Electrical Machines - i

Transformers

1 Introduction

Michael Faraday propounded the principle of electro-magnetic induction in 1831.

It states that a voltage appears across the terminals of an electric coil when the flux linked

with the same changes. The magnitude of the induced voltage is proportional to the rate of

change of the flux linkages. This finding forms the basis for many magneto electric machines.

The earliest use of this phenomenon was in the development of induction coils. These coils

were used to generate high voltage pulses to ignite the explosive charges in the mines. As

the d.c. power system was in use at that time, very little of transformer principle was made

use of. In the d.c. supply system the generating station and the load center have to be

necessarily close to each other due to the requirement of economic transmission of power.

Also the d.c. generators cannot be scaled up due to the limitations of the commutator. This

made the world look for other efficient methods for bulk power generation and transmis-

sion. During the second half of the 19th century the alternators, transformers and induction

motors were invented. These machines work on alternating power supply. The role of the

transformers became obvious. The transformer which consisted of two electric circuits linked

by a common magnetic circuit helped the voltage and current levels to be changed keeping

the power invariant. The efficiency of such conversion was extremely high. Thus one could

choose a moderate voltage for the generation of a.c. power, a high voltage for the transmis-

sion of this power over long distances and finally use a small and safe operating voltage at

the user end. All these are made possible by transformers. The a.c. power systems thus got

well established.

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Transformers can link two or more electric circuits. In its simple form two electric

circuits can be linked by a magnetic circuit, one of the electric coils is used for the creation

of a time varying magnetic filed. The second coil which is made to link this field has an

induced voltage in the same. The magnitude of the induced emf is decided by the number

of turns used in each coil. Thus the voltage level can be increased or decreased by changing

the number of turns. This excitation winding is called a primary and the output winding

is called a secondary. As a magnetic medium forms the link between the primary and the

secondary windings there is no conductive connection between the two electric circuits. The

transformer thus provides an electric isolation between the two circuits. The frequency on

the two sides will be the same. As there is no change in the nature of the power, the re-

sulting machine is called a ‘transformer’ and not a ‘converter’. The electric power at one

voltage/current level is only ‘transformed’ into electric power, at the same frequency, to an-

other voltage/current level.

Even though most of the large-power transformers can be found in the power systems,

the use of the transformers is not limited to the power systems. The use of the principle

of transformers is universal. Transformers can be found operating in the frequency range

starting from a few hertz going up to several mega hertz. Power ratings vary from a few

milliwatts to several hundreds of megawatts. The use of the transformers is so wide spread

that it is virtually impossible to think of a large power system without transformers. Demand

on electric power generation doubles every decade in a developing country. For every MVA

of generation the installed capacity of transformers grows by about 7MVA. These figures

show the indispensable nature of power transformers.

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Indian Institute of Technology Madras

2 Basic Principles

As mentioned earlier the transformer is a static device working on the principle of

Faraday’s law of induction. Faraday’s law states that a voltage appears across the terminals

of an electric coil when the flux linkages associated with the same changes. This emf is

proportional to the rate of change of flux linkages. Putting mathematically,

e =dψ

dt(1)

Where, e is the induced emf in volt and ψ is the flux linkages in Weber turn. Fig. 1 shows a

Figure 1: Flux linkages of a coil

coil of N turns. All these N turns link flux lines of φ Weber resulting in the Nφ flux linkages.

In such a case,

ψ = Nφ (2)

and

e = Ndφ

dtvolt (3)

The change in the flux linkage can be brought about in a variety of ways

• coil may be static and unmoving but the flux linking the same may change with time.

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• flux lines may be constant and not changing in time but the coil may move in space

linking different value of flux with time.

• both 1 and 2 above may take place. The flux lines may change in time with coil moving

in space.

These three cases are now elaborated in sequence below, with the help of a coil with a simple

geometry.

L

B

X

+-

Figure 2: Static coil

Fig. 2 shows a region of length L m, of uniform flux density B Tesla, the

flux lines being normal to the plane of the paper. A loop of one turn links part of this flux.

The flux φ linked by the turn is L ∗B ∗X Weber. Here X is the length of overlap in meters

as shown in the figure. If now B does not change with time and the loop is unmoving then

no emf is induced in the coil as the flux linkages do not change. Such a condition does not

yield any useful machine. On the other hand if the value of B varies with time a voltage is

induced in the coil linking the same coil even if the coil does not move. The magnitude of B

4





is assumed to be varying sinusoidally, and can be expressed as,

B = Bm sinωt (4)

where Bm is the peak amplitude of the flux density. ω is the angular rate of change with

time. Then, the instantaneous value of the flux linkage is given by,

ψ = Nφ = NLXBm sinωt (5)

The instantaneous value of the induced emf is given by,

e =dψ

dt= Nφm.ω cosωt = Nφm.ω. sin(ωt+

π

2) (6)

Here φm = Bm.L.X. The peak value of the induced emf is

em = Nφm.ω (7)

and the rms value is given by

E =Nφm.ω√

2volt.

Further, this induced emf has a phase difference of π/2 radian with respect to the

flux linked by the turn. This emf is termed as ‘transformer’ emf and this principle is used

in a transformer. Polarity of the emf is obtained by the application of Lenz’s law. Lenz’s

law states that the reaction to the change in the flux linkages would be such as to oppose

the cause. The emf if permitted to drive a current would produce a counter mmf to oppose

this changing flux linkage. In the present case, presented in Fig. 2 the flux linkages are

assumed to be increasing. The polarity of the emf is as indicated. The loop also experiences

a compressive force.

Fig. 2(b) shows the same example as above but with a small difference. The flux

density is held constant at B Tesla. The flux linked by the coil at the current position is

5





φ = B.L.X Weber. The conductor is moved with a velocity v = dx/dt normal to the flux,

cutting the flux lines and changing the flux linkages. The induced emf as per the application

of Faraday’s law of induction is e = N.B.L.dx/dt = B.L.v volt.(Here N=1)

Please note,the actual flux linked by the coil is immaterial. Only the change in the

flux linkages is needed to be known for the calculation of the voltage. The induced emf is

in step with the change in ψ and there is no phase shift. If the flux density B is distributed

sinusoidally over the region in the horizontal direction, the emf induced also becomes sinu-

soidal. This type of induced emf is termed as speed emf or rotational emf, as it arises out of

the motion of the conductor. The polarity of the induced emf is obtained by the application

of the Lenz’s law as before. Here the changes in flux linkages is produced by motion of the

conductor. The current in the conductor, when the coil ends are closed, makes the conductor

experience a force urging the same to the left. This is how the polarity of the emf shown in

fig.2b is arrived at. Also the mmf of the loop aids the field mmf to oppose change in flux

linkages. This principle is used in d.c machines and alternators.

The third case under the application of the Faraday’s law arises when the flux changes

and also the conductor moves. This is shown in Fig. 2(c).

The uniform flux density in space is assumed to be varying in magnitude in time as

B = Bm sinωt. The conductor is moved with a uniform velocity of dx

dt= v m/sec. The

change in the flux linkages and hence induced emf is given by

e = N.d(Bm. sinωt.L.X)

dt= N.L.X.Bm.ω. cosωt.+N.Bm. sinωt.L.

dx

dtV olt. (8)

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The first term is due to the changing flux and hence is a transformer emf. The second

term is due to moving conductor or is a speed emf. When the terminals are closed such as

to permit a current the conductor experiences a force and also the mmf of the coil opposes

the change in flux linkages. This principle is used in a.c. machines where the field is time

varying and conductors are moving under the same.

The first case where there is a time varying field and a stationary coil resulting in

a transformer emf is the subject matter in the present section. The case two will be re-

visited under the study of the d.c machines and synchronous machines. Case three will be

extensively used under the study of a.c machines such as induction machines and also in a.c.

commutator machines.

Next in the study of the transformers comes the question of creating a time varying

filed. This is easily achieved by passing a time varying current through a coil. The winding

which establishes the field is called the primary. The other winding, which is kept in that

field and has a voltage induced in it, is called a secondary. It should not be forgotten that

the primary also sees the same time varying field set up by it linking its turns and has an

induced emf in the same. These aspects will be examined in the later sections. At first

the common constructional features of a transformer used in electric power supply system

operating at 50 Hz are examined.

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3 Constructional features

Transformers used in practice are of extremely large variety depending upon the

end use. In addition to the transformers used in power systems, in power transmission and

distribution, a large number of special transformers are in use in applications like electronic

supplies, rectification, furnaces, traction etc. Here the focus is on power transformers only.

The principle of operation of these transformers also is the same but the user requirements

differ. Power transformers of smaller sizes could be air cooled while the larger ones are

oil cooled. These machines are highly material intensive equipments and are designed to

match the applications for best operating conditions. Hence they are ‘tailor made’ to a

job. This brings in a very large variety in their constructional features. Here more common

constructional aspects alone are discussed. These can be broadly divided into

1. Core construction

2. Winding arrangements

3. Cooling aspects

3.1 Core construction

Transformer core for the power frequency application is made of highly permeable

material. The high value of permeability helps to give a low reluctance for the path of

the flux and the flux lines mostly confine themselves to the iron. Relative permeability µr

well over 1000 are achieved by the present day materials. Silicon steel in the form of thin

laminations is used for the core material. Over the years progressively better magnetic prop-

erties are obtained by going in for Hot rolled non-oriented to Hot rolled grain oriented steel.

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Later better laminations in the form of cold Rolled Grain Oriented (CRGO), -High B (HiB)

grades became available. The thickness of the laminations progressively got reduced from

over 0.5mm to the present 0.25mm per lamination. These laminations are coated with a thin

layer of insulating varnish, oxide or phosphate. The magnetic material is required to have

a high permeability µ and a high saturation flux density, a very low remanence Br and a

small area under the B-H loop-to permit high flux density of operation with low magnetizing

current and low hysteresis loss. The resistivity of the iron sheet itself is required to be high

to reduce the eddy current losses. The eddy current itself is highly reduced by making the

laminations very thin. If the lamination is made too thin then the production cost of steel

laminations increases. The steel should not have residual mechanical stresses which reduce

their magnetic properties and hence must be annealed after cutting and stacking.

In the case of very small transformers (from a few volt-amperes to a few kilo volt-

amperes) hot rolled silicon steel laminations in the form of E & I, C & I or O as shown in

Fig. 3 are used and the core cross section would be a square or a rectangle. The percentage

of silicon in the steel is about 3.5. Above this value the steel becomes very brittle and also

very hard to cut. The saturation flux density of the present day steel lamination is about 2

Tesla.

Broadly classifying, the core construction can be separated into core type and

shell type. In a core type construction the winding surrounds the core. A few examples of

single phase and three phase core type constructions are shown in Fig. 4. In a shell type on

the other hand the iron surrounds the winding.

In the case of very small transformers the conductors are very thin and round.

These can be easily wound on a former with rectangular or square cross section. Thus no

special care is needed for the construction of the core. The cross section of the core also

would be square or rectangular. As the rating of the transformer increases the conductor size

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(a ) (b)

(c)

Figure 3: E and I,C and I and O Type Laminations

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HV LVHVLV

coreHVLV

Single phase Three phase

1.phase

3.phase

(a)Core type (b) Shell type

Figure 4: Core and Shell Type Construction

also increases. Flat conductors are preferred to round ones. To wind such conductor on a

rectangular former is not only difficult but introduces stresses in the conductor, at the bends.

From the short circuit force with stand capability point of view also this is not desirable.

Also, for a given area enclosed the length of the conductor becomes more. Hence it results in

more load losses. In order to avoid all these problems the coils are made cylindrical and are

wound on formers on heavy duty lathes. Thus the core construction is required to be such as

to fill the circular space inside the coil with steel laminations. Stepped core construction thus

becomes mandatory for the core of large transformers. Fig. 5 shows a few typical stepped core

constructions. When the core size increases it becomes extremely difficult to cool the same

(Even though the core losses are relatively very small). Cooling ducts have to be provided

in the core. The steel laminations are grain oriented exploiting the simple geometry of the

transformer to reduce the excitation losses. The iron losses in the lamination, when the flux

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d d dduct

duct

0.71D

0.160.16

0.1 0.1

0.53

0.14 0.14

0.42

0.12 0.120.09 0.09

0.07 0.07

0.3

Figure 5: Stepped Core Construction

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is oriented in the direction of grain orientation, is about 30% of that in the normal direction.

Another important aspect to be carefully checked and monitored is the air gaps in

Windings

Core

Path of

flux

LV

HV

(a) (b)

Figure 6: Typical stacked Core and wound core Construction

series in the path of the main flux. As the reluctance of air path is about 1000 times more

than that of the steel, an air path of 1mm will require a mmf needed by a 1 meter path in iron.

Hence butt joints between laminations must be avoided. Lap joints are used to pro-

vide alternate paths for flux lines thus reducing the reluctance of the flux paths. Some typical

constructional details are shown in Fig. 6. In some power transformers the core is built up

by threading a long strip of steel through the coil in the form of a toroid. This construction

is normally followed in instrument transformers to reduce the magnetizing current and hence

the errors.

13




Large cores made up of laminations must be rendered adequately stiff by the provi-

sion of stiffening plates usually called as flitch plates. Punched through holes and bolts are

progressively being avoided to reduce heating and melting of the through bolts. The whole

stack is wrapped up by strong epoxy tapes to give mechanical strength to the core which

can stand in upright position. Channels and angles are used for the frame and they hold the

bottom yoke rigidly.

3.2 Windings

Windings form another important part of transformers. In a two winding trans-

former two windings would be present. The one which is connected to a voltage source and

creates the flux is called as a primary winding. The second winding where the voltage is

induced by induction is called a secondary. If the secondary voltage is less than that of the

primary the transformer is called a step down transformer. If the secondary voltage is more

then it is a step up transformer. A step down transformer can be made a step up transformer

by making the low voltage winding its primary. Hence it may be more appropriate to desig-

nate the windings as High Voltage (HV) and Low Voltage (LV) windings. The winding with

more number of turns will be a HV winding. The current on the HV side will be lower as

V-I product is a constant and given as the VA rating of the machines. Also the HV winding

needs to be insulated more to withstand the higher voltage across it. HV also needs more

clearance to the core, yoke or the body. These aspects influence the type of the winding

used for the HV or LV windings.

Transformer coils can be broadly classified in to concentric coils and sandwiched

coils Fig. 7. The former are very common with core type transformers while the latter one

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LV

HV

Core

HV LV

(a)Concentric coil

LVHV

Core

(b) Sandwich coil

Figure 7: Concentric and Sandwich Coils

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are common with shell type transformers. In the figure the letters L and H indicate the low

voltage and high voltage windings. In concentric arrangement, in view of the lower insulation

and clearance requirements, the LV winding is placed close to the core which is at ground

potential. The HV winding is placed around the LV winding. Also taps are provided on HV

winding when voltage change is required. This is also facilitated by having the HV winding

as the outer winding.

Three most common types of coils viz. helical, cross over and disc coils are shown in Fig. 8.

cross over coilsDisc coils

Helical coils

Figure 8: Disc, Crossover and Helical Coil Construction

Helical Windings One very common cylindrical coil arrangement is the helical winding.

This is made up of large cross section rectangular conductor wound on its flat side.

The coil progresses as a helix. This is commonly used for LV windings. The insulation

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requirement also is not too high. Between layers no insulation (other than conductor

insulation) is needed as the voltage between layers is low. The complexity of this

type of winding rapidly increases as the current to be handled becomes more. The

conductor cross section becomes too large and difficult to handle. The eddy current

losses in the conductor rapidly increases. Hence two or more conductors have to be

wound and connected in parallel. The parallel circuits bring in problems of current

sharing between the circuits. Transpositions of the parallel paths have to be adopted

to reduce unequal current distribution. The modern practice is to use continuously

transposed and bunched conductors.

Cross over coils The second popular winding type is the cross over coil. These are made

of circular conductors not exceeding 5 to 6 sq mm in cross section. These are used for

HV windings of relatively small transformers. These turns are wound in several layers.

The length and thickness of each block is made in line with cooling requirements. A

number of such blocks can be connected in series, leaving cooling ducts in between the

blocks, as required by total voltage requirement.

Disc coils Disc coils consist of flat conductors wound in a spiral form at the same place

spiralling outwards. Alternate discs are made to spiral from outside towards the center.

Sectional discs or continuous discs may be used. These have excellent thermal prop-

erties and the behavior of the winding is highly predictable. Winding of a continuous

disc winding needs specialized skills.

Sandwich coils Sandwich windings are more common with shell type core construction.

They permit easy control over the short circuit impedance of the transformer. By

bringing HV and LV coils close on the same magnetic axis the leakage is reduced

and the mutual flux is increased. By increasing the number of sandwiched coils the

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reactance can be substantially reduced.

3.3 Insulation

The insulation used in the case of electrical conductors in a transformer is varnish

or enamel in dry type of transformers. In larger transformers to improve the heat transfer

characteristics the conductors are insulated using un-impregnated paper or cloth and the

whole core-winding assembly is immersed in a tank containing transformer oil. The trans-

former oil thus has dual role. It is an insulator and also a coolant. The porous insulation

around the conductor helps the oil to reach the conductor surface and extract the heat. The

conductor insulation may be called the minor insulation as the voltage required to be with-

stood is not high. The major insulation is between the windings. Annular bakelite cylinders

serve this purpose. Oil ducts are also used as part of insulation between windings. The oil

used in the transformer tank should be free from moisture or other contamination to be of

any use as an insulator.

3.4 Cooling of transformers

Scaling advantages make the design of larger and larger unit sizes of transformers

economically attractive. This can be explained as below. Consider a transformer of certain

rating designed with certain flux density and current density. If now the linear dimensions

are made larger by a factor of K keeping the current and flux densities the same the core and

conductor areas increase by a factor of K2. The losses in the machine, which are proportional

to the volume of the materials used, increase by a factor of K3.The rating of the machine

increases by a factor of K4.

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The surface area however increases by a factor of K2 only. Thus the ratio of loss per

surface area goes on increasing by a factor of K. The substantial increase in the output is

the major attraction in going in for larger units. However cooling of the transformer becomes

more and more difficult. As the rating increases better cooling techniques are needed.

Simple air cooling of the transformers is adopted in dry type transformers. The limit

for this is reached by the time the rating is a few kVA. Hence air cooling is used in low

voltage machines. This method of cooling is termed as AN(Air Natural). Air Blast(AB)

method improves on the above by directing the blast of air at the core and windings. This

permits some improvement in the unit sizes.

Substantial improvement is obtained when the transformer is immersed in an oil tank.

The oil reaches the conductor surface and extracts the heat and transports the same to the

surface of the tank by convection. This is termed as ON (Oil Natural) type of cooling. This

method permits the increase in the surface available for the cooling further by the use of

ducts, radiators etc.

OB(Oil Blast) method is an improvement over the ON-type and it directs a blast of

air on the cooling surface. In the above two cases the flow of oil is by natural convective

forces. The rate of circulation of oil can be increased with the help of a pump, with the

cooling at the surface remaining natural cooling to air. This is termed as OFN (Oil Forced

Natural). If now a forced blast of air is also employed, the cooling method become OFB(

Oil Forced Blast). A forced circulation of oil through a radiator is done with a blast of air

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Tubes

Radiator

Main tank

(a)

Radiator

water inlet

water outlet

oil pump

Bushing

Conservator

& Breather

(b)

Conservator&

Breather

Radiator

Fan motorOil pump

for O.F.B

Bushing

(c)

Figure 9: Some Typical Cooling Arrangements20




over the radiator surface. Substantial amount of heat can be removed by employing a water

cooling. Here the hot oil going into the radiator is cooled by a water circuit. Due to the

high specific heat of water, heat can be evacuated effectively. Next in hierarchy comes OFW

which is similar to OFB except that instead of blast of air a forced circulation of cool water

in the radiator is used in this. Some cooling arrangements are shown in Fig. 9.

In many large sized transformers the cooling method is matched with the amount

of heat that is required to be removed. As the load on the transformer changes the heat

generated within also changes. Suitable cooling method can be pressed into service at that

time. This gives rise to the concept of mixed cooling technique.

ON/OB Works as ON but with increased load additional air blast is adopted. This gives

the ratings to be in the ratio of 1:1.5

ON/OB/OFB Similarly gives the ratings in the ratio of 1:1.5:2

The temperature rise permitted in the British standard specification for power transformers

are tabulated below.

Type winding oil core

Class A Class B

◦C ◦C ◦C

AN,AB 55 75 - As

ON,OB,OW 60 - 50 for

OFN,OFB 65 - 50 adjacent

OFW 70 - 50 winding

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3.4.1 Properties of the transformer coil

Even though the basic functions of the oil used in transformers are a) heat conduc-

tion and b) electrical insulation, there are many other properties which make a particular oil

eminently suitable. Organic oils of vegetative or animal origin are good insulators but tend

to decompose giving rise to acidic by-products which attack the paper or cloth insulation

around the conductors.

Mineral oils are suitable from the point of electrical properties but tend to form sludge.

The properties that are required to be looked into before selecting an oil for transformer

application are as follows:

Insulting property This is a very important property. However most of the oils naturally

fulfil this. Therefore deterioration in insulating property due to moisture or contami-

nation may be more relevant.

Viscosity It is important as it determines the rate of flow of the fluid. Highly viscous fluids

need much bigger clearances for adequate heat removal.

Purity The oil must not contain impurities which are corrosive. Sulphur or its compounds

as impurities cause formation of sludge and also attack metal parts.

Sludge formation Thickening of oil into a semisolid form is called a sludge. Sludge for-

mation properties have to be considered while choosing the oil as the oil slowly forms

semi-solid hydrocarbons. These impede flows and due to the acidic nature, corrode

metal parts. Heat in the presence of oxygen is seen to accelerate sludge formation. If

the hot oil is prevented from coming into contact with atmospheric air sludge formation

22




can be greatly reduced.

Acidity Oxidized oil normally produces CO2 and acids. The cellulose which is in the paper

insulation contains good amount of moisture. These form corrosive vapors. A good

breather can reduce the problems due to the formation of acids.

Flash point And Fire point Flash point of an oil is the temperature at which the oil

ignites spontaneously. This must be as high as possible (not less than 160◦C from the

point of safety). Fire point is the temperature at which the oil flashes and continuously

burns. This must be very high for the chosen oil (not less than 200◦C).

Inhibited oils and synthetic oils are therefore used in the transformers. Inhibited oils

contain additives which slow down the deterioration of properties under heat and moisture

and hence the degradation of oil. Synthetic transformer oil like chlorinated diphenyl has

excellent properties like chemical stability, non-oxidizing, good dielectric strength, moisture

repellant, reduced risk due fire and explosion.

It is therefore necessary to check the quality of the oil periodically and take corrective

steps to avoid major break downs in the transformer.

There are several other structural and insulating parts in a large transformer. These

are considered to be outside the scope here.

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4 Ideal Transformer

Earlier it is seen that a voltage is induced in a coil when the flux linkage associated

with the same changed. If one can generate a time varying magnetic field any coil placed in

the field of influence linking the same experiences an induced emf. A time varying field can

be created by passing an alternating current through an electric coil. This is called mutual

induction. The medium can even be air. Such an arrangement is called air cored transformer.

Indeed such arrangements are used in very high frequency transformers. Even though the

principle of transformer action is not changed, the medium has considerable influence on the

working of such devices. These effects can be summarized as the followings.

1. The magnetizing current required to establish the field is very large, as the reluctance

of the medium is very high.

2. There is linear relationship between the mmf created and the flux produced.

3. The medium is non-lossy and hence no power is wasted in the medium.

4. Substantial amount of leakage flux exists.

5. It is very hard to direct the flux lines as we desire, as the whole medium is homogeneous.

If the secondary is not loaded the energy stored in the magnetic field finds its way

back to the source as the flux collapses. If the secondary winding is connected to a load then

part of the power from the source is delivered to the load through the magnetic field as a link.

The medium does not absorb and lose any energy. Power is required to create the field and

not to maintain the same. As the winding losses can be made very small by proper choice

of material, the ideal efficiency of a transformer approaches 100%. The large magnetizing

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x

Primary

Leakage

flux

Mutual flux

Secondary

(a)

Leakage flux

Primary

Mutual flux

Secondary

Iron core

X

(b)

Figure 10: Mutual Induction a) air core b) iron core

25





current requirement is a major deterrent. However if now a piece of magnetic material is

introduced to form the magnetic circuit Fig. 10(b) the situation changes dramatically. These

can be enumerated as below.

1. Due to the large value for the permeance ( µr of the order of 1000 as compared to

air) the magnetizing current requirement decreases dramatically. This can also be

visualized as a dramatic increase in the flux produced for a given value of magnetizing

current.

2. The magnetic medium is linear for low values of induction and exhibits saturation type

of non-linearity at higher flux densities.

3. The iron also has hysteresis type of non-linearity due to which certain amount of power

is lost in the iron (in the form of hysteresis loss), as the B-H characteristic is traversed.

4. Most of the flux lines are confined to iron path and hence the mutual flux is increased

very much and leakage flux is greatly reduced.

5. The flux can be easily ‘directed’ as it takes the path through steel which gives great

freedom for the designer in physical arrangement of the excitation and output windings.

6. As the medium is made of a conducting material eddy currents are induced in the

same and produce losses. These are called ‘eddy current losses’. To minimize the

eddy current losses the steel core is required to be in the form of a stack of insulated

laminations.

From the above it is seen that the introduction of magnetic core to carry the flux

introduced two more losses. Fortunately the losses due to hysteresis and eddy current for

the available grades of steel is very small at power frequencies. Also the copper losses in the

26





winding due to magnetization current is reduced to an almost insignificant fraction of the

full load losses. Hence steel core is used in power transformers.

In order to have better understanding of the behavior of the transformer, initially

certain idealizations are made and the resulting ‘ideal’ transformer is studied. These ideal-

izations are as follows:

1. Magnetic circuit is linear and has infinite permeability. The consequence is that a van-

ishingly small current is enough to establish the given flux. Hysteresis loss is negligible.

As all the flux generated confines itself to the iron, there is no leakage flux.

2. Windings do not have resistance. This means that there are no copper losses, nor there

is any ohmic drop in the electric circuit.

In fact the practical transformers are very close to this model and hence no major

departure is made in making these assumptions.

Fig. 11 shows a two winding ideal transformer. The primary winding has T1 turns and is

connected to a voltage source of V1 volts. The secondary has T2 turns. Secondary can be

connected to a load impedance for loading the transformer. The primary and secondary are

shown on the same limb and separately for clarity.

As a current I0 amps is passed through the primary winding of T1 turns it sets up an

mmf of I0T1 ampere which is in turn sets up a flux φ through the core. Since the reluctance

of the iron path given by R = l/µAis zero as µ −→ ∞, a vanishingly small value of current

I0 is enough to setup a flux which is finite. As I0 establishes the field inside the transformer

27





++

+

-

-

T1

T2

e1

e2

φ µ

~

8v1=V1mcosωt

io 0

+

e1

i1

+

e2

i2

+ -

v1=V1sinωt

(a)Unloaded machine (b) Circuit

form

N

++

+

-

-

T1

T2

e1

e2

φ µ 8

-

i1

i2

ZL

v1=V1cosωt

(c)Loaded machine

Figure 11: Two winding Ideal Transformer unloaded and loaded

28





it is called the magnetizing current of the transformer.

F lux φ =mmf

Reluctance=I0T1

l

µA

=I0T1Aµ

l. (9)

This current is the result of a sinusoidal voltage V applied to the primary. As the

current through the loop is zero (or vanishingly small), at every instant of time, the sum of

the voltages must be zero inside the same. Writing this in terms of instantaneous values we

have,

v1 − e1 = 0 (10)

where v1 is the instantaneous value of the applied voltage and e1 is the induced emf due to

Faradays principle. The negative sign is due to the application of the Lenz’s law and shows

that it is in the form of a voltage drop. Kirchoff’s law application to the loop will result in

the same thing.

This equation results in v1 = e1 or the induced emf must be same in magnitude to

the applied voltage at every instant of time. Let v1 = V1peak cosωt where V1peak is the peak

value and ω = 2πf t. f is the frequency of the supply. As v1 = e1; e1 = dψ1/dt but

e1 = E1peak cosωt ∴ E1 = V1 . It can be easily seen that the variation of flux linkages can

be obtained as ψ1 = ψ1peak sinωt. Here ψ1peak is the peak value of the flux linkages of the

primary.

