ee09 404-module 1

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EE09 404-DC MACHINES AND

TRANSFORMERS

Prof. THANKACHEN P.V

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TRANSFORMERS

MODULE I

1.1 Magnetic Circuit

A magnetic circuitis made up of one or more closed loop paths containing a magnetic flux.

The flux is usually generated bypermanent magnetsor electromagnetsand confined to the path by

magnetic coresconsisting offerromagneticmaterials like iron, although there may be air gaps or

other materials in the path. Magnetic circuits are employed to efficiently channel magnetic fieldsin

many devices such as electric motors, generators, transformers, relays, lifting electromagnets,

SQU!s,galvanometers,and magneticrecording heads.

"ig #.#.#$ A simple magnetic circuit %ith an air gap

"igure #.#.# sho%s a simple magnetic circuit %ith an air gap of length &lg cut in the middle of

a leg. The %inding providesNI ampere'turn. The spreading of the magnetic flux lines outside the

common area of the core for the air gap is kno%n as fringing field (figure #.#.) *a+. "or simplicity,

this effect is negligible and the flux distribution is assumed to be as in figure #.#.) *b+. t can be

sho%n that the magnetic flux generated in the air gap is e-ual to the magneto motive force NI divided

by the sum of the reluctances of the core and of the air gap.

*a+ *b+

"igure #.#.)$ Air gaps *a+ %ith fringing and *b+ ideal

Dept. Of EEE 1 SIMAT,Vavanoor
http://en.wikipedia.org/wiki/Magnetic_fluxhttp://en.wikipedia.org/wiki/Magnetic_fluxhttp://en.wikipedia.org/wiki/Permanent_magnethttp://en.wikipedia.org/wiki/Electromagnethttp://en.wikipedia.org/wiki/Magnetic_corehttp://en.wikipedia.org/wiki/Ferromagnetichttp://en.wikipedia.org/wiki/Ferromagnetichttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Electric_motorhttp://en.wikipedia.org/wiki/Electric_generatorhttp://en.wikipedia.org/wiki/Transformerhttp://en.wikipedia.org/wiki/Transformerhttp://en.wikipedia.org/wiki/Transformerhttp://en.wikipedia.org/wiki/Relayhttp://en.wikipedia.org/wiki/Electromagnethttp://en.wikipedia.org/wiki/Electromagnethttp://en.wikipedia.org/wiki/Electromagnethttp://en.wikipedia.org/wiki/SQUIDhttp://en.wikipedia.org/wiki/Galvanometerhttp://en.wikipedia.org/wiki/Galvanometerhttp://en.wikipedia.org/wiki/Galvanometerhttp://en.wikipedia.org/wiki/Recording_headhttp://en.wikipedia.org/wiki/Recording_headhttp://en.wikipedia.org/wiki/Permanent_magnethttp://en.wikipedia.org/wiki/Electromagnethttp://en.wikipedia.org/wiki/Magnetic_corehttp://en.wikipedia.org/wiki/Ferromagnetichttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Electric_motorhttp://en.wikipedia.org/wiki/Electric_generatorhttp://en.wikipedia.org/wiki/Transformerhttp://en.wikipedia.org/wiki/Relayhttp://en.wikipedia.org/wiki/Electromagnethttp://en.wikipedia.org/wiki/SQUIDhttp://en.wikipedia.org/wiki/Galvanometerhttp://en.wikipedia.org/wiki/Recording_headhttp://en.wikipedia.org/wiki/Magnetic_flux

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TRANSFORMERS

Some corresponding -uantities in electric and magnetic circuit are listed as belo%$

Electric quantity Magnetic quantity

urrent in ampere *+ Magnetic flux in %ebers */+

urrent density 0 Magnetic flux density 1

onductivity 2 3ermeability 4

5lectromotive force in volt6resistance x Magneto motive force in ampere

turns6reluctance x /

5lectric field intensity 5 Magnetic field intensity 7

onductance6#8resistance 3ermeance6#8reluctance

9esistance6#82A. 9eluctance6#84A

The differences bet%een electric and magnetic circuits are as belo%$

: The path of the magnetic flux flo%s is perpendicular to the current flo%s in the circuit. n other

%ords, the directions of 1 and 0 are perpendicular.

