This document describes the course EEE 2207: Electrical Machines 1. The course covers various electrical machines including DC generators and motors, transformers, induction motors, synchronous generators and motors. It provides details on the operating principles, construction, characteristics and testing of these machines. The document also outlines the syllabus, evaluation criteria, textbooks and reference books for the course. Key topics to be covered include armature reactions, speed control methods, transformer circuits and performance, induction motor equivalent circuits, and synchronous generator and motor operation.

1. EEE 2207: Electrical Machines 1
Course Credit: 3 CP, 3hrs/week
Pre-requisite: EEE-2101
DC generator: operating principle, classifications, constructions, armature
windings, voltage build up, commutation technique, armature reactions,
performance and testing.
DC motor: operating principle, types of dc motors, dc motor characteristics,
methods of speed control.
Transformer: operating principle, structural details, vector diagrams of a
single-phase transformer, equivalent circuits, transformer at load and no load
conditions, transformer losses and efficiency, voltage regulation.
Induction motor: operating principle, structural details, equivalent circuits,
speed-torque relations, circle diagram, losses and efficiency.
Synchronous generator: operating principle, salient poles and non-salient
poles, armature and field cores, armature windings, voltage regulation, armature
reaction, losses and efficiency, parallel operation of synchronous generators.
Synchronous motor: operating principle, vector diagrams, V-curves, losses,
efficiency and starting.
Syllabus
Quizzes: Marks of the best two quizzes will be taken out of 3
quizzes for both Midterm and Final exam.
(No makeup quiz will be taken.)
Marking system (Midterm and Final term):
i) Attendance - - - - - - - - - - - - - - - - - - - - - - 20%
ii) Quiz - - - - - - - - - - - - - - - - - - - - - - - - - 40%
iii)Term Exam - - - - - - - - - - - - - - - - - - - - - 40%
Evaluation
Total - - - - - - - - - - - - - - - - - - - - - - - - - - 100%
Final Grade: Midterm- 40% and Final Term- 60%
Text and Reference Books
[1] B.L. Theraja, A.K. Theraja, “A textbook of Electrical Technology”,
Volume- II, S. Chand & company Ltd.
[2] Jack Rosenblat and M. Harold Friedman, “Direct and Alternating
Current Machinery”, CBS Publishers and Distributors.
[3] Irving L. Kosow, “Electrical Machinery and Transformers”, Second
Edition, Prentice –Hall India Pvt. Limited
[4] Stephen J. Chapman, “Machinery Fundamentals”, Third Edition,
McGraw-Hill International Edition
[5] Charles S. Siskind, “Electrical Machines”, Second or latest Edition,
McGraw-hill intl.
[6] E. R. R. K. