EEC 233 Theory

1

UNESCO-NIGERIA TECHNICAL &

VOCATIONAL EDUCATION

REVITALISATION PROJECT-PHASE II

Ia IbIc

A BC

N

YEAR II- SEMESTER III

THEORY

Version 1: December 2008

NATIONAL DIPLOMA IN

ELECTRICAL ENGINEERING TECHNOLOGY

ELECTRICAL MACHIENS I I

COURSE CODE: EEC233

Table of Contents

Chapter 1: Basic Principles of electric machines: ............................... 1keeW

1.1 Introduction .........................................................................................1

1.2 Electro- mechanical energy convertion ........................................... 2

1.3 Alignment devices .................................................................................. 6

1.4 Interaction devices ................................................................................ 7

1.5 Induction devices ................................................................................... 7

1.6 Work Examples ....................................................................................... 8

1.7Electromagnets ...................................................................................... 11

1.8 Faraday's Law ........................................................................................ 12

1.9Lenz's Law ............................................................................................... 13

1.10 Rotating magnetic field ............................................................ Week2

1.11 Synchronous speed: .......................................................................... 14

Chapter 2 Three phase induction motor ....................................... Week3

2.1 Introduction ........................................................................................... 17

2.2 Construction of Induction Motor ...................................................... 18

2.2 The principle of operation of the Induction Motor ............. Week4

2.3 The slip ................................................................................................... 20

2.4 Name Plate ............................................................................................. 22

Chapter 3: Synchronous Machine: ....................................................... 5keeW

3.1 Introduction ........................................................................................... 18

3.2 Stator construction .............................................................................. 18

3.3 Rotor construction ............................................................................... 18

3.4 Principle of operation of the synchronous generator ................ 20

3.5 Principle of operation of the synchronous motor: ...................... 20

3.6 Excitation Methods .............................................................................. 21

Chapter4:Control & protection of electric motors ............................. 6keeW

4.1 Need for Circuit Protection ............................................................... 22

4.2 Types of Overcurrent Protective Devices ............................. Week7

4.2.0 Protection and control devices............................................ Week8

4.2.1 Fuses .................................................................................................... 25

4.2.2 Circuit Breakers ................................................................................ 27

4.3 Control devices ............................................................................. Week9

4.3.1 Relay ................................................................................. 30

4.3.2 Contactors ....................................................................... 31

4.3.3Pushbuttons ............................................................Week10

4.3.4 Selector Switches ........................................................... 35

4.3.5 Indicator Lights .............................................................. 35

Chapter 5: Energy convertion ............................................................. 11keeW

5.1 Electro-mechanical energy convertion .......................................... 37

5.1.1Major energy convertion principle ........................................ 38

5.2 Energy convertion ................................................................................ 39

5.3 Linked energy system ............................................................................ 40

5.4 Energy storage ...................................................................................... 41

5.5 Energy ballance ......................................................................... Week12

5..5.1 Block diagram of energy balance equation ......................... 43

5.6 Magnetic field energy and force ........................................... Week13

5.6.1 Magnetic field .............................................................................. 45

5.6.2 Magnetic circuit ......................................................................... 46

5.7 Magnetic field energy ............................................................................ 47

5.8 Maxwell stress .................................................................................. 48

5.9 Energy density ........................................................................... Week14

5.10 Faraday's Lenz Law ............................................................................. 49

5.11 Energy Convertion ............................................................................. 50

5.11.1 Constant current ..................................................................... 51

5.11.2 Constant flux ........................................................................... 52

5.11.3 General Condition .................................................................. 53

5.11.4 Diffirencial foam ..................................................................... 54

5.12 Alignment force and torque; single excitation .................... Week15

5.11 Work examples ................................................................................... 56

5.11.3 General Condition

1. Basic Principles of Electric Machines Week 1

1

1.1 Introduction

It may be necessary to define what we mean by the term electrical machines. A machine is a

device that does useful work in a predictable way according to some physical laws. It acts as

a transducer, or convertors, accepting an input of energy in one physical from and

transforming it, more or less effectively, into another.

An electromagnetic machine, in the essential conversion process, uses energy in an

intermediate magnetic form. As a motor the machine takes in electrical energy and converts

it into mechanical work, such as driving a machine tool or a lift, or operating a loudspeaker.

An electro-magnetic machine is usually reversible and cab, as a generator, producer

electrical energy form some other kind, such as the mechanical energy of prime- movers or

the a caustic energy of microphones and gramophone pickups.

Electrical energy is versatile and controllable. Its special lie in that can be transfer

continuously and economically from to place (Transmission), made widely available as a

services (distribution), used in conveying intelligence (Telecommunication and data

processing), and applied to indicate an supervise production systems (control,

instrumentation and computation). It is readily converted into sound, light, heat and useful

forms of energy. In particular it is easily converted to or from mechanical energy in the

electromagnetic machines


2

1.2 Electro-mechanical energy conversion

1.2.1 Principal of electrical machines

The operation of electromagnetic mechanical devices can be explained in terms of basic

principals concerned with

i The development of magneto-mechanical forces and

ii. The induction of emf (electromotive force) by the rate of change of the linkage.

Thus, electromagnetic energy conversion is based on three bask principles namely (i)

induction (ii) interaction and (iii) alignment

1. Principle of induction

It is known that when electrons are in motion, they produce a magnetic field. Conversely,

when, a magnetic field embracing a conductor moves relative to the conductor, it produce a

flow of electrons in the conductor.

The phenomenon whereby on e.m.f and hence current (i.e flow of electrons) is induced in

any conductor which is cut across or is cut by a magnetic flux is known as electromagnetic

induction

The induced emf E is given by

(a) E = NdØ OR (B) e = Bluw ……..volts

dt

Where N = number of turns of the coil

Ø = flux in webers linking the coil

T = time in seconds


3

This is the equation for the induced emf when the magnetic flux moves relatively to the

conductor.

In equation 1.1(b), B = flux density in wb/m2

L = effective length of conductor in metre , U = velocity of the conductor in m/s

And this is the equation for the induced emf when the conductor moves relatively to the flux.

The induction principle is employed in devices such as induction motors generators,

transformers, controlling instrument etc.

1.2.2 Sketchmatic explanation of the induction principle

Fig:1.1a. Voltage & Current induced in the secondary Fig: 1.1b Conductor stationary, while the

circuit due to flux linkage with the primary winding. field moves (current will be induced on the

galvanometer)

Fig: 1.1c Conductor moves, while the field stationary (current will be induced on the

galvanometer)


4

Fig. 1.1 (a) shows an irobn- cored solenoid with a permanent magnetic place adjascent ot it. If the

magnet‟s position is changed from position CD to position AB, the flux linking with the

coils of the solenoid will change, leading to an induced emf in the coil which can be

detected by the sensitive galvanometer G. in this arrangement, the conductor (coil) i

stationary whilst the filed (magnet) moves as in alternators i.e a.c generators.

Fig 1.1 (b) shows a filed arrangement that is stationary while the conduct a-b is free to move about

the vertical axis. An emf, detectable by galvanometer G, will be induced in the conductor as

it cuts through the flux through the flux. This principle is employed in the construction of

d.c. generator,.

F ig 1.1(c) when a coil (Ni) is made to carry an alternative current (ii) it produces an alternative flux

(g). if a second coil (N2) is now placed in a region whereby the alternative flux produced by

the first coil links with the second coil, an emf ( usually of the some frequency) will be

induced in the second coil. This is the principle of the transformer and the induction motors

2. Principle of interaction

An electric current flowing in a direction making an angle (preferably a right-angle) with a

magnetic filed produced by another current ( or a magnet) experience a force fe, the relative

direction being shown in Fig 1.2.

Fig: 1.2 Principle of interaction.


5

The force, fe, arises from the interaction of the flux (created by the current l‟ flowing in the

conductor with the flux produced by a second current or magnet. Since lines of flux do not

cross, the two fluxes will realign. Resulting in a stronger fie ld one side. The conductor and

weaker filed on t6he other side. The conductor then tends to move from the region of

stronger field to the region of weaker filed. Employed in electric motors.