: "or a given temperature, electric resistance is constant and does not depend on current density.

7o%ever, the magnetic reluctance depends on magnetic field and flux intensity since the

permeability is not constant.

: urrent flo%ing in an electric circuit involves dissipation of energy, but for magnetic circuit, energy

is needed to generate magnetic flux.

1.2 Magneto-Motive Force

The amount of flux density setup in the core is dependent upon five factors'the current,number of turns, material of the magnetic core, length of core and the cross'sectional area of the

core. More current and the more turns of %ire %e use, the greater %ill be the magneti;ing effect.

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reluctance. t is a scalar, extensive -uantity, akin to electrical resistance. The units for magnetic

reluctance are inverse 7enries, 7>#.

n a ! field, the reluctance is the ratio of the ?magneto motive force@ *MM"+ in a magnetic

circuitto the magnetic fluxin this circuit.

The definition can be expressed as follo%s$

S = mmf/ *#..#+

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TRANSFORMERS

applied field 7. This property is called magnetic hysteresis. The 1'7 loop is called hysteresis loop.

The shape and area of the loop are different for different materials .

1.5.1 ysteresis loo!"

Get us take an unmagnified bar of iron A1 and magneti;e in by placing it %ithin the magneti;ing

field of a solenoid *7+. The field can be increased or decreased by increasing or decreasing current

through it. Get &7B be increased in step from ;ero up to a certain maximum value and the

corresponding of induction flux density *1+ is noted. f %e plot the relation bet%een 7 and 1, a curve

like DA, as sho%n in fig, is obtained. The material becomes magnetically saturated at 76DM and

has, at that time, a maximum flux density, established through it.

*a+ *b+

"ig #.F.#$ *a+ magneti;ation of an iron bar *b+ hysteresis loop.

f 7 is no% decreased gradually *by decreasing solenoid current+ flux density 1 %ill not

decrease along AD *as might be expected+ but %ill decrease less rapidly along A.

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TRANSFORMERS

t is seen that 1 al%ays lags behind 7 the t%o ne%er attain ;ero value simultaneously. This

lagging of 1, behind 7 is given the name hysteresis %hich literally means &to lag behind.B The closed

loop A!5"HA, %hich is obtained %hen iron bar is taken through one complete cycle of reversal of

magneti;ation is kno%n as 7ysteresis loop.

1.5.2 ysteresis loss"

7ysteresis loss is %hen the effect of a cause lags behind the cause itself. This is noticed %hen

changes in magnetism of a body lag behind the changes in the magnetic field. ron, for example,

depends not only on the magnetic field, but also any previous exposures. !eformations in the shapes

of substances that continue indefinitely, once the deforming force has been removed, are an example

of hysteresis.ysteresis lossis energy %asted in the form of heat %hen alternating current reversesrapidly and molecular dipoles lag the magneti;ing force.

n other %ords %e can say that, if the magnetic field applied to a magnetic material isincreased and then decreased back to its original value, the magnetic field inside the material does

not return to its original value. The internal field &lagsB behind the external field. This behaviour

results in a loss of energy, called the hysteresis loss, %hen a sample is repeatedly magneti;ed and

demagneti;ed.

5nergy loss in 08m8cycle 6 Area of hysteresis loop.

7ysteresis po%er loss, Ph= kh(volume) f Bmn *#.F.).#+

3h 6 7ysteresis loss in %atts

f 6 "re-uency in 7;.

