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

182 Capítulo 2. La máquina sincrónica
Ejercicio 2.20. Si:
Y:
⎡
[ ]
R x + L ∗ q s L ⎤
dΩ L 1xmax Ω
Z11 = ⎣ −L ∗ qΩ R x + L d s L 1xmax s ⎦ ,
0 L 1xmax s R 1 + L 1 s
⎡ ⎤
[ ]
L xDmax Ω
Z12 = ⎣L xDmax s⎦ ,
L 1D s
[ ] [ ]
−1 1
Z22 =
R D +L D s
,
[ ]
Z21 = [ 0 L xDmax s L 1D s ] .
[
Z
′ ] = [ Z 11
]
−
[
Z12
][
Z22
] −1 [
Z21
]
.
Comprobar que:
donde:
⎡
[
Z
′ ] R x + L ∗ qs L ∗ d Ω ⎤
L∗ 1x max
Ω
= ⎣ −L ∗ q Ω R x + L ∗ d s L∗ 1x max
s ⎦ ,
0 L ∗ 1x max
s R 1 + L ∗ 1 s
L ∗ 1x max
L ∗ d = L d − L2 xD max
s
R D + L D s ,
= L 1xmax − L xD max
L 1D s
R D + L D s ,
L ∗ 1 = L 1 − L2 1D s
R D + L D s .
Ejercicio 2.21. Para los valores de L ∗ d , L∗ 1x max
y L ∗ 1 dados en el numeral anterior, comprobar
que:
L ∗ d s = (L d − L xDmax )s + L xD max
[R D + (L D − L xDmax )s]
L xDmax + [R D + (L D − L xDmax )s] ,
L ∗ 1x max
s = (L 1xmax − L 1xDmax L 1D )s + L xD max
L 1D s [R D + (L D − L xDmax L 1D )s]
L xDmax L 1D s + [R D + (L D − L xDmax L 1D )s] ,
L ∗ 1s = (L 1 − L 1D )s + L 1Ds [R D + (L xDmax − L 1D )s]
L 1D + [R D + (L xDmax − L 1D )s] .
Ejercicio 2.22.
R x + L ∗∗
d s = R x +
(
)
L ∗ d − L∗2 1x max
s
R 1 + L ∗ 1 s s.
⎡
(
L
R x + L ∗∗
d s = R x + ⎢
⎣ L d −
L2 xD max
s 1xmax − L )
xD max
L 1D s 2
⎤
s
R D + L D s − R D + L D s
(
R 1 + L 1 −
L2 1D s ) ⎥
⎦ s.
s
R D + L D s