3. Principle of alignment

A pieces of ferromagnetic materials in a magnetic field experience of force urging it towards

a region where the field is stronger, or tending to align it so as to shorten the magnetic flux

path as shown in fig: 1.3

Fig: 1.3a Moving coil meter Fig: 1.3b The force „fe‟ on shaped high

permeability pieces in a field

Fig: 1.3c Polar attraction & repulsion on separately magnetized bodies


6

(a) Lifting magnet (f) Actuator

(b) Relay (g) Electromagnetic pump

( c) Telephone (h) Loudspeaker

(d) Moving-iron indicator (i) Moving –coil indicator

(e) Reluctance motor (k) Industrial rotating machine

1.3 Alignment devices

(a) The lifting magnet: Attract ferromagnetic loads such as beams, plates, and scrap-

iron.

(b) The relay: the coil current causes the armature to be attracted towards the cover

against a spring load: Millions of such relays do useful work in automatic telephone

exchanges, traffic light installation and simple control systems,.

(c) The telephone receivers: has a ferromagnetic diaphragm attracted by a permanent

magnet, the field is caused to fluctuated by the speech currents in the coil, so varying

the deflection of the claptrap and producing sound waves in the air.

(d) The moving- iron indicator, uses the force between the fixed and moving irons to

deflect a pointed against a spring.

(e) The Reluctance motor- the forces urge a displaced rotor in alignment with the

magnetized stator.

(f) The actuator-the current-carrying coil “suck” a displaced ferromagnetic plunger into

a position of symmetry: this is a useful and forceful device.


7

1.4 Interaction devices

(g) Electromagnetic pump: current passed through a conducting liquid in an enclosed

channel forces the liquid to move by interaction with a magnetic cross field; liquid

sodium-potassium or lithium can be pumped in thy way for the extraction of heat

from a nuclear reactor.

(h) Loudspeaker: alternating current in the coil flow in the radial magnet filed of the port

magnet,. And the consequent movement of the attached diaphragm sets up sound

waves. This is the same essential arrangement as a “generator‟ of mechanical

vibrations

(i) Moving –coil indicator-current (normally direct) in the coil of the indirect develops a

force in the radial permanent- magnet filed to move pointed against a control spring.

(k) Industrial rotating machines: Current caused to flow in conductors the surface of a

rotor, mounted within a magnetic stator develop interaction forces tending to turn the

rotor.

1.5 Induced voltage devices

Recalling that a conductor moving or cutting magnetic lines of flux or that the flux

moves relative to the conductor will proan induced voltage, the following devices

employ the induced voltage arrangement.

(i) The transformer- an alternating current flowing in the primary coil (winding) set up

an alternating flux that links with the secondary coil inducing a voltage in the latter.

(m) The generatopr-usually constructed like (k) but with the rotor mechanical energy (via

the prime –mover) will have emf induced in the stator coils. ( the stator is slotted to

house conductors)


8

(n) The induction motor- the stator usually carried one or htree –phawindings whilst the

rotor may have a similar arrangement of coil as the stator or just carry or alirmium

bars. Electrical energy supplied to the stator windings produced a rotating magnetic

field with cuts the rotor conductors and hence induced voltages in them. A complete

rotor circult will have current flowing in the rotor conductors (caused by the induced

voltage) and by interaction forces produced motion of the rotor.

1.6 Work Examples

Examples 1

A conductor carries a current of 800 A at right- angle to magnetic field having a density of

0.5wb/m2 calculated the force on a metre length of the conductor.

Solution

The force F is given by F = Bli

= 0.5 X 1 X 800

= 400N

Example 2

A four –pole generator has a magnetic flux of 12 mnb /pole calculated the average value of

the emf generated in one of the armature conductors while it is moving through the

magnetic flux of one pole, if armature is driven at 900 r.p.m

Solution

When a conductor moves through the magnetic field of one pole, it cuts a magnetic flux of

12 x 10-3

wb.

Time taken for a conductor to move through one revolution

= 60 = 1 second


9

900 15

Since the machine has 4 poles, time taken for a conductor to move through the field of one

pole = ¼ x 1/15 = 1/60s

:. Average emf generated in one conductor rate of change of flux

= Ø = 12 x 10-3

1/60

t

= 0.012 – 0.01667 = 0.72v

= 0.72v

Example 4

A magnetic flux of 400 uwb passing through a coil of 1200 turns is reversed in 0.1s calculate

the average emf induced in the coil.

Solution

The magnetic flux has to decrease form 400 uwb to zero and then increase to 400wwb in the

reverse direction, hence the increase of flux is 400 (-400-400) uwb = -800 x 10-6

wb.

:. Average emf induced in coil

= (change in flux x No of turns) = NdØ

Time taken. Dt


10

1.7 Electromagnets

Anything with an electrical current running through it has a magnetic field. Figure1 shows different

sources of magnetic field.

Figure1.4: Different sources of magnetic field

The most common forms of electromagnets are the Solenoids .When the wire is shaped into a coil

as shown in Figure1.1, all the individual flux lines produced by each section of wire join together to

form one large magnetic field around the total coil.

As with the permanent magnet, these flux lines leave the north of the coil and re-enter the coil at its

south pole. The magnetic field of a wire coil is much greater and more localized than the magnetic

field around the plain conductor before being formed into a coil. This magnetic field around the coil

can be strengthened even more by placing a core of iron or similar metal in the center of the core.

The metal core presents less resistance to the lines of flux than the air, thereby causing the field

strength to increase. (This is exactly how a stator coil is made; a coil of wire with a steel core.) The

advantage of a magnetic field which is produced by a current carrying coil of wire is that when the

current is reversed in direction the poles of the magnetic-as shown in Figure1.2- field will switch

positions since the lines of flux have changed direction. Without this magnetic phenomenon

existing, the AC motor as we know it today would not exist.


11

Battery

Iron Core

S

NMagnetic field Lines

N

SThe Current

Figure1.5: Reversing the polarity of the solenoid by reversing the current direction

1.8 Faraday's Law

Faradays law states whenever the magnetic flux linked with a circuit changes, an e.m.f. is always

induced in it, or Whenever a conductor cuts magnetic flux, an e.m.f. is induced in that conductor.

The phenomenon of inducing a current by changing the magnetic field in a coil of wire is known as

electromagnetic induction.

Figure1.3 shows an electromagnet which is connected to an AC power source. Another

electromagnet is placed above it. The second electromagnet is in a separate circuit. There is no

physical connection between the two circuits. Voltage and current are zero in both circuits at Time1.

At Time2 voltage and current are increasing in the bottom circuit


12

00 0

Time1 Time2 Time3

Figure 1.6: Experment showing the electromagnetic induction phenomena

A magnetic field builds up in the bottom electromagnet. Lines of flux from the magnetic field

building up in the bottom electromagnet cut across the top electromagnet. A voltage is induced in

the top electromagnet and current flows through it. At Time 3 current flow has reached its peak.

Maximum current is flowing in both circuits. The magnetic field around the coil continues to build

up and collapse as the alternating current continues to increase and decrease. As the magnetic field

moves through space, moving out from the coil as it builds up and back towards the coil as it

collapses, lines of flux cut across the top coil. As current flows in the top electromagnet it creates its

own magnetic field.

1.9 Lenz's Law

Lenz's law enables us to determine the direction of the induced current: "The direction of the

induced current is such as to oppose the change causing it." The Figure 1.4a shows the north pole of

a bar magnet approaching a solenoid. According to Lenz's law, the current which is thereby

generated in the coil must cause an effect which opposes the approaching magnetic field.


13

Iron Core

N

Ammeter

N

NSN

a

b

Figure1.7: Experiment demonstrating Lenz's law

This is achieved if the direction of the induced current creates a north pole at the end of the

solenoid closest to the approaching magnet, as the induced north pole tends to repel the approaching

north pole. The Figure1.4b shows the north pole of a bar magnet withdrawing from a solenoid.

According to Lenz's law, the current which is thereby generated in the coil must cause an effect

which opposes the departing magnetic field. This is achieved if the direction of the induced current

creates a south pole at the end of the solenoid closest to the departing magnet, as the induced south

pole tends to attract the departing north pole

Basic Principles of Electric Machines Week Two

5

1. 1.4 Rotating magnetic field

The three-phase induction motor also operates on the principle of a rotating magnetic

field. The following discussion shows how the stator windings can be connected to a three-

phase ac input and have a resultant magnetic field that rotates.

Figure 1.5 shows how the three phases are tied together in a Y-connected stator. The dot in

each diagram indicates the common point of the Y-connection. You can see that the

individual phase windings are equally spaced around the stator. This places the windings

120° apart.

Ia IbIc

A BC

N

Figure 1.5:- Three-phase, Y-connected stator.

Using the left-hand rule the electromagnetic polarity of the poles can be determined at any

given instant.


