Efecto del desbalance en las cargas sobre la

52
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Recibido 25 de septiembre de 2006, aprobado 19 de abril de 2007.
Oscar Gómez Carmona
Carlos J. Zapata
Ingeniero Electricista, M.Sc. en Ingeniería Eléctrica. Pro-
Ingeniero Electricista, M.Sc. en Ingeniería Eléctrica. Pro-
fesor auxiliar, Facultad de Ingeniería, Universidad Tec-
fesor asociado, Facultad de Ingeniería, Universidad Tec-
QROyJLFDGH3HUHLUD3HUHLUD&RORPELD
QROyJLFDGH3HUHLUD3HUHLUD&RORPELD
[email protected].
[email protected].
RESUMEN Muchos circuitos primarios de distribución tri-
se asume lo contrario se obtienen valoraciones pesimis-
fásicos son desbalanceados porque, primero, atienden
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a sus usuarios por medio de transformadores de distri-
decisiones de inversión erróneas.
bución monofásicos; segundo, utilizan componentes de
3$/$%5$6&/$9(
operación monopolar; y, tercero, la mayoría de las fallas
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que afectan sus componentes son monofásicas. Este im-
de distribución de energía eléctrica, simulación de
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Montecarlo.
bilidad pues, como se muestra en este artículo, cuando
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ABSTRACT Many three-phase distribution feeders are
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by means of single–phase distribution transformers;
assessments of the reliability indices are obtained which
could lead to erroneous investment decisions.
.(<:25'6
second, they use components which operate in single-
Power system reliability, power distribution systems,
phase manner; third, most of the failures that affect
Montecarlo simulation.
their components are single–phase. This important fact
must be included in reliability studies because, as shown
in this paper, when the contrary is assumed pessimistic
#25 revista de ingeniería. Universidad de los Andes. rev.ing. ISSN. 0121-4993. Mayo de 2007
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Tabla 1. Población de transformadores de distribución en la ciudad de Pereira [1].
# 25 revista de ingeniería
técnica
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CASO DE ESTUDIO 1: ¿QUÉ PASA SI LA
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Tabla 4. Probabilidad de ocurrencia de fallas en el sistema de prueba [%].
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# 25 revista de ingeniería
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Tabla 5. Probabilidad de ocurrencia de fallas sobre las fases del sistema de prueba [%].
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CONCLUSIONES Y RECOMENDACIONES
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REFERENCIAS
BIBLIOGRAFÍA
[1] C.J. Zapata, D. Cataño, H.F. Suárez.
R. Billinton, R. Allan.
´ÌQGLFHVGHFRQILDELOLGDGGHWUDQVIRUPDGRUHVGH
Reliability Evaluation of Power Systems. 3OHQXP3UHVV
GLVWULEXFLyQµRevista Mundo Eléctrico,1R
IEEE.
[2] L. J. Blackburn.
´5HFRPPHQGHG3UDFWLFHIRUWKH'HVLJQRI5HOLDEOH
Protective Relaying: Principles and Applications,0DUFHO'HNNHU
,QGXVWULDODQG&RPPHUFLDO6\VWHPVVWDQGDUGµ,(((
[3] R. Billinton, R. Allan.
*.MROOH/5ROIVHJQ('DKO
Reliability evaluation of engineering systems.3OHQXP3UHVV
´7KH(FRQRPLF$VSHFWRI5HOLDELOLW\LQ'LVWULEXWLRQ
6\VWHP3ODQQLQJµ,(((7UDQVDFWLRQVRQ3RZHU'HOLYHU\
9RO1R
[4] C.J. Zapata.
Confiabilidad de sistemas Eléctricos, 8QLYHUVLGDG7HFQROyJLFD
GH3HUHLUD
R. Billinton and P. Wang.
´7HDFKLQJ'LVWULEXWLRQ6\VWHP5HOLDELOLW\HYDOXDWLRQ
8VLQJ0RQWH&DUOR6LPXODWLRQµ,(((7UDQVDFWLRQRQ
[5] C.J. Zapata, O.Gómez.
3RZHUV\VWHPV9RO1R0D\
´5HOLDELOLW\DVVHVVPHQWRIXQEDODQFHGGLVWULEXWLRQ
V\VWHPVXVLQJVHTXHQWLDO0RQWHFDUORVLPXODWLRQµ,(((
C. J. Zapata, L.C. Piñeros, D.A. Castaño.
7UDQVPLVVLRQ'LVWULEXWLRQ/DWLQ$PHULFD&RQIHUHQFH
´(OPpWRGRGHVLPXODFLyQGH0RQWHFDUORHQHVWXGLRV
GHFRQILDELOLGDGGHVLVWHPDVGHGLVWULEXFLyQGHHQHUJtD
HOpFWULFDµRevista Scientia et Technica1R
[6] C.J. Zapata, O.Gómez.
'LVSRQLEOHHQZZZXWSHGXFRFLHQFLD
´9DORUDFLyQGHFRQILDELOLGDGGHVLVWHPDVGHGLVWULEXFLyQ
GHVEDODQFHDGRVXWLOL]DQGRVLPXODFLyQGH0RQWHFDUORµ
O. Gómez.
Revista Scientia et Technica,1R'LVSRQLEOHHQ
´$QiOLVLVGH&RQILDELOLGDGHQ6LVWHPDVGH'LVWULEXFLyQ
ZZZXWSHGXFRFLHQFLD
'HVEDODQFHDGRVµ7HVLVGH0DHVWUtD8QLYHUVLGDG
7HFQROyJLFDGH3HUHLUD
[7] IEEE.
´*XLGHIRU(OHFWULF3RZHU'LVWULEXWLRQ5HOLDELOLW\
,QGLFHVµ6WDQGDUG,(((
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