Autotransformer

Autotransformer

AU: Dec.-03, 04, 05, 06, 07, 11, 14, 15, May-04, 05, 10

• Uptill now the two winding transformers are discussed in which the windings are electrically isolated and the e.m.f. in secondary gets induced due to induction. In practice, it is possible to use only one winding for the transformer so that part of this winding is common to the primary and secondary. Such a special type of transformer having only one winding such that part of the winding is common to the primary and secondary is called autotransformer. Obviously the two windings are electrically connected and it works on the principle of conduction as well as induction. Such an autotransformer is very much economical where the voltage ratio is less than 2 and the electrical isolation of the two windings is not necessary. The power transfer in 2 winding transformer is fully inductively while in autotransformer the power is transferred from primary to secondary by both inductively as well as conductively.

 

1. Construction of Autotransformers

•  In an autotransformer only one winding is wound on a laminated magnetic core while in 2 winding transformer, two windings are wound. The single winding of the autotransformer is used as primary and secondary. The part of the winding is common to both primary and secondary. The voltage can be stepped down or stepped up using an autotransformer. Accordingly the autotransformers are classified as step up autotransformer and step down autotransformer.

• The Fig. 7.1.1 (a) shows the conventional two winding transformer while the Fig. 7.1.1 (b) and (c) show the step down and step up autotransformers tep down and st respectively.

. • In step down autotransformer shown in the Fig. 7.1.1 (b), the entire winding acts as a primary while the part of the winding is used common to both primary and secondary. Thus AB forms the primary having N₁ turns while BC forms the secondary with N₂ turns. As N₂ < N₁, the output voltage V₂ < V₁ and it acts as a step down autotransformer. In step up autotransformer shown in the Fig. 7.1.1 (c), the entire winding acts as secondary while the part of the winding is used common to both primary and secondary. Thus AB forms the secondary having N₂ turns while BC forms the primary with N₁ turns. As N₂ > N₁, the output voltage V₂ > V₁ and it acts as a step up autotransformer.

•  The current distribution in the step down and step up autotransformers is shown in the Fig. 7.1.2 (a) and (b) respectively.

 

2. Transformation Ratio of an Autotransformer

• Neglecting the losses, the leakage reactance and the magnetising current, the transformation ratio of an autotransformer can be obtained as,

K=  V₂ / V₁ = I₁ / I₂ = N₂  / N1

• K is greater than unity for step up autotransformer while K is less than unity for step down autotransformer.

• Due to the use of single winding, compared to the normal two winding transformer, for the same capacity and voltage ratio, there is substantial saving in copper in case of autotransformers.

• Let us obtain the expression for the copper saving in the autotransformers.

 

3. Copper Saving in Autotransformer

For any winding, the cross-section of winding is proportional to the current I. While the total length of the winding is proportional to the number of turns N. Hence the weight of copper is proportional to the product of N and I.

Weight of copper ∞ N_I

where I =  Current in the winding

and N = Number of turns of the winding

• Consider a two winding transformer and step down autotransformer as shown in the Fig. 7.1.3. (a) and (b).

Let W_TW = Total weight of copper in two winding transformer

W_AT = Weight of copper in autotransformer

In two winding transformer,

Weight of copper of primary ∞ N₁ I₁

Thus saving copper is K times the total weight of copper in two winding transformer.

And Saving of copper = (1/K) W_TW    …. For step pu autotransformer

Key Point: As the transformation ratio increases, the saving in copper is more and more.

 

4. Power Transfer in Autotransformer

It is mentioned earlier that the power input to an autotransformer gets transferred to the secondary by two ways i.e.

1. By electromagnetic induction i.e. inductively

2. By conduction i.e. directly as windings are electrically connected.

Consider a loaded autotransformer shown in the Fig. 7.1.4.

The current drawn from the supply is I, while the input voltage is V₁.

Input power = V₁ I₁

While the load current is I₂ at a load voltage V₂.

