Chapter 10 - Electrical Machine
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Transcript of Chapter 10 - Electrical Machine
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ENT188
ELECTRICAL TECHNOLOGY
(Electrical Machine)
-
MUTUAL INDUCTANCE
INTRODUCTION TO TRANSFORMER
STEP-UP AND STEP-DOWN TRANSFORMER
LOADING THE SECONDARY WINDING
IDEAL TRANSFORMER
DC GENERATOR
DC MOTORS
INTRODUCTION TO MACHINE THEORY
Electrical Machine
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MUTUAL INDUCTANCE
When a second coil is placed very close to the first coil so that the
changing magnetic lines of force cut through the second coil, the coils
are magnetically coupled and a voltage is induced.
When two coils are magnetically coupled, they provide electrical
isolation because there is no electrical connection between them,
only magnetic link.
-
MUTUAL INDUCTANCE
The amount of voltage induced in the second coil as a result of the
current in the first coil is dependent on the mutual inductance.
The mutual inductance is established by the inductance of each coil
(L1 and L2) and by the amount of coupling k between the two coils.
Mutual inductance is the ability of one inductor to induce a
voltage across a neighboring inductor, measured in Henrys (H).
To maximize coupling, the two coils are wound on the same core.
Coefficient of
Coupling
= the flux ( lines of force) produced by the primary linking of secondary
=the total flux produced by the primary
Coefficient coupling (k) is depends
on the physical closeness of the coils
and the type of core material that
they are wound. Also the construction
and shape of the core.
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MUTUAL INDUCTANCE Formula for Mutual Inductance
Example 1
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A transformer is a stationary electric machine which transfers electrical energy (power) from one voltage level to another voltage level.
Unlike in rotating machines, there is no electrical to mechanical energy conversion.
INTRODUCTION TO ELECTRICAL MACHINE
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INTRODUCTION TO TRANSFORMER
The Basic Transformer
A basic transformer is an electrical device constructed of two coils of wire (windings) magnetically coupled to each other so that there is a mutual inductance for the transfer of power from one winding to the other.
A schematic of a transformer
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INTRODUCTION TO TRANSFORMER
The source voltage is applied to the primary winding, and the
load is connected to the secondary winding.
The primary winding is the input winding, and the secondary
winding is the output winding.
There are three general categories of core material: air, ferrite,
and iron.
Schematic symbols based on type of core.
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INTRODUCTION TO TRANSFORMER
The amount of magnetic coupling between the primary winding and
the secondary winding is set by the type of core material and by the
relative positions of the windings.
Transformers with cylindrical-
shaped cores.
Iron-core transformer construction with
multilayer windings.
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INTRODUCTION TO TRANSFORMER Some common types of transformers.
Turns Ratio
Function of transformer stepping up or stepping down ac voltage
or currents
Planar transformer
Low-voltage transformer
Common type of small
transformers
-
Example 2
A transformer primary winding has 100 turns, and the secondary
winding has 400 turns. What is the turns ratio?
Solution:
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INTRODUCTION TO TRANSFORMER
How does a transformer work? An AC current in the primary coil creates a changing magnetic
field in the iron core.
This changing magnetic field induces a current in the secondary coil as described by Faradays Law.
Primary voltage Iron core
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INTRODUCTION TO TRANSFORMER
Direction of winding
The direction of the windings determines the polarity of the voltage
across the secondary winding (secondary voltage) with respect to the
voltage across the primary winding (primary voltage).
Phase dots indicate relative polarities of primary and secondary
voltages.
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What is a step-up transformer?
STEP-UP AND STEP DOWN TRANSFORMERS
A transformer in which the secondary voltage is greater than the
primary voltage.
The amount that the voltage is stepped up depends on the turns
ratio.
1N
N
V
V
1
2
rms1
rms2
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STEP-UP TRANSFORMERS
Applications
Power plants to increase the generated voltage and send it to high
voltage transmission lines.
To increase the voltage in order to get higher electrical field (TVs,
Radar and Microwaves,)
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Example 3
The transformer in Figure has a turns ratio of 3. What is the voltage
across the secondary winding?
Solution:
Note that the turns ratio of 3 is indicated on the schematic as 1:3. meaning that
there are three secondary turns for each primary turn.
-
What is a step-down transformer?
