Chapter 07 Transformer

Electric Submersible Pumps Mohamed Dewidar 2013

Chapter 7

1

Transformers

Table of Content

Section Content Page

1 Introduction 2

2 Principal of operation 3

3 Induced voltage (EMF equation) 4

4 Transformer construction 7

4.1 Transformer construction of the core 8

4.2 Transformer laminations 9

4.3 Transformer core types 9

4.4 Transformer winding arrangement 10

5 Transformer dot orientation 11

6 Transformer Primary tap change 12

7 Transformer core losses 13

7.1 Hysteresis losses 13

7.2 Eddy current losses 13

7.3 Copper losses 14

8 Transformer loading 15

8.1 Transformer at NO-Load 15

8.2 Transformer On-Load 16

9 Three phase ideal transformer 20

10 Three phase transformer construction 26

11 Equivalent circuit transformer 26

11.1 Equivalent circuit of an ideal transformer

at No-Load 27

11.2 Equivalent circuit of an ideal transformer

On-Load 30

11.3 Equivalent circuit of real transformer 31

11.4 Approximate Equivalent circuit of

Transformer 34

12 Losses and efficiency of transformer 35

12.1 Iron losses or core losses 36

12.2 Core losses 38

12.3 Short circuit test 39

12.4 Efficiency of single phase transformer 40

13 Current transformer 39

14 Autotransformer 44


Chapter 7

2

Transformers

7.1. Introduction

In its simplest form a single-phase transformer consists

of two windings, wound on an iron core one of the windings is

connected to an ac source of supply f. The source supplies a

current to this winding (called primary winding) which in turn

produces a flux in the iron core.

This flux is alternating in nature (Refer Figure 6.1). If the

supplied voltage has a frequency f, the flux in the core also

alternates at a frequency f. the alternating flux linking with

the second winding, induces a voltage E2 in the second winding

(called secondary winding). [Note that this alternating flux

linking with primary winding will also induce a voltage in the

primary winding, denoted as E1. Applied voltage V1 is very

nearly equal to E1].

If the number of turns in the primary and secondary windings

is N1 and N2 respectively, we shall see later in this unit that

E1 / E2 = N1 / N2.

The load is connected across the secondary winding, between

the terminals a1, a2. Thus, the load can be supplied at a

voltage higher or lower than the supply voltage, depending

upon the ratio N1 / N2.

Figure (7.1) Basic arrangement of transformer

.When a load is connected across the secondary winding it

carries a current I2, called load current. The primary current

correspondingly increases to provide for the load current, in

addition to the small no load current. The transfer of power

from the primary side (or source) to the secondary side (or

load) is through the mutual flux and core. There is no direct

electrical connection between the primary and secondary sides.

In an actual transformer, when the iron core carries

alternating flux, there is a power loss in the core called

core loss, iron loss or no load loss. Further, the primary and

secondary windings have a resistance, and the currents in


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3

primary and secondary windings give rise to I2R losses in

transformer windings, also called copper losses.

The losses lead to production of heat in the transformers, and

a consequent temperature rise. Therefore, in transformer,

cooling methods are adopted to ensure that the temperature

remains within limit so that no damage is done to windings

insulation and material.

7.2. Principal of operation

A transformer operates on the principle of mutual

inductance between two (and sometimes more) inductively

coupled coils. It consists of two windings in close proximity

as shown in fig (7.2).

The two windings are coupled by magnetic induction. (There is

no conductive connection between the windings). One of the

windings called primary, has N1 turns is energized by a

sinusoidal voltage E1. The second winding, called secondary,

has N2 turns and feeds the load. The alternating current in the

primary winding sets up an alternating flux in the core. The

secondary winding is linked by most of this flux and emfs are

induced in the two windings. The emf induced in the secondary

winding drives a current through the load connected to this

winding. Energy is transferred from the primary circuit to the

secondary circuit through the medium of the magnetic field.

A power transformer in which the secondary voltage is higher

than the primary is called a step-up power transformer; if the

secondary voltage is less than the primary, the device is

known as a step-down power transformer. The product of current

times voltage is constant in each set of coils, so that in a

step-up power transformer, the voltage increase in the

secondary is accompanied by a corresponding decrease in the

current.

Figure (7.2)

A transformer makes use of Faraday's law and the ferromagnetic

properties of an iron core to efficiently raise or lower AC

voltages. It of course cannot increase power so that if the

voltage is raised, the current is proportionally lowered and

vice versa.

Faraday's Law

Any change in the magnetic environment of a coil of wire will


Chapter 7

4

cause a voltage (emf) to be "induced" in the coil. No matter

how the change is produced, the voltage will be generated. The

change could be produced by changing the magnetic field

strength, moving a magnet toward or away from the coil, moving

the coil into or out of the magnetic field, rotating the coil

relative to the magnet, etc.

Figure (7.3)

7.3. Induced voltage (EMF equation)

If the flux, , linking a coil of N turns and inductance,

L, varies sinusoidally at frequency f, then

t sinmax ---------------------------(6.1)

Where max is the peak value of the flux

Then the induced emf (voltage) , from Faradays law (voltage =

rate of change of flux linkage) is,

tNtdt

dN

dt

dNe

cossin

maxmax

2sin2cos2

maxmax

tfNtfNe ---------(6.2)

The peak value of the induced emf is max2 fN .

The rms (root mean square) value, E, of the induced emf is,

maxmax 44.422

1fNfNE volt ----------(6.3)


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Example 1

The primary winding of a 50 hz transformer has 480

turns and is fed from 6400 v supply, find,

(a) the peak value of the flux in the core.

(b) Secondary voltage if the secondary winding has 20 turns.

Solution:

(a) From eqn. 6.3

06.04805044.4

6400max

Wb

(b) Voltage induced in secondary winding = 4.44x50x20x0.06 = 266.4 V

Transformation ratio

If Np and Ns are the number of turns in the primary and

secondary winding and Ep and Es are the rms values of primary

and secondary induced emf, eqn 6.3 gives

max44.4 NfE pp ---------------- (6.4a)

max44.4 NfE ss ----------------- (6.4b)

Therefore,

N

N

E

E

s

p

s

p ------------------------ (6.5)

Thus the ratio of primary to secondary voltage is the same as

the ratio of primary winding turns to the secondary winding

turns. This ratio (Np/Ns) is known as transformation ratio. By

selecting this ratio properly the transformation can be done

from any convenient input voltage to any convenient output

voltage. If Np is greater than Ns, the secondary voltage will

be lower than the primary voltage and the transformer is known

as step down transformer. If Ns is greater than Np, the

secondary voltage would be higher than the primary voltage and

then the device is known as step up transformer.

If the losses in a two winding transformer are neglected, the

volt amperes in the primary and secondary must be equal.

Therefore,

IEIE sspp

N

N

I

I

E

E

s

p

p

s

s

p ---------------------- (6.6)

Where Ip and Is are the currents in the primary and secondary

windings respectively. Thus the current is transformed in the

reverse ratio of the voltage. If the transformer steps up the

voltage, it steps down the current and vise verse.


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Figure (7.4)

Figure (7.5)

Examples:

1. step down transformer

2. Step up transformer


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7

3. Transformation ratio

Primary

Windings

Secondary

Voltage

Turns

Ratio

Primary

Voltage

Secondary

Voltage

Terns

Ratio

480 240 2/1 600 120 5/1

480 120 4/1 600 208 2.88/1

480 24 20/1 208 120 1.73/1

7.4. Transformer construction

The construction of a simple two-winding transformer

consists of each winding being wound on a separate limb or

core of the soft iron form which provides the necessary

magnetic circuit.