6

1. The results of this analysis are shown for voltage points 1 through 7 in figure 2. At point 1,

the magnetic field in coils A is maximum with polarities as shown. At the same time,

negative voltages are being felt in the B and C windings. These create weaker magnetic

fields, which tend to aid the A field. At point 2, maximum negative voltage is being felt in

the C windings. This creates a strong magnetic field which, in turn, is aided by the weaker

fields in A and B. As each point on the voltage graph is analyzed, it can be seen that the

resultant magnetic field is rotating in a clockwise direction. When the three-phase voltage

completes one full cycle (point 7), the magnetic field has rotated through360°.


5

1. 10

5

-10

-5

1 2 3 4 5 6 7

Point6

Point7

Point1 Point2 Point3

Point4

Point5

Point 5


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1.5 Synchronous speed:

The speed of the rotating magnetic field is referred to as synchronous speed (Ns). Synchronous

speed is equal to 120 times the frequency (f), divided by the number of poles (P).

p

fNs

120

If the frequency of the applied power supply for the two-pole stator used in the previous example is

50 Hz, synchronous speed is 3000 RPM.

RPMNs 30002

50120

The synchronous speed decreases as the number of poles increase. The following table shows the

synchronous speed at 50 Hz for the corresponding number of poles.

No of poles Synchronous speed

2 3000rpm

4 1500rpm

6 1000rpm

8 750rpm

Table 1.1: Different speeds for different number of poles

Point5

2. Three phase induction motor Week 3

1

2.1 Introduction

Three-phase AC induction motors are widely used in industrial and commercial applications. They

are classified either as squirrel cage or wound-rotor motors.

These motors are self-starting and use no capacitor, start winding, centrifugal switch or other

starting device.

They produce medium to high degrees of starting torque. The power capabilities and efficiency in

these motors range from medium to high compared to their single-phase counterparts.

Popular applications include grinders, lathes, drill presses, pumps, compressors, conveyors, also

printing equipment, farm equipment, electronic cooling and other mechanical duty applications.

Simple and rugged construction

Low cost and minimum maintenance

High reliability and sufficiently high efficiency since there is no losses in brush contacts

or mechanical friction

Needs no extra starting motor and need not be synchronized

Need only one source of power

2.2 Construction of Induction Motor:

An Induction motor has basically two parts, Stator and Rotor. Also some of other parts were

acknowledged in the following section


2

2.2.1 Stator construction:

Figure2.1: Diagram construction of the stator

The stator is made up of several thin laminations of aluminum or cast iron. They are punched and

clamped together to form a hollow cylinder (stator core) with slots as shown in Figure 2.1. Coils of

insulated wires are inserted into these slots.

The iron core on the figure has paper liner insulation placed in some of the slots.

Each grouping of coils, together with the core it surrounds, forms an electromagnet (a pair of poles)

on the application of AC supply. The number of poles of an AC induction motor depends on the

internal connection of the stator windings. The stator windings are connected directly to the power

source. Internally they are connected in such a way, that on applying AC supply, a rotating magnetic

field is created

2.2.2 Rotor construction:

There are two main types


3

Squirrel cage type

Wound rotor

2.2.2.1 Squirrel cage rotor:

This rotor has a laminated iron core with slots(Figure2.2), and is mounted on a shaft. Aluminum

bars are molded in the slots and the bars are short circuited with two end rings. The bars are skewed

on a small rotor to reduce audible noise. Fins are placed on the ring that shorts the bars. These fins

also work as a fan and improve cooling.

Most motors use the squirrel-cage rotor because There are no commutators, slip rings or brushes.

Hence this is a most rugged and maintenance-free construction.

Rotor bars ) slightly skewed(

End ring

Figure2.2:Squriell cage rotor

2.2.2.2 Wound rotor:


4

Wound Rotor

Brush

Slip RingsExternal Rotor

Resistances

Figure 2.3: Schemtic diagram showing Induction motor, wound rotor type

The wound rotor or slip-ring induction motor differs from the squirrel-cage motor only in the rotor

winding. The rotor winding consists of insulated coils, grouped to form definite polar areas of

magnetic force having the same number of poles as the stator. The ends of these coils are brought

out to slip-rings. By means of brushes, a variable resistance is placed across the rotor winding

(Fig.2.3). By varying this resistance, the speed and torque of the motor is varied. The wound rotor

motor is an excellent motor for use on applications that require an adjustable-varying speed (an

adjustable speed that varies with load) and high starting torque.

Shaft

CoilsFan

Slip ringsBearings

Laminated core

Terminals

Figure 2.4:Wound rotor

2.2.3 Enclosure

Enclosure or the frame (Figure2.5) ,its main

application to hold the parts together. also it Helps

with heat dissipation. In some cases, protects internal


5

components from the environment. A cooling fan is attached to the shaft at the left-hand side. This

fan blows air over the ribbed stator frame

2.2.3 Bearings:

There are two main types, the sleeve bearings and ball bearings .Ball (Roller) Bearings

(Figure2.6a) Support shaft in any position. Its Grease lubricated and required no maintenance

The Sleeve Bearings(figure2.6b) are Standard on most motors. They are only used with horizontal

shafts and its oil lubricated.

2.2.5 Conduit Box

Point of connection of electrical power to the motor’s stator windings.

2.2.6 Eye Bolt

Used to lift heavy motors with a hoist or crane to prevent motor damage, as it can be seen in the

following figure.

Figure2.5:Induction Motor enclosure

Figure2.6: a)Ball Bearings

b)Sleeve bearings

(a) (b)

b


6

Figure2.7: Sectional view of Induction Motor


1

2.2 The principle of operation of the Induction Motor:

The three-phase current with which the motor is supplied establishes a rotating magnetic

field in the stator. This rotating magnetic field cuts the conductors in the rotor inducing

voltages and causing currents to flow. These currents set up an opposite polarity field in the

rotor(Lenz's law). The attraction between these opposite stator and rotor fields produces the

torque which causes the rotor to rotate. This simply is how the squirrel-cage motor works

2.3 The Slip:

There must be a relative difference in speed between the rotor and the rotating magnetic

field. If the rotor and the rotating magnetic field were turning at the same speed no relative

motion would exist between the two, therefore no lines of flux would be cut, and no voltage

would be induced in the rotor. The difference in speed is called slip. Slip is necessary to

produce torque. Slip is dependent on load. An increase in load will cause the rotor to slow

down or increase slip. A decrease in load will cause the rotor to speed up or decrease slip.

Slip is expressed as a percentage and can be determined with the following formula.

Ns

NrNsSlip

100)((%)

Figure2.8:The magnetic field created in the stator and the rooted in the squirrel cage induction motor


2

Where Nr is the actual speed of the rotor

For Example, a four-pole motor operated at 60Hz has a synchronous speed (Ns) of

1800 RPM. If the rotor speed at full load is 1765 RPM (Nr), then the slip will be

calculated

%9.11800

100)17651800((%)

Slip

2.4 Name Plate:

It is essential that all motors have nameplates with certain information useful in the

identification of the type of motor, The following Table explain the indication of each code

used on the shown nameplate

Name Of Manufacturer

ORD. No.

TYPE

H.P.

AMPS

R.P.M

DUTY

CLASS INSUL.

FRAME

SERVICE

FACTOR

VOLTS

HERTZ

DATE

NEMANOM. EFF.

IN123456789

HIGH EFFICIENCY

42

40

1790

CONT

F B

286T

1.10

415

60

01/15/2003

95

3PH

Y

4POLE

NEMADesign

Address Of Manufacturer

Term Description

Volts Rated Supply voltage

HP Rated motor output

Amps Rated full load current

RPM Rated full load speed of the motor

Figure2.9:Typical Nameplate of an AC induction motor


3

Hertz Rated supply frequency

Frame External dimensions based on NEMA Regulations

Duty Motor load condition ,either its continuities load, short time,etc

Date Date of manufacturing

Class Insulation Specifies the max. limit temperature of the winding

NEMA Design Types of NEMA design, A,B,C etc

Service factor Factor by which the motor can be overloaded beyond the full load.

NEMA Nom

Efficiency

Motor efficiency at rated load

PH Number of phases

Pole Number of poles

Motor safety standard

Y The connection either star or delta

Table 2.1:Explanation of the codes used on AC motor nameplates

3. Synchronous machine Week 5

1

3.1 Introduction:

Synchronous motors are motors that always run at the same speed regardless of load.

