Electrical Transformers and Rotating Machines
Electrical Transformers and Rotating Machines
4th Edition
ISBN: 9781337264419
Author: Stephen L. Herman
Publisher: Cengage Learning US
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Chapter 5, Problem 6RQ
To determine

The voltages between the points AB, AC, AD, AE, BC, BD, BE, CD, CE and DE.

Expert Solution & Answer
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Explanation of Solution

Given:

The number of turns between the windings AB (NAB) is 120.

The number of turns between the windings BC (NBC) is 180.

The number of turns between the windings CD (NCD) is 250.

The number of turns between the windings DE (NDE) is 300.

The voltage connected across windings BE (EBE) is 240volts.

The below figure represents the autotransformer windings.

Electrical Transformers and Rotating Machines, Chapter 5, Problem 6RQ

Calculation:

Calculate the voltage per unit turns (voltsperturn) using the relation.

  voltsperturn=EBENBE

  voltsperturn=240volts(180+250+300)voltsperturn=2473

Calculate the voltage between the windings AB (EAB) using the relation.

  EAB=(voltsperturn)×NAB

  EAB=2473×120EAB=39.452volts

Calculate the voltage between the windings AC, (EAC) using the relation.

  EAC=(voltsperturn)×NAC

  EAC=2473×(120+180)EAC=98.63volts

Calculate the voltage between the windings AD (EAD) using the relation.

  EAD=(voltsperturn)×NA-D

  EAD=2473×(120+180+250)EAD=180.82volts

Calculate the voltage between the windings AE (EAE) using the relation.

  EAE=(voltsperturn)×NAE

  EAE=2473×(120+180+250+300)EAE=279.452volts

Calculate the voltage between the windings BC (EBC) using the relation.

  EBC=(voltsperturn)×NBC

  EBC=2473×(180)EBC=59.178volts

Calculate the voltage between the windings BD (EBD) using the relation.

  EBD=(voltsperturn)×NBD

  EBD=2473×(180+250)EBD=141.37volts

Calculate the voltage between the windings BE (EBE) using the relation.

  EBE=(voltsperturn)×NBE

  EBE=2473×(180+250+300)EBE=240volts

Calculate the voltage between the windings CD (ECD) using the relation.

  ECD=(voltsperturn)×NCD

  ECD=2473×(250)ECD=82.19volts

Calculate the voltage between the windings CE (ECE) using the relation.

  ECE=(voltsperturn)×NCE

  ECE=2473×(250+300)ECE=180.82volts

Calculate the voltage between the windings DE (EDE) using the relation.

  EDE=(voltsperturn)×NDE

  EDE=2473×(300)EDE=98.63volts

Thus, the voltages between the windings AB is 39.452volts_, between windings AC is 98.63volts_, between windings AD is 180.82volts_, between windings AE is 279.452volts_, between windings BC is 59.178volts_, between windings BD is 141.37volts_, between windings BE is 240volts_, between windings CD is 82.19volts_, between windings CE is 180.82volts_ and between windings DE is 98.63volts_.

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