AUTO TRANSFORMER

             Generally we know about two winding transformer but there is another special type of transformer , namely autotransformer which is also used in several applications. Auto transformer is a single winding transformer in which a part of the winding is common to both high voltage and low voltage sides. That is only one winding is shared by the input and output side. The part of the  winding which is common to both high voltage and low voltage side is termed as ‘common winding’ and the remaining part of the main winding is called ‘series winding’. This series winding is connected in series with the common winding.
             Auto transformer is kind of electrical transformer where primary and secondary shares same common single winding.

Types of autotransformer:

According to the operation, the autotransformers are classified in two general categories.

•  Step up autotransformer –  In this type of autotransformer, the source voltage is connected to the common winding  and the load is connected across the main single winding .

• Step down autotransformer – In this type of autotransformer, the source voltage is applied to the main winding and common winding is connected across the load.

• Working principle of autotransformer

  The figure shows the circuit diagram of a stepup autotransformer. Now we are going to discuss the working principle of autotransformer. Here we can see that, the alternating voltage source is connected to the winding section ‘bc’ and the load is connected across the full winding section, that is ‘abc’. So, the single winding is shared by low voltage and high voltage side. Assume, TH= Number of turns of full winding abc, TL= Number of turns of the common winding bc, Tab= Number of turns of the series winding ab, VH= Voltage of high voltage side, VL= voltage of low voltage side, IH = Current in high voltage side, IL= Current in the low voltage side.
  So, balancing the part winding emf , IHTab= ITbc ………………..(1)
  Consider, the transformation is y= Tab / Tbc = VH / VL
  So, from the equation (1); I / IH = Tab / Tbc
  But, from the circuit diagram,  Tab = Tac - Tbc
  ∴ I / IH = (Tac - Tbc) / Tbc
  ∴ I / IH  = (Tac / Tbc )H
  ∴ I / IH = y-1.
  So from this equation we can say that, (I+IH) / IH = y………………(2)
  But, I + IH = IL
  Therefore, from  eqation (2),  IL / IH = y.
  And, I / IL= (y-1) / y.
  Applying KVL at high voltage side,
  Eab+Ebc = Eac
  ∴ Eab = Eac - Ebc  = yEbc - Ebc  =yEL-EL.
  Thus, Eab = (y-1)EL
  We can see from the equtaion that, Eab, that is the output voltage is nothing but the product of input voltage EL and (y-1). So, the output voltage is greater than the input volatge. Hence, the voltage level is increased after the transformation. In this way, by using a common winding, the transformer action is accompolished.

Copper Savings in Auto Transformer

Now we will discuss the savings of copper in auto transformer compared to conventional two winding electrical power transformer.

We know that weight of copper of any winding depends upon its length and cross - sectional area. Again length of conductor in winding is proportional to its number of turns and cross - sectional area varies with rated current.

So weight of copper in winding is directly proportional to product of number of turns and rated current of the winding.

Therefore, weight of copper in the section AC proportional to

(N1 − N2)I1

and similarly, weight of copper in the section BC proportional to

N2( I2 − I1)

Hence, total weight of copper in the winding of Auto Transformer proportional to

(N1 − N2)I1 + N2( I2 − I1)

In similar way it can be proved, the weight of copper in two winding transformer is proportional to,

N1I1 + N2I2

⇒ 2N1I1    (Since, in a transformer N1I1 = N2I2)

Let's assume, Wa and Wtw are weight of copper in auto transformer and two winding transformer respectively,

∴ Saving of copper in auto transformer compared to two winding transformer,

Auto transformer employs only single winding per phase as against two distinctly separate windings in a conventional power transformer. Advantages of using auto transformer. For transformation ratio = 2, the size of the auto transformer would be approximately 50% of the corresponding size of two winding transformer. For transformation ratio say 20 however the size would be 95%. The saving in cost is of course not in the same proportion. The saving of cost is appreciable when the ratio of transformer is low, that is lower than 2.

Important features of an autotransformer

• The transformation ratio ( we considered y) of an autotransformer is always greater than unity.

• VA rating of an autotransformer is greater than VA rating of two winding transformer.
  That is, VA autotransformer > VA two winding transformer.

