )35533553 5 3 σδδ δ −−∗∗∗= SenYVV d dP ( )905,239,225125,1897219,0902086,0 5 3 −+−∗∗∗= Sen d dP δ 2241,1 5 3 −= d dP ( )4334434 3 4 σδδ −−∗∗= CosYV d d V P ( )909,229,2211 3 4 −+−∗∗= Cos d d V P 0 3 4 = V P d d ( )43344334 3 4 σδδ δ −−∗∗∗= SenYVV d dP ( )909,229,221902086,01 3 4 −+−∗∗∗= Sen d dP δ 902086 4 3 −= δd dP
- 26. ( )43344334 4 4 σδδ δ −−∗∗∗−= SenYVV d dP ( )909,229,221902086,01 4 4 −+−∗∗∗−= Sen d dP δ 902086,0 4 4 = δd dP ( )90003611,3897219,0 2 5 −−∗∗= Cos d d V P 331443,0 2 5 −= V P d d ( )5335335 3 5 σδδ −−∗∗= CosYV d d V P ( )909,225,235125,1897219,0 3 5 −+−∗∗= Cos d d V P 014211,0 3 5 −= V P d d ( ) ( ) ( )5335533522552255555 5 5 2 σδδσδδσ −−∗∗+−−∗+−∗∗∗= CosYVCosYVCosYV d d V P ( ) ( ) ( 5,235125,1902086,09019,175,233611,3924781,0908736,4897219,02 5 5 −∗∗+−+−∗∗+∗∗∗= CosCosCos d d V P 355912,0 5 5 −= V P d d ( )52255225 2 5 σδδ δ −−∗∗∗= SenYVV d dP ( )9019,175,233611,3924781,0897219,0 2 5 −+−∗∗∗= Sen d dP δ 77191,2 2 5 −= δd dP ( )53355335 3 5 σδδ δ −−∗∗∗= SenYVV d dP ( )909,225,235125,1902086,0897219,0 3 5 −+−∗∗∗= Sen d dP δ 2241,1 3 5 −= δd dP ( ) ( )5335533552255225 5 5 σδδσδδ δ −−∗∗∗−−−∗∗∗−= SenYVVSenYVV d dP ( )5225525 2 5 σδδ −−∗∗= CosYV d d V P
- 27. ( ) ( 9,225,235125,1902086,0897219,09019,175,233611,3924781,0897219,0 5 5 −+−∗∗∗−−+−∗∗∗−= SenSen d dP δ 8702,3 5 5 = δd dP ( ) ( ) ( ) ( )25522552332233211221122222 2 2 2 σδδσδδσδδσ −−∗∗+−−∗∗+−−∗∗+−∗∗∗= SenYVSenYVSenYVSenYV d d V Q ( ) ( ) ( )909,2219,17.84,4902086,090019,17333,3190532,11924781,02 2 2 +−+−∗∗+−−−∗∗+∗∗∗= SenSenSen d d V Q 5299,10 2 2 = V Q d d ( )2332232 3 2 σδδ −−∗∗= SenYV d d V Q ( )909,2219,1784,4924781,0 3 2 −+−∗∗= Sen d d V Q 45373,4 3 2 −= V Q d d ( )2552252 5 2 σδδ −−∗∗= SenYV d d V Q ( )905,2319,173611,3924781,0 5 2 −+−∗∗= Sen d d V Q 08945,3´ 5 2 −= V Q d d ( ) ( ) ( )255225522332233221122112 2 2 σδδσδδσδδ δ −−∗∗∗+−−∗∗∗+−−∗∗∗= CosYVVCosYVVCosYVV d dQ ( ) ( ) 92478,0909,2219,1784,4902086,0924781,090019,17333,31924781,10 2 2 +−+−∗∗∗+−−−∗∗∗= CosCos d dQ δ 202711,0 2 2 −= δd dQ
- 28. ( )23322332 3 2 σδδ δ −−∗∗∗−= CosYVV d dQ ( )909,2219,1784,4902086,0924781,0 3 2 −+−∗∗∗−= Cos d dQ δ 401723,0 3 2 −= δd dQ ( )25522552 5 2 σδδ δ −−∗∗∗−= CosYVV d dQ ( )905,2319,173611,3897219,0924781,0 5 2 −+−∗∗∗−= Cos d dQ δ 306512,0 5 2 −= δd dQ ( )3223323 2 3 σδδ −−∗∗= SenYV d d V Q ( )9019,179,2284,4*902086,0 2 3 −+−∗= Sen d d V Q 24443,4 2 3 −= V Q d d ( ) ( ) ( ) ( )35533553443344322332233333 3 3 2 σδδσδδσδδσ −−∗∗+−−∗∗+−−∗∗+−∗∗∗= SenYVSenYVSenYVSenYV d d V Q ( ) ( ) ( ) 897219,0909,229,2211909,2284,4924781,090353,7902086,02 3 3 ∗+−+−∗∗+−−∗∗+∗∗∗= SenSenSen d d V Q 45538,6 3 3 = V Q d d ( )3553353 5 3 σδδ −−∗∗= SenYV d d V Q ( )905,239,225125,1924781,0 5 3 −+−∗∗= Sen d d V Q 36433,1 5 3 −= V Q d d ( )32233223 2 3 σδδ δ −−∗∗∗−= CosYVV d dQ ( )9019,179,2284,492478,0902086,0 2 3 −+−∗∗∗−= Cos d dQ δ 401723,0 2 3 = δd dQ