STEP-UP AND STEP DOWN TRANSFORMERS
A transformer in which the secondary voltage is less than the primary
voltage.
The amount by which the voltage is stepped down depends on the
turns ratio.
1N
N
V
V
1
2
rms1
rms2
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STEP DOWN TRANSFORMERS
Electrical distribution networks (to reduce the voltage from medium
voltage (10,000 V 30 000 V) to low voltage (110 V 208 V) for
different customers).
Applications
Distribution Transformers used by Hydro companies to deliver the electric energy
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STEP DOWN TRANSFORMERS
To reduce plug voltage (110 V) to lower voltages in electronic.
Equipments/ circuits such as radio, phone, laptop, adaptors,
Applications
-
Example 4
The transformer in Figure has a turns ratio of 0.2, What is the
secondary voltage?
Solution:
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LOADING THE SECONDARY WINDING
When a resistive load is connected to the secondary winding of a
transformer, the relationship of the load (secondary) current and the
current in the primary circuit is determined by the turns ratio.
Thus, for a step-up transformer, in which n is greater than 1, the
secondary current is less than the primary current.
For a step-down transformer, n is less than 1, and Isec is greater than
Ipri When the secondary voltage is greater than the primary voltage, the
secondary current is lower than the primary current and vice versa.
-
Example 5 The two transformers in Figure have loaded secondary windings. If the
primary current is 100 mA in each case. what is the load current?
SOLUTION
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IDEAL TRANSFORMER
Ideal transformer is one with perfect coupling (k=1).
Ideal transformer is a unity-coupled, lossless transformer in which
the primary and secondary coils have infinite self inductances.
Iron core transformers are close approximation to ideal transformer.
These are used in power systems and electronics.
Ideal Transformer Circuit Symbol for Ideal Transformers
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IDEAL TRANSFORMER
Relating primary and secondary quantities in an ideal transformer.
The turns ratio or transformation ratio:
nI
I
N
N
V
V
2
1
1
2
1
2
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1. A transformer primary winding has 100 turns, and the secondary
winding has winding 400 turns. What is the turns ratio?
n = Nsec / Npri = 400/100 = 4
2. A certain transformer has a turn ratio of 10. If Npri = 500, what is
Nsec?
n = 10, Npri = 500
Nsec = n X Npri = 10 X 500 = 5000
Example 5
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For an ideal transformer , the complex power (VA) in the primary winding is equal to the secondary:
P1 = V1I1 = V2I2 = P2
where, P1= power in the primary winding
P2=power in secondary winding
(This shows that the complex power supplied to the primary is
delivered to the secondary without loss, since ideal transformer is
lossless).
IDEAL TRANSFORMER
Transformer Efficiency
The efficiency () of the transformer is measure of the percentage
of the input power that delivered to the output.
100% P
P
in
out
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DC GENERATOR
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Simplified dc generator. Consist of:
A single loop of wire rotates in a permanent magnetic field
Commutator split-ring arrangement, connected at each end
of the loop.
Brushes the fixed contacts that connects wire to external
circuit.
DC GENERATOR
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DC GENERATOR
When driven by an external mechanical force the wire loop rotates
through the magnetic field and cuts through the flux lines at varying
angles.
End view of wire loop cutting through the magnetic field.
At position A the loop of wire is effectively moving parallel with the
magnetic field the rate at which it is cutting through the magnetic
flux lines is zero.
-
DC GENERATOR
As the loop moves from position A to position B the loop cuts
through the flux lines at an increasing rate.
At position B, it is moving effectively perpendicular to the magnetic
field and thus is cutting through a maximum number of lines.
As the loop rotates from position B to position C, the rate at which it
cuts the flux lines decreases to minimum (zero) at C.
From position C to position D, the rate at which the loop cuts the flux
lines increase to a maximum at D and then back to a minimum again at
A.
End view of wire loop cutting through the magnetic field.
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DC GENERATOR
Recall from Faradays law:
1. When a wire moves through a magnetic field, a voltage is
induced.
2. According to Faradays Law amount of induced voltage is
proportional to the number of loops turns in the wire and the
rate at which it is moving with respect to the magnetic field.
3. The angle at which the wire moves with respect to the magnetic
flux lines determines the amount of induced voltage because
the rate at which the wire cuts through the flux lines depends
on the angle of motion.