• Weight of conductor material in a winding is proportional to the product of current and number of turns. Hence there is a saving of the conductor material in the autotransformer as it consist of only a single winding. In more simple words, as we use only a single winding instead of two separtae winding, so, much less amount of core winding material (copper) is required and in this way, for the same purpose or application much less conductor is used. Saving of conductor material is more if the
  (1 / transformation ratio) approaches unity.

• Efficiency of autotransformer is more than 2 winding transformer. In the former one energy is transferred from primary to secondary side partly by induction and partly by direct electrical connection ie conduction . So losses are much less.

• Advantages of autotransformer

  • Autotransformers are smaller in size and cheaper than the two winding transformer of the same rating . Therefore it is little more economical than a convenient two winding transformer.
  •  In autotransformer, only a single winding is used. So, voltage regulation is superior because of the reduced voltage drop in resistance and reactance of the winding. Due to elimination of one winding, resistance and leakage flux for that is zero.
  • Autotransformer has more efficient than two winding transformer.

  • Disadvantages of Using Auto Transformer

    But auto transformer has the following disadvantages:
    1. Because of electrical conductivity of the primary and secondary windings the lower voltage circuit is liable to be impressed upon by higher voltage. To avoid breakdown in the lower voltage circuit, it becomes necessary to design the low voltage circuit to withstand higher voltage.
    2. The leakage flux between the primary and secondary windings is small and hence the impedance is low. This results into severer short circuit currents under fault conditions.
    3. The connections on primary and secondary sides have necessarily to be same, except when using interconnected starring connections. This introduces complications due to changing primary and secondary phase angle particularly in the case-by-case of delta / delta connection.
    4. Because of common neutral in a star / star connected auto transformer it is not possible to earth neutral of one side only. Both their sides have to have their neutrality either earth or isolated.
    5. It is more difficult to preserve the electromagnetic balance of the winding when voltage adjustment tappings are provided. It should be known that the provision of adjusting tapping on an auto transformer increases considerably the frame size of the transformer. If the range of tapping is very large, the advantages gained in initial cost is lost to a great event. 

  • Applications of autotransformer

    •  Autotransformer is used widely in interconnection of power systems of different voltage levels. As an instance, autotransformer is used to make an interconnection of a 132 KV line and 230 Kv line.
    •  They are also used in boosting the supply voltage in distribution system to compensate voltage drop.
    •   Autotransformers with several number of tappings are used for starting of induction and synchronous motors. This starting methos is termed as autotransformer starting method.
    •  They are also used as variac in laboratories where continuous variable voltage is required and this variac is nothing but a variable AC voltage source.
    .

                                       TRANSFORMER

Definition of Transformer

A transformer is a static machine used for transforming power from one circuit to another without changing frequency

History of Transformer

The history of transformer commenced in the year of 1880. In the year of 1950 400KVelectrical power transformer first introduced in high voltage electrical power system. In the early 1970s unit rating as large as 1100MVA were produced and 800KV and even higher KV class transformers were manufactured in year of 1980.

Actually, the word Transformer refers to transfer something from one place to other. In very simple words, a Electrical Transformer is a static electrical device, which transfers the electrical energy from one  circuit to another circuit by mutual induction method. No direct electrical connection is needed to perform this transformation, that is the two circuits are physically isolated from each other. When a transformer transfers the electrical energy in between two circuits, then the operating frequency remains the constant. The KVA rating of input and output side is also remains the constant. Therefore, a transformer can change the voltage level from low to high or high to low with a corresponding decrease or increase in the current. In this way, the product of voltage and current (VA, in large transformers KVA) is equal in both sides of a transformer. As the transformer does not contain any rotary part so it is termed as static device. In a typical transformer, two or more stationary electrical circuits are interlinked with each other by a common magnetic field.

This is a very simple and basic concept of transformer. This device only operates in AC, and modern power transmission and distribution system is totally depnded on this device. To get more vivid concept about transformer, we have to proceed to the illustrative section of transformer, from where we will understand more easily what is transformer.

