Electrical machines lecture notes

AC Generator
By
Eng. Jean De Dieu IYAKAREMYE
(Msc, Bsc )

Components of an AC generator:
a. Field
b. Armature
c. Prime mover
d. Rotor
 e. Stator
f. Slip rings

Field
The field in an AC generator consists of coils of
conductors within the generator that receive a voltage
from a source (called excitation) and produce a magnetic
flux.
The magnetic flux in the field cuts the armature to produce
a voltage. This voltage is ultimately the output voltage of
the AC generator.

Armature
The armature is the part of an AC generator in which
voltage is produced.
This component
consists of many coils of wire that are large enough
to carry the full-load current of the generator.

Prime Mover
The prime mover is the component that is used to drive
the AC generator.
The prime mover may be any type of rotating machine,
such as a diesel engine, a steam turbine, or a motor.

Rotor
The rotor of an AC generator is the rotating component of
the generator, as shown in Figure 1.
The rotor is driven by the generator’s prime mover, which
may be a steam turbine, gas turbine, or diesel engine.
Depending on the type of generator, this component may
be the armature or the field.
 The rotor will be the armature if the voltage output is
generated there; the rotor will be the field if the field
excitation is applied there.

Stator
The stator of an AC generator is the part that is stationary
(refer to Figure 1).
 Like the rotor, this component may be the armature or the
field, depending on the type of generator.
The stator will be the armature if the voltage output is
generated there; the stator will be the field if the field
excitation is applied there.

Slip Rings
Slip rings are electrical connections that are used to
transfer power to and from the rotor of an AC generator
(refer to Figure 1).
The slip ring consists of a circular conducting material
that is connected to the rotor windings and insulated from
the shaft.
 Brushes ride on the slip ring as the rotor rotates.
 The electrical connection to the rotor is made by
connections to the brushes.
Slip rings are used in AC generators because the desired
output of the generator is a sine wave.

Slip Rings
In a DC generator, a commutator was used to provide an
output whose current always flowed
in the positive direction, as shown in Figure 2.
 This is not necessary for an AC generator.
Therefore, an AC generator may use slip rings, which will
allow the output current and voltage to oscillate through
positive and negative values.
This oscillation of voltage and current takes the shape of a
sine wave.

Figure 2 - Comparison of DC and AC Generator
Outputs

Theory of Operation
 The strong magnetic field is produced by a current flow through
the field coil of the rotor.
 The field coil in the rotor receives excitation through
the use of slip rings and brushes.
 Two brushes are spring-held in
contact with the slip rings to provide the continuous
connection between the field coil and the external excitation
circuit.
 The armature is contained within the windings of the stator and is
connected to the output.

Theory of Operation
 Each time the rotor makes one complete revolution, one
complete cycle of AC is developed.
 A generator has many turns of wire wound into the slots of the
rotor.
 The magnitude of AC voltage generated by an AC generator is
dependent on the field strength and speed of the rotor.
 Most generators are operated at a constant speed; therefore, the
generated voltage depends on field excitation, or strength.

A simple AC generator consists of:
 (a) a strong magnetic field,
 (b) conductors that rotate through that magnetic field, and
 c) a means by which a continuous connection is
provided to the conductors as they are rotating (Figure
3).

The frequency of the generated voltage is dependent on the number of
field poles and the speed at which the generator is operated,
as indicated in Equation .
f = NP/120
where:
f = frequency (Hz)
P = total number of poles
N = rotor speed (rpm)
120 = conversion from minutes to seconds and from poles to
pole pairs
The 120 in Equation is derived by multiplying the following conversion
factors.
60 seconds x 2 poles
1 minute pole pair
In this manner, the units of frequency (hertz or cycles/sec.) are derived.

1.) Internal Voltage Drop
 The load current flows through the armature in all AC generators.
The armature has some amount of resistance and inductive
reactance.
 The combination of these make up what
is known as the internal resistance, which causes a loss in a
n AC generator.
 When the load
current flows, a voltage drop is developed across the internal
resistance.
 This voltage drop subtracts from the output voltage and,
therefore, represents generated voltage and power that is
lost and not available to the load.

The voltage drop in an AC generator can be found
using Equation.
Voltage drop = IaRa IaXLa
where :
Ia = armature current
Ra = armature resistance
XLa = armature inductive reactance

2.) Hysteresis Losses
 Hysteresis losses occur when iron cores in an AC generat
or are subject to effects from a magnetic field.
 The magnetic domains of the cores are held in alignment
with the field in varying numbers, dependent upon field
strength.
 The magnetic domains rotate, with respect to
the domains not held in alignment, one complete turn duri
ng each rotation of the rotor.
 This
rotation of magnetic domains in the iron causes friction a
nd heat.

2.) Hysteresis Losses
The heat produced by this friction is called
magnetic hysteresis loss.
After the heat-treated silicon steel is formed to the
desired shape, the laminations are heated to a dull red
and then allowed to cool.
This process, known as annealing, reduces hysteresis
losses to a very low value.
To reduce hysteresis losses, most AC armatures ar
e constructed of heat-treated silicon steel, which
has an inherently low hysteresis loss.

3.)Mechanical Losses
 Rotational or mechanical losses can be caused by bearing f
riction, brush friction on the
commutator, and air friction (called windage), which is cau
sed by the air turbulence due to armature rotation.
 Careful maintenance can be instrumental in keeping bearing
friction to a minimum.
 Clean bearings and proper lubrication are essential to the
reduction of bearing friction.
 Brush friction is reduced by ensuring: proper brush seating,
proper brush use, and maintenance of proper brush tension.
 A smooth and clean commutator also aids in the reduction
of brush friction.
 In very large generators, hydrogen is used within the generator
for cooling; hydrogen, being less dense than air, causes less
windage losses than air.

Efficiency
Efficiency of an AC generator is the ratio of the useful
power output to the total power input.
Because any mechanical process experiences some losses,
no AC generators can be 100 percent efficient.
Efficiency of an AC generator can be calculated using
Equation.
Efficiency =(Output /Input )x 100

Example:
Given a 5 hp motor acting as the prime mover of a g
enerator that has a load demand of 2 kW, what is the
efficiency of the generator?
Solution: In order to calculate efficiency, the input and
output power must be in the same
units. As described in Thermodynamics, the horsepow
er and the watt are equivalent units of power.
Input Power = 5 hp x 746W hp=3730 W
Output Power = 2 kW =2000 W
Efficiency =(output/input)x100= (2000 W /3730 W)=
0.54 x 100 =54%

Ratings
Typical name plate data for an AC generator (Figure 4) includes:
 (1) manufacturer;
 (2) serial number and type number;
 (3) speed (rpm), number of poles, frequency of output,
number of phases, and maximum supply voltage;
 (4) capacity rating in KVA and kW
at a specified power factor and maximum output voltage;
 (5) armature and field current per phase; and
 (6) maximum temperature rise.
Power (kW) ratings of an AC generator
 are based on the ability of the prime mover to
overcome generator losses and the ability of
the machine to dissipate the internally generated heat.
 The current rating of an AC generator is based on the insulation
rating of the machine.

Figure 4 AC Generator Nameplate Ratings

Types of AC Generators
 there are two types of AC generators:
1.) the stationary field, rotating armature;
2.) and the rotating field, stationary armature.
 Small AC generators usually have a stationary
field and a rotating armature (Figure 5).
 One important disadvantage to this arrangement is that the slip-ring
and brush assembly is in series with
the load circuits and, because of worn or dirty components, may
interrupt the flow of current.