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DC GENERATOR
Operation of Basic DC Generator
1. Assume that the loop is in its instantaneous horizontal position, so
the induced voltage is zero.
2. As the loop continues in its rotation, the induced voltage builds up
to a maximum at position B. as shown in part (a) of the figure.
3. Then, as the loop continues from B to C, the voltage decreases to
zero at position C, as shown in part (b).
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DC GENERATOR
During the second half of the revolution ,the brushes switch to
opposite commutator sections, so the polarity of the voltage remains
the same across the output.
Thus, as the loop rotates from position C to position D and then back
to position A, the voltage increases from zero at C to a maximum at D
and back to zero at A.
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DC GENERATOR
Induced voltage over three rotations of the wire loop in the dc generator.
The induced voltage for a two-loop generator. There is much less variation in the induced voltage.
When more wire loops are added, the voltage induced across each loop are combined across the output resulting a smoother dc voltage
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DC GENERATOR
Operation of Basic DC Generator
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DC MACHINE
The direct current (dc) machine can be used as a motor or as a
generator.
DC Machine is most often used for a motor.
The major advantages of dc machines are the easy speed and
torque regulation.
However, their application is limited to mills, mines and trains.
As examples, trolleys and underground subway cars may use dc
motors.
In the past, automobiles were equipped with dc dynamos to
charge their batteries.
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DC MOTOR
Direct current (DC) motors convert the electrical energy
into mechanical motion.
They drive devices such as hoists, fan, pumps, punch-presses
and cars.
These devices may have a definite torque-speed characteristic
(such as a pump or fan ) or a highly variable one ( such as hoist
or automobile).
-
38
Fundamental characteristics of DC
Motors
N
S
Stator
Coils
N
SS
N
Rotor
Stator
S
N
S
N
N
S
End view Time 0
N
S
Stator
Coils
N
S NRotor
Stator
S
N
S
N
N
S
S
End view Time 0+
Shifting magnetic field in rotor causes rotor to be forced to turn
-
39
Nature of commutation Power is applied to armature
windings
From V+
Through the +brush
Through the commutator contacts
Through the armature (rotor) winding
Through the brush
To V-
Rotation of the armature moves the commutator, switching the armature winding connections
Stator may be permanent or electromagnet
Rotor
V-
V+Brush
Assembly
S
S
N
N
N
Stator
Stator
Comutator
V-
V+
-
LP11 40
Armature of a DC Motor
-
Figure : Cutaway view of a dc motor.
DC Machines Construction
-
DC Machines Construction
-
Motor Ratings
Some motor are rated by the torque they can
provide, others are rated by the power they are
produce.
Torque and power are different physical
parameters. If one is known, the other can be
obtained. Torque tend to rotate the object. In dc motors, torque is
proportional to the amount of flux and to the armature current.
AIKT T = Torque (newton-meter) (N-m)
K = constant
= magnetic flux (weber @ Wb)
IA = armature current ( Amperes)
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Motor Rating
Power is defined as the rate of doing work.
The equation to determine the power from
torque is given by:
TsP 105.0 P = Power in watts
T = Torque in newton-meter (N-m)
s = speed of motor
-
The torque-speed characteristic of the motor must be adapted to
the type of the load it has to drive.
DC motors are classified based on the connection between field
coil and armature coil.
i) Series wound motor
ii) Shunt wound motor
iii) Compound wound motor
iv) Separate wound motor Shunt motors
Types of Motors
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12/3/2002 BAE 4353 46
DC motor wiring topologies P
erc
en
t o
f ra
ted
Sp
ee
d
Percent of Rated Torque
120
Series
Com
pound
Shunt100
80
60
40
20
0
400300200100
0
Sh
un
t F
ield
Series Field
Sh
un
t F
ield
Series Field
Shunt
Series
Compound
Torque Speed Characteristic
-
In shunt motor, armature and filed windings are connected parallel and at same voltage.
Field winding resistance is higher compared to armature winding. High torque characteristics for wide range of speed.
Torque can be increased by increasing current in the motor. Generally field resistance is changed to achieve this. Starting torque is 1.5 times of rated torque.
To reverse the direction of the rotor, armature or field polarity is to be reversed.
DC Shunt Motor
-
DC Shunt Motor
-
Armature and field windings are connected in series. The current is same in both the windings.
