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A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is 30Ω per phase. The load angle is 30o. The power delivered to the motor in kW is _______
Correct answer is between '835,842'. Can you explain this answer?
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A three-phase, 50Hz, star-connected cylindrical-rotor synchronous mach...
P = 838.31 kW
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A three-phase, 50Hz, star-connected cylindrical-rotor synchronous mach...
Ω per phase and the rotor resistance is 0.2 Ω per phase. The stator current is 500 A and the power output of the motor is 5 MW.
To find:
a) The voltage across each phase of the stator.
b) The power factor angle of the motor.
c) The torque developed by the motor.
Solution:
a) The voltage across each phase of the stator can be found using the formula:
Vs = Vgrid / √3
where Vgrid = 6.6 kV is the voltage of the grid.
Vs = 6.6 kV / √3 = 3.81 kV
Therefore, the voltage across each phase of the stator is 3.81 kV.
b) The power factor angle of the motor can be found using the formula:
cos(θ) = Pout / (√3 x Vs x Is)
where Pout = 5 MW is the power output of the motor and Is = 500 A is the stator current.
cos(θ) = 5 x 10^6 / (√3 x 3.81 x 10^3 x 500) = 0.925
θ = cos^-1(0.925) = 22.3 degrees
Therefore, the power factor angle of the motor is 22.3 degrees.
c) The torque developed by the motor can be found using the formula:
T = Pout / (2 x π x f)
where f = 50 Hz is the frequency of the supply.
T = 5 x 10^6 / (2 x π x 50) = 15,915 Nm
Therefore, the torque developed by the motor is 15,915 Nm.
To find:
a) The voltage across each phase of the stator.
b) The power factor angle of the motor.
c) The torque developed by the motor.
Solution:
a) The voltage across each phase of the stator can be found using the formula:
Vs = Vgrid / √3
where Vgrid = 6.6 kV is the voltage of the grid.
Vs = 6.6 kV / √3 = 3.81 kV
Therefore, the voltage across each phase of the stator is 3.81 kV.
b) The power factor angle of the motor can be found using the formula:
cos(θ) = Pout / (√3 x Vs x Is)
where Pout = 5 MW is the power output of the motor and Is = 500 A is the stator current.
cos(θ) = 5 x 10^6 / (√3 x 3.81 x 10^3 x 500) = 0.925
θ = cos^-1(0.925) = 22.3 degrees
Therefore, the power factor angle of the motor is 22.3 degrees.
c) The torque developed by the motor can be found using the formula:
T = Pout / (2 x π x f)
where f = 50 Hz is the frequency of the supply.
T = 5 x 10^6 / (2 x π x 50) = 15,915 Nm
Therefore, the torque developed by the motor is 15,915 Nm.
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A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is 30Ωper phase. The load angle is 30o. The power delivered to the motor in kW is _______Correct answer is between '835,842'. Can you explain this answer?
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A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is 30Ωper phase. The load angle is 30o. The power delivered to the motor in kW is _______Correct answer is between '835,842'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is 30Ωper phase. The load angle is 30o. The power delivered to the motor in kW is _______Correct answer is between '835,842'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is 30Ωper phase. The load angle is 30o. The power delivered to the motor in kW is _______Correct answer is between '835,842'. Can you explain this answer?.
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