- 29. ( ) ( ) ( )355335533443344332233223 3 3 σδδσδδσδδ δ −−∗∗∗+−−∗∗∗+−−∗∗∗= CosYVVCosYVVCosYVV d dQ ( ) ( ) 0902086,0909,229,2211902086,09019,179,2284,4924781,0902086,0 3 3 ∗+−+−∗∗∗+−+−∗∗∗= CosCos d dQ δ 388904,0 3 3 −= δd dQ ( )34433443 4 3 σδδ δ −−∗∗∗−= CosYVV d dQ ( )909,229,2211902086,0 4 3 −+−∗∗∗−= Cos d dQ δ 0 4 3 = δd dQ ( )35533553 5 3 σδδ δ −−∗∗∗−= CosYVV d dQ ( )905,239,225125,189729,0902086,0 5 3 −+−∗∗∗−= Cos d dQ δ 012819,0 5 3 −= δd dQ ( )5225525 2 5 σδδ −−∗∗= senYV d d V Q ( )9019,175,233611,3897219,0 2 5 −+−∗∗= sen d d V Q 99737,2 2 5 −= V Q d d ( )5335535 3 5 σδδ −−∗∗= senYV d d V Q ( )909,225,235125,1897219,0 3 5 −+−∗∗= sen d d V Q 35697,1 3 5 −= V Q d d ( ) ( ) ( )5335533522552255555 5 5 2 σδδσδδσ −−∗∗+−−∗∗+−∗∗∗= SenYVSenYVSenYV d d V Q ( ) ( ) ( ,235125,11902086,09019,175,233611,3924781,0908736,4897219,02 5 5 −∗∗+−+−∗∗+∗∗∗= SenSenSen d d V Q 29159,4 5 5 = V Q d d
- 30. ( )52255225 2 5 σδδ δ −−∗∗∗−= CosYVV d dQ ( )9019,175,233611,3924781,0897219,0 2 5 −+−∗∗∗−= Cos d dQ δ 306512,0 2 5 = δd dQ ( )53355335 3 5 σδδ δ −−∗∗∗−= CosYVV d dQ ( )909,225,235125,1902086,0897219 2 5 −+−∗∗∗−= Cos d dQ δ 012819,0 2 5 = δd dQ ( ) ( )5335533552255225 5 5 σδδσδδ δ −−∗∗∗+−−∗∗∗= CosYVVCosYVV d dQ ( ) ( 99,225,235125,1902086,0897219,09019,175,233611,3924781,0897219,0 5 5 −+−∗∗∗+−+−∗∗∗= CosCos d dQ δ 319331,0 5 5 −= δd dQ − − − − − − ∗ −−− −−−− −−−−− −−−− − −−−−− −−− = ∆ ∆ ∆ ∆ ∆ ∆ ∆ − 02,0 3,0,0 178,0 7,0,0 0 111,0 104,0 319331,00012819,0306512,029159,435697,199737,2 012819,00388904,0401723,036433,145538,634443,4 306512,00401723,0202711,008945,345373,48032,10 8702,302241,177191,2355912,0014211,0331443,0 0902086,0902086,00000 2241,1902086,014384,601765,4014288,043311,0434398,0 7719,2001765,473417,9341624,0445327,0250605,0 1 5 4 3 2 5 3 2 δ δ δ δ V V V °=°−°−→−=∆ °−=°−°−→−=∆ °−=°−°−→−=∆ °−=°−°−→−=∆ =+−=∆ =+−=∆ =+−=∆ 3818,305,238818,612011,0 47721,299,2257721,6114794,0 47721,299,2257721,6114794,0 91668,2019,1772668,3065043,0 789003,0897219,0108216,0 805138,0902086,0096948,0 828472,0924781,0096309,0 5 4 3 2 5 3 2 rad rad rad rad vV vV vV δ δ δ δ
- 31. Determine las potencias activas y reactivas de cada una de las líneas (Inicio y término) 408374,0 82596,1 408374,082596,16067,1287107,15701,3538313,147721,29805138,0 508791,0 89892,1 508791,089892,19994,149659,15701,3538313,191668,20828472,0 .5701,3538313,19020661,0/2499,54285768,0 2499,54285768,047721,29805138,091668,20828472,0 3 3 3 2 2 2 32 32 = = +=∠=∠∗−∠= = = +=∠=∠∗−∠= −∠=∠∠== ∠=−∠−−∠=∆ − − − Q P JS JQ P JS ampI vV JQ P JS JQ P JS ampI vV 074758,0 361299,0 074758,0361299,06904,11368952,00722,42467618,03818,30789003,0 139816,0 361299,0 139816,0361299,01555,21387409,00722,42467618,091668,20828472,0 .0722,42467618,09029752,0/9278,47139126,0 9278,47139126,03818,30789003,091668,20828472,0 5 5 5 2 2 2 52 52 = = +=∠=∠∗−∠= = = +=∠=∠∗−∠= −∠=∠∠== ∠=−∠−−∠=∆ − − JQ P JS JQ P JS ampI vV 019135,0 015169,0 019135,0015169,05953,51024419,09771,81030949,03818,30789003,0 019769,0 015169,0 019769,0015169,04999,52024918,09771,81030949,047721,29805138,0 .9771,81030949,09066115,0/02289,8020462,0 02289,8020462,03818,30789003,047721,29805138,0 5 5 5 3 3 3 53 53 = = +=∠=∠∗−∠= = = +=∠=∠∗−∠= −∠=∠∠= ∠=−∠−−∠=∆ − − Segunda Iteración con Programa Power – world
