Auto-Transformer

 

27.1 Goals of the lesson

In this lesson we shall learn about the working principle of another type of transformer called autotransformer and its uses. The differences between a 2-winding and an autotransformer will be brought out with their relative advantages and disadvantages. At the end of the lesson some objective type questions and problems for solving are given.

Key Words: tapping's, conducted VA, transformed VA.

After going through this section students will be able to understand the following.

 

1. Constructional differences between a 2-winding transformer and an autotransformer.

 

2. Economic advantages/disadvantages between the two types.

 

3. Relative advantages/disadvantages of the two, based on technical considerations.

 

4. Points to be considered in order to decide whether to select a 2-winding transformer or an autotransformer.

 

5. The difference between an autotransformer and variac (or dimmerstat).

 

6. The use of a 2-winding transformer as an autotransformer.

 

7. The connection of three identical single phase transformers to be used in 3-phase system.

 

27.2 Introduction

So far we have considered a 2-winding transformer as a means for changing the level of a given voltage to a desired voltage level. It may be recalled that a 2-winding transformer has two separate magnetically coupled coils with no electrical connection between them. In this lesson we shall show that change of level of voltage can also be done quite effectively by using a single coil only. The idea is rather simple to understand. Suppose you have a single coil of 200 turns (= N_BC) wound over a iron core as shown in figure 27.1. If we apply an a.c voltage of 400 V, 50 Hz to the coil (between points B and C), voltage per turn will be 400/200 = 2 V. If we take out a wire from one end of the coil say C and take out another wire tapped from any arbitrary point E, we would expect some voltage available between points E and C. The magnitude of the voltage will obviously be 2 × N_EC where N_EC is the number of turns between points E and C. If tapping has been taken in such a way that N_EC = 100, voltage between E and C would be 200 V. Thus we have been able to change 400 V input voltage to a 200 V output voltage by using a single coil only. Such transformers having a single coil with suitable tapings are called autotransformers.

It is possible to connect a conventional 2-winding transformer as an autotransformer or one can develop an autotransformer as a single unit. Tapping E output 400 V 50 Hz B CC 400 V50 HzCCE B

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27.3 2-winding transformer as Autotransformer

Suppose we have a single phase 200V/100V, 50Hz, 10kVA two winding transformer with polarity markings. Then the coils can be connected in various ways to have voltage ratios other than 2 also, as shown in figure 27.2.

Let us explain the one of the connections in figure 27.2(a) in detail. Here the LV and the HV sides are connected in additive series. For rated applied voltage (100V) across the LV winding, 200V must be induced across the HV winding. So across the whole combination we shall get a voltage of 300V. Thus the input voltage is stepped up by a factor of 3 (300 V/100 V). Now how much current can be supplied to a load at 300 V? From the given rating of the transformer we know, I_{HV rated} = 50 A and I_{LV rated} = 100 A. Therefore for safe operation of the transformer, these rated currents should not be exceeded in HV and LV coils. Since the load is in series with the HV coil, 50A current can be safely supplied. But a current of 50A in the HV demands that the LV winding current must be 100A and in a direction as shown, in order to keep the flux in the core constant. Therefore by applying KCL at the junction, the current drawn from the supply will be 150A. Obviously the kVA handled by the transformer is 30 kVA and without overloading either of the windings. It may look a bit surprising because as a two winding transformer its rating is only 10 kVA. The explanation is not far to seek. Unlike a two winding transformer, the coils here are connected electrically. So the kVA transferred from supply to the load side takes place both inductively as well as conductively - 10kVA being transferred inductively and remaining 20kVA transferred conductively. The other connections shown in (b), (c) and (d) of figure 27.2 can similarly explained and left to the reader to verify.

27.4 Autotransformer as a single unit

Look at the figure 27.3 where the constructional features of an auto transformer is shown. The core is constructed by taking a rectangular long strip of magnetic material (say CRGO) and rolled to give the radial thickness. Over the core, a continuous single coil is wound the free terminals of which are marked as C and A. A carbon brush attached to a manually rotating handle makes contact with different number of turns and brought out as a terminal, marked E. The number of turns between E & C, denoted by N_EC can be varied from zero to a maximum of total number of turns between A & C i.e, N_AC. The output voltage can be varied smoothly from zero to the value of the input voltage simply by rotating the handle in the clockwise direction. 200V 150A HV 300VLV 100V 100A 50A (a) 100V 150A LV300VHV200V 50A 100A(b) 300V100V200V150AHVLV100A50A(c) 300V 200V100V150ALV HV 50A 100A (d) Figure 27.2: A two winding transformer connected as an autotransformer in various ways.

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This type of autotransformers are commercially known as varic or dimmerstat and is an important piece of equipment in any laboratory.

Now we find that to change a given voltage V₁ to another level of voltage V₂ and to transfer a given KVA from one side to the other, we have two choices namely by using a Two Winding Transformer or by using an Autotransformer. There are some advantages and disadvantages associated with either of them. To understand this aspect let us compare the two types of transformers in equal terms. Let,

Input voltage = V₁

Output voltage required across the load = V₂

Rated current to be supplied to the load = I₂

Current drawn from the supply at rated condition = I₁

KVA to be handled by both types of transformers = V₁I₁ = V₂I₂

The above situation is pictorially shown in figures 27.5(a) and (b). Let for the two winding transformer,

For the two winding transformer:

Primary number of turns = N₁

Secondary number of turns = N₂

For the autotransformer:

Number of turns between A & C = N₁

Number of turns between E & C = N₂

Therefore, number of turns between A & E = N₁ - N₂ Carbon brush Moving handle ECoreCAFigure 27.3: Autotransformer or Variac. AE CFixed input Variable outputFigure 27.4: Schematic representation of autotransformer.

