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FUNDAMENTALS OF ELECTRICAL
ENGINEERING
[ ENT 163 ]
LECTURE #10
ELECTRICAL MACHINES
HASIMAH ALI
Programme of Mechatronics,
School of Mechatronics Engineering, UniMAP.
Email: [email protected]
CONTENTS
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INTRODUCTION TO TRANSFORMER
MUTUAL INDUCTANCE
COEFFICIENT OF COUPLING
IDEAL TRANSFORMER
DC GENERATOR
INTRODUCTION TO TRANSFORMER
 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
 A transformer is a static device and
all currents and voltages are AC.
 The transfer of energy takes place
through the magnetic filed.
INTRODUCTION TO TRANSFORMER
 When two loops with or without contacts between them affect each
other through the magnetic field generated by one of them, they are
said to be magnetically coupled.
 Transformer is an electrical device designed on the basis of the
concept of magnetically coupling. It uses magnetically coupled coils to
transfer energy from one circuit to another.
 Function of transformer – stepping up or stepping down ac voltage or
currents
INTRODUCTION TO TRANSFORMER
Transformer Principles
 It has 2 electric circuits called
primary and secondary.
 A magnetic circuit provides the link
between primary and secondary.
 When an AC voltage is applied to
the primary winding (Vp) of
transformer, an AC current will
result (Ip). Ip sets up a time-varying
magnetic flux in the core.
 A voltage is induced to the
secondary circuit (Vs) according
to the Faraday’s law.
Primary voltage
Iron core
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.
 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
 Coefficient of coupling, k, between the primary and secondary
windings of a transformer is the ratio of the flux ( lines of force)
produced by the primary linking of secondary ( 1-2) to the total flux
produced by the primary ( 1):
k=
1-2/ 1
 E.g. if half of the total flux produced by coil 1 links coil 2, then k=0.5.
 Greater value of k means that more voltage is induced in coil 2 for a
certain rate of change of current in coil 1.
 k- depends on the physical closeness of the coils, the type of core
material on which they are wound, the construction and shape of the
cores.
COEFFICIENT OF COUPLING
Example:
One coil produces a total magnetic flux of 50µW, and 20µW link coil
2. What is the coefficient of coupling k?
IDEAL TRANSFORMER
 Transformer is a magnetic device, constructed of four-terminal device
comprising two magnetically coupled coils which have the mutual
inductance phenomenon.
 One coil – primary winding ( connected to the voltage source), other
coil – secondary winding (connected to the load):
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.
V2 N 2 I1

 n
V1 N1 I 2
IDEAL TRANSFORMER
 An important characteristic in ideal transformer = turns ratio/
transformation ratio n:
V2 N 2 I1

 n
V1 N1 I 2
Where,
V1 = primary voltage
V2 = secondary voltage
N1 = number of turns of the primary winding
N2 = number of turns of the secondary winding
I1 = primary current
I2 = secondary current
IDEAL TRANSFORMER
1. A transformer primary winding has 100 turns, and the secondary
winding has winding 400 turns. What is the turns ratio?
2. A certain transformer has a turn ratio of 10. If Npri = 500, what is
Nsec?
IDEAL TRANSFORMER
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
IDEAL TRANSFORMER
 For an ideal transformer , the complex power (VA) in the primary winding is
equal to the secondary:
S1 = V1I1 = V2I2 =S2
where, S1= power in the primary winding
S2=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).
 There are two types of a transformer:
 A step-down transformer
 A step-up transformer
IDEAL TRANSFORMER
Step-down Transformer
A step-down transformer is one whose secondary is less than its primary voltage
 Applications:
 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).
 To reduce plug voltage (110 V) to
lower voltages in electronic.
Equipments/ circuits such as radio,
phone, laptop, adaptors,…
Distribution Transformers used
by Hydro companies to deliver
the electric energy
IDEAL TRANSFORMER
Step-up Transformer
A step-up transformer is one whose secondary is greater than its primary voltage
 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,…)
DC GENERATOR
 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
DC GENERATOR
 When driven by an external mechanical force – loop rotates through the
magnetic field and cuts through the flux lines at varying angles:
 At A – loop is effectively moving parallel with the magnetic field – the rate
at which it is cutting through the magnetic flux lines is zero.
 From A to B – the loop cuts through the flux lines at an increasing rate.
 From B to C – the rate at which it cuts the flux lines decreases to
minimum (zero) at C.
N
D
C
A
B
S
DC GENERATOR
 From C to D – the rate at which the loop cuts the flux lines increases to
a maximum at D, and then back to minimum again at A.
 Recall from Faraday’s law:
 When a wire moves through a magnetic field, a voltage is induced.
 According to Faraday’s 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.
 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.
DC GENERATOR
 Operation:
 Assume that the loop is in its instantaneous horizontal position
(induced voltage = 0).
 As the loop continuous in its rotation, the induced voltage builds up
to a maximum at B.
 As the loop continuous to rotate from B to C, the voltage
decreases to zero at C.
 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 D and then back to A,
the voltage increase from zero at C to a maximum at D and back to
zero at A.
DC GENERATOR
DC GENERATOR
DC GENERATOR
 Final output (shows how the induced voltage varies as a wire in a dc
generator goes through several rotations)
DC GENERATOR
 Voltage = dc voltage (polarity does not change)
 When more wire loops are added, the voltage induced across each
loop are combined across the output – resulting a smoother dc voltage.
DC GENERATOR
 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.
FURTHER READING
1. Electrical Machines, Drives, And Power System, 6th Edition,
Pearson Prientice Hall, Wildi.
2. Principles of Electric Circuits; Conventional Current version, 8th
Edition, Pearson, Floyd.