This magnetic circuit, know more commonly as the "transformer

core" is designed to provide a path for the magnetic field to

flow around, which is necessary for induction of the voltage

between the two windings.

However, this type of transformer construction were the two

windings are wound on separate limbs is not very efficient

since the primary and secondary windings are well separated

from each other.

This results in a low magnetic coupling between the two

windings as well as large amounts of magnetic flux leakage

from the transformer itself. But as well as this "O" shapes

construction, there are different types of "transformer

construction" and designs available which are used to overcome

these inefficiencies producing a smaller more compact

transformer.

The efficiency of a simple transformer construction can be

improved by bringing the two windings within close contact

with each other thereby improving the magnetic coupling.

Increasing and concentrating the magnetic circuit around the

coils may improve the magnetic coupling between the two

windings, but it also has the effect of increasing the

magnetic losses of the transformer core. As well as providing

a low reluctance path for the magnetic field, the core is

designed to prevent circulating electric currents within the

iron core itself.

Circulating currents, called "eddy currents", cause heating

and energy losses within the core decreasing the transformers

efficiency. These losses are due mainly to voltages induced in

the iron circuit, which is constantly being subjected to the

alternating magnetic fields setup by the external sinusoidal

supply voltage.

One way to reduce these unwanted power losses is to construct

the transformer core from thin steel laminations. In all types

of transformer construction, the central iron core is


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constructed from of a highly permeable material made from thin

silicon steel laminations assembled together to provide the

required magnetic path with the minimum of losses.

The resistivity of the steel sheet itself is high reducing the

eddy current losses by making the laminations very thin. These

steel laminations vary in thicknesses from between 0.25 mm to

0.5 mm and as steel is a conductor, the laminations are

electrically insulated from each other by a very thin coating

of insulating varnish or by the use of an oxide layer on the

surface.

Figure (7.6)

7.4.1. Transformer construction of the core

Generally, the name associated with the construction of

a transformer is dependant upon how the primary and secondary

windings are wound around the central laminated steel core.

The two most common and basic designs of transformer

construction are the Closed-core Transformer and the Shell-

core Transformer. In the "closed-core" type (core form)

transformer, the primary and secondary windings are wound

outside and surround the core ring. In the "shell type" (shell

form) transformer, the primary and secondary windings pass

inside the steel magnetic circuit (core) which forms a shell

around the windings as shown below.

Figure (7.7)

In both types of transformer core design, the magnetic flux

linking the primary and secondary windings travels entirely

within the core with no loss of magnetic flux through air.


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9

In the core type transformer construction, one half of each

winding is wrapped around each leg (or limb) of the

transformers magnetic circuit as shown above.

The coils are not arranged with the primary winding on one leg

and the secondary on the other but instead half of the primary

winding and half of the secondary winding are placed one over

the other concentrically on each leg in order to increase

magnetic coupling allowing practically all of the magnetic

lines of force go through both the primary and secondary

windings at the same time.

However, with this type of transformer construction, a small

percentage of the magnetic lines of force flow outside of the

core, and this is called "leakage flux".

Shell type transformer cores overcome this leakage flux as

both the primary and secondary windings are wound on the same

centre leg or limb which has twice the cross-sectional area of

the two outer limbs. The advantage here is that the magnetic

flux has two closed magnetic paths to flow around external to

the coils on both left and right hand sides before returning

back to the central coils. This means that the magnetic flux

circulating around the outer limbs of this type of transformer

construction is equal to /2.

As the magnetic flux has a closed path around the coils, this

has the advantage of decreasing core losses and increasing

overall efficiency.

7.4.2. Transformer laminations

But you may be wondering as to how the primary and

secondary windings are wound around these laminated iron or

steel cores for this types of transformer constructions. The

coils are firstly wound on a former which has a cylindrical,

rectangular or oval type cross section to suit the

construction of the laminated core. In both the shell and core

type transformer constructions, in order to mount the coil

windings, the individual laminations are stamped or punched

out from larger steel sheets and formed into strips of thin

steel resembling the letters "E's", "L's", "U's" and "I's" as

shown below.

7.4.3. Transformer core types

These lamination stampings when connected together form

the required core shape. For example, two "E" stampings plus

two end closing "I" stampings to give an E-I core forming one

element of a standard shell-type transformer core. These

individual laminations are tightly butted together during the

transformers construction to reduce the reluctance of the air

gap at the joints producing a highly saturated magnetic flux

density. Transformer core laminations are usually stacked

alternately to each other to produce an overlapping joint with

more lamination pairs being added to make up the correct core

thickness. This alternate stacking of the laminations also


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gives the transformer the advantage of reduced flux leakage

and iron losses. E-I core laminated transformer construction

is mostly used in isolation transformers, step-up and step-

down transformers as well as auto transformers.

Figure (7.8)

7.4.4. Transformer winding arrangements

Transformer windings form another important part of a

transformer construction, because they are the main current-

carrying conductors wound around the laminated sections of the

core. In a single-phase two winding transformer, two windings

would be present as shown.

The one which is connected to the voltage source and creates

the magnetic flux called the primary winding, and the second

winding called the secondary in which a voltage is induced as

a result of mutual induction. If the secondary voltage is less

than that of the primary the transformer is called a "step-

down transformer", and if the secondary voltage is greater

then it is called a "step-up transformer".

The type of wire used as the main current carrying conductor

in a transformer winding is either copper or aluminum. While

aluminum wire is lighter and generally less expensive than

copper wire, a larger cross sectional area of conductor must

be used to carry the same amount of current as with copper so

it is used mainly in larger power transformer applications.

Small kVA power and voltage transformers used in low voltage

electrical and electronic circuits tend to use copper

conductors as these have a higher mechanical strength and

smaller conductor size than equivalent aluminum types. The

downside is that when complete with their core, these

transformers are much heavier.

Transformer windings and coils can be broadly classified in to

concentric coils and sandwiched coils. In core-type

transformer construction, the windings are usually arranged

concentrically around the core limb as shown above with the

higher voltage primary winding being wound over the lower

voltage secondary winding. Sandwiched or "pancake" coils

consist of flat conductors wound in a spiral form and are so

named due to the arrangement of conductors into discs.

Alternate discs are made to spiral from outside towards the

centre in an interleaved arrangement with individual coils

being stacked together and separated by insulating materials


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such as paper of plastic sheet. Sandwich coils and windings

are more common with shell type core construction.

Helical Windings also known as screw windings are another very

common cylindrical coil arrangement used in low voltage high

current transformer applications. The windings are made up of

large cross sectional rectangular conductors wound on its side

with the insulated strands wound in parallel continuously

along the length of the cylinder, with suitable spacers

inserted between adjacent turns or discs to minimize

circulating currents between the parallel strands.

The coil progresses outwards as a helix resembling that of a

corkscrew. The insulation used to prevent the conductors

shorting together in a transformer is usually a thin layer of

varnish or enamel in air cooled transformers. This thin

varnish or enamel paint is painted onto the wire before it is

wound around the core. In larger power and distribution

transformers the conductors are insulated from each other

using oil impregnated paper or cloth.

The whole core and windings is immersed and sealed in a

protective tank containing transformer oil. The transformer

oil acts as an insulator and also as a coolant.