1m 6 Maximum flux density, T

&nB varies from #.F to ).F depending on the material used. The constant khalso depends on the

material. "or a particular machine, the volume of material also constant, so that 3hcan be %ritten as

Ph= Khf Bmn *#.F.).)+

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TRANSFORMERS

The bar magnet represents the armature and the coil of %ire represents the field. The arro%

sho%s the direction of the armatureBs rotation. =otice that the arro% sho%s the armature starting to

rotate in the clock%ise direction. The north pole of the field coil is repelling the north pole of the

armature, and the south pole the field coil is repelling the south pole of the armature.

"ig #.J.#$ *a+ magnetic diagram that explains the operation of a ! motor. The rotating

magnets moves clock%ise because like poles repel. *b+ The rotating magnet being attracted because

the poles are unlike. *c+ The rotating magnet is no% sho%n as the armature coil, and its polarity is

determined by the brushes and commutator segments.

As the armature begins to move, the north pole of the armature comes closer to the armature

comes closer to the south pole of the field, and the south pole of the armature is coming closer to the

north pole of the field. As the t%o unlike poles near each other, they begin to attract. This attraction

becomes stronger until the armatureBs north pole moves directly in line %ith the fieldBs south pole,and its south pole moves directly in line %ith the fieldBs north pole *fig #.J.# *b++.

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TRANSFORMERS

Since the armature is no% a coil of %ire, it %ill need ! current flo%ing through it to

become magneti;ed. This presence another problemL since the armature %ill be rotating, the !c

voltage %ires cannot be connected directly to the armature coil. A stationary set of carbon brushes is

used to make contact to the rotating armature. The brushes ride on the commutator segments to make

contact so that current %ill flo% through the armature coil.

n fig #.J.# *c+ you can see that the ! voltage applied to the field and to the brushes. Since

negative ! voltage is connected to one of the brushes, the commutator segment the negative brush

rides on %ill also be negative. The armatureBs magnetic field causes the armature to begin to rotate.

This time %hen the armature gets to the point %here it becomes locked up %ith the magnetic field,

the negative brush begin to touch the end of the armature coil that %as negative. This action s%itches

the direction of current flo% through the armature, %hich also s%itches the polarity of the armature

coilBs magnetic field at Eust the right time so that the repelling and attracting continues. The armature

continues to s%itch its magnetic polarity t%ice during each rotation, %hich causes it to continually be

attracted and repelled %ith the field poles.

This is a simple t%o pole motor that is used primarily for instructional purposes. Since the

motor has only t%o poles, the motor %ill operate rather roughly and not provide too much tor-ue.

Additional field poles and armature poles must be added to the motor for it to become useful for

industry.

An electrical current in a magnetic field *produced by some other currents+ experiences a

force perpendicular to both the direction of the current and the direction of the magnetic field, and

reverses if either of these reverses in direction. The force is proportional to the current and to the

strength of the magnetic field *fig #.J.)+. This principle can be called Kmotor action.@

"ig #.J.)$ A force is exerted on a current in a magnetic field perpendicular to the plane of themagnetic field and the current.

1.) *evelo!e& torque

"ig #. sho%s a coil carrying a current and lying in a magnetic field of flux density 1. t is

seen that an up%ard force is exerted on the left hand conductor and a do%n%ard force on the right

hand conductor.


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TRANSFORMERS

"ig #.$ Tor-ue on a coil in a magnetic field

"orce on each conductor, F = B I l=e%ton *#..#+

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TRANSFORMERS

n #P# Michael "araday discovered that if a conductor is moved through a magnetic field, an

electrical voltage is induced in the conductor.

The magnitude of this generated voltage is directly proportional to the strength of the

magnetic field and the rate at %hich the conductor crosses the magnetic field. The induced voltagehas a polarity that %ill oppose the change causing the induction'Gen;Bs la%

This natural phenomenon is kno%n as generator action and is described today by "aradayBs

la% of electromagnetic induction$ *ind6 R/8Rt+, %here ind6 induced voltage, R/ 6 change in flux

density, Rt 6 change in time.

