Práctica 1 Construccion de Zbus

PRÁCTICA NO. 1: CONSTRUCCIÓN DE Z BUS

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PRÁCTICA NO. 1 CONSTRUCCI ÓN DE Z BUS

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PROCEDI7IENTO PARTICIPACIÓN CO7PRENSIÓN CONCLUSIONES CALIFICACIÓN DE LA PRÁCTICA

O BJ ET IV O

Introducir lo !rinci!io d" t"or#$ d" r"d" !$r$ l$ o%t"nci&n d" l$ '$tric" d" Z%u.

TEORÍA FUNDAMENTAL L$ '$tri( Z%u " un$ )"rr$'i"nt$ i'!ort$nt" "n "l $n*lii d" it"'$ d" !ot"nci$. Aun+u" co',n'"nt" no " utili($d$ !$r$ "tudio d" -uo d" !ot"nci$/ l$ '$tri( Z%u " un$ )"rr$'i"nt$ 'u0 i'!ort$nt" !$r$ $n*lii d" corto circuito 0 "tudio d" $ll$. Por "t$ r$(&n " 2u"l2" d" int"r3 !$r$ "l $lu'no conoc"r l$ or'$ "n +u" " contru0" l$ '$tri( Z%u. Uno d" lo "no+u" !$r$ contruir l$ '$tri( d" Z%u " !or !or '" '"di dio o d" 4r$ 4r$o o.. El 4r$ 4r$o o d" un$ un$ r"d "l3c "l3ctr tric ic$ $ d"cri%" l$ "tructur$ "l3ctric$ d" l$ r"d. El 4r$o conit" "n r"di%u$r l$ r"d/ dond" lo %u" on r"!r""nt$do !or nodo o 23rtic" 0 l$ i'!"d$nci$ o "l"'"nto !or l#n"$ . L$ '$tri( d" i'!"d$nci$ Z%u !u"d" "r contruid$

PRÁCTICA NO. 1: CONSTRUCCIÓN DE Z BUS

co'"n($ndo con un olo "l"'"nto 0 "l !roc"o " continu$ )$t$ +u" todo lo nodo 0 "l"'"nto "$n incluido. S" cu"nt$ con un nodo 8/ "l cu$l conid"r$ l$ con"9ion" $ ti"rr$.

L$ or'$ d" ir contru0"ndo Z%u con lo di"r"nt" ti!o d" nodo " "9!lic$ $ continu$ci&n:

Agregar un ee!en"# nue$# a n#%# %e re&eren'(a S" co'i"n($ $ contruir Z%u $4r"4$ndo un nodo ! $l nodo d" r""r"nci$. Eto i'!l"'"nt" " r"$li($ indic$ndo un$ '$tri( d" 191 con "l 2$lor d" l$ i'!"d$nci$ Z !8. Z bus =[ Z  p 0 ]

A4r"4$ un nodo nu"2o + 0 $l %u d" r""r"nci$ $ l$ Z%u 2i"$ d" ord"n '9';/ r"ult$r* "n un$ nu"2$ '$tri( Z%u d" ord"n '<1;9'<1;. Et$ '$tri( " di$4on$l con lo 2$lor" d" i'!"d$nci$ "n l$ di$4on$l. L$ nu"2$ Z%u " !u"d" 2"r d" l$ i4ui"nt" or'$:

Z bus =

[

Z 11 …

0

0

0

0

⋮

⋱

0

0

Z mm

0

0

⋯

0

Z  p 0

]

Agregar un ee!en"# en"re un )u* nue$# + un# +a 'rea%# S" continu$ con lo "l"'"nto r"t$nt" +u" con"ct$n $ un %u nu"2o + con uno 0$ cr"$do !. Eto r"ult$r* +u" t"ni"ndo un$ '$tri( 2i"$ Z%u d" '9';/ " o%t"n4$ un$ nu"2$ '$tri( Z%u d" ord"n '<1;9'<1;. Lo cu$l o%t"ndr#$'o d" l$ i4ui"nt" or'$:

