GATE EE 2023 Set 1 — Question 47
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Electrical Machines → Synchronous Machines → Synchronizing Power & Power Angle
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Question
A three-phase synchronous motor with synchronous impedance of per unit per phase has a static stability limit of per unit. The corresponding excitation voltage in per unit is ___________ (Round off to 2 decimal places).
Correct answer
1.58 to 1.59
Solution
Given:
Synchronous impedance pu
Resistance pu
Reactance pu
Magnitude of synchronous impedance pu
Static stability limit pu
Terminal voltage pu (assumed for per-unit calculations)The maximum power (static stability limit) for a synchronous motor is given by the power-angle equation at the limit:Substituting the given values into the equation:Rearranging into a standard quadratic equation form :Solving for using the quadratic formula :Rounding off to 2 decimal places, the excitation voltage is pu.
Synchronous impedance pu
Resistance pu
Reactance pu
Magnitude of synchronous impedance pu
Static stability limit pu
Terminal voltage pu (assumed for per-unit calculations)The maximum power (static stability limit) for a synchronous motor is given by the power-angle equation at the limit:Substituting the given values into the equation:Rearranging into a standard quadratic equation form :Solving for using the quadratic formula :Rounding off to 2 decimal places, the excitation voltage is pu.
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