Thus the RMS primary induced emf is

e1 =dψ1

dt=d(ψ1peak sinωt)

dt(11)

= ψ1peak.ω. cosωt or the rms value (12)

E1 =ψ1peak.ω

√2

=2πfT1φm

√2

= 4.44fφmT1 volts

29





Here ψ1peak is the peak value of the flux linkages of the primary. The same mutual

flux links the secondary winding. However the magnitude of the flux linkages will be ψ2peak =

T2.φm. The induced emf in the secondary can be similarly obtained as ,

e2 =dψ2

dt=d(ψ2peak sinωt)

dt(13)

= ψ2peak.ω. cosωt or the rms value (14)

E2 =2πfT2φm

√2

= 4.44fφmT2 volt

which yields the voltage ratio as

E1

E2

=T1

T2

(15)

+

-

E1

I1

V1

+

-

E2

I2

V2

Figure 12: Dot Convention

The voltages E1 and E2 are obtained by the same mutual flux and hence they are

in phase. If the winding sense is opposite i.e., if the primary is wound in clockwise sense

and the secondary counter clockwise sense then if the top terminal of the first winding is

at maximum potential the bottom terminal of the second winding would be at the peak

potential. Similar problem arises even when the sense of winding is kept the same, but the

30





two windings are on opposite limbs (due to the change in the direction of flux). Hence in

the circuit representation of transformers a dot convention is adopted to indicate the ter-

minals of the windings that go high (or low) together. (Fig. 12). This can be established

experimentally by means of a polarity test on the transformers. At a particular instant of

time if the current enters the terminal marked with a dot it magnetizes the core. Similarly

a current leaving the terminal with a dot demagnetizes the core.

So far, an unloaded ideal transformer is considered. If now a load impedance ZL is

connected across the terminals of the secondary winding a load current flows as marked in

Fig. 11(c). This load current produces a demagnetizing mmf and the flux tends to collapse.

However this is detected by the primary immediately as both E2 and E1 tend to collapse.

The current drawn from supply increases up to a point the flux in the core is restored back

to its original value. The demagnetizing mmf produced by the secondary is neutralized by

additional magnetizing mmf produces by the primary leaving the mmf and flux in the core

as in the case of no-load. Thus the transformer operates under constant induced emf mode.

Thus,

i1T1 − i2T2 = i0T1 but i0 → 0 (16)

i2T2 = i1T1 and the rms value I2T2 = I1T1. (17)

If the reference directions for the two currents are chosen as in the Fig. 12, then the above

equation can be written in phasor form as,

I1T1 = I2T2 or I1 =T2

T1

.I2 (18)

AlsoE1

E2

=T1

T2

=I2I1

E1I1 = E2I2 (19)

31





Thus voltage and current transformation ratio are inverse of one another. If an impedance

of ZL is connected across the secondary,

I2 =E2

ZL

or ZL =E2

I2(20)

The input impedance under such conditions is

Zi =E1

I1= (

T1

T2

)2.E2

I2= (

T1

T2

)2.ZL (21)

An impedance of ZL when viewed ‘through’ a transformer of turns ratio (T1

T2

) is seen

as (T1

T2

)2.ZL. Transformer thus acts as an impedance converter. The transformer can be

interposed in between a source and a load to ‘match’ the impedance.

E1

I1

θ1

φ

V1

E2

I2

θ2

φ

V2

Figure 13: Phasor diagram of Operation of an Ideal Transformer

Finally, the phasor diagram for the operation of the ideal transformer is shown in

Fig. 13 in which θ1 and θ2 are power factor angles on the primary and secondary sides. As

32





the transformer itself does not absorb any active or reactive power it is easy to see that

θ1 = θ2.

Thus, from the study of the ideal transformer it is seen that the transformer provides

electrical isolation between two coupled electric circuits while maintaining power invariance

at its two ends. However, grounding of loads and one terminal of the transformer on the

secondary/primary side are followed with the provision of leakage current detection devices

to safe guard the persons working with the devices. Even though the isolation aspect is

a desirable one its utility cannot be over emphasized. It can be used to step up or step

down the voltage/current at constant volt-ampere. Also, the transformer can be used for

impedance matching. In the case of an ideal transformer the efficiency is 100% as there are

no losses inside the device.

33





5 Practical Transformer

An ideal transformer is useful in understanding the working of a transformer. But it

cannot be used for the computation of the performance of a practical transformer due to the

non-ideal nature of the practical transformer. In a working transformer the performance as-

pects like magnetizing current, losses, voltage regulation, efficiency etc are important. Hence

the effects of the non-idealization like finite permeability, saturation, hysteresis and winding

resistances have to be added to an ideal transformer to make it a practical transformer.

Conversely, if these effects are removed from a working transformer what is left behind is an

ideal transformer.

Finite permeability of the magnetic circuit necessitates a finite value of the current

to be drawn from the mains to produce the mmf required to establish the necessary flux.

The current and mmf required is proportional to the flux density B that is required to be

established in the core.

B = µH ; B =φ

A(22)

where A is the area of cross section of the iron core m2. H is the magnetizing force which is

given by,

H = i.T1

l(23)

where l is the length of the magnetic path, m. or

φ = B.A =Aµ(iT1)

l= permeance ∗ mmf(here that of primary) (24)

The magnetizing force and the current vary linearly with the applied voltage as long

as the magnetic circuit is not saturated. Once saturation sets in, the current has to vary in

34





a nonlinear manner to establish the flux of sinusoidal shape. This non-linear current can be

resolved into fundamental and harmonic currents. This is discussed to some extent under

harmonics. At present the effect of this non-linear behavior is neglected as a secondary

effect. Hence the current drawn from the mains is assumed to be purely sinusoidal and

directly proportional to the flux density of operation. This current can be represented by a

current drawn by an inductive reactance in the circuit as the net energy associated with the

same over a cycle is zero. The energy absorbed when the current increases is returned to

the electric circuit when the current collapses to zero. This current is called the magnetizing

current of the transformer. The magnetizing current Im is given by Im = E1/Xm where Xm

is called the magnetizing reactance. The magnetic circuit being lossy absorbs and dissipates

the power depending upon the flux density of operation. These losses arise out of hysteresis,

eddy current inside the magnetic core. These are given by the following expressions:

Ph ∝ B1.6f (25)

Pe ∝ B2f 2t2 (26)

Ph -Hysteresis loss, Watts

B- Flux density of operation Tesla.

f - Frequency of operation, Hz

t - Thickness of the laminations of the core, m.

For a constant voltage, constant frequency operation B is constant and so are these

losses. An active power consumption by the no-load current can be represented in the input

circuit as a resistance Rc connected in parallel to the magnetizing reactance Xm. Thus the

no-load current I0 may be made up of Ic(loss component) and Im (magnetizing component

35





as )

I0 = Ic − jIm (27)

I2

cRc– gives the total core losses (i.e. hysteresis + eddy current loss)

I2

mXm- Reactive volt amperes consumed for establishing the mutual flux.

Finite µ of the magnetic core makes a few lines of flux take to a path through the air.

Thus these flux lines do not link the secondary winding. It is called as leakage flux. As the

path of the leakage flux is mainly through the air the flux produced varies linearly with the

primary current I1. Even a large value of the current produces a small value of flux. This

flux produces a voltage drop opposing its cause, which is the current I1. Thus this effect of

the finite permeability of the magnetic core can be represented as a series inductive element

jxl1. This is termed as the reactance due to the primary leakage flux. As this leakage flux

varies linearly with I1, the flux linkages per ampere and the primary leakage inductance

are constant (This is normally represented by ll1 Henry). The primary leakage reactance

therefore becomes

xl1 = 2πfll1 ohm (28)

A similar effect takes place on the secondary side when the transformer is loaded.

The secondary leakage reactance jxl2 arising out of the secondary leakage inductance ll2 is

given by

xl2 = 2πfll2 (29)

Finally, the primary and secondary windings are wound with copper (sometimes alu-

minium in small transformers) conductors; thus the windings have a finite resistance (though

36





~

+

+

+

-

Rc

I2

φ

-

ZL

I’2

V2

r1

r2

I1

jXm

E1

-

V1

E2 T2

Io

jxl1

jxl2

T1

(a)Physical arrangement

r1

RcjXm

V1

Ic Im

Io

ZLV2

E1 E2

I’2I1I2

r2

jXl1

jXl2

(b)Equivalent circuit

Figure 14: A Practical Transformer

37





small). This is represented as a series circuit element, as the power lost and the drop pro-

duced in the primary and secondary are proportional to the respective currents. These are

represented by r1 and r2 respectively on primary and secondary side. A practical transformer

sans these imperfections (taken out and represented explicitly in the electric circuits) is an

ideal transformer of turns ratio T1 : T2 (voltage ratio E1 : E2). This is seen in Fig. 14. I′

2

in the circuit represents the primary current component that is required to flow from the

mains in the primary T1 turns to neutralize the demagnetizing secondary current I2 due to

the load in the secondary turns. The total primary current

vectorially is I1 = I′

2+ I0 (30)

Here I′

2T1 = I2T2 or I

′

2= I2

T2

T1

(31)

Thus I1 = I2

T2

T1

+ I0 (32)

By solving this circuit for any load impedance ZL one can find out the performance of the

loaded transformer.

The circuit shown in Fig. 14(b). However, it is not very convenient for use due to

the presence of the ideal transformer of turns ratio T1 : T2. If the turns ratio could be made

unity by some transformation the circuit becomes very simple to use. This is done here by

replacing the secondary by a ‘hypothetical’ secondary having T1 turns which is ‘equivalent ’

to the physical secondary. The equivalence implies that the ampere turns, active and reactive

power associated with both the circuits must be the same. Then there is no change as far

as their effect on the primary is considered. Thus

V′

2= aV2, I

′

2=

I2

a, r

′

2= a2r2, x

′

l2= a2xl2 Z

′

L= a2ZL.

where a -turns ratio T1

T2

38





This equivalent circuit is as shown in Fig. ??(a). As the ideal transformer in this

case has a turns ratio of unity the potentials on either side are the same and hence they

may be conductively connected dispensing away with the ideal transformer. This particular

equivalent circuit is as seen from the primary side. It is also possible to refer all the pri-

mary parameters to secondary by making the hypothetical equivalent primary winding on

the input side having the number of turns to be T2. Such an equivalent circuit having all

the parameters referred to the secondary side is shown in fig. 15.

The equivalent circuit can be derived, with equal ease, analytically using the Kir-

choff’s equations applied to the primary and secondary. Referring to fig. 14(a), we have (by

neglecting the shunt branch)

V1 = E1 + I1(r1 + jxl1) (33)

E2 = V2 + I2(r2 + jxl2) (34)

T1I0 = T1I1 + T2I2 or I1 = −I2

a+ I0 (35)

= −I2

a+ Ic + Im

a =T1

T2

.

Multiply both sides of Eqn.34 by ‘a’ [This makes the turns ratio unity and retains the power

invariance].

aE2 = aV2 + aI2(r2 + jxl2) but aE2 = E1 (36)

Substituting in Eqn.33 we have

39





V1 = aV2 + aI2(r2 + jxl2) + I1(r1 + jxl1)

= V′

2+ I1(a

2r2 + ja2xl2) + I1(r1 + jxl1)

= V′

2+ I1(r1 + r

′

2+ jxl1 + x

′

l2) (37)

A similar procedure can be used to refer all parameters to secondary side. (Shown in fig. 15.)

r’1

R’c jX’

mV’1

I’o

ZLV2

jx’l1 jxl2r2

I2I’1

I’c I’m

Figure 15: Equivalent Circuit Referred to the Secondary Side

40




6 Phasor diagrams

r1

RcjXmV1

Io

Z’LV’

2

jxl1 jx’l2r’2

Ic Im

I1

(a)

r1

Io

Z’L

jxl1 jx’l2r’2

I’2I1

Ic Im

jxmRcV1

V’2V’

2V1

I1R jX

I’2

R=r1+r’2

x=xl1+x’l2

I1=I’2

(b) (c)

Figure 16: Exact,approximate and simplified equivalent circuits

The resulting equivalent circuit as shown in Fig. 16 is known as the exact

equivalent circuit. This circuit can be used for the analysis of the behavior of the transform-

ers. As the no-load current is less than 1% of the load current a simplified circuit known

as ‘approximate’ equivalent circuit (see Fig. 16(b)) is usually used, which may be further

41




simplified to the one shown in Fig. 16(c).

On similar lines to the ideal transformer the phasor diagram of operation can be

drawn for a practical transformer also. The positions of the current and induced emf phasor

are not known uniquely if we start from the phasor V1. Hence it is assumed that the phasor

φ is known. The E1 and E2 phasor are then uniquely known. Now, the magnetizing and loss

components of the currents can be easily represented. Once I0 is known, the drop that takes

place in the primary resistance and series reactance can be obtained which when added to

E1 gives uniquely the position of V1 which satisfies all other parameters. This is represented

in Fig. 17(a) as phasor diagram on no-load.

Next we proceed to draw the phasor diagram corresponding to a loaded transformer.

The position of the E2 vector is known from the flux phasor. Magnitude of I2 and the load

power factor angle θ2 are assumed to be known. But the angle θ2 is defined with respect

to the terminal voltage V2 and not E2. By trial and error the position of I2 and V2 are

determined. V2 should also satisfy the Kirchoff’s equation for the secondary. Rest of the

construction of the phasor diagram then becomes routine. The equivalent primary current

I′

2is added vectorially to I0 to yield I1. I1(r1 + jxl1)is added to E1 to yield V1. This is shown

in fig. 17(b) as phasor diagram for a loaded transformer.

42




V1

E1

IoXl1

Ior1

Io

Im Il

φ φ

E2

(a)No-load

V1

E1

I1Xl1

I1r1

Io

I’2

Il

φ φ

E2

V2

I2

I2x2I2r2

(b)On-load

Figure 17: Phasor Diagram of a Practical Transformer

43




7 Testing of Transformers

The structure of the circuit equivalent of a practical transformer is developed earlier.

The performance parameters of interest can be obtained by solving that circuit for any load

conditions. The equivalent circuit parameters are available to the designer of the transformers

from the various expressions that he uses for designing the transformers. But for a user

these are not available most of the times. Also when a transformer is rewound with different

primary and secondary windings the equivalent circuit also changes. In order to get the

equivalent circuit parameters test methods are heavily depended upon. From the analysis of

the equivalent circuit one can determine the electrical parameters. But if the temperature

rise of the transformer is required, then test method is the most dependable one. There are

several tests that can be done on the transformer; however a few common ones are discussed

here.

7.1 Winding resistance test

This is nothing but the resistance measurement of the windings by applying a small

d.c voltage to the winding and measuring the current through the same. The ratio gives

the winding resistance, more commonly feasible with high voltage windings. For low voltage

windings a resistance-bridge method can be used. From the d.c resistance one can get the

a.c. resistance by applying skin effect corrections.

44




V1

V2

V3

Vs

~

A2

A1

a2

a1

V

S

+

-

+

A2

A1

a2

a1

(a)A.C.test (b)D.C.test

Figure 18: Polarity Test

7.2 Polarity Test

This is needed for identifying the primary and secondary phasor polarities. It is

a must for poly phase connections. Both a.c. and d.c methods can be used for detecting

the polarities of the induced emfs. The dot method discussed earlier is used to indicate the

polarities. The transformer is connected to a low voltage a.c. source with the connections

made as shown in the fig. 18(a). A supply voltage Vs is applied to the primary and the

readings of the voltmeters V1, V2 and V3 are noted. V1 : V2 gives the turns ratio. If V3 reads

V1−V2 then assumed dot locations are correct (for the connection shown). The beginning and

end of the primary and secondary may then be marked by A1 −A2 and a1 − a2 respectively.

If the voltage rises from A1 to A2 in the primary, at any instant it does so from a1 to a2 in

the secondary. If more secondary terminals are present due to taps taken from the windings

they can be labeled as a3, a4, a5, a6. It is the voltage rising from smaller number towards

larger ones in each winding. The same thing holds good if more secondaries are present.

45




Fig. 18(b) shows the d.c. method of testing the polarity. When the switch S is closed if the

secondary voltage shows a positive reading, with a moving coil meter, the assumed polarity

is correct. If the meter kicks back the assumed polarity is wrong.

7.3 Open Circuit Test

A

VV1

W

V2

Rc

jXmV1

IcIm

Io

(a)Physical Arrangement

(b)Equivalent Circuit

Figure 19: No Load Test

As the name suggests, the secondary is kept open circuited and nominal value

of the input voltage is applied to the primary winding and the input current and power are

measured. In Fig. 19(a) V, A, W are the voltmeter, ammeter and wattmeter respectively.

Let these meters read V1, I0 and W0 respectively.Fig. 19(b) shows the equivalent circuit of

the transformer under this test. The no load current at rated voltage is less than 1 percent of

nominal current and hence the loss and drop that take place in primary impedance r1 + jxl1

due to the no load current I0 is negligible. The active component Ic of the no load current I0

46




represents the core losses and reactive current Im is the current needed for the magnetization.

Thus the watt meter reading

W0 = V1Ic = Pcore (38)

∴ Ic =W0

V1

(39)

∴ Im =√

I2

0− I2

cor (40)

Rc =V1

Ic

andXm =V1

Im

(41)

Io

V1

Figure 20: Open Circuit Characteristics

The parameters measured already are in terms of the primary. Sometimes the pri-

mary voltage required may be in kilo-Volts and it may not be feasible to apply nominal

voltage to primary from the point of safety to personnel and equipment. If the secondary

voltage is low, one can perform the test with LV side energized keeping the HV side open

circuited. In this case the parameters that are obtained are in terms of LV . These have to

be referred to HV side if we need the equivalent circuit referred to HV side.

47




Sometimes the nominal value of high voltage itself may not be known, or in doubt,

especially in a rewound transformer. In such cases an open circuit characteristics is first

obtained, which is a graph showing the applied voltage as a function of the no load current.

This is a non linear curve as shown in Fig. 20. This graph is obtained by noting the current

drawn by transformer at different applied voltage, keeping the secondary open circuited. The

usual operating point selected for operation lies at some standard voltage around the knee

point of the characteristic. After this value is chosen as the nominal value the parameters

are calculated as mentioned above.

7.4 Short Circuit Test

The purpose of this test is to determine the series branch parameters of the equiv-

alent circuit of Fig. 21(b). As the name suggests, in this test primary applied voltage, the

current and power input are measured keeping the secondary terminals short circuited. Let

these values be Vsc, Isc and Wsc respectively. The supply voltage required to circulate rated

current through the transformer is usually very small and is of the order of a few percent

of the nominal voltage. The excitation current which is only 1 percent or less even at rated

voltage becomes negligibly small during this test and hence is neglected. The shunt branch

is thus assumed to be absent. Also I1 = I′

2as I0 ≃ 0. Therefore Wsc is the sum of the

copper losses in primary and secondary put together. The reactive power consumed is that

absorbed by the leakage reactance of the two windings.

Wsc = I2

sc(r1 + r

′

2) (42)

Zsc =Vsc

Isc

(43)

(xl1 + x′

l2) =

√

Z2sc− (r1 + r

′

2)2 (44)

48




A

VVsc

W

(a)Physical Arrangement

r1

Isc

Vsc

jxl1 jx’l2r’2

(b)Equivalent Circuit

Figure 21: Short Circuit Test

49




If the approximate equivalent circuit is required then there is no need to separate r1

and r′

2or xl1 and x

′

l2. However if the exact equivalent circuit is needed then either r1 or

r′

2is determined from the resistance measurement and the other separated from the total.

As for the separation of xl1 and x′

l2is concerned, they are assumed to be equal. This is a

fairly valid assumption for many types of transformer windings as the leakage flux paths are

through air and are similar.

7.5 Load Test

Load Test helps to determine the total loss that takes place, when the transformer

is loaded. Unlike the tests described previously, in the present case nominal voltage is applied

across the primary and rated current is drown from the secondary. Load test is used mainly

1. to determine the rated load of the machine and the temperature rise

2. to determine the voltage regulation and efficiency of the transformer.

Rated load is determined by loading the transformer on a continuous basis and observ-

ing the steady state temperature rise. The losses that are generated inside the transformer

on load appear as heat. This heats the transformer and the temperature of the transformer

increases. The insulation of the transformer is the one to get affected by this rise in the

temperature. Both paper and oil which are used for insulation in the transformer start get-

ting degenerated and get decomposed. If the flash point of the oil is reached the transformer

goes up in flames. Hence to have a reasonable life expectancy the loading of the transformer

must be limited to that value which gives the maximum temperature rise tolerated by the

insulation. This aspect of temperature rise cannot be guessed from the electrical equivalent

circuit. Further, the losses like dielectric losses and stray load losses are not modeled in the

50




equivalent circuit and the actual loss under load condition will be in error to that extent.

Many external means of removal of heat from the transformer in the form of different cooling

methods give rise to different values for temperature rise of insulation. Hence these permit

different levels of loading for the same transformer. Hence the only sure way of ascertaining

the rating is by conducting a load test.

It is rather easy to load a transformer of small ratings. As the rating increases it

becomes difficult to find a load that can absorb the requisite power and a source to feed the

necessary current. As the transformers come in varied transformation ratios, in many cases

it becomes extremely difficult to get suitable load impedance.

Further, the temperature rise of the transformer is due to the losses that take place

‘inside’ the transformer. The efficiency of the transformer is above 99% even in modest sizes

which means 1 percent of power handled by the transformer actually goes to heat up the

machine. The remaining 99% of the power has to be dissipated in a load impedance external

to the machine. This is very wasteful in terms of energy also. ( If the load is of unity power

factor) Thus the actual loading of the transformer is seldom resorted to. Equivalent loss

methods of loading and ‘Phantom’ loading are commonly used in the case of transformers.

The load is applied and held constant till the temperature rise of transformer reaches a

steady value. If the final steady temperature rise is lower than the maximum permissible

value, then load can be increased else it is decreased. That load current which gives the

maximum permissible temperature rise is declared as the nominal or rated load current and

the volt amperes are computed using the same.

51




In the equivalent loss method a short circuit test is done on the transformer. The

short circuit current is so chosen that the resulting loss taking place inside the transformer

is equivalent to the sum of the iron losses, full load copper losses and assumed stray load

losses. By this method even though one can pump in equivalent loss inside the transformer,

the actual distribution of this loss vastly differs from that taking place in reality. Therefore

this test comes close to a load test but does not replace one.

A

V

Io

I2I’2

V

A

I2I’2

Vs

W 2

W 1

2Io

V1

Io

Figure 22: Back to Back Test - Phantom Loading

In Phantom loading method two identical transformers are needed. The windings

are connected back to back as shown in Fig. 22. Suitable voltage is injected into the loop

formed by the two secondaries such that full load current passes through them. An equiv-

52




alent current then passes through the primary also. The voltage source V1 supplies the

magnetizing current and core losses for the two transformers. The second source supplies

the load component of the current and losses due to the same. There is no power wasted

in a load ( as a matter of fact there is no real load at all) and hence the name Phantom

or virtual loading. The power absorbed by the second transformer which acts as a load is

pushed back in to the mains. The two sources put together meet the core and copper losses

of the two transformers. The transformers work with full flux drawing full load currents and

hence are closest to the actual loading condition with a physical load.

53





8 Per Unit Calculations

As stated earlier, transformers of various sizes, ratings, voltage ratios can be seen

being used in a power system. The parameters of the equivalent circuits of these machines

also vary over a large range. Also the comparison of these machines are made simple if all

the parameters are normalized. If simple scaling of the parameters is done then one has

to carry forward the scaling factors in the calculations. Expressing in percent basis is one

example of scaling. However if the scaling is done on a logical basis one can have a simple

representation of the parameters without the bother of the scaling factors. Also different

units of measurement are in use in the different countries (FPS, CGS, MKS, etc;). These

units also underwent several revisions over the years. If the transformer parameter can be

freed from the units then the system becomes very simple. The ‘per unit’ system is developed

keeping these aspects in mind. The parameters of the transformer are referred to some base

values and thus get scaled. In the case of power system a common base value is adopted

in view of different ratings of the equipments used. In the case of individual equipments,

its own nominal parameters are used as base values. Some base parameters can be chosen

as independent base values while some others become derived base parameters. Once the

base values are identified the per unit values are calculated for any parameter by dividing

the same by its base value. The units must be the same for both the parameters and their

bases. Thus the per unit value is a unit-less dimensionless number. Let us choose nominal

voltage and nominal current on the primary side of a transformer as the base values Vbase

and Ibase. Other base values like volt ampere Sbase, short circuit impedance Zbase can be

54





calculated from those values.

Pbase, Qbase, Sbase = Vbase ∗ Ibase (45)

Rbase, Xbase, Zbase =Vbase

Ibase

(46)

Gbase, Bbase, Ybase =Ibase

Vbase

(47)

Normally Sbase and Vbase are known from name plate details. Other base values can be

derived from them.

Vp.u =V (volt)

Vbase(volt),

Ip.u =I(Amps)

Ibase(amps)=

I(amps)Sbase

Vbase

(48)

Zp.u =Z(ohm)

Zbase(ohm)= Z(ohm) ∗

Ibase

Vbase

= Z(ohm).Sbase

V 2

base

(49)

Many times, when more transformers are involved in a circuit one is required to choose

a common base value for all of them. Parameters of all the machines are expressed on this

common base. This is a common problem encountered in the case of parallel operation of

two or more transformers. The conversion of the base values naturally lead to change in the

per unit values of their parameters. An impedance Zp.u.old on the old base of Sbaseold and

Vbaseold shall get modified on new base Sbasenew,Vbasenew as

Zp.u.new = (Zp.u.old.V 2

base old

Sbase old

)Sbase new

V 2

base new

(50)

The term inside the bracket is nothing but the ohmic value of the impedance and this gets

converted into the new per unit value by the new Sbase and Vbase.

If all the equivalent circuit parameters are referred to the secondary side and per unit

values of the new equivalent circuit parameters are computed with secondary voltage and

55





current as the base values, there is no change in the per unit values. This can be easily seen by,

Z′

p.u.= Z

′

ohm.S

′

base

V′2

base

but Z′

ohm=

1

a2.Zohm (51)

Where a - is the turns ratio of primary to secondary

Z - impedance as seen by primary,

Z′

- impedance as seen by secondary.

S′

base= Sbase - as the transformer rating is unaltered.

V′

base= Vbase.

1

a

From the above relationships it can be seen that Z′

p.u.= Zp.u..

This becomes obvious if we realize that the mmf of the core for establishing a given

flux is the same whether it is supplied through primary or the secondary. Also the active

power and reactive power absorbed inside the transformer are not dependant on the winding

connected to supply. This is further illustrated by taking the equivalent circuit of a trans-

former derived earlier and expressing the same in per unit form.

Thus the per unit values help in dispensing away the scaling constants. The veracity

of the parameters can be readily checked. Comparison of the parameters of the machines

with those of similar ones throw in useful information about the machines. Comparing the

efficiencies of two transformers at any load one can say that the transformer with a higher

p.u.resistance has higher copper losses without actually computing the same.

Application of per unit values for the calculation of voltage regulation, efficiency and

load sharing of parallel connected transformers will be discussed later at appropriate places.

56





9 Voltage Regulation

Modern power systems operate at some standard voltages. The equipments work-

ing on these systems are therefore given input voltages at these standard values, within

certain agreed tolerance limits. In many applications this voltage itself may not be good

enough for obtaining the best operating condition for the loads. A transformer is interposed

in between the load and the supply terminals in such cases. There are additional drops

inside the transformer due to the load currents. While input voltage is the responsibility of

the supply provider, the voltage at the load is the one which the user has to worry about.

If undue voltage drop is permitted to occur inside the transformer the load voltage becomes

too low and affects its performance. It is therefore necessary to quantify the drop that takes

place inside a transformer when certain load current, at any power factor, is drawn from its

output leads. This drop is termed as the voltage regulation and is expressed as a ratio of

the terminal voltage (the absolute value per se is not too important).

The voltage regulation can be defined in two ways - Regulation Down and Regulation

up. These two definitions differ only in the reference voltage as can be seen below.

Regulation down: This is defined as ” the change in terminal voltage when a load current

at any power factor is applied, expressed as a fraction of the no-load terminal voltage”.

Expressed in symbolic form we have,

Regulation =|Vnl| − |Vl|

|Vnl|(52)

Vnl and Vl are no-load and load terminal voltages. This is the definition normally used

in the case of the transformers, the no-load voltage being the one given by the power

57





supply provider on which the user has no say. Hence no-load voltage is taken as the

reference.

Regulation up: Here again the regulation is expressed as the ratio of the change in the

terminal voltage when a load at a given power factor is thrown off, and the on load

voltage. This definition if expressed in symbolic form results in

Regulation =|Vnl| − |Vl|

|Vl|(53)

Vnl is the no-load terminal voltage.

Vl is load voltage. Normally full load regulation is of interest as the part load regulation

is going to be lower.

This definition is more commonly used in the case of alternators and power systems

as the user-end voltage is guaranteed by the power supply provider. He has to generate

proper no-load voltage at the generating station to provide the user the voltage he has asked

for. In the expressions for the regulation, only the numerical differences of the voltages are

taken and not vector differences.