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I II

Let us now right down the mmf balance equation of the transformers.

For the two winding transformer:

MMF balance equation is N₁I₁ = N₂I₂

For the autotransformer:

MMF balance equation is (N₁ - N₂)I₁ = N₂(I₂ - I₁)

or, N₁I₁ = N₂I₂

It may be noted that in case of an autotransformer, the portion EC is common between the primary and the secondary. At loaded condition current flowing through N_EC is (I₂ - I₁). Therefore, compared to a two winding transformer lesser cross sectional area of the conductor in the portion EC can be chosen, thereby saving copper. We can in fact find out the ratio of amount of copper required in two types of transformers noting that the volume of copper required will be proportional to the product of current and the number of turns of a particular coil. This is because, length of copper wire is proportional to the number of turns and crossectional area of wire is proportional to the current value i.e.,

Volume of copper ∝ length of the wire × cross sectional area of copper wire

∝ N × I

Hence,

Amount of copper required in an autotransformerAmount of copper required in a two winding transformer = ()(1212211122N-NI+NI-INI+NI

Noting that N₁I₁ = N₂ I₂ = 1121112N2N

= 121N- A ECV2 V1

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= 11- where, is the turns ratio.aa

Here we have assumed that N₁ is greater than N₂ i.e., a is greater than 1. The savings will of course be appreciable if the value of a is close to unity. For example if a = 1.2, copper required for autotransformer will be only 17% compared to a two winding transformer, i.e, saving will be about 83%. On the other hand, if a = 2, savings will be only 50%. Therefore, it is always economical to employ autotransformer where the voltage ratio change is close to unity. In fact autotransformers could be used with advantage, to connect two power systems of voltages say 11 kV and 15 kV.

Three similar single units of autotransformers could connected as shown in the figure 27.6 to get variable balanced three phase output voltage from a fixed three phase voltage. Such connections are often used in the laboratory to start 3-phase induction motor at reduced voltage.

Apart from being economical, autotransformer has less leakage flux hence improved regulation. Copper loss in the common portion of the winding will be less, so efficiency will be slightly more. However its one major disadvantage is that it can not provide isolation between HV and LV side. In fact, due to an open circuit in the common portion between E & C, the voltage on the load side may soot up to dangerously high voltage causing damage to equipment. This unexpected rise in the voltage on the LV side is potentially dangerous to the personnel working on the LV side.

27.5 Tick the correct answers

 

1. Savings of copper, in an autotransformer will be significant over a two winding transformer of same rating when the ratio of the voltages is

 

(A) ≈ 1 (B) >> 1 (C) = 1 (D) << 1

 

2. 110 V, 50 Hz single phase supply is needed from a 220 V, 50 Hz source. The ratio of weights of copper needed for a two winding and an autotransformer employed for the purpose is:

3 - phase output voltage 3 - phase input voltage Figure 27.6: 3 - phase autotransformer connection A1 E1 A2 A3 E2 E3 C1 C2 C3

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(A) 2 (B) 0.5 (C) 4 (D) 0.25

 

3. The two winding transformer and the autotransformer of the circuit shown in Figure 27.7 are ideal. The current in the section BC of the autotransformer is

 

(A) 28 A from B to C (B) 12 A from C to B

(C) 28 A from C to B (D) 12 A from B to C

 

4. A 22 kVA, 110 V/ 220 V, 50 Hz transformer is connected in such away that it steps up 110 V supply to 330 V. The maximum kVA that can be handled by the transformer is

 

(A) 22 kVA (B) 33 kVA (C) 11 kVA (D) 5.5 kVA

27.6 Problems

 

1. The following figure 27.8 shows an ideal autotransformer with number of turns of various sections as N_AB = 100, N_CB = 60 and N_DB = 80. Calculate the current drawn from the supply and the input power factor when the supply voltage is 400V, 50Hz.

400 V50 Hz60Ω20ΩAB CDFigure 27.8: Figure 27.7: 200 V 50 Hz N1=200N2=100N1:N2NBC=20NBA=30AB C10A

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2. An ideal autotransformer steps down a 400 V, single phase voltage to 200 V, single phase voltage. Across the secondary an impedance of (6 + j8)Ω is connected. Calculate the currents in all parts of the circuit.

 

 

3. Calculate the values of currents and show their directions in the various branches of a 3-phase, star connected autotransformer of ratio of 400 / 500 V and loaded with 600 kW at 0.85 lagging. Autotransformer may be considered to be ideal. It may be noted that, unless otherwise specified, voltage value of a 3-phase system corresponds to line to line voltage.

 

 

4. A delta-star connected 3-phase transformer is supplied with a balanced 3-phase, 400 V supply as shown in figure 27.9. A 3-phase auto transformer is fed from the output of the 3-phase transformer. Finally the at the secondary of the autotransformer a balanced 3-phase load is connected. The per phase primary and secondary turns of both the transformers are given in figure 27.9.

 

Calculate line to line voltage at which the load receives power. If the load draws 10 A current, calculate currents (a) in the section XZ & ZY of the autotransformer and (b) line currents and coil currents of both the sides of the 3-phase, delta-star connected transformer. Z 3-phase transformer XBalanced 3-phase supply Balanced 3-phase load N1 = 100 b Figure 27.9:400 V, 50 Hz N2 = 125 Y3-phase auto transformer NXY = 200 & NZY = 175

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