Synchronous motors are somewhat more complex than squirrel-cage and wound rotor motors and,

hence, are more expensive. There is no slip in a synchronous motor, that is, the rotor always moves

at exactly the same speed as the rotating stator field.. The machine consists of three main parts:

Stator, which carries the three phase winding,

Rotor, with one DC winding or permanent magnets

Slip rings or excitation machine (exciter) (in case of electrical excitation).

Synchronous motors are used whenever exact speed must be maintained or for power factor

correction. Synchronous motors are more expensive than other types for the lower horsepower

ratings, but may possibly be more economical for 100 hp and larger ratings.

3.2 Stator construction:

The stator of a synchronous generator holds a three-phase winding where the individual phase

windings are distributed 120° apart in space and is sometimes called the armature winding. The

stator must be made of laminated iron sheets in order to reduce eddy currents.

3.3 Rotor construction:

The rotor holds a field winding,which is magnetized

by a DC current( the field current). The rotating

field winding can be energized through a set of slip

rings and brushes (external excitation), or from a

diode-bridge mounted on the rotor (self-excited). The

rectifier-bridge is fed from a shaft-mounted

alternator, which is itself excited by the pilot exciter.

In externally fed fields, the source can be a shaft-

driven dc generator, a separately excited dc generator, or a solid-state rectifier. Several variations to

these arrangements exist. There are two types of rotors:

Salient-pole rotor (Fig.2) for low-speed machines (e.g.hydro-generators)

Cylindrical rotor (Fig.3) for high-speed machines (e.g. turbo-generators).

Laminated iron

core with slots

Insulated copper

bars are placed in

the slots to form

the three-phase

winding

Metal frame


2

DC current terminals

Shaft

Steel

retaining

ring

DC current

terminals

Wedges

Shaft

3-Phase Stator Winding

Rotor Field

Winding

Brushes

Slip Rings

Cylindrical

Pole Rotor Field current

+-

a- Schematic diagram showing a cylindrical rotor of a synchronous machine

b- cylindrical rotor of a synchronous machine

Figure3.1: cylindrical rotor of a synchronous machine


3

3-Phase Stator Winding

Rotor Field

Winding

Brushes

Slip Rings

Salient Pole

Rotor Field current

+-

a- Schematic diagram showing a salient-pole rotor of a synchronous machine

b- salient-pole rotor of a synchronous machine

Figure3.2: Salient-Pole rotor of a synchronous machine

3.4 Principle of operation of the synchronous generator:

When the 3phase rotor is rotated (by an external prime-mover) the rotating magnetic

flux(induced by DC current) induces voltages in the stator windings. These voltages are sinusoidal

with a magnitude that depends on the field current, and also differ by 120° in time and have a

frequency determined by the angular velocity of the rotation.

3.5 Principle of operation of the synchronous motor:

The stator is supplied with three phase supply in order to develop a rotating magnetic field. Also

the rotor is supplied with DC supply to produce constant

magnetic field. As a result of the interaction of these two fields, the rotor will start to move.

However, the synchronous motor is not self started. Consequently, it usually equipped with squirrel

cage windings that mounted on the pole faces of the synchronous motor rotor. These rotor windings

Pole

DC excitation

windingFan

Slip

rings


4

are frequently referred to as damper or amortisseur windings. Thus, the synchronous motor starts as

an induction motor. When the motor accelerates to near synchronizing speed (about 95%

synchronous speed), DC current is introduced into the rotor field windings. This current creates

constant polarity poles in the rotor, causing the motor to operate at synchronous speed as the rotor

poles "lock" onto the rotating AC stator poles.

3.6 Excitation Methods

Two methods are commonly utilized for the application of the direct current (DC) field current to

the rotor of a synchronous motor.

Brush-type systems apply the output of a separate DC generator (exciter) to the slip rings of the

rotor.

Brushless excitation systems utilize an integral exciter and rotating rectifier assembly that

eliminates the need for need for brushes and slip rings.

3.7 Method of Synchronization

There are three basic method of synchronizing two or more machine:

. Bright lamp method

. Dark lamp method

. automatic method

3. Protection & control of electric motors Week 6

1

4.1 Need for Circuit Protection

Current flow in a conductor always generates heat(Figure1). The greater the current flow, the

hotter the conductor. Excess heat is damaging to electrical components. For that reason, conductors

have a rated continuous current carrying capacity or ampacity. Overcurrent protection devices, such

as circuit breakers, are used to protect conductors from excessive current flow. These protective

devices are designed to keep the flow of current in a circuit at a safe level to prevent the circuit

conductors from overheating.

Excessive current Flow

Normal Current Flow

Figure4. 1:The effect of current flowing in conductors

overcurrent is defined as any current in excess of the rated current of equipment of a conductor. It

may result from overload, short circuit, or ground fault

Overloads: An overload occurs when too many devices are operated on a single circuit, or a piece of

electrical equipment is made to work harder than it is designed for. For example, a motor rated for

10 amps may draw 20, 30, or more amps in an overload condition.


2

Good Insulation

Damaged Insulation

Figure4. 2: Insulation of electric conductors

Conductor Insulation Motors, of course, are not the only devices that require circuit protection for

an overload condition. Every circuit requires some form of protection against overcurrent. Heat is

one of the major causes of insulation failure of any electrical component. High levels of heat can

cause the insulation to breakdown and deteriorated, exposing conductors (Figure4.2).

Short Circuits When two bare conductors touch, a short circuit occurs (Figure4.3).

When a short circuit occurs, resistance drops to almost zero. Short circuit current can be thousands

of times higher than normal operating current.

The heat generated by this current will cause extensive damage to connected equipment and

conductors. This dangerous current must be interrupted immediately when a short circuit occurs.


3

Insulation

conductorShort Circuit

Figure4. 3: Short circuit fault between two condu

4.Protection & control of electric motors Week 7

1

4.2 Types of Overcurrent Protective Devices

Circuit protection would be unnecessary if overloads and short circuits could be eliminated.

Unfortunately, overloads and short circuits do occur. To protect a circuit against these currents, a

protective device must determine when a fault condition develops and automatically disconnect the

electrical equipment from the voltage source. An overcurrent protection device must be able to

recognize the difference between overcurrents and short circuits and respond in the proper way.

Slight overcurrents can be allowed to continue for some period of time, but as the current magnitude

increases, the protection device must open faster. Short circuits must be interrupted instantly.

Several devices are available to accomplish this.

4.2.1 Fuses

A fuse is a one-shot device (Figure1). The heat produced by overcurrent causes the current

carrying element to melt open, disconnecting the load from the source voltage. There are three types

of fuses, namely

Semi-enclosed (Rewireable) fuse

Cartridge fuses

High Breaking Capacity(HBC)

Fuse Cap

Glass or Ceramic

Body

Open

Element

Good Element

Figure 4.4: Plug fuse

4.2.1.1 Cartridge

The cartridge type have fuses which look similar to those you would

find in a standard household plug. This type is improvement of the

rewirable fuse type. It is main advantages, is easy to replace, totally


2

enclosed and its current rating is very accurate

4.2.1.2 HBC

HBC stands for "high blow current (sometimes described as HRC = high rupture current). HBC

fuses are designed not to explode when failing under currents

many times their normal working current (e.g. 1500 amps in a 10

amp circuit). They are therefore to be preferred for the

protection of main voltage circuits where the power source may

be capable of providing very high currents. HBC types can

usually be recognized by being sand filled though they may have

a thick ceramic body.

4.2.1.3 Semi-enclosed(Rewireable) fuses

As the name indicates, the rewireable type have a fuse wire held at both

ends by a small retaining screw. Once the fuse is blown, the fuse wire is

the only pieces to be replaced. It is cheap, but replacing a wrong size of

element can cause catastrophic consequences.

Figure 4.5: A cartridge fuse and its holder

Figure 4.5: A HBC fuse

Figure 4.6: Rewireable fuses


27

Figure 4.7:Miniature circuit breakers with different poles

The problem with fuses is they only work once. Every time you blow a fuse, you

have to replace it with a new one. A circuit breaker(Figure 4.7) does the same thing

as a fuse .It opens a circuit as soon as current climbs to unsafe levels ,but you can

use it over and over again.

The basic circuit breaker consists of a simple switch,(see figure 4.8) connected to

either a bimetallic strip or an electromagnet. The diagram below shows a typical

electromagnet design.

