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ProblemsAndSolutions_Ch-5

# ProblemsAndSolutions_Ch-5 - 5-22 If a 60-Hz synchronous...

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95 5-22. If a 60-Hz synchronous motor is to be operated at 50 Hz, will its synchronous reactance be the same as at 60 Hz, or will it change? (Hint: Think about the derivation of X S .) S OLUTION The synchronous reactance represents the effects of the armature reaction voltage stat E and the armature self-inductance. The armature reaction voltage is caused by the armature magnetic field S B , and the amount of voltage is directly proportional to the speed with which the magnetic field sweeps over the stator surface. The higher the frequency, the faster S B sweeps over the stator, and the higher the armature reaction voltage stat E is. Therefore, the armature reaction voltage is directly proportional to frequency. Similarly, the reactance of the armature self-inductance is directly proportional to frequency, so the total synchronous reactance X S is directly proportional to frequency. If the frequency is changed from 60 Hz to 50 Hz, the synchronous reactance will be decreased by a factor of 5/6. 5-23. A 480-V 100-kW 0.85-PF leading 50-Hz six-pole Y-connected synchronous motor has a synchronous reactance of 1.5 and a negligible armature resistance. The rotational losses are also to be ignored. This motor is to be operated over a continuous range of speeds from 300 to 1000 r/min, where the speed changes are to be accomplished by controlling the system frequency with a solid-state drive. (a) Over what range must the input frequency be varied to provide this speed control range? (b) How large is E A at the motor’s rated conditions?

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