GATE EE 2019 Set 1 — Question 58
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Electrical Machines → Synchronous Machines → Synchronous Reactance & Regulation
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Question
A 220 V (line), three-phase, Y-connected, synchronous motor has a synchronous impedance of . The motor draws the rated current of 10 A at 0.8 pf leading. The rms value of line-to-line internal voltage in volts (round off to two decimal places) is _____.
Correct answer
240 to 250
Solution
Given:
Y-connected synchronous motor
Line voltage
Synchronous impedance per phase
Rated current
Power factor leading
(Current leads voltage)
So, First, calculate :
Now, calculate :
Rounding off to two decimal places, the rms value of line-to-line internal voltage is .
This value falls within the given range of to .
Y-connected synchronous motor
Line voltage
Synchronous impedance per phase
Rated current
Power factor leading
1.Calculate phase voltage:
For a Y-connected system, 2.Represent phase voltage as a phasor:
Let be the reference phasor.3.Represent line current as a phasor:
Since the power factor is leading, the current leads the voltage.(Current leads voltage)
4.Represent synchronous impedance as a phasor:
5.Calculate internal generated voltage (back EMF) per phase :
The phasor equation for a synchronous motor is:So, First, calculate :
Now, calculate :
6.Calculate the magnitude of the internal generated voltage per phase:
7.Calculate the line-to-line internal voltage:
For a Y-connected system, Rounding off to two decimal places, the rms value of line-to-line internal voltage is .
This value falls within the given range of to .
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