Figure4.8: Cut view of a miniature circuit breaker


28

circuit breakers generally employ a bimetal strip to sense overload

conditions(Figure4.9b). When sufficient overcurrent flows through the circuit

breaker’s current path, heat build up causes the bimetal strip to bend. After bending

a predetermined distance the bimetal strip makes contact with the tripper bar

activating the trip mechanism.

A bimetal strip is made of two dissimilar metals bonded together(Figure4.8). The

two metals have different thermal expansion characteristics, so the bimetal bends

when heated. As current rises, heat also rises. The hotter the bimetal becomes the

more it bends, until the mechanism is released.

Material 1

Material2

Heat source

} Bi-metal

Figure 4.8:The effect of heat on a bimetal strip

Short circuit protection is accomplished with an electromagnet (Figure4.8a). The

electromagnet is connected in series with the overload bimetal strip. During

normal current flow, or an overload, the magnetic field created by the

electromagnet is not strong enough to attract the armature. When a short circuit

current flows in the circuit, the magnetic field caused by the electromagnet attracts

the electromagnet’s armature. The armature hits the tripper bar rotating it up and to

the right. This releases the trip mechanism and operating mechanism, opening the

contacts. Once the circuit breaker is tripped current no longer flows through the

electromagnet and the armature is released. (See figure 4.9).


29

Curr

ent in

Latching

mechanisim

Current out

Magnetic

coil

Electrical

contacts

Spring

Normal Conditions

Current in

Latching

mechanisim

Current out

Magnetic

coil

Electrical

contacts

Spring

Overload Conditions

Thermal-magnetic Circuit Breaker(b)

Current in

Latching

mechanisim

Current

out

Magnetic

coil

Electrical

contacts

Spring

Overload Conditions

Magnetic Circuit Breaker(a)

Current in

Latching

mechanisim

Current

out

Magnetic

coil

Electrical

contacts

Spring

Normal Conditions

Figure4.9: The principle of operation of circuit breakers


1

4.3 Control devices

4.3.1 Relay:

BatteryRelay Coil

Contacts

To Power Circuit

Iron Core

Switch

Relay Coil

Contacts

To Power Circuit

Iron Core

Switch

Relay Open Relay Close Figure4.10:The principle of operation of the relay

The relay is a remotely controlled switch. In the diagram above, a power circuit contains a

switch which is opened and closed by operation of a

relay. The relay is activated by a magnetic core which is

energised when a controlling switch is closed. As the

core is energised, it lifts and closes a pair of contacts in a

second circuit - usually a power circuit. The current

required for the relay is usually much lower than that used

for the power circuit so it can be provided by a battery

In the left hand of figure4.10,the diagram shows the

controlling switch is open, so the relay is de-energised and the

power circuit contacts are open. If the controlling switch is

closed, as in the right hand diagram, the relay is therefore energised and its core magnet lifts

to close the contacts in the power circuit.

Figure4.11: a relay


2

4.3.2 Contactors:

( a ) ( b)

Figure4.12a shows the interior of a basic contactor. There are two circuits involved with the

operation of a contactor, the control circuit and the power circuit. The control circuit is

connected to the coil of an electromagnet, and the power circuit is connected to the

stationary contacts.

When the control circuit supplies power to the coil, a magnetic field is produced,

magnetizing the electromagnet. The magnetic field attracts the armature to the magnet,

which, in turn, closes the contacts. With the contacts closed, current flows through the power

circuit from the line to the load. Figure(4.13)

When current no longer flows through the control circuit, the electromagnet's coil is de-

energized, the magnetic field collapses, and the movable contacts open under spring

pressure.

Figure4.12: a)Construction of a contactor ,b) A contactor


3

4.3.2.1 Overload relays

Overload relays (Figure4.14)are designed to meet the special protective needs of motor

control circuits. Overload relays allow harmless temporary overloads that occur when a

motor starts.

Overload relays trip and disconnect power to the motor if an overload condition persists.

Overload relays can be reset after the overload condition has been corrected.

Figure4.13:Principle of operation of the contactor

Figure4.14: Overload relay


4

4.3.2.2 Contactors and Overload Relays

Contactors are used to control power in a variety of applications. When used in motor-

control applications, contactors can only start and stop the motors. Contactors cannot sense

when the motor is being overloaded and provide no overload protection.

Most motor applications require overload protection, although some smaller motor, such as

household garbage disposals, have overload protection built into the motor. Where overload

protection is required, overload relays (such as the one shown here) provide such protection.

4.3.2.3 Motor Starter

Contactors and overload relays are separate control devices. When a contactor is combined

with an overload relay, it is called a motor starter.Figure4.15


1

4.3.3Pushbuttons

A pushbutton is a control device used to manually open and close a set of contacts. Pushbuttons may

be illuminated or non-illuminated and are available in a variety of configurations and actuator

colors.

Figure 4.16: Different types of pushbuttons

i) Normally Open Pushbuttons

Pushbuttons are used in control circuits to perform various functions such as starting and stopping a

motor. A typical pushbutton uses an operating plunger, a return spring, and one set of contacts.

This illustration shows a pushbutton with normally open contacts. Pressing the button causes the

contacts to close (figure4.17). This pushbutton has momentary contacts which means that the

contacts will open when the pushbutton is released.

ii) Normally Closed Pushbuttons

Pushbuttons with normally closed contacts, such as the one shown here, are also used in control

circuits. The contacts remain in the closed position allowing current to flow through them until the

pushbutton is pressed(figure4.17). Pressing the pushbutton opens the contacts and interrupts current

flow. The pushbutton shown here also has momentary contacts; however, normally open and

normally closed pushbuttons with maintained contacts are also available.

.


2

Normally Open Pushbutton

Normally Close Pushbutton

Figure 4.17: The mechanism of the pushbuttons

4.3.4 Selector Switches

Selector switches are another means to manually open and close contacts and are commonly used

to select one of two or more circuit possibilities.

Selector switches may be maintained, spring return, or key operated and are available in two-

position, three-position, and four-position types.

The basic difference between a pushbutton and a selector switch is the operator mechanism. A

selector switch operator mechanism is rotated to open and close contacts.


3

Figure 4.18: Different types of selector switches

4.3.5 Indicator Lights:

Indicator lights, often referred to as pilot lights, provide a visual indication of a circuit's operating

condition. An indicator light may be wired to turn on for any predetermined condition. Indicator

lights are available in round designs with 16 mm, 22 mm, or 30 mm mounting diameters as well as

in square designs.

Figure 4.19: Different types of push buttons switch

5. energy conversion Week 11

5.1 Electro-mechanical energy conversion

Energy is converted to electrical form because of the advantages listed in the introductory

part of the note. It is seldom available or used in electrical form, but converted into electrical

form at the input to a system and back to non-electrical form at the output of a system. A

typical example is the processing of energy from and hydro generating plant. It is converted

into electrical form at the power plant. Transmitted through transmission lines and

distribution lines, and converted to mechanical energy in an electric motor are the point use.

A second example is in the conversion of the energy in sound pressure waves, and the

transmission in electrical form from the taker to the listener in a telephone system. Few more

energy conversion principles will be mentioned.

5.1.1 Major energy coversion principles

Energy conversion between electrical and non- electrical forms includes

(i) Electrochemical eg battery

(ii) Electrothermal eg. Thermocouple

(iii) Photo electrical eg photo cell

5.2 Energy coversion

Theoretically, only a sourceless current is needed to develop a mechanical force

magnetically. But in a machine the production of force is hardly enough: something must

move in order to do useful work done demands a corresponding energy supply form

somewhere.

In a device energized only by a permanent magnet, the only energy source is the magnet

itself. If the displacable part of the machine moves under force and does work, this can only

be at the expense of the field energy of the permanent magnet, which must decrease. Such an


arrangement has obvious limitations. It may also be inconvenient a permanent magnet”

lifting magnet, for example would not e capable of releasing its load. Where the magnetic

affected by the movement is produced by a current circuit, changes of field energy have to

be supplied electrically from a source. This implies the appearance in the circuit of an

electromotive force e, which, with the current I, represents the delivery or absorption by the

source of energy at the rate ei consider the elementary system of fig 2.1 A sources of voltage

is connected to a device (e.g a secondary battery or a machine) in which the energy-

conversion process results in the appearance of an e.f.m.

The effective resistance of the circuit is represented by R. if current flows into the circuit

form the positive terminal of the source, and the input power p = Vi Rl + el, has the

direction as shown at (a). However¸ if e >, the current reverses and we can now call it –e. the

power input from the now p = v (-i) = Rl2 + e (-l), which is negative, i.e it is an output from

the device into the source, as at (b). to illustrate this simple but fundamental point, suppose

that v = 10v d.c nad R = 1-2. then if e = 8vd.c.