In the case of transformers both definitions result in more or less the same value for

the regulation as the transformer impedance is very low and the power factor of operation is

quite high. The power factor of the load is defined with respect to the terminal voltage on

load. Hence a convenient starting point is the load voltage. Also the full load output voltage

is taken from the name plate. Hence regulation up has some advantage when it comes to its

application. Fig. 23 shows the phasor diagram of operation of the transformer under loaded

condition. The no-load current I0 is neglected in view of the large magnitude of I′

2. Then

58





Re jXe

V1

I’2

V’2

(a) Equivalent Circuit

O

V1

C

I2’

φ V’2

θ B

D

I2’Re

I2’Xe

E

A

(b)Phasor Diagram

Figure 23: Regulation of Transformer

59





I1= I′

2.

V1 = I′

2(Re + jXe) + V

′

2(54)

OD = V1 =√

[OA + AB + BC]2 + [CD]2

=√

[V′

2+ I

′

2Re cos φ + I

′

2Xe sin φ]2 + [I

′

2Xe cos φ − I

′

2Re sin φ]2 (55)

φ - power factor angle,

θ- internal impedance angle=tan−1 Xe

Re

Also,

V1 = V′

2+ I

′

2.(Re + jXe) (56)

= V′

2+ I

′

2(cos φ − j sin φ)(Re + jXe)

∴ RegulationR =|V1| − |V

′

2|

|V′

2|

=√

(1 + v1)2 + v2

2− 1 (57)

(1 + v1)2 + v2

2≃ (1 + v1)

2 + v2

2.2(1 + v1)

2(1 + v1)+ [

v2

2

2(1 + v1)]2 = (1 + v1 +

v2

2

2(1 + v1))2 (58)

Taking the square root (59)√

(1 + v1)2 + v2

2= 1 + v1 +

v2

2

2(1 + v1)(60)

where v1 = er cos φ + ex sin φ and v2 = ex cos φ − er sin φ

er =I′

2Re

V′

2

=per unit resistance drop

ex =I′

2Xe

V′

2

=per unit reactance drop

as v1 and v2 are small.

∴ R ≃ 1 + v1 +v2

2

2(1 + e1)− 1 ≃ v1 +

v2

2

2(61)

∴ regulation R = er cos φ ± ex sin φ +(ex sin φ − er cos φ)2

2(62)

60





v2

2

2(1 + v1)≃

v2

2

2.(1 − v1)

(1 − v2

1)≃

v2

2

2.(1 − v1) ≃

v2

2

2(63)

Powers higher than 2 for v1 and v2 are negligible as v1 and v2 are already small. As

v2 is small its second power may be neglected as a further approximation and the expression

for the regulation of the transform boils down to

regulation R = er cos φ ± ex sin φ

The negative sign is applicable when the power factor is leading. It can be seen from

the above expression, the full load regulation becomes zero when the power factor is leading

and er cos φ = ex sin φ or tan φ = er/ex

or the power factor angle φ = tan−1(er/ex) = tan−1(Re/Xe) leading.

Similarly, the value of the regulation is maximum at a power factor angle φ =

tan−1(ex/er) = tan−1(Xe/Re) lagging.

An alternative expression for the regulation of a transformer can be derived by the

method shown in Fig. 24. Here the phasor are resolved along the current axis and normal

to it.

We have,

OD2 = (OA + AB)2 + (BC + CD)2 (64)

= (V′

2cos φ + I

′

2Re)

2 + (V′

2sin φ + I

′

2Xe)

2 (65)

∴ RegulationR =OD − V

′

2

V′

2

=OD

V′

2

− 1 (66)

√

(V′

2cos φ + I

′

2Re)

V′

2

2

+(V

′

2sin φ + I

′

2Xe)

V′

2

2

− 1 (67)

=√

(cos φ + Rp.u)2 + (sin φ + X2

p.u)− 1 (68)

61





A

B

O

D

C

θφ

I2’

I2’Re

I2’Xe

V1

V2

Figure 24: An Alternate Method for the Calculation of Regulation

Thus this expression may not be as convenient as the earlier one due to the square root

involved.

Fig. 25 shows the variation of full load regulation of a typical transformer as the

power factor is varied from zero power factor leading, through unity power factor, to zero

power factor lagging.

It is seen from Fig. 25 that the full load regulation at unity power factor is nothing but

the percentage resistance of the transformer. It is therefore very small and negligible. Only

with low power factor loads the drop in the series impedance of the transformer contributes

substantially to the regulation. In small transformers the designer tends to keep the Xe very

low (less than 5%) so that the regulation performance of the transformer is satisfactory.

62





1

2

3

4

5

leading lagging

power factor

%Regulation

1.0 0.50

0 0.5

-1

-2

-3

-4

-5

Figure 25: Variation of Full Load Regulation with Power Factor

63





A low value of the short circuit impedance /reactance results in a large short circuit

current in case of a short circuit. This in turn results in large mechanical forces on the

winding. So, in large transformers the short circuit impedance is made high to give better

short circuit protection to the transformer which results in poorer regulation performance.

In the case of transformers provided with taps on windings, so that the turns ratio can be

changed, the voltage regulation is not a serious issue. In other cases care has to be exercised

in the selection of the short circuit impedance as it affects the voltage regulation.

64




10 Efficiency

Transformers which are connected to the power supplies and loads and are in op-

eration are required to handle load current and power as per the requirements of the load.

An unloaded transformer draws only the magnetization current on the primary side, the

secondary current being zero. As the load is increased the primary and secondary currents

increase as per the load requirements. The volt amperes and wattage handled by the trans-

former also increases. Due to the presence of no load losses and I2R losses in the windings

certain amount of electrical energy gets dissipated as heat inside the transformer. This gives

rise to the concept of efficiency.

Efficiency of a power equipment is defined at any load as the ratio of the power output to

the power input. Putting in the form of an expression,

Efficiency η =output power

input power=

Input power − losses inside the machine

Input power(69)

= 1 −losses inside the machine

input power= 1 − defficiency

=output power

output + losses inside the machine

More conveniently the efficiency is expressed in percentage. %η = output power

input power∗ 100

While the efficiency tells us the fraction of the input power delivered to the load, the

deficiency focuses our attention on losses taking place inside transformer. As a matter of

fact the losses heat up machine. The temperature rise decides the rating of the equipment.

The temperature rise of the machine is a function of heat generated the structural configu-

ration, method of cooling and type of loading (or duty cycle of load). The peak temperature

attained directly affects the life of the insulations of the machine for any class of insulation.

These aspects are briefly mentioned under section 7.5 on load test.

65




25

50

75

100

0.5 1x

Effic

iency%

0

Figure 26: Efficiency

A typical curve for the variation of efficiency as a function of output is given in Fig. 26

The losses that take place inside the machine expressed as a fraction of the input is some

times termed as deficiency. Except in the case of an ideal machine, a certain fraction of

the input power gets lost inside the machine while handling the power. Thus the value for

the efficiency is always less than one. In the case of a.c. machines the rating is expressed

in terms of apparent power. It is nothing but the product of the applied voltage and the

current drawn. The actual power delivered is a function of the power factor at which this

current is drawn. As the reactive power shuttles between the source and the load and has a

zero average value over a cycle of the supply wave it does not have any direct effect on the

efficiency. The reactive power however increases the current handled by the machine and

the losses resulting from it. Therefore the losses that take place inside a transformer at any

66




given load play a vital role in determining the efficiency. The losses taking place inside a

transformer can be enumerated as below:

1. Primary copper loss

2. Secondary copper loss

3. Iron loss

4. Dielectric loss

5. Stray load loss

These are explained in sequence below.

Primary and secondary copper losses take place in the respective winding resistances

due to the flow of the current in them.

Pc = I2

1r1 + I2

2r2 = I

′2

2Re (70)

The primary and secondary resistances differ from their d.c. values due to skin effect and the

temperature rise of the windings. While the average temperature rise can be approximately

used, the skin effect is harder to get analytically. The short circuit test gives the value of Re

taking into account the skin effect.

The iron losses contain two components - Hysteresis loss and Eddy current loss. The

Hysteresis loss is a function of the material used for the core.

Ph = KhB1.6f

67




For constant voltage and constant frequency operation this can be taken to be con-

stant. The eddy current loss in the core arises because of the induced emf in the steel

lamination sheets and the eddies of current formed due to it. This again produces a power

loss Pe in the lamination.

Pe = KeB2f 2t2

where t is the thickness of the steel lamination used. As the lamination thickness is much

smaller than the depth of penetration of the field, the eddy current loss can be reduced by

reducing the thickness of the lamination. Present day laminations are of 0.25 mm thickness

and are capable of operation at 2 Tesla. These reduce the eddy current losses in the core.

This loss also remains constant due to constant voltage and frequency of operation. The

sum of hysteresis and eddy current losses can be obtained by the open circuit test.

The dielectric losses take place in the insulation of the transformer due to the large

electric stress. In the case of low voltage transformers this can be neglected. For constant

voltage operation this can be assumed to be a constant.

The stray load losses arise out of the leakage fluxes of the transformer. These leakage

fluxes link the metallic structural parts, tank etc. and produce eddy current losses in them.

Thus they take place ’all round’ the transformer instead of a definite place , hence the name

’stray’. Also the leakage flux is directly proportional to the load current unlike the mutual

flux which is proportional to the applied voltage. Hence this loss is called ’stray load’ loss.

This can also be estimated experimentally. It can be modeled by another resistance in the

series branch in the equivalent circuit. The stray load losses are very low in air-cored trans-

formers due to the absence of the metallic tank.

68




Thus, the different losses fall in to two categories Constant losses (mainly voltage

dependant) and Variable losses (current dependant). The expression for the efficiency of the

transformer operating at a fractional load x of its rating, at a load power factor of θ2, can

be written as

η =xS cos θ2

xS cos θ2 + Pconst + x2Pvar

(71)

Here S in the volt ampere rating of the transformer (V′

2I

′

2at full load), Pconst being constant

losses and Pvar the variable losses at full load.

For a given power factor an expression for η in terms of the variable x is thus obtained.

By differentiating η with respect to x and equating the same to zero, the condition for

maximum efficiency is obtained. In the present case that condition comes out to be

Pconst = x2Pvar or x =

√

Pconst

Pvar

(72)

That is, when constant losses equal the variable losses at any fractional load x the

efficiency reaches a maximum value. The maximum value of that efficiency at any given

power factor is given by,

ηmax =xS cos θ2

xS cos θ2 + 2Pconst

=xS cos θ2

xS cos θ2 + 2x2Pvar

(73)

From the expression for the maximum efficiency it can be easily deduced that this

maximum value increases with increase in power factor and is zero at zero power factor of

the load. It may be considered a good practice to select the operating load point to be at the

maximum efficiency point. Thus if a transformer is on full load, for most part of the time

then the ηmax can be made to occur at full load by proper selection of constant and variable

69




losses. However, in the modern transformers the iron losses are so low that it is practically

impossible to reduce the full load copper losses to that value. Such a design wastes lot of

copper. This point is illustrated with the help of an example below.

Two 100 kVA transformers A nd B are taken. Both transformers have total full load

losses to be 2 kW. The break up of this loss is chosen to be different for the two transformers.

Transformer A: iron loss 1 kW, and copper loss is 1 kW. The maximum efficiency of 98.04%

occurs at full load at unity power factor. Transformer B: Iron loss =0.3 kW and full load

copper loss =1.7 kW. This also has a full load η of 98.04%. Its maximum η occurs at

a fractional load of√

0.3

1.7= 0.42. The maximum efficiency at unity power factor being

42

42+0.6∗ 100 = 98.59%. At the corresponding point the transformer A has an efficiency of

42

42+1.0+0.1764∗ 100 = 97.28%. Transformer A uses iron of more loss per kg at a given flux

density, but transformer B uses lesser quantity of copper and works at higher current density.

10.1 All day efficiency

Large capacity transformers used in power systems are classified broadly into Power trans-

formers and Distribution transformers. The former variety is seen in generating stations and

large substations. Distribution transformers are seen at the distribution substations. The

basic difference between the two types arise from the fact that the power transformers are

switched in or out of the circuit depending upon the load to be handled by them. Thus at

50% load on the station only 50% of the transformers need to be connected in the circuit.

On the other hand a distribution transformer is never switched off. It has to remain in the

circuit irrespective of the load connected. In such cases the constant loss of the transformer

continues to be dissipated. Hence the concept of energy based efficiency is defined for such

70




50

100

6 12 18 24

Load %

of

full load

Time,hrs

s

P

50

100

1224

Po

we

r L

oss %

(a)Load factor (b) Loss factor

Figure 27: Calculation of Load Factor and Loss Factor

71




transformers. It is called ’all day’ efficiency. The all day efficiency is thus the ratio of the

energy output of the transformer over a day to the corresponding energy input. One day

is taken as a duration of time over which the load pattern repeats itself. This assumption,

however, is far from being true. The power output varies from zero to full load depending

on the requirement of the user and the load losses vary as the square of the fractional loads.

The no-load losses or constant losses occur throughout the 24 hours. Thus, the comparison

of loads on different days becomes difficult. Even the load factor, which is given by the

ratio of the average load to rated load, does not give satisfactory results. The calculation

of the all day efficiency is illustrated below with an example. The graph of load on the

transformer, expressed as a fraction of the full load is plotted against time in Fig. 27. In an

actual situation the load on the transformer continuously changes. This has been presented

by a stepped curve for convenience. The average load can be calculated by

Average load over a day =

∑

n

i=1Pi

24=

Sn

∑

n

i=1xiti cos θi

24(74)

where Pi is the load during an interval i. n intervals are assumed. xi is the fractional load.

Si = xiSn where Sn is nominal load. The average loss during the day is given by

Average loss = Pi +Pc

∑

n

i=1x2

iti

24(75)

This is a non-linear function. For the same load factor different average loss can be

there depending upon the values of xi and ti. Hence a better option would be to keep the

constant losses very low to keep the all day efficiency high. Variable losses are related to

load and are associated with revenue earned. The constant losses on the other hand has to

be incurred to make the service available. The concept of all day efficiency may therefore be

more useful for comparing two transformers subjected to the same load cycle.

72




The concept of minimizing the lost energy comes into effect right from the time of

procurement of the transformer. The constant losses and variable losses are capitalized and

added to the material cost of the transformer in order to select the most competitive one,

which gives minimum cost taking initial cost and running cost put together. Obviously the

iron losses are capitalized more in the process to give an effect to the maximization of energy

efficiency. If the load cycle is known at this stage, it can also be incorporated in computation

of the best transformer.

73





11 Auto Transformer

V1

T1

T2

I1

V2 ZL

I1

I2

I2

A

B

C

Figure 28: Autotransformer - Physical Arrangement

The primary and secondary windings of a two winding transformer have

induced emf in them due to a common mutual flux and hence are in phase. The currents

drawn by these two windings are out of phase by 180◦. This prompted the use of a part

of the primary as secondary. This is equivalent to fusing the secondary turns into primary

turns. The fused section need to have a cross sectional area of the conductor to carry (I2−I1)

ampere! This ingenious thought led to the invention of an auto transformer. Fig. 28 shows

the physical arrangement of an auto transformer. Total number of turns between A and C

are T1. At point B a connection is taken. Section AB has T2 turns. As the volts per turn,

which is proportional to the flux in the machine, is the same for the whole winding,

V1 : V2 = T1 : T2 (76)

For simplifying analysis, the magnetizing current of the transformer is neglected.

74





When the secondary winding delivers a load current of I2 ampere the demagnetizing ampere

turns is I2T2 . This will be countered by a current I1 flowing from the source through the

T1 turns such that,

I1T1 = I2T2 (77)

A current of I1 ampere flows through the winding between B and C . The current

in the winding between A and B is (I2 − I1) ampere. The cross section of the wire to be

selected for AB is proportional to this current assuming a constant current density for the

whole winding. Thus some amount of material saving can be achieved compared to a two

winding transformer. The magnetic circuit is assumed to be identical and hence there is

no saving in the same. To quantify the saving the total quantity of copper used in an auto

transformer is expressed as a fraction of that used in a two winding transformer as,

copper in auto transformer

copper in two winding transformer=

(T1 − T2)I1 + T2(I2 − I1)

T1I1 + T2I2

(78)

= 1 −2T2I1

T1I1 + T2I2

But T1I1 = T2I2 (79)

∴ The Ratio = 1 −2T2I1

2T1I1

= 1 −T2

T1

(80)

This means that an auto transformer requires the use of lesser quantity of copper

given by the ratio of turns. This ratio therefore denotes the savings in copper. As the

space for the second winding need not be there, the window space can be less for an auto

transformer, giving some saving in the lamination weight also. The larger the ratio of the

voltages, smaller is the savings. As T2 approaches T1 the savings become significant. Thus

auto transformers become ideal choice for close ratio transformations. The savings in mate-

rial is obtained, however, at a price. The electrical isolation between primary and secondary

75





V1

I1+I2

V1+V2

V2

I2

I1

ZL

I1+I2 I1

I2

I2

φ

Figure 29: Two Winding Transformer used as auto transformer

has to be sacrificed.

If we are not looking at the savings in the material, even then going in for the auto

transformer type of connection can be used with advantage, to obtain higher output. This

can be illustrated as follows. Fig. 29 shows a regular two winding transformer of a voltage

ratio V1 : V2, the volt ampere rating being V1I1 = V2I2 = S. If now the primary is connected

across a supply of V1 volt and the secondary is connected in series addition manner with the

primary winding, the output voltage becomes (V1 + V2) volt. The new output of this auto

transformer will now be

I2(V1 + V2) = I2V2(1 +V1

V2

) = S(1 +V1

V2

) (81)

= V1(I1 + I2) = S(1 +I2

I1

) (82)

76





Thus an increased rating can be obtained compared to a two winding transformer

with the same material content. The windings can be connected in series opposition fashion

also. Then the new output rating will be

I2(V1 − V2) = I2V2(V1

V2

− 1) = S(V1

V2

− 1) (83)

The differential connection is not used as it is not advantageous as the cumulative

connection.

11.1 Equivalent circuit

V1

(I2 -I1)

V2

I2

I1

I1

I1 I2

r1,xl1

r2,xl2

Figure 30: Kirchoff’s Law Application to auto transformer

As mentioned earlier the magnetizing current can be neglected, for simplicity. Writing

77





the Kirchoff’s equation to the primary and secondary of Fig. 30 we have

V1 = E1 + I1(r1 + jxl1) − (I2 − I1)(r2 + jxl2) (84)

Note that the resistance r1 and leakage reactance xl1 refer to that part of the winding where

only the primary current flows. Similarly on the load side we have,

E2 = V2 + (I2 − I1)(r2 + jxl2) (85)

The voltage ratio V1 : V2 = E1 : E2 = T1 : T2 = a where T1 is the total turns of the

primary.

Then E1 = aE2 and I2 = aI1

multiplying equation(84) by ’a’ and substituting in (83) we have

V1 = aV2 + a(I2 − I1)(r2 + jxl2) + I1(r1 + jxl1) − (I2 − I1)(r2 + jxl2)

= aV2 + I1(r1 + jxl1 + r2 + jxl2 − ar2 − ajxl2) + I2(ar2 + jaxl2 − r2 − jxl2)

= aV2 + I1(r1 + jxl1 + r2 + jxl2 + a2r2 + ja2xl2 − ar2 − ajxl2 − ar2 − jaxl2)

= aV2 + I1(r1 + r2(1 + a2 − 2a) + jxl1 + xl2(1 + a2 − 2a))

= aV2 + I1(r1 + (a − 1)2r2 + jxl1 + (a − 1)2xl2) (86)

Equation (85) yields the equivalent circuit of Fig. 31 where Re = r1 + (a − 1)2r2 and

Xe = xl1 + (a − 1)2xl2.

The magnetization branch can now be hung across the mains for completeness. The

above equivalent circuit can now be compared with the approximate equivalent circuit of

a two winding case Re = r1 + a2r2 and Xe = xl1 + a2xl2. Thus in the case of an auto

transformer total value of the short circuit impedance is lower and so also the percentage

resistance and reactance. Thus the full load regulation is lower. Having a smaller value

of short circuit impedance is sometimes considered to be a disadvantage. That is because

78





Re jXe

Rc jXmV1

Ic Im

Io

V’2=aV1

Re=r1+(a-1)2r2

Xl=xl1+(a-1)2xl2

Figure 31: Equivalent Circuit of auto transformers

the short circuit currents become very large in those cases. The efficiency is higher in auto

transformers compared to their two winding counter part at the same load. The phasor

diagram of operation for the auto transformer drawing a load current at a lagging power

factor angle of θ2 is shown in Fig. 32. The magnetizing current is omitted here again for

simplicity.

From the foregoing study it is seen that there are several advantages in going in for the

autotransformer type of arrangement. The voltage/current transformation and impedance

conversion aspects of a two winding transformer are retained but with lesser material (and

hence lesser weight) used. The losses are reduced increasing the efficiency. Reactance is

reduced resulting in better regulation characteristics. All these benefits are enhanced as

the voltage ratio approaches unity. The price that is required to be paid is loss of electri-

cal isolation and a larger short circuit current (and larger short circuit forces on the winding).

79





φ

I1

E1

I1r1

I1x1

(I2-I1)x2

V1

(I2-I1)r2

(I2-I1)x2

(I2-I1)r2

V2

I2

E2

I2

θ1

θ2

Figure 32: Phasor Diagram of Operation of an autotransformer

80





Auto transformers are used in applications where electrical isolation is not a critical

requirement. When the ratio V2 : V1 is 0.3 or more they are used with advantage. The

normal applications are motor starters, boosters or static balancers.

Vin

M oving contact

Variable

a.c output

Figure 33: Variable Secondary Voltage Arrangement

Another wide spread application of auto transformer type of arrangement is in ob-

taining a variable a.c. voltage from a fixed a.c. voltage supply. Here only one winding is used

as in the auto transformer. The secondary voltage is tapped by a brush whose position and

hence the output voltage is variable. The primary conductor is bared to facilitate electrical

contact Fig. 33. Such arrangement cannot exploit the savings in the copper as the output

voltage is required right from zero volts upwards.

The conductor is selected based on the maximum secondary current that could be

drawn as the output voltage varies in practically continuous manner. These are used in

81





voltage stabilizers, variable d.c. arrangements (with a diode bridge) in laboratories, motor

starters, dimmers etc.

82





12 Harmonics

In addition to the operation of transformers on the sinusoidal supplies, the harmonic

behavior becomes important as the size and rating of the transformer increases. The effects

of the harmonic currents are

1. Additional copper losses due to harmonic currents

2. Increased core losses

3. Increased electro magnetic interference with communication circuits.

On the other hand the harmonic voltages of the transformer cause

1. Increased dielectric stress on insulation

2. Electro static interference with communication circuits.

3. Resonance between winding reactance and feeder capacitance.

In the present times a greater awareness is generated by the problems of harmonic

voltages and currents produced by non-linear loads like the power electronic converters.

These combine with non-linear nature of transformer core and produce severe distortions in

voltages and currents and increase the power loss. Thus the study of harmonics is of great

practical significance in the operation of transformers. The discussion here is confined to the

harmonics generated by transformers only.

83





e

t’ t’’ t iϕi’ϕ

i’’ϕiϕ

i’ϕ i’’ϕ

ϕ

ϕ’

ϕ’’

ϕ

ϕ’

ϕ’’

Figure 34: Harmonics Generated by Transformers

12.1 Single phase transformers

Modern transformers operate at increasing levels of saturation in order to reduce

the weight and cost of the core used in the same. Because of this and due to the hysteresis,

the transformer core behaves as a highly non-linear element and generates harmonic voltages

and currents. This is explained below. Fig. 34 shows the manner in which the shape of the

magnetizing current can be obtained and plotted. At any instant of the flux density wave

the ampere turns required to establish the same is read out and plotted, traversing the

hysteresis loop once per cycle. The sinusoidal flux density curve represents the sinusoidal

applied voltage to some other scale. The plot of the magnetizing current which is peaky is

analyzed using Fourier analysis. The harmonic current components are obtained from this

analysis. These harmonic currents produce harmonic fields in the core and harmonic voltages

in the windings. Relatively small value of harmonic fields generate considerable magnitude

of harmonic voltages. For example a 10% magnitude of 3rd harmonic flux produces 30%

84





magnitude of 3rd harmonic voltage. These effects get even more pronounced for higher

order harmonics. As these harmonic voltages get short circuited through the low impedance

of the supply they produce harmonic currents. These currents produce effects according to

Lenz’s law and tend to neutralize the harmonic flux and bring the flux wave to a sinusoid.

Normally third harmonic is the largest in its magnitude and hence the discussion is based on

it. The same can be told of other harmonics also. In the case of a single phase transformer

the harmonics are confined mostly to the primary side as the source impedance is much

smaller compared to the load impedance. The understanding of the phenomenon becomes

more clear if the transformer is supplied with a sinusoidal current source. In this case current

has to be sinusoidal and the harmonic currents cannot be supplied by the source and hence

the induced emf will be peaky containing harmonic voltages. When the load is connected on

the secondary side the harmonic currents flow through the load and voltage tends to become

sinusoidal. The harmonic voltages induce electric stress on dielectrics and increased electro

static interference. The harmonic currents produce losses and electro magnetic interference

as already noted above.

12.2 Three phase banks of single phase transformers

In the case of single phase transformers connected to form three phase bank, each

transformer is magnetically decoupled from the other. The flow of harmonic currents are

decided by the type of the electrical connection used on the primary and secondary sides.

Also, there are three fundamental voltages in the present case each displaced from the other

by 120 electrical degrees. Because of the symmetry of the a.c. wave about the time axis

only odd harmonics need to be considered. The harmonics which are triplen (multiples of

three) behave in a similar manner as they are co-phasal or in phase in the three phases. The

85





non-triplen harmonics behave in a similar manner to the fundamental and have ±120◦ phase

displacement between them. The harmonic behavior of poly-phase banks can be discussed

now.

Dd connection In three phase banks with mesh connection on both primary side and sec-

ondary side a closed path is available for the triplen harmonics to circulate currents.

Thus the supply current is nearly sinusoidal (but for the non-triplen harmonic cur-

rents). The triplen harmonic currents inside the closed mesh winding correct the flux

density wave to be nearly sinusoidal. The secondary voltages will be nearly sinusoidal.

Third harmonics currents flow both in the primary and the secondary and hence the

magnitudes of these currents, so also the drops due to them will be lower.

Dy and Yd connection (without neutral connection) Behavior of the bank with mesh

connection on one side is similar to the one discussed under Dd connection. The har-

monic currents and drops and the departure of the flux density from sinusoidal are

larger in the present case compared to Dd banks.

Yy connection without neutral wires With both primary and secondary connected in

star no closed path exists. As the triplen harmonics are always in phase, by virtue

of the Y connection they get canceled in the line voltages. Non-triplen harmonics

like fundamental, become√

3 times phase value and appear in the line voltages. Line

currents remain sinusoidal except for non-triplen harmonic currents. Flux wave in each

transformer will be flat topped and the phase voltages remain peaked. The potential

of the neutral is no longer steady. The star point oscillates due to the third harmonic

voltages. This is termed as ”oscillating neutral”.

Yy connection with neutral wires When a neutral wire is provided the triplen har-

86





monic current can flow and the condition is similar to the single phase case (with a

star connected 4 wire source or with the system earth). The neutral wire carries three

times the triplen harmonic current of one transformer as these currents are co-phasal.

Unloaded secondary neutral will not be operative. Other polyphase connections not

discussed above explicitly will fall under one type or the other of the cases discussed.

In a Yy connection, to obtain third harmonic suppression one may provide a third

winding which is connected in mesh, which can be an unloaded winding. It is called a

tertiary. This winding improves the single phase to earth fault detection also. Further,

this winding can be used to feed some permanent station loads also. Such transform-

ers are designated as Yyd transformers. If the neutral wires are provided and also

mesh connected winding is present, then triplen harmonics are ’shared’ between them

depending upon their impedances.

12.3 Three phase transformers units

As against a bank of three single phase transformers connected to three phase

mains, a three phase transformer generally has the three magnetic circuits that are inter-

acting. The exception to this rule is a 3-phase shell type transformer. In the shell type of

construction, even though the three cores are together, they are non-interacting. Three limb

core type 3-phase transformer is the one in which the phases are magnetically also linked.

Flux of each limb uses the other two limbs for its return path. This is true for fundamental

and non-triplen harmonics. The triplen harmonics being co-phasal cannot use other limbs

for the return path (this holds good for zero sequence, unbalanced fundamental mmf also).

The flux path is completed through the air. So substantially large value of the mmf produces

a low value of third harmonic flux as the path of the flux is through the air and has a very

87





high reluctance. Thus the flux in the core remains nearly sinusoidal, so also the induced emf.

This happens irrespective of the type of connection used. The triplen order flux, sometimes

links the tank and produces loss in the same.

Other harmonics can be suppressed by connecting tuned filters at the terminals.

Harmonic current compensation using special magnetic circuit design is considered to be

outside the scope here.

