Working of Auto transformer, Saving in Copper Material

• 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.

 

• 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 ( E_t ) = V₁ / N₁

As we know that the value of E_t is same for both winding

Secondary voltage V₂ = E_t × N₂

      

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 ( W_O ) = N₁I₁ + N₂I₂

Weight of copper in the auto transformer ( W_a ) =

Weight of copper in part PQ a I₁ ( N₁ – N₂ )

Weight of copper in part QR a ( I₂ – I₁ ) N₂

Total weight of copper in the auto transformer a I₁ ( N₁ – N₂ ) + ( I₂ – I₁ )

                                                                                                                  N₂

                                                                           a ( I₁N₁ + I₂N₂ – 2N₂I₁ )

Weight of copper in auto transformer ( W_a ) / Weight of copper in ordinary transformer ( W_O ) =  ( 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 W_a = ( 1 – K ) W_O

Saving in Copper = W_O – W_a

                           = W_O – ( 1 – K ) W_O

                           = KW_O

• 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

Weight of the copper in the ordinary transformer ( W_O ) = N₁I₁ + N₂I₂

Weight of copper in the auto transformer ( W_a ) =

Weight of copper in part PR a I₂ ( N₂ – N₁ )

Weight of copper in part QR 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 ( W_a ) / Weight of copper in ordinary transformer ( W_O ) = ( 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 W_a = [ ( 1 – 1 / K ) ] W_O

Saving in copper = W_O – [ ( 1 – 1 / K ) ] W_O

                           = [ 1 – 1 + 1 / K ] W_O

                           = ( 1 / K ) W_O

• 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 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 

             

Conversion of Two winding Transformer into Step down Auto Transformer

Conversion of Two winding Transformer into Step up Auto Transformer

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