Use of Power Transformer

Generation of electrical power in low voltage level is very much cost effective. Hence electrical power are generated in low voltage level. Theoretically, this low voltage level power can be transmitted to the receiving end. But if the voltage level of a power is increased, the electric current of the power is reduced which causes reduction in ohmic or I2R losses in the system, reduction in cross sectional area of the conductor i.e. reduction in capital cost of the system and it also improves the voltage regulation of the system. Because of these, low level power must be stepped up for efficient electrical power transmission. This is done by step up transformer at the sending side of the power system network. As this high voltage power may not be distributed to the consumers directly, this must be stepped down to the desired level at the receiving end with help of step down transformer. These are the use of electrical power transformer in the electrical power system.

Two winding transformers are generally used where ratio between high voltage and low voltage is greater than 2. It is cost effective to use auto transformer where the ratio between high voltage and low voltage is less than 2. Again three phase single unit transformer is more cost effective than a bank of three single phase transformer unit in a three phase system. But still it is preferable to use later where power dealing is very large since such large size of three phase single unit power transformer may not be easily transported from manufacturer's place to work site.

Constructional Parts of a Transformer

Initially we have to know about the main parts of a transformer. A typical transformer is constructed with three basic parts. They are: primary winding, seondary winding and a magnetic core. Now we will discuss about those parts separately.

Primary winding: This is a simple coil which is wound by copper wires. This winding generates the required magnetic flux whenever a active AC source is connected across it. It is a closed coil, so whenever an AC voltage is applied across it, current starts flowing. And this flow of current leads to develope an alternating magnetic field surrounding the coil. This winding is used to develop the main magnetic field into the transformer. As the flux generation and creation of magnetic field is initiated from here, so this winding is termed as the primary winding. The primary winding is the input section of a transformer.

Core: Core is very important part of a transformer, which gives the strong mechanical support for the windings as well as serves the necessary path for the magnetic fluxes. Each horizontal legs are termed as limbs of the core, and the primary and secondary windings are wound on different limbs. Core is generally made up with soft iron or laminated silicon steel. Actually, these materials have high permeability and low reluctance. So, when the magnetic fluxes are generated in the primary winding, it confines them and after that those fluxes are passing through the core. Both primary and secondary windings are connected with a common core. As this magnetic core offers a low reluctance path for the generated magnetic fluxes, so most of the fluxes will go through the core. So they are guided to the secondary winding through the magnetic core.

Secondary winding: This is also a copper winding simillar to the primary, but the number of turns are different. The generated magnetic fluxes will link this secondary winding by mutual induction method after passing through the magnetic core. Output of a transformer is always taken from the secondary winding terminal that is the load is always connected with this terminal.

Working Principle of Transformer

To understand the working principle of a transformer, we need to know about the term ‘electromagnetic induction’ and the faradey’s law of electromagnetic induction. Whenever a closed conductor is placed into a varying magnetic field, a potential differance is developed across the terminals of the conductor. This phenomenon is known as electromagnetic induction. This is the basic principle of working of any transformer.

Faradey’s law:
This law states that, if a closed conductor is subjected to a varying magnetic field, then the induced emf in the conductor is equal to the rate of change of flux linkages of that magnetic field. So, we can say that, the induced voltage is:e = – Ndφ / dt volt.

Now, coming to the point of working principle of transformer. Think you have two copper coils and an alternating AC source. Now if you connect the AC source with any of the copper coils then obviously an alternating voltage will induced in the coil and as the source voltage is sinusoidal in nature so a varing magnetic field will also developed around the coil. And if you bring the other coil closer to the energised coil, then according to faradey’s law of electromagnetic induction an alternating emf will induced in this coil. By nature, the induced emf in this coil is equal to the rate of change of flux linkages of the magnetic field which is created by the main coil. This is the basic transformer action. But in high voltage application, dealing with natural air as the flux circulation path is quite inconvenient as only very few amount of flux can be induced by using air. So, a very low reluctance path should be used as the flux circulating path instead of natural air.

