ADDIS ABABA SCIENCE and TECHNOLOGY UNIVERSITY
SCHOOL of MECHANICAL and MANUFACTURING ENGINEERING
DEPARTMENT of ELECTROMECHANICAL ENGINEERING
LECTURE NOTE of
INTRODUCTION to ELECTRICAL MACHINES
(ECEG - 2261 )
OUTLINE
1.
Magnetics
2.
Transformers
3.
AC 3-Phase Induction Machines (IM)
4.
DC Machines
5.
Synchronous Machines
Chapter 1. Magnetics
Magnetism and Electromagnetism
Magnet:- is a material which has the property of
attracting small bits of iron-containing objects.
Magnets are generally classified in two categories
 Permanent magnets
 Electro-magnets
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Permanent magnets
Are magnets which have the inherence property of
retaining their magnetism indefinitely and they don’t
require electrical energy for retaining their magnetism.
A permanent magnet will position itself in a north and
south direction when freely suspended. The northseeking end of the magnet is called the North Pole, N,
and the south-seeking end the South Pole, S.
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Electromagnets
Is the magnetization due to flow of an electric current
through a coil.
Electromagnets sometimes called as Artificial Magnets.
Whenever an electric current flows through a
conductor, a magnetic field is produced.
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Electromagnets
Hans Christian Oersted (1771-1851), who demonstrated
in the year 1819 that a current-carrying conductor
produced a magnetic field.
The higher the
current flow,
the stronger
the magnetic
field produced.
This is what we measure
with a clamp on ammeter.
The magnetic field produced in a conductor is
proportional to the current moving through the
conductor and the number of turns wound on the
materials.
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Magnetic Field
Magnetic field:- is the area around a magnet and it is in
this area that the effects of the magnetic force
produced by the magnet can be detected.
Michael Faraday suggested that the magnetic field
could be represented pictorially, by imagining the field
to consist of lines of magnetic flux, which enables
investigation of the distribution and density of the field
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Magnetic flux (magnetic line of force)
 Is total magnetic lines of force produced by a magnet
The quantity of magnetism which exists in a magnetic
field
How much of magnetic force exist on the surface
Magnetic fields may be produced by permanent
magnets or electromagnets.
Magnetic fields are created by alternating and directcurrent sources
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Properties of Magnetic Lines of Force
The direction of magnetic lines of force radiates from
North Pole to South Pole outside the magnet and is
from South to North Pole inside the magnet.
Thus such lines of flux always form complete closed
loops or paths; they never intersect and always have a
definite direction.
A magnetic field cannot be seen, felt, smelt or heard
and therefore is difficult to represent.
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Properties of Magnetic Lines of Force
 The laws of magnetic attraction and repulsion can be
demonstrated by using two bar magnets. Unlike poles
attract each other and like poles repel each other. This
is indicated in the fig 1.1 below
Figure 1.1
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Electromagnetism
A magnetic field is always associated with a currentcarrying conductor.
Ampere's Right hand rule
A magnetic field is always associated with a currentcarrying conductor.
Field or flux
line
Current-carrying
conductor
The thumb pointing in the direction of the current
 Our fingers will point in the direction of magnetic field
Another form of Ampere's right-hand rule
Solenoid:- a cylindrical coil with large no of turns
If we grasp the coil with our right hand the fingers
pointing in the direction of the current, thumb will
point in the direction of the north pole.
Magnetic Properties of Materials
Magnetic materials can be classified generally as
 Diamagnetic
 Paramagnetic
 Ferromagnetic
Diamagnetic Materials
Materials that experience a feeble or very weak force
of repulsion by a magnetic field are called diamagnetic,
such as bismuth, silver, and copper are diamagnetic
materials.
The permeability of a diamagnetic material is slightly
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less than the permeability of free space.
Magnetic Properties of Materials
Paramagnetic Materials
Materials that experience a feeble force of attraction by a
magnetic field are called Paramagnetic materials but the
permeability is slightly greater than the permeability of
free space. Example Air, Aluminum, oxygen, Manganese,
platinum and palladium
Since the force experienced by a paramagnetic or a
diamagnetic substance is quite feeble, for all practical
purposes we can group them together and refer to them
as nonmagnetic materials.
Ferromagnetic materials
These materials exhibit strong attraction and hence the
permeability much greater than free space. Principal
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ferromagnetic materials are Iron and various steel
Is the magnetic flux per unit cross-sectional area.
The total magnetic flux that comes out of the magnet is
not uniformly distributed
The magnetic flux density increases as we approach closer
to the end of the magnet, as we move away the magnetic
flux spreads out, and therefore the magnet flux density
decreases.
A greater amount of magnetic flux passing through an area