The current o = v-e = 10-8 =2A

R 1

And the source provides an input power p = 10 x 2 = 20w The converting device accepts 8

x 2 W as a motor And power loss due to plissipation = 1 x RT2 = 4W Conversely, if e

12V, The current again is 10 -12 -2A (I.e reversed) The device produces 12 x 2 = 24 W as

a generator of which RT2 2

2 x 1 = 4W is dissipated in R, and 10 x 20W is delivery as an

output to the source. In the case of the electromagnetic machine, the relationship between

the emf and the magnetic field is obtained from the faraday induction law (which had been

mentioned in 1.1)


5.3 Linked energy systems

An electromechanical machine forms a coverting link between an electrical energy system (

such as a main power –supply network) and a mechanical one (such as a prime- mover or a

train). In action a machine is not an isolated things, but has a behavious strongly influenced

by its terminal systems. A relay, for instance, will be affected if its operating battery

becomes discharged; a loudspeaker will behave very differently it enclosed in an evacuated

vessels with the air loading thus removed; a hydro electric generator, suddenly short-

circuited, will react severely on the turbine and pipe-line.

A machine can, of course, be studies initially in isolation, but the engineering interest

begins in fact when the complete linked system is considered. Again, the steady-state

behavious is informative up to a point, but operation in responses to change – i.e, the

transient responses is fro move important and fundamental.

Fig 2.1 Electro–mechanical linked energy system

System analysis can be complicated. Fig 2.2 shows diagrammatically a typical electric

supply system feeding a mechanical load through an electromechanical machine. In some

cases we might simplify the analysis by assuming, say, that the terminal voltage and

frequency of the machine were constant. This is good enough if the machine is a small

contactor but if it is a 25MW motor the effects of its behaviour reach for back through even

an extensive supply system. Methods are available for evaluating such a complex for any


given stimulus, such as the occurrence of a transmission- line fault or starting of a large

motor.

5.4 Energy storage

We now consider how a flux is established and energy is stored in simple toroidal magnetic

Circuit of cross sectional area A, path length L, and of material of constant permeability u,

The flux is to be established by a current i, in a uniformly wound coil of N-turns. In order

To concentrate on energy storage we neglect the coil resistance. With i initially zero, let a

Voltage V, be applied to the coil terminals, what happen thereafter depends on Faraday’s

Law of electromagnetic induction.


5.5 Energy balance

Fig: 2.1 Electromechanical machine conventions

A machine accepts energy in a variety of forms from its attached terminal systems. By

conversion we take energy input as positive, so that an output is regarded as a negative input.

The machine internally electrical energy- mechanical energy is a motor mechanical energy to

electrical energy is a generator converts some energy, stores some, and dissipates the rest:

these energies are positive if they increase with time. As the prime object of a machine is

conversion to useful output, one of the terminal inputs will normally be negative. Recalling

the principle of conservation of energy which states that energy is neither created nor

destroyed and combining it with the laws of electric and magnetic fields, electric circuits and

Newtonian mechanics, the energy balance can be expressed as:-

Total terminal energy input internal energy + Dissipation 2.1 for an electromechanical

machine using a magnetic field as the means of conversion, the balance can be stated in more

specific terms as electrical energy input + mechanical energy input

= stored magnetic –field energy + stored mechanical energy + Dissipation


Reckoned from an initial condition of zero energy, w = o.A comparable relation must apply

to energy changes dw, and also to energy rate dw/dt i.e to power, P. in corresponding

symbols these relations are total energy wf + ws + w 2.2(a)

Energy change dwe + dwm = dwf + dws + dw 2.2(b)

Energy rate Pe + pm = dwf + dws + p 2.2(c)

dt dt

The rates of change of stored field energy wf and stored mechanical energy, ws, are left in

differential form because there is always a practical limit to storage. A magnetic field can not

grow in strength indefinitely when ferromagnetic materials is employed; and if the kinetic

energy in a flywheel is continually increased, the speed must rise and the wheel may burst

under centrifugal force.

We shall now examine the electromechanical machine in more detail with fig 2.3. The

machine links an electric source of voltages supplying a current; and a mechanical sources

represented by a bar moving to positive directions, thus both vi and fmu are inputs ( The

mechanical source could alternatively be a shaft rotated at angular speed wr by a tongue mm

to give an input power mnwr ). The electrical end of the machine is precisely that of fig 2.1

(a), with opposing v. the mechanical end has the magnetically developed force fe opposing

fm > fm it can reverse speed w so that the mechanical system is driven and absorbs a

mechanical output.

The behavior can now be summarized. With the machine operating in the steady state as a

motor, the applied voltage u drive +I against e to give a total electrical power input pe =

u(+e), of which the part ei is converted. The outcome of conversion is the force fe which

drives the bar against fm to develop the mechanical input pm = fm (-u) which, being


negative, is actually an output. With the machine as a generator; the bar is driven at speed u

by the force fm to provide the mechanical input pm = fm ( +u), as a result which e now

exceeds u and reverse the current to provide the negative electrical input (i.e output (i.e

output) pe = u (-i) the sum of the inputs (pe +pm) must be rate of rise of internal energy

storage plus the rate of energy dissipation.

A real electromagnetic machine has fairly obvious points of attachment (e.g the electrical

terminals and the shaft) by which it is connected to the electrical and mechanical sources to

form a link between them. But it is very to concentrate source to from link between them.

But it is very convenient attention on the conversion region enclosed by the chain- dotted

line in fig 2.3, for it contains only the essential quantities e and i,. U and fe. Various losses,

and the mechanical storage, are excluded so that attention can be directed on to the physical

process if useful energy conversion by electromagnetic means outside the conversion region

we can account for conduction and core losses associated with the electrical end and

represented rough by the resistance R in fig 2.3, and friction and similar losses on the

mechanical side. It is to be noted that the externally applied force fm is not necessarily equal

to –fe because there may be force-absorbing components of inertial and elasticity in the

mechanical working parts of the machine itself, as well as internal friction.

The machine has new been reduced to an analyzable form. Its behaviors under specified

conditions involves the forces and movement of the mechanical parts, the voltages and

current at the electrical terminals and processes of energy conversion and storage and

dissipation going on inside. Evaluation is based on the well-established principles and laws

summarized in the following table.


Part of system Quantities Principles

Electrical Voltage, current Faraday-Lenz and

Kirchhoff laws

Conversion

Mechanical

E.M.F current magnetic

field,. Force, displacement

Force, displacement speed

Magneto- mechanical

Principles induction and

thermal laws Newton law

5.5.1 Block diagram for energy balance equation

The energy balance equation is given by equation 2.2 as electrical energy input mechanical

energy input

= stored magnetic-=field energy + stored mechanical energy + dissipation

The dissipation (energy lossess) arise from three main causes

(ii) Part of electrical energy is converted directly to heat in the resistance of current path.

(ii) Part of mechanical energy developed with the device is absorbed in friction ad

windage and converted to heat.

(iii) Part of the energy absorbed by the coupling field is converted to heat in magnetic

core losses (for magnetic coupling ) or dielectric loss) for electric coupling).

if we associate the various losses with the corresponding energies, equation 2.2 be written as

Electrical energy mechanical energy increase in energy stored

Input minus = Output plus friction + in the coupling field

Resistance losess and windage losses plus associated losses


Equation 2.3 is obtained ( for a motor) with the mechanical energy transferred to the R.H.S

of the equality sign and neglecting the energy mechanical stored energy ( for a machine

without a flywheel and neglecting the mass of the shaft). If there is a flywheel, the stored

mechanical energy is 1/2mu2 or ½ mr2w2

Where m = mass of flywheel

V = linear velocity of rotating wheel

w = angular velocity of rotating wheel

r = radius of flywheel

Equation 2.3 may be represented in the form of a block diagram as shown in fig 2.4

Fig 2.4 General representation of electromagnetic energy conversion. Fro a generator action, the

positions of the electrical system and that or the mechanical system will be interchanged.


5.6 Magnetic field energy and forces

In order to be able to analyse mathematically the electromechanical system that is

completely described by the energy balance equation, we need to be able to determine

qualitatively the energy of the magnetic field and the associated force.