Z bus =

[

 Z 11

⋯

Z 1 p

⋯

Z 1 m

Z 1 p

⋮

⋮

⋮

⋮

⋮

⋮

Z  pp

⋯

Z  pm

Z  pp

Z  p 1 ⋯ ⋮

⋮

Z m 1 ⋯ Z  p 1 ⋯

⋮

⋮

Z mp ⋯ Z  pp ⋯

⋮

⋮

Z mm Z  pm

Z mp Z  pp+ Z  pq

]

Agregar un ee!en"# en"re %#* )u*e* +a 'rea%#*

PRÁCTICA NO. 1: CONSTRUCCIÓN DE Z BUS

Cu$ndo " $4r"4$ un$ i'!"d$nci$ "ntr" do %u" 0$ cr"$do ! 0 +/ l$ '$tri( " +u"d$r* d"l 'i'o t$'$=o/ " d"cir/ d" ord"n '9';/ in "'%$r4o/ co'o !$rt" d"l !roc"di'i"nto " utili($r* un$ nu"2$ '$tri( Z%u d" ord"n '<1;9'<1;/ +u" " cr"$ d" l$ i4ui"nt" or'$:

[

Z 11

Z 1 p

Z 1 q

⋯

Z 1 m

Z 1 q −Z 1 p

⋮

⋮

⋮

⋮

⋮

⋮

Z  p 1

Z  pp

Z  pq

⋯

Z  pm

Z  pq− Z  pp

Z q 1

Z qp

Z qq

⋯

Z qm

Z qq− Z qp

⋮

⋮

⋮

⋮

⋮

⋮

Z m 1 Z 1 q− Z 1 p

Z mp Z 1 q −Z 1 p

Z mq Z 1 q− Z 1 p

⋯

 z bus =

Z mm ⋯ Z 1 q −Z 1 p

Z mq− Z mp Z ¿

]

dond" Z ¿ = z pq+ Z  pp + Z qq − 2 Z  pq

L$ nu"2$ >l$ 0 colu'n$ " "li'in$d$/ !or '"dio d" l$ r"l$ci&n new bus =

Z 

T 

DZ ∗ DZ  Z   –  Z ¿ old bus

En l$ $ctu$lid$d "9it"n $l4orit'o +u" " "nc$r4$n d" contruir l$ '$tri( Z%u $ !$rtir d" d$to +u" " l" d$n d" "ntr$d$. Eto $l4orit'o 2$n i4ui"ndo lo !$o d"crito $nt"rior'"nt" !$r$ or'$r l$ '$tri( Z%u. Uno d" "to $l4orit'o " l" !ro!orcion$r* 0 d"cri%ir* $l $lu'no/ !$r$ +u" co'!r"nd$ l$ or'$ "n +u" "l $l4orit'o contru0" Z%u.

ACTIVIDAD 1 An$li($r "l $l4orit'o d" contrucci&n d" Z%u !ro!orcion$do.

O%t"n"r lo d$to d"l it"'$ lin"d$t$;: Bu 8 8 1 1 5 6 6 5

Bu R"it"n ci$ 1 8 5 8 5 8 6 8 6 8 1 8 5 8 1 8

R"$ct$nc i$ 8.6 8.5 8.? 8.@ 8.6? 8.@ 8.6? 8.?

A !$rtir d" lo d$to d" l$ t$%l$/ o%t"n"r l$ '$tri( Z%u !$r$ "l it"'$/ u$ndo "l $l4orit'o !ro!orcion$do Z%uildlin"d$t$;: Z%u 8.8888 < 8.1i 8.8888 < 8.81i 8.8888 < 8.18@i

8.8888 < 8.81i 8.8888 < 8.116i 8.8888 < 8.151i

8.8888 < 8.18@i 8.8888 < 8.151i 8.8888 < 8.5?8i

ACTIVIDAD , O%t"n"r lo "l"'"nto d" di$4on$l" d" l$ '$tri( Z%u/ !$r$ "l it"'$ d" ? %u" u$ndo "l $l4orit'o !ro!orcion$do Z%uild!ilin"d$t$/4"nd$t$;. Lo d$to d"l it"'$ " !r""nt$n "n l$ t$%l$ i4ui"nt":

 Escriba a uí la ecuación.