7.5. Transformer dot orientation

We can not just simply take a laminated core and wrap one

of the coil configurations around it. We could but we may find

that the secondary voltage and current may be out-of-phase

with that of the primary voltage and current. The two coil

windings do have a distinct orientation of one with respect to

the other. Either coil could be wound around the core

clockwise or anticlockwise so to keep track of their relative

orientations "dots" are used to identify a given end of each

winding. This method of identifying the orientation or

direction of a transformers windings is called the "dot

convention". Then a transformer windings are wound so that the

correct phase relations exist between the winding voltages

with the transformers polarity being defined as the relative

polarity of the secondary voltage with respect to the primary

voltage as shown below.

Figure (7.9)


Chapter 7

12

The first transformer shows its two "dots" side by side on the

two windings. The current leaving the secondary dot is "in-

phase" with the current entering the primary side dot. Thus

the polarities of the voltages at the dotted ends are also in-

phase so when the voltage is positive at the dotted end of the

primary coil, the voltage across the secondary coil is also

positive at the dotted end. The second transformer shows the

two dots at opposite ends of the windings which means that the

transformers primary and secondary coil windings are wound in

opposite directions. The result of this is that the current

leaving the secondary dot is 180o "out-of-phase" with the

current entering the primary dot. So the polarities of the

voltages at the dotted ends are also out-of-phase so when the

voltage is positive at the dotted end of the primary coil, the

voltage across the corresponding secondary coil will be

negative. Then the construction of a transformer can be such

that the secondary voltage may be either "in-phase" or "out-

of-phase" with respect to the primary voltage.

In transformers which have a number of different secondary

windings, each of which is electrically isolated from each

other it is important to know the dot polarity of the

secondary windings so that they can be connected together in

series-aiding (secondary voltage is summed) or series-opposing

(the secondary voltage is the difference) configurations.

The ability to adjust the turns ratio of a transformer is

often desirable to compensate for the effects of variations in

the primary supply voltage, the regulation of the transformer

or varying load conditions. Voltage control of the transformer

is generally performed by changing the turns ratio and

therefore its voltage ratio whereby a part of the primary

winding on the high voltage side is tapped out allowing for

easy adjustment.

The tapping is preferred on the high voltage side as the volts

per turn are lower than the low voltage secondary side.

7.6. Transformer primary tap changes

Figure (7.10)

In this simple example, the primary tap changes are calculated

for a supply voltage change of 5%, but any value can be

chosen. Some transformers may have two or more primary or two

or more secondary windings for use in different applications

providing different voltages from a single core.


Chapter 7

13

7.7. Transformer core losses

The ability of iron or steel to carry magnetic flux is

much greater than it is in air, and this ability to allow

magnetic flux to flow is called permeability. Most transformer

cores are constructed from low carbon steels which can have

permeabilities in the order of 1500 compared with just 1.0 for

air. This means that a steel laminated core can carry a

magnetic flux 1500 times better than that of air. However,

when a magnetic flux flows in a transformers steel core, two

types of losses occur in the steel. One termed "eddy current

losses" and the other termed "hysteresis losses".

7.7.1. Hysteresis losses

Transformer Hysteresis Losses are caused because of the

friction of the molecules against the flow of the magnetic

lines of force required to magnetise the core, which are

constantly changing in value and direction first in one

direction and then the other due to the influence of the

sinusoidal supply voltage. This molecular friction causes heat

to be developed which represents an energy loss to the

transformer. Excessive heat loss can overtime shorten the life

of the insulating materials used in the manufacture of the

windings and structures. Therefore, cooling of a transformer

is important. Also, transformers are designed to operate at a

particular supply frequency. Lowering the frequency of the

supply will result in increased hysteresis and higher

temperature in the iron core. So reducing the supply frequency

from 60 Hertz to 50 Hertz will raise the amount of hysteresis

present, decreased the VA capacity of the transformer.

7.7.2. Eddy current losses

Transformer Eddy Current Losses on the other hand are caused

by the flow of circulating currents induced into the steel

caused by the flow of the magnetic flux around the core. These

circulating currents are generated because to the magnetic

flux the core is acting like a single loop of wire.

Since the iron core is a good conductor, the eddy currents

induced by a solid iron core will be large. Eddy currents do

not contribute anything towards the usefulness of the

transformer but instead they oppose the flow of the induced

current by acting like a negative force generating resistive

heating and power loss within the core.

Figure (7.11) laminating the Iron Core


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14

Eddy current losses within a transformer core cannot be

eliminated completely, but they can be greatly reduced and

controlled by reducing the thickness of the steel core.

Instead of having one big solid iron core as the magnetic core

material of the transformer or coil, the magnetic path is

split up into many thin pressed steel shapes called

"laminations".

The laminations used in a transformer construction are very

thin strips of insulated metal joined together to produce a

solid but laminated core as we saw above. These laminations

are insulated from each other by a coat of varnish or paper to

increase the effective resistivity of the core thereby

increasing the overall resistance to limit the flow of the

eddy currents.

The result of all this insulation is that the unwanted induced

eddy current power-loss in the core is greatly reduced, and it

is for this reason why the magnetic iron circuit of every

transformer and other electro-magnetic machines are all

laminated. Using laminations in a transformer construction

reduces eddy current losses. The losses of energy, which

appears as heat due both to hysteresis and to eddy currents in

the magnetic path, is known commonly as "transformer core

losses".

Since these losses occur in all magnetic materials as a result

of alternating magnetic fields. Transformer core losses are

always present in a transformer whenever the primary is

energized, even if no load is connected to the secondary

winding. Also these hysteresis and the eddy current losses are

sometimes referred to as "transformer iron losses", as the

magnetic flux causing these losses is constant at all loads.

7.7.3. Copper losses

But there is also another type of energy loss associated

with transformers called "copper losses". Transformer Copper

Losses are mainly due to the electrical resistance of the

primary and secondary windings.

Most transformer coils are made from copper wire which has

resistance in Ohms, (). This resistance opposes the

magnetizing currents flowing through them. When a load is

connected to the transformers secondary winding, large

electrical currents flow in both the primary and the secondary

windings, electrical energy and power (or the I2 R) losses

occur as heat.

Generally copper losses vary with the load current, being

almost zero at no-load, and at a maximum at full-load when

current flow is at maximum. Transformers with high voltage and

current ratings require conductors of large cross-section to

help minimize their copper losses.

Then we can define an ideal transformer as having:


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1. No Hysteresis loops or Hysteresis losses 0

2. Infinite Resistivity of core material giving zero Eddy

current losses 0

3. Zero winding resistance giving zero I2R copper losses 0

7.8. Transformer loading

In the previous transformer section, we have assumed that

the transformer is ideal, that is one in which there are no

core losses or copper losses in the windings.

However, in real transformers there will always be losses

associated with the transformer loading as the transformer is

put "on-load". But what do we mean by:

7.8.1. Transformer at No-Load

Well first let's look at when the transformer is in a

"no-load" condition that is without a secondary current

flowing.

A transformer is said to be on "no-load" when its secondary

side winding is open circuited, in other words, the

transformer loading is zero.

When an AC sinusoidal supply is connected to the primary

winding of a transformer, a small current, IOPEN will flow

through the primary coil winding due to the presence of the

primary supply voltage. With the secondary circuit open,

nothing connected a back EMF along with the primary winding

resistance acts to limit the flow of this primary current.

Obviously, this no-load primary current (Io) must be

sufficient to maintain enough magnetic field to produce the

required back emf. Consider the circuit below.