5.6.1 Magnetic field

A magnetic field is a region of space in which certain physical effects occurs in particular

the development of mechanical force. A pictorial model of the field can be made by drawing

closed loops of magnetic flux, such that their direction and spacing at any point are a

measure of the flux density. The magnetic circuit in the present context is composed partly

of ferromagnetic material such as iron, and partly of an airgap. The iron serves to “guide” the

flux in a desired path; the airgap is necessary to make useful magnetic effects readily

accessible.

The lines in a flux plot have no real existence. In a given region a magnetic field may change

direction, become weaker in some place and stronger in others.

5.6.2 Magnetic circuit n/a

Engineers look upon magnetic flux (Weber) as produced by electric current. A current I

develops around any path that links it a magneto motive force (M.M.F) F = I (ampere). The

effect of a current can be multiplied. By coiling the electric circuit into N turns so that

around a path linking all N turns the m.m.f is N times as great, giving F =- ampere- turn.

The m.m.f is distributed along the path, to give along a path element of length dx the

magnetic field intensity h (ampere-turn/ metre). The summation of Hdx around a single loop

closed with F i.e F = Hdx = m.m.d.


At any point, H gives rise to a flux density B = NH (tesla or Weber/m2) our Henry/meter]

Flux summation of the flux density over the area available to the flux path given the total

flux [ i.e Ø i.e. BA. (Weber).-2.6 where A is the are of flux path.

The „ law of the magnetic circuit relates the total flux Ø to the mmf f through the

expression.

Ø = F =F Comparable to the law of electric circuit 2.7

S

I = V

R = v.g (ohm‟s law)

Where s = the total reluctance (ampere-turn per weber]

And = 1/s = total permeance [ weber per ampere-turn]

For a path- length x of materials of absolute permeability U, and having a uniform cross-

sectional area A over which the density B is everywhere the same, the mmf f require = N x x

= Hx…………..2.8

From equation 2.6, 2.7 and 2.8, F Øs F = mmf 2.9

And the reluctance of the path S = f/Ø = Hx = x……….2.10

And the 1/s UA/x

For a succession of parts , x, y, z 2.11

F = fx + fy + f2 + and S = SX + SY + SZ + 2.12

If, however the parts are in parallel and share the flux

F = fx =fy =fz and

For fields in ferromagnetic materials U is very much greater, and the relative permeability Nr

=u =Uo 4 /107 1/80000


Which means that H = Ub = 800000B

For field ferromagnetic materials U is very much greater,

Ad the relative permeability Ur = U

Uo

Since, usually Ur is large, then it is convenient ( it simplies analysis) to assume that the

whole mmf is required for the excitation of the air gap i.e the whole of the field energy is

stored in the air-gap

5.7 Magnetic field energy

With the assumption that the magnetic filed energy is concentrated within the air gap. It

becomes easy to calculated the magnetic field energy.

A magnet attract on iron bar. If the iron bar is light enough and the magnet filed is enough,

the bar will be seen to move up to get attached to the magnet. The movement of the bar

signifies that work is done, since the iron bar has mass and covered some distance

(work done = force x distance). This means that the space that the file occupies (the field

region) can demonstrated or has on attribute of force. And hence, the filed region must

process some energy. If can be easily noticed that the force is strong when the air gap is short

but rapidly diminishes as the air gap length is increased.

5.8 Maxwell stress

Fig 2.5 maxwell forces

Maxwell formulated the concept that the forces is transmitted across the gap between a pair

of magnetized surface as a result of two stresses. If at a point in the gap the flux density is B

and the corresponding field intensity is H =B/U,. then there is a tensile stress of magnitude


1.2 BH along the direction of a flux line and a compressive stress ½ BH along all directions

at right angles to a flux line.

Fig 2.5 shows two iron bars forming part of magnetic circuit when, as at (a), the polar

surfaces are close together, the flux is mainly concentrated between the surfaces. The density

B is large, and so therefore is H, and ½ BH represented a strong tensile force of attraction

between the faces. Not all the flux is useful; some, of the leakage flux, exists at the sides of

each bar. Flux crossing the boundary between air and a high permeable materials must enter

or leave the boundary between air and a high permeable materials must enter or leave the

boundary almost at right angles, so that the tensile stress due to faces. All the comprehensive

stresses balance out by symmetry.

In case (b), the greater reluctance of the long air gap reduces the total flux, the useful flux

density of the pole faces is smaller while the leakage flux is much greater hence the forces of

attraction between the pole faces is much less than in case (a)

In most practical applications, the air gap is small enough to enable us assumes a uniform

flux density over the polar area. i.e in the air gap.

.


5.9 ENERGY DENSITY

The Maxwell stress concept is another way of saying that the energy to the value

½ BH is stored in a unity cube of the space occupied by = magnetic, thus ½ BH is the energy density

[weber (metre2) x (amper/metre] = volt –second x ampere/cubic metre

= Joule /cubic metre.

Fig 2.6 magnetic energy.

Consider an air gap, initially unmagnetized. Apply a magnetic force to the gap, an increase of H

from zero causes the flux density B = μoH to increase proportionately, Fig 2.6(o). The energy (m3

is [HdB, and for and values Bi and H1 the final energy density (shaded area) is clearly ½ B1H1 . The

some summation applies to a filed set up by in a ferromagnetic matter, with similar result Fig. 2.6

(b0, if the permeability U is constant; but for the same and density B1 a much smaller magnetizing

force Hii is need and much less energy is stored.

If the ferromagnetic materials is subjected to saturation, the stored energy is as shown in Fig 2.6(c0

and is calculated by piece-wise approximation to composite area of DOAD plus area of trapezium

AB,CD.


5.10 FARADAY- LENZ LAW

When the flux 4 associated with an electric increase in time at by amount d4, an emf, e = de/dt

appears in the circuit. The minus sign implies that the direction of the emf is such that a current

produced by it in the circuit opposes the change d4.

Flux-linkage 4 (weber- turn] is the product of a magnetic flux and the number of turns through

which it passes in the same direction. Since the current is proportional the flux,

then flux likage Ų = NQ

Since we are neglecting the coil resistance, then around the electric circuit loop formed by the

voltage source and the N turns of coil on the toroid, the KVL gives

u = +Dq/DT =-E. 2.17

The instantaneous electric power input to the coil

P =vi = (dw/dt)i

The total energy required to establish from zero a flux Q1 and a linkage Q1, (corresponding to a

current mmf F1 =Ni) is

Wf = (t pdt = (

4 idQ =(

Q fdQ

Since the core of the toroid has constant permeability.

Which is represented by the shaded area in Fig, 2. 6 (d). this magnetically stored energy can be

assumed to be uniformly distributed through the active volume Al of the core. Then because

Q1 = QIN =NB,A and Nli =Fi =H il

The energy density = ½ 4ili/Al =1/2 Bi Hi

The total magnetic energy can be stated in several ways

[f =1/24I =1/2QF =1/2Q2S =1/2 F

2S =1/2Q / 1/2F

2 =1/2Li

2]


Also, since Q BA and F =Hl and H =B/U

Then wf =1/2 QF =1/2 BAHL =1/2AL

U

But al = volume

Wf = Vol. B2

2U

Any expression for the energy of the field wf in equation 2.32 and 2.23 may be employed

depending on the parameters given.

5.11 ENERGY CONVERSION

Fig. 2.7 Energy change with position

Fig 2.7 (a) shows airgap region and existing coil of a magnetic circuit, the ferromagnetic

core of which has a high. Permeability, the plane parallel polar faces. Have an area A and are

spaced x apart. The n-turn coil carrying current I magnetic the system. The problem is to find

the magnetic force of alteraction between the polar faces.

In the comparable system Fig 2.7 (b), with a rotatable part (rotor) port (stator), the problem is

to find the tongue.

Insight into the inteplay of energy can be obtained from a study of finite mobvements, say

from an initial position (1) to afinal direction position (2). At (a0. this movement -∆x (i.e


against the positive direction of x) of the right-hand member’ are ( b) it is a rotation -∆Q of

the rotor. The static 4/I relations for the two positions are shown in Fig 2.7 © differ because

the gap reluctance for (2) is less than for (1). Clearly the filed energy will differ too. How it

changes depends on the conditions wholly in the gap, and the effect of coil resistance will

initially be ignored.

(1) CONSTANT CURRENT

Let the current be held constant at is throughout, as shown at Fig 2.7 (d). for

position the linkage is 41 and the filed energy is ½ Fig 4. to reach position (2) a

linkage 42 with constant current, an electrical energy input + ∆we =(Ų2-Ų1 ) i0 must

be fig 2.7 (d). the current sources. This is represented by the hatched area at Fig

2.7(d0. Now, the increase in field energy is ∆WF =1/2 (Ų2-Ų1)io, which, comparing

the expressions or the hatched areas at (d), is only one-half of∆we. What has

happened to the other half?

