maquinas de corriente alterna.pdf - Universidad Tecnológica de ...

1.10. Componentes simétricas en la máquina de corriente alterna 77
⎡ ⎤ ⎡
⎤ ⎡ ⎤
v α s 3 + 2ρ −ρ −ρ i α s
⎣v β s⎦ = ⎣ −ρ 3 + 2ρ −ρ ⎦ ⎣i β s⎦
v γ s −ρ −ρ 3 + 2ρ i γ s
En fasores, para régimen permanente:
⎡ ⎤ ⎡
⎤
V α s 3 + 4j −2j −2j
⎣V β s⎦ = ⎣ −2j 3 + 4j −2j ⎦
V γ s −2j −2j 3 + 4j
⎡
⎣
I α s
⎤
I β s⎦
I γ s
i α s = √ 2 5sen 2t I α s = 5∠0 ◦ = 5,
i β s = √ 2 5sen(2t − 120 ◦ ) I β s = 5∠ − 120 ◦ = −2,5 − 4,3j,
i γ s = √ 2 5sen(2t + 120 ◦ ) I β s = 5∠120 ◦ = −2,5 + 4,3j,
V α s = (3 + 4j)5 − 2j(−2,5 − 4,3j) − 2j(−2,5 + 4,3j).
V α s = 22,54∠63,43 ◦ ,
V β s = 33,54∠ − 56,56 ◦ ,
V γ s = 33,54∠ − 183,43 ◦ .
v α s
v β s
v γ s
= √ 2 33,54sen(2t + 63,43 ◦ ) ◭
= √ 2 33,54sen(2t − 56,56 ◦ ) ◭
= √ 2 33,54sen(2t + 183,43 ◦ ) ◭
b)
P α s
P β s
P γ s
= (33,54)(5)cos 63,43 ◦ = 75,01 W ◭
= (33,54)(5)cos 63,43 ◦ = 75,01 W ◭
= (33,54)(5)cos(183, 43 ◦ − 120 ◦ ) = 75,01 W ◭
c) Con
P 1,2 = P α,β,γ .
√ [ ]
2 1 −1/2 −1/2
=
3 0 √ 3/2 − √ [i
3/2 α,β,γ ],
√ [ ] ⎡ ⎤
5
2 1 −1/2 −1/2
=
3 0 √ 3/2 − √ ⎣−2,5 − 4,3j⎦ ,
3/2
−2,5 + 4,3j
√ [ ] [ ]
2 7,5 6,12
= = .
3 7,439j −6,12