All rotary generators built use the basic principles of Henerator Action.

An electrical conductor, such as a copper %ire, moving in a magnetic field has an electrical

current induced in it. This is expressed by the creation of an electromotive force or voltage, %hich

causes current to flo% Eust as the voltage of a battery does. The effect is maximum %hen the %ire, the

motion, and the magnetic field are all mutually perpendicular *fig #.P.#+. This principle can be called

Kgenerator action.@

"ig #.P.#$ A voltage is induced in a conductor moved in a magnetic field. =ote that the voltage is

opposite to the current causing a force in the direction of motion.

1., Energy conversion in rotating electrical machines

onverters that are used to continuously translate electrical input to mechanical output or viceversa are called electric machines. The process of translation is kno%n as electromechanical energy

conversion. 5lectro mechanical energy conversion occurs %hen there is a change in magnetic flux

linking a coil, associated %ith mechanical motion. An electric machine is therefore a link bet%een an

electrical system and a mechanical system. n these machines the conversion is reversible. f the

conversion is from mechanical to electrical energy, the machine is said to act as a generator. f the

conversion is from electrical to mechanical energy, the machine is said to act as a motor. These t%o

effects are sho%n in fig #.. n these machines, conversion of energy from electrical to mechanical

form or vice versa results from the follo%ing t%o electromagnetic phenomena$

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TRANSFORMERS

"ig #.$ The energy directions in generator and motor actions.

These t%o effect occur simultaneously %henever energy conversion takes place from

electrical to mechanical or vice versa. n motoring action, the electrical system makes current flo%

through conductors that are placed in the magnetic field. A force is produced on each conductor. f

the conductors are placed on a structure free to rotate, an electromagnetic tor-ue %ill be produced,

tending to make the rotating structure rotate at some speed. f the conductors rotate in a magnetic

field, a voltage %ill also be induced in each conductor. n generating action, the process is reversed.

n this case, the rotating structure, the rotor, is driven by a prime mover *such as a steam turbine or

diesel engine+. A voltage %ill be induced in the conductors that are rotating %ith the rotor. f an

electrical load is connected the %inding formed by these conductors, a current %ill flo%, delivering

electrical po%er to the load. Moreover, the current flo%ing through the conductor %ill interact %ith

the magnetic field to produce a reaction tor-ue, %hich %ill tend to oppose the tor-ue applied by the

prime mover. =ote that in both motor and generator actions, the coupling magnetic field is involved

in producing a tor-ue and an induced voltage.

1.1 E&&y currents an& e&&y current losses

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TRANSFORMERS

This circulating current creates a magnetic field that opposes the external magnetic field. The

direction of the eddy current is described by Gen;Bs la%. The stronger of the external magnetic field

or the greater of the electrical conductivity of the material, the eddy current that is developed %ill be

stronger and also yields stronger opposing force.

5ddy current creates losses through 0oule heating, and it reduces the efficiency of device that

operates under alternating magnetic field condition such as iron core of transformers and alternating

current motors. This po%er loss is kno%n as eddy current loss due to the induced eddy current in the

metal or magnetic materials.

n order to reduce the eddy current loss, the resistivity of the material is increased by adding

silicon in the metal or ferromagnetic materials. Another effective %ay to achieve lo% eddy current

loss is by using lamination of electrical metal sheets. These metal sheets are coated %ith insulator

%hich breaks the eddy currents path as illustrated in the diagram belo%.

"igure #.#.)$ 5ddy currents in a laminated toroidal core.

The po%er due to the eddy current loss is given asL

e/ 0e t

2 %2 m2'volume( , unit$

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TRANSFORMERS

parts, one stationary and one moving, called the field and the armature. An essential example of a !

machine is a copper coil spinning on its o%n axis bet%een t%o magnets. A practical ! machine also

needs a commutator, brushes, poles and bearings.