88




Electrical Machines I Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao


13 Poly Phase connections and Poly phase Transform-

ers

The individual transformers are connected in a variety of ways in a power system.

Due to the advantages of polyphase power during generation, transmission and utilization

polyphase power handling is very important. As an engineering application is driven by

techno-economic considerations, no single connection or setup is satisfactory for all appli-

cations. Thus transformers are deployed in many forms and connections. Star and mesh

connections are very commonly used. Apart from these, vee or open delta connections, zig

zag connections , T connections, auto transformer connections, multi winding transformers

etc. are a few of the many possibilities. A few of the common connections and the tech-

nical and economic considerations that govern their usage are discussed here. Literature

abounds in the description of many other. Apart from the characteristics and advantages

of these, one must also know their limitations and problems, to facilitate proper selection of

a configuration for an application. Many polyphase connections can be formed using single

phase transformers. In some cases it may be preferable to design, develop and deploy a

polyphase transformer itself. In a balanced two phase system we encounter two voltages

that are equal in magnitude differing in phase by 90◦. Similarly, in a three phase system

there are three equal voltages differing in phase 120 electrical degrees. Further there is an

order in which they reach a particular voltage magnitude. This is called the phase sequence.

In some applications like a.c. to d.c. conversion, six phases or more may be encountered.

Transformers used in all these applications must be connected properly for proper function-

ing. The basic relationship between the primary and secondary voltages (brought about by

a common mutual flux and the number of turns), the polarity of the induced emf (decided

by polarity test and used with dot convention) and some understanding of the magnetic

89






circuit are all necessary for the same. To facilitate the manufacturer and users, interna-

tional standards are also available. Each winding has two ends designated as 1 and 2. The

HV winding is indicated by capital letters and the LV winding by small letters. If more

terminals are brought out from a winding by way of taps there are numbered in the increas-

ing numbers in accordance to their distance from 1 (eg A1, A2, A3...). If the induced emf

at an instant is from A1 to A2 on the HV winding it will rise from a1 to a2 on the LV winding.

Out of the different polyphase connections three phase connections are mostly en-

countered due to the wide spread use of three phase systems for generation, transmission

and utilization. Three balanced 3-phase voltages can be connected in star or mesh fashion

to yield a balanced 3-phase 3-wire system. The transformers that work on the 3-phase sup-

ply have star, mesh or zig-zag connected windings on either primary secondary or both. In

addition to giving different voltage ratios, they introduce phase shifts between input and

output sides. These connections are broadly classified into 4 popular vector groups.

1. Group I: zero phase displacement between the primary and the secondary.

2. Group II: 180◦ phase displacement.

3. Group III: 30◦ lag phase displacement of the secondary with respect to the primary.

4. Group IV: 30◦ lead phase displacement of the secondary with respect to the primary.

A few examples of the physical connections and phasor diagrams are shown in Fig. 35

and Fig. 36 corresponding to each group. The capital letters indicates primary and the

small letters the secondary. D/d stand for mesh, Y/y - for star, Z/z for zig-zag. The angu-

lar displacement of secondary with respect to the primary are shown as clock position, 0◦

90






Group1 00 Phase shift

W indings & Term inals E.M .F Vector diagram s

A2 a2

B2 b2

C2 c2

N n

a1

b1

c1

A1

B1

C1

A2 a2

B2 b2

C2 c2

A1

B1

C1

a1

b1

c1

a4

b4

c4

A2

B2

C2

A1

B1

C1

n

a1

b1

c1

A2

C2B2

a2

A2

C2

B2

a2

A2

C2

B2

(a)



A2

C2B2

A2 a1

B2 b1

C2 c1

n

A1

B1

C1

a1

b1

c1

N

a1

b1

c1

a1

b1

c1

a2

b2

c2

A2

B2

C2

A1

B1

C1

a3

b3

c3

n

a1

b1

c1

A2

B2

C2

A1

B1

C1

A2

C2 B2

A2

C2 B2

(b)

Figure 35: Vector Groups for 3-phase Transformer Connections91








A2 a2

B2 b2

C2 c2

n

A1

B1

C1

a1

b1

c1

A2 a2

B2 b2

C2 c2

N

A1

B1

C1

a1

b1

c1

A2 a4

B2 b4

C2 c4

N

A1

B1

C1

n

a1

b1

c1

A2

C2B2

a2

A2

C2B2

A2

C2B2

a2

(a)

Group4 + 300 Phase shift


A2

B2

A1

B1

C1

a2

b2

c2

n

a1

b1

c1

A2

B2

C2

N

A1

B1

C1

a1

b1

c1

a1

b1

c1

a2

b2

c2

A2

B2

C2

N

A1

B1

C1

n

a1

b1

c1

a3

b3

c3

a4

b4

c4

A2

C2

B2

a2

C2B2

C2

B2

A2

B2

C2

(b)

Figure 36: Vector Groups for 3-phase Transformer Connections92






referring to 12 o’clock position. These vector groups are especially important when two or

more transformers are to be connected in parallel.

Star connection is normally cheaper as there are fewer turns and lesser cost of insula-

tion. The advantage becomes more with increase in voltage above 11kv. In a star connected

winding with earthed-neutral the maximum voltage to the earth is ( 1√

3)of the line voltage.

Also star connection permits mixed loading due to the presence of the neutral. Mesh con-

nections are advantageous in low voltage transformers as insulation costs are insignificant

and the conductor size becomes ( 1√

3) of that of star connection and permits ease of winding.

The common polyphase connections are briefly discussed now.

Star/star (Yy0, Yy6)connection This is the most economical one for small high voltage

transformers. Insulation cost is highly reduced. Neutral wire can permit mixed load-

ing. Triplen harmonics are absent in the lines. These triplen harmonic currents cannot

flow, unless there is a neutral wire. This connection produces oscillating neutral. Three

phase shell type units have large triplen harmonic phase voltage. However three phase

core type transformers work satisfactorily. A tertiary mesh connected winding may be

required to stabilize the oscillating neutral due to third harmonics in three phase banks.

Mesh/mesh (Dd0, Dd6) This is an economical configuration for large low voltage trans-

formers. Large amount of unbalanced load can be met with ease. Mesh permits a cir-

culating path for triplen harmonics thus attenuates the same. It is possible to operate

with one transformer removed in open delta or Vee connection meeting 58 percent of

the balanced load. Three phase units cannot have this facility. Mixed single phase

loading is not possible due to the absence of neutral.

93






Star/mesh(Dy or Yd ) This arrangement is very common for power supply transform-

ers. The delta winding permits triplen harmonic currents to circulate in the closed

path and attenuates them.

Zig zag/ star (ZY1 or Zy11) Zigzag connection is obtained by inter connection of phases.

4-wire system is possible on both sides. Unbalanced loading is also possible. Oscillat-

ing neutral problem is absent in this connection. This connection requires 15% more

turns for the same voltage on the zigzag side and hence costs more.

Generally speaking a bank of three single phase transformers cost about 15% more

than their 3-phase counter part. Also, they occupy more space. But the spare capac-

ity cost will be less and single phase units are easier to transport.

Mesh connected three phase transformers resemble 3- single phase units but kept in

a common tank. In view of this single tank, the space occupied is less. Other than

that there is no big difference. The 3-phase core type transformer on the other hand

has a simple core arrangement. The three limbs are equal in cross section. Primary

and secondary of each phase are housed on the same limb. The flux setup in any limb

will return through the other two limbs as the mmf of those limbs are in the proper

directions so as to aid the same. Even though magnetically this is not a symmetrical

arrangement, as the reluctance to the flux setup by side limbs is different from that of

the central limb, it does not adversely affect the performance. This is due to the fact

that the magnetizing current itself forms a small fraction of the total phase current

drawn on load. The added advantage of 3-phase core is that it can tolerate substantially

94






large value of 3rd harmonic mmf without affecting the performance. The 3rd harmonic

mmf of the three phases will be in phase and hence rise in all the limbs together.

The 3rd harmonic flux must therefore find its path through the air. Due to the high

reluctance of the air path even a substantially large value of third harmonic mmf

produces negligible value of third harmonic flux. Similarly unbalanced operation of the

transformer with large zero sequence fundamental mmf content also does not affect its

performance. Even with Yy type of poly phase connection without neutral connection

the oscillating neutral does not occur with these cores. Finally, three phase cores

themselves cost less than three single phase units due to compactness.

95






14 Parallel operation of one phase and two phase trans-

formers

By parallel operation we mean two or more transformers are connected to the same

supply bus bars on the primary side and to a common bus bar/load on the secondary side.

Such requirement is frequently encountered in practice. The reasons that necessitate parallel

operation are as follows.

1. Non-availability of a single large transformer to meet the total load requirement.

2. The power demand might have increased over a time necessitating augmentation of the

capacity. More transformers connected in parallel will then be pressed into service.

3. To ensure improved reliability. Even if one of the transformers gets into a fault or is

taken out for maintenance/repair the load can continued to be serviced.

4. To reduce the spare capacity. If many smaller size transformers are used one machine

can be used as spare. If only one large machine is feeding the load, a spare of similar

rating has to be available. The problem of spares becomes more acute with fewer

machines in service at a location.

5. When transportation problems limit installation of large transformers at site, it may

be easier to transport smaller ones to site and work them in parallel.

Fig. 37 shows the physical arrangement of two single phase transformers working in

parallel on the primary side. Transformer A and Transformer B are connected to input

voltage bus bars. After ascertaining the polarities they are connected to output/load bus

96






E1 E2

V1 V2IA

E1 E2

load

A

B

supply bus Load bus

IB

Figure 37: Parallel Operation of Two Single Phase Transformers - Physical

97






bars. Certain conditions have to be met before two or more transformers are connected in

parallel and share a common load satisfactorily. They are,

1. The voltage ratio must be the same.

2. The per unit impedance of each machine on its own base must be the same.

3. The polarity must be the same, so that there is no circulating current between the

transformers.

4. The phase sequence must be the same and no phase difference must exist between the

voltages of the two transformers.

These conditions are examined first with reference to single phase transformers and then the

three phase cases are discussed.

Same voltage ratio Generally the turns ratio and voltage ratio are taken to be the same.

If the ratio is large there can be considerable error in the voltages even if the turns ratios

are the same. When the primaries are connected to same bus bars, if the secondaries

do not show the same voltage, paralleling them would result in a circulating current

between the secondaries. Reflected circulating current will be there on the primary

side also. Thus even without connecting a load considerable current can be drawn

by the transformers and they produce copper losses. In two identical transformers

with percentage impedance of 5 percent, a no-load voltage difference of one percent

will result in a circulating current of 10 percent of full load current. This circulating

current gets added to the load current when the load is connected resulting in unequal

sharing of the load. In such cases the combined full load of the two transformers can

never be met without one transformer getting overloaded.

98






Per unit impedance Transformers of different ratings may be required to operate in par-

allel. If they have to share the total load in proportion to their ratings the larger

machine has to draw more current. The voltage drop across each machine has to be

the same by virtue of their connection at the input and the output ends. Thus the

larger machines have smaller impedance and smaller machines must have larger ohmic

impedance. Thus the impedances must be in the inverse ratios of the ratings. As the

voltage drops must be the same the per unit impedance of each transformer on its

own base, must be equal. In addition if active and reactive power are required to be

shared in proportion to the ratings the impedance angles also must be the same. Thus

we have the requirement that per unit resistance and per unit reactance of both the

transformers must be the same for proper load sharing.

Polarity of connection The polarity of connection in the case of single phase transform-

ers can be either same or opposite. Inside the loop formed by the two secondaries

the resulting voltage must be zero. If wrong polarity is chosen the two voltages get

added and short circuit results. In the case of polyphase banks it is possible to have

permanent phase error between the phases with substantial circulating current. Such

transformer banks must not be connected in parallel. The turns ratios in such groups

can be adjusted to give very close voltage ratios but phase errors cannot be compen-

sated. Phase error of 0.6 degree gives rise to one percent difference in voltage. Hence

poly phase transformers belonging to the same vector group alone must be taken for

paralleling.

Transformers having −30◦ angle can be paralleled to that having +30◦ angle by re-

versing the phase sequence of both primary and secondary terminals of one of the

transformers. This way one can overcome the problem of the phase angle error.

99






Phase sequence The phase sequence of operation becomes relevant only in the case of

poly phase systems. The poly phase banks belonging to same vector group can be

connected in parallel. A transformer with +30◦ phase angle however can be paralleled

with the one with −30◦ phase angle, the phase sequence is reversed for one of them

both at primary and secondary terminals. If the phase sequences are not the same

then the two transformers cannot be connected in parallel even if they belong to same

vector group. The phase sequence can be found out by the use of a phase sequence

indicator.

Performance of two or more single phase transformers working in parallel can be com-

puted using their equivalent circuit. In the case of poly phase banks also the approach

is identical and the single phase equivalent circuit of the same can be used. Basically

two cases arise in these problems. Case A: when the voltage ratio of the two trans-

formers is the same and Case B: when the voltage ratios are not the same. These are

discussed now in sequence.

14.1 Case A: Equal voltage ratios

Always two transformers of equal voltage ratios are selected for working in parallel.

This way one can avoid a circulating current between the transformers. Load can be switched

on subsequently to these bus bars. Neglecting the parallel branch of the equivalent circuit the

above connection can be shown as in Fig. 38(a),(b). The equivalent circuit is drawn in terms

of the secondary parameters. This may be further simplified as shown under Fig. 38(c). The

voltage drop across the two transformers must be the same by virtue of common connection

at input as well as output ends. By inspection the voltage equation for the drop can be

100






V2’

V1

ZA

ZB

IA

IB

RA

RB

jXA

jXB

V2’

IV1

IA

IB

RA

RB

jXA

jXB

(a) (b)

V’L

IA

IB

ZL

I

ZA

ZB

VLoad

VL

(c)

Figure 38: Equivalent Circuit for Transformers working in Parallel -Simplified circuit and

Further simplification for identical voltage ratio

101






written as

IAZA = IBZB = IZ = v (say) (87)

HereI = IA + IB (88)

And Z is the equivalent impedance of the two transformers given by,

Z =ZAZB

ZA + ZB

(89)

Thus IA =v

ZA

=IZ

ZA

= I.ZB

ZA + ZB

(90)

and IB =v

ZB

=IZ

ZB

= I.ZA

ZA + ZB

If the terminal voltage is V = IZL then the active and reactive power supplied by each of

the two transformers is given by

PA = Real(V I∗

A) and QA = Imag(V I∗

A) and (91)

PB = Real(V I∗

B) and QB = Imag(V I∗

B) (92)

From the above it is seen that the transformer with higher impedance supplies lesser

load current and vice versa. If transformers of dissimilar ratings are paralleled the trans-

former with larger rating shall have smaller impedance as it has to produce the same drop

as the other transformer, at a larger current. Thus the ohmic values of the impedances must

be in the inverse ratio of the ratings of the transformers. IAZA = IBZB, therefore IA

IB

= ZB

ZA

.

Expressing the voltage drops in p.u basis, we aim at the same per unit drops at any load for

the transformers. The per unit impedances must therefore be the same on their respective

bases.

Fig. 39 shows the phasor diagram of operation for these conditions. The drops are

magnified and shown to improve clarity. It is seen that the total voltage drop inside the

102






φBφA

E

θBθA

IB

IA

φ

IL

V2

V

IARA

IRIBRB

IBXBIX

IAXA

Figure 39: Phasor Diagram of Operation for two Transformers working in Parallel

transformers is v but the currents IA and IB are forced to have a different phase angle due

to the difference in the internal power factor angles θA and θB. This forces the active and

reactive components of the currents drawn by each transformer to be different ( even in

the case when current in each transformer is the same). If we want them to share the load

current in proportion to their ratings, their percentage ( or p.u) impedances must be the

same. In order to avoid any divergence and to share active and reactive powers also properly,

θA = θB . Thus the condition for satisfactory parallel operation is that the p.u resistances

and p.u reactance must be the same on their respective bases for the two transformers. To

determine the sharing of currents and power either p.u parameters or ohmic values can be

used.

103






14.2 Case B :Unequal voltage ratios

VL

IA

IB

ZL

EA EB

I

RAjXA

RB jXB

Figure 40: Equivalent Circuit for unequal Voltage Ratio

One may not be able to get two transformers of identical voltage ratio in

spite of ones best efforts. Due to manufacturing differences, even in transformers built as

per the same design, the voltage ratios may not be the same. In such cases the circuit

representation for parallel operation will be different as shown in Fig. 40. In this case the

two input voltages cannot be merged to one, as they are different. The load brings about a

common connection at the output side. EA and EB are the no-load secondary emf. ZL is

the load impedance at the secondary terminals. By inspection the voltage equation can be

written as below:

EA = IAZA + (IA + IB)ZL = V + IAZA ·

EB = IBZB + (IA + IB)ZL = V + IBZB· (93)

Solving the two equations the expression for IA and IB can be obtained as

104






IA =EAZB + (EA − EB)ZL

ZAZB + ZL(ZA + ZB)and (94)

IB =EBZA + (EB − EA)ZL

ZAZB + ZL(ZA + ZB)

ZA and ZB are phasors and hence there can be angular difference also in addition to

the difference in magnitude. When load is not connected there will be a circulating current

between the transformers. The currents in that case can be obtained by putting ZL = ∞

( after dividing the numerator and the denominator by ZL ). Then,

IA = −IB =(EA − EB)

(ZA + ZB)(95)

If the load impedance becomes zero as in the case of a short circuit, we have,

IA =EA

ZA

and IB =EB

ZB

(96)

Instead of the value of ZL if the value of V is known , the currents can be easily determined

( from Eqns. 93 ) as

IA =EA − V

ZA

and IB =EB − V

ZB

(97)

If more than two transformers are connected across a load then the calculation of

load currents following the method suggested above involves considerable amount of compu-

tational labor. A simpler and more elegant method for the case depicted in Fig. 41 is given

below. It is known by the name parallel generator theorem.

IL = IA + IB + IC + ......

But IA =EA − V

ZA

, IB =EB − V

ZB

, IC =EC − V

ZC

V = IL.ZL (98)

105






V

IA

IB

IC

ZL

EA

EB

EC

I

RA

RB

jXA

jXB

RCjXC

Figure 41: Parallel Generator Theorem

Combining these equations

V

ZL

=EA − V

ZA

+EB − V

ZB

+EC − V

ZC

+ ... (99)

Grouping the terms together

V (1

ZL

+1

ZA

+1

ZB

+1

ZC

+ ...) =EA

ZA

+EB

ZB

+EC

ZC

+ ...

= ISCA + ISCB + ISCC + .... (100)

(1

ZL

+1

ZA

+1

ZB

+1

ZC

+ ...) =1

Z(101)

V = Z(ISCA + ISCB + ISCC + ....) (102)

From this V can be obtained. Substituting V in Eqn. 98, IA, IB etc can be obtained.

Knowing the individual current phasor, the load shared by each transformer can be com-

puted.

106




15 Transformer voltage control and Tap changing

Regulating the voltage of a transformer is a requirement that often arises in a power

application or power system.

In an application it may be needed

1. To supply a desired voltage to the load.

2. To counter the voltage drops due to loads.

3. To counter the input supply voltage changes on load.

On a power system the transformers are additionally required to perform the task of

regulation of active and reactive power flows.

Reverser

Booster transformer

Regulation

transformer

Booster transformer

Reverser

Main

transformer

tertiary

B B

1

2

1

2

Figure 42: Tap changing and Buck Boost arrangement

The voltage control is performed by changing the turns ratio. This is done by provi-

sion of taps in the winding. The volts per turn available in large transformers is quite high

and hence a change of even one turn on the LV side represents a large percentage change

in the voltage. Also the LV currents are normally too large to take out the tapping from

the windings. LV winding being the inner winding in a core type transformer adds to the

107




difficulty of taking out of the taps. Hence irrespective of the end use for which tapping is put

to, taps are provided on the HV winding. Provision of taps to control voltage is called tap

changing. In the case of power systems, voltage levels are some times changed by injecting a

suitable voltage in series with the line. This may be called buck-boost arrangement. In ad-

dition to the magnitude, phase of the injected voltage may be varied in power systems. The

tap changing arrangement and buck boost arrangement with phase shift are shown in Fig. 42.

Tap changing can be effected when a) the transformers is on no- load and b) the load

is still remains connected to the transformer. These are called off load tap changing and

on load tap changing. The Off load tap changing relatively costs less. The tap positions

are changed when the transformer is taken out of the circuit and reconnected. The on-load

tap changer on the other hand tries to change the taps without the interruption of the load

current. In view of this requirement it normally costs more. A few schemes of on-load tap

changing are now discussed.

108




HV LV

Reactor

s

1

2

3

4

5

Figure 43: Reactor Method of Tap Changer ( with table of switching)

109




Tap switches closed

1 1,s

2 1,2

3 2,s

4 2,3

5 3,s

6 3,4

7 4,s

8 4,5

9 5,s

Reactor method The diagram of connections is shown in Fig. 43. This method employs

an auxiliary reactor to assist tap changing. The switches for the taps and that across

the reactor(S) are connected as shown. The reactor has a center tapped winding on

a magnetic core. The two ends of the reactor are connected to the two bus bars to

which tapping switches of odd/even numbered taps are connected. When only one tap

is connected to the reactor the shorting switch S is closed minimizing the drop in the

reactor. The reactor can also be worked with both ends connected to two successive

taps. In that case the switch ’S’ must be kept open. The reactor limits the circulating

current between the taps in such a situation. Thus a four step tapped winding can be

used for getting seven step voltage on the secondary(see the table of switching). The

advantage of this type of tap changer are

1. Load need not be switched off.

2. More steps than taps are obtained.

3. Switches need not interrupt load current as a alternate path is always provided.

110




The major objection to this scheme seems to be that the reactor is in the circuit always

generating extra loss.

Parallel winding, transformer method In order to maintain the continuity of supply

the primary winding is split into two parallel circuits each circuit having the taps as

shown in Fig. 44. Two circuit breakers A and B are used in the two circuits. Initially

tap 1a and 1b are closed and the transformer is energized with full primary voltage.

To change the tap the circuit breaker A is opened momentarily and tap is moved from

1a to 2a. Then circuit breaker A is closed. When the circuit A is opened whole of the

primary current of the transformer flows through the circuit B. A small difference in

the number of turns between the two circuit exists. This produces a circulating current

between them. Next, circuit breaker B is opened momentarily, the tap is changed from

1b to 2b and the breaker is closed. In this position the two circuits are similar and there

is no circulating current. The circulating current is controlled by careful selection of

the leakage reactance. Generally, parallel circuits are needed in primary and secondary

to carry the large current in a big transformer. Provision of taps switches and circuit

breakers are to be additionally provided to achieve tap changing in these machines.

Series booster method In this case a separate transformer is used to buck/boost the

voltage of the main transformer. The main transformer need not be having a tapped

arrangement. This arrangement can be added to an existing system also. Fig. 42shows

the booster arrangement for a single phase supply. The reverser switch reverses the

polarity of the injected voltage and hence a boost is converted into a buck and vice

versa. The power rating of this transformer need be a small fraction of the main

transformer as it is required to handle only the power associated with the injected

voltage. One precaution to be taken with this arrangement is that the winding must

111




A B

HVLV

a1a2

a3a4

b1 b2 b3 b4

Figure 44: Parallel Primary Winding Tap Changing

112




not be open circuited. If it gets open circuited the core (B in fig) gets highly saturated.

In spite of the small ratings and low voltages and flexibility, this method of voltage

control costs more mainly due to the additional floor space it needs. The methods of

voltage regulation discussed so far basically use the principle of tap changing and hence

the voltage change takes place in steps. Applications like a.c. and d.c. motor speed

control, illumination control by dimmers, electro-chemistry and voltage stabilizers need

continuous control of voltage. This can be obtained with the help of moving coil voltage

regulators.

Vin

5%

95%

a1

b1

S

a2

b2

Vout

Figure 45: Moving Coil Voltage Regulator

moving coil voltage regulators Fig. 45 shows the physical arrangement of one such trans-

former. a, b are the two primary windings wound on a long core, wound in the opposite

113




sense. Thus the flux produced by each winding takes a path through the air to link

the winding. These fluxes link their secondaries a2 and b2. A short circuited moving

coil s is wound on the same limb and is capable of being held at any desired position.

This moving coil alters the inductances of the two primaries. The sharing of the total

applied voltage thus becomes different and also the induced emf in the secondaries a2

and b2. The total secondary voltage in the present case varies from 10 percent to 20

percent of the input in a continuous manner. The turns ratios of a1 : a2 and b1 : b2

are 4.86 and 10.6 respectively. 5

4.86+ 95

10.6= 10% when s is in the top position. In

the bottom position it becomes 95

4.86+ 5

10.6= 20%. By selecting proper ratios for the

secondaries a2 and b2 one can get the desired voltage variation.

V1

sliding contact

Variable secondary

a.c voltage

V2

a) without electrical isolation

V1

b) with electrical isolation

Figure 46: Sliding Contact Regulator

Sliding contact regulators These have two winding or auto transformer like construction.

The winding from which the output is taken is bared and a sliding contact taps the

voltage. The minimum step size of voltage change obtainable is the voltage across a

single turn. The conductor is chosen on the basis of the maximum load current on the

114




output side. In smaller ratings this is highly cost effective. Two winding arrangements

are also possible. The two winding arrangement provides electrical isolation also.These

are shown in Fig. 46.

115




D.C Machines

1 Introduction

The steam age signalled the beginning of an industrial revolution. The advantages

of machines and gadgets in helping mass production and in improving the services spurred

the industrial research. Thus a search for new sources of energy and novel gadgets received

great attention. By the end of the 18th century the research on electric charges received

a great boost with the invention of storage batteries. This enabled the research work on

moving charges or currents. It was soon discovered ( in 1820 ) that, these electric currents

are also associated with magnetic field like a load stone. This led to the invention of an

electromagnet. Hardly a year later the force exerted on a current carrying conductor placed

in the magnetic field was invented. This can be termed as the birth of a motor. A better

understanding of the inter relationship between electric and magnetic circuits was obtained

with the enumeration of laws of induction by Faraday in 1831. Parallel research was contem-

porarily being done to invent a source of energy to recharge the batteries in the form of a

d.c. source of constant amplitude (or d.c. generator). For about three decades the research

on d.c. motors and d.c. generators proceeded on independent paths. During the second half

of the 19th century these two paths merged. The invention of a commutator paved the way

for the birth of d.c. generators and motors. These inventions generated great interest in the

generation and use of electrical energy. Other useful machines like alternators, transformers

and induction motors came into existence almost contemporarily. The evolution of these

machines was very quick. They rapidly attained the physical configurations that are being

used even today. The d.c. power system was poised for a predominant place as a preferred

1




system for use, with the availability of batteries for storage, d.c. generators for conversion of

mechanical energy into electrical form and d.c. motors for getting mechanical outputs from

electrical energy.

The limitations of the d.c. system however became more and more apparent

as the power demand increased. In the case of d.c. systems the generating stations and the

load centers have to be near to each other for efficient transmission of energy. The invention

of induction machines in the 1880s tilted the scale in favor of a.c. systems mainly due to

the advantage offered by transformers, which could step up or step down the a.c.voltage

levels at constant power at extremely high efficiency. Thus a.c. system took over as the

preferred system for the generation transmission and utilization of electrical energy. The

d.c. system, however could not be obliterated due to the able support of batteries. Further,

d.c. motors have excellent control characteristics. Even today the d.c. motor remains an

industry standard as far as the control aspects are concerned. In the lower power levels and

also in regenerative systems the d.c. machines still have a major say.

In spite of the apparent diversity in the characteristics, the underlying princi-

ples of both a.c. and d.c. machines are the same. They use the electromagnetic principles

which can be further simplified at the low frequency levels at which these machines are used.

These basic principles are discussed at first.

2




1.1 Basic principles

Electric machines can be broadly classified into electrostatic machines and electro-

magnetic machines. The electrostatic principles do not yield practical machines for commer-

cial electric power generation. The present day machines are based on the electro-magnetic

principles. Though one sees a variety of electrical machines in the market, the basic under-

lying principles of all these are the same. To understand, design and use these machines the

following laws must be studied.

1. Electric circuit laws - Kirchoff ′s Laws

2. Magnetic circuit law - Ampere′s Law

3. Law of electromagnetic induction - Faraday′s Law

4. Law of electromagnetic interaction -BiotSavart′s Law

Most of the present day machines have one or two electric circuits linking a common

magnetic circuit. In subsequent discussions the knowledge of electric and magnetic circuit

laws is assumed. The attention is focused on the Faraday’s law and Biot Savart’s law in the

present study of the electrical machines.