Figure (7.12) transformer "No-load"

The ammeter above will indicate a small current flowing

through the primary winding even though the secondary circuit

is open circuited. This no-load primary current is made up of

the following two components:

1. An in-phase current, IE which supplies the core losses (eddy current and hysteresis).

2. A current, IM at 90o to the voltage which sets up the magnetic flux.


Chapter 7

16

Figure (7.13)

Note that this no-load primary current, Io is very small

compared to the transformers normal full-load current. Also

due to the iron losses present in the core as well as a small

amount of copper losses in the primary winding, Io does not

lag behind the supply voltage, Vp by exactly 90o, (cos = 0),

there will be some small phase angle difference.

Example

A single phase transformer has an energy component, IE of 2

Amps and a magnetizing component, IM of 5 Amps. Calculate the

no-load current, Io and resulting power factor.

7.8.2. Transformer On-Load

When an electrical load is connected to the secondary winding

of a transformer and the transformer loading is therefore

greater than zero, current flows in the secondary winding due

to the induced secondary voltage, set up by the magnetic flux

created in the core from the primary current.

This secondary current, IS which is determined by the

characteristics of the load, creates a secondary magnetic

field, S in the transformer core which flows in the exact

opposite direction to the main primary field, P.

These two magnetic fields oppose each other resulting in a

combined magnetic field of less magnetic strength than the

single field produced by the primary winding alone when the

secondary circuit was open circuited. This combined magnetic

field reduces the back EMF of the primary winding causing the

primary current, IP to increase slightly.

The primary current continues to increase until the cores

magnetic field is back at its original strength, and for a

transformer to operate correctly, a balanced condition must

always exist between the primary and secondary magnetic

fields. This results in the power to be balanced and the same


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17

on both the primary and secondary sides. Consider the circuit

below.

Figure (7.14) Transformer "On-load"

We know that the turns ratio of a transformer states that the

total induced voltage in each winding is proportional to the

number of turns in that winding and also that the power output

and power input of a transformer is equal to the volts times

amperes, (V x I). Therefore:

But we also know previously that the voltage ratio of a

transformer is equal to the turns ratio of a transformer as:

"voltage ratio = turns ratio". Then the relationship between

the voltage, current and number of turns in a transformer can

be linked together and is therefore given as:

Where:

NP/NS = VP/VS represents the voltage ratio

NP/NS = IS/IP represents the current ratio

Note that the current is inversely proportional to both the

voltage and the number of turns. This means that with a

transformer loading on the secondary winding, in order to

maintain a balanced power level across the transformers

windings, if the voltage is stepped up, the current must be

stepped down and vice versa. In other words, higher voltage lower current or lower voltage higher current. The total current drawn from the supply by the primary winding is the

vector sum of the no-load current, Io and the additional

supply current, I1 as a result of the secondary transformer


Chapter 7

18

loading and which lags behind the supply voltage by an angle

of . We can show this relationship as a phasor diagram.

Figure (7.15) Transformer Loading Current

If we are given currents, IS and Io, we can calculate the

primary current, IP by the following methods.

Figure (7.16)

Example

A single phase transformer has 1000 turns on its primary

winding and 200 turns on its secondary winding. The

transformers "no-load" current taken from the supply is 3 Amps

at a power factor of 0.2 lagging. Calculate the primary

winding current, IP and its corresponding power factor, when

the secondary current supplying a transformer loading is 280

Amperes at 0.8 lagging.


Chapter 7

19

You may have noticed that the phase angle of the primary

current, P is very nearly the same as that of the secondary

current phase angle, S. This is due to the fact that the no-

load current of 3 amperes is very small compared to the larger

56 amperes drawn by the primary winding from the supply.

Actual real life, transformer windings have impedances of XL

and R.

These impedances need to be taken into account when drawing

the phasor diagrams as these internal impedances cause voltage

drops to occur within the transformers windings.

The internal impedances are due to the resistance of the

windings and an inductance drop called the leakage reactance

resulting from the leakage flux.

These internal impedances are given as:

Figure (7.17)

So the primary and secondary windings of a transformer possess

both resistance and reactance. Sometimes, it can be more

convenient if all these impedances are on the same side of the

transformer to make the calculations easier.

It is possible to move the primary impedances to the secondary

side or the secondary impedances to the primary side. The

combined values of R and L impedances are called "Referred

Impedances" or "Referred Values". The object here is to group

together the impedances within the transformer and have just

one value of R and XL in our calculations as shown.

Figure (7.18) Combining Transformer Impedances


Chapter 7

20

In order to move a resistance from one side of the transformer

to the other, we must first multiply them by the square of the

turns ratio, (Turns Ratio2) in our calculations.

So for example, to move a resistance of 2 from one side to

the other in a transformer that has a turns ratio of 8:1 will

have a new resistive value of: 2 x 82 = 128 's.

Note that if you move a resistance from a higher voltage side

the new resistance value will increase and if you move the

resistance from a lower voltage side its new value will

decrease. This applies to the load resistance and reactance as

well.

7.9. Three phase ideal transformer

Since three-phase is used so often for power distribution

systems, it makes sense that we would need three-phase

transformers to be able to step voltages up or down. This is

only partially true, as regular single-phase transformers can

be ganged together to transform power between two three-phase

systems in a variety of configurations, eliminating the

requirement for a special three-phase transformer. However,

special three-phase transformers are built for those tasks,

and are able to perform with less material requirement, less

size, and less weight than their modular counterparts. A

three-phase transformer is made of three sets of primary and

secondary windings, each set wound around one leg of an iron

core assembly. Essentially it looks like three single-phase

transformers sharing a joined core as in Figure below.

Figure (7.19)

Three phase transformer core has three sets of windings.

Those sets of primary and secondary windings will be connected

in either or Y configurations to form a complete unit. The

various combinations of ways that these windings can be

connected together in will be the focus of this section.

Whether the winding sets share a common core assembly or each

winding pair is a separate transformer, the winding connection

options are the same:

Primary - Secondary

Y - Y

Y

Y

-


Chapter 7

21

The reasons for choosing a Y or configuration for

transformer winding connections are the same as for any other

three-phase application: Y connections provide the opportunity

for multiple voltages, while connections enjoy a higher

level of reliability (if one winding fails open, the other two

can still maintain full line voltages to the load).

Probably the most important aspect of connecting three sets of

primary and secondary windings together to form a three-phase

transformer bank is paying attention to proper winding phasing

(the dots used to denote polarity of windings).

Remember the proper phase relationships between the phase

windings of and Y: (Figure below)

Figure (7.20)

(Y) The center point of the Y must tie either all the - or

all the + winding points together.

() The winding polarities must stack together in a

complementary manner (+ to -).

Getting this phasing correct when the windings aren't shown in

regular Y or configuration can be tricky. Let me illustrate,

starting with Figure below.

Figure (7.21)

Inputs A1, A2, A3 may be wired either or Y, as may

outputs B1, B2, B3. Three individual transformers are to be

connected together to transform power from one three-phase

system to another. First, I'll show the wiring connections for

a Y-Y configuration: Figure below


Chapter 7

22

Figure (7.22)

Phase wiring for Y-Y transformer.

Note in Figure above how all the winding ends marked with dots

are connected to their respective phases A, B, and C, while

the non-dot ends are connected together to form the centers of

each Y. Having both primary and secondary winding sets

connected in Y formations allows for the use of neutral

conductors (N1 and N2) in each power system.

Now, we'll take a look at a Y- configuration: (Figure below)

Figure (7.23)

Phase wiring for Y- transformer.

Note how the secondary windings (bottom set, Figure above) are

connected in a chain, the dot side of one winding connected

to the non-dot side of the next, forming the loop. At

every connection point between pairs of windings, a connection

is made to a line of the second power system (A, B, and C).

Now, let's examine a -Y system in Figure below.

Figure (7.24)

Phase wiring for -Y transformer.


Chapter 7

23

Such a configuration (Figure above) would allow for the

provision of multiple voltages (line-to-line or line-to-

neutral) in the second power system, from a source power

system having no neutral. And finally, we turn to the -

configuration, (Figure below)

Figure (7.25)

Phase wiring for - transformer.

When there is no need for a neutral conductor in the secondary

power system, - connection schemes (Figure above) are

preferred because of the inherent reliability of the

configuration.

Three phase transformer configurations and calculations

In a delta connected group of transformers, the line voltage,

VL is equal to the phase voltage, VL = VPH. But the current in

each phase winding is given as: IL / 3 (or IL = IPH x 3) where

IL is the line current.

In a star connected group of transformers, the line voltage, VL

is equal to 3 the phase voltage, VL = 3VPH. But the current

in each phase winding is given as: IPH = IL where IL is the line

current.

Example of Delta-Delta


Chapter 7

24

Example of Delta-Star

Example of Star-Star

Example of Star-Delta


Chapter 7

25

TR 1:5 1:n

Connection Line Voltage Line Current

Primary Secondary Primary Secondary

-

EL

n*EL

IL

ILn

- 3*n*EL IL3*n

- n*EL ILn

- n*EL3 3*ILn

-

480

5*480=2400

100

1005=20

- 3*480*5=4156 1003*5=11.55

- 5*480=2400 1005=20

- 5*4803=1386 3*1005=34.64

Example 1

150 KVA Delta-Star transformer bank, 480 v primary, 208/120 v

secondary. Calculate, TR, ILP, ILS

Example 2

3 Star-Delta transformer, ELP=6600, ILP=10 A, TR 12:1,

calculate ELS, EphP, and ILS


Chapter 7

26

7.10. Three phase transformer construction

Figure (7.26)

The three-limb core-type three-phase transformer is the most

common method of three-phase transformer construction allowing

the phases to be magnetically linked. Flux of each limb uses

the other two limbs for its return path with the three

magnetic fluxes in the core generated by the line voltages

differing in time-phase by 120 degrees. Thus the flux in the

core remains nearly sinusoidal, producing a sinusoidal

secondary supply voltage.

The shell-type five-limb type three-phase transformer

construction is heavier and more expensive to build than the

core-type. Five-limb cores are generally used for very large

power transformers as they can be made with reduced height.

Shell-type transformers core materials, electrical windings,

steel enclosure and cooling are much the same as for the

larger single-phase types.

7.11. Equivalent circuit of transformer

The performance of a transformer at no load and at load is

influenced by mutual flux, the leakage fluxes, the winding

resistances and the iron losses. For the purpose of

performance evaluation, the effect of these is represented on

an electrical circuit, in the form of resistances and

reactances. Such an electrical circuit is called equivalent

circuit.

In this section, we will develop the equivalent circuit of a

single-phase transformer in the following steps:

(a) Equivalent circuit of an ideal transformer at no load

(b) Equivalent circuit of an ideal transformer on load

(c) Equivalent circuit at load

(d) Equivalent circuit referred to primary side

(e) Approximate equivalent circuit.


Chapter 7

27

7.11.1. Equivalent circuit of an ideal transformer at No

Load

Under certain conditions, the transformer can be treated as an

ideal transformer. The assumptions necessary to treat it as an

ideal transformer are :

(a) Primary and secondary windings have zero resistance. This

means that ohmic loss (I2R loss), and resistive voltage drops

in windings are zero.

(b) There is no leakage flux, i.e. the entire flux is mutual

flux that links both the primary and secondary windings.

(c) Permeability of the core is infinite this means that the

magnetizing current needed for establishing the flux is zero.

(d) Core loss (hysteresis as well as eddy current losses) are

zero.

We have earlier learnt that:

(n is a constant, known as voltage transformation ratio or

turns ratio).

For an ideal transformer, V1 = E1 and E2 = V2.

Even at no load, a transformer draws some active power from

the source to provide the following losses in the core:

(a) Eddy-current loss, and

(b) Hysteresis loss.

The current responsible for the active power is nearly in

phase with V1 (applied voltage) and is known as core-loss

current. A transformer when connected to supply, draws a

current to produce the flux in the core. At no-load, this flux

lags nearly by 90o behind the applied voltage V1. The

magnetizing current, denoted by Im is in phase with the flux

and thus, lags behind the applied voltage by nearly 90o.

The phasor sum of the core loss component of current Ic and the

magnetizing current Im is equal to the no-load current I0.

Ic = I0 cos 0 and Im = I0 sin 0

Core loss = P0 = V1 I0 (cos 0)

Where 0 is the phase angle between V1 and I0, and, (cos 0) is the no load power factor.

The phase relationship between applied voltage V1, no-load

current I0, and its components Ic, Im is shown in Fig 7.27(a).


Chapter 7

28

Figure (7.27)

In the form of equivalent circuit, this can be represented as

Fig 7.27(b), in which Rc is a resistance representing core loss

and Xm is an inductive reactance (called magnetizing

reactance).

Note that the current in the resistance is in phase with V1 and

Xm being an inductive reactance, the current Im in this branch

lags V1 by 90o as shown in the phasor diagram of Fig 7.27(a).

(The representation in Fig 7.27, assumes that V1 = E1 (equal to

and in opposition to V1).

This implies that the primary winding resistance and leakage

reactance are neglected.

Similarly, in the secondary winding of transformer mutually

induced emf is antiphase with V1 and its magnitude is

proportional to the rate of change of flux and the number of

secondary turns. (You will learn about the concept of leakage

reactance when you study about the equivalent circuit at

load).

The equivalent circuit parameters Rc and Xm can also be

expressed as conductance and susceptance Gc, Bm such that


Chapter 7

29

Example

At no-load a transformer has a no-load loss of 50 W, draws a

current of 2A (RMS) and has an applied voltage of 230V (RMS).

Determine:

(i) no-load power factor, (ii) core loss current, and (iii) magnetizing current. Also, calculate the no-load circuit parameter (Rc, Xm) of the transformer.

Solution

Pc = 40 W, Io = 2 A, E1 = 230 V

Pc = V1 Io coso

Magnetizing current,

Im = I0 sino

= 2 sin(83.76o)

= 1.988 A

Core-loss current,

Ic = Io coso

= 2 0.108

= 0.216 A

This equivalent circuit is shown below.


Chapter 7

30

7.11.2. Equivalent circuit of an ideal transformer On Load

Under certain conditions the transformer can be

treated as an ideal transformer. The idealizing assumptions

are listed below

(a) Both primary and secondary windings have zero resistance.

This means, no ohmic power loss and no resistive voltage

drop.

(b) No leakage flux, i.e. all the flux produced is confined to

the core and links both the windings

(c) Infinite permeability of the core. This means no zero

magnetizing current is needed to establish the requisite

amount of flux in the core, i.e. Im = 0.

(d) Core-loss (hysteresis as well as eddy-current loss) is

zero, i.e. Ic = 0.

Assumptions (a), (b) and (d) mean that copper losses, and

iron losses being zero, the efficiency of the transformer

is 100%. Since Im = Ic = 0, Io = 0.

Figure (7.28)

As per earlier derived equation

where, V1 is supply voltage and V2 is voltage across load

terminals.