Watch the diagram carefully, you can see there are two windings ( copper coil) which are wound in a common magnetic core.These two windings are insulated from each other so there is no electrical connection present in between those windings. Whenever an alternating voltage source connected across the primary winding, an alternating voltage E1 is induced and an alternating current starts flowing through the primary winding of a transformer. This alternating current in the primary winding develops a alternating magnetic flux φ which further developes a varying magnetic field around the primary coil. Due to transformer action, an alternating emf get induced in the secondary coil. The common magnetic core helps to circulate the mutual flux φm in between primary coil and seconsary coil. As the secondary coil is nothing but a closed conductor circuit so the induced emf  causes to produce an alternating volatge E2 in the secondary winding. Generally, the load is connected across the secondary winding terminals. So, an alternating current starts flowing through the closed secondary winding as well as through the load. Thus, the electrical energy is transferred from the primary winding to the secondary winding with the help of a common magnetic circuit. As, all those coils are static, that is no relative motion is present in between the coils, so ultimately the frequency of the voltage is remain constant. This the description of working principle of transformer. So, hope you understood the working principle of transformer very easily.

Types of Power Transformer

Actually, there are several varity of transformers according to their functions and purposes of use. So, here we discuss about the severaltypes of transformers.

• According to the core construction:

(a) Core type.

(b) Shell type.

(c) Berry type.

• According to the voltage ratio:

(a) Step Up transformer: These type of transformers are used for step up the voltage level during the transmission of power from the generating stations to electrical substations.

(b) Step down transformer: These type of transformers are used to step down the voltage level during transmission of power from substation to the consumer.

• According to the phase:

(a) Single Phase Transformer: This type of transformer is used for operating only in single phase AC network.

(b) Three Phase Transformer: Three phase transformer is used in three phase system. A interesting fact is, it is preferable to use 3 single phase transformers instead of a single three phase transformer.

• According to the method of cooling:

(a) Self Cooled:- Here the transformer is subjected to natural air circulation and this natural flow of air demolishes the generated heat. This cooling procedure is suitable for low voltage transformer.

(b) Air forced cooled:- Here some high speed fans are connected near the transformer radiator and in this way high velocity air is foced to demolish the generated heat of the transformer.

(c) Oil cooled:- Here oil is used to as the cooling medium.

(d) forced oil cooled:- Here a pump is included with the transformer in order to circulate the oil rapidly.

• According to the frequency groups:

(a) Power frequency transformers.

(b) Audio frequency transformers.

(c) Radio frequency transformers.

There are many other types of transformers are present according to the specific applications.

• Distribution Transformer: Distribution transformers are used in distribution network to step down the voltage level for feeding the local consumers.

• Power Transformer: Power transformers are used at each end of transmission line in generating stations and substations for stepping up or down the voltage level.

• Current transformer: This transformer is used for the measurement of electric current.

• Potential transformer: These type of  transformers are used to step down the voltage to low value which can be fed to relay for protection purpose.

• Instrument transformers:Current transformers and potential transformer both are called the instrument transformer because their main fuction is to transform  high currents and voltages to a standardized low and easily measurable values.
• Auto transformer : It is a single winding transformer and a common winding is used as both primary and secondary winding.

Theory of transformer e.m.f. equation

Basically, the e.m.f. equation of  transformer represents the primary side voltage and secondary side voltage of a transformer. The term emf means “electro motive force”. A a coil is subjected to time varying magnetic field, then it will automatically induces a alternating current. The EMF is a type of potential, which signifies the amount of energy per unit charge. In case of battery and transformers, the EMF is denoted by Volt. We know that, transformer is a static device which transfers the electrical energy from one circuit to another circuit by mutual induction method. Actually, transformers are working on AC voltage so, all the terminology is based upon the AC waveshape that is sinusoidal wave. So, by nature derivation of the emf equation of transformer is a very easy process by implimenting the derivation process.

As the alternationg current source is applied across the primary winding so, when this primary coil induced voltage is also sinusoidal type. When the primary side links the secondary by mutual induction method, obviously the secondary induced voltage is also alternating type. Determination of the e.m.f. equation of transformer is very imporatant to know the input and output voltage parameter of the transformer. And it also shows the relation of developed emf with the number of turns, magnetic flux and the frequency.

