Chapter 1 1page

8/2/2019 Chapter 1 1page

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Electric MachinesElectric Machines

ELECELEC 312312

Textbookextbook Electric Machinery FundamentalsElectric Machinery FundamentalsStephen Chapman,tephen Chapman, 4thh edition, McGraw Hilldition, McGraw Hill 2005005p ,p , ,

Instructor: Dr Ahmednstructor: Dr Ahmed M.. MassoudassoudAssistant professor, Electrical Department,ssistant professor, Electrical Department,College of Engineering , Qatar Universityollege of Engineering , Qatar UniversityOffice hours:ffice hours:ffice hours:ffice hours: --


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Referenceseferenceseferenceseferences. . en r nc p e o ec r c ac nes an power

Electronics 2nd

edition, JohnWiley Sons, NY, 1997

Mohamed El-Hawary Principle of Electric Machines

w power ec ron cs pp ca ons , u y , ey-IEEE Press

Dr Ahmed MassoudQatar University, College of Engineering2


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Course contentourse contentCourse contentourse contentTransformersDC machines

Synchronous generators



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ELECLEC 23434 Assessment methodsssessment methodsLECLEC 23434 Assessment methodsssessment methodsHome work 5%

Quizzes 10%

Term project 10%

Midterm II 20%

na exam



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Quizzes:Quizzes:

5 quizzes (the best 4 quizzes will be considered)

Midterm exam dates:Midterm exam dates:

Exam II week 12



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Chapterhapter 1:Introduction to Machineryntroduction to MachineryPrinciplesrinciples



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Cha ter contentCha ter content

Basic concept of electrical machines fundamentals

Magnetic Behaviour of Ferromagnetic Materials

How magnetic field can affect its surroundings



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Electric Machines and transformerlectric Machines and transformerAn electricelectric machinemachine is a rotating device that converts mechanical energy

to e ectrica energy generatorgenerator or converts e ectrica energy to

mechanical energy (motor)(motor) depending on the action of magnetic filed.

A transformertransformer is a stationary device that converts electrical energy from

one voltage level to another depending on the action of magnetic filed.

Importance of electric motors and generators:

. ectric power is a c ean an e icient energy source t at is very easy to

transmit over long distances and easy to control.

-.

combustion engine), free from pollutant associated with combustion.



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Basicasic conceptoncept off electricallectrical machinesachinesfundamentalsundamentals1 Rotationalotational Motionotion Newtonsewtons Lawaw andnd Powerower. Rotationalotational Motion,otion, Newton sewton s Lawaw andnd PowerowerRelationshipelationship

Almost all electric machines rotate around an axis, called the shaft of the machines. It

is important to have a basic understanding of rotational motion.

Angular position, : is the angle at which it is oriented, measured from some. .

is similar to the linear concept of distance along a line.

Conventional notation: +ve value for anticlockwise rotation-ve value for clockwise rotation



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Angular Velocity, : Defined as the velocity at which the measured point ismoving. Similar to the concept of standard velocity where:

where:

dtdxv

t time taken to travel the distance r

For a rotating body, angular velocity is formulated as:

d

where: - Angular position

dt

Angular acceleration, : is defined as the rate of change in angularvelocity with respect to time. Its formulation is as shown:

(rad/s2)d

dt



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Torque, ,

change. The greater the force applied to the object, the more rapidly its

velocity changes.

Similarly in the concept of rotation, the greater the torque, the more

.

Torque is known as a rotational force applied to a rotating body giving

angular acceleration.

