Question 4.8: A three-phase, four-pole, 50 Hz induction motor rotates at a...
A three-phase, four-pole, 50 Hz induction motor rotates at a full-load speed of 1470 rpm. The EMF measured between the slip-ring terminals when the rotor is not rotating is 200 V. The rotor windings are star connected and has resistance and stand-still reactance per phase of 0.1 Ω and 1.0 Ω, respectively. Calculate the rotor current on full load.
N_{r} = 1470 rpm
N_{s} = \frac{120 f}{p}= \frac{120 ×50 }{4}= 1500 rpm
S=\frac{N_{s}-N_{r}}{N_{s}}= \frac{1500-1470}{1500}=0.02Rotor-induced EMF between the slip rings at standstill, E_{20} = 200 V.
As the rotor windings are star connected,
E_{20} per phase =\frac{200}{\sqrt{3}}=115.4 V
When the rotor is rotating at a speed of 1470 rpm the rotor-induced EMF per phase, E_{2} is
E_{2} = S E_{20} = 0.02 × 115.4 = 2.3 V
Rotor current when the rotor is rotating at 1470 rpm,
I_{2} = \frac{ S E_{20}}{Z_{2}}=\frac{ S E_{20}}{\sqrt{R_{2}^{2}+(S X_{20})^{2}}}Substituting values
I_{2} = \frac{2.3}{\sqrt{(0.1)^{2}+(0.02×1)^{2}}}=\frac{2.3}{0.102}=22.5 A