that is nearer the magnet pole
B
A
B = magnetic flux density, T
 = magnetic flux, Wb
A = area through which  penetrates perpendicularly, m2
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Example
1. The total magnetic flux out of a cylindrical permanent
magnet is found to be 0.032 mWb. If the magnet has a
circular cross section and a diameter of 1 cm.
what is the magnetic flux density at the end of the
magnet?
Solution
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 A driving force causing to establish magnetic flux.
 The magnetic flux is proportional to the products of amperes
and turns.
 Ability of a coil to produce magnetic flux is magnetomotive
force
Fm  NI
Magneto motive force (MMF), AT
N = number of turns of coil
I = excitation current in coil, A
Magneto motive force in the magnetic circuit is analogous to electromotive force
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Example
2. The coil below has 1000 turns wound on a
cardboard toroid. The mean diameter D of the toroid
is 10 cm, and the cross section is 1 cm. The total
magnetic flux in the toroid is 3Wb when there is an
excitation current of 10 mA in the coil.
a. What is the magnetic flux when the current is
increased to 20 mA?
b. What is the magnetic flux density within the coil when
the current is 20 mA
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Solution
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Magnetic Reluctance
 It is Opposition of the material to establish magnetic flux.
Fm

 m
The MMF, AT
 = magnetic flux, Wb
m= reluctance of the magnetic circuit. At/Wb
Transposing, we have
Fm  m ………………..Ohm's law of magnetic circuits.
m
l

μA
Doubling the MMF in the circuit results in a doubling of the flux
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Permeability
Permeability (μ) – the magnetic property of a
material to allow itself to be magnetized.
It determines the characteristics of magnetic
materials and nonmagnetic materials.
 0  4  10 7 H / m
 The reluctance of magnetic materials is much
lower than that of air or nonmagnetic material.
The permeability of magnetic materials is much
greater than that of air or non magnetic material
Magnetic materials (iron steel cobalt nickel )
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Example
3. In Figure below we assume that the magnetic flux is practically
uniform in the cross-sectional area of the toroid. The mean
path length is 0.314 m and the cross-sectional area through
which the flux exists is 78.5 x 10-6 m2. Calculate the number of
ampere-turns required to set up magnetic flux of 1 Wb.
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Solution
 This is obviously a very large number and we may conclude that the
path reluctance is very high. This means that it is comparatively
difficult to establish a large magnetic flux in air.
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Relative Permeability
 Compares the permeability of magnetic materials with that
of air
 r