When load is applied, let the impedance of load be ZL, as shown

in Fig (7.28) Sinusoidal current i2 flows through the

secondary.

Therefore, secondary winding creates an mmf F2 = N2i2 which

opposes the flux .

But mutual flux is invariant with respect to load (otherwise

V1 = e1 balance is disturbed).

As a result, the primary winding starts drawing a current i1

from the source so as to create mmf F1 = N1i1 which at all

times cancels out the load-caused mmf N2i2 so that is

maintained constant independent of the magnitude of the load


Chapter 7

31

current which flows in the secondary winding. This implies

that for higher load, more power will be drawn from the supply

(Instantaneous power into primary) = (Instantaneous power out

of secondary)

In terms of rms values,

i.e. VA output = VA input, i.e. V1I1 = V2I2

The circuit representation of Fig (7.28), can be simplified by

referring the load impedance and secondary current to the

primary side. From Fig (7.28), we see that

V2 = I2ZL

Where

is said to be the load impedance referred to the primary side.

From V2 = I2 ZL we can also easily obtain V2 = I2 ZL

Where

is secondary terminal voltage referred to primary side, and

is secondary current referred to primary side.

In the ideal transformer, I1 = I2 and V1 = V2.

7.11.3. Equivalent circuit of a real transformer

In real conditions, in addition to the mutual flux which links

both the primary and secondary windings transformer, has a

component of flux, which links either the primary winding or

the secondary, but not both.

This component is called leakage flux. The flux which links

only with primary is called primary leakage flux, and the flux

which links only with secondary is called secondary leakage

flux. Fig 7.28 shows schematically the mutual and the leakage

flux.


Chapter 7

32

From our knowledge of magnetic circuits, we know that a flux

lining with a winding is the cause of inductance of the

winding (Inductance = Flux linkage per ampere).

Since in a transformer the flux is alternating, its flux

linkage gives rise to an induced voltage in the winding. Thus,

primary leakage flux (which is proportional to I1) causes an

induced voltage, which acts as a voltage drop.

Similarly for the secondary leakage flux. The effect of these

induced EMFs are, therefore, represented as inductive leakage

reactances Xl1, Xl2.

Xl1 and Xl2 are called leakage reactances of the primary and

secondary respectively. These are also denoted as X1, X2.

The windings of the transformer have resistance R1, R2. These

resistances cause a voltage drop I1R1 and I2R2, as also ohmic

loss I12R1 and I2

2R2.

To sum up, in a Real Transformer,

(a) Both the primary and secondary windings possesses resistance. As a result, the value of actual impressed

voltage across the transformer is the voltage V1 less the

drop across the resistance R1. Moreover, the copper loss in

the primary winding is I21R1 and in the secondary winding

I22R1.

(b) A Real Transformer has some leakage flux, as shown in the

Fig 7.28 These fluxes, as discussed earlier, lead to self-

reactances Xl1 and Xl2 for the two windings respectively.

(c) The magnetizing current cannot be zero. Its value is

determined by the mutual flux m. The mutual flux also

determines core-loss taking place in the iron parts of the

transformer. The value of Io does not depend on load and

hence the iron-loss or core-loss is constant which is not

zero.

Considering the effects of resistances and leakage reactances,

a transformer can be visualized as shown in Fig 7.29.

Figure (7.29) Representation of transformer showing leakage

reactances

In the form of equivalent circuit, this can be represented as

in Fig 7.30.


Chapter 7

33

Figure (7.30) Exact equivalent circuit of real transformer

The use of this equivalent circuit is difficult and

calculations involved are laborious. For most practical

purposes (like calculations of voltage regulation and

efficiency) we need only a simplified form of equivalent

circuit. We will now proceed to first obtain a simplified

equivalent circuit and then to obtain an approximate

equivalent circuit.

Equivalent Circuit Referred to Primary Side

We will now refer the impedance R2 + jXl2 to the primary side

i.e. to the left hand side of the ideal transformer. We have

seen earlier that a load impedance ZL can be referred to

primary side as Z'L, where

Similarly Z2 = R2 + jXl2 can be referred to the primary side as

where Z'2 is said to be the secondary winding impedance

referred to the primary side.

Eq. (4) can be re-written as

Equating real and imaginary parts

R'2 is the secondary winding resistance referred to primary,

and X'l2 is the secondary winding leakage reactance referred to

primary side.

Fig (7.30) can now be modified (i.e. referring the secondary

resistance and reactance to the primary side) to get the

equivalent circuit shown in Fig (7.31)


Chapter 7

34

Figure (7.31) Exact Circuit with secondary parameters referred

to primary side

The secondary terminal voltage V2 and secondary current I2 can

also be referred to the primary side using the relations.

These referred quantities V'2 and I'2 are also marked in Fig

(7.31)

7.11.4. Approximate equivalent circuit of transformer

Transformers which are used at a constant power frequency (say

50 Hz), can have very simplified approximate equivalent

circuits, without having a substantial effect on the

performance evaluation (efficiency and voltage regulation).

It should be borne in mind that higher the VA or KVA rating

of the transformers, better are the approximation-based

evaluation results.

It is assumed that V1 ~ E1 (V1 is approximately equal to E1)

even under conditions of load.

This assumption is justified because the values of winding

resistance and leakage reactances are very small. Therefore,

the exciting current drawn by the parallel combination of

conductance Gc and susceptance Bm would not be affected

significantly by shifting it to the input terminals. With this

change, the equivalent circuit becomes as shown in Fig (7.32).

Figure (7.32) Equivalent circuit referred to primary side


Chapter 7

35

Denoting

R1 + R'2 = R'eq

and

Xl2 + X'l2 = X'eq

The equivalent circuit becomes as shown in Fig (7.33) R'eq, X'eq

are called the equivalent resistance and equivalent reactance

referred to primary side.

Figure (7.33) Approximate Equivalent Circuit

If only voltage regulation is to be calculated even the

excitation branch can be neglected and the equivalent circuit

becomes as shown in Fig (7.34).

Figure (7.34) Most simplified form of approximate equivalent

circuit

7.12. Losses and efficiency of transformer

A transformer doesn't contain any rotating part so it is

free from friction and windage losses. In transformer the

losses occur in iron parts as well as in copper coils. In iron

core the losses are sum of hysteresis and eddy current losses.

The hysteresis losses are Ph fBxmax and eddy current loss is

equal to Pe a f2Bmax.

Where f is frequency Bmax is maximum flux density.

We know that the maximum flux density is directly proportional

to applied voltage so, if the applied voltage is constant then


Chapter 7

36

the flux density is constant and the hysterises losses are

proportional to f and eddy current losses are proportional to

f2.

7.12.1 Iron losses or core losses

To minimize hysteresis loss in transformer, we use Cold Rolled

Grain Oriented (CRGO) silicon steel to build up the iron core.

Eddy current loss

When the primary winding variable flux links with iron core

then it induces some EMF on the surface of core. The

magnitude of EMF is different at various points in core. So,

there is current between different points in Iron Core having

unequal potential.

These currents are known at eddy currents. I2R loss in iron

core is known as eddy current loss.

These losses depend on thickness of core. To minimize the

eddy current losses we use the Iron Core which is made of

laminated sheet stampings. The thickness of stamping is

around 0.5 mm.

Determination of iron or core losses

Practically we can determine the iron losses by performing

the open circuit test.

Open circuit test

We perform open circuit test in low voltage winding in

transformer keeping the high voltage winding open.

The circuit is connected as shown in Fig (7.35). The

instruments are connected on the LV side. The advantage of

performing the test from LV side is that the test can be

performed at rated voltage.