Tor ue Definition: Nm

Product of force applied to the object and the smallest distance between the line of

action of the force and the objects axis of rotation



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Direction

o ro a on

rsinrsin

Force perpendicular distance

sinF r



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Power, P is defined as rate of doing work. Hence,

(watts)dWPdt

Applying this for rotating bodies,

d

Pdt

ddt



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Newtons Law of Rotation

Newtons law for objects moving in a straight line gives a relationship between the

force applied to the object and the acceleration experience by the object as the resultof force applied to it. In general,

where:

F Force applied

F ma

m mass o o ject

a resultant acceleration of object

Applying these concept for rotating bodies,where:

m

-Torque

moment of inertia

- angular acceleration



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2. Thehe Magneticagnetic FieldieldMagnetic fields are the fundamental mechanism by which energy is convertedfundamental mechanism by which energy is converted fromone form to another in motors, generators and transformers.

rs , we are go ng o oo a e as c pr nc p e currencurren --carry ng w re pro uces acarry ng w re pro uces a

magnetic field in the area around it.magnetic field in the area around it.

Production of a Magnetic Field

Amperes LawAmperes Law the basic law governing the production of a magnetic field by a

where H is the magnetic field intensity produced by the current Inet and dlis a

netIdlH

differential element of length along the path of integration. H is measured in

Ampere-turns per meter.



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Consider a current currying conductor is wrapped around a ferromagnetic core;



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Applying Amperes law, the total amount of magnetic field induced will be

turns around the ferromagnetic material as shown. Since the core is made of

ferromagnetic material, it is assume that a majority of the magnetic field will be

confined to the core.

The ath of inte ration in Am eres law is the mean ath len th of the core l . Thec

current passing within the path of integration Inet is then Ni, since the coil of wires

cuts the path of integration N times while carrying the current i. Hence Amperes

aw ecomes,

Hl Ni

Ni

H c



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In this sense, H (Ampere turns per metre) is known as the effort required to

.

core also depends on the material of the core. Thus,

B = magnetic flux density (webers per square meter, Tesla (T))

H = magnetic field intensity (ampere-turns per meter)

The constant may be further expanded to include relative permeabilitywhich can be defined as below:

r

o

where: o permeability of free space (4107 Vs/(Am) )



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Hence the permeability value is a combination of the relative permeability and

the ermeabilit of free s ace. The value of relative ermeabilit is de endent u on

the type of material used. The higher the permeability, the higher the amount of fluxinduced in the core. Relative permeability is a convenient way to compare the

magnet za ty o mater a s.

Also, because the ermeabilit of iron is so much hi her than that of air, themajority of the flux in an iron core remains inside the core instead of travelling

through the surrounding air, which has lower permeability. The small leakage flux

coils and the self-inductances of coils in transformers and motors.

In a core such as in the figure,

= = Nicl



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Now, to measure the total flux flowing in the ferromagnetic core, consideration has

. ,

BdA

Where: A cross sectional area throughout the core

A

Assuming that the flux density in the ferromagnetic core is constant A, the

e uation is sim lified to be:

BATaking into account past derivation of B,

NiA

cl



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Magneticsagnetics CircuitsircuitsThe flow of magnetic flux induced in the ferromagnetic core can be made analogous

.

The analogy is as follows:

Electric Circuit Analogy Magnetic Circuit Analogy



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Referring to the magnetic circuit analogy, F is denoted as magnetomotivemagnetomotive

f rcef rce mmf which is similar to Electromotive force in an electrical circuit emf .

Therefore, we can safely say that F is the prime mover or force which pushesmagnetic flux around a ferromagnetic core at a value of Ni (refer to amperes law).

ence is measure in ampere turns. ence t e magnetic circuit equiva ent

equation is as shown:

(similar to V=IR)F R

The polarity of the mmf will determine the direction of flux. To easily

,

1.The direction of the curled fingers determines the current flow.

2.The resultin thumb direction will show the ma netic flux flow.



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The element of R in the magnetic circuit analogy is similar in concept to the

.

magnetic flux. ReluctanceReluctance in this analogy obeys the rule of electrical resistance

(Series and Parallel Rules). Reluctance is measured in Ampere-turns per weber.

Series Reluctance,

=eq .

