¡Descarga Análisis de circuitos cortos trifásicos con y sin intervención de tierra y más Apuntes en PDF de Ingenieria Eléctrica solo en Docsity!
Corto trifásico con o sin intervención de tierra
a) Con tierra: Condiciones: Va = 0 Vb = 0 Vc = 0
[
V (^) a V (^) a
V a2]^
= 1
3 [
1 1 1 1 a a^2
1 a^2 a ] [
V (^) a V (^) b
V c ]^
= 1
3 [
1 1 1 1 a a^2
1 a^2 a ] [
0 0
0 ]^
=
[
0 0
0 ]
[
V (^) a V (^) a
V a2]^
=
[
0 E
0 ]^
−
[
z 0 0 0 0 z 1 0
0 0 z 2 ] [^
I (^) a I (^) a
I a2 ]^
→
[
0 0
0 ]^
=
[
0 E
0 ]
−
[
z 0 0 0 0 z 1 0
0 0 z 2 ] [
I (^) a I (^) a
I a2]^
→
[
I (^) a I (^) a
I a2]^
=
[
0 E z 1 0
]
[
I (^) a I (^) b
I c ]^
=
[
1 1 1 1 a^2 a
1 a a^2 ] [
I (^) a I (^) a
I a2]^
=
[
1 1 1 1 a^2 a
1 a a^2 ] [^
0 E z 1 0
]
=
[
E z 1 a^2 E z 1 a E z 1
]
=
E
z 1 [
1 (^1) ∣ 240
1 ∣ 120 ]
I (^) D = I (^) a + I (^) b + I (^) c = 0
a) Sin tierra: Condiciones: I (^) a + I (^) b + Ic = 0 Va = Vb = V (^) c
De I (^) a +I (^) b +Ic =0 sacamos que Ia0 = 0 y dado que Va0 = - z 0 Ia0 obtenemos que Va0 = 0
[
V (^) a V (^) a
V a2]^
= 1
3 [
1 1 1 1 a a^2
1 a^2 a ] [
V (^) a V (^) b
V c ]^
= 1
3 [
1 1 1 1 a a^2
1 a^2 a ] [
V (^) a V (^) a
V a ]^
=
[
V (^) a 0
0 ]^
=
[
0 0
0 ]^
como el caso con tierra
I (^) D
a b c a b c
Corto monofásico
Condiciones:
Va = 0 → V (^) a0 + V (^) a1 + V (^) a2 = 0 I (^) b = 0 I (^) c = 0
[
I (^) a I (^) a
I a2]^
= 1
3 [
1 1 1 1 a a^2
1 a^2 a ] [
I (^) a 0
0 ]^
=
I (^) a
3 [
1 1
1 ]^
→ I (^) a0 = I (^) a1 = I (^) a2 =
I (^) a 3
V (^) a0+V (^) a1+V (^) a2 = 0 → − I (^) a0 z 0 + E− I (^) a1 z 1 − I (^) a2 z 2 = 0 → −
I (^) a 3
z 0 + E−
I (^) a 3
z 1 −
I (^) a 3
z 2 = 0
→
I (^) a 3
= E z 0 + z 1 + z 2
= I (^) a0 = I (^) a1 = I (^) a
[
I (^) a I (^) b
I c ]^
=
[
1 1 1 1 a^2 a
1 a a^2 ] [
I (^) a I (^) a
I a2]^
=
E
z 0 + z 1 + z 2 [
1 1 1 1 a^2 a
1 a a^2 ] [
1 1
1 ]^
=
3 E
z 0 + z 1 + z 2 [
1 0
0 ]
[
V (^) a V (^) a
V a2]^
=
[
0 E
