A 3-phase induction motor, 440-V, 50-Hz, 6-pole, delta-connected has the following equivalent-circuit parameters at normal frequency:R1.2 ohm, R'2=0.18 ohm, X1= x'2=0.58 ohm, all per phase values.The machine is subjected in service to an occasional fall of 40% in both voltage and frequency. What total mechanical load torque is it safe to drive so that the machine just does not stall under these conditions?When operating at normal voltage and frequency, calculate the speed when delivering this torque and the power developed. Calculate also the speed at which maximum torque occurs.If V and f were both halved, what would be the increase in starting torque from the normal direct-on-line start at rated voltage and frequency?If now the machine is run up to speed from a variable-voltage, variable-frequency supply, calculate the required terminal voltage and frequency to give the 'safe' torque calculated above: (i) at starting, (ii) at 500 rev/min.Repeat (d) for the machine to develop a torque equal to the maximum value occurring at rated voltage and frequency. In both (d) and (e), the criteria is that the air-gap flux per pole is maintained constant for any particular torque.

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Answered: A 3-phase induction motor, 440-V,…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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A 3-phase induction motor, 440-V, 50-Hz, 6-pole, delta-connected has the following equivalent-circuit parameters at normal frequency:R1.2 ohm, R'2=0.18 ohm, X1= x'2=0.58 ohm, all per phase values.

The machine is subjected in service to an occasional fall of 40% in both voltage and frequency. What total mechanical load torque is it safe to drive so that the machine just does not stall under these conditions?
When operating at normal voltage and frequency, calculate the speed when delivering this torque and the power developed. Calculate also the speed at which maximum torque occurs.
If V and f were both halved, what would be the increase in starting torque from the normal direct-on-line start at rated voltage and frequency?
If now the machine is run up to speed from a variable-voltage, variable-frequency supply, calculate the required terminal voltage and frequency to give the 'safe' torque calculated above: (i) at starting, (ii) at 500 rev/min.
Repeat (d) for the machine to develop a torque equal to the maximum value occurring at rated voltage and frequency. In both (d) and (e), the criteria is that the air-gap flux per pole is maintained constant for any particular torque.

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