GATE 2019 EE – Question 57
A delta-connected, 3.7 kW, 400 V(line), three-phase, 4-pole, 50-Hz squirrel-cage induction motor has the following equivalent circuit parameters per phase referred to the stator: $R_1=5.39\ \Omega$, $R_2=5.72\ \Omega$, $X_1=X_2=8.22\ \Omega$. Neglect shunt branch in the equivalent circuit. The starting line current in amperes (round off to two decimal places) when it is connected to a 100 V (line), 10 Hz, three-phase AC source is ________.
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Correct answer: 14.43 to 14.57
Explanation
At 10 Hz the reactances scale by $\frac{10}{50}=0.2$: $X_1+X_2=16.44\times0.2=3.29\ \Omega$. At start the slip is 1, so $Z=(5.39+5.72)+j3.29=11.11+j3.29$, $|Z|=11.59\ \Omega$ per phase. The phase voltage of the delta connection is 100 V, so the phase current is $\frac{100}{11.59}=8.63$ A and the line current is $\sqrt3\times8.63=14.9$ A.