Parallel Reluctance,

1 2 3

1 1 1 1 ...eq

R R R R



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The inverse of electrical resistance is conductance which is a measure of

conductivit of a material. Hence the inverse of reluctance is known as

permeancepermeance, P, P where it represents the degree at which the material permits theflow of magnetic flux.

c

NiA

l

c

ANi

l

c

AF

l

, c

c

AP R

l A



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in a ferromagnetic material, however, this approach has inaccuracy embedded into it

due to assumptions made in creating this approach (within 5% of the real answer).

Possible reason of inaccuracy is due to:

. ,

reality a small fraction of the flux escapes from the core into the surrounding

low-permeability air, and this flux is called leakage fluxleakage flux..

2. The reluctance calculation assumes a certain mean path length and cross

sectional area csa of the core. This is correct if the core is ust one block of

ferromagnetic material with no corners, for practical ferromagnetic cores which

have cornerscorners due to its design, this assumption is not accurate.



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3. In ferromagnetic materials, the permeability varies with the amount of flux

a rea y in t e materia . e materia permea i ity is not constant ence t ere isan existence ofnonnon--linearity of permeability.linearity of permeability.

4. For ferromagnetic core which has air gaps, there are fringing effectsfringing effects that

should be taken into account as shown:



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Examplexample 1.1A ferromagnetic core is shown. Three sides of this core are of uniform width, while

the fourth side is somewhat thinner. The de th of the core into the a e is 10cm

and the other dimensions are shown in the figure. There is a 200 turn coil wrapped

around the left side of the core. Assuming relative permeability r of 2500, howmuc ux w e pro uce y a nput current

Solution:3 sides of the core have the same csa, while the 4th side has a different area.

Thus the core can be divided into 2 regions:(1) the single thinner side



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The magnetic circuit corresponding to this core:



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Examplexample 1.2Figure shows a ferromagnetic core whose mean path length is 40cm. There is a smallgap of 0.05cm in the structure of the otherwise whole core. The csa of the core is

12cm , t e re ative permea i ity o t e core is 4000, an t e coi o wire on t e core

has 400 turns. Assume that fringing in the air gap increases the effective csa of the gap

b 5%. Given this information find1.the total reluctance of the flux path (iron plus air gap)

2.the current required to produce a flux density of 0.5T in the air gap.



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Solution:

The ma netic circuit corres ondin to this core is shown below:



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Examplexample 1.3Figure shows a simplified rotor and stator for a dc motor. The mean path length ofthe stator is 50cm, and its csa is 12cm2. The mean path length of the rotor is 5 cm,

an its csa a so may e assume to e 12cm . Eac air gap etween t e rotor an

the stator is 0.05cm wide, and the csa of each air gap (including fringing) is 14cm2.

The iron of the core has a relative ermeabilit of 2000 and there are 200 turns ofwire on the core. If the current in the wire is adjusted to be 1A, what will the

resulting flux density in the air gaps be?



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Solution:


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To determine the flux density in the air gap, it is necessary to first calculate the mmf

applied to the core and the total reluctance of the flux path. With this information,the total flux in the core can be found. Finally, knowing the csa of the air gaps

enables the flux densit to be calculated.

The magnetic cct corresponding to this machine is shown below.



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Magneticagnetic Behaviourehaviour off Ferromagneticerromagnetic MaterialsaterialsMaterials which are classified as non-magnetic all show a linear relationshipbetween the flux density B and coil current I. In other words, they have constant

permea ty. us, or examp e, n ree space, t e permea ty s constant. ut n

iron and other ferromagnetic materials it is not constant.

For magnetic materials, a much larger value of B is produced in these materials

than in free space. Therefore, the permeability of magnetic materials is much higher

an o. owever, e permea y s no near anymore u oes epen on e

current over a wide range.

Thus, the permeability is the property of a medium that determines its

magnetic characteristics. In other words, the concept of magnetic permeability

through it.



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Energynergy Lossesosses inn a Ferromagneticerromagnetic Coreore

y ry r discussions made before concentrates

on the application of a DC currentthrough the coil.