Output power = V₂ I₂

Now BC portion has N₂ turns and acts as secondary. The current induced in this secondary due to transformer action is I₂ – I₁ while secondary induced voltage is V₂.

P_t = Power transformed inductively i.e. transformer action

While the remaining power which is (K × Input power) gets transferred directly i.e. conductively as windings are electrically connected.

P_t  = Power transformed = (1 - K) × Input power

and P_c = Power conducted through = K × Input power

P_c = (Load power output) - Pt

Key Point: Thus for the same excitation voltage and winding currents, the autotransformer gives more output than two winding transformer. Hence autotransformer has higher efficiency.

 

5. VA Rating of Autotransformer

• Let us compare the VA rating of two winding transformer and the VA rating of two winding transformer when connected as an autotransformer.

• Consider an autotransformer connected to the load as shown in the Fig. 7.1.5 (a).

• For the autotransformer the transformation ratio, neglecting the losses is,

K = V₂ / V₁ = I₁ / I₂ = N₂ / N₁

• The VA rating of autotransformer is,

(VA)_AT = V₁ I₁ = V₂ 1₂

• If the same transformer is used as a two winding transformer with AC as primary and BC as secondary then its VA rating can be obtained as,

• This is step down autotransformer with K < 1. So (1 – K) < 1 and we get (VA)AT > (VA) TW.

• Now consider the step up autotransformer as shown in the Fig. 7.1.5 (b).

• For the autotransformer, the ratio remains same as,

K = V2 / V1 = I1 / I2

• Hence VA rating of autotransformer is same as,

(VA)AT +  V1  I1 = V2 I2

• If the same transformer is used as two winding transformer then BC acts as primary with current I1 – I2 while AB acts as secondary.

• Hence its VA rating is,

Key Point: So whether autotransformer is step up or step down, its VA rating is always more than the corresponding two winding version.

So the VA transferred in autotransformer, from primary to secondary is more as it is due to both conduction and induction.

 

6. Conversion of Two Winding Transformer to an Autotransformer

• Consider a two winding transformer with the polarities as shown in the Fig. 7.1.6. 

• The transformer turns ratio is 1 : 1 and V₂ = V₁ 400 V.

• This transformer can be converted to an autotransformer in two ways, i) Additive polarity ii) Subtractive polarity.

a. Additive Polarity

• The primary and secondary windings can b connected in series with additive polarity, as shown in the Fig. 7.1.7.

• The common point A which is common to inpu and output can be taken as the top of autotransformer. The corresponding autotransforme is shown in the Fig. 7.1.8.

• Thus if input is V₁ then the output is V₁ + V₂ due to additive polarities.

• With common point A at the bottom autotransformer can be shown as in the Fig. 7.1.9.

b. Subtractive Polarity

• The primary and secondary windings can be connected in series opposition as shown in the Fig. 7.1.10 (a) which is called subtractive polarity.

•The common point A which is common to input and output can be taken as the top of the autotransformer as shown in the Fig. 7.1.10 (b).

Thus if input is V₁ then the output voltage is V₁-V₂ due to subtractive polarities.

• With common point A at the bottom, autotransformer can be shown as in the Fig. 7.1.11. A

 

7. Advantages of Autotransformer

• The various advantages of an autotransformer are,

1. Copper required is very less.

2. The efficiency is higher compared to two winding transformer.

3. The size and hence cost is less compared to two winding transformer.

4. The resistance and leakage reactance is less compared to two winding transformer.

5. The copper losses ^I2R, are less.

6. Due to less resistance and leakage reactance, the voltage regulation is superior than the two winding transformer.

7. VA rating is more compared to two winding version.

8. A smooth and continuous variation of voltage is possible.

 

8. Limitations of Autotransformer

• Apart from its advantages, an autotransformer suffers from following limitations,

1. Low impedance hence high short circuit currents for short circuits on secondary side.

2. If a section of winding common to primary and secondary is opened, full primary voltage appears across the secondary resulting in higher voltages on secondary and danger of accidents.

