GATE EE 2019 Set 1 — Question 57
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Electrical Machines → Three-Phase Induction Machines → Slip & Equivalent Circuit
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Question
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: , , . 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 _____.
Correct answer
13 to 16
Solution
Given:
Delta-connected induction motor
Rated power
Rated line voltage
Rated frequency
Stator parameters per phase: , ,
Shunt branch neglected.
Starting conditions: Line voltage , Frequency For starting, the slip .
The equivalent impedance per phase at starting, referred to the stator, is:
However, the reactances depend on frequency.
and .
The given are at rated frequency .
So,
And At starting frequency :
Now, calculate the total equivalent impedance per phase at starting:
Magnitude of starting impedance:
For a delta-connected motor, the phase voltage is equal to the line voltage.
Starting phase current:
Starting line current for a delta connection:
Rounding off to two decimal places, the starting line current is .
This value falls within the given range of to .
Delta-connected induction motor
Rated power
Rated line voltage
Rated frequency
Stator parameters per phase: , ,
Shunt branch neglected.
Starting conditions: Line voltage , Frequency For starting, the slip .
The equivalent impedance per phase at starting, referred to the stator, is:
However, the reactances depend on frequency.
and .
The given are at rated frequency .
So,
And At starting frequency :
Now, calculate the total equivalent impedance per phase at starting:
Magnitude of starting impedance:
For a delta-connected motor, the phase voltage is equal to the line voltage.
Starting phase current:
Starting line current for a delta connection:
Rounding off to two decimal places, the starting line current is .
This value falls within the given range of to .
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