,

residual flux when moving from thepositive half cycle to the negative cycle of

the ac current flow and vice versa.


Explanation of Hysteresis Loop


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. .

As current increases, the flux traces the path ab. (saturation curve)

W en t e current ecreases, t e ux traces out a i erent pat rom t e one

when the current increases (path bcd).

en t e current ncreases aga n, t traces out pat e .

HYSTERESIS is the dependence on the preceding flux history and the

resu ng a ure o re race ux pa s.

When a large mmf is first applied to the core and then removed, the flux

.

When mmf is removed, the flux does not go to zero residual flux. This is

.

To force the flux to zero, an amount of mmf known as coercive mmfmust

be a lied in the o osite direction.


Wh d h t i ?


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Why does hysteresis occur?

To understand hysteresis in a ferromagnetic core, we have to look into the

behaviour of its atomic structure before, during, and after the presence of a magnetic

.

The atoms of iron and similar metals (cobalt, nickel, and some of their alloys) tend

to have their magnetic fields closely aligned with each other. Within the metal, there

presence of a small magnetic field which randomly aligned through the metalstructure.

This as shown below:



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Eddyddy Currenturrent LossossA time-changing flux induces voltage within a ferromagnetic core.

ese vo tages cause sw r s o current to ow w t n t e core e y currents.

Ener is dissi ated in the form of heat because these edd currents are flowin ina resistive material (iron)

e amoun o energy os o e y curren s s propor ona o e s ze o e

paths they follow within the core.

To reduce energy loss, ferromagnetic core should be broken up into small strips, or

laminations, and build the core up out of these strips. An insulating oxide or resin is

,small areas.



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FARADAYSARADAYS LAWAW Inducednduced Voltageoltage fromrom a Timeime-


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Ch gi gh gi g M g tig ti Fi ldi ldhanginghanging Magneticagnetic FieldieldFaradays Law:

If a flux passes through a turn of a coil of wire, voltage will be induced in the turn of the

wire that is directly proportional to the rate of change in the flux with respect of time

dt

deind

If there is N number of turns in the coil with the same amount of flux flowingthrou h it hence:

dt

dNeind


where: N number of turns of wire in coil.

N h i i h i b hi h i i d L L


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Note the ne ative si n at the e uation above which is in accordance to Lenz Law

which states:The direction of the build-up voltage in the coil is as such that if the coils were short circuited,

it wou pro uce current t at wou cause a ux opposing t e origina ux c ange.

Examine the figure below


If the flux shown is increasin in stren th then the volta e built u in the coil will


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If the flux shown is increasin in stren th, then the volta e built u in the coil will

tend to establish a flux that will oppose the increase.

curren ow ng as s own n e gure wou pro uce a ux oppos ng e

increase.

So, the voltage on the coil must be built up with the polarity required to drive the

current through the external circuit. So, -eind



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Productionroduction off Inducednduced Forceorce onn a Wireire


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A current carrying conductor present in a uniform magnetic field of flux density B,would produce a force to the conductor/wire. Dependent upon the direction of the

surrounding magnetic field, the force induced is given by:

F i l B where:i represents the current flow in the conductor

,

current flowB magnetic field density

The direction of the force is given by the leftleft--handhand rulerule. Direction of the force

magnetic field. A rule of thumb to determine the direction can be found using the

right-hand rule as shown below:



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Current

Force

Left hand rule


Inducednduced Voltageoltage onn a Conductoronductor Movingoving inn a Magneticagnetic


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Fi ldi ldIf a conductor moves or cuts through a magnetic field, voltage will be induced

Fieldieldbetween the terminals of the conductor at which the magnitude of the induced

voltage is dependent upon the velocity of the wire assuming that the magnetic field

.eind= (v x B) l

where:

v velocity of the wire

B magnetic field density

The induction of voltages in a wire moving in a magnetic field is fundamental to the

operation of all types ofgenerators.



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Voltage

Flux

Right hand rule


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