1.1.1 Law of electro magnetic induction

Faraday proposed this law of Induction in 1831. It states that if the magnetic

flux lines linking a closed electric coil changes, then an emf is induced in the coil. This

emf is proportional to the rate of change of these flux linkages. This can be expressed

mathematically,

e ∝dψ

dt(1)

3




where ψ is the flux linkages given by the product of flux lines in weber that are linked

and N the number of turns of the coil. This can be expressed as,

e ∝ NdΦ

dt(2)

Here N is the number of turns of the coil, and Φ is the flux lines in weber link-

ing all these turns. The direction of the induced emf can be determined by the application of

Lenz’s law. Lenz’s law states that the direction of the induced emf is such as to produce an

effect to oppose this change in flux linkages. It is analogous to the inertia in the mechanical

systems.

The changes in the flux linkages associated with a turn can be brought about by

(i) changing the magnitude of the flux linking a static coil

(ii) moving the turn outside the region of a steady field

(iii) moving the turn and changing the flux simultaneously

These may be termed as Case(i), Case(ii), and Case(iii) respectively.

This is now explained with the help of a simple geometry. Fig. 1 shows a rectan-

gular loop of one turn (or N=1). Conductor 1 is placed over a region with a uniform flux

density of B Tesla. The flux lines, the conductor and the motion are in mutually perpendic-

ular directions. The flux linkages of the loop is BLN weber turns. If the flux is unchanging

and conductor stationary, no emf will be seen at the terminals of the loop. If now the flux

alone changes with time such that B = Bm. cosωt, as in Case(i), an emf given by

e =d

dt(Bm.L.N cosωt) = −(Bm.L.Nω). sinωt.

= −jBm.L.Nω. cosωt volt (3)

4




+-

L

X

B

Figure 1: Faraday’s law of Induction

appears across the terminals. This is termed as a ”transformer” emf.

If flux remains constant at Bm but the conductor moves with a velocity v, as in Case(ii),

then the induced emf is

e =dψ

dt=d(Bm.L.N)

dt= Bm.L.N

dX

dtvolts (4)

but

dX

dt= v ∴ e = Bm.L.N.v volts (5)

The emf induced in the loop is directly proportional to the uniform flux density under which

it is moving with a velocity v. This type of voltage is called speed emf (or rotational emf).

The Case(iii) refers to the situation where B is changing with time and so also is X. Then

the change in flux linkage and hence the value of e is given by

e =dψ

dt=d(Bm.L.X.N. cosωt)

dt= Bm. cosωt.L.N.

dX

dt−Bm.L.X.N.ω. sinωt. (6)

In this case both transformer emf and speed emf are present.

5




The Case(i) has no mechanical energy associated with it. This is the principle

used in transformers. One coil carrying time varying current produces the time varying field

and a second coil kept in the vicinity of the same has an emf induced in it. The induced emf

of this variety is often termed as the transformer emf.

The Case(ii) is the one which is employed in d.c. machines and alternators. A

static magnetic field is produced by a permanent magnet or by a coil carrying a d.c. current.

A coil is moved under this field to produce the change in the flux linkages and induce an emf

in the same. In order to produce the emf on a continuous manner a cylindrical geometry

is chosen for the machines. The direction of the field, the direction of the conductor of the

coil and the direction of movement are mutually perpendicular as mentioned above in the

example taken.

In the example shown above, only one conductor is taken and the flux ’cut’ by

the same in the normal direction is used for the computation of the emf. The second con-

ductor of the turn may be assumed to be far away or unmoving. This greatly simplifies the

computation of the induced voltage as the determination of flux linkages and finding its rate

of change are dispensed with. For a conductor moving at a constant velocity v the induced

emf becomes just proportional to the uniform flux density of the magnetic field where the

conductor is situated. If the conductor, field and motion are not normal to each other then

the mutually normal components are to be taken for the computation of the voltage. The

induced emf of this type is usually referred to as a rotational emf (due to the geometry).

Application of Faradays law according to Case(iii) above for electro mechani-

6




cal energy conversion results in the generation of both transformer and rotational emf to be

present in the coil moving under a changing field. This principle is utilized in the induction

machines and a.c. commutator machines. The direction of the induced emf is

Force Motion

B

emf and

current

F

(a) (b)

Figure 2: Law of induction-Generator action

decided next. This can be obtained by the application of the Lenz’s law and the law of

interaction. This is illustrated in Fig. 3.

In Case(i), the induced emf will be in such a direction as to cause a opposing

mmf if the circuit is closed. Thus, it opposes the cause of the emf which is change in ψ and

hence φ. Also the coil experiences a compressive force when the flux tries to increase and

a tensile force when the flux decays. If the coil is rigid, these forces are absorbed by the

supporting structure.

In Case(ii), the direction of the induced emf is as shown. Here again one could

derive the same from the application of the Lenz’s law. The changes in the flux linkages is

7




Motion,Force

B

emf

current

F

(a) (b)

Figure 3: Law of interaction- Motor action

brought about by the sweep or movement of the conductor. The induced emf, if permitted

to drive a current which produces an opposing force, is as shown in the figure. If one looks

closely at the field around the conductor under these conditions it is as shown in Fig. 2(a)and

(b). The flux lines are more on one side of the conductor than the other. These lines seem

to urge the conductor to the left with a force F . As F opposes v and the applied force,

mechanical energy gets absorbed in this case and the machine works as a generator. This

force is due to electro magnetic interaction and is proportional to the current and the flux

swept. Fig. 3(a)and (b) similarly explain the d.c.motor operation. The current carrying con-

ductor reacts with the field to develop a force which urges the conductor to the right. The

induced emf and the current are seen to act in opposite direction resulting in the absorption

of electric energy which gets converted into the mechanical form.

In Case (iii) also the direction of the induced emf can be determined in a

similar manner. However, it is going to be more complex due to the presence of transformer

8




emf and rotational emf which have phase difference between them.

Putting mathematically, in the present study of d.c.machines,

F = B.L.I Newton

When the generated voltage drives a current, it produces a reaction force on the

mechanical system which absorbs the mechanical energy. This absorbed mechanical energy

is the one which results in the electric current and the appearance of electrical energy in

the electrical circuit. The converse happens in the case of the motor. If we force a current

against an induced emf then the electrical power is absorbed by the same and it appears

as the mechanical torque on the shaft. Thus, it is seen that the motoring and generating

actions are easily changeable with the help of the terminal conditions.

9




2 Principles of d.c. machines

D.C. machines are the electro mechanical energy converters which work from a d.c.

source and generate mechanical power or convert mechanical power into a d.c. power. These

machines can be broadly classified into two types, on the basis of their magnetic structure.

They are,

1. Homopolar machines

2. Heteropolar machines.

These are discussed in sequence below.

2.1 Homopolar machines

Homopolar generators

Even though the magnetic poles occur in pairs, in a homopolar generator the conductors

are arranged in such a manner that they always move under one polarity. Either north pole

or south pole could be used for this purpose. Since the conductor encounters the magnetic

flux of the same polarity every where it is called a homopolar generator. A cylindrically

symmetric geometry is chosen. The conductor can be situated on the surface of the rotor

with one slip-ring at each end of the conductor. A simple structure where there is only

one cylindrical conductor with ring brushes situated at the ends is shown in Fig. 4. The

excitation coil produces a field which enters the inner member from outside all along the

periphery. The conductor thus sees only one pole polarity or the flux directed in one sense.

A steady voltage now appears across the brushes at any given speed of rotation. The polarity

of the induced voltage can be reversed by reversing either the excitation or the direction of

10




Brush

Field

coil

Flux

+

A

N

S

S

N+

A B

B

-

-

Figure 4: Homopolar Generator

11




rotation but not both. The voltage induced would be very low but the currents of very large

amplitudes can be supplied by such machines. Such sources are used in some applications

like pulse-current and MHD generators, liquid metal pumps or plasma rockets. The steady

field can also be produced using a permanent magnet of ring shape which is radially mag-

netized. If higher voltages are required one is forced to connect many conductors in series.

This series connection has to be done externally. Many conductors must be situated on the

rotating structure each connected to a pair of slip rings. However, this modification intro-

duces parasitic air-gaps and makes the mechanical structure very complex. The magnitude

of the induced emf in a conductor 10 cm long kept on a rotor of 10 cm radius rotating at

3000 rpm, with the field flux density being 1 Tesla every where in the air gap, is given by

e = BLv

= 1 ∗ 0.1 ∗ 2π ∗ 0.1 ∗3000

60= 3.14 volt

The voltage drops at the brushes become very significant at this level bringing down the

efficiency of power conversion. Even though homopolar machines are d.c. generators in a

strict sense that they ’generate’ steady voltages, they are not quite useful for day to day use.

A more practical converters can be found in the d.c. machine family called ”hetero-polar”

machines.

2.2 Hetero-polar d.c. generators

In the case of a hetero-polar generator the induced emf in a conductor goes through a

cyclic change in voltage as it passes under north and south pole polarity alternately. The

induced emf in the conductor therefore is not a constant but alternates in magnitude. For

12




A

-B

a

b

c

d

S

N

+

Load

Figure 5: Elementary hetro-polar machine

vArmature core

v

Pole

Yokev

-

N

S

A B

F3

S1

S2

S3

F1

F2

+

Field coil

v

v

Commutator

F4

S4

1

2

3

4

5

6

7

8

9

10

11

12

Figure 6: Two pole machine -With Gramme ring type armature

13




a constant velocity of sweep the induced emf is directly proportional to the flux density

under which it is moving. If the flux density variation is sinusoidal in space, then a sine

wave voltage is generated. This principle is used in the a.c generators. In the case of d.c.

generators our aim is to get a steady d.c. voltage at the terminals of the winding and not

the shape of the emf in the conductors. This is achieved by employing an external element,

which is called a commutator, with the winding.

Fig. 5 shows an elementary hetero-polar, 2-pole machine and one-coil arma-

ture. The ends of the coil are connected to a split ring which acts like a commutator. As

the polarity of the induced voltages changes the connection to the brush also gets switched

so that the voltage seen at the brushes has a unidirectional polarity. This idea is further

developed in the modern day machines with the use of commutators. The brushes are placed

on the commutator. Connection to the winding is made through the commutator only. The

idea of a commutator is an ingenious one. Even though the instantaneous value of the in-

duced emf in each conductor varies as a function of the flux density under which it is moving,

the value of this emf is a constant at any given position of the conductor as the field is sta-

tionary. Similarly the sum of a set of coils also remains a constant. This thought is the one

which gave birth to the commutator. The coils connected between the two brushes must be

”similarly located” with respect to the poles irrespective of the actual position of the rotor.

This can be termed as the condition of symmetry. If a winding satisfies this condition then

it is suitable for use as an armature winding of a d.c. machine. The ring winding due to

Gramme is one such. It is easy to follow the action of the d.c. machine using a ring winding,

hence it is taken up here for explanation.

14




Fig. 6 shows a 2-pole, 12 coil, ring wound armature of a machine. The 12 coils

are placed at uniform spacing around the rotor. The junction of each coil with its neighbor

is connected to a commutator segment. Each commutator segment is insulated from its

neighbor by a mica separator. Two brushes A and B are placed on the commutator which

looks like a cylinder. If one traces the connection from brush A to brush B one finds that

there are two paths. In each path a set of voltages get added up. The sum of the emfs is

constant(nearly). The constancy of this magnitude is altered by a small value corresponding

to the coil short circuited by the brush. As we wish to have a maximum value for the output

voltage, the choice of position for the brushes would be at the neutral axis of the field. If

the armature is turned by a distance of one slot pitch the sum of emfs is seen to be constant

even though a different set of coils participate in the addition. The coil which gets short

circuited has nearly zero voltage induced in the same and hence the sum does not change

substantially. This variation in the output voltage is called the ’ripple’. More the number of

coils participating in the sum lesser would be the ’percentage’ ripple.

Another important observation from the working principle of a heterogeneous

generator is that the actual shape of the flux density curve does not matter as long as the

integral of the flux entering the rotor is held constant; which means that for a given flux

per pole the voltage will be constant even if the shape of this flux density curve changes

(speed and other conditions remaining unaltered). This is one reason why an average flux

density over the entire pole pitch is taken and flux density curve is assumed to be rectangular.

A rectangular flux density wave form has some advantages in the derivation

of the voltage between the brushes. Due to this form of the flux density curve, the induced

15




emf in each turn of the armature becomes constant and equal to each other. With this back

ground the emf induced between the brushes can be derived. The value of the induced in

one conductor is given by

Ec = Bav.L.v Volt (7)

where

Bav- Average flux density over a pole pitch, Tesla.

L- Length of the ’active’ conductor, m.

v- Velocity of sweep of conductor, m/sec.

If there are Z conductors on the armature and they form b pairs of parallel circuits between

the brushes by virtue of their connections, then number of conductors in a series path is

Z/2b.

The induced emf between the brushes is

E = Ec.Z

2b(8)

E = Bav.L.v.Z

2bVolts (9)

But v = (2p).Y.n where p is the pairs of poles Y is the pole pitch, in meters, and n is the

number of revolutions made by the armature per second.

Also Bav can be written in terms of pole pitch Y , core length L, and flux per pole φ as

Bav =φ

(L.Y )Tesla (10)

Substituting in equation Eqn. 9,

E =φ

(L.Y ).L.(2p.Y.n).

Z

2b=

φpZn

bvolts (11)

The number of pairs of parallel paths is a function of the type of the winding chosen. This

16




will be discussed later under the section on the armature windings.

2.2.1 Torque production

When the armature is loaded, the armature conductors carry currents. These current

carrying conductors interact with the field and experience force acting on the same. This

force is in such a direction as to oppose their cause which in the present case is the relative

movement between the conductors and the field. Thus the force directly opposes the motion.

Hence it absorbs mechanical energy. This absorbed mechanical power manifests itself as the

converted electrical power. The electrical power generated by an armature delivering a

current of Ia to the load at an induced emf of E is EIa Watts. Equating the mechanical and

electrical power we have

2πnT = EIa (12)

where T is the torque in Nm. Substituting for E from Eqn. 11, we get

2πnT =p.φ.Z.n

b.Ia (13)

which gives torque T as

T =1

2π.p.φ.(

Ia

b)Z Nm (14)

This shows that the torque generated is not a function of the speed. Also,

it is proportional to ’total flux’ and ’Total ampere conductors’ on the armature, knowing that

Ia/2b is Ic the conductor current on the armature. The expression for the torque generated

can also be derived from the first principles by the application of the law of interaction. The

law of interaction states that the force experienced by a conductor of length L kept in a

17




uniform field of flux density B carrying a current Ic is proportional to B,L and Ic.

Force on a single conductor Fc is given by,

Fc = B.L.Ic Newton (15)

The total work done by an armature with Z conductors in one revolution is given by,

Wa = Bav.L.Ic.Z.(2p.Y ) Joules =φ

L.Y.L.Ic.Z.2p.Y Joules (16)

The work done per second or the power converted by the armature is,

Pconv = φ.2p.Z.Ic.n watts (17)

AsIc =Ia

2b(18)

= φ.p.Z.n.Ia

b(19)

which is nothing but EIa.

The above principles can easily be extended to the case of motoring mode

of operation also. This will be discussed next in the section on motoring operation of d.c.

machines.

2.2.2 Motoring operation of a d.c. machine

In the motoring operation the d.c. machine is made to work from a d.c. source and

absorb electrical power. This power is converted into the mechanical form. This is briefly

discussed here. If the armature of the d.c. machine which is at rest is connected to a d.c.

source then, a current flows into the armature conductors. If the field is already excited then

18




these current carrying conductors experience a force as per the law of interaction discussed

above and the armature experiences a torque. If the restraining torque could be neglected the

armature starts rotating in the direction of the force. The conductors now move under the

field and cut the magnetic flux and hence an induced emf appears in them. The polarity of

the induced emf is such as to oppose the cause of the current which in the present case is the

applied voltage. Thus a ’back emf’ appears and tries to reduce the current. As the induced

emf and the current act in opposing sense the machine acts like a sink to the electrical power

which the source supplies. This absorbed electrical power gets converted into mechanical

form. Thus the same electrical machine works as a generator of electrical power or the

absorber of electrical power depending upon the operating condition. The absorbed power

gets converted into electrical or mechanical power. This is briefly explained earlier with the

help of Figure 3(a) and 3(b). These aspects would be discussed in detail at a later stage.

19





3 Constructional aspects of d.c. machines

As mentioned earlier the d.c. machines were invented during the second half of the 19th

century. The initial pace of development work was phenomenal. The best configurations

stood all the competition and the test of time and were adopted. Less effective options were

discarded. The present day d.c. generator contains most, if not all, of the features of the

machine developed over a century earlier. To appreciate the working and the characteristics

of these machines, it is necessary to know about the different parts of the machine - both

electrical and non-electrical. The description would also aid the understanding of the reason

for selecting one form of construction or the other. An exploded view of a small d.c.

Figure 7: Exploded view of D.C.Machine

machine is shown in Fig. 7.

Click here to see the assembling of the parts.

The major parts can be identified as,

1. Body

2. Poles

20





3. Armature

4. Commutator and brush gear

5. Commutating poles

6. Compensating winding

7. Other mechanical parts

The constructional aspects relating to these parts are now discussed briefly in sequence.

Body The body constitutes the outer shell within which all the other parts are housed.

This will be closed at both the ends by two end covers which also support the bearings

required to facilitate the rotation of the rotor and the shaft. Even though for the

generation of an emf in a conductor a relative movement between the field and the

conductor would be enough, due to practical considerations of commutation, a rotating

conductor configuration is selected for d.c. machines. Hence the shell or frame supports

the poles and yoke of the magnetic system. In many cases the shell forms part of the

magnetic circuit itself. Cast steel is used as a material for the frame and yoke as the

flux does not vary in these parts. In large machines these are fabricated by suitably

welding the different parts. Those are called as fabricated frames. Fabrication as

against casting avoids expensive patterns. In small special machines these could be

made of stack of laminations suitably fastened together to form a solid structure.

Main poles Solid poles of fabricated steel with seperate/integral pole shoes are fastened

to the frame by means of bolts. Pole shoes are generally laminated. Sometimes pole

body and pole shoe are formed from the same laminations. Stiffeners are used on both

21





sides of the laminations. Riveted through bolts hold the assembly together. The pole

shoes are shaped so as to have a slightly increased air gap at the tips.

Inter-poles These are small additional poles located in between the main poles. These can

be solid, or laminated just as the main poles. These are also fastened to the yoke by

bolts. Sometimes the yoke may be slotted to receive these poles. The inter poles could

be of tapered section or of uniform cross section. These are also called as commutating

poles or compoles. The width of the tip of the compole can be about a rotor slot pitch.

Armature The armature is where the moving conductors are located. The armature is

constructed by stacking laminated sheets of silicon steel. Thickness of these lamination

is kept low to reduce eddy current losses. As the laminations carry alternating flux

the choice of suitable material, insulation coating on the laminations, stacking it etc

are to be done more carefully. The core is divided into packets to facilitate ventilation.

The winding cannot be placed on the surface of the rotor due to the mechanical forces

coming on the same. Open parallel sided equally spaced slots are normally punched in

the rotor laminations. These slots house the armature winding. Large sized machines

employ a spider on which the laminations are stacked in segments. End plates are

suitably shaped so as to serve as ’Winding supporters’. Armature construction process

must ensure provision of sufficient axial and radial ducts to facilitate easy removal of

heat from the armature winding.

Field windings In the case of wound field machines (as against permanent magnet excited

machines) the field winding takes the form of a concentric coil wound around the main

poles. These carry the excitation current and produce the main field in the machine.

Thus the poles are created electromagnetically. Two types of windings are generally

employed. In shunt winding large number of turns of small section copper conductor is

22





used. The resistance of such winding would be an order of magnitude larger than the

armature winding resistance. In the case of series winding a few turns of heavy cross

section conductor is used. The resistance of such windings is low and is comparable

to armature resistance. Some machines may have both the windings on the poles.

The total ampere turns required to establish the necessary flux under the poles is

calculated from the magnetic circuit calculations. The total mmf required is divided

equally between north and south poles as the poles are produced in pairs. The mmf

required to be shared between shunt and series windings are apportioned as per the

design requirements. As these work on the same magnetic system they are in the form

of concentric coils. Mmf ’per pole’ is normally used in these calculations.

Armature winding As mentioned earlier, if the armature coils are wound on the surface of

the armature, such construction becomes mechanically weak. The conductors may fly

away when the armature starts rotating. Hence the armature windings are in general

pre-formed, taped and lowered into the open slots on the armature. In the case of

small machines, they can be hand wound. The coils are prevented from flying out due

to the centrifugal forces by means of bands of steel wire on the surface of the rotor in

small groves cut into it. In the case of large machines slot wedges are additionally used

to restrain the coils from flying away. The end portion of the windings are taped at

the free end and bound to the winding carrier ring of the armature at the commutator

end. The armature must be dynamically balanced to reduce the centrifugal forces at

the operating speeds.

Compensating winding One may find a bar winding housed in the slots on the pole

shoes. This is mostly found in d.c. machines of very large rating. Such winding is

called compensating winding. In smaller machines, they may be absent. The function

23





and the need of such windings will be discussed later on.

4

3

21

5

2

1.Clamping cone

2.Insulating cups

3.Commutator bar

4.Riser

5.Insulating gasket

Figure 8: Cylindrical type commutator-a longitudinal section

Commutator Commutator is the key element which made the d.c. machine of the present

day possible. It consists of copper segments tightly fastened together with mica/micanite

insulating separators on an insulated base. The whole commutator forms a rigid and

solid assembly of insulated copper strips and can rotate at high speeds. Each com-

mutator segment is provided with a ’riser’ where the ends of the armature coils get

connected. The surface of the commutator is machined and surface is made concentric

with the shaft and the current collecting brushes rest on the same. Under-cutting the

mica insulators that are between these commutator segments has to be done periodi-

cally to avoid fouling of the surface of the commutator by mica when the commutator

gets worn out. Some details of the construction of the commutator are seen in Fig. 8.

Brush and brush holders Brushes rest on the surface of the commutator. Normally

electro-graphite is used as brush material. The actual composition of the brush depends

on the peripheral speed of the commutator and the working voltage. The hardness of

the graphite brush is selected to be lower than that of the commutator. When the

24





brush wears out the graphite works as a solid lubricant reducing frictional coefficient.

More number of relatively smaller width brushes are preferred in place of large broad

brushes. The brush holders provide slots for the brushes to be placed. The connection

Brush holder box

Brush

Pressure

spring

Pigtail

(a)

Radial Trailing

Reaction

Motion of commutator

(b)

Figure 9: Brush holder with a Brush and Positioning of the brush on the commutator

from the brush is taken out by means of flexible pigtail. The brushes are kept pressed

on the commutator with the help of springs. This is to ensure proper contact between

25





the brushes and the commutator even under high speeds of operation. Jumping of

brushes must be avoided to ensure arc free current collection and to keep the brush

contact drop low. Fig. 9 shows a brush holder arrangement. Radial positioning of the

brushes helps in providing similar current collection conditions for both direction of

rotation. For unidirectional drives trailing brush arrangement or reaction arrangement

may be used in Fig. 9-(b) Reaction arrangement is preferred as it results in zero side

thrust on brush box and the brush can slide down or up freely. Also staggering of the

brushes along the length of the commutator is adopted to avoid formation of ’tracks’

on the commutator. This is especially true if the machine is operating in a dusty

environment like the one found in cement plants.

Other mechanical parts End covers, fan and shaft bearings form other important me-

chanical parts. End covers are completely solid or have opening for ventilation. They

support the bearings which are on the shaft. Proper machining is to be ensured for

easy assembly. Fans can be external or internal. In most machines the fan is on the

non-commutator end sucking the air from the commutator end and throwing the same

out. Adequate quantity of hot air removal has to be ensured.

Bearings Small machines employ ball bearings at both ends. For larger machines roller

bearings are used especially at the driving end. The bearings are mounted press-fit

on the shaft. They are housed inside the end shield in such a manner that it is not

necessary to remove the bearings from the shaft for dismantling. The bearings must be

kept in closed housing with suitable lubricant keeping dust and other foreign materials

away. Thrust bearings, roller bearings, pedestal bearings etc are used under special

cases. Care must be taken to see that there are no bearing currents or axial forces on

the shaft both of which destroy the bearings.

26





4 Armature Windings

X

X

X

xx

x

x

x

xx

x

x

x

X

x

x

x

x

x

x

x

x

N

N

SS

v

X

X

XX

Main field

Compole field

Compensating

winding

Commutator

& Brush

Shaft

Armature

winding

Yoke

Figure 10: Cross sectional view

Fig. 10 gives the cross sectional view of a modern d.c. machine show-

ing all the salient parts. Armature windings, along with the commutators, form the heart

of the d.c. machine. This is where the emf is induced and hence its effective deployment

enhances the output of the machine. Fig. 11(a) shows one coil of an armature of Gramme

ring arrangement and Fig. 11(b) shows one coil as per drum winding arrangement. Earlier,

a simple form of this winding in the form of Gramme ring winding was presented for easy

understanding. The Gramme ring winding is now obsolete as a better armature winding has

27





X

X

φ/2 φ/2

φ

Ν X

X

φ/2 φ/2

φ

Ν

ΑΑ’Α

Α’

(a) Ring winding (b) Drum winding

Figure 11: Ring winding and drum winding

28





been invented in the form of a drum winding. The ring winding has only one conductor in

a turn working as an active conductor. The second conductor is used simply to complete

the electrical connections. Thus the effectiveness of the electric circuit is only 50 percent.

Looking at it differently, half of the magnetic flux per pole links with each coil. Also, the

return conductor has to be wound inside the bore of the rotor, and hence the rotor diameter

is larger and mounting of the rotor on the shaft is made difficult.

In a drum winding both forward and return conductors are housed in slots cut

on the armature (or drum). Both the conductors have emf induced in them. Looking at it

differently the total flux of a pole is linked with a turn inducing much larger voltage induced

in the same. The rotor is mechanically robust with more area being available for carrying

the flux. There is no necessity for a rotor bore. The rotor diameters are smaller. Mechanical

problems that existed in ring winding are no longer there with drum windings. The coils

could be made of single conductors (single turn coils) or more number of conductors in series

(multi turn coils). These coils are in turn connected to form a closed winding. The two sides

of the coil lie under two poles one north and the other south, so that the induced emf in

them are always additive by virtue of the end connection. Even though the total winding

is a closed one the sum of the emfs would be zero at all times. Thus there is no circulating

current when the armature is not loaded. The two sides of the coil, if left on the surface, will

fly away due to centrifugal forces. Hence slots are made on the surface and the conductors

are placed in these slots and fastened by steel wires to keep them in position. Each armature

slot is partitioned into two layers, a top layer and a bottom layer. The winding is called as

a double layer winding. This is a direct consequence of the symmetry consideration. The

distance, measured along the periphery of the armature from any point under a pole to a

similar point under the neighboring pole is termed as a pole pitch. The forward conductor

is housed in the top layer of a slot and the return conductor is housed in the bottom layer

29





Active

Lower coil sideUpper coil side

Inactive

B

S NA

A’

Inactive

C D

A’

D

C

AB

S

Lower

coil side

Upper coil side

N

S

N

S

Armature

(a) End view

(b) Developed view

Figure 12: Arrangement of a single coil of a drum winding

30





of a slot which is displaced by about one pole pitch. The junction of two coils is terminated

on a commutator segment. Thus there are as many commutator segments as the number of

coils. In a double layer winding in S slots there are 2S layers. Two layers are occupied by a

coil and hence totally there are S coils. The S junctions of these S coils are terminated on S

commutator segments. The brushes are placed in such a manner that a maximum voltage

appears across them. While the number of parallel circuits in the case of ring winding is

equal to the number of poles, in the case of drum winding a wide variety of windings are

possible. The number of brushes and parallel paths thus vary considerably. The physical

arrangement of a single coil is shown in Fig. 12 to illustrate its location and connection to

the commutators.

Fig. 13 shows the axial side view while Fig. 13-(b) shows the cut and spread view

of the machine. The number of turns in a coil can be one (single turn coils) or more (multi

turn coils ). As seen earlier the sum of the instantaneous emfs appears across the brushes.

This sum gets altered by the voltage of a coil that is being switched from one circuit to the

other or which is being commutated. As this coil in general lies in the magnetic neutral

axis it has a small value of voltage induced in it. This change in the sum expressed as the

fraction of the total induced voltage is called as the ripple. In order to reduce the ripple,

one can increase the number of coils coming in series between the brushes. As the number

of coils is the same as the number of slots in an armature with two coil sides per slot one is

forced to increase the number of slots. However increasing the slot number makes the tooth

width too narrow and makes them mechanically weak.

To solve this problem the slots are partitioned vertically to increase the number

of coil sides. This is shown in Fig. 14. In the figure, the conductors a, b and c belong to a

coil. Such 2/3 coils occupy the 2/3 top coil sides of the slot. In the present case the number

of coils in the armature is 2S/3S.