When we apply rated voltage then watt meter shows iron losses

[There is some copper loss but this is negligible when

compared to iron loss]. The ammeter shows no load current I0

which is very small [2-5 % of rated current]. Thus, the drops

in R1 and Xl1 can be neglected.

Figure (7.35) Open Circuit Test

We have

Wo = iron loss


Chapter 7

37

Io = no load current

Under no load conditions the PF is very low (near to 0) in

lagging region.

By using the above data we can draw the equivalent parameter

shown in Fig (7.36).

Figure (7.36) No Load equivalent circuit from Open Circuit

test

Example

At no load test, a transformer draws a current of 0.2 Ampere

lagging behind the applied voltage by 80o, when the low

voltage winding of the transformer is connected to a 500 V

source. Calculate:

(a) iron loss and

(b) components of the no load current.

Solution

We have V1 = 500 V, Io = 0.2 A and o = 80o

cos80o = 0.1736

PF = cosf ~ 0.174 lagging

(a) Iron loss = V1Iocos = 500 0.2 0.174 = 17.4 watts

(b) Components of no load current

Ic = Iocos = 0.0348 A

Im = Io sin = 0.197 A or Im = I2o I

2c = 0.197


Chapter 7

38

7.12.2. Copper losses

In a transformer the primary and secondary winding

currents increase with increases in load. Due to these

currents there is some I2R losses. These are known as copper

losses or ohmic losses. The total I2R loss in both windings at

rated or full load current is equal to I12R1+I2

2R2

[assuming I'1 = I1 , i.e. shunt branch neglected].

= I12Ro1

Similarly, it can be shown that

Copper loss = I22Ro2

Here I1 and I2 are primary and secondary current. R1 is primary

winding resistance and R2 is secondary winding resistance.

R01 is total resistance of winding referred to primary

Ro2 is total resistance of windings referred to secondary.

By performing short circuit test we find out copper loss

experimentally.

7.12.3. Short circuit test

Its an indirect method to find out the copper losses. To

perform this test, we apply a reduced voltage to the primary

winding through instruments keeping LV winding short

circuited. The connections are shown in Figure (7.37a).

We need to apply only 5-10% of rated voltage to primary to

circulated rated current in the primary and secondary winding.

The applied voltage is adjusted so that the ammeter shows

rated current of the winding.

Under this condition, the watt-meter reading shows the copper

losses of the transformer. Because of low value of applied

voltage, iron losses, are very small and can be neglected.

As applied voltage is very small, small voltage across the

excitation branch produces very small percentage of exciting

current in comparison to its full load current and can

therefore, be safely ignored. As a result, equivalent circuit

with secondary short circuited can be represented as Fig

(7.37b).


Chapter 7

39

Figure (7.37)

At a rated current watt meter shows full load copper loss. We

have:

Vs = applied voltage

Is = rated current

Ws = copper loss

So we calculate equivalent reactance:

These Req and Xeq are equivalent resistance and reactance of

both windings referred in HV side. These are known as

equivalent circuit resistance and reactance.

7.12.4. Efficiency of single phase transformer

Generally we define the efficiency of any machine as a

ratio of output power to the input power, i.e.

7.13. Current transformer

The Current Transformer (C.T.), is a type of "instrument

transformer" that is designed to produce an alternating


Chapter 7

40

current in its secondary winding which is proportional to the

current being measured in its primary. Current transformers

reduce high voltage currents to a much lower value and provide

a convenient way of safely monitoring the actual electrical

current flowing in an AC transmission line using a standard

ammeter. The principal of operation of a current transformer

is no different from that of an ordinary transformer.

Figure (7.38)

Typical Current Transformer Unlike the voltage or power

transformer looked at previously, the current transformer

consists of only one or very few turns as its primary winding.

This primary winding can be of either a single flat turn, a

coil of heavy duty wire wrapped around the core or just a

conductor or bus bar placed through a central hole as shown.

Due to this type of arrangement, the current transformer is

often referred too as a "series transformer" as the primary

winding, which never has more than a very few turns, is in

series with the current carrying conductor.

The secondary winding may have a large number of coil turns

wound on a laminated core of low-loss magnetic material which

has a large cross-sectional area so that the magnetic flux

density is low using much smaller cross-sectional area wire,

depending upon how much the current must be stepped down. This

secondary winding is usually rated at a standard 1 Ampere or 5

Amperes.

There are three basic types of current transformers: "wound",

"toroidal" and "bar".

Wound current transformers

The transformers primary winding is physically connected in

series with the conductor that carries the measured current

flowing in the circuit. The magnitude of the secondary

current is dependent on the turns ratio of the transformer.

Toroidal current transformers

These do not contain a primary winding. Instead, the line

that carries the current flowing in the network is threaded

through a window or hole in the toroidal transformer. Some

current transformers have a "split core" which allows it to


Chapter 7

41

be opened, installed, and closed, without disconnecting the

circuit to which they are attached.

Bar-type current transformers

This type of current transformer uses the actual cable or

bus-bar of the main circuit as the primary winding, which is

equivalent to a single turn. They are fully insulated from

the high operating voltage of the system and are usually

bolted to the current carrying device.

Current transformers can reduce or "step-down" current levels

from thousands of amperes down to a standard output of a

known ratio to either 5 Amps or 1 Amp for normal operation.

Thus, small and accurate instruments and control devices can

be used with CT's because they are insulated away from any

high-voltage power lines. There are a variety of metering

applications and uses for current transformers such as with

wattmeter's, power factor meters, watt-hour meters,

protective relays, or as trip coils in magnetic circuit

breakers, or MCB's.

Figure (7.38) Current transformer

Generally current transformers and ammeters are used together

as a matched pair in which the design of the current

transformer is such as to provide a maximum secondary current

corresponding to a full-scale deflection on the ammeter.

In most current transformers an approximate inverse turns

ratio exists between the two currents in the primary and

secondary windings. This is why calibration of the CT is

generally for a specific type of ammeter. For most current

transformers the primary and secondary currents are expressed

as a ratio such as 100/5.

This means that when 100 Amps is flowing in the primary

winding it will result in 5 Amps flowing in the secondary

winding. By increasing the number of secondary windings, N2,

the secondary current can be made much smaller than the


Chapter 7

42

current in the primary circuit being measured. In other

words, as N2 increases, I2 goes down by a proportional

amount. We know from our tutorial on double wound

transformers that its turns ratio is equal to:

As the primary usually consists of one or two turns whilst

the secondary can have several hundred turns, the ratio

between the primary and secondary can be quite large. For

example, assume that the current rating of the primary

winding is 100A. The secondary winding has the standard

rating of 5A. Then the ratio between the primary and the

secondary currents is 100A-to-5A, or 20:1.

In other words, the primary current is 20 times greater than

the secondary current.

It should be noted however, that a current transformer rated

as 100/5 is not the same as one rated as 20/1 or subdivisions

of 100/5. This is because the ratio of 100/5 expresses the

"input/output current rating" and not the actual ratio of the

primary to the secondary currents.

Also note that the number of turns and the current in the

primary and secondary windings are related by an inverse

proportion. But relatively large changes in current

transformers turns ratio can be achieved by modifying the

primary turns through the CT's window where one primary turn

is equal to one pass and more than one pass through the

window results in the electrical ratio being modified.

So for example, a current transformer with a relationship of

say, 300/5 A can be converted to another of 150/5 A or even

100/5 A by passing the main primary conductor through its

interior window two or three times as shown.

