 #1
 103
 6
 Homework Statement:
 Find currents Is (stator current), Ir (rotor current) and Im (magnetic current)
 Relevant Equations:

Kirchoff's Law
Ohm's Law
Hi,
Please find attached below the Induction Generator circuit.
I have the following parameters:
I am requested to find the currents.
Kirchoff's Law I_{m} = I_{s} + I_{r}
$$Is = \frac{Vsl} { Zoverall} $$
$$Zoverall = Zs+Zparallel$$
$$Zs = Rs+iXs = 0.2+1.8849 Ω $$
$$Zm = iXm = (0+37.6991i) Ω $$
$$Zr = \frac {Rr} {s} + iXr = (10 +1.8849i)Ω $$
$$Zparallel = \frac {Zm*Zr} {Zm+Zr} = \frac { (0+37.6991i)*(10 +1.8849i)} {(0+37.6991i)+(10 +1.8849i)} $$
$$Zparallel = (8.5261+3.9490i) Ω $$
Hence $$Zoverall = Zs+Zparallel = (0.2+1.8849 Ω) + (8.5261+3.9490i) Ω $$
$$Zoverall =(8.3261+5.8339i)$$
$$Is = \frac{220V} {8.3261+5.8339i } $$
$$Is = (17.7222 12.4175i) A = 21.6395 A$$
Now we have to find currents Ir and Im
$$Vs = Is*Zs = 21.6395 A *1.8954 Ω = 41.0172 V$$
$$Vm=220VVs = 220V41.0172V = 178.9828 V$$
$$Im = \frac {Vm} {Zm} = \frac {178.9828 V} {(0+37.6991i) Ω}$$
$$Im = (04.7476i)A = 4.7466 A $$
$$Ir = Im  Is = (04.7476i)A  (17.7222 12.4175i) A$$
$$Ir = (17.72227.6699i)A$$
$$Ir = 19.3107 A$$
Do these calculations for Im and Ir make any sense? Current through the stator (Is) seems to be all right, but I'm not sure if what I did to calculate Im and Ir makes any sense.
Can we say m and r branches are in parallel?
I would be more than grateful if someone can check the calculation for Im and Ir.
Many thanks!
Please find attached below the Induction Generator circuit.
I have the following parameters:
Parameter  Value 
R_{s} = R_{r} (Resistance on stator and rotor)  0.2 Ω 
L_{s} = L_{r} (inductance on stator and rotor)  5 mH = 0.005 H 
p (number of pairs of poles)  2 
f (frequency)  60 Hz 
Vsl (stator line voltage)  delta connection  220 V 
s (slip of the generator)  0.02 
I am requested to find the currents.
Kirchoff's Law I_{m} = I_{s} + I_{r}
$$Is = \frac{Vsl} { Zoverall} $$
$$Zoverall = Zs+Zparallel$$
$$Zs = Rs+iXs = 0.2+1.8849 Ω $$
$$Zm = iXm = (0+37.6991i) Ω $$
$$Zr = \frac {Rr} {s} + iXr = (10 +1.8849i)Ω $$
$$Zparallel = \frac {Zm*Zr} {Zm+Zr} = \frac { (0+37.6991i)*(10 +1.8849i)} {(0+37.6991i)+(10 +1.8849i)} $$
$$Zparallel = (8.5261+3.9490i) Ω $$
Hence $$Zoverall = Zs+Zparallel = (0.2+1.8849 Ω) + (8.5261+3.9490i) Ω $$
$$Zoverall =(8.3261+5.8339i)$$
$$Is = \frac{220V} {8.3261+5.8339i } $$
$$Is = (17.7222 12.4175i) A = 21.6395 A$$
Now we have to find currents Ir and Im
$$Vs = Is*Zs = 21.6395 A *1.8954 Ω = 41.0172 V$$
$$Vm=220VVs = 220V41.0172V = 178.9828 V$$
$$Im = \frac {Vm} {Zm} = \frac {178.9828 V} {(0+37.6991i) Ω}$$
$$Im = (04.7476i)A = 4.7466 A $$
$$Ir = Im  Is = (04.7476i)A  (17.7222 12.4175i) A$$
$$Ir = (17.72227.6699i)A$$
$$Ir = 19.3107 A$$
Do these calculations for Im and Ir make any sense? Current through the stator (Is) seems to be all right, but I'm not sure if what I did to calculate Im and Ir makes any sense.
Can we say m and r branches are in parallel?
I would be more than grateful if someone can check the calculation for Im and Ir.
Many thanks!
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