Writing the energy balance and excluding the loss and mechanical storage terms:

∆we + ∆wf

i.e (42-41)io + ∆wm =1/2 (Ų2-Ų1)io

Hence ∆wm =1/2 (Ų2-Ų1) io]

As 41 the mechanical input is negative: it is in fact an output work

(force x displacement). A precisely similar consideration gives for the rotary case (b)

the output work (torgue x angular displacement). For constant current, therefore, the

source provides ∆we, of which one-half is taken as energy into the filed and the

other half is converted into mechanical energy output.


(2) CONSTANT FLUX

Let the flux be kept constant so that linkage is always . the condition implies that the

current fall from Li to i1 to compensate for the rise in permeance in Fig (e). there is

no electrical energy transfer between the source and system for with constant linkage

there is no induced e.m.f to be balance. Hence ∆we =o. but there is change of filed

energy ∆wf =1/2Ų0 (l2-l1) which is negative because l2 <l1. the energy balance is

O +∆wm =1/2 Ų0 (l2 –l1)

Hence ∆wm =fm (-∆x) =1/2 Ų0 (l2 –l1)

For constant flux, therefore, the mechanical work done comes from an equal

reduction in filed energy.

(3) GENERAL CONDITION

In a practical device neither of condition (1) and (2) is likely to apply consistently.

The transition will follow some arbitrary contour, such as that in Fig 2.7 (f), with

changes in both 4 and i. the energy balance is then some combination of cases (1) and

(2). The change in field energy is the shaded area ∆wf, and this will correspond, as

before in magnitude to the mechanical energy ∆wm even, if owing to saturation

effect, the Q/I relation is non- linear, they are ∆wf can still be found by graphical

integration. Ni any case,

The mean force = ∆wf, = fm 2.28

∆x

The mean torgue ∆wf, = mm 2.29


(4) DIFFENTIAL FORM

IF ∆ AND ∆Q are reduced to the infinitesimal differentials dx and dq, the force and

torgue are obtained for a single position x or Q. Then

Force, fm = dwf 2.30

dx

torgue, mm = dwf 2.31

dQ


5.12 ALIGNMENT FORCE AND TORQUE: SINGLE EXCITATION

Fig: 2.8 Reluctance motor

The reluctance motor shown in figure above depend on the tendency of the rotor to

Align itself magnetically with the stator. A flux plot for the machine shows that,

provided there is ad equate ove4rlop, all the active flux and all the field energy can be

assumed to occupy the overlap regions. The active gap volume changes with angle Q

between the two magnetic exes, and the torgue is d e f/dQ eqtn 2.31 using equation

2.22 a basis. An angular increase Dq others the active volume of each gap by - rlg

dQ and the gap energy by -1/2 B2 Lr Dq/Uo

the torgue for the two poles is consequently

me = dwe = B2Lrlg 2.24

Dq uo = 4π x10-7

(const.)

The minus sign indicating that the force acts to reduce Q.

Example 1

With the rotor dimentions shown and a coil of 400 turns carrying 1.6A, calculated the

torgue acting on the rotor.


Solution

The mmf (F) = NI 400 X 1.6 = 640 A.t HX 21g

Area fine B =UOH =>

Then F = 640 BX2lg

Uo

:. B =640 x UO 640 X 4π X 190-7

= 0.40 tesla

2lg 2 x 10-3

0.43

i.e The flux density in each 1mm gap B = 0.40T.

:.

me = -0.42 X 0.025 X0.03 X0.001 X10

7 = 0.0955N-M

-B2l/g4 π

Example 2

The 4-l characteristics of a magnetic circuit are frequently described with straight

segments as shown below. The act is considered linear up to pt. a and in saturation

from a to 5 find the field energy

Example 3

A dynamic phonograph pickup consists of a 20-turn coil length of each coil =1cm)

moving normal to a field of B=0.2t. if the maximum allowable amplitude is 0.02mm,

calculated the output voltage at 100-HZ and at 100Hz

Solution


A dynamic phonograph pickup for vertical recording the effective length of

conductor in moving coil is

L = 20turns =20cm =0.2m

For a sinusoidal displacement of amplitude 2 x 10-5

m =0.02mm

X (t) =Asinwt = 2x 10-5

sinwt

The velocity at 100HZ is d x /dt or

U =dx =2 x10-5

x 2π x 103conwt m/s.

Neglecting internal impedance, the output voltage is

V = e =Blu =0.2 x 0.2 x 4π x 10-2 coswt colt

The r.m.s value of output voltage is V = vmax = 0.2 x0.2 x 4 π x10-2

2 2

= 0.0036v =3.6mv

(ii) The velocity at 100HZ is

U = dx =2 x 100-5

x 2 π x 102 coswt m/s

And output voltage (neglecting internal impedance) is

V =e bLu = 0.2 x 0.2 4 π x 10-3

coswt volt

And r.m.s value of output voltage = 0.2 x 0.2 x 4 π x 10-3

2

= 0.00036v =0.36mv


Example4.

In a d.c machine, shown above, the armature is wound on a laminated iron cylinder

15cm long and 15cm in diameter. The N and S role faces are 15cm long (into the

paper) and 10cm along the circumference the average flux density in the air gap

under the pole faces is 1T. If there are 80 conductors in series between the brushes

and the machine turning at N =1500rpm, calculated the no-load terminal voltage

Solution

For Ns conductor (no coils) in series, the average emf is

E =NS ∆Ø wb =Ns Ø wb P poles n rev No 2 conductor in sec)

∆t s pole rev 60 sec

= Ns Øpn volts

Where the flux per pole Ø = BA = 1 x0. 15 x 0.1 = 0.015 wb.

:. E = 80 x 0.015 x 2 x 1500

60

= 60 volts

Example 5.


A magnetic circuit is completed through a soft –iron rotor as shown in the figure

above. Assuming (1) all the reluctance of the magnetic circuit is in the air gaps of

length L

(ii) There is no fringing so the effective area of each gap is the area

Derive on expression for the torgue as a function of angular position.

Solution

The total reluctance for two air gaps in series is

R = 2l (since Ur =1 for air) R = F =1L

UOA Q A

= 2L

Urwq

For an N-turn coil, the inductance is

L = NØ = NF N2I = N

2 trwØ

I IR IR 2L

Since torgue =1/2 I2

dL = Uo N2rw

dØ 2L

The torgue is independent of Ø under the assume conditions.

Example 6

(a) Wiring diagram (b)Steady state model

A commutator machine, with the wiring diagram and steady-state model showed

above, is rated 5KW , 250V, 2000rmp. The armature resistance RA is 1. Drive from

the electrical and at 2000rmp, the no-load powder input to the armature is IA = 1.2A

at 250V with the field winding (RE =250) excited by IF =1A. Calculate the efficiency

of this machine.


Solution

In fig (a), input power IF 2RF = 1

2 X 250 =250W is required to provide the necessary

magnetic flux. This is power lost and it appears as heat.

In no-load steady operation, there is no output and no change is all loss

[The armature cooper loss at no load is negligible (1.22 x 1=1.44w) and most of the

input power at no- load goes to supply air, bearing brush friction, eddy cumenty and

hystersis losses] the losses are associated with flux changes in the rotting armature

core, are dependent on speed but are nearly independent of load.

Hence, field loss = IF2RF = 250W

And rotational loss = IAV = 300w p =iv :.i = p1

v

At full-load of 5KW, IA =5000W = 20A

And the armature copper loss = IA2 Ra =20

2 x1 =400w

The energy balance equation gives

Mech. Energy + field elect = increase energy

:input input output energy stored converted

Field to heat

i.e

Mech. input + 250-5000 = 0 field arm rotat

less less less

Mech. input + 250 -5000 = 0 + 250 +300 + 400

(field input is all loss and appears o n both sides)

Mech. Input = 500 + 300 + 400 =5700W.

Hence efficiency = output = elect output

Input mech. output + elect input

= 5000 = 0.84. or 84%

5700 + 250


Example 7

In the relay shown above, the contacts are held open by the spring excerting a force

of 0.1N . The gap length is 4mm when the contacts are open and 1mm when

closed. The coil of 5000 turns would on core 1cm2 in cross- section. Assuming

1) All reluctance is in a uniform air gap

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EEC 233 Theory