GATE EE 2015 Set 2 — Question 59
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Electrical Machines → Synchronous Machines → Synchronizing Power & Power Angle
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Question
A three-phase, , , , star connected, cylindrical rotor synchronous motor is connected to an , source. Its synchronous reactance is per phase, and its stator resistance is negligible. The motor has a constant field excitation. At a particular load torque, its stator current is at unity power factor. If the load torque is increased so that the stator current is , then the load angle (in degrees) at this load is ______.
Correct answer
-48 to -46
Solution
Step 1: Calculate the phase voltage :
Step 2: Calculate the excitation voltage at unity power factor ():
For a synchronous motor, . Given :
Magnitude Step 3: Since the field excitation is constant, remains when the load torque increases and the stator current becomes .Step 4: Use the phasor relationship to find the load angle :
Step 5: For a synchronous motor, the rotor lags the stator magnetic field, so the load angle is negative.
The value lies within the specified range of to .
Step 2: Calculate the excitation voltage at unity power factor ():
For a synchronous motor, . Given :
Magnitude Step 3: Since the field excitation is constant, remains when the load torque increases and the stator current becomes .Step 4: Use the phasor relationship to find the load angle :
Step 5: For a synchronous motor, the rotor lags the stator magnetic field, so the load angle is negative.
The value lies within the specified range of to .
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