Figure 5: Stationary Field, Rotating Armature
AC Generator

 If DC field excitation is connected to the rotor,
the stationary coils will have AC induced into them
(Figure 6).
 This arrangement is called a rotating field, stationary
armature AC generator.
The rotating field, stationary
armature type AC generator is used when large power
generation is involved.
 In this type of generator, a DC source is supplied
to the rotating field coils, which
produces a magnetic field around the rotating element.
 As the rotor is turned by the prime mover, the field will
cut the conductors of the
stationary armature, and an EMF will be induced into
the armature windings.

 This type of AC generator has several advantages over the
stationary field, rotating armature AC generator:
(1) a load can be connected to the armature without
moving contacts in the circuit;
(2) it is much easier to insulate stator fields than
rotating fields; and
(3) much higher voltages and currents can be
generated.

Figure 6: Simple AC Generator - Rotating Field,
Stationary Armature

Three-Phase AC Generators
The principles of a three-phase generator are basically
the same as that of a single-phase generator, except that
there are three equally-spaced windings and three
output voltages that are all 120° out of phase with one
another.
 Physically adjacent loops (Figure 7) are separated by 60° of
rotation; however, the loops are
connected to the slip rings in such a manner that
there are 120 electrical degrees between phases.
The individual coils of each winding are combined and
represented as a single coil. The significance of
Figure 7 is that it shows that the three-phase
generator has three separate armature windings that are
120 electrical degrees out of phase

Figure 7 Stationary Armature 3f Generator

AC Generator Connections
As shown in Figure 7, there are six leads from the
armature of a three-phase generator, and the output is
connected to an external load.
In actual practice, the windings are connected together, and
only three leads are brought out and connected to the external
load.
Two means are available to connect the three armature
windings.
In one type of connection, the windings are connected in
series, or delta-connected (D) (Figure 8).

In a delta-connected generator, the voltage between any
two of the phases, called line voltage, is the same as the
voltage generated in any one phase.
As shown in Figure 9, the three phase voltages are equal,
as are the three line voltages.
The current in any line is times the phase current. You
can 3 see that a delta-connected generator provides an
increase in current, but no increase in voltage.

Figure 9 : Characteristics of a Delta-Connected
Generator

An advantage of the delta-
connected AC generator is that if one phase beco
mes damaged or Figure 9 Characteristics of a Delta-
Connected Generator open, the remaining two phases
can still deliver three-phase power.
The capacity of the generator is reduced to 57.7% of
what it was with all three phases in operation.

 In the other type of connection, one of the Connection
leads of each winding is connected, and the remaining
three leads are connected to an external load.
 This is called a wye connection (Y) (Figure 10).
 The voltage and current characteristics of the wye-
connected AC generator are
opposite to that of the delta connection.
 Voltage between any two lines in a wye-
connected AC generator is 1.73 (or ) 3
times any one phase voltage, while line currents are
equal to phase currents.
 The wye-connected AC generator provides an increase in
voltage, but no increase in current (Figure 11).

Figure 11: Characteristics of a Wye-
Connected AC Generator

An advantage of a wye-connected AC generator is that
each phase only has to carry 57.7% of line voltage and,
therefore, can be used for high voltage generation.

45
AC Motors
AC motors convert AC electrical energy to Mechanical energy.

46
AC Motors
 AC motors:
1. the armature of rotor is a magnet (different to DC motors).
2. the stator is formed by electromagnets (like in DC motors).

47
Effects of AC Supply on Magnetic Poles
 Consider the rotor to be a permanent magnet.
 Current flowing through conductors energize the magnets and develop N
and S poles.
 The strength of electromagnets depends on current.
 First half cycle current flows in one direction.
 Second half cycle it flows in opposite direction.
As AC voltage changes, the poles alternate.

48
Using AC Supply to Make an Elementary
Motor (1)
 Consider the AC voltage at 0 degrees, then, no current will flow, and
there is no magnetism.

49
Motor (2)
 As voltage increases, current starts to flow and electromagnets gain
strength and North and South poles appear.
 (Use left hand rule to find poles).
 The rotor magnet is pushed CW, and the rotor and motor starts to
rotate.

50
Motor (3)
 When voltage decreases, the current decreases also, the electromagnet
loses the strength, and when V=0 there is no magnetism.

51
Motor (4)
 Now, AC voltage builds up as part of the negative cycle.
 Then, current flows in opposite direction, and the magnets reverse
polarity.
 Therefore, the CW rotation continues.

52
Motor (5)
 This process is repeated over and over, as AC voltage goes through its
cycles, and we have continuous rotation.

53
AC Motor Rotation The whole
picture

54
Limitation of the Elementary Motor
 The initial position of the rotor determines the direction of the motor
rotation.
 Indicate the rotation in the figures below:

55
Practical AC Motor
 By adding another pair of electromagnets the limitation mentioned
before is removed.
 Two electromagnets = Vertical & Horizontal
 Two phases with phase difference = 90 deg.

56
Effect of Two Pole-Pairs
(Observe the pole rotation)

57
Operation of the Practical AC Motor
 Fig. of page 124 shows a CCW rotation
Can you see it?

58
Magnetic Poles Revolve in AC Motors
 From the previous slide we can see that the poles rotate around the
circumference of the motor.
 The rotor, no matter how it is positioned at rest, will be locked-in with
the magnetic field and will turn in one direction only.
 (Same rotation as the poles).

59
Phase Splitting Method (1)
 So, two voltage sources with 90 degree phase connected to
electromagnets make the rotor turn.
 Question is: Can we do the same using only one voltage
source?

60
Phase Splitting Method (2)
 The answer is yes!
 Because we can use inductors and capacitors to produce a
voltage out of phase with the source!

61
Reactor Start AC Motor
(One phase + Inductor)
 Two parallel branches connected to the power supply.
 First branch: Start winding through a centrifugal switch.
 Second branch: Run winding (through an inductor).
 The current in the second branch lags the current in the first branch
(Remember “ELI”).
 This phase difference makes motor work.

62
Reactor Start AC Motor
The Centrifugal Switch

63
Capacitor Start AC Motor
(One phase + Capacitor)
 Here the capacitor provides the phase difference.
 The difference is that the current in the star winding leads the current
in the run winding (ICE).
 Similar effect as with the inductor, but it creates a motor with higher
starting power.
 Refrigerators, compressors, air conditioners
8

64
Three Types of Capacitor Start Motors
1. Capacitor Start (disconnects capacitor after motor
speed picks up)
2. Capacitor Run (Keeps the capacitor connected during
the operation of the motor, in order to keep the electric
power consumption low)
3. Capacitor Start-Run (uses two capacitors, one for
starting and one for running. This further improves
Power Consumption)

65
Synchronous Speed
 AC motors always rotate with the speed of their revolving magnetic
field.
 The speed of the revolving poles is the maximum possible speed of
rotation of the motor.
 It is called “Synchronous Speed”.

66
Motor Construction
The Stator
 The stator forms a hollow cylinder with coils of insulated wire inserted
into slots of the stator core.
 The coils, plus the steel core form the electromagnets.