0 ]^
−
[
z 0 0 0 0 z 1 0
0 0 z 2 ] [^
I (^) a I (^) a
I a2]^
=
[
0 E
0 ]^
− E
z 0 + z 1 + z 2 [
z 0 0 0 0 z 1 0
0 0 z 2 ] [
1 1
1 ]^
= E
z 0 + z 1 + z 2 [
−z 0 z 0 + z 2
−z 2 ]
[
V (^) a V (^) b
V c^ ]^
=
[
1 1 1 1 a^2 a
1 a a^2 ] [
V (^) a V (^) a
V a2^ ]^
= E
z 0 + z 1 + z 2 [
1 1 1 1 a^2 a
1 a a^2 ] [^
− z 0 z 0 + z 2
− z 2 ]^
= E z 0 + z 1 + z (^2) [
0 (a^2 − 1 ) z 0 +(a^2 −a) z (^2) (a− 1 ) z 0 +(a−a^2 ) z 2 ]
[
V (^) a V (^) b
V c ]^
= √^3 E
z 0 + z 1 + z (^2) [
0 z 0 ∣ 210 + z 2 ∣ 270 z 0 ∣ 150 + z 2 ∣ 90 ]
I (^) D = 3 E z 0 + z 1 + z 2
I (^) a=I (^) D
I (^) b
I (^) c
Corto bifásico a tierra
Condiciones:
I (^) a = 0 → I (^) a0 + Ia1 + I (^) a2 = 0 V (^) b= V (^) c.= 0
[
V (^) a V (^) a
V a2]^
= 1
3 [
1 1 1 1 a a^2
1 a^2 a ] [
V (^) a 0
0 ]^
=
V (^) a
3 [
1 1
1 ]^
→ V (^) a0 = V (^) a1 = V (^) a2 =
V (^) a 3
I (^) a0+ I (^) a1+ I (^) a2 = 0 → −
V (^) a z 0
E− V (^) a z 1
−
V (^) a z 2
= 0 → −
V (^) a z 0
E− V (^) a z 1
−
V (^) a z 2
= 0
→ E z 1
= V (^) a0 (^) [ 1 z 0
→ V (^) a0 =
E z 1 1 z 0
→
[
V (^) a V (^) a
V a2^ ]^
=
E z 1 1 z 0
[
1 1
1 ]
[
V (^) a V (^) b
V c^ ]^
=
[
1 1 1 1 a^2 a
1 a a^2 ] [
V (^) a V (^) a
V a2^ ]^
=
E z 1 1 z 0
[
1 1 1 1 a^2 a
1 a a^2 ] [
1 1
1 ]^
=
3 E z 0 z 2
z 0 z 1 + z 0 z 2 + z 1 z 2 [
1 0
0 ]
[
I (^) a I (^) a
I a2]^
=
[
I (^) a − I (^) a0− I (^) a
I a2 ]^
= V (^) a
[
− 1 z 0 1 z 0
]
=
E z 1 1 z 0
− 1 z 0 1 z 0
]
= E
z 0 z 1 + z 0 z 2 + z 1 z 2 [
− z 2 z 0 + z 2
− z 0 ]
[
I (^) a I (^) b
I c^ ]^
= E
z 0 z 1 + z 0 z 2 + z 1 z 2 [
1 1 1 1 a^2 a
1 a a^2 ] [^
−z 2 z 0 + z 2
−z 0 ]^
= E z 0 z 1 + z 0 z 2 + z 1 z (^2) [
0 (a^2 − 1 ) z 2 +(a^2 −a) z 0 ( a− 1 ) z 2 +(a−a^2 ) z 0 ]
[
I (^) a I (^) b
I c ]^
= √^3 E
z 0 z 1 + z 0 z 2 + z 1 z (^2) [
0 z 0 ∣ 270 + z (^2) ∣ 210 z 0 ∣ 90 + z (^2) ∣ 150 ]^
I (^) D = I (^) b+ I (^) c =
3 E z (^2) z 0 z 1 + z 0 z 2 + z 1 z 2
I (^) D
I (^) b
I (^) a
I (^) c
