The weight of conductor for
any winding depends upon two parameters:

- Current carried by the winding

- Number of turns required in the winding

Thus we can say that weight
of conductor in a winding is directly proportional to its Ampere Turns i.e.
MMF.

Now, we will focus our
attention on the weight of conductor required for Auto Transformer and a Two
Winding Transformer.

As discussed in earlier post
Basic principle of Auto Transformer, the current carried by winding AC i.e. I

_{AC}= I_{1}and that of winding BC i.e. I_{BC}= (I_{2}-I_{1}). Also the number of turns for winding AC is (N_{1}-N_{2}) and that for winding BC is N_{2}.
Therefore,

The weight of conductor
required for Auto Transformer, W

_{CAT}_{}

∝
Ampere turns of winding AC + Ampere turns of winding BC

∝ (N

_{1}-N_{2})xI_{1}+ N_{2}x(I_{2}-I_{1})
∝
N

_{1}I_{1}+N_{2}I_{2}-2N_{2}I_{1}_{}

But N

_{2}/ N_{1}= I_{1}/ I_{2}_{}

So, N

_{2}I_{2}= N_{1}I_{1}_{}

Therefore,

The weight of conductor
required for Auto Transformer, W

_{CAT}_{}

∝ N

_{1}I_{1}+N_{2}I_{2}-2N_{2}I_{1}_{}

∝ 2N

_{1}I_{1 }- 2N_{2}I_{1}_{}

∝ 2(N

_{1}– N_{2})xI_{1}…………………….(1)
If we want to compare the
weight of conductor required for Auto Transformer and Two Winding Transformer,
then both the Transformers must have same voltage ratio (V

_{2}/ V_{1}), current ratio (I_{2}/ I_{1}), input VA i.e. V_{1}I_{1}and output VA i.e. V_{2}I_{2}.
Assuming all the above
parameters to be same for Two Winding and Auto Transformer,

Weight of conductor in Two
Winding Transformer W

_{CTWT,}_{}

∝
Ampere Turns of Primary + Ampere Turns of Secondary

∝ N

_{1}I_{1}+ N_{2}I_{2}_{}

But N

_{1}I_{1}= N_{2}I_{2}_{}

So,

Weight of conductor in Two
Winding Transformer W

_{CTWT},
∝ 2N

_{1}I_{1}……………………………………….(2)
Therefore from equation (1)
and (2),

W

_{CAT}/ W_{CTWT}= [2(N_{2}– N_{1})xI_{1}] / 2N_{1}I_{1}_{}

= 1 – N

_{2}/N_{1}_{}

= (1
– k)

As for step down Auto
Transformer k<1, hence the weight of conductor required for Auto Transformer
is less than that required for Two Winding Transformer.

Saving in Conductor = 1 – W

_{CAT}/ W_{CTWT}_{}

= 1 – (1 - k)

= k

Hence there is net saving of
conductor in case of Auto Transformer. Let us assume that k =0.1, thus the
saving in conductor for Auto Transformer will be only 10% but if k = 0.9 then
saving in conductor will be 90% which is quite lucrative. Thus we can conclude
that Auto Transformer is more economical when the voltage ratio k is more near
to unity.

Another important aspect is
core. As the conductor required for Auto Transformer is less than that required
for Two Winding Transformer that means for Auto Transformer lower window dimension
will be required. Thus by using Auto
Transformer, there is net saving in Core material as well as conductor
material, the saving will be more and more as we tend toward voltage ratio
unity.

Owing to reduction in conductor
and core material, the Ohmic loss in conductor and core loss is reduced
considerably. Therefore an Auto Transformer has higher efficiency than Two
Winding Transformer of same output.

Reduction in conductor material
means lower value of winding resistance. Since a part of winding is common to
both the Primary and Secondary circuit in Auto Transformer, leakage reactance
will be less. Because of lower value of leakage reactance, a superior voltage
regulation is achieved with Auto Transformer.

**Disadvantage of Auto Transformer:**

- As seen earlier in this post that saving of conductor in Auto Transformer is k so saving in conductor decreases as the value of voltage ratio k decreases.

- Another biggest disadvantage of Auto Transformer is direct electrical connection between the Primary and Secondary circuit. If Primary is supplied with high voltage then any open circuit in common winding will lead to dangerously high voltage on LV side which may damage load as well as this dangerously high voltage will be very harmful of working personnel. Thus special protection must be provided to prevent such an occurrence.

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