Auto Transformer

In this article, we are going to learn about the most important topic of the Transformer section, which is Autotransformer. We will see what is autotransformers, the advantages and disadvantages of autotransformers, application of autotransformers in detail. So let’s start from the basics of Autotransformer.

What is Autotransformer

We have seen in the previous lectures, where we have seen all about the normal transformer. The normal transformer has separate primary winding and secondary winding. But today we will discuss the Autotransformer.

The Autotransformer is a special transformer in which a part of the winding is common for the primary and secondary winding.

The construction of an autotransformer is shown in the below figure.

It consists of only one winding wound on a laminated magnetic core, with a rotary movable contact. Thus from the autotransformer three terminals are brought out for connection.

The autotransformer can operate as:

1. step-down autoansfromer
2. step-up autotransformer

Now we will discuss each type in detail.

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Autotransformer as Step Down Transformer

The connection of the autotransformer to work as the step-down transformer is shown in the below figure.

It shows that two fixed terminals A and B are connected to the single-phase AC supply V₁. Thus winding AB acts as the primary winding.

A part of the complete winding i.e. CB acts as the secondary winding across which the load is connected.

The operating principle of an autotransformer is the same as the operating principle of a normal transformer.

Therefore the load voltage for this configuration is given by,

V_2 = \frac{N_2}{N_1}\times V_1

Where, N₂ = Number of turns corresponding to secondary i.e. CB, N₁ = Number of turns corresponding to primary i.e. AB.

As the number of turns corresponding to secondary winding CB i.e. N₂ is less than that of primary winding AB i.e. N₁, this configuration operates as a step-down transformer.

If we neglect the losses in transformer, the magnetizing current, and the leakage reactances, then the transformation ratio is defined as,

\boxed{\mathbf{K = \frac{V_2}{V_1} = \frac{N_2}{N_1} = \frac{I_1}{I_2}}}

Where I₁ = Primary current and I₂ = Load current

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Autotransformer as Step Up Transformer

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

Note that the part CB of the complete winding acts as the primary winding. The AC input voltage V₁ is applied between terminals C and B. The full winding AB acts as a secondary winding and the load is connected between these terminals.

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

Neglecting the losses in the transformer, the magnetizing current, and the leakage reactances, the load voltage V₂ is given by,

\boxed{\mathbf{V_2 = \frac{N_2}{N_1} \times V_1}}

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Copper Saving in Autotransformer

The cross-sectional area of a wire is decided by the value of the current flowing through it. The larger than rea, the smaller the resistance, and the higher the current carrying capacity.

∴ Area ∝ I

The length of the wire is proportional to the number of turns.

∴ length l ∝ N

The weight of copper required is proportional to area and length.

∴ Weight of copper ∝ Area x Length

But Area ∝ I and l ∝ N.

∴ Weight of copper ∝ N I

Wight of Copper in two winding Transformer

Consider a two-winding transformer of the figure shown. Let the total weight of copper be W_c.

W_c = W₁ + W₂

Where W₁ is the weight of copper for primary and W₂ is the weight of copper for secondary.

But W₁ ∝ N₁ I₁ and W₂ ∝ N₂ I₂

∴ Total Weight of Copper W_c ∝ (N₁ I₁ + N₂ I₂) …… Eq.1

Weight of copper in a step-down Autotransformer

Consider the step-down autotransformer of the figure shown.

Wight of copper of section XY ∝ (N1 – N2) I1

Wight of copper of section YZ ∝ N2(I2 – I1)

Hence the total weight of copper is given by,

W_A ∝ [(N₁– N₂) I₁ + N₂ (I₂ – I₁)] …… Eq.2

Saving of Copper

Take the ratio of Equation 1 and 2 to get,

\frac{W_C}{W_A} = \frac{N_1I_1 + N_2I_2}{(N_1 - N_2)I_1 + N_2(I_2 - I_1)}

But K = \frac{N_2}{N_1} = \frac{I_1}{I_2}

∴ I₂ = I₁/K and N₂ = KN₁,

\frac{W_C}{W_A} = \frac{N_1I_1 + KN_1(I_1/K)}{(N_1 - KN_1)I_1 + KN_1(I_1/K - I_1)}

= \frac{2N_1I_1}{N_1I_1 - KN_1I_1 + N_1I_1 - KN_1I_1}

= \frac{2N_1I_1}{2N_1I_1 - 2KN_1I_1}

\therefore \frac{W_C}{W_A}= \frac{1}{(1-K)}

\therefore W_A=(1-K)W_C

This shows that the copper required for the autotransformer is less than that of required for a winding transformer.

∴ Saving Copper = W_C – W_A = W_C – (1 -K)W_C = KW_C

So the saving of copper for a step-down autotransformer is K times the total copper weight of two winding transformers.

For the step-up transformer, we can prove that,

\mathbf{Copper\; saving = \frac{W_C}{K}}

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Advantage of Auto Transformer

• As we have seen in the above section on copper saving, as only one winding is used, the copper required for the autotransformer is much less.

• The size is reduced, hence the cost is also reduced as compared to the conventional transformer.

• The losses taking place in the winding are reduced hence the efficiency is higher than the conventional transformer.

• Due to reduced resistance, the voltage regulation is better than the conventional transformer.

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Disadvantage of Auto Transformer

• There is no electrical isolation between the primary and secondary windings. This can prove to be dangerous for high-voltage applications.

• If the common part of the winding (winding CB) breaks (open-circuited) then the transformer action is lost and a full primary voltage appears across the secondary as shown in the figure.

• It possesses a low impedance, hence if the secondary circuit is short-circuited, then a large current will flow on the secondary side.

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Application of Autotransformer

• It can be used as variac, i.e. variable AC supply to vary the AC voltage applied to the load smoothly from oV to about 270 V.

• In order to start the AC machines such as induction motors or synchronous motors.

• To vary the supply voltage of the furnace.

• As a Dimmerstat: when the variac autotransformer is used to control the intensity of lamps in cinema halls etc. It is called a Dimmerstat.

Dimmerstat

When an autotransformer is used for the application of light dimming in cinema halls or on the stage of a play, it is called a Dimmestat.

By varying the position of the variable contact we can adjust the AC voltage applied to the lamps as shown in the figure below.

The secondary voltage \boxed{\mathbf{V_2 = \frac{N_2}{N_1} \times V_1}}

With a change in the position of the variable contact, the value of N2 changes. This will change the value of V2 and hence the intensity of lamps that are acting as load.

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FAQs

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Also Read

• Losses in Transformer
• EMF Equation of a Transformer
• Voltage and Current Ratio of Transformer
• What is an Ideal Transformer? Properties, Working, Phasor Diagram