0
B
 
H
Where  = absolute permeability of the material. H/m
0 = 410-7H/m = permeability of free space
r = relative permeability
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Magnetic Field Intensity
 Magnetizing force or magnetic field strength.
 It is the magneto motive force gradient per unit length of
magnetic circuit
Fm
H =
l
 The magnetic field intensity for the air path is much larger
than for the iron path
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Magnetization (B-H) Curve
 The nonlinear relationship between magnetic flux density
and magnetic field intensity
 The magnetic flux density increases almost linearly with an
increase in the magnetic field intensity up to the knee point
 Beyond the knee a continued increase in the magnetic field
intensity results in a relatively small increase in the
magnetic flux density
 A slight increase in magnetic flux density for a relatively
large increase in magnetic field intensity the materials are
said to be saturated
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Magnetization (B-H) Curve
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Magnetization (B-H) Curve
Magnetic material theory
 Magnetic materials are composed of many tiny magnets (magnetic
domains) that are randomly positioned when the material is totally
demagnetized
 Application of a magnetizing force the tiny magnets will tend to align
themselves in the direction of this force
 The aligned tiny magnets increase proportionally until the knee of the
curve.
 Beyond the knee fewer tiny magnets remain to be aligned
 When there are no more tiny magnets to be aligned, the ferromagnetic
material is completely saturated.
 Saturation region practical implications in the operation of electrical
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machines
Hysteresis loop
 Hysteresis is lagging of flux density B
behind the magnetizing force H
 If the specimen has been completely
demagnetized and the magnetizing force H
is increased oa is the normal magnetization
curve
 The trace of B is higher than oa
 A residual flux density referred to as
remnant flux (retentivity) density ob.
 In order to reduce B to zero, a negative
field strength oc must be applied. The
magnetic field intensity oc required to wipe
out the residual magnetism ob is called
coercive force (coercive)
 -H to +H, the path defa is similar to the
curve abcd.
 The closed loop abcdefa thus traced out is
called the hysteresis loop
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HYSTERESIS is the dependence on the preceding flux
history and the resulting failure to retrace flux paths.
 When mmf is removed, the flux does not go to zero –
Residual Flux.
 To force the flux to zero, extra energy must be applied in
the opposite direction.
This extra energy requirement is known as hysteresis
loss.
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Hysteresis loop
Conclusions
A. Flux density B always lags with respect to the
magnetizing force H.
B. An expenditure of energy is essential to get a
complete cycle of magnetization.
C. Energy loss is proportional to the area of
hysteresis loop and depends upon the quality
of the magnetic material.
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Eddy current loss
 A time-changing flux induces voltage within a ferromagnetic
core.
 These voltages cause swirls of current to flow within the core –
eddy currents.
 Energy is dissipated (in the form of heat) because these eddy
currents are flowing in a resistive material (iron)
 The amount of energy lost to eddy currents is proportional to
the size of the 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 used between the strips, so
that the current paths for eddy currents are limited to small
areas
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Conclusion:
 Core loss analysis is extremely important in practice, since it
greatly affects operating temperatures, efficiencies, and ratings of
magnetic devices.
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 A current-carrying wire produces a magnetic field in
the area around it.
 H dl  I
net
 where H is the magnetic field intensity produced by
the current I𝒏𝒆𝒕 and dl is a 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;

I
CSA
N turns
mean path length, lc
 Applying Ampere’s law, the total amount of magnetic field induced
will be proportional to the amount of current flowing through the
conductor wound with N turns around the ferromagnetic material
as shown above.
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 The path of integration in Ampere’s law is the mean path length
of the core, lc.
 The 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 Ampere’s Law becomes,
Hlc  Ni
Ni
H 
lc
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 In a core such as in the above figure,
B = H =
Ni
lc
 Now, to measure the total flux flowing in the ferromagnetic core,
   BdA
A
where
 A - cross sectional area throughout the core
 - total flux flowing in the ferromagnetic core (webers)
Assuming B is constant throughout hence constant A, the equation
simplifies to be:
 NiA
  BA 

lc
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ELECTROMAGNETIC INDUCTION
Faraday's laws of electromagnetic induction
1) Whenever the magnetic flux is changed or when a conductor is cut by the
magnetic flux an emf is induced
2) The magnitude of the induced emf generated in a coil is directly
proportional to the rate of change of magnetic flux.
 The change of flux can be produced in two different ways:
I. Dynamically induced emf :-By the motion of the conductor or the
coil in a magnetic field
II. Statically induced emf :-By changing the current (either increasing
or decreasing)
 Statically induced emf can be further subdivided into
(a) self-induced emf and
(b) mutually induced emf.
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Self induced emf
 Any electrical circuit in which the change of current is
accompanied by the change of flux, and therefore by an induced
emf is said to be inductive or to possess self inductance.
 The property of the coil which enables to induce an emf in it,
whenever the current changes is called self-induction
d
e  N
dt
di
e  L
dt
A coil with changing current and flux
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Mutually induced emf (Transformer)
 The phenomenon of generation of induced emf in a circuit by changing the
current in a neighboring circuit is called mutual induction.