67
Motor Construction
The Rotor
 There are two types of motor rotors:
 The wound rotor
 The squirrel cage
 The wound rotor has coils of wire wound in the slots of the rotor
(Similar to generator coils).
 The “Squirrel cage” consists of bars of copper or aluminum electrically
connected at each end with conducting rings.
 As the rotor rotates inside a magnetic field, it receives
electromagnetic induction, then current flows and form the rotor
electromagnet.
0

68
Types of Motor Enclosures
1. ODP – Open Drip Proof
2. TENV – Totally Enclosed Non-Ventilating
3. TEFC – Totally enclosed Fan Cooled
4. XP – Explosion Proof

69
 ODP – Open Drip Proof
 Air flows through motor (fan blades help flow)
 Used in environments free from contaminants

70
 TENV – Totally Enclosed Non-Ventilating
 Protect motor from corrosive and harmful elements
 Frame fins help to dissipate heat

71
 TEFC – Totally enclosed Fan Cooled
 Similar to TENV except has external fan for cooling

72
 XP – Explosion Proof
 Similar to TEFC but enclosures are cast iron

73
Slip
 Slip is associated with synchronous speed.
 If the motor turned at the same RPM as the magnetic field, there
would be no relative motion between the rotor and the field.
 Therefore, no current would be induced into the rotor, and no
magnetic field would exist.
Rotor speed < synchronous speed
Slip = synchronous speed – rotor speed
% slip = ( Ns – Nr / Ns ) 100

74
Three Phase AC Motor
 It has three pairs of electromagnets, connected to one of the three
phases of the power supply.
 It provides a lot higher power that what single phase motor can deliver.

75
AC Motor Data Plate
 Each motor has a plate mounted on its frame, with electrical and
mechanical information.

Summary AC Motors
 AC motors can be divided into two main forms:
 synchronous motors
 induction motors
 High-power versions of either type invariably operate from a
three-phase supply, but single-phase versions of each are
also widely used – particularly in a domestic setting
23.7

 Synchronous motors
 just as a DC generator can be used as a DC motor, so AC generators (or
alternators) can be used as synchronous AC motors
 three phase motors use three sets of stator coils
 the rotating magnetic field drags the rotor around with it
 single phase motors require some starting mechanism
 torque is only produced when the rotor is in sync with the rotating
magnetic field
 not self-starting – may be configured as an induction motor until
its gets up to speed, then becomes a synchronous motor

 Induction motors
 these are perhaps the most important form of AC motor
 rather than use slip rings to pass current to the field coils
in the rotor, current is induced in the rotor by transformer
action
 the stator is similar to that in a synchronous motor
 the rotor is simply a set of parallel conductors shorted
together at either end by two conducting rings

 A squirrel-cage induction motor

 In a three-phase induction motor the three phases
produce a rotating magnetic field (as in a three-phase
synchronous motor)
 a stationary conductor will see a varying magnetic field
and this will induce a current
 current is induced in the field coils in the same way that
current is induced in the secondary of a transformer
 this current turns the rotor into an electromagnet which
is dragged around by the rotating magnetic field
 the rotor always goes slightly slower than the magnetic
field – this is the slip of the motor

 In single-phase induction motors other techniques
must be used to produce the rotating magnetic field
 various techniques are used leading to various forms of
motor such as
 capacitor motors
 shaded-pole motors
 such motors are inexpensive and are widely used in
domestic applications

Universal Motors
 While most motors operate from either AC or DC, some can
operate from either
 These are universal motors and resemble series-wound
DC motors, but are designed for both AC and DC operation
 typically operate at high speed (usually > 10,000 rpm)
 offer high power-to-weight ratio
 ideal for portable equipment such as hand drills and
vacuum cleaners
23.8

Electrical Machines – A Summary
 Power generation is dominated by AC machines
 range from automotive alternators to the synchronous
generators used in power stations
 efficiency increases with size (up to 98%)
 Both DC and AC motors are used
 high-power motors are usually AC, three-phase
 domestic applications often use single-phase induction motors
 DC motors are useful in control applications
23.9

Key Points
 Electrical machines include both generators and motors
 Motors can usually function as generators, and vice versa
 Electrical machines can be divided into AC and DC forms
 The rotation of a coil in a uniform magnetic field produces a sinusoidal
e.m.f. This is the basis of an AC generator
 A commutator can be used to produce a DC generator
 The magnetic field in an electrical machine is normally produced
electrically using field coils
 DC motors are often similar in form to DC generators
 Some forms of AC generator can also be used as motors
 The most widely used form of AC motor is the induction motor

Course Code_52 Subj. Code 5261 87SLIDE
ELECTRICAL MACHINES-I EXIT
GENERALISED TREATMENT OF ELECTRICAL MACHINES
D.C MOTORS

LECTURE 5 OF 40
APPLICATION CONCEPT OF ALIGNMENT OF TWO MAGNETIC FIELDS
DC MACHINES
+ +
+
FIELD
POLES
N
S
FIELD
WINDING
ARMATURE
CONDUCTORS
ARMATURE
YOKE
BRUSH
MAIN FIELD AXIS
BRUSH
AXIS + _
+
+
+
+
.
.
.
.
+
+

LECTURE 5 OF 40
DC MACHINES
N
S

Te
A B
_
+ 









S N
( GENERATOR )
ELECTRICAL
LOAD
Tm

LECTURE 5 OF 40
DC MACHINES
N
S

Te
A B
_
+ 








S N
TL
( MOTOR )
v
DC
SUPPLY

LECTURE 5 OF 40
DC MACHINES
Electrical machines can be classified
mainly into DC Machines and AC
Machines. Slide no 1 shows the view
of a dc machine. For simplicity , only
main component parts have been
shown.

LECTURE 5 OF 40
DC MACHINES
The field windings are shown as
excited from external source.The
polarity of electro-magnetic field will
depend upon the direction of field
current as shown in the fig. of slide
no.1 .

LECTURE 5 OF 40
DC MACHINES
The armature carries conductors in
side the slots.Two brushes are placed
at the right angle to the main field axis.
The brushes are stationary whereas
armature is free to rotate.

LECTURE 5 OF 40
DC MACHINES
When the armature is rotated in the
magnetic field, an e.m.f will be induced
in the armature conductors.The
direction of the induced e.m.f can be
found by applying Fleming’s Right
Hand Rule.

LECTURE 5 OF 40
DC MACHINES
The direction of induced e.m.f will
depend upon the direction of rotation
of armature , if polarity of field poles to
be kept unchanged.When load is
connected across the armature
terminals , the current will flow through
the armature circuit.

LECTURE 5 OF 40
DC MACHINES
The direction of current will be same as
that of induced e.m.f. The armature will
now be considered as electro-magnet
and its polarity is shown in the fig. of
slide no. 2 .The electro-magnetic
torque Te will be developed in the anti-
clock wise direction as shown in the
fig.of slide no. 1 and 2.

LECTURE 5 OF 40
DC MACHINES
The magnitude of Te will depend on the
strength of the field poles and armature
field which further depends upon the
currents flowing through the respective
windings. As the external load on the
generator is increased, the magnitude
of Te increases.

LECTURE 5 OF 40
DC MACHINES
As Te acts in the opposite direction to
the applied mechanical torque, more
torque will be required through the
prime mover to maintain the speed of
armature .

LECTURE 5 OF 40
DC MACHINES
The direction of currents in the upper
conductors in the armature are
indicated by ‘dots’ and conductors in
lower half of armature are indicated by
‘cross’ .

LECTURE 5 OF 40
DC MACHINES
The brush ‘B’ will collect dot currents
and brush ‘A’ will collect cross currents
as the armature continues to rotate in
clockwise direction. In the out put
circuit, across terminals ‘A’ and ‘B’,
current will flow in one direction.

LECTURE 5 OF 40
DC MACHINES
The dc machine shown in fig. of slide
no. 2 is working as generator.The same
machine will work as motor , if the
armature is provided with electric
supply as shown in fig. of slide no. 3 .

LECTURE 5 OF 40
DC MACHINES
The armature is connected across a
supply voltage ‘V’ and the field
windings are excited from the same
supply or from any external dc
source.The magnetic polarities due to
the current in armature winding will be
as shown in fig. of slide no. 3 .

LECTURE 5 OF 40
DC MACHINES
The electro-magnetic torque Te will be
developed in the anti-clockwise
direction as opposite poles of armature
field and main field will attract each
other. The armature will rotate in anti-
clockwise direction due to Te .

LECTURE 5 OF 40
DC MACHINES
To reverse the direction of rotation of
armature, either the direction of current
in the field winding or armature
winding will have to be reversed.If the
direction of currents in both the
windings are reversed, direction of
rotation of armature will be
unchanged.

LECTURE 5 OF 40
DC MACHINES
As the mechanical load on the
armature i.e. rotor shaft represented by
load torque TL is increased, more and
more electro-magnetic torque will be
developed by the armature to balance
the mechanical torque requirements for
which the armature will draw more
current from the supply mains.

B
Q
LOAD
A
B
AA
P

MAGNETIC FIELD
0o

B
Q
LOAD
A
B
A
P

MAGNETIC FIELD
_+
e
30o
t

B
Q
LOAD
A
B
A
P

MAGNETIC FIELD
+ _
e
60o
t

Q
LOAD
A
B
A

MAGNETIC FIELD
B P
+ _
e
90o
t

Q
LOAD
BA
A
A P

MAGNETIC FIELD
B
+ _
e
120o
t

Q
LOAD
A
B
A
A
P

MAGNETIC FIELD
B
+ _
e
150o
t

A
Q
LOAD
A
B
AB
P

MAGNETIC FIELD
+
e
180o
t

A
Q
LOAD
A
B
B
P

MAGNETIC FIELD
+ _
e
210o
t

A
Q
LOAD
B
A
B
P

MAGNETIC FIELD
+ _
e
240o
t

Q
LOAD
B
A
B

MAGNETIC FIELD
A P
+ _
e
270o
t

B
Q
LOAD
AB
AA
P

MAGNETIC FIELD
+ _
e
300o
t

B
Q
LOAD
B
A
AA
P

MAGNETIC FIELD
+ _
e
330o
t

B
Q
LOAD
B
A
AA
P

MAGNETIC FIELD
e
360o
t

MAIN CONSTRUCTIONAL FEATURES
LECTURE 7 OF 40
DC MACHINES
INTODUCTION
A DC machine is an electro-mechanical
energy conversion device. It can convert
Mechanical power into Electrical Power.
When output electrical power is DC , it is
called DC Generator. When it converts
DC electrical power into mechanical
power , it is known as DC Motor.

LECTURE 7 OF 40
DC MACHINES
3. FIELD or EXCITING COILS
1. BODY OR MAGNETIC FRAME OR YOKE
2. POLE CORE AND POLE SHOES
4. ARMATURE CORE
5. ARMATURE WINDING
6. COMMUTATOR

LECTURE 7 OF 40
DC MACHINES
9. BEARINGS
7. BRUSHES
8. END HOUSINGS
10. SHAFT

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DC MACHINES
Body / Yoke
Field Winding
Shaft
Commutator
Armature
Pulley
Brush
Brush
holder
Field Core
Bearing
Click here to see photograph
End Housing

LECTURE 7 OF 40
DC MACHINES
+
-
YOKE
ARMATURE
COMMUTATOR
SHAFT
BRUSH
FIELD POLE
& COIL

LECTURE 7 OF 40
DC MACHINES
The outer cylindrical
frame to which main
poles and inter poles are
fixed and by means of
the machine is fixed to
the foundation is called
YOKE.
1. MAGNETIC FRAME or YOKE :

LECTURE 7 OF 40
DC MACHINES
It serves two purposes:
a) It provides
mechanical protection
to the inner parts of the
machines.

LECTURE 7 OF 40
DC MACHINES
b) It provides a low
reluctance path for the
magnetic flux.
The yoke is made of
cast iron for smaller …

LECTURE 7 OF 40
DC MACHINES
machines and cast steel
or fabricated rolled
steel for larger
machines.

LECTURE 7 OF 40
DC MACHINES
The pole core and pole
shoes are fixed to the
yoke by bolts. They
serves the following
purpose :
a) They support
the field or exciting
coils.
2. POLE CORE AND POLE SHOES :
POLE CORE

LECTURE 7 OF 40
DC MACHINES
b) They distribute the
magnetic flux on the
armature periphery
more uniformly.

LECTURE 7 OF 40
DC MACHINES
c) The pole shoes have
larger X- section, so,
the reluctance of the
magnetic path is
reduced. The pole core

LECTURE 7 OF 40
DC MACHINES
and pole shoes are
made of laminated
steel assembled by
riveting together under
hydraulic pressure.

LECTURE 7 OF 40
DC MACHINES
Field coils or exciting
coils are used to
magnetise the pole core.
Enameled copper wire is
used for the construction
of these coils.When direct
3. FIELD or EXCITING COILS :

LECTURE 7 OF 40
DC MACHINES
current is passed through
these coils/ winding, it
sets up the magnetic field
which magnetise the pole
core to the reqd. flux.
3. FIELD or EXCITING COILS :

LECTURE 7 OF 40
DC MACHINES
Armature is a rotating part of the DC
machine, reversal of flux takes place,
so hysteresis losses are produced.
To minimise this loss, silicon steel is
used for the construction.
4. ARMATURE CORE:

LECTURE 7 OF 40
DC MACHINES
The rotating armature cuts the main
magnetic field , therefore an e.m.f is
induced in the armature core.This e.m.f
circulates eddy currents in the core
which results in eddy current loss in it.
4. ARMATURE CORE:

LECTURE 7 OF 40
DC MACHINES
The armature core is laminated to reduce
the eddy current loss.
Armature core serves the following
purposes:
a) It houses the conductors in the slots.
b) It provides an easy path for magnetic
flux
4. ARMATURE CORE:

LECTURE 7 OF 40
DC MACHINES
The no. of
conductors in form
of coils placed in
the slots of the
armature and
suitably inter
connected are
called winding .
5. ARMATURE WINDING ;
ARMATURE WINDING

LECTURE 7 OF 40
DC MACHINES
This is the
armature winding
where conversion
of power takes
place i.e. in case
of generator ,

LECTURE 7 OF 40
DC MACHINES
mechanical power
is converted into
electrical power
and in case of a
motor, electrical

LECTURE 7 OF 40
DC MACHINES
power is
converted into
mechanical
power.

LECTURE 7 OF 40
DC MACHINES
Depending upon the types of inter
connection. of coils , the winding can
be classified into two types;
i) Lap Winding;
The conductors/coils are
connected in such a way that no of
parallel paths are equal to no. of poles.

LECTURE 7 OF 40
DC MACHINES
If machine has ‘P’ no. of poles and ‘Z’
no. of conductors, then there will be ‘P’
no. of parallel paths.And each path will
have ‘Z/P’ no of conductors in series.
Also the no. of brushes are equal to no.
of parallel paths.

LECTURE 7 OF 40
DC MACHINES
Out of which half of the brushes will be
positive and remaining will be negative.
ii) Wave Winding;
The conductors are so connected
that they are divided into two parallel
paths only , irrespective of the no. of
poles. If machines has ‘Z’ no. of …

LECTURE 7 OF 40
DC MACHINES
conductors, there will be only two
parallel paths and each will be having
‘Z/2’ no. of conductors connected in
series with only two brushes.
Click here to study detailed contents of winding

LECTURE 7 OF 40
DC MACHINES
6. COMMUTATOR
It is the most
important part of
a DC machine and
serves the
following purpose
:- i) It connects …

LECTURE 7 OF 40
DC MACHINES
6. COMMUTATOR
the rotating
armature
conductors to the
stationary external
circuit through the
brushes.

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DC MACHINES
ii) It converts
altering current
induced in the
armature
conductors into
unidirectional …..
COMMUTATOR
6. COMMUTATOR

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DC MACHINES
6. COMMUTATOR
current in the
external load
circuit in
generating action
and it converts
alternating torque
into unidirectional COMMUTATOR

LECTURE 7 OF 40
DC MACHINES
6. COMMUTATOR COPPER SEGMENT
RISER
END RING
ADJUSTING NUT
METAL SLEEVESHAFT
MICA INSULATION

LECTURE 7 OF 40
DC MACHINES
6. COMMUTATOR
torque produced in the armature in
motoring action.
The commutator is of cylindrical
shape and is made of wedge shaped
hard drawn copper segments.The
segments are insulated from each ….

LECTURE 7 OF 40
DC MACHINES
6. COMMUTATOR
other by a thin sheet of mica.The
segments are held together by means
of two V-shaped rings that fit into the
V-grooves cut into the segments.
Each armature coil is connected to
the commutator segment through
riser.

LECTURE 7 OF 40
DC MACHINES
7. BRUSHES
Brushes are made of high grade
carbon.They form the connecting link
between armature winding and the
external circuit. The brushes are held in
particular position around the
commutator by brush holders.

LECTURE 7 OF 40
DC MACHINES
8. END HOUSINGS
They are attached
to the ends of
main frame and
support bearing .
The front housing
supports ….. END HOUSING

LECTURE 7 OF 40
DC MACHINES
8. END HOUSINGS
the bearing and
the brush
assembly whereas
rear housing
supports the
bearing only.
END HOUSING

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DC MACHINES
9. BEARINGS
The function of the bearing is to reduce
friction between the rotating and
stationary parts of the machines.These
are fitted in the end housings.
Generally, high carbon steel is used for
the construction of the bearings.

LECTURE 7 OF 40
DC MACHINES
10. SHAFT
The function of
shaft is to transfer
mechanical power
to the machine or
from the machine .
SHAFT

LECTURE 7 OF 40
DC MACHINES
Shaft is made of
mild steel with
maximum breaking
strength. All the
rotating parts like
SHAFT
10. SHAFT

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DC MACHINES
armature core,
commutator,
cooling fan etc. are
keyed to the shaft.
SHAFT
10. SHAFT
See Also

LECTURE 9 OF 40
DIFFERENT TYPES OF EXCITATIONS ( DC MOTORS )
TYPES OF EXCITATIONS ( DC MOTORS )
Depending upon the type if excitation to
the field winding , The dc machine can
be classified into three categories viz.
Machines with permanent field,

LECTURE 9 OF 40
separately excited and self excited type
dc machines. Dc motors with
permanent magnetic field, are
manufactured for small rating
applications such as toys, cassette tape
recorders etc.large rating dc motors …

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are constructed with electro-magnetic
field i.e field winding is placed on the
field core and this winding is supplied
with dc current called excitation.
Depending upon the type of
connections to the field winding for ….

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excitation , the dc motors can be
classified into two categories ;
1) Separately excited dc motors
2) Self excited dc motors.

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SEPARATELY EXCITED DC MOTORS
A
AA
E
Ra
Ia
V
+
_VDC
If
+ _
F FF
+
_
M
Supply
Rf

LECTURE 9 OF 40
• The field winding is excited from a
supply which is not connected to the
armature winding. It may be noted
that current flowing through the field
winding is independent of load and
is equal to V / Rf , where Rf is the….

LECTURE 9 OF 40
field circuit resistance. The flux
produced is proportional to the field
current i.e. Ø  If

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SUPPLYE
Ra
IL
V
FF
If
Ia
AA
+
_
F
M
A
SELF EXCITED DC MOTORS ( DC SHUNT MOTORS )

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SELF EXCITED DC MOTORS ( DC SHUNT MOTORS )
In this type of excitation , armature and
field windings are connected across a
constant source of supply. The field
current If is drawn from the same
source as that of armature current. As
shown in fig.
See Fig.

LECTURE 9 OF 40
SELF EXCITED DC MOTORS ( DC SERIES MOTORS )
A
E
Ra
IL
V
+
_
Ia
AA
ISE
YYY
+
_
M SUPPLY

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The field winding is connected in series
with the armature so that If = Ia = IL .
Therefore field winding is made up of
thick winding wire of less no. of turns
as compared to that of shunt field
winding so that armature current can ...

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flow through it without overheating. In
case of dc series machine , Ø  If  Ia ..
The relationship between induced
e.m.f. and terminal voltage is as follows
; …..
See Fig.

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V = E + Ia Ra + Ia Rse
or
E = V - Ia ( Ra + Rse )
Ia = Ise = ILand

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SELF EXCITED DC MOTORS ( DC COMPOUND MOTORS )
A
E
Ra
IL
V
Ia
AA
ISE
YYY
+
_
ISh
Z
ZZ
Rsh
SUPPLY
M

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There are two field windings , namely a
shunt field winding and a series field
winding. The shunt field winding is
connected in parallel with the armature
and series field winding is connected in
series with the combination .
See Fig.

LECTURE 9 OF 40
Series field winding will carry a large
armature current Ia or IL and therefore it
is made of wire of large cross section
and has a few turns only. The
resistance of series field winding is
very small.

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The shunt field winding is made up of
wires of small cross section and has
high resistance. Since the resistance of
shunt field winding is high , the current
flowing through it is very small as
compared to that of series field winding

LECTURE 9 OF 40
or armature current Ia . The main
magnetic field flux is produced by the
shunt field current / winding but it is
modified by the field of series winding.
A compound machine therefore
combines the best features of dc shunt
machines and dc series machines.

LECTURE 9 OF 40
Depending up on the connections of
shunt field winding in the combination
of armature and series field winding, dc
compound generators can be named as
i) Short shunt compound generators.
ii) Long shunt compound generators.

