3 November 2017

Working of Auto transformer, Saving in Copper Material and Applications

  • It consists of only single winding which is common to both primary and secondary winding. 
  • It has two end terminals ( PR) acts as primary and one end terminal ( either P or R ) and inter mediate terminal Q acts as a secondary winding ( Figure A ). 
  • The position of the intermediate terminal Q determines whether auto – transformer works as step down transformer or step up transformer. 
  • The theory and operation of the auto-transformer is similar to that of conventional two winding transformer. 
  • The auto transformer is cheaper than the ordinary transformer because of single winding uses less copper than the two winding. Since the voltage / turn is equal in both winding, the voltage develops across each winding depends on number of turns.
auto-transformer.png

  • Figure B shows a step down transformer in which PQ winding acts as a primary having N1 turns and QR winding acts as a secondary winding consists of N2 turns.
  • If the supply voltage V1 is given to primary winding.
        Induced emf per turn ( Et ) = V1 / N1
        As we know that the value of Et is same for both windings.

        Secondary voltage V2 = Et × N2

auto-transformer-as-step-down-transformer.png
Saving of copper in auto transformer as step down transformer
  • The weight of winding material ( copper ) is proportional to the length and area of cross section of the conductors.
        W a Volume of material
        W a ( a × L )
  • The cross section of the conductor depends on current ( I ) and length of conductors is proportional to the number of turns ( N ). 
  • Therefore the weight of copper is directly proportional to ampere - turns ( NI ).
        Weight of the copper in the ordinary transformer ( WO ) = N1I1 + N2I2
        Weight of copper in the auto transformer ( Wa ) =
        Weight of copper in part PQ a I1 ( N1 – N2 ) +
        Weight of copper in part QR a ( I2 – I1 ) N2
        Weight of copper in the auto transformer a I1 ( N1 – N2 ) + ( I2 – I1 ) N2
                                                                      a ( I1N1 + I2N2 – 2N2I1 )
  • Weight of copper in auto transformer ( Wa ) / Weight of copper in ordinary transformer ( WO ) =  ( I1N1 + I2N2 – 2N2I1 ) / ( I1N1 + I2N2 )

                                    = ( I1N1 + I1N1 – 2N2I1 ) / 2N1I1  ( As N1I1 = N2I2 )
                                    = ( 2I1N1 / 2I1N1 ) – ( 2N2I1 / 2I1N1 )
                                    = ( 1 ) – ( K )     ( As K = N2 / N1 = I1 / I2 )
                                    = 1 – K
              Therefore Wa = ( 1 – K ) WO
         Saving in copper = WO – Wa
                                   = WO – ( 1 – K ) WO
                                   = KWO
  • Therefore the saving in copper material depends on the value of K ( Voltage transformation ratio ). 
  • Higher value of K, more saving in copper material

Saving of copper in auto transformer as step up transformer

auto-transformer-as-step-up-transformer.png

Weight of the copper in the ordinary transformer ( WO ) = N1I1 + N2I2
Weight of copper in the auto transformer ( Wa ) =
Weight of copper in part PR a I2 ( N2 – N1 ) +
Weight of copper in part RQ a ( I1 – I2 ) N1
Total weight of copper in the auto transformer a I2 ( N2 – N1 ) + ( I1 – I2 ) N1
                                                                      a ( I1N1 + I2N2 – 2N1I2 )
Weight of copper in auto transformer ( Wa ) / Weight of copper in ordinary transformer ( WO ) = ( I1N1 + I2N2 – 2N1I2 ) / ( I1N1 + I2N2 )
           = ( I1N1 + I1N1 – 2N1I2 ) / 2N1I1  ( As N1I1 = N2I2 )
           = ( 2I1N1 / 2I1N1 ) – ( 2N1I2 / 2 N1I1 )
           = ( 1 ) – ( 1 / K )     ( As K = N2 / N1 = I1 / I2 )
           = ( 1 – 1 / K )
  • Therefore Wa = [ ( 1 – 1 / K ) ] WO
  • Saving in copper = WO – [ ( 1 – 1 / K ) ] WO

                                 = [ 1 – 1 + 1 / K ] WO
                                 = ( 1 / K ) WO
  • Therefore the saving in copper material depends on the value of 1 / K. 
  • Lower value of K, more saving in copper material
Application
  • The auto transformer is used for starting of synchronous motor and induction motor. Its winding is used only during starting period of the motor for a few seconds.
  • It is used as a furnace transformer for getting suitable supply voltage for furnace winding from 230 V supply.
  • It is used as laboratory equipment to get suitable supply voltage as per requirement.
  • To compensate the small voltage drop in a distribution cable by giving small voltage boost.
  • It may be used as interconnecting transformer in 132 kV / 66 kV supply system.

Connection of two winding transformer into a auto transformer
  • The winding connection diagram of an auto transformer from two winding transformer may be as ( I ) Step down transformer ( II ) Step up transformer

               two-winding-transformer.png
  • Conversion of two winding transformer into step down auto transformer

conversion-of-two-winding-transformer-into-step-down-auto-transformer.png

  • Conversion of two winding transformer into step up auto transformer

conversion-of-two-winding-transformer-into-step-up-auto-transformer.png

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1 comment:

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