Single-phase Autotransformer

Single-phase Autotransformer

The normal transformer has two windings; primary winding and secondary winding. The autotransformer is a special kind of which has a common winding for primary and secondary winding.

The operating principle of autotransformer is same as the normal transformer. But, the construction of autotransformer is different compared to the normal transformer.

It consists of only one winding wound on a laminated magnetic core. It has a rotary movable contact. Therefore, from the autotransformer three terminals are brought out for connection. Out of these three contacts, two contacts are fixed (A and B) and one contact is moving (C).

The construction of autotransformer is as shown in below figure.

construction of autotransformer
construction of autotransformer

The same autotransformer used as step-up transformer as well as step-down transformer.

Autotransformer as Step-down Transformer

The connection of autotransformer is as shown in below figure for use as a step-down transformer.

Autotransformer as step-down transformer
Autotransformer as step-down transformer

As shown in above figure, fixed contact is connected with the single-phase supply. Therefore, winding AB acts as the primary winding.

A part of the complete winding, CB winding act as secondary winding across which the load is connected.

Therefore, the load voltage for this configuration is given by,

    \[ V2 = \frac{N2}{N1} \times V1 \]

Where,
N2 = Number of turns in Secondary winding, CB
N1 = Number of turns in Primary winding, AB

As the number of turns corresponding to winding CB (N2) is less than the number of turns of winding AB (N1), this configuration operates as step down transformer.

If we assume that, the transformer losses are zero, then the transformer ratio is defined as,

    \[ K = \frac{V2}{V1} = \frac{N2}{N1} = \frac{I1}{I2} \]

Where,
I1 = Primary current
I2 = Load current

Autotransformer as a Step-up Transformer

Below figure shows the connection of an autotransformer for operating it as a step-up transformer.

Autotransformer as a Step-up Transformer
Autotransformer as a Step-up Transformer

In this condition, the part of winding CB acts as the primary winding. The AC input voltage V1 is applied between the terminal C and B.

The full winding AB acts as a secondary winding and the load is connected between terminal A and B.

The number of turns of winding AB (N2) is higher than the number of turns of winding CB (N1), the autotransformer now acts as a step-up transformer.

Now, if you consider the losses are zero, then the load voltage V2 is given by,

    \[ V2 = \frac{N2}{N1} \times V1 \]

Copper Saving in Autotransformer

The value of current flowing through the conductor will decide the cross-section area of conductor. For larger current capacity, the area is large. Therefore, the resistance is smaller.

The area of conductor is directly proportional to the amount of current passing through the conductor.

    \[ Area \propto I \]

The length depends on the number of turns. And the length of conductor is directly proportional to the number of turns.

    \[ Length \quad l \propto N \]

The weight of copper of proportional to the area and length of conductor.

    \[ Weight \, of \, Copper \propto NI \]

Now compare the weight of copper in both autotransformer and normal two winding transformer.

Weight of Copper in Autotransformer

Consider step down transformer to calculate the weight of copper.

    \[ XZ = N1 \]

    \[ YZ = N2 \]

    \[ XY = N1 + N2 \]

Weight of Copper in Autotransformers
Weight of Copper in Autotransformer

Weight of copper of section in XY,

    \[ XY \propto (N1-N2)I1 \]

Weight of copper of section in YZ,

    \[ YZ \propto N2 (I1-I2) \]

Hence, the total weight of copper is given by,

    \[ Wa = (N1-N2)I1 + N2 (I1-I2) \]

Weight of Copper in Normal Two Winding Transformer

Consider below figure for normal two winding transformer. It has two winding, a primary winding and secondary winding.

Weight of copper in normal two winding transformer
Weight of copper in normal two winding transformer

Consider the total weight of transformer is Wc. And W1 is the weight of primary winding and W2 is the weight of secondary winding.

    \[ Wc = W1 + W2 \]

Where,

    \[ W1 \propto N1I1 \quad and \quad W2 \propto N2I2 \]

Hence, total weight of transformer is ,

    \[ Wc = (N1I1+N2I2) \]

Saving of Copper

Now take a ratio of weight of both types of transformer,

    \[ \frac{Wc}{Wa} = \frac{N1I1+N2I2}{(N1-N2)I1 + N2(I2-I1)} \]

But from the transformation ratio K,

    \[ K = \frac{N2}{N1} = \frac{I1}{I2} \]

    \[ I2 = \frac{I1}{K} \quad and \quad N2 = KN1 \]

    \[ \frac{Wc}{Wa} = \frac{N1I1+ kN1(\frac{I1}{K})}{(N1-KN1)I1 + KN1(\frac{I1}{K} - I1} \]

    \[ \frac{Wc}{Wa} = \frac{N1I1+ N1I1}{(N1I1-KN1I1 + N1I1 - KN1I1} \]

    \[ \frac{Wc}{Wa} = \frac{2N1I1}{2N1I1-2KN1I1} \]

    \[ \frac{Wc}{Wa} = \frac{2N1I1}{2N1I1(1-K) } \]

    \[ \frac{Wc}{Wa} = \frac{1}{1-K} \]

    \[ Wa = (1-K)Wc \]

The above calculation shows that, the copper required for the autotransformer is less than the copper required for the normal two winding transformer.

Hence, total saving of copper,

    \[ W = Wc - Wa \]

    \[ W = Wc - (1-K)Wc \]

    \[ W = KWc \]

So, for step down transformer, the saving of copper is K times the total copper weight of the two-winding transformer.

Advantages of Autotransformer

Autotransformer is better in some terms compared to the normal transformer. Here, listed some advantages of autotransformer over conventional transformer.

  • The copper required for the autotransformer is very less compared to the copper required for normal two winding transformer.
  • The size of Autotransformer is small. Therefore, the cost of the entire device is less compared to the normal transformer.
  • It requires less copper. So, the loss in winding (copper loss) is less. So, transformer losses are less and it increase the efficiency of transformer.
  • Voltage regulation of autotransformer is better than the conventional transformer.

Disadvantages of Autotransformer

Here below lists shows the disadvantages of autotransformer over conventional transformer.

  • There is no electrical isolation between the primary and secondary winding. This is very dangerous for high voltage transformers.
  • Due to any reason if the secondary winding is short circuited, a large amount of current will flow on the secondary side because it possesses low impedance.
  • Here, on single winding divided in two parts, if the common part of winding (CB) breaks, the transformer action is lost and full primary voltage appears across the secondary.

Applications of an Autotransformer

The autotransformer used in various applications that listed below.

  • It is used in AC machines like induction motor and synchronous motor, as an autotransformer starter.
  • As per requirement, it is used to vary the supply voltage. For this purpose, it used in applications like furnace.
  • It can used as a variac. Variable AC supply to vary the AC voltage applied to the load smoothly from 0V to rated voltage.

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