3. No electrical separation between primary and secondary which is risky in case of high voltage levels.

4. Economical only where the voltage ratio is less than 2.

 

9. Applications of Autotransformer

• The various applications of an autotransformer are,

1. For safely starting the machines like induction motors, synchronous motors i.e. as a startor.

2. To give a small boost to a distribution cable to compensate for a voltage drop i.e. as a booster.

3. As a furnace transformer to supply power to the furnaces at the required supply voltage.

4. For interconnecting the systems which are operating roughly at same voltage level.

5. It can be used to vary the voltage to the load, smoothly from zero to the rated voltage. Such a device giving smooth and continuous supply using an autotransformer is called variac. A single phase autotransformer used as variac is shown in the Fig. 7.1.12.

The portion AB forms primary while with the help of sliding contacts, the secondary turns can bag be changed. Thus by rotating sliding contact smooth variable voltage can be obtained. Such variacs are commonly used for dimming the lights in the cinema halls. Hence the variacs are also called dimmerstats.

The principle of dimmerstat is shown in the Fig. 7.1.13.

6. In various control systems as well as appliances.

 

10. Comparison with Two Winding Transformer

 

11. Equivalent Circuit of Autotransformer

• Consider an autotransformer as shown in the Fig. 7.1.14.

• R₁ and X₁ are the resistance and inductance of that part of the winding which carries only current I₁.

• R₂ and X₂ are the resistance and inductance of that part of the winding which behaves as secondary.

• Applying Kirchhoff's law,

• For the analysis, magnetising branch is neglected which can be added across the voltage V₁.

Ex. 7.1.1 The Fig. 7.1.16 shows an autotransformer used to supply a load of 2 kW at 230 V from a 400 V a.c. supply. Find the currents in parts AC and BC, neglecting losses and no load current. Also find the copper saving due to the use of autotransformer instead of using two winding transformer. Assume purely resistive load.

Sol. :

Ex. 7.1.2 A 10 kVA, 230/110 V transformer is to be used as an autotransformer. What will be the voltage ratio and output rating of an autotransformer ?

Solution: The given values are,

Two winding transformer = 230/110 V

kVA rating = 10 kVA

• Now as secondary voltage of two winding transformer is 110 V, let us assume that autotransformer output voltage required is 110 V. So it can be connected as an autotransformer as shown in the Fig. 7.1.17.

• The part AC is primary of two winding while BC is secondary of two winding transformer.

• Thus for an autotransformer,

Note: The problem may be solved by assuming output voltage required from an autotransformer as 230 V in which case also the input voltage is 110 + 230 = 340 V. In such case we get voltage ratio as 23/24 and output rating as 30.909 kVA. Students are expected to solve this case.

Ex. 7.1.3 A 2200/220 V, 20 kVA, two winding transformer is connected as an autotransformer to transform 2200 V to 2420 V. Find:

i) The transformation ratio of autotransformer

ii) The kVA rating of autotransformer

iii) The currents in various parts of winding

iv) The efficiency at full load, 0.8 p.f. if the core loss is 150 W and full load copper loss 275 W. Compare it with the two winding transformer.

Sol. :

Review Questions

1. Draw the circuit and explain the principle of an autotransformer. Also derive the expression for the volume of copper of an autotransformer. AU: Dec.-03, 04, 05, 06, 11, Marks 10

2. Explain the working principle of autotransformer. AU May-04, 05, Dec.-05, Marks 6

3. Explain how two winding transformer can be connected in autotransformer mode. AU: Dec.-07, Marks 4

4. Prove that the amount of copper saved in autotransformer is (1- K) times that of ordinary transformer. AU May-10, Dec.-14, Marks 6

5. Derive the expression for saving of copper in autotransformer. AU:Dec.-15, Marks 6

6. State the advantages and limitations of an autotransformer.

7. State the various applications of an autotransformer.

8. A 10 kVA, 230/110 V transformer is to be used as an autotransformer. What will be the voltage ratio and output rating of an autotransformer. [Ans.: 11/34, 14.782 KVA]