Very high starting torque compared to shunt motors and very high speed at no load.
Series motor can fail on sudden removal of load and this condition is called run-away. Parabolic variation between speed and torque and nearly constant power output over a wide range.
Reversing the supply voltage has no effect on the direction of motor rotation because both field direction and armature current directions are changed.
DC Series Motor
-
DC Series Motor
-
It is a combination of shunt and series motor. Contain two coils one in series and another in parallel. Maximum speed is limited, but the speed regulation is not as good as shunt motor.
DC Compound Motor
-
1. DC motor control is achieved by changing the armature current or field current.
2. Control system is added in the low power part of the system. For example field coil of shunt motor.
3. In a series motor, control resistor is put parallel to field coil to control current in it.
4. To understand how these changes will effect the output detail study on DC motor operation is required.
DC Motor Control
-
Braking: DC motor can be stopped by switching off the power supply and let it coast. Large motors may take lot of time due to large inertia.
Electromechanical braking is used for quick slow down. In this case the stator is kept energized and it is used as generator.
It means that the output of the rotor is given to resistor or fed back to the power supply. It is very effective at high
speeds. Another method is armature current direction is changed and it is switched off when it comes to halt.
DC Motor Control
-
DC Motor Control
-
Motor efficiency
-
Comparison of a DC generator and a DC motor:
DC Generator DC Motor
No source is connected to the commutator circuit
A DC source is connected to the commutator circuit, producing current through the wire loop.
External mechanical energy is used to rotate the loop to produce an induced voltage
External electrical energy is used to rotate the loop to produce a mechanical rotation.
DC Generator Vs DC Motor
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INTRODUCTION TO MACHINE THEORY
In electrical machine, electrical energy is used to
drive machines.
All electrical machines operate on a common set
of principles operate either in alternating
current or direct current.
-
CONTENTS
Basic Principles:
CONVERSION PROCESS IN A MACHINE
MAGNETIC FIELD ENERGY
ANALYSIS OF FORCE OF ALIGNMENT
DIVISION OF CONVERTED ENERGY AND
POWER
-
Introduction
All electrical machine operate on a common set
of principles.
The most simple electrical machine involve with
linear movement (e.g. relay and contactor).
Rotating machine (e.g. motors)
-
Conversion Process In A Machine
An electromagnetic machine is one that links an
electrical energy system to another energy
system by providing a reversible mean of energy
flow in its magnetic field.
The coupling between two system is called
mutual link.
The energy transferred from one to another
system is temporarily stored in the field.
-
Conversion Process In A Machine
Energy conversion:
Mechanical to electrical energy (generator)
Electrical to mechanical energy (motor)
An electromagnetic system can develop a
mechanical force in two ways:
By alignment
By interaction
-
The force of alignment
The figure show two poles situated opposite
one to another.
A flux pass through the surfaces are said to be
magnetized surface.
They are attracted towards one another.
The force of alignment act in any direction will
increase the magnetic energy stored in the
arrangement.
It will try to bring the poles together since this
decreases the reluctance of the air gap in
magnetic circuit and hence will increase the
flux and the energy stored.
Force of attraction
Force of Attraction
-
The force of alignment
The poles are not situated opposite one to
another.
The resultant force tries to achieve greater
stored magnetic energy by two component
action:
By attraction of the poles toward one another as
before.
By aligning poles laterally
If the poles move laterally, the cross-section
area of air gap is increased and the reluctance
is reduced.
Both action attempt to align the poles to
point of maximum stored energy.
Lateral Force of Alignment
Lateral force of alignment
-
Application of force of alignment
Electromagnetic relay demonstrate the force of
alignment giving rise to linear motion.
The force of alignment can also be used to produce the
rotary motion.
i. When the coil is energized, a flux set
up in the relay core and their air gap.
ii. The surface adjacent to the air gap
become magnetized and are attracted. (
pulling the armature plate in the
direction indicated in a figure given).
i. The rotor experiences a torque due to the
magnetized rotor and pole surfaces attempting to
align themselves.
ii. Torque occurs in any rotating machine.
Alignment torque
-
The force of interaction
Advantage : simplicity in its application
Many application involving the force of
interaction to give rise the rotary motion include
synchronous and induction machines.