This allows a higher value current transformer to provide the

maximum output current for the ammeter when used on smaller

primary current lines.

Figure (7.39) Current transformer primary Turns Ratio


Chapter 7

43

Example

A bar-type current transformer which has 1 turn on its primary

and 160 turns on its secondary is to be used with a standard

range of ammeters that have an internal resistance of 0.2 .

The ammeter is required to give a full scale deflection when

the primary current is 800 Amps. Calculate the maximum

secondary current and secondary voltage across the ammeter.

We can see above that since the secondary of the current

transformer is connected across the ammeter, which has a very

small resistance, the voltage drop across the secondary

winding is only 1.0 volts at full primary current.

If the ammeter is removed, the secondary winding becomes open-

circuited and the transformer acts as a step-up transformer

resulting in a very high voltage equal to the ratio of:

Vp(Ns/Np) being developed across the secondary winding.

So for example, assume our current transformer from above is

connected to a 480 volt three-phase power line.

Therefore:

This is why a current transformer should never be open

circuited or operated with no-load attached when the main

primary current is flowing.

If the ammeter is to be removed, a short-circuit should be

placed across the secondary terminals first. This is because

when the secondary is open-circuited the iron core of the

transformer operates at a high degree of saturation, which

produces an abnormally large secondary voltage, and in our

simple example above, this was calculated at 76.8 kV!. This

high secondary voltage could damage the insulation or cause

electric shock if the CT's terminals are accidentally touched.

Handheld Current Transformers

There are many specialized types of current transformers now

available. A popular and portable type which can be used to

measure circuit loading are called "clamp meters" as shown

below.

Clamp meters open and close around a current carrying

conductor and measure its current by determining the magnetic

field around it, providing a quick measurement reading usually

on a digital display without disconnecting or opening the

circuit.

As well as the handheld clamp type CT, split core current

transformers are available which has one end removable so that


Chapter 7

44

the load conductor or bus bar does not have to be disconnected

to install it.

These are available for measuring currents from 100 up to 5000

amps, with square window sizes from 1" to over 12" (25 to 300

mm).

Then to summarize, the Current Transformer, (CT) is a type of

instrument transformer used to convert a primary current into

a secondary current through a magnetic medium. Its secondary

winding then provides a much reduced current which can be used

for detecting overcurrent, undercurrent, peak current, or

average current conditions.

A current transformers primary coil is always connected in

series with the main conductor giving rise to it also being

referred to as a series transformer. The nominal secondary

current is rated at 1 A or 5 A for ease of measurement.

Construction can be one single primary turn as in Toroidal,

Donut, or Bar types, or a few wound primary turns, usually for

low current ratios.

Current transformers are intended to be used as proportional

current devices. Therefore a current transformers secondary

winding should never be operated into an open circuit, just as

a voltage transformer should never be operated into a short

circuit. Very high voltages will result from open circuiting

the secondary circuit of an energized CT so their terminals

must be short-circuited if the ammeter is to be removed or

when a CT is not in use before powering up the system.

7.14. Autotransformer

Autotransformer Basics

Unlike the previous voltage transformer which has two

electrically isolated windings, the primary and the secondary.

An Autotransformer has only one single voltage winding which

is usually "tapped" at various points along it to provide a

percentage of the primary voltage supply across its secondary

load.

The autotransformer has the usual magnetic core but only one

winding, which is common to both the primary and secondary

circuits.


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45

Therefore in an autotransformer the primary and secondary

windings are both linked together electrically and

magnetically. This type of transformer design is a lot cheaper

but the main disadvantage of an autotransformer is that it

does not have the primary/secondary winding isolation of a

conventional double wound transformer.

The section of winding designated as the primary part of the

winding is connected to the AC power source with the secondary

being part of this primary winding.

An autotransformer can also be used to step the supply voltage

up or down by reversing the connections. If the primary is the

total winding and is connected to a supply, and the secondary

circuit is connected across only a portion of the winding,

then the secondary voltage is "stepped-down" as shown.

Figure (7.40) Autotransformer design

When the primary current IP is flowing through the single

winding in the direction of the arrow as shown, the secondary

current, IS, flows in the opposite direction. Therefore, in the

portion of the winding that generates the secondary voltage, VS

the current flowing out of the winding is the difference of IP

and IS.

The Autotransformer can also be constructed with more than one

single tapping point. Autotransformers can be used to provide

different voltage points along its winding or increase its

supply voltage with respect to its supply voltage VP as shown.

Figure (7.41) Autotransformer with multiple tapping points


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46

The standard method for marking an auto-transformer windings

is to label it with capital (upper case) letters. So for

example, A, B, Z etc to identify the supply end. Generally the

common neutral connection is marked as N or n.

For the secondary tapings, suffix numbers are used for all

tapping points along the auto-transformers primary winding.

These numbers generally start at number 1 and continue in

ascending order for all tapping points as shown.

Figure (7.41) Autotransformer terminal markings

An autotransformer is used mainly for the adjustments of line

voltages to either change its value or to keep it constant. If

the voltage adjustment is by a small amount, either up or

down, then the transformer ratio is small as VP and VS are

nearly equal.

Currents IP and IS are also nearly equal. Therefore, the

portion of the winding which carries the difference between

the two currents can be made from a much smaller conductor

size, since the currents are much smaller saving on the cost

of an equivalent double wound transformer.

However, the regulation, leakage inductance and physical size

(since there is no second winding) of an autotransformer for a

given VA or KVA rating are less than for a double wound

transformer. Autotransformers are clearly much cheaper than

conventional double wound transformers of the same VA rating.

When deciding upon using an autotransformer it is usual to

compare its cost with that of an equivalent double wound type.

This is done by comparing the amount of copper saved in the

winding. If the ratio "n" is defined as the ratio of the lower

voltage to the higher voltage, then it can be shown that the

saving in copper is: n.100%. For example, the saving in copper

for the two autotransformers would be:


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47

Example

An autotransformer is required to step-up a voltage from 220

volts to 250 volts. The total number of coil turns on the

transformer main winding is 2000. Determine the position of

the primary tapping point, the primary and secondary currents

when the output is rated at 10KVA and the economy of copper

saved.

Then the primary current is 45.4 amperes, the secondary

current drawn by the load is 40 amperes and 5.4 amperes flows

through the common winding. The economy of copper is 88%.

Disadvantages of an Autotransformer

1. The main disadvantage of an autotransformer is that it does not have the primary to secondary winding isolation of a

conventional double wound transformer.

Then autotransformer's can not safely be used for stepping

down higher voltages to much lower voltages suitable for

smaller loads.

2. If the secondary side winding becomes open-circuited, current stops flowing through the primary winding stopping

the transformer action resulting in the full primary voltage

being applied to the secondary circuit.

3. If the secondary circuit suffers a short-circuit condition, the resulting primary current would be much larger than an

equivalent double wound transformer due to the increased

flux linkage damaging the autotransformer.

4. Since the neutral connection is common to both the primary and secondary windings, earthing of the secondary winding

automatically earths the primary as there is no isolation


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48

between the two windings. Double wound transformers are

sometimes used to isolate equipment from earth.

The autotransformer has many uses and applications including

the starting of induction motors, used to regulate the voltage

of transmission lines, and can be used to transform voltages

when the primary to secondary ratio is close to unity. An

autotransformer can also be made from conventional two-winding

transformers by connecting the primary and secondary windings

together in series and depending upon how the connection is

made, the secondary voltage may add to, or subtract from, the

primary voltage

Chapter 07 Transformer

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