Transformer e.m.f. equation derivation

We know that, in AC system, flux at any instant is given by:

Φ = Φmsinωt…………………….(1)

But at the peak value Φ becomes Φm. By the faradey’s law of electromagnetism, the instanneous e.m.f. induced in any coil of T turns by this flux is,

e = – d(ΦT) / dt

=  -T (dΦ / dt)

= -T d(Φmsinωt) / dt

= -TωΦmcosωt

= TωΦmsin(ωt-π / 2)

This equation can be written as, e = Emsin(ωt-π / 2)………………………………(2)

Where, Em = TωΦm= maximum value of e…………………………………………..(3)

So, for a sinusoidal wave, the r.m.s value of that e.m.f. is;
Erms = E = Em / √2………………………………………………………………………(4)

So, E = TωΦm / √2

= T(2πfΦm / √2)

      So, E = 4.44ΦmfT Volt

 This highlighted eqation is called the e.m.f. equation of transformer.

In this way, suppose the number of turns in the primary winding and secondary winding are T1 and T2 respectively.

Then, the primary rms voltage is;

       E1 = 4.44ΦmfT1Volt

And secondary rms voltage is;

        E2 = 4.44ΦmfT2Volt

In those equations,Φm is the maximum value of flux in Webers.
The e.m.f. equation of transformer signifies that, the winding with higher number of turns will induce greater EMF into it, and it will develope higher voltage. So, the widing with greater turns is termed as high voltage (HV) winding and vice versa. From the EMF euation, it is quite easy to say that, the EMF of any winding can be varied either by changing the number of turns, or by changing the flux, or even by changing the frequency. This is a  standard equation for all types of power transformers, and according this principle, all transformers are designed with proper turns ratio.

Voltage ratio and turns ratio:

When E is the voltage and T is the number of turns in a coil then voltage per turn is the E / T ratio.
So, from the e.m.f. equation of transformer, primary volts per turn, E1 / T1 = 4.44Φmf.
In this way, secondary volts per turn, E2 / T2 = 4.44Φmf.

We can see that, voltage per turn ratio is equal in the both side of a transformer.So, we can say that, E1 / T1 = E2 / T2

            ∴ E1 / E2 = T1 / T2

This ratio T1 / T2 is termed as turns ratio.

This turns ratio is also termed as voltage ratio or transformation ratio. Because, the turns ratio is nothing but a  relationship in between the number of turns and the induced voltage. So, we can say that, transformation ratio a = E1 /  E2 = T1  / T2

So, we can see that, we can get any desired voltage ratio by adjusting the number of turns in the primary and secondary winding.

Definition of Ideal Transformer

An Ideal Transformer is an imaginary transformer which does not have any loss in it, means no core losses, copper losses and any other losses in transformer. Efficiency of this transformer is considered as 100%.

Ideal Transformer Model

Ideal Transformer Model is developed by considering a transformer which does not have any loss. That means the windings of the transformer are purely inductive and core of transformer is loss free. There is zero Leakage Reactance of Transformer. As we said, whenever we place a low reluctance core inside the windings, maximum amount of flux passes through this core, but still there is some flux which does not pass through the core but passes through the insulation used in the transformer. This flux does not take part in the transformation action of the transformer. This flux is called leakage flux of transformer. In an Ideal Transformer, this leakage flux is considered also nil. That means 100% flux passes through the core and linked with both primary and secondary windings of transformer. Although every winding is desired to be purely inductive but it has some resistance in it which causes voltage drop and I2R loss in it. In such ideal transformer model, the winding are also considered, ideal that means resistance of the winding is zero.

Now if an alternating source voltage V1 is applied in the primary winding of that Ideal Transformer, there will be a counter self emf E1 induced in the primary winding which is purely 180o in phase opposition with supply voltage V1.

For developing counter emf E1 across the the primary winding it draws electric current from the source to produces required magnetizing flux. As the primary winding is purely inductive, that current is in 90o lags from the supply voltage. This current is called magnetizing current of transformer Iμ.

This alternating current, Iμ produces a alternating magnetizing flux Φ which is proportional to that electric current and hence in phase with it. As this flux is also linked with secondary winding through the core of transformer, there will be another emf E2 induced in the secondary winding, this is mutually induced emf. As the secondary is placed on the same core where the primary winding is placed, the emf induced in the secondary winding of transformer, E2 is in the phase with primary emf E1 and in phase opposition with source voltage V1.

The above chapter was about a brief discussion about ideal transformer it has also explained the basic ideal transformer model.

REMAINING CONCEPT WILL BE CAPSULED IN A WEEK