Auto transformer


Auto transformer

This transformer is used for step up and step down applications.
In this primary and secondary are not electrically isolated. An auto transformer has winding common to both primary and secondary, the input and output windings are electrically connected as one continues winding. Its application include starters and interconnection of high voltage lines.



Advantage of auto transformer over 2 winding transformer

  1. Autotransformer required less volume of core materials.
  2. In this no isolation required between primary and secondary winding as it has common winding between input and output circuit.
  3. Size and weight are less due to common winding.
  4. KVA rating of auto transformer is high as compared to 2 winding transformer.
  5. Efficiency of auto transformer will be high as low loss as copper requirement will be less.

Analysis of single phase  Autotransformer

 A single-phase autotransformer having N1 turns primary with N2 turns tapped for a lower voltage secondary. There is a winding section of N2 turns is common to both primary and secondary circuits. The winding section (N1− N2) must be provided with extra insulation, being at higher voltage. It will be assumed here that the magnetizing current is negligible.
For 2 winding turn ratio is given by ;


Let a’ be turn ratio for autotransformer,
                    a’ =  VHIGH/VLOW = V1/V2=  N1/N2....1
Always a’ > 1;

MMF produced in the winding bc reduce main flux, but current in the winding ac increase in such a way to neutralize the effect

                      Iac (N1− N2)  =  Ibc N2 .....2
                      I1 (N1− N2)  =  I1’ N2   …..3


                        a’ – 1 =   I1’/I1 …..4     

now apply kcl at  ‘c’

                     I1 + I1’ =  I2

                   I1’ =   (I2 –  I1) …5

                    a’ =    I2 /I1 …6

                        =     I2/ (I2  –  I1’)…7

….8


Volt ampere in auto transformer
Energy transferred takes place in the auto transformer by both induction and conduction.  

Total KVA in auto transformer =  SIN

KVA by induction =    ST
KVA by conduction =   SC
                             SIN    =  ST  + SC
                             Eac Iac =   Ebc Ibc =   ST
For ideal transformer
                            Vac Iac =   Vbc Ibc =   ST

input volt ampere     =     ( Vac  +  Vbc) Iac

                             SIN    =  ST  + Vbc Iac
                             SC  =  Vbc Iac
                             SC  =  V2 I1’  
        
Ratio of autotransformer to two winding transformer

…..9
From eq.  8 in eq. 9

Saving in conductor material of auto transformer

The cross section of a conductor is proportional to current through it and length is proportional to number of turns.

Weight is proportional to current × turns.
let Wauto be weight of conductor in autotransformer
let Wtf  be the weight of conductor in 2 winding transformer 

Total weight of  two winding transformer is proportional to

                (I2N2  +  I1N1)

In autotransformer, the weight is proportional to
For section ac
               I1(N1 –  N2)
For section bc
               N2(I2 –  I1)
Total weight is proportional to

             I1(N1  –  N2) + N2(I2  –  I1)



     As   I1N1 =   I2N2 being equal MMF

                             ….....10
 apply eq 1 in eq 10 , we have 

                             

Comments

  1. UnknownJanuary 3, 2020 at 4:25 AM

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    ReplyDelete
  2. UnknownJanuary 3, 2020 at 4:42 AM

    Waah mere bhai

    ReplyDelete

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