When the switch K is closed to start current in the coil P the
galvanometer gives a sudden "kick" in one direction.
 when K is opened, the galvanometer again shows a deflection but in the
opposite direction.
di
e  M 12
2
dt
M
12
1
2
M N
N
21
2 I
1 I
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Lenz’s Law
 The voltage built up in the coil will tend to establish a flux that
will oppose the change in the original flux.
 The induced current opposes the cause that produced it
 used to fix the direction of statically induced emf.
 The direction of the induced emf is always opposite to the
change of flux responsible for producing that emf.
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Induced Voltage on a Conductor Moving in a
Magnetic Field (ELECTRIC GENERATOR)
 If a conductor moves or ‘cuts’ through a magnetic field,
voltage will be induced between the terminals of the
conductor.
eind = (v x B) l
Ein = (VX B)l cos θ
Where: θ - angle between the conductor and the direction of (v x B)
 The magnitude of the induced voltage is dependent upon
the velocity of the wire assuming that the magnetic field
is constant.
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Direction of Induced emf
 Fleming's right hand rule
 To
obtain
direction
dynamically induced emf
of
 Stretch the right hand fingers in
three mutually perpendicular
directions
 If the forefinger points in the
direction of the magnetic flux
 the thumb points in the direction
of motion of the conductor
relative to the magnetic field
 then the middle finger represents
the direction of the induced emf.
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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.
F  i l  B 
F  ilB sin 
Where:  - angle between the conductor and the
direction of the magnetic field.
 Direction of the force depends on the direction of current
flow and the direction of the surrounding magnetic field
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and is given by the Flemings left-hand rule.
Left-hand rule.
Thumb
(resultant force)
Index Finger
(current direction)
Middle
Finger
(Magnetic Flux Direction)
(a)
(b)
Figure(b) shows a conductor moving with a velocity
v to the right and the direction of the flux density is
into the page.
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Magnet circuit is the path followed by magnetic flux.
In fact the laws of magnetic circuit are almost similar (but
not exactly same) to those of the electric circuit.

A
+
V
-
Electric Circuit Analogy
R
F=Ni
(mmf)
+
-
Reluctance, R
Magnetic Circuit Analogy
F  R
(similar to V=IR)
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Composite Series Magnetic Circuits
 A magnetic circuit of varying length of different materials
of different parameters through which the same flux
flows is known as a series magnetic circuit.
 This is also called composite magnetic circuit. Hence the
total reluctance is the sum of reluctance of individual
parts or magnetic path.
(Rm)= (L1/1o A1) + (L2/2o A2) + (L3/3o A3)
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Leakage Flux in Magnetic Circuit
 Leakage flux is the flux which does not follow the designed
path intended to be followed in a magnetic circuit.
 The flux passing through the air gap is known as useful flux.
 However, as air is not perfect magnetic insulator, hence a part
of the total flux returns by paths(outside the designed
magnetic path) is leakage flux.
The total flux =flux in air gap(useful flux) + leakage flux.
Leakage factor ==Total fux ( flux through iron path)
useful flux flux through air gap
 For electrical machine vary between 1.1 to 1.25
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Comparison between Electrical and Magnetic
Circuit
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The major applications of magnets
 They are used in Transformers, motors and generators,
old telephones, relays, loudspeakers, computer hard
drives and floppy disks, anti-lock brakes, cameras, fishing
reels, electronic ignition systems, keyboards, T.V and
radio components and in transmission equipments
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