31





(a)End view

- +- +

1 2 3 4 5 6 7 8 9 10 11

1 2 3 4 5 6 7 8 9 10 11

12

12

SNSN

Motion

2’

1’

1’

3’

2’11

10

12

12

11

(b)Developed view

Figure 13: Lap Winding32





Press board

Press board

Copper

Mica Tape

(a) Single coil-side perlayer

(b) More coil sides perlayer

Figure 14: Partitioning of slots

33





As mentioned earlier, in a drum winding, the coils span a pole pitch where

ever possible. Such coils are called ’full pitched’ coils. The emf induced in the two active

conductors of such coils have identical emfs with opposite signs at all instants of time. If the

span is more than or less than the full pitch then the coil is said to be ’chorded’. In chorded

coils the induced emfs of the two conductor may be of the same sign and hence oppose each

other( for brief intervals of time). Slight short chording of the coil reduces overhang length

and saves copper and also improves commutation. Hence when the pole pitch becomes frac-

tional number, the smaller whole number may be selected discarding the fractional part.

Similar to the pitch of a coil one can define the winding pitch and commutator

pitch. In a d.c. winding the end of one coil is connected to the beginning of another coil

(not necessarily the next), this being symmetrically followed to include all the coils on the

armature. Winding pitch provides a means of indicating this. Similarly the commutator

pitch provides the information regarding the commutators to which the beginning and the

end of a coil are connected. Commutator pitch is the number of ’micas’ between the ends of

a coil. For all these information to be simple and useful the numbering scheme of the coils

and commutator segments becomes important. One simple method is to number only the

top coil side of the coils in sequence. The return conductor need not be numbered. As a

double layer is being used the bottom coil side is placed in a slot displaced by one coil span

from the top coil side. Some times the coils are numbered as 1 − 1′

, 2 − 2′

etc. indicating

the second sides by 1′

, 2′

etc. The numbering of commutators segments are done similarly.

The commutator segment connected to top coil side of coil 1 is numbered 1. This method

of numbering is simple and easy to follow. It should be noted that changing of the pitch

34





of a coil slightly changes the induced emf in the same. The pitch of the winding however

substantially alters the nature of the winding.

The armature windings are classified into two families based on this. They are

called lap winding and wave winding. They can be simply stated in terms of the commutator

pitch used for the winding.

4.1 Lap winding

The commutator pitch for the lap windings is given by

yc = ±m, m = 1, 2, 3... (20)

where yc is the commutator pitch, m is the order of the winding.

For m = 1 we get a simple lap winding, m = 2 gives duplex lap winding etc. yc = m

gives a multiplex lap winding of order m. The sign refers to the direction of progression

of the winding. Positive sign is used for ‘progressive’ winding and the negative sign for the

‘retrogressive’ winding. Fig. 15 shows one coil as per progressive and retrogressive lap wind-

ing arrangements. Fig. 16 shows a developed view of a simple lap winding for a 4-pole

armature in 12 slots. The connections of the coils to the commutator segments are also

shown. The position of the armature is below the poles and the conductors move from left

to right as indicated. The position and polarity of the brushes are also indicated. Single

turn coils with yc = 1 are shown here. The number of parallel paths formed by the winding

equals the number of poles. The number of conductors that are connected in series between

the brushes therefore becomes equal to Z/2b. Thus the lap winding is well suited for high

current generators. In a symmetrical winding the parallel paths share the total line current

35





1 2 3

Progressive

yc =+1

s1 s2 F1 F2

1 2 3 4

Retrogressive

yc = -1

s3F3s2

F2

(a) Lap winding

Coil span

1

s1 F1

2 c 1+_

p

(b) Wave winding

Figure 15: Typical end connections of a coil and commutator

36





1 2 3 4 5 6 7 8 9 10 11 1213 14

1 2

SN NS S

Motion

A1 A2B1 B2+ - + -

Figure 16: Developed view of a retrogressive Lap winding

37





equally.

The increase in the number of parallel paths in the armature winding brings

about a problem of circulating current. The induced emfs in the different paths tend to

differ slightly due to the non-uniformities in the magnetic circuit. This will be more with the

increase in the number of poles in the machine. If this is left uncorrected, circulating currents

appear in these closed parallel paths. This circulating current wastes power, produces heat

and over loads the brushes under loaded conditions. One method commonly adopted in d.c.

machines to reduce this problem is to provide equalizer connections. As the name suggests

these connections identify similar potential points of the different parallel paths and connect

them together to equalize the potentials. Any difference in the potential generates a local

circulating current and the voltages get equalized. Also, the circulating current does not

flow through the brushes loading them. The number of such equalizer connections, the

cross section for the conductor used for the equalizer etc are decided by the designer. An

example of equalizer connection is discussed now with the help of a 6-pole armature having

150 commutator segments. The coil numbers 1, 51 and 101 are identically placed under the

poles of same polarity as they are one pole-pair apart. There are 50 groups like that. In

order to limit the number of links to 5(say), the following connections are chosen. Then

1,11,21,31, and 41 are the coils under the first pair of poles. These are connected to their

counter parts displaced by 50 and 100 to yield 5 equalizer connections. There are 10 coils

connected in series between any two successive links. The wave windings shall be examined

next.

38





Motion-+

S N S N

+ A1 B1- A2 B2

17 18 1920 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1

(a)Winding layout

Span : 1 to 6

Full pitch: 21/4=5.25 5~_

Yc=C 1+_

2

21 1+_

2= =

11

10}

Commutator pitch 1-11 for retrogressive winding

1-11-21-10-20-9-19-8-18-7-17-

6-16-5-15-4-14-3-13-2-12-1

B2

A1

A2

B1

v

v

(b)Parallel paths

Figure 17: Developed view of a Retrogressive Wave winding

39





4.2 Wave windings

In wave windings the coils carrying emf in the same direction at a time are all

grouped together and connected in series. Hence in a simple wave winding there are only

two paths between the brushes, the number of conductors in each path being 50 percent of

the total conductors. To implement a wave winding one should select the commutator pitch

as

yc =C ± 1

p(21)

where C is the total segments on the commutator. yc should be an integer number; C and

p should satisfy this relation correctly. Here also the positive sign refers to the progressive

winding and the negative sign yields a retrogressive winding. yc = (C ±m)/p yields a multi-

plex wave winding of order m. A simple wave winding for 4 poles in 21 slots is illustrated in

Fig. 17. As could be seen from the figure, the connection to the next (or previous) adjacent

coil is reached after p coils are connected in series. The winding closes on itself after all the

coils are connected in series. The position for the brushes is indicated in the diagram.

It is seen from the formula for the commutator pitch, the choice of commutator

segments for wave winding is restricted. The number of commutator segments can only be

one more or one less than some multiple of pole pairs. As the number of parallel circuits is

2 for a simple wave winding irrespective of the pole numbers it is preferred in multi polar

machine of lower power levels.

As mentioned earlier the simple wave winding forms two parallel paths, duplex

wave winding has 2*2=4 etc. The coils under all the north poles are grouped together in

40





one circuit and the other circuit collects all the coils that are under all the south poles. Two

brush sets are therefore adequate. Occasionally people employ brush sets equal to the num-

ber of poles. This arrangement does not increase the number of parallel circuits but reduces

the current to be collected by each brush set. This can be illustrated by an example. A

4-pole wave connected winding with 21 commutator segments is taken. yc = (21−1)/2 = 10

. A retrogressive wave winding results. The total string of connection can be laid out as

shown below. If coil number 1 is assumed to be in the neutral axis then other neutral axis

coils are a pole pitch apart i.e. coils 6, 11, 16.

If the brushes are kept at commutator segment 1 and 6, nearly half the num-

ber of coils come under each circuit. The polarity of the brushes are positive and negative

alternately. Or, one could have two brushes at 11 and 16 or any two adjacent poles. By

having four brushes at 1, 6, 11 and 16 and connecting 1,11 and 6,16 still only two parallel

circuits are obtained. The brush currents however are halved. This method permits the use

of commutator of shorter length as lesser current is to be collected by each brush and thus

saving on the cost of the commutator. Fig. 17(b) illustrates this brush arrangement with

respect to a 21 slot 4 pole machine. Similarly proceeding, in a 6-pole winding 2,4 or 6 brush

sets may be used.

Multiplex windings of order m have m times the circuits compared to a simplex

winding and so also more restriction on the choice of the slots, coil sides, commutator

and brushes. Hence windings beyond duplex are very uncommon even though theoretically

possible. The duplex windings are used under very special circumstances when the number

of parallel paths had to be doubled.

41





4.3 Dummy coils and dummy commutator segments

Due to the restrictions posed by lap and wave windings on the choice of number

of slots and commutator segments a practical difficulty arises. Each machine with a certain

pole number, voltage and power ratings may require a particular number of slots and com-

mutator segments for a proper design. Thus each machine may be tailor made for a given

specification. This will require stocking and handling many sizes of armature and commu-

tator.

Sometimes due to the non-availability of a suitable slot number or commu-

tator, one is forced to design the winding in an armature readily available in stock. Such

designs, obviously, violate the symmetry conditions as armature slots and commutator seg-

ment may not match. If one is satisfied with approximate solutions then the designer can

omit the surplus coil or surplus commutator segment and complete the design. This is called

the use of a ’dummy’. All the coils are placed in the armature slots. The surplus coil is

electrically isolated and taped. It serves to provide mechanical balance against centrifugal

forces. Similarly, in the case of surplus commutator segment two adjacent commutator seg-

ments are connected together and treated as a single segment. These are called dummy coils

and dummy commutator segments. As mentioned earlier this approach must be avoided as

far as possible by going in for proper slot numbers and commutator. Slightly un-symmetric

winding may be tolerable in machines of smaller rating with very few poles.

42






5 Armature reaction

Earlier, an expression was derived for the induced emf at the terminals of the

armature winding under the influence of motion of the conductors under the field established

by field poles. But if the generator is to be of some use it should deliver electrical output to a

load. In such a case the armature conductors also carry currents and produce a field of their

own. The interaction between the fields must therefore must be properly understood in order

to understand the behavior of the loaded machine. As the magnetic structure is complex

and as we are interested in the flux cut by the conductors, we primarily focus our attention

on the surface of the armature. A sign convention is required for mmf as the armature and

field mmf are on two different members of the machine. The convention used here is that

the mmf acting across the air gap and the flux density in the air gap are shown as positive

when they act in a direction from the field system to the armature. A flux line is taken

and the value of the current enclosed is determined. As the magnetic circuit is non-linear,

the field mmf and armature mmf are separately computed and added at each point on the

surface of the armature. The actual flux produced is proportional to the total mmf and the

permeance. The flux produced by field and that produced by armature could be added to

get the total flux only in the case of a linear magnetic circuit. The mmf distribution due to

the poles and armature are discussed now in sequence.

5.0.1 MMF distribution due to the field coils acting alone

Fig. 18 shows the distribution of mmf due to field coils over two pole pitches. It

is a step curve with the width being equal to the pole arc. The permeance variation at the

surface is given by Fig. 18 assuming the air gap under the pole to be uniform and neglecting

43






Practical

Flux density

N S

Ideal flux density

mmf

Permeance

Figure 18: Mmf and flux variation in an unloaded machine

44






the slotting of the armature. The no-load flux density curve can be obtained by multiplying

mmf and permeance. Allowing for the fringing of the flux, the actual flux density curve

would be as shown under Fig. 18.

5.0.2 MMF distribution due to armature conductors alone carrying currents

N-Pole

A

N

S-PoleFlux

mmf

S

Generator

Figure 19: Mmf and flux distribution under the action of armature alone carrying current

The armature has a distributed winding, as against the field coils which

are concentrated and concentric. The mmf of each coil is shifted in space by the number of

slots. For a full pitched coil, each coil produces a rectangular mmf distribution. The sum

of the mmf due to all coils would result in a stepped triangular wave form. If we neglect

slotting and have uniformly spaced coils on the surface, then the mmf distribution due to the

armature working alone would be a triangular distribution in space since all the conductors

carry equal currents. MMF distribution is the integral of the ampere conductor distribution.

45






This is depicted in Fig. 19. This armature mmf per pole is given by

Fa =1

2.Ic.Z

2p

where Ic is the conductor current and Z is total number of conductors on the armature. This

peak value of the mmf occurs at the inter polar area, shifted from the main pole axis by half

the pole pitch when the brushes are kept in the magnetic neutral axis of the main poles.

5.0.3 Total mmf and flux of a loaded machine

N S

c

a

A

b

Generator

B

C

D

oo’

Total flux

Bru

sh

axis

A B

Armature flux

Field

flux

Figure 20: Flux distribution in a loaded generator without brush shift

The mmf of field coils and armature coils are added up and the re-

sultant mmf distribution is obtained as shown in Fig. 20.

46






This shows the decrease in the mmf at one tip of a pole and a substantial rise

at the other tip. If the machine has a pole arc to pole pitch ratio of 0.7 then 70% of the

armature reaction mmf gets added at this tip leading to considerable amount of saturation

under full load conditions. The flux distribution also is shown in Fig. 20. This is obtained

by multiplying mmf and permeance waves point by point in space. Actual flux distribution

differs from this slightly due to fringing. As seen from the figure, the flux in the inter polar

region is substantially lower due to the high reluctance of the medium. The air gaps under

the pole tips are also increased in practice to reduce excessive saturation of this part. The

advantage of the salient pole field construction is thus obvious. It greatly mitigates the

effect of the armature reaction. Also, the coils under going commutation have very little

emf induced in them and hence better commutation is achieved. Even though the armature

reaction produced a cross magnetizing effect, the net flux per pole gets slightly reduced,

on load, due to the saturation under one tip of the pole. This is more so in modern d.c.

machines where the normal excitation of the field makes the machine work under some level

of saturation.

5.0.4 Effect of brush shift

In some small d.c. machines the brushes are shifted from the position of the mag-

netic neutral axis in order to improve the commutation. This is especially true of machines

with unidirectional operation and uni-modal (either as a generator or as a motor) operation.

Such a shift in the direction of rotation is termed ‘lead’ (or forward lead). Shift of brushes

in the opposite to the direction of rotation is called ‘backward lead’. This lead is expressed

in terms of the number of commutator segments or in terms of the electrical angle. A pole

pitch corresponds to an electrical angle of 180 degrees. Fig. 21 shows the effect of a forward

47






N S

a

c

b

Rotation

Ge

om

etr

ic N

eu

tra

l a

xis

Bru

sh

axis

Total flux

Armature flux

Field

flux

(a)Armature reaction with brush shift

S

N

θa

b

a’

b’

Rotation

(b)Calculation of demagnetizing mmf per pole

Figure 21: Effect of brush shift on armature reaction

48






brush lead on the armature reaction. The magnetization action due to the armature is no

longer entirely cross magnetizing. Some component of the same goes to demagnetize the

main field and the net useful flux gets reduced. This may be seen as the price we pay for

improving the commutation. Knowing the pole arc to pole pitch ratio one can determine

the total mmf at the leading and trailing edges of a pole without shift in the brushes.

Fmin = Ff − α.Fa (22)

Fmax = Ff + α.Fa

where Ff is the field mmf, Fais armature reaction mmf per pole, and α is the pole arc to

pole pitch ratio.

Fa =1

2

Z.Ic

2p. (23)

The net flux per pole decreases due to saturation at the trailing edge and

hence additional ampere turns are needed on the pole to compensate this effect. This may

be to the tune of 20 percent in the modern d.c. machines.

The brush shift gives rise to a shift in the axis of the mmf of the armature

reaction. This can be resolved into two components, one in the quadrature axis and sec-

ond along the pole axis as shown in Fig. 21.(b) The demagnetizing and cross magnetizing

component of the armature ampere turn per pole can be written as

Fd =2θ

π.Fa (24)

Fq = (1 −2θ

π).Fa (25)

where θ is the angle of lead . In terms of the number of commutator segments they are

Fd =Cl

C

4p

.IcZ

4por

Cl

C.Ic.Z (26)

49






where, Cl is the brush lead expressed in number of commutator segments.

5.0.5 Armature reaction in motors

As discussed earlier, for a given polarity of the field and sense of rotation, the

motoring and generating modes differ only in the direction of the armature current. Alter-

natively, for a given sense of armature current, the direction of rotation would be opposite

for the two modes. The leading and trailing edges of the poles change positions if direction

of rotation is made opposite. Similarly when the brush leads are considered, a forward lead

given to a generator gives rise to weakening of the generator field but strengthens the motor

field and vice-versa. Hence it is highly desirable, even in the case of non-reversing drives,

to keep the brush position at the geometrical neutral axis if the machine goes through both

motoring and generating modes.

The second effect of the armature reaction in the case of motors as well as

generators is that the induced emf in the coils under the pole tips get increased when a

pole tip has higher flux density. This increases the stress on the ‘mica’ (micanite) insulation

used for the commutator, thus resulting in increased chance of breakdown of these insulating

sheets. To avoid this effect the flux density distribution under the poles must be prevented

from getting distorted and peaky.

The third effect of the armature reaction mmf distorting the flux density is

that the armature teeth experience a heavy degree of saturation in this region. This increases

the iron losses occurring in the armature in that region. The saturation of the teeth may

be too great as to have some flux lines to link the thick end plates used for strengthening

50






the armature. The increase in iron loss could be as high as 50 percent more at full load

compared to its no-load value.

The above two effects can be reduced by providing a ’compensating’ mmf at

N S

NS

s

s

NN

Commutating pole

Main pole

Compensating

winding

Figure 22: Compensating winding

the same spatial rate as the armature mmf. This is provided by having a compensating

winding housed on the pole shoe which carries currents that are directly proportional to the

armature current. The ampere conductors per unit length is maintained identical to that of

51






+ + + + +

+

++++ ++

+++

+ + + + +

mmf of

compensating

winding

Resultant

mmf

Armature

mmf

Main field

mmf

compole mmf

N S

Rotation

Figure 23: Armature reaction with Compensating winding

52






the armature. The sign of the ampere conductors is made opposite to the armature. This is

illustrated in Fig. 22 and Fig. 23 . Since the compensating winding is connected in series with

the armature, the relationship between armature mmf and the mmf due to compensating

winding remains proper for all modes of working of the machine. The mmf required to be

setup by the compensating winding can be found out to be

Fc =Ic.Z

4p.

polearc

polepitch(27)

Under these circumstances the flux density curve remains unaltered under the poles between

no-load and full load.

The axis of the mmf due to armature and the compensating winding being

the same and the signs of mmf being opposite to each other the flux density in the region

of geometric neutral axis gets reduced thus improving the conditions for commutation. One

can design the compensating winding to completely neutralize the armature reaction mmf.

Such a design results in overcompensation under the poles. Improvement in commutation

condition may be achieved simply by providing a commutating pole which sets up a local

field of proper polarity. It is better not to depend on the compensating winding for improv-

ing commutation.

Compensating windings are commonly used in large generators and motors

operating on weak field working at high loads.

From the analysis of the phenomenon of armature reaction that takes place

in a d.c. machine it can be inferred that the equivalent circuit of the machine need not be

modified to include the armature reaction. The machine can simply be modelled as a voltage

53






source of internal resistance equal to the armature circuit resistance and a series voltage drop

equal to the brush contact drop, under steady state. With this circuit model one can arrive

at the external characteristics of the d.c. machine under different modes of operation.

5.1 Commutation

As seen earlier, in an armature conductor of a heteropolar machine a.c. voltages

are induced as the conductor moves under north and south pole polarities alternately. The

frequency of this induced emf is given by the product of the pole-pairs and the speed in

revolutions per second. The induced emf in a full pitch coil changes sign as the coil crosses

magnetic neutral axis. In order to get maximum d.c. voltage in the external circuit the coil

should be shifted to the negative group. This process of switching is called commutation.

During a short interval when the two adjacent commutator segments get bridged by the

brush the coils connected in series between these two segments get short circuited. Thus in

the case of ring winding and simple lap winding 2p coils get short circuited. In a simple wave

winding in a 2p pole machine 2 coils get short circuited. The current in these coils become

zero and get reversed as the brush moves over to the next commutator segment. Thus brush

and commutator play an important role in commutation. Commutation is the key process

which converts the induced a.c. voltages in the conductors into d.c. It is important to learn

about the working of the same in order to ensure a smooth and trouble free operation of the

machine.

54






Leaving EdgeEntering Edge

Thickness

Le

ng

th Wid

th

123

12

1

1

2

2

3

34

4

(a)

(b)

tb

34

4

13

12

(c)tb

34

4 2

Motion

tb

IaIa

2Ia

2Ia

2Ia

2Ia

IaIa

2Ia

I1I2

Ia Ia

i

x

(a)Location of Brush (b)Process of commutation

Figure 24: Location of the brush and Commutation process

55






5.1.1 Brushes

Brush forms an important component in the process of commutation. The coil

resistance is normally very small compared to the brush contact resistance. Further this

brush contact resistance is not a constant. With the brushes commonly used, an increase in

the current density of the brushes by 100 percent increases the brush drop by about 10 to

15 percent. Brush contact drop is influenced by the major factors like speed of operation,

pressure on the brushes, and to a smaller extent the direction of current flow.

Major change in contact resistance is brought about by the composition of

the brush. Soft graphite brushes working at a current density of about 10A/cm2 produce a

drop of 1.6V (at the positive and negative brushes put together) while copper-carbon brush

working at 15A/cm2 produces a drop of about 0.3V. The coefficient of friction for these

brushes are 0.12 and 0.16 respectively. The attention is focussed next on the process of

commutation.

5.1.2 Linear Commutation

If the current density under the brush is assumed to be constant through out the

commutation interval, a simple model for commutation is obtained. For simplicity, the brush

thickness is made equal to thickness of one commutator segment. In Fig. 24(b), the brush

is initially solely resting on segment number 1. The total current of 2Ia is collected by

the brush as shown. As the commutator moves relative to the brush position, the brush

position starts to overlap with that of segment 2. As the current density is assumed to be

constant, the current from each side of the winding is proportional to the area shared on the

56






two segments. Segment 1 current uniformly comes down with segment 2 current increasing

uniformly keeping the total current in the brush constant. The currents I1 and I2 in brush

segments 1 and 2 are given by

I1 = 2Ia(1 −x

tb) and I2 = 2Ia

x

tb(28)

giving I1 + I2 to be 2 Ia.

Here ‘x’ is the width of the brush overlapping on segment 2. The process of commutation

would be over when the current through segment number 1 becomes zero. The current in

the coil undergoing commutation is

i = I1 − Ia = Ia − I2 =(I1 − I2)

2= Ia(1 −

2x

tb) (29)

The time required to complete this commutation is

Tc =tbvc

(30)

where vc is the velocity of the commutator. This type of linear commutation is very close

to the ideal method of commutation. The time variation of current in the coil undergoing

commutation is shown in Fig. 25.(a). Fig. 25.(b) also shows the timing diagram for the

currents I1 and I2 and the current densities in entering edge αe, leaving edge αl and also the

mean current density αm in the brush. Machines having very low coil inductances, operating

at low load currents, and low speeds, come close to this method of linear commutation.

In general commutation will not be linear due to the presence of emf of self

induction and induced rotational emf in the coil. These result in retarded and accelerated

commutation and are discussed in sequence.

57






Ia

0 Tc

-Ia

Time of

communication

Time

i

2Ia

TcTime of

commutation0

I1 I2

α’ = αm = α"

(a) (b)

Figure 25: Linear commutation

5.1.3 Retarded commutation

Retarded commutation is mainly due to emf of self induction in the coil. Here

the current transfer from 1 to 2 gets retarded as the name suggests. This is best explained

with the help of time diagrams as shown in Fig. 26.(a). The variation of i is the change in

the current of the coil undergoing commutation, while i′

is that during linear commutation.

Fig. 26(b) shows the variation of I1 and current density in the brush at the leaving edge and

Fig. 26.(c) shows the same phenomenon with respect to I2 at entering edge. The value of

current in the coil is given by i undergoing commutation. αm is the mean current density in

the brush given by total current divided by brush area of cross section. αl and αe are the

current density under leaving and entering edges of the brush. As before,

I1 = Ia + i and I2 = Ia − i (31)

58






0

+Ia

t

i

-Ia

Tc

i’

αm

α’=AB/AC

+Ia

P

0

Q

t

I1=Ia+i

Tc

2Ia

A

C

B

(a) commutation (b) Leaving edge density

E

F

Dt0 Tc

I2=Ia-i

t

2Ia

α"=DF/DE

(c)Entry edge density

Figure 26: Diagrams for Retarded commutation

59






The variation of densities at leaving and entering edges are given as

αl =AB

AC.αm (32)

αe =DF

DE.αm (33)

At the very end of commutation, the current density

αe = αm.di

dt/di

′

dt(34)

= αm.di

dt/2Ia

Tc

If at this point di/dt = 0 the possibility of sudden breaking of the current and

hence the creation of an arc is removed .

Similarly at the entering edge at the end of accelerated commutation, shown

in Fig. 27.(b).

αe = αm.di

dt/2Ia

Tc

(35)

Thus retarded communication results in di/dt = 0 at the beginning of commutation

(at entering edge) and accelerated communication results in the same at the end of commu-

tation (at leaving edge). Hence it is very advantageous to have retarded commutation at the

entry time and accelerated commutation in the second half. This is depicted in Fig. 27.(b1).

It is termed as sinusoidal commutation.

Retarded commutation at entry edge is ensured by the emf of self induction

which is always present. To obtain an accelerated commutation, the coil undergoing com-

mutation must have in it an induced emf of such a polarity as that under the pole towards

which it is moving. Therefore the accelerated commutation can be obtained by i) a forward

60






B

0

Ia

Tc

-Ia

ii’

C

B

A

0

Ia

Tc

-Ia

ii’

α"

αm

α’

α’=AB/AC

α"=DB/DC

D

(a1) (a2)

0

Ia

Tc

-Ia

i’

time

i

B

0

Ia

Tc

-Ia

A

i

α"

αm

C

α’

time

Leaving edge

Entering

edge

P

Q

R

S

α’=PR/PQ

α"=SR/SQ

(b1) (b2)

Figure 27: Accelerated and Sinusoidal commutation

61






lead given to the brushes or by ii) having the field of suitable polarity at the position of the

brush with the help of a small pole called a commutating pole. In a non-inter pole machine

the brush shift must be changed from forward lead to backward lead depending upon gener-

ating or motoring operation. As the disadvantages of this brush shifts are to be avoided, it

is preferable to leave the brushes at geometric neutral axis and provide commutating poles

of suitable polarity (for a generator the polarity of the pole is the one towards which the

conductors are moving). The condition of commutation will be worse if commutating poles

are provided and not excited or they are excited but wrongly.

The action of the commutating pole is local to the coil undergoing commu-

tation. It does not disturb the main field distribution. The commutating pole winding

overpowers the armature mmf locally and establishes the flux of suitable polarity. The com-

mutating pole windings are connected in series with the armature of a d.c. machine to get

a load dependent compensation of armature reaction mmf.

The commutating pole are also known as compole or inter pole. The air gap

under compole is made large and the width of compole small. The mmf required to be

produced by compole is obtained by adding to the armature reaction mmf per pole Fa the

mmf to establish a flux density of required polarity in the air gap under the compole Fcp

.This would ensure straight line commutation. If sinusoidal commutation is required then

the second component Fcp is increased by 30 to 50 percent of the value required for straight

line commutation.

The compole mmf in the presence of a compensating winding on the poles

62






will be reduced by Fa * pole arc/pole pitch. This could have been predicted as the axis of

the compensating winding and armature winding is one and the same. Further, the mmf of

compensating winding opposes that of the armature reaction.

5.2 Methods of excitation

It is seen already that the equivalent circuit model of a d.c. machine becomes very

simple in view of the fact that the armature reaction is cross magnetizing. Also, the axis

of compensating mmf and mmf of commutating poles act in quadrature to the main field.

Thus flux under the pole shoe gets distorted but not diminished (in case the field is not

saturated). The relative connections of armature, compole and compensating winding are

unaltered whether the machine is working as a generator or as a motor; whether the load

is on the machine or not. Hence all these are connected permanently inside the machine.

The terminals reflect only the additional ohmic drops due to the compole and compensating

windings. Thus commutating pole winding, and compensating winding add to the resistance

of the armature circuit and can be considered a part of the same. The armature circuit

can be simply modelled by a voltage source of internal resistance equal to the armature

resistance + compole resistance + compensating winding resistance. The brushes behave

like non-linear resistance; and their effect may be shown separately as an additional constant

voltage drop equal to the brush drop.

5.2.1 Excitation circuit

The excitation for establishing the required field can be of two types a) Permanent

magnet excitation(PM) b) Electro magnetic excitation. Permanent magnet excitation is

63






lp

lg lg lp

da

lt lt

la

lyYoke

Pole

Armature

Field

coil

Figure 28: Magnetization of a DC machine

64






employed only in extremely small machines where providing a field coil becomes infeasible.