Rotary Machine illustrate force of interaction
By passing a current through the coil, it experiences
a force on each of the coil sides resulting in a torque
about the axis rotation.
Alignment torque
-
Method Analysis of Machine
Performance
There are two possible approaches to analysing the energy conversion. i. The so-called classical approach.
The operation of machine can be predicted from study of the machine losses.
This classical approach can be use in order to analyze the characteristic of AC Synchronous Machine, Induction Motor, DC Motor, and in motor selection and efficiency.
Disadvantage It deals almost exclusively with machine operating under steady state
conditions, thus transient response conditions are virtually ignore
( i.e. when it is accelerating and decelerating.)
The losses of each machine are different. It follows that each type of machine requires to be separately analysed.
-
Method Analysis of Machine
Performance
ii. The generalized-machine approach.
This approach depends on a full analysis of the coupling field as observed from terminals of the machine windings.
The losses are recognized as necessary digressions from the main line of the analysis.
The coupling field is described in term of mutual inductance.
The measured quantities are voltage, current, power, frequency, torque and rotational speed, from which may be derived the resistance and inductance values for the coils.
It is possible to analyze to performance both under steady state and transient conditions.
-
Air Gap on Magnetic circuit
Let us consider the effects that an
air gap has on magnetic circuit.
The spreading of the flux line
outside the common area of core
for the air gap known as fringing.
Ignore the fringing effect and
assume the flux distribution to be
as in Figure (b).
g
g
gA
B
bygiven is gapair theofdensity Flux
Where;
g = core Ag = Acore
-
In most practical applications, the permeability
of air is taken to be equal to that of free space.
Magnetizing force of the air gap determined by
o
g
g
BH
Air Gap on Magnetic circuit
-
Magnetic Field Energy
The energy in magnetic field is given by
Energy storage
However, there are a number of way in which the inductance can be expressed.
These expressions can be substituted in the energy relation to give
Where;
= magnetic flux linkage, electric flux
= magnetic flux
F= force
i = Current
2
2
1Liw f
l
AN
S
N
ii
NL r
022
SFiw f2
1
2
1
2
1
All of these expressions for the energy
depend on the flux and the m.m.f being
directly proportional, i.e. the inductance is
constant.
-
Magnetic Field Energy
In the case of an air gap, the B/H characteristic
is straight, the energy stored given by
Fw
lBHw
l
BHw
f
f
f
2
1
A x 2
1
length andA area sectional-cross a has gapair theif
gapair of x volume2
1
Wf
B
H
The stored energy density is thus given by
o
f
Bw
2
2
-
Simple analysis of force of
alignment
Consider the force alignment between 2 poles of
the magnetic circuit.
Let there be a flux in the air gap and let there be
no fringing of the flux.
The uniform flux density in the air gap is given
by
CSA
A
Flux
And force F
x
AB
-
The poles separated by a small distance dx. There is
mechanical experience by poles and the work done is given
by
Assume the magnetic core is ideal ( infinity permeability and
no m.m.f to create a magnetic field in it)
The air gap has been increase by a volume A.dx
Since the flux density is constant, energy density must remain
unchanged.
Therefore, the increase in the stored energy
Simple analysis of force of
alignment
dxB
dWo
f A.x 2
2
dxFdWm .
-
Simple analysis of force of
alignment
Since the system is ideal and the motion has
takes slowly form one point to another, this
energy must be due to the input of mechanical
energy
o
ABF
2
2
dxAB
dxFo
.2
.2
fm dWdW
Force of magnetic field
-
Example 5
An electromagnetic is made using a horseshoe core as shown in Fig.36.14. the
core has an effective length of 600 mm and a cross-sectional area of 500 mm2.
A rectangular block of steel is held by the electromagnets force of alignment
and a force of 20 N is required to free it. The magnetic circuit through the
block is 200 mm long and the effective cross-sectional area is again 500 mm2.
the relative permeability of both core and block is 700. if the magnetic is
energized by a coil of 100 turns, estimate the coil current.
20 N
-
1. Principles of Electric Circuits; Conventional Current version, 8th Edition, Pearson, Floyd.
2. Fundamental of Electric Circuits. 2nd Edition, McGrawHill, Alexander & Sadiku.
3. Electrical Machines, Drives, And Power System, 6th Edition, Pearson Prientice Hall, Wildi.
Further reading