LECTURE 9 OF 40
SHORT SHUNT TYPE ( DC COMPOUND MOTORS )
A
E
Ra
IL
V
Ia
AA
ISE
YYY
+
_
ISh
Z
ZZ
Rsh
SUPPLY
M

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SHORT SHUNT TYPE ( DC COMPOUND MOTORS )
In this case the shunt field winding is
connected across the armature winding
only as shown in the fig of slide no.
i) SHORT SHUNT DC COMPOUND MOTORS
Ise = IL = Ia + Ish
V = E + Ia Ra+ Ise Rse
= E + Ia Ra+ ( Ia + Ish ) Rse

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LONG SHUNT TYPE ( DC COMPOUND MOTORS )
A
E
Ra
IL
V
Ia
AA
ISE
YYY
+
_
ISh
Z
ZZ
Rsh
SUPPLY
M

LECTURE 9 OF 40
LONG SHUNT TYPE ( DC COMPOUND MOTORS )
In this case the shunt field winding is
connected across the combination of
armature and series field winding as
shown in the fig.
Ise = Ia and IL= Ia +
IshV = E + Ia Ra+ Ise Rse
= Ish Rsh
ii) LONG SHUNT DC COMPOUND MOTORS

LECTURE 9 OF 40
Depending upon the direction of flow of
current through series field, we can
classify dc compound motors into two
categories namely ;
I) Cumulative compound dc motors
II) differential compound dc motors

LECTURE 9 OF 40
CUMULATIVE TYPE ( DC COMPOUND MOTORS )
A
E
Ra
IL
V
Ia
AA
ISE
YYY
+
_
ISh
Z
ZZ
Rsh
SUPPLY
M
Ø = Øsh + Øse

LECTURE 9 OF 40
CUMULATIVE TYPE ( DC COMPOUND MOTORS )
The direction of current in the series field
winding is such that magnetic field
produced by it is in the direction to that
of shunt field. Total magnitude of the
field is the sum of shunt field and series
field so that Ø = Øsh + Øse. .
See Fig.

LECTURE 9 OF 40
DIFFERENTIAL TYPE ( DC COMPOUND MOTORS )
A
E
Ra
IL
V
Ia
AA
ISE
YYY +
_
ISh
Z
ZZ
Rsh
SUPPLY
M
Ø = Øsh - Øse

LECTURE 9 OF 40
DIFFERENTIAL TYPE ( DC COMPOUND MOTORS )
The direction of current in the series field
winding is such that magnetic field
produced by it is in the opposite
direction to that of shunt field. Total
magnitude of the field is the difference
of shunt field and series field so that
Ø = Øsh - Øse.
See Fig.

FACTORS DETERMINING THE SPEED OF DC MOTOR
LECTURE 10 OF 40
The expression for back e.m.f.
developed in the armature of a dc motor
is given as follows :
P Ø Z N
60 A
E = …..(i)
E = V - Ia Ra
…..(ii)

LECTURE 10 OF 40
P Ø Z N
60 A
= V - Ia Ra
Comparing expressions (i) and (ii)
K Ø N = V - Ia RaOR
N =
V - Ia Ra
K Ø

LECTURE 10 OF 40
Where K is the constant of
proportionality and equal to PZ / 60 A
Now in the above expression for speed,
the speed can be varied by varying the
applied voltage ‘V’ , field flux Ø and
resistance of the armature .

LECTURE 10 OF 40
It is clear that speed is directly
proportional to the supply voltage ‘V’. So
the speed increases with increase in
voltage ‘V’ and vice versa.
The speed is inversely proportional to the
field flux Ø . So speed decreases as the
Flux Ø increases and vice versa.

PERFORMANCE AND CHARACTERISTICS OF DC MOTORS
LECTURE 11 OF 40
The important characteristics of dc
motors are :
1) Speed - armature current ( Load )
characteristics
2) Torque - armature current ( Load )
characteristics
3) Speed - Torque characteristics
CHARACTERISTICS OF DC MOTORS

LECTURE 11 OF 40
It is very much important to know the
characteristics mentioned above for
different types of dc motors because it
enables the selection of a specific type
of dc motor for specific purpose.
CHARACTERISTICS OF DC MOTORS

LECTURE 11 OF 40
CHARACTERISTICS OF DC SHUNT MOTORS
SUPPLYE
Ra
IL
V
FF
If
Ia
AA
+
_
F
M
A

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N
Ia
FULL LOAD
0
( Amps)

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For a dc motor , we know that ;
N =
V - Ia Ra
K Ø
A dc shunt motor is connected across
the mains having supply voltage ‘V’ .
N
Ia
FULL
LOAD
0
( Amps)
1. Speed - Armature current (Load ) characteristics

LECTURE 11 OF 40
This supply voltage is assumed to be
constant.The field winding is connected
across the armature as shown in Fig. The
magnetic flux Ø produced by field
current If will be constant as V remains
constant.
Speed - Armature current (Load ) characteristics
See Fig.

LECTURE 11 OF 40
But in actual practice, the air gap flux is
slightly reduced due to the effect of
armature reaction. From the expression
for the speed mentioned earlier, it is
evident that as the armature current Ia …...

LECTURE 11 OF 40
increases , speed will decrease by a
small amount due to an increase in Ia Ra
drop is very small as compared to V .
The speed verses armature current
characteristics is shown in Fig.
See Fig.

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The shunt motor being thus more or less
a constant speed motor , can be used in
the applications such as driving of line
shafts, lathes conveyors etc.

LECTURE 11 OF 40
T
Ia
0
( Amps)
2. Torque - Armature current (Load ) characteristics

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2. Torque - Armature current (Load ) characteristics
The equation for torque can be written as
follows ; T = kt Ø Ia
If flux Ø is taken as constant, the torque
T becomes directly proportional to
armature current (Load current) Ia . It is a
straight line passing through the origin.

LECTURE 11 OF 40
N
T
0
( N-m)
3. Speed - Torque characteristics

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And The relationship between speed and
torque can be drawn as shown in Fig .
N =
V - Ia Ra
K Ø
The relation between T and Ia and N
and Ia are as under ;
T = kt Ø Ia

LECTURE 11 OF 40
CHARACTERISTICS OF DC SERIES MOTORS
A
E
Ra
IL
V
+
_
Ia
AA
ISE
YYY
+
_
M SUPPLY

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1. Speed - Load characteristics
N
0
Ia( Amps)

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From the expression ; N =
V - Ia Ra
K Ø
It is seen that the speed N is inversely
proportional to flux Ø
For a dc series motor ,magnetic flux Ø is
proportional to Ia.

LECTURE 11 OF 40
Thus , if V is constant, N is inversely
proportional to Ia. The N verses Ia
characteristics is therefore a rectangular
hyperbola as shown in Fig . It is seen
from the characteristics that ….
See Fig.

LECTURE 11 OF 40
the speed decreases as the load on the
motor increases. At a very low load , the
speed is dangerously high . Thus if a dc
series motor is allowed to run on very
light load or at No- Load , its speed will
become much higher than its ……..

LECTURE 11 OF 40
normal speed which may cause damage
to the motor. For this reason , dc series
motors are never started on No- Load
and are not used in the applications
where there is a chance of Load being
completely removed , when the motor ...

LECTURE 11 OF 40
remains connected to the supply. The
load on the dc series motor is connected
through the gears and not through the
belt pulley arrangement.This is because,
in case of failure of belt , the load will be
removed from the motor and thereby the

LECTURE 11 OF 40
motor will attain a dangerously high
speed . In case of load connected
through the gears, however in the event
of an accidental release of load, gears
will provide some load on account of the
frictional resistance of the gear teeth.