- 33. Usando programa PowerWorld Se cambia la potencia activa por una mas elevada ya que la carga supera a la potencia entregada en el sistema Potencia antigua = 60 MW Potencia Nueva = 100 MW • Con que nivel de potencia activa en la barra 3 se llega a tener 100% de la línea 2-3 5% Para lograr obtener tener el 100% de la línea 2-3 se tiene que disminuir la Potencia Activa a 0 MW como se muestra en la figura siguiente
- 34. • Con que nivel de potencia reactiva en la barra 2 se llega a tener 100% de la línea 2-3 5% Cuando se comienza a variar la potencia reactiva en la barra 2 se comienza por disminuir y la línea 2-3 comienza a aumentar el porcentaje, entonces se comienza a aumentar la potencia reactiva de5 MVAR a 25 MVAR , y se produce un backout lo cual no permite llegar a obtener el 100 % de la linea y esta se mantiene con un 344%.
- 35. • Con que nivel de potencia activa en la barra 3 se genera el Blackaut. 5% El blackout se produce cuando se aumenta la potencia activa en la barra 3, llegando a 62 MW, lo cual el generador 2 queda en 112MW, y el generador 4, queda con 50 MW. La línea 2-3 se encuentra sobrecargada en 427 %
- 36. • Con que nivel de potencia activa en la barra 5 el generado 1 llega a su nivel máximo de generación reactiva. 5% Para que el generador uno llegue al máximo de generación de potencia reactiva se tiene que desminuir la potencia activa de la barra 5, A 7 MW lo que implica que la potencia activa del generador también disminuye.
- 37. . CONCLUCIÓN SE PUEDE CONCLUIR QUE TANTO LOS CALCULOS REALIZADOS DAN LO MISMO QUE LOS DEL PROGRAMA, Y LA LINEA 2-3 LA CAPACIDAD MAXIMA DE TRANSPORTE ES EXEDIDA EN UN 356 %, Y EL TRANSFORMADOR XT1 TAMBIEN SOBREPASA EL LIMITE DE LA POTENCIA NOMINAL EN 133 % Giuliano Bozzo Moncada Giuliano Bozzo Moncada Giulianno Bozzo Moncada Giuliano David Bozzo Moncada Giulianno Bozzo Moncada Giuliano-Bozzo-Moncada Giulianno-Bozzo-Moncada Giuliano-David-Bozzo-Moncada Giulianno-Bozzo-Moncada Giuliano Bozzo Moncada Giulianno Bozzo Moncada Giuliano David Bozzo Moncada Giulianno Bozzo Moncada Giuliano-Bozzo-Moncada Giulianno-Bozzo-Moncada Giuliano-David-Bozzo-Moncada Giulianno-Bozzo-Moncada Giuliano Bozzo Moncada Giulianno Bozzo Moncada Giuliano David Bozzo Moncada Giulianno Bozzo Moncada
- 38. Giuliano-Bozzo-Moncada Giulianno-Bozzo-Moncada Giuliano-David-Bozzo-Moncada Giulianno-Bozzo-Moncada Giuliano Bozzo Moncada Giulianno Bozzo Moncada Giuliano David Bozzo Moncada Giulianno Bozzo Moncada Giuliano-Bozzo-Moncada Giulianno-Bozzo-Moncada Giuliano-David-Bozzo-Moncada Giulianno-Bozzo-Moncada Giuliano Bozzo Moncada Giulianno Bozzo Moncada Giuliano David Bozzo Moncada Giulianno Bozzo Moncada Giuliano-Bozzo-Moncada Giulianno-Bozzo-Moncada Giuliano-David-Bozzo-Moncada Giulianno-Bozzo-Moncada Giuliano Bozzo Moncada Giulianno Bozzo Moncada Giuliano David Bozzo Moncada Giulianno Bozzo Moncada Giuliano-Bozzo-Moncada Giulianno-Bozzo-Moncada Giuliano-David-Bozzo-Moncada Giulianno-Bozzo-Moncada