A
Transformer, in which a part of the winding is common to both the Primary and
Secondary circuit is called an Auto Transformer. It shall be noted that in Two
Winding Transformer, Primary and Secondary windings are electrically isolated
but in Auto Transformer, the two windings are not electrically isolated.

A
simplified diagram of a Step-down Auto Transformer is shown in figure below.

As shown in the figure
above, N

_{1}and N_{2}are the number of turns between winding AB and AC respectively. If a voltage V_{1}is applied across AB, an exciting current will start flowing through the full winding. Therefore, voltage per turn in winding AB is V_{1}/N_{1}and hence voltage across CB is (V_{1}/N_{1})N_{2}.
As the load current is I

_{2}and the current taken from the source is I1, neglecting losses
Input Power = Output Power

V

_{1}I_{1}CosØ_{1}= V_{2}I_{2}CosØ_{2}………………….(1)
Assuming internal impedance
drop and losses to be negligible, power factor for primary and secondary will
be almost same.

CosØ

_{1}= CosØ_{2}_{}

Therefore from equation (1),

V

_{1}I_{1}= V_{2}I_{2}_{}

So,

V

_{2}/ V_{1}= I_{1}/ I_{2}= N_{2}/ N_{1}=k(say)
In our case of Step down
Auto Transformer, k<1.

Again, since the direction
of flow of load current is in the opposite to the current flowing in the
Primary because of Lenze’s Law, hence the current flowing in winding BC = (I

_{2}-I_{1})
ICB = (I

_{2}– I_{1})
Now the primary MMF = I

_{AC}x(N_{1}-N_{2})
= I

_{1}x(N_{1}– N_{2})
= N

_{1}I_{1}– N_{2}I_{1}_{}

But N

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

So, N

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

Therefore,

Now the primary MMF = N

_{2}I_{2}– N_{2}I_{1}_{}

= (I

_{2}– I_{1})xN_{2}_{}

= I

_{CB}xN_{2}= Secondary MMF
Thus we see that in Auto
Transformer, Transformer action take place between winding AC and BC. Thus VA
of winding AC will be transferred to winding BC by Transformer action.

Therefore,

Transformed VA = V

_{AB}xI_{AB}_{}

= (V

_{1}-V_{2})xI_{1}………………………(2)
Now, total VA input = V

_{1}xI_{1}_{}

Therefore,

Transformed VA / Input VA =
[(V

_{1}-V_{2})xI_{1}] / V_{1}I_{1}_{}

= 1 – V

_{2}/V_{1}_{}

= 1-k

Thus we see that out of
total input VA, only a part of it is transformed by Transformer action and
remaining is therefore transferred by conduction.

So,

Conducted VA = Total Input –
Transformed VA

= V

_{1}I_{1}- (V_{1}-V_{2})xI_{1}.....................From equation (1)
= V

_{2}I_{1}
So,

Conducted VA / Input VA = V

_{2}I_{1}/ V_{1}I_{1}_{}

= V

_{2}/V_{1}= k
Thus in an Auto Transformer,
a part of input power is delivered to the load by Transformer action while the
remaining is by conduction method. Power transfer because of conduction method
is possible in Auto Transformer because a part of winding is common to both the
primary as well as secondary circuit.

## No comments:

Post a Comment