LECTURE 11 OF 40
1. Torque - Load characteristics
T
0
Ia ( Amps)
SATURATION OF
SERIES FIELD CORE

LECTURE 11 OF 40
The equation for the torque for dc motor
is given by ; T = kt Ø Ia
The magnetic flux for a dc series motor is
proportional to armature current Ia. Thus
the torque T = kt Ia Ia.
Or T  Ia
2

LECTURE 11 OF 40
The relationship between torque and
armature current , is therefore of the form
of a parabola . With increase in Ia , the
field flux increases linearly but due to
saturation of the core, beyond a certain
magnitude of Ia the increase in flux is

LECTURE 11 OF 40
negligible.. Thus T is proportional to the
square of Ia up to the saturation point
beyond which T varies linearly with Ia.
From the torque load characteristics , it
can be observed that a dc series motor ..

LECTURE 11 OF 40
started on-load , develops a very high
starting torque.
Hence dc series motors are used in
applications where high starting torque is
required such as in electric trains ,
hoists, trolleys etc.

LECTURE 11 OF 40
1. Torque - Speed characteristics
T
0
N

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From the characteristics shown in slide
no. , it can be seen that for low speeds ,
the torque is high and for high speeds
the torque is very small. This is why dc
series motor is widely used in the … ..

LECTURE 11 OF 40
applications where motor is to be started
on bulk loads such as electric loco-
motive.

LECTURE 11 OF 40
CHARACTERISTICS OF DC COMPOUND MOTORS
A
E
Ra
IL
V
Ia
AA
ISE
YYY
+
_
ISh
Z
ZZ
Rsh
SUPPLY
M

LECTURE 11 OF 40
0
N
Ia ( Amps)
DIFFERENTIAL
COMPOUND
SHUNT
CUMULATIVE
COMPOUND

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In cumulative compound motors , series
field winding is connected in such a way
that magnetic flux produced by it helps
the flux produced by shunt field winding.
Series field is directly proportional to the
load current , ….. . … .

LECTURE 11 OF 40
therefore total flux increases with
increase in load current / armature
current due to the series field in addition
to the voltage drop in the armature
winding.The speed of dc motor is
inversely proportional to the . .. . ..

LECTURE 11 OF 40
total main flux Ø . Therefore speed drops
more sharply as compared to dc shunt
motor.Refer Fig.
See Fig.

LECTURE 11 OF 40
T
0
Ia ( Amps)
DIFFERENTIAL
COMPOUND
SHUNTCUMULATIVE
COMPOUND

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The torque developed by a cumulative
compound motor increases with sudden
increase in load and at no-load , it has a
definite speed. Cumulative compound
motors are therefore, suitable where
there is sudden application . . . . . . .

LECTURE 11 OF 40
of heavy loads like sheers, punches,
rolling mills etc. The speed of differential
compound motors remains more or less
constant. With increase in load but its
torque decreases with load. Since the dc
shunt motor develops a good torque and

LECTURE 11 OF 40
its speed does not vary appreciably with
increase in load, differential compound
motors are not preferred over dc shunt
motors and hence are rarely used.

LECTURE 11 OF 40
0
N
T (N-m)
DIFFERENTIAL
COMPOUND
CUMULATIVE
COMPOUND

APPLICATION OF DC MACHINES
(i) Shunt motors are used in situations,
such as driving a line shafting etc. where
the speed as to be maintained
approximately constant between no-load
and full-load.
APPLICATIONS OF DC MOTORS
(a) DC SHUNT MOTORS

(ii) In situations where variable load is to
be driven at different speeds but at each
load, the speed is to be kept constant.
Such as driving a lathe.
(a) DC SHUNT MOTORS

DC Series Motors are used in
applications such as driving hoists,
cranes, trains, etc., as in these cases a
large starting torque is required. They are
also used where the motor can be
permanently coupled to the load, such as
(b) DC SERIES MOTORS

Fans , whose torque increases with speed.
Where constancy in speed is not
essential, the decrease of speed with
increase of load has the advantage that
the power absorbed by the motor does
not increase as rapidly as the torque .

Series motors acquire very high speed at
no-load or at very light load . That is why
they should not be used for a belt drive
where there is a possibility of the load
decreasing to very small value.

DC Compound Motors are used in
application where large starting torque
are required but where the load may fall
to such a small value that a series motor
would reach a dangerously high speed.
(c) DC COMPOUND MOTORS

Where the supply voltage may fluctuate ,
for instance on a traction system, the
series winding reduces the fluctuation of
armature current partly by its inductance
and partly by its influence on the value of

flux and therefore on that of the induced
e.m.f.
When the load is of a fluctuating nature ,
e.g. for driving stamping processes, etc.
the shunt excitation prevents the speed …

Becoming excessive on light load, and
the decrease of speed with increase of
load enables the flywheel, usually fitted
to such a machine, to assist the motor in
in dealing with the peak load by giving

up some of its kinetic energy.
* THANKS *

ELECTRICAL MACHINES
TRANSFORMER
By Jean de Dieu IYAKAREMYE

Transformer
An A.C. device used to change high voltage low current
A.C. into low voltage high current A.C. and vice-versa
without changing the frequency
In brief,
1. Transfers electric power from one circuit to another
2. It does so without a change of frequency
3. It accomplishes this by electromagnetic induction
4. Where the two electric circuits are in mutual inductive
influence of each other.

Principle of operation
It is based on
principle of MUTUAL
INDUCTION.
According to which
an e.m.f. is induced
in a coil when
current in the
neighbouring coil
changes.

Constructional detail : Shell type
• Windings are wrapped around the center leg of a
laminated core.

Core type
• Windings are wrapped around two sides of a laminated square
core.

Sectional view of transformers
Note:
High voltage conductors are smaller cross section conductors
than the low voltage coils

GENERALISED TREATMENT OF ELECTRICAL MACHINESConstruction of transformer from
stampings

Core type
Fig1: Coil and laminations of
core type transformer
Fig2: Various types of cores

Shell type
• The HV and LV
windings are split
into no. of sections
• Where HV winding
lies between two
LV windings
• In sandwich coils
leakage can be
controlledFig: Sandwich windings

Cut view of transformer

Transformer with conservator
and breather

Working of a transformer
1. When current in the primary coil
changes being alternating in
nature, a changing magnetic field
is produced
2. This changing magnetic field gets
associated with the secondary
through the soft iron core
3. Hence magnetic flux linked with
the secondary coil changes.
4. Which induces e.m.f. in the
secondary.