Also, permanent magnet excited fields cannot be varied for control purposes. Permanent

magnets for large machines are either not available or expensive. However, an advantage

of permanent magnet is that there are no losses associated with the establishment of the field.

Electromagnetic excitation is universally used. Even though certain amount

of energy is lost in establishing the field it has the advantages like lesser cost, ease of control.

The required ampere turns for establishing the desired flux per pole may be

computed by doing the magnetic circuit calculations. MMF required for the poles, air gap,

armature teeth, armature core and stator yoke are computed and added. Fig. 28 shows two

poles of a 4-pole machine with the flux paths marked on it. Considering one complete flux

loop, the permeance of the different segments can be computed as,

P = A.µ/l

Where P- permeance

A- Area of cross section of the part

mu- permeability of the medium

l- Length of the part

A flux loop traverses a stator yoke, armature yoke, and two numbers each

of poles, air gap, armature teeth in its path. For an assumed flux density Bg in the pole

region the flux crossing each of the above regions is calculated. The mmf requirement for

65






establishing this flux in that region is computed by the expressions

Flux = mmf . permeance

= B.A

From these expressions the mmf required for each and every part in the path of

the flux is computed and added. This value of mmf is required to establish two poles. It

is convenient to think of mmf per pole which is nothing but the ampere turns required to

be produced by a coil wound around one pole. In the case of small machines all this mmf

is produced by a coil wound around one pole. The second pole is obtained by induction.

This procedure saves cost as only one coil need be wound for getting a pair of poles. This

produces an unsymmetrical flux distribution in the machine and hence is not used in larger

machines. In large machines, half of total mmf is assigned to each pole as the mmf per pole.

The total mmf required can be produced by a coil having large number of turns but taking a

small current. Such winding has a high value of resistance and hence a large ohmic drop. It

can be connected across a voltage source and hence called a shunt winding. Such method of

excitation is termed as shunt excitation. On the other hand, one could have a few turns of

large cross section wire carrying heavy current to produce the required ampere turns. These

windings have extremely small resistance and can be connected in series with a large current

path such as an armature. Such a winding is called a series winding and the method of

excitation, series excitation. A d.c. machine can have either of these or both these types of

excitation.

These are shown in Fig. 29. When both shunt winding and series winding are

present, it is called compound excitation. The mmf of the two windings could be arranged to

aid each other or oppose each other. Accordingly they are called cumulative compounding

and differential compounding. If the shunt winding is excited by a separate voltage source

66






Shunt field

F2

F1

A2

A1

Shunt field

F2

F1

A2

A1

(a)Separate excitation (b) Self excitation

Series

field

S2

S1

A2

A1

Diverter

Long shunt

Short shunt

F2

F1

A2

A1

S2

S1

(c)Series excitation (d)Compound excitation

Figure 29: D.C generator connections

67






then it is called separate excitation. If the excitation power comes from the same machine,

then it is called self excitation. Series generators can also be separately excited or self excited.

The characteristics of these generators are discussed now in sequence.

5.2.2 Separately excited shunt generators

E

If

Prime

mover

n=const

Ia=0

+

-

F1

F2

A1

A2

Vdc

Exciting Current

Induced e

.m.f

Decreasing

Magnetisation

Increasing

magnetisation

e.m.f. due to Residual Magnetism

(a) (b)

Figure 30: Magnetization characteristics

Fig. 30 shows a shunt generator with its field connected to a voltage

source Vf through a regulating resistor in potential divider form. The current drawn by

the field winding can be regulated from zero to the maximum value. If the change in the

excitation required is small, simple series connection of a field regulating resistance can be

used. In all these cases the presence of a prime mover rotating the armature is assumed. A

68






separate excitation is normally used for testing of d.c. generators to determine their open

circuit or magnetization characteristic. The excitation current is increased monotonically

to a maximum value and then decreased in the same manner, while noting the terminal

voltage of the armature. The load current is kept zero. The speed of the generator is held

at a constant value. The graph showing the nature of variation of the induced emf as a

function of the excitation current is called as open circuit characteristic (occ), or no-load

magnetization curve or no-load saturation characteristic. Fig. 30(b). shows an example. The

magnetization characteristic exhibits saturation at large values of excitation current. Due

to the hysteresis exhibited by the iron in the magnetic structure, the induced emf does not

become zero when the excitation current is reduced to zero. This is because of the remnant

field in the iron. This residual voltage is about 2 to 5 percent in modern machines. Separate

excitation is advantageous as the exciting current is independent of the terminal voltage

and load current and satisfactory operation is possible over the entire voltage range of the

machine starting from zero.

5.2.3 Self excitation

In a self excited machine, there is no external source for providing excitation current.

The shunt field is connected across the armature. For series machines there is no change in

connection. The series field continues to be in series with the armature.

Self excitation is now discussed with the help of Fig. 31.(a) The pro-

cess of self excitation in a shunt generator takes place in the following manner. When the

armature is rotated a feeble induced emf of 2 to 5 percent appears across the brushes de-

pending upon the speed of rotation and the residual magnetism that is present. This voltage

69






F2

F1

A2

A1

Prime

movern

1500 rev/min

1000 rev/min

500 rev/min

1.0

375 o

hm

s280 o

hm

s

250 o

hm

s

170 ohms

140 o

hm

s

Exciting current,Amperes

Open c

ircuit e

.m.f,v

olts

0

30

60

90

120

150

180

210

(a)Physical connection (b) characteristics

400200

40

80

120

160

200

Total field circuit resistance, ohms

In

du

ce

d e

mf o

n o

pe

n circu

it

Critica

l R

esista

nce

125 o

hm

s

60 o

hm

s

250 o

hm

s

Op

en

cir

cu

it e

.m

.f,vo

lts

speed in rev/min15000

30

60

90

120

150

180

210

(c)Critical resistance (d) Critical speed

Figure 31: Self excitation

70






P’

Q’

R’

O’Q1

PL

0 P" Q" A

P

Excitation current If

Vo

lta

ge

P1

RL

QL

Armature current Ia

Open circuit

characteristic

Armature drop

characteristicA’

R

Q

CD

Figure 32: External characteristics of a self excited of a shunt generator

gets applied across the shunt field winding and produces a small mmf. If this mmf is such

as to aid the residual field then it gets strengthened and produces larger voltage across the

brushes. It is like a positive feed back. The induced emf gradually increases till the voltage

induced in the armature is just enough to meet the ohmic drop inside the field circuit. Under

such situation there is no further increase in the field mmf and the build up of emf also stops.

If the voltage build up is ‘substantial’, then the machine is said to have ‘self excited’.

Fig. 31(b) shows the magnetization curve of a shunt generator. The field resistance

line is also shown by a straight line OC. The point of intersection of the open circuit charac-

71






teristic (OCC) with the field resistance line, in this case C, represents the voltage build up

on self excitation. If the field resistance is increased, at one point the resistance line becomes

a tangent to the OCC. This value of the resistance is called the critical resistance. At this

value of the field circuit resistance the self excitation suddenly collapses. See Fig. 31(c). In-

stead of increasing the field resistance if the speed of the machine is reduced then the same

resistance line becomes a critical resistance at a new speed and the self excitation collapses

at that speed. In this case, as the speed is taken as the variable, the speed is called the

critical speed. In the linear portion of the OCC the ordinates are proportional to the speed

of operation, hence the critical resistance increases as a function of speed Fig. 31.(b) and (d).

The conditions for self excitation can be listed as below.

1. Residual field must be present.

2. The polarity of excitation must aid the residual magnetism.

3. The field circuit resistance must be below the critical value.

4. The speed of operation of the machine must be above the critical speed.

5. The load resistance must be very large.

Remedial measures to be taken if the machine fails to self excite are briefly

discussed below.

1. The residual field will be absent in a brand new, unexcited, machine. The field may

be connected to a battery in such cases for a few seconds to create a residual field.

72






2. The polarity of connections have to be set right. The polarity may become wrong

either by reversed connections or reversed direction of rotation. If the generator had

been working with armature rotating in clockwise direction before stopping and if one

tries to self excite the same with counter clockwise direction then the induced emf

opposes residual field, changing the polarity of connections of the field with respect to

armature is normally sufficient for this problem.

3. Field circuit resistance implies all the resistances coming in series with the field winding

like regulating resistance, contact resistance, drop at the brushes, and the armature

resistance. Brush contact resistance is normally high at small currents. The dirt on

the commutator due to dust or worn out mica insulator can increase the total circuit

resistance enormously. The speed itself might be too low so that the normal field

resistance itself is very much more than the critical value. So ensuring good speed,

clean commutator and good connections should normally be sufficient to overcome this

problem.

4. Speed must be increased sufficiently to a high value to be above the critical speed.

5. The load switch must be opened or the load resistance is made very high.

5.2.4 Self excitation of series generators

The conditions for self excitation of a series generator remain similar to that of

a shunt machine. In this case the field circuit resistance is the same as the load circuit

resistance and hence it must be made very low to help self excitation. To control the field

mmf a small resistance called diverter is normally connected across the series field. To help

in the creation of maximum mmf during self excitation any field diverter if present must be

73






Load Current

Term

inal voltage

Q

S

RB

0

Open circuit

characteristic

Armature

characteristic

External

characteristicP

A

PS=PQ-PR

Figure 33: External characteristics of a Series Generator

open circuited.In a series generator load current being the field current of the machine the

self excitation characteristic or one and the same. This is shown in Fig. 33

5.2.5 Self excitation of compound generators

Most of the compound machines are basically shunt machines with the series wind-

ing doing the act of strengthening/weakening the field on load, depending up on the con-

nections. In cumulatively compounded machines the mmf of the two fields aid each other

and in a differentially compounded machine they oppose each other. Due to the presence of

the shunt winding, the self excitation can proceed as in a shunt machine. A small difference

exists however depending up on the way the shunt winding is connected to the armature. It

can be a short shunt connection or a long shunt connection. In long shunt connection the

shunt field current passes through the series winding also. But it does not affect the process

of self excitation as the mmf contribution from the series field is negligible.

74






Both series field winding and shunt field winding are wound around the main

poles. If there is any need, for some control purposes, to have more excitation windings

of one type or the other they will also find their place on the main poles. The designed

field windings must cater to the full range of operation of the machine at nominal armature

current. As the armature current is cross magnetizing the demagnetization mmf due to pole

tip saturation alone need be compensated by producing additional mmf by the field.

The d.c. machines give rise to a variety of external characteristics with consid-

erable ease. The external characteristics are of great importance in meeting the requirements

of different types of loads and in parallel operation. The external characteristics, also known

as load characteristics, of these machines are discussed next.

5.3 Load characteristics of d.c. generators

Load characteristics are also known as the external characteristics. External char-

acteristics expresses the manner in which the output voltage of the generator varies as a

function of the load current, when the speed and excitation current are held constant. If

they are not held constant then there is further change in the terminal voltage. The terminal

voltage V can be expressed in terms of the induced voltage E and armature circuit drop as

V = E − IaRa − Vb (36)

Vb - brush contact drop, V

Ia - armature current, A

Ra - armature resistance + inter pole winding resistance+ series winding resistance + com-

75






Volts

Ohmic Drop IaRa

Open circuit e.m.f

Terminal voltage V

Induced e.m.f

Load current,Ia

A0

C

B

Figure 34: External characteristics of a separately excited shunt generator

pensating winding resistance.

As seen from the equation E being function of speed and flux per pole it will

also change when these are not held constant. Experimentally the external characteristics

can be determined by conducting a load test. If the external characteristic is obtained by

subtracting the armature drop from the no-load terminal voltage, it is found to depart from

the one obtained from the load test. This departure is due to the armature reaction which

causes a saturation at one tip of each pole. Modern machines are operated under certain

degree of saturation of the magnetic path. Hence the reduction in the flux per pole with

load is obvious. The armature drop is an electrical drop and can be found out even when

the machine is stationary and the field poles are unexcited. Thus there is some slight droop

in the external characteristics, which is good for parallel operation of the generators.

76






One could easily guess that the self excited machines have slightly higher droop

in the external characteristic as the induced emf E drops also due to the reduction in the

applied voltage to the field. If output voltage has to be held constant then the excitation

current or the speed can be increased. The former is preferred due to the ease with which it

can be implemented. As seen earlier, a brush lead gives rise to a load current dependent mmf

along the pole axis. The value of this mmf magnetizes/demagnetizes the field depending on

whether the lead is backward or forward.

5.4 External characteristics of a shunt generator

For a given no-load voltage a self excited machine will have more voltage drop at

the terminals than a separately excited machine, as the load is increased. This is due to

the dependence of the excitation current also on the terminal voltage. After certain load

current the terminal voltage decreases rapidly along with the terminal current, even when

load impedance is reduced. The terminal voltage reaches an unstable condition. Also, in a

self excited generator the no-load terminal voltage itself is very sensitive to the point of inter-

section of the magnetizing characteristics and field resistance line. The determination of the

external characteristics of a shunt generator forms an interesting study. If one determines

the load magnetization curves at different load currents then the external characteristics

can be easily determined. Load magnetization curve is a plot showing the variation of the

terminal voltage as a function of the excitation current keeping the speed and armature cur-

rent constant. If such curves are determined for different load currents then by determining

the intersection points of these curves with field resistance line one can get the external

characteristics of a shunt generator. Load saturation curve can be generated from no-load

saturation curve /OCC by subtracting the armature drop at each excitation point. Thus

77






it is seen that these family of curves are nothing but OCC shifted downwards by armature

drop. Determining their intercepts with the field resistance line gives us the requisite result.

Instead of shifting the OCC downwards, the x axis and the field resistance line is shifted ‘up-

wards’ corresponding to the drops at the different currents, and their intercepts with OCC

are found. These ordinates are then plotted on the original plot. This is shown clearly in

Fig. 32. The same procedure can be repeated with different field circuit resistance to yield

external characteristics with different values of field resistance. The points of operation up to

the maximum current represent a stable region of operation. The second region is unstable.

The decrease in the load resistance decreases the terminal voltage in this region.

5.4.1 External characteristics of series generators

In the case of series generators also, the procedure for the determination of the

external characteristic is the same. From the occ obtained by running the machine as a sep-

arately excited one, the armature drops are deducted to yield external /load characteristics.

The armature drop characteristics can be obtained by a short circuit test as before.

Fig. 33 shows the load characteristics of a series generator. The first half of

the curve is unstable for constant resistance load. The second half is the region where series

generator connected to a constant resistance load could work stably. The load characteristics

in the first half however is useful for operating the series generator as a booster. In a booster

the current through the machine is decided by the external circuit and the voltage injected

into that circuit is decided by the series generator. This is shown in Fig. 35

78






E1

E2

- +

E=E1

Main generator

E2+-

F1

F2

A1

A2

S1 S2

A2A1

Booster

Generator

Figure 35: Series generator used as Booster

5.4.2 Load characteristics of compound generators

In the case of compound generators the external characteristics resemble those of

shunt generators at low loads. The load current flowing through the series winding aids

or opposes the shunt field ampere turns depending upon whether cumulative or differential

compounding is used. This increases /decreases the flux per pole and the induced emf E.

Thus a load current dependant variation in the characteristic occurs. If this increased emf

cancels out the armature drop the terminal voltage remains practically same between no

load and full load. This is called as level compounding. Any cumulative compounding below

this value is called under compounding and those above are termed over- compounding.

These are shown in Fig. 36. The characteristics corresponding to all levels of differential

compounding lie below that of a pure shunt machine as the series field mmf opposes that of

the shunt field.

79






F2

F1

A2

A1

S2

S1

Vf

If

IL

Load

#Prime

mover

(a)-Connection

Over compounded

Level compounded

Under compounded

Differential

compounding

Te

rmin

al vo

ltag

e

Load current

Shunt machine

(b)-Characteristics

Figure 36: External characteristic of Compound Generator

80






External characteristics for other voltages of operation can be similarly derived

by changing the speed or the field excitation or both.

5.5 Parallel operation of generators

D.C. generators are required to operate in parallel supplying a common load when

the load is larger than the capacity of any one machine. In situations where the load is small

but becomes high occasionally, it may be a good idea to press a second machine into operation

only as the demand increases. This approach reduces the spare capacity requirement and its

cost. In cases where one machine is taken out for repair or maintenance, the other machine

can operate with reduced load. In all these cases two or more machines are connected to

operate in parallel.

5.5.1 Shunt Generators

Parallel operation of two shunt generators is similar to the operation of two storage

batteries in parallel. In the case of generators we can alter the external characteristics easily

while it is not possible with batteries. Before connecting the two machines the voltages of

the two machines are made equal and opposing inside the loop formed by the two machines.

This avoids a circulating current between the machines. The circulating current produces

power loss even when the load is not connected. In the case of the loaded machine the

difference in the induced emf makes the load sharing unequal.

Fig. 37 shows two generators connected in parallel. The no load emfs are made

equal to E1 = E2 = E on no load; the current delivered by each machine is zero. As the load

is gradually applied a total load current of I ampere is drawn by the load. The load voltage

81






G1 G2

v

Prime

moverLoad

Vf1 Vf2

s1

s2

F1

F2 F2

F1

A2 A2

A1 A1

Figure 37: Connection of two shunt generators in Parallel

A B CV

I1

I2

I=I1+I2

V2 k j

V1

E1

E2

V2

V0

Load current

Term

inal

Vo

ltag

e

DO

Total characteristic

Figure 38: Characteristics of two shunt generators in Parallel

82






under these conditions is V volt. Each machines will share this total current by delivering

currents of I1 and I2 ampere such that I1 + I2 = I.

Also terminal voltage of the two machines must also be V volt. This is dictated

by the internal drop in each machine given by equations

V = E1 − I1Ra1 = E2 − I2Ra2 (37)

where Ra1 and Ra2 are the armature circuit resistances. If load resistance RL is known these

equations can be solved analytically to determine I1 and I2 and hence the manner in which

to total output power is shared. If RL is not known then an iterative procedure has to be

adopted. A graphical method can be used with advantage when only the total load current is

known and not the value of RL or V . This is based on the fact that the two machines have a

common terminal voltage when connected in parallel. In Fig. 38 the external characteristics

of the two machines are first drawn as I and II . For any common voltage the intercepts OA

and OB are measured and added and plotted as point at C. Here OC = OA + OB . Thus

a third characteristics where terminal voltage is function of the load current is obtained.

This can be called as the resultant or total external characteristics of the two machines put

together. With this, it is easy to determine the current shared by each machine at any total

load current I.

The above procedure can be used even when the two voltages of the machines

at no load are different. At no load the total current I is zero ie I1 + I2 = 0 or I1 = −I2.

Machine I gives out electrical power and machine II receives the same. Looking at the voltage

equations, the no load terminal equation Vo becomes

Vo = E1 − I1nlRa1 = E2 + I2nlRa2 (38)

83






As can be seen larger the values of Ra1 and Ra2 larger is the tolerance for the error

between the voltages E1 and E2. The converse is also true. When Ra1 and Ra2 are nearly zero

implying an almost flat external characteristic, the parallel operation is extremely difficult.

5.5.2 Series generators

Series generators are rarely used in industry for supplying loads. Some applications

like electric braking may employ them and operate two or more series generates in parallel.

Fig. 39 shows two series generators connected in parallel supplying load current of I1 and I2.

If now due to some disturbance E1 becomes E1 + ∆E1 then the excitation of the machine I

increases, increasing the load current delivered. As the total current is I the current supplied

by machine II reduces, so also its excitation and induced emf. Thus machine I takes greater

and greater fraction of the load current with machine II shedding its load. Ultimately the

current of machine II becomes negative and it also loads the first machine. Virtually there is

a short circuit of the two sources, the whole process is thus highly unstable. One remedy is

for a problem as this is to make the two fields immune to the circulating current between the

machines. This is done by connecting an equalizer between the fields as shown in Fig. 39-a

. With the equalizer present, a momentary disturbance does not put the two machines out

of action. A better solution for such problems is to cross connect the two fields as shown in

Fig. 39-b. A tendency to supply a larger current by a machine strengthens the field of the

next machine and increases its induced emf . This brings in stable conditions for operation

rapidly.

84






I1 I1+I2

I1+I2

I1 I2

F1F2

+

-

+

-

Equaliser

VI1+I2

S1

S2

A2

A1

A2

A1

S1

S2

(a)Equalizer connection

I1

I1+I2I1 I2

G1 G2

+

-

+

- I1+I2

I2

I2

VLoad

S1

S2

S1

S2

A1

A2

A1

A2

- -

(b)Cross connection of fields

Figure 39: Series Generator working in parallel

85






S1

A1

A2+ +

S2

VLoad

F2

F1

F2

F1

A2

A1

S1

S2

- -

Equalizer

(a)Equalizer connection

S1

A1

A2+ +

S2

VLoad

F2

F1

F2

F1

A2

A1

S1

S2

- -

(b)Cross connection of series fields

Figure 40: Compound generators operating in parallel

86






5.5.3 Compound Generators

The parallel operation of compound machines is similar to shunt generators. Dif-

ferential compounding would produce a drooping external characteristics and satisfactory

parallel operation is made easy. But most of the generators are used in the cumulatively

compounded mode. In such cases the external characteristics will be nearly flat making the

parallel operation more difficult. By employing equalizer connection for the series windings

this problem can be mitigated. Fig. 40 shows the connection diagram for parallel operation

of two compound generators.

5.6 D.C. motors

D.C. motors have a place of pride as far as electrical drives are considered. The

simplicity, and linearity of the control method makes them highly preferred machines in

precision drives. In spite of the great advancements in a.c. drives these machines are still

sought after by the industries. Apart from high precision application they are preferred in

stand alone systems working on batteries and high speed drives off constant voltage mains.

After the field is excited if we pass a current through the armature the rotor experiences

a torque and starts rotating. The direction of the torque can be readily obtained from the

law of interaction. These moving conductors cut the field and induce emf, usually called the

’back emf’ according to Lenz’s law and act as a sink of electrical power from the electrical

source. This absorbed power appears as mechanical power. The converted mechanical power

should overcome the frictional and iron losses before useful work could be done by the same.

The connections to the supply of a d.c. shunt motor are given in Fig. 41.

87






+

-

A2

A1

F2

F1

+

-

A2

A1

F2

F1

(a)Separate excitation (b) Shunt excitation

s2

+

-

s1

F1

F2

A2

A1

DC

Supply

(c)Practical arrangement

Figure 41: Shunt motor connections

88






Commonly used connection is where in both the field and the armature are

energized simultaneously Fig. 41(b). As the field has higher inductance and time constant

torque takes some time to reach the full value corresponding to a given armature current.

In Fig. 41.(c), the switch S1 is closed a few seconds prior to switch S2 . By then the field

current would have reached the steady value. So the torque per ampere is high in this case.

The only difference in the second connection Fig. 41.(a) is that the shunt field

winding is connected to a separate source. This connection is used when the armature and

field voltage are different as is common in high voltage d.c. machines. The field voltage is

kept low in such cases for the sake of control purposes. Here again the field circuit must

be energized prior to the armature. Suitable interlock should be provided to prevent the

armature switch being closed prior to / without closing of field circuit as the armature

currents reach very large values still not producing any torque or rotation. The relevant

equations for the motoring operation can be written as below

V − E − IaRa − Vb = 0 or E = V − IaRa − Vb (39)

E =p.φ.Z.n

b= Keφ.n where Ke =

pZ

b(40)

TM =1

2π.p.φ.ZIa

b= KtφIa where Kt =

1

2π.pZ

b(41)

and TM − TL = Jdw

dt(42)

where

TL- Load torque

TM - Motor torque

J - polar moment of inertia.

w - angular velocity = 2π.n

89






The first one is an electrical equation, the second and the third are electro

mechanical in nature and the last equation is the mechanical equation of motion. Ke and

Kt are normally termed as back emf constant and torque constant respectively. Under

steady speed of operation the fourth equation is not required. Using these equations one

can determine the torque speed characteristics of the machine for a given applied voltage.

These characteristics are similar to the external characteristics for a generator. Here the

torque on the machine is assumed to be varying and the corresponding speed of operation

is determined. This is termed as the torque speed characteristic of the motor.

5.7 Torque speed characteristics of a shunt motor

A constant applied voltage V is assumed across the armature. As the armature

current Ia, varies the armature drop varies proportionally and one can plot the variation of

the induced emf E. The mmf of the field is assumed to be constant. The flux inside the

machine however slightly falls due to the effect of saturation and due to armature reaction.

The variation of these parameters are shown in Fig. 42.

Knowing the value of E and flux one can determine the value of the speed.

Also knowing the armature current and the flux, the value of the torque is found out. This

procedure is repeated for different values of the assumed armature currents and the values

are plotted as in Fig. 42-(a). From these graphs, a graph indicating speed as a function of

torque or the torque-speed characteristics is plotted Fig. 42-(b)(i).

As seen from the figure the fall in the flux due to load increases the speed due

to the fact that the induced emf depends on the product of speed and flux. Thus the speed

90






No load speedLine voltage

A B

C

E

F

0

G

Torque Flux

Speed

Back emf

Flu

x, S

peed a

nd T

orq

ue

Armature current

(a)Load characteristics

Torque

Sp

eed

0

(ii)

(i)

(b)Torque speed curve

Figure 42: DC Shunt motor characteristics

91






of the machine remains more or less constant with load. With highly saturated machines

the on-load speed may even slightly increase at over load conditions. This effects gets more

pronounced if the machine is designed to have its normal field ampere turns much less

than the armature ampere turns. This type of external characteristics introduces instability

during operation Fig. 42(b)(ii) and hence must be avoided. This may be simply achieved by

providing a series stability winding which aids the shunt field mmf.

5.8 Load characteristics of a series motor

Following the procedure described earlier under shunt motor, the torque speed

characteristics of a series motor can also be determined. The armature current also happens

to be the excitation current of the series field and hence the flux variation resembles the

magnetization curve of the machine. At large value of the armature currents the useful flux

would be less than the no-load magnetization curve for the machine. Similarly for small

values of the load currents the torque varies as a square of the armature currents as the flux

is proportional to armature current in this region. As the magnetic circuit becomes more

and more saturated the torque becomes proportional to Ia as flux variation becomes small.

Fig. 43(a) shows the variation of E1, flux , torque and speed following the above procedure

from which the torque-speed characteristics of the series motor for a given applied voltage

V can be plotted as shown in Fig. 43.(b) The initial portion of this torque-speed curve is

seen to be a rectangular hyperbola and the final portion is nearly a straight line. The speed

under light load conditions is many times more than the rated speed of the motor. Such

high speeds are unsafe, as the centrifugal forces acting on the armature and commutator

can destroy them giving rise to a catastrophic break down. Hence series motors are not

recommended for use where there is a possibility of the load becoming zero. In order to

92






Terminal voltage

Useful

Torque

Speed

Back emf

To

rqu

e, F

lux a

nd

Sp

ee

d

Load current

Developed

Torque

Useful

Flux

No load

Magnetisation

curve

(a)Load characteristics

Torque

Sp

eed

0

(b)-Torque speed curve

Figure 43: Load characteristics of a Series Motor

93






safeguard the motor and personnel, in the modern machines, a ‘weak’ shunt field is provided

on series motors to ensure a definite, though small, value of flux even when the armature

current is nearly zero. This way the no-load speed is limited to a safe maximum speed. It is

needless to say, this field should be connected so as to aid the series field.

5.9 Load characteristics of a compound motor

Two situations arise in the case of compound motors. The mmf of the shunt field

and series field may oppose each other or they may aid each other. The first configuration

is called differential compounding and is rarely used. They lead to unstable operation of

the machine unless the armature mmf is small and there is no magnetic saturation. This

mode may sometimes result due to the motoring operation of a level-compounded generator,

say by the failure of the prime mover. Also, differential compounding may result in large

negative mmf under overload/starting condition and the machine may start in the reverse

direction. In motors intended for constant speed operation the level of compounding is very

low as not to cause any problem.

Cumulatively compounded motors are very widely used for industrial drives.

High degree of compounding will make the machine approach a series machine like charac-

teristics but with a safe no-load speed. The major benefit of the compounding is that the

field is strengthened on load. Thus the torque per ampere of the armature current is made

high. This feature makes a cumulatively compounded machine well suited for intermittent

peak loads. Due to the large speed variation between light load and peak load conditions, a

fly wheel can be used with such motors with advantage. Due to the reasons provided under

shunt and series motors for the provision of an additional series/shunt winding, it can be

94






seen that all modern machines are compound machines. The difference between them is only

in the level of compounding.

95





6 Parallel operation of d.c. motors

As in the case of generators motors may also be required to operate in parallel

driving a common load. The benefits as well as the problems in both the cases are similar.