The construction of ! machines is discussed here. An actual generator consists of the follo%ingparts$

magnetic frame or yoke

pole cores and pole shoes

armature core

armature %indings or conductors

field %inding

commutator

brushes

bearing

The yoke, pole cores, armature core and air gaps bet%een the poles and the armature core

form the magnetic field. The rest form the electrical circuit. "igure #.## sho%s the construction of a

! machine in %hich the above parts have been depicted.

"igure #.##$ Sectional vie% of a O pole ! Machine

"agnetic frame or #o$e: The magnetic frame or yoke gives mechanical support for poles as

%ell as protects the %hole machine as a protecting cover. t also carries the magnetic flux

produced by the poles. n small generators yokes are made of cast iron, %hereas for largemachines cast steel is used. The yoke carries F per cent of total flux per pole.


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TRANSFORMERS

%ole cores and pole soes:The pole core and pole shoe stacked together under hydraulic

pressure and then attached to the yoke. These t%o structures are assigned for different

purposes, the pole core is of small cross sectional area and its function is to Eust hold the pole

shoe over the yoke, %hereas the pole shoe having a relatively larger cross'sectional area

spreads the flux produced over the air gap bet%een the stator and rotor to reduce the loss dueto reluctance. The pole shoe also carries slots for the field %indings that produce the field

flux.

&rmature core:The armature or rotor core, %hich carries the armature or rotor %inding, is

made of sheet'steel laminations, and as a result is subEected to altering magnetic field in the

path of its rotation %hich directly results in magnetic losses. "or this reason the rotor is made

of armature core, thatBs made %ith several lo%'hysteresis silicon steel laminations, to reduce

the magnetic losses like hysteresis and eddy current loss respectively. The laminations are

stacked together to form a cylindrical structure.

&rmature 'inding or conductors:Armature %inding is an arrangement of conductors to

develop desired emfs by relative motion in a magnetic field. These %indings are first %ound

in the form of flat rectangular coils and are pulled into proper shape in a coil puller. The

conductors are placed in the armature slots %hich are lined %ith a tough insulating material

called Gatheroide paper. 7ere normally t%o layer %inding %ith diamond shaped coils are

used.

ield 'inding:The field %inding of dc motor are made %ith field coils *copper %ire+ %ound

over the slots of the pole shoes in such a manner that %hen field current flo%s through it, then

adEacent poles have opposite polarity are produced. The field %indings basically form an

electromagnet, that produces field flux %ithin %hich the rotor armature of the dc motor

rotates, and results in the effective flux cutting.

ommutator: The commutator is cylindrical structure and is built up of %edge shaped

segments of high conductivity hard dra%n copper. These segments are insulated from each

other by thin layers of mica usually .F to # mm thickness. The commutator is a form of

rotating s%itch placed bet%een the armature and the external circuit. "ollo%ing purposes are

served by the commutator$

t provides electrical connections bet%een rotating armature coils and stationary external

circuit.

t collects current from armature conductors. t rectifies alternating current induced in the

armature conductors into unidirectional current for external load circuit

*ruses: The brushes of dc motor are made %ith carbon or graphite structures, making

sliding contact over the rotating commutator. The function of brush is to collect current from

the armature conductors and supply it to the external load circuit. The brushes are rectangular

in shape and rests on commutator.

*earings: n small motors ball bearings are used at both ends. "or larger motor, roller

bearings are used at driving end and ball bearing at commutator end.

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1.12 Flu &istriution curve in the air ga!

To estimate the correct reluctance of the air gap, the magnetic field distribution in the

space bet%een the pole shoes and the armature is plotted. onsider a smooth armature, the half pole

pitch of it is divided into suitable number of sections. ts flux lines are plotted by method of

curvilinear s-uares. All these lines must leave and enter the surface at right angle.