Ideal Transformers
• Zero leakage flux:
-Fluxes produced by the primary and secondary currents
are confined within the core
• The windings have no resistance:
- Induced voltages equal applied voltages
• The core has infinite permeability
- Reluctance of the core is zero
- Negligible current is required to establish magnetic
flux
• Loss-less magnetic core
- No hysteresis or eddy currents

When two coils are placed close to each other, a
changing flux in one coil will cause an induced voltage
in the second coil. The coils are said to have mutual
inductance (LM), which can either add or subtract
from the total inductance depending on if the fields are
aiding or opposing.
Mutual Inductance
LM
k
The coefficient of
coupling is a measure of
how well the coils are
linked; it is a number
between 0 and 1.
1 2L1 L2

The formula for mutual inductance is
Mutual Inductance
LM
k
k = the coefficient of coupling (dimensionless)
L1, L2 = inductance of each coil (H)
The coefficient of coupling
depends on factors such
as the orientation of the
coils to each other, their
proximity, and if they are
on a common core.
1 2L1 L2

The basic transformer is formed from two coils that are
usually wound on a common core to provide a path for
the magnetic field lines. Schematic symbols indicate the
type of core.
Basic Transformer
Air core Ferrite core Iron core
Small power transformer

A useful parameter for ideal transformers is the turns
ratio defined* as
Turns ratio
Nsec = number of secondary windings
Npri = number of secondary windings
* Based on the IEEE dictionary definition for electronics power transformers.
Most transformers are not marked with turns ratio, however it
is a useful parameter for understanding transformer operation.
A transformer has 800 turns on the primary and a turns
ratio of 0.25. How many turns are on the secondary? 200

The direction of the windings determines the polarity of
the voltage across the secondary winding with respect to
the voltage across the primary. Phase dots are
sometimes used to indicate polarities.
Direction of windings
In phase Out of phase

120 Vrms
Vpri
In a step-up transformer, the secondary voltage is
greater than the primary voltage and n > 1.
Step-up and step-down transformers
In a step-down transformer, the secondary voltage is
less than the primary voltage and n < 1.
What is the secondary voltage?
4:1
?30 Vrms
What is the turns ratio? 0.25

A special transformer with a turns ratio of 1 is called an
isolation transformer. Because the turns ratio is 1, the
secondary voltage is the same as the primary voltage,
hence ac is passed from one circuit to another.
Isolation transformers
The purpose of an isolation transformer is to break a dc
path between two circuits while maintaining the ac path.
The DC is blocked by the transformer, because the
magnetic flux is not changing.

Transformers cannot increase power. If the secondary
voltage is higher than the primary voltage, then the
secondary current must be lower than the primary
current and vice-versa.
Current
pri
sec
I
n
I

The ideal transformer turns ratio equation for
current is
Notice that the primary
current is in the numerator.

The ideal transformer does not dissipate power. Power
delivered from the source is passed on to the load by the
transformer. This important idea can be summarized as
Power
pri sec
pri pri sec sec
prisec
pri sec
P P
V I V I
IV
V I


 These last ratios are, of
course, the turns ratio, n.

A transformer changes both the voltage and current on
the primary side to different values on the secondary
side. This makes a load resistance appear to have a
different value on the primary side.
From Ohm’s law, and
pri sec
pri L
pri sec
V V
R R
I I
 
Taking the ratio of Rpri to RL,
2
1 1 1
=
pri pri sec
L sec pri
R V I
R V I n n n
     
            
Reflected resistance

Reflected resistance
The resistance “seen” on the primary side is called the
reflected resistance. 2
1
pri LR R
n
 
  
 
If you “look” into the primary side of the circuit, you
see an effective load that is changed by the reciprocal
of the turns ratio squared.
You see the primary
side resistance, so the
load resistance is
effectively changed.
RL

Impedance matching
The word impedance is used in ac work to take into
account resistance and reactance effects. To match a
load resistance to the internal source resistance (and
hence transfer maximum power to the load), a special
impedance matching transformer is used.
RL
Rint
Vs
Impedance matching
transformers are designed
for a wider range of
frequencies than power
transformers, hence tend
to be not ideal.
Impedance
matching
transformer

Non-ideal transformers
An ideal transformer has no power loss; all power applied to the
primary is all delivered to the load. Actual transformers depart from
this ideal model. Some loss mechanisms are:
Winding resistance (causing power to be dissipated in the
windings.)
Hysteresis loss (due to the continuous reversal of the magnetic
field.)
Core losses due to circulating current in the core (eddy currents).
Flux leakage flux from the primary that does not link to the
secondary
Winding capacitance that has a bypassing effect for the windings.

Transformer efficiency
The efficiency of a transformer is the ratio of power
delivered to the load (Pout) to the power delivered to
the primary (Pin). That is
120 Vrms
Vpri
What is the efficiency of the transformer?
RL
100 W
15 Vrms
20 mA
94%
(See next
slide for
method.)

Transformer efficiency
100%out
in
P
P

 
  
 
120 Vrms
Vpri
What is the efficiency of the transformer?
RL
100 W
15 Vrms
20 mA
     
2
2
15 V
100100% 100% 94%
120 V 0.020 A
L
L
pri pri
V
R
V I
     W           
94%

Tapped and multiple-winding transformers
Frequently, it is useful to tap a transformer to allow for a
different reference or to achieve different voltage ratings,
either on the primary side or the secondary side.
Multiple windings can be on either the primary or
secondary side. One application for multiple windings is
to be able to use the same transformer for either 120 V or
240 V operation.
Secondary with center-tap Primary with multiple-windings

Mutual
inductance
Transformer
Primary
winding
Secondary
winding
The inductance between two separate coils, such
as in a transformer.
An electrical device constructed of two or more
coils that are magnetically coupled to each
other so that there is mutual inductance from
one coil to the other.
The input winding of a transformer; also
called primary.
The output winding of a transformer; also called
secondary.
Selected Key Terms

Magnetic
coupling
Turns ratio
Reflected
resistance
Impedance
matching
The ratio of the turns in the secondary
winding to the turns in the primary winding.
The resistance of the secondary circuit
reflected into the primary circuit.
The magnetic connection between two coils as
a result of the changing magnetic flux lines of
one coil cutting through the second coil.
Selected Key Terms
A technique used to match a load resistance to a
source resistance in order to achieve maximum
transfer of power.

Quiz
1. The measurement unit for the coefficient of coupling is
a. ohm
b. watt
c. meter
d. dimensionless

Quiz
2. A step-up transformer refers to one in which
a. The voltage across the secondary is higher than
the primary.
b. The current in secondary is higher than the
primary.
c. The power to the load is higher than delivered to
the primary
d. All of the above

Quiz
3. An isolation transformer
a. blocks both ac and dc
b. blocks ac but not dc
c. blocks dc but not ac
d. passes both ac and dc

Quiz
4. If the current in the secondary is higher than in the
primary, the transformer is a
a. a step-up transformer
b. an isolation transformer
c. a step-down transformer
d. not enough information to tell

Quiz
5. An ideal transformer has
a. no winding resistance
b. no eddy current loss
c. power out = power in
d. all of the above

Quiz
6. Assume a step-down transformer is used between a
source and a load. From the primary side, the load
resistance will appear to be
a. smaller
b. the same
c. larger

Quiz
7. A transformer that can deliver more power to the load
than it receives from the source is a(n)
a. step-up type
b. step-down type
c. isolation type
d. none of the above

Quiz
8. Generally, the purpose of an impedance matching
transformer is to
a. make the load voltage appear to be the same as
the source voltage
b. make the load resistance appear to be the same as
the source resistance
c. make the load current appear to be the same as
the source current
d. provide more power to the load than is delivered
from the source

Quiz
9. A type of transformer that tends to not be ideal because it
is designed for a good frequency response is a
a. step-up type
b. step-down type
c. isolation type
d. impedance matching type

Quiz
10. A transformer that could be used for 120 V or 240 V
operation is a
a. multiple-winding type
b. center-tapped type
c. isolation type
d. all of the above

Quiz
Answers:
1. d
2. a
3. c
4. c
5. d
6. c
7. d
8. b
9. d
10. a

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