As the two machines are coupled to a common load the speed of the load is the common

parameter in the torque speed plane. The torque shared by each machine depends on the

intersection of the torque speed curves. If the torque speed lines are drooping the point

of intersection remains reasonably unaltered for small changes in the characteristics due to

temperature and excitation effects. However if these curves are flat then great changes occur

in torque shared by each machine. The machine with flatter curve shares a larger portion

of the torque demand. Thus parallel operation of two shunt motors is considerably more

difficult compared to the operation of the same machines as generators. The operation of

level compounded generators is much more difficult compared to the same machines work-

ing as cumulative compounded motor. On a similar count parallel operation of cumulative

compounded motors is easier than shunt motors. Series motors are, with their highly falling

speed with the load torque, are ideal as far as the parallel operation is considered. Consid-

erable differences in their characteristics still do not affect adversely their parallel operation.

One application where several series motors operate in parallel is in electric locomotives.

Due to the uneven wear and tear of the wheels of the locomotive the speeds of the rotation

of these motors can be different to have the same common linear velocity of the locomotive.

The torque developed by each machine remains close to the other and there is no tendency

for derailment.The torque speed curves for parallel operation of series motors are given in

Fig. 44

96





Torque

Sp

ee

d A B C D

I II

Motors I and II

in parallel

0

Figure 44: Parallel operation of Series motors

97





7 Series operation of motors

In the case of series operation the motors shafts of the two machines are connected

to the same load and also the two armatures are series connected. This forces a common

armature current through both the machines and the torques developed by the machines

are proportional to the flux in each machine. Series operation of series motors is adopted

during starting to improve the energy efficiency. This method is ideally suited for shunt

and compound machines with nearly flat torque speed characteristics. Such machines can go

through high amount of dynamics without the fear of becoming unstable. This configuration

is used in steel mills. Having two smaller machines connected to the shaft is preferred over

there in place of one large machine as the moment of inertia of the motors is much reduced,

thus improving the dynamics.

98




8 Application of d.c. motors

Some elementary principles of application alone are dealt with here. The focus is

on the mechanical equation of dynamics which is reproduced here once again.

TM − TL = Jdw

dt(43)

Here TM and TL are the motor torque and the load torques respectively which are expressed

as functions of ω. Under steady state operation dω/dt will be zero. The application of

motors mainly looks at three aspects of operation.

1. Starting

2. Speed control

3. Braking

The speed of the machine has to be increased from zero and brought to the op-

erating speed. This is called starting of the motor. The operating speed itself should be

varied as per the requirements of the load. This is called speed control. Finally, the running

machine has to be brought to rest, by decelerating the same. This is called braking. The

torque speed characteristics of the machine is modified to achieve these as it is assumed

that the variation in the characteristics of the load is either not feasible or desirable. Hence

the methods that are available for modifying the torque speed characteristics and the actual

variations in the performance that these methods bring about are of great importance. When

more than one method is available for achieving the same objective then other criteria like,

initial cost, running cost, efficiency and ease operation are also applied for the evaluation of

the methods. Due to the absence of equipment like transformer, d.c. machine operation in

99




general is assumed to be off a constant voltage d.c. supply.

The relevant expressions may be written as,

n =E

Keφ=

V − IaRa − Vb

pZφ/b(44)

TM = Kt.φ.Ia =1

2π.p.Z

b.φIa (45)

TM − TL = Jdω

dt(46)

As can be seen, speed is a function of E and φ and T is a function of φ and Ia. Using these

equations, the methods for starting , speed control and braking can be discussed.

8.1 Starting of d.c. machines

For the machine to start, the torque developed by the motor at zero speed must

exceed that demanded by the load. Then TM − TL will be positive so also is dω/dt, and the

machine accelerates. The induced emf at starting point is zero as the ω = 0 The armature

current with rated applied voltage is given by V/Ra where Ra is armature circuit resistance.

Normally the armature resistance of a d.c. machine is such as to cause 1 to 5 percent drop

at full load current. Hence the starting current tends to rise to several times the full load

current. The same can be told of the torque if full flux is already established. The machine

instantly picks up the speed. As the speed increases the induced emf appears across the

terminals opposing the applied voltage. The current drawn from the mains thus decreases,

so also the torque. This continues till the load torque and the motor torque are equal to

each other. Machine tends to run continuously at this speed as the acceleration is zero at

this point of operation.

The starting is now discussed with respect to specific machines.

100




8.1.1 DC shunt motor

If armature and field of d.c. shunt motor are energized together, large current is

drawn at start but the torque builds up gradually as the field flux increases gradually. To

improve the torque per ampere of line current drawn it is advisable to energize the field

first. The starting current is given by V/Ra and hence to reduce the starting current to a

safe value, the voltage V can be reduced or armature circuit resistance Ra can be increased.

Variable voltage V can be obtained from a motor generator set. This arrangement is called

Ward-Leonard arrangement. A schematic diagram of Ward-Leonard arrangement is shown

in Fig. 45. By controlling the field of the Ward-Leonard generator one can get a variable

voltage at its terminals which is used for starting the motor.

The second method of starting with increased armature circuit resistance can

be obtained by adding additional resistances in series with the armature, at start. The

current and the torque get reduced. The torque speed curve under these conditions is shown

in Fig. 46(a) . It can be readily seen from this graph that the unloaded machine reaches its

final speed but a loaded machine may crawl at a speed much below the normal speed. Also,

the starting resistance wastes large amount of power. Hence the starting resistance must

be reduced to zero at the end of the starting process. This has to be done progressively,

making sure that the current does not jump up to large values. Starting of series motor and

compound motors are similar to the shunt motor. Better starting torques are obtained for

compound motors as the torque per ampere is more. Characteristics for series motors are

given in fig. 47.

101




M GLoad

M

+ -

+

-

+ +

--

variable

voltage

constant

voltage

mains

F1

F2

F1

F2

F1

F2

A2

A1

A2

A1

A2

A1

(a)

+

-

+

-

Static Ward

Leonard system

Constant

voltage

ac mains

Auto

transformerDiode

bridge

Variable

voltage

dc

Load

A1

A2

F1

F2

(b)

Figure 45: Ward-Leonard arrangement

102




E1

v

Constant voltage

source

A2

A1

Rext

+ -

F1

F2

Sp

ee

d

Torque

Rext = 0

Rext increasing

0

(a)

E1

v

Constant voltage

source

A2

A1

Rext

+ -

F1

F2 >If

Vf

Speed

Torque

If2

If rated

0

If2 < If rated

(b)

E1

Variable voltage

source

A2

A1

+ -

F1

F2

Vf V

V1

V2

V3

Torque

Sp

ee

d

V3 < V2 < V1

0

(c)

Figure 46: Shunt Motor characteristics

103




E1

v

Constant voltage

sources

A2

A1

S2

S1

Rext

+ -

Torque

Sp

ee

d

Rext = 0

Rext > 0

0

(a)

E1

v

Constant

voltage

sources

A2

A1

S2

S1

Rd

+ -

Torque

Sp

eed

Rd reducing

0

Rd = 8

(b)

VVariable

voltage

A2

A1

S2

S1

+ -

M

Torque

Sp

eed

V reducing

0

Vrated

(c)

Figure 47: Series motor control

104




r1

R1

R2

R3

Rn+1

n+1

n-1

n

1

2

3

rn

rn-1

r2

ra

A2

A1

F1

F2

(a)Physical connection

Vo

lts

IaImin Imax

R1

Rn-1

R2

R3

Rn

Rn+1

graphical method

0

Imin

Imax

Time

Starting current with time

0

(b) Characteristics (c) Time-current plot

Figure 48: Calculation of starter resistance steps

105




8.1.2 Grading of starting resistance for a shunt motor

If the starting resistor is reduced in uniform steps then the current peaks reached

as we cut down the resistances progressively increase. To ascertain that at no step does

the current jump to a large value non-uniform reduction of resistances must be assorted to.

This use of a non-uniform resistance step is called ‘grading’ of the resistors. The calculations

for a starter resistance of a shunt motor are shown below with the help of Fig. 48. In

the figure an n element or n+1 step starter is shown. The armature resistance when all

the external resistances are cut off is ra. The total armature circuit resistance at step 1 is

R1 = (r1 + r2 + ... + rn) + ra. The field winding is connected across the supply. The starting

current reaches a maximum value Imax when we move on to a step. One resistance element

is cut from the circuit when the current falls down to Imin . During the instant when the

element is cut the speed and hence the induced emf does not change but the current jumps

back to Imax . Thus during the starting the current changes between two limits Imax and

Imin. Writing the expression for the current before and after the resistance is changed on

step Ri and Ri+1, we have

Imin =V − E

Ri

Imax =V − E

Ri+1

orImax

Imin=

Ri

Ri+1

(47)

Proceeding this way for all the steps

Imax

Imin=

R1

R2

=R2

R3

= ... =Rn−1

Rn

=Rn

Rn+1

= k(say) (48)

kn =R1

R2

∗R2

R3

∗ ... ∗Rn

Rn+1

=R1

Rn+1

=R1

ra

k = n

√

R1

ra

(49)

106




Sometimes the ratio k may be required to be fixed. Then the number of steps required can

be calculated as

n log k = logR1

ra

, n =log R1

ra

log k(50)

log R1 − log Rn

log k

Also,

R = n

√

V

I1ra

= n

√

V

RI2ra

= n+1

√

V

I2ra

(51)

From these expressions it is seen that to have the ratio k to be unity, the number

of steps should be infinity. Smaller the number of steps larger is the ratio of maximum to

minimum current. Also, it is not possible to choose n and k independently. Imax is set

by the maximum possible starting current from the point of view of commutation. Imin

is found from the minimum torque against which the starting is required to be performed.

Similar method exists in the case of series motors and compound motors. In these cases the

ratio of currents and the ratio of fluxes are needed. The equation becomes non-linear and a

graphical method is normally adopted for the design of the resistances in those cases.

Resistance method of starting is cheaper and simple and hence is used univer-

sally. But it wastes energy in the starting resistor. Hence this method is not advised when

frequent starting of the motor is required. Ward-Leonard method gives a energy efficient

method of starting. With the help of a auto transformer and rectifier set one can get variable

voltage d.c. supply from a constant voltage a.c power source. This is some times called a

static Ward-Leonard arrangement. This method is becoming more popular over the rotating

machine counter part.

107




8.2 Speed control of d.c. motors

In the case of speed control, armature voltage control and flux control methods

are available. The voltage control can be from a variable voltage source like Ward-Leonard

arrangement or by the use of series armature resistance. Unlike the starting conditions the

series resistance has to be in the circuit throughout in the case of speed control. That means

considerable energy is lost in these resistors. Further these resistors must be adequately

cooled for continuous operation. The variable voltage source on the other hand gives the

motor the voltage just needed by it and the losses in the control gear is a minimum. This

method is commonly used when the speed ratio required is large, as also the power rating.

Field control or flux control is also used for speed control purposes. Normally

field weakening is used. This causes operation at higher speeds than the nominal speed.

Strengthening the field has little scope for speed control as the machines are already in a

state of saturation and large field mmf is needed for small increase in the flux. Even though

flux weakening gives higher speeds of operation it reduces the torque produced by the ma-

chine for a given armature current and hence the power delivered does not increase at any

armature current. The machine is said to be in constant power mode under field weakening

mode of control. Above the nominal speed of operation, constant flux mode with increased

applied voltage can be used; but this is never done as the stress on the commutator insulation

increases.

Thus operation below nominal speed is done by voltage control. Above the

nominal speed field weakening is adopted. For weakening the field, series resistances are used

for shunt as well as compound motors. In the case of series motors however field weakening

108




is done by the use of ’diverters’ . Diverters are resistances that are connected in parallel to

the series winding to reduce the field current without affecting the armature current.

8.3 Braking the d.c. motors

When a motor is switched off it ‘coasts’ to rest under the action of frictional forces.

Braking is employed when rapid stopping is required. In many cases mechanical braking

is adopted. The electric braking may be done for various reasons such as those mentioned

below:

1. To augment the brake power of the mechanical brakes.

2. To save the life of the mechanical brakes.

3. To regenerate the electrical power and improve the energy efficiency.

4. In the case of emergencies to step the machine instantly.

5. To improve the through put in many production process by reducing the stopping time.

In many cases electric braking makes more brake power available to the braking

process where mechanical brakes are applied. This reduces the wear and tear of the me-

chanical brakes and reduces the frequency of the replacement of these parts. By recovering

the mechanical energy stored in the rotating parts and pumping it into the supply lines

the overall energy efficiency is improved. This is called regeneration. Where the safety of

the personnel or the equipment is at stake the machine may be required to stop instantly.

Extremely large brake power is needed under those conditions. Electric braking can help

in these situations also. In processes where frequent starting and stopping is involved the

109




process time requirement can be reduced if braking time is reduced. The reduction of the

process time improves the throughput.

Basically the electric braking involved is fairly simple. The electric motor can

be made to work as a generator by suitable terminal conditions and absorb mechanical energy.

This converted mechanical power is dissipated/used on the electrical network suitably.

Braking can be broadly classified into:

1. Dynamic

2. Regenerative

3. Reverse voltage braking or plugging

These are now explained briefly with reference to shunt ,series and compound motors.

8.3.1 Dynamic braking

• Shunt machine

In dynamic braking the motor is disconnected from the supply and connected to a

dynamic braking resistance RDB. In and Fig. 49 this is done by changing the switch

from position 1 to 2 . The supply to the field should not be removed. Due to the

rotation of the armature during motoring mode and due to the inertia, the armature

continues to rotate. An emf is induced due to the presence of the field and the rotation.

This voltage drives a current through the braking resistance. The direction of this

current is opposite to the one which was flowing before change in the connection.

Therefore, torque developed also gets reversed. The machine acts like a brake. The

110




torque speed characteristics separate by excited shunt of the machine under dynamic

braking mode is as shown in Fig. 49(b) for a particular value of RDB. The positive

torque corresponds to the motoring operation. Fig. 50 shows the dynamic braking of

a shunt excited motor and the corresponding torque-speed curve. Here the machine

behaves as a self excited generator.

Below a certain speed the self-excitation collapses and the braking action becomes

Zero.

• Series machine

In the case of a series machine the excitation current becomes zero as soon as the

armature is disconnected from the mains and hence the induced emf also vanishes. In

order to achieve dynamic braking the series field must be isolated and connected to

a low voltage high current source to provide the field. Rather, the motor is made to

work like a separately excited machine. When several machines are available at any

spot, as in railway locomotives, dynamic braking is feasible. Series connection of all

the series fields with parallel connection of all the armatures connected across a single

dynamic braking resistor is used in that case.

• Compound generators

In the case of compound machine, the situation is like in a shunt machine. A separately

excited shunt field and the armature connected across the braking resistance are used.

A cumulatively connected motor becomes differentially compounded generator and the

braking torque generated comes down. It is therefore necessary to reverse the series

field if large braking torques are desired.

111




-

-

++

Vf E

RDB

2

2

1

1

A2

A1

F1

F2

(a)Connections

RDBS

peed

0Torque

increasing

(b)Characteristics

Figure 49: Dynamic Braking of a shunt motor

112




-

-

++

Vf E

RDB

2

2

1

1

A2

A1

F1

F2

(a)Connections

RDBS

peed

0Torque

increasing

(b)Characteristics

Figure 50: Dynamic braking of shunt excited shunt machine

113




8.3.2 Regenerative braking

In regenerative braking as the name suggests the energy recovered from the rotating

masses is fed back into the d.c. power source. Thus this type of braking improves the energy

efficiency of the machine. The armature current can be made to reverse for a constant voltage

operation by increase in speed/excitation only. Increase in speed does not result in braking

and the increase in excitation is feasible only over a small range, which may be of the order of

10 to 15%. Hence the best method for obtaining the regenerative braking is to operate, the

machine on a variable voltage supply. As the voltage is continuously pulled below the value of

the induced emf the speed steadily comes down. The field current is held constant by means

of separate excitation. The variable d.c. supply voltage can be obtained by Ward-Leonard

arrangement, shown schematically in Fig. 51. Braking torque can be obtained right up to

zero speed. In modern times static Ward-Leonard scheme is used for getting the variable

d.c. voltage. This has many advantages over its rotating machine counter part. Static set

is compact, has higher efficiency, requires lesser space, and silent in operation; however it

suffers from drawbacks like large ripple at low voltage levels, unidirectional power flow and

low over load capacity. Bidirectional power flow capacity is a must if regenerative braking is

required. Series motors cannot be regeneratively braked as the characteristics do not extend

to the second quadrant.

8.3.3 Plugging

The third method for braking is by plugging.Fig. 52 shows the method of connection

for the plugging of a shunt motor. Initially the machine is connected to the supply with the

switch S in position number 1. If now the switch is moved to position 2, then a reverse

voltage is applied across the armature. The induced armature voltage E and supply voltage

114




E

+ -

VVf

Variable

votage

source

IfA2

A1F1

F2


B

A

V1

V2

V1 > V2

Speed

Torque0

C

(b)Characteristics

Figure 51: Regenerative braking of a shunt machine

115




-

-

+

+

VfE

RB2

2

1

1

V

A2

A1

F1

F2


B

A

Spee

d

TorqueC 0

(b)Characteristics

Figure 52: Plugging or reverse voltage braking of a shunt motor

116




V aid each other and a large reverse current flows through the armature. This produces a

large negative torque or braking torque. Hence plugging is also termed as reverse voltage

braking. The machine instantly comes to rest. If the motor is not switched off at this instant

the direction of rotation reverses and the motor starts rotating the reverse direction. This

type of braking therefore has two modes viz. 1) plug to reverse and 2) plug to stop. If we

need the plugging only for bringing the speed to zero, then we have to open the switch S

at zero speed. If nothing is done it is plug to reverse mode. Plugging is a convenient mode

for quick reversal of direction of rotation in reversible drives. Just as in starting, during

plugging also it is necessary to limit the current and thus the torque, to reduce the stress on

the mechanical system and the commutator. This is done by adding additional resistance in

series with the armature during plugging.

• Series motors

In the case of series motors plugging cannot be employed as the field current too gets

reversed when reverse voltage is applied across the machine. This keeps the direction

of the torque produced unchanged. This fact is used with advantage, in operating a

d.c. series motor on d.c. or a.c. supply. Series motors thus qualify to be called as

‘Universal motors’.

• Compound motors

Plugging of compound motors proceeds on similar lines as the shunt motors. However

some precautions have to be observed due to the presence of series field winding. A

cumulatively compounded motor becomes differentially compounded on plugging. The

mmf due to the series field can ’over power’ the shunt field forcing the flux to low values

or even reverse the net field. This decreases the braking torque, and increases the

duration of the large braking current. To avoid this it may be advisable to deactivate

117




the series field at the time of braking by short circuiting the same. In such cases the

braking proceeds just as in a shunt motor. If plugging is done to operate the motor

in the negative direction of rotation as well, then the series field has to be reversed

and connected for getting the proper mmf. Unlike dynamic braking and regenerative

braking where the motor is made to work as a generator during braking period, plugging

makes the motor work on reverse motoring mode.

8.4 Application of d.c motors and generators

It is seen from the earlier sections that the d.c.machine is capable of having variety of

torque-speed characteristics depending on the circuit conditions. The need for generating

these characteristics will be clear only when they are seen along with the characteristics of

the loads that they operate with. Even though a detailed treatment of motor load systems is

outside the scope here, it may be useful to look into the typical torque-speed characteristics

of some of the common loads.

Loads are broadly divided into,

(a) Passive loads

(b) Active loads

They may be unidirectional in operation or work in either direction (Reversible loads).

Passive loads absorb the mechanical energy developed by the motors while

active loads are capable of working as both sinks and sources for mechanical energy. The

direction of rotation may be taken to be clockwise/counter clockwise rotation. Normally the

118




direction in which the load operates most of the time, is taken as the positive direction of

rotation. Any torque which accelerates the motor load system in the positive direction of

rotation is termed as a positive toque. With this rotation torques of motors, generators or

loads can be represented graphically on a four quadrantal diagram. The torque being taken

as an independent variable, is represented along the x-axis. Y-axis represents the speed.

Quadrants. I and III in Fig. 53(a) represent ‘forward motoring’ and ‘reverse motoring’ op-

eration respectively. Quadrants II and IV similarly represent generating/braking quadrants

as they absorb mechanical power and cause braking action.

Fig. 53(b) shows a few typical load characteristics on a four quadrantal dia-

gram.

The characteristics a, b,and c correspond to frictional torque, cutting torque and fan torque

respectively. While the frictional torque is not a function of speed, the cutting toque is pro-

portional to the speed and the fan torque varies as the square of the speed. These can only

absorb mechanical power and hence are represented in quadrantal II for positive direction

of rotation. Similar loads produce characteristics in quadrant IV for negative direction of

rotation.

Fig. 54 shows a typical behaviour of an active load. Here an elevator is taken as an example.

Here the counter weight is assumed to be heavier than the cage and similarly the loaded

cage in assumed to be heavier than the counter weight. As seen from the Fig. 54 the torque

is constant and depends on the difference in the weight of the case and the counter weight,

and the radius of the drum. The characteristics of the load exists in all the four quadrants

and is capable of delivering as well as absorbing mechanical power. Hence it is called as an

active load. The governing equation when the motor and a load are connected together is

TM (w) − TL(w) = Jdw

dt(52)

119




II I

I I I I V

Torque

Speed

(a)

a

a

b

c

b

c

Torque

Speed

(b)

Figure 53: Typical load characteristics on a four quadrantal diagram

120




Torque

Hoisting an

empty cage Hoisting a

loaded cage

Lowering a

loaded cageLowering an

empty cage

o

speedT

WT

W

TW

T

W

Figure 54: Four quadrantal diagram

121




where TM(w) and TM(w) are motor and load torques respectively. J is the polar moment of

inertia of the motor and load put together at the motor shaft. dw

dtis made positive when the

speed has to be increased in the positive direction and negative when reducing the speed.

Under steady operation TM(w)− TL(W ) = 0. Both motor and load torques are expressed as

functions of the speed. The speed at which motor and load torques are equal and opposite is

the steady state operating speed. By varying the characteristics of the motor (or the load),

this speed can be changed to suit our requirements. Normally the torque speed characteris-

tics of a load cannot be changed easily. Thus most speed control methods adopt, varying the

motor characteristics to achieve speed control. Some typical loads and the motors commonly

used to drive the same are tabulated in Table.

d.c. shunt motor lathes,fans,pumps disc and band saw drive requiring moderate torques.

d.c. series motor Electric traction, high speed tools

d.c. compound motor Rolling mills and other loads requiring large momentary toques.

122




9 Testing of d.c. machines

A d.c. machine has to be tested for proper fabrication and trouble free operation.

From the tests one can determine the external characteristics needed for application of these

machines. Also, one can find the efficiency, rating and temperature rise of the machine.

Some of the tests are discussed in sequence now.

9.1 Measurement of armature resistance

Measurement of winding resistances of field windings and armature winding are

performed by v-i method. Field is not excited during this test.

Even though any value of applied voltage can be used, the highest permissible

voltage/current is chosen during the test to minimize the errors. The armature circuit

consists of two resistances in series. They are armature winding resistance and resistance

due to the brushes and the brush drop. The brush contact drop behaves like a non-linear

resistance. To separate this from the armature circuit resistance and brush resistance a

number of v-i readings are taken. An equation of V = Vb + IRa form is fitted through

these test points shown graphically in Fig. 55. For large values of I the equivalent armature

resistance is taken to be V/I ohm. If the value of brush drop Vb can be neglected then the

armature resistance Ra = V/I ohm.

9.2 Open Circuit Characteristic (OCC)

The OCC is of great value as it shows the mmf and hence the field current required

to generate a given voltage at any speed, on no load. It is a graph showing the variation

123




v

+

-

V

A

A2

A1

DC Supply


V

I

Vb

I.V. Characteristic

dv

di

Ra = dv

di

0

(b)Characteristics

Figure 55: Measurement of Armature resistance and Brush drop

124




of the induced emf as a function of excitation current, when the speed is held constant,

with the load current being zero. It is also called the no-load saturation curve or no load

magnetization characteristic. This is experimentally determined by running the machine

as a separately excited generator on no-load at a constant speed and noting the terminal

voltage as a function of the excitation current. This curve can be used to find the OCC at

other speeds and also the self excited voltage when the machine works as a shunt generator.

9.3 Short circuit characteristics:(SCC)

In the case of short circuit test the armature is kept short circuited through an

ammeter. The machine is demagnetized and an extremely small field current is passed

through the field. The variation of the short circuit current as a function of excitation

current is plotted as the SCC. The speed is to be held constant during this test also. The

short circuit test gives an idea of the armature drop at any load current.

9.4 Load test

To assess the rating of a machine a load test has to be conducted. When the

machine is loaded, certain fraction of the input is lost inside the machine and appears as

heat, increasing the temperature of the machine. If the temperature rise is excessive then

it affects the insulations, ultimately leading to the breakdown of the insulation and the

machine. The load test gives the information about the efficiency of a given machine at any

load condition. Also, it gives the temperature rise of the machine. If the temperature rise

is below the permissible value for the insulation then the machine can be safely operated

at that load, else the load has to be reduced. The maximum continuous load that can be

125




delivered by the machine without exceeding the temperature rise for the insulation used, is

termed as the continuous rating of the machine. Thus the load test alone can give us the

proper information of the rating and also can help in the direct measurement of the efficiency.

9.5 Measurement of rotor inertia

The moment of inertia value is very important for the selection of a proper motor

for drives involving many starts and stops or requiring very good speed control characteris-

tics. The inertia can be determined by a retardation test.

The test works on the principle that when a motor is switched off from the

mains it decelerates and comes to rest. The angular retardation at any speed is proportional

to the retarding torque and is inversely proportional to the inertia. The torque lost at

any speed is calculated by running the motor at that speed steadily on no load and noting

the power input.From this power the losses that takes place in the armature and field are

deducted to get the power converted into mechanical form. All this power is spent in over

coming the mechanical losses at that speed. This can be repeated at any defined speed to

get the lost power (PL) and torque lost (Tlost) due to mechanical losses. In a retardation

test the motor speed is taken to some high value and the power to the motor is switched off.

The torque required by the losses is supplied by the energy stored in the motor inertia. The

lost torque at any speed can be written as

PL = Tlost.ω (53)

Tlost = PL/w = Jdw

dt

Here the dw

dtis the slope of the retardation curve and the (Tlost) is the torque required to be

126




met at the given speed. From these values the moment of inertia can be computed as

J =Tlost

dw

dt

=PL

w.dw

dt

kgm2 (54)

9.6 Efficiency of a d.c. machine

A machine when loaded yields an output. The input to the machine is measured

at that operating point. The the efficiency in per unit is given as the ratio of output power

to input power.

η =output power

input power(55)

=Input power − power lost inside the machine

input power

=output power

output power + power lost inside the machine

The first definition is used in the direct estimation of the efficiency . The other

two definitions are known as determination of efficiency using the loss segregation. For the

segregation of losses one must know the losses that take place inside a d.c. machine. The

losses that take place inside a d.c. machine can be listed as below.

1. Armature copper loss.

2. Brush and brush contact loss.

3. Shunt field loss

4. Series field loss

5. Commutating pole loss

127




6. Compensating winding loss

7. Mechanical losses

8. Iron losses

9. Stray load losses

Out of these items 1,2,7,8 and 9 will be present in all the d.c. machines. Out of

the remaining one or more may be present depending on which winding is present. These

losses change with temperature of operation. Mechanical losses vary with variation in speed.

Iron losses change with the degree of saturation and distortion of the shape of the field flux

distribution under the poles.

When a d.c. machine is loaded using a suitable load the output delivered by

the machine increases. The input requirement also increases along with the output. The

difference between the input and output powers is the power lost inside the machine as loss.

The efficiency of power conversion is given by the ratio of output power to input power.

Putting in mathematical form for a motor,

η =V I − losses

V I(56)

for constant speed operation, the speed dependant losses remain constant. The load depen-

dant losses form the variable losses. While the loss that takes place in the brush drop in the

brushes is proportional to the load current, the loss that takes place in the resistance of the

armature is proportional to the square of the load current. Even though the loss that takes

place in a field winding is proportional to the square of the current through that winding, it

is classified under constant losses as the excitation current is held constant during loading.

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Thus the total losses in a d.c. motor can be expressed in the form

PL = a + bI + cI2 (57)

η =V I − PL

V I= 1 − (

A

I+ B + CI) (58)

When A = a

V, B = b

Vand C = cV .

The term inside the brackets is sometimes referred to as the deficiency. For a

typical d.c.motor these are plotted in Fig. 56(a) as a function of the load current. The

curves a,b,c in the figure represent the efficiency curve taking one component of the loss

at a time. The curve d is the efficiency curve with all three components taken together.

The resultant curve exhibits a maximum. This can be easily seen from the graph that

this maximum occurs when constant losses equal the variable losses.A

I= CI or A = CI2.

Fig. 56(b) depicts a typical output vs η curve of a d.c.machine.

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a

b

c

d

current

Effic

iency

(a)Efficiency Vs Load current

Output

Effic

iency

(b)Output Vs Efficiency

Figure 56: Efficiency of a D.C.machine

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Electrical Machines - i

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