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The !c armature %indings are al%ays of the closed continuous type of double layer

lap or %ave %inding. "or small machines, the coils are directly %ound in the armature slots using

automatic %inders. n large machines, the coils are performed and then inserted into the armature

slots. 5ach coil consists of a number of turns of %ire, each turn taped and insulated from the other

turns and form the rotor slots. 5ach side of the turn is called the con&uctor. The number of the

conductors on a machineVs armature is given by

"= 2#N

*#.#.#+

%here $

W6 numbers of conductors on rotor

6 numbers of coils on rotor=6 number of turns per coil

Since the voltage generated in conductor under the south pole opposite the voltage

generated in the conductor under the =orth pole, the coil span is e-ual to #P electrical

degrees, one pole pitch. n a ) pole machine #P electrical degrees is e-ual to #P mechanical

degrees, %hereas in a O'pole machine #P electrical degrees is e-ual to mechanical

degrees. n general, the relationship bet%een the electrical angle and mechanical angle is

electrical angle 6 *38)+ mechanical angle

%here 3 is the number of poles.

1.14 7a! an& 6ave

T%o types of %inding mostly employed are kno%n as lap %inding and %ave %inding.

1.14.1 7a! 6in&ing"

n lap %inding, the finishing end of one coil is connected to a commutator segment

and to the starting end of the adEacent coil situated under the same pole and so on, till all the

coils have been connected. This type of %inding derives its name from the fact it doubles or

laps back %ith its succeeding coils.

"or a progressive lap %inding the commutator pitch y 6 #.

A typical coil of = turns for a simplex lap %inding is sho%n in fig #.#O.#


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TRANSFORMERS

"ig #.#O.#.a$ Simplex lap %inding

n the simplex lap %inding the number of parallel path is e-ual to the number of poles and

also to the number of brushes.

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n the %ave %inding, the t%o ends of a coil are connected to a commutator segments

that are approximately J degrees apart. This %ay all the coils carrying current in the same

direction are connected in series. Therefore, there are only t%o parallel paths bet%een the brushes,

a6) independent of the number of poles. This type of %inding is used lo%'current, high voltage

application.

"ig #.#O.).a$ Simplex %ave %inding

"ig #.#O.).b represents an unrolled %ave %inding of a dc armature, along %ith the

commutator segments *bars+ and stationary brushes. oils are laid out in a %ave pattern and cross all

the poles. n %ave %indings, the number of parallel paths, a, is al%ays t%o *)+, and there may be t%o

or more brush positions.

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TRANSFORMERS

"ig #.#O.).b$ unrolled %ave %inding and e-uivalent coil representation

1.15 Equalizer rings

The existence of many parallel paths, in a lap %inding, can lead to the serious

problem of circulating currents. The fluxes from all the poles are not exactly e-ual. 1ecause

of %ear on the bearings, the air gap does not remain uniform around the %hole periphery. Asthe armature conductor rotate, the voltage induced in some conductors may be slightly more

than that in the others. Since all the parallel paths are in parallel, a resultant emf acting

around a closed path may cause circulating current in the %inding. The resistance of %inding

being very small, even a small imbalance in the emfs can give rise to a large circulating

current. 5vidently these circulating currents cause energy loss and heating. Therefore the

points %hich should be the same potential, in different parallel paths, are connected together

by a ring made of copper. 5ach ring is insulated from the other. These rings, kno%n as

e-uali;er rings or bars, help in keeping the circulating currents inside the small sections

shorted together, so that these circulating currents may not flo% through the brushes.

1.1# *ummy coils


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These coils are used %ith %ave %inding and restored to %hen the re-uirement of the

%inding are not met by the standard armature punching available in armature %inding shops, these

dummy coils does not influence the electrical character of the %inding. 1ecause, they are not

connected to the commutator. They are exactly similar to the other coils except that their ends are

short and tapped. The dummy coils inserted into the slots in the same %ay as the others to make the

armature dynamically *an armature having some slots %ithout %indings %ould be out of balance

mechanically+ balanced but it is not a part of the armature %inding.

ee09 404-module 1

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