Gendata: Bus 1 2 3 6 8 9 12

R 0 0 0 0 0 0 0

X 0.20 0.15 0.25 0.25 0.20 0.20 0.15

Elementos de la diagonal de Zbus: 1 2 3 4 5 6 ! 8 9 10 11 12 13

0.0045  0.0501i 0.0051  0.0512i 0.00!!  0.0529i 0.0139  0.0666i 0.0341  0.0!63i 0.010!  0.0666i 0.0134  0.0845i 0.0053  0.058!i 0.0048  0.0530i 0.0183  0.1029i 0.0153  0.0823i 0.0051  0.0534i 0.00!!  0.0558i

14 15 16 1! 18 19 20 21 22 23 24 25 26

0.0128  0.0!02i 0.00!9  0.0555i 0.0158  0.1002i 0.01!3  0.1064i 0.0465  0.5033i 0.2225  0.!0!!i 0.14!!  0.6!!2i 0.1066  0.2408i 0.0450  0.1380i 0.0526  0.1488i 0.11!3  0.2508i 0.1365  0.6940i 0.11!8  0.25!9i

2! 28 29 30 31 32 33 34 35 36 3! 38 39 53 54 55

0.0901  0.2128i 0.0518  0.160!i 0.01!!  0.1193i 0.2211  0.!890i 0.3280  0.930!i 0.2212  0.8960i 0.2604  0.9320i 0.1!64  0.3452i 0.1352  0.2!!4i 0.0981  0.228!i 0.0!81  0.1991i 0.0305  0.11!6i 0.0980  0.2329i 0.1188  0.2680i 0.0306  0.3243i 0.1360  0.486!i

40 41 42 43 44 45 46 4! 48 49 50 51 52 56 5!

0.0163  0.20!9i 0.03!8  0.13!5i 0.0160  0.1266i 0.0182  0.1219i 0.0363  0.1445i 0.0418  0.1458i 0.0232  0.1100i 0.0635  0.1!04i 0.0252  0.1490i 0.1181  0.2332i 0.1440  0.2651i 0.1286  0.2639i 0.0131  0.1586i 0.1134  0.4313i 0.1!4!  0.5!25i

ACTIVIDAD Ecri%$ u concluion" 4"n"r$l" 0 !$rticul$r" d" "t$ !r*ctic$. Co'o " $%" )$0 ditint$ or'$ d" c$lcul$r Z%u/ un$ d" "ll$ " "ncontr$ndo G%u 0 $c$rl" u in2"r$/ !"ro in dud$ $l4un$ " un !roc"di'i"nto un !oco '* l$r4o 0 '* cu$ndo )$%l$'o d" un 4r$n n,'"ro d" %u". Ad"'* " i'!ort$nt" '"ncion$r +u" Z%u " c$!$( d" %rind$rno 'uc)$ inor'$ci&n/ !or ""'!lo l$ di$4on$l d" l$ '$tri( no 'u"tr$ "l "+ui2$l"nt" d" t)"2"nin 2ito d"d" c$d$ %u/ t$'%i3n ll$'$d$ i'!"d$nci$ d" !unto d" o!"r$ci&n d" lo %u"/ 0 $ l$ i'!"d$nci$ u"r$ d" l$ di$4on$l " l" conoc" co'o i'!"d$nci$ d" tr$n"r"nci$ "ntr" %u". Con l$ $0ud$ d" 7$tl$% " !u"d" "ncontr$r Z%u d" un$ '$n"r$ '* r*!id$/ i'!li>c$ndo "l l$r4o !roc"di'i"nto 0 '* i " tr$t$ d" un 4r$n n,'"ro d" %u".