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3.6. La máquina de inducción monofásica 211
⎡
⎢
⎣
⎡
⎤
R 1 + jωL 1 R 1 + jωL 1 jωL ′ 1x max
jωL ′ ⎤
1x max ⎡
⎥
⎦ = 1 R 1 + jωL 1 R 1 + jωL 1 jωL ′ 1x max
jωL ′ ( 1x max
R
2
jωL ′ 1x max
jωL ′ ′
)
1x max
2 x
br /(2 − s) ⎢
s + jL′ x0 0
⎢
⎣
( ) ⎥
⎣
R
jωL ′ 1x max
jωL ′ ′
1x max
0 2 x
2 − s + ⎦
jL′ x0
V fs
′
V bs
′
V fr ′ /s
V ′
Sumando las primeras dos ecuaciones de 3.53:
V ′
fs + V ′
bs = (R 1 + jωL 1 )(I ′ fs + I′ bs ) + jωL′ 1x max
I ′ fr + jωL′ 1x max
I ′ br .
I fs
′
I bs
′
I ′ fr
I ′ br
⎤
⎥
⎦ .
(3.53)
Como:
I 1 = (I′ fs + I′ bs )
√
2
,
y,
V 1 = (V fs ′ + V bs ′
√ )
.
2
⎡
⎣
V 1
V fr ′ /s
V ′
V 1 = (R 1 + jωL 1 )I 1 + jωL ′ 1x max
I ′ fr + jωL′ 1x max
I ′ br . (3.54)
⎤ ⎡
R 1 + jωL 1 jωL ′ 1x max
jωL ′ 1x max
⎦ ⎢1
= ⎣
br /(2 − s) 2 jωL′ R ′ x
1x max s
+ jωL ′ x0 0
1
2 jωL′ 1x max
0
R ′ x
2−s + jωL′ x0
El siguiente circuito (figura 3.21), satisface las ecuaciones anteriores:
⎤ ⎡
⎥
⎦ ⎣
I 1
I ′ fr
I ′ br
⎤
⎦. (3.55)
R 1 L 1 − L ′ 1x max
L ′ x0 − L ′ 1x max
R ′ x
s
+ +
I fr
′
L ′ 1x max
I
V 12 1
L ′ 1x max
V ′
I ′ br
fr
s
−
+
V ′
br
2−s
−
−
R 1 L 1 − L ′ 1x max
L ′ x0 − L ′ 1x max
R ′ x
2−s
Figura 3.21: Circuito equivalente para la máquina monofásica.