1. Basic Principles of Electric Machines
Week 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 convert 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
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1. Basic Principles of Electric Machines
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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
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1. Basic Principles of Electric Machines
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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)
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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.
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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
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1. Basic Principles of Electric Machines
1.3
(a)
Lifting magnet
(f)
(b)
Relay
(g)
Electromagnetic pump
( c)
Telephone
(h)
Loudspeaker
(d)
Moving-iron indicator (i)
Moving –coil indicator
(e)
Reluctance motor
(k)
Week 1
Actuator
Industrial rotating machine
Alignment devices
(a)
The lifting magnet: Attract ferromagnetic loads such as beams, plates, and scrapiron.
(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.
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1. Basic Principles of Electric Machines
1.4
Week 1
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)
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1. Basic Principles of Electric Machines
(n)
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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
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1. Basic Principles of Electric Machines
900
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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
=
0.012 – 0.01667 = 0.72v
=
0.72v
1/60
t
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
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1. Basic Principles of Electric Machines
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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.
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Iron Core
N
Magnetic field Lines
S
The Current
Battery
S
N
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
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1. Basic Principles of Electric Machines
0
Time1
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0
0
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.
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1. Basic Principles of Electric Machines
N
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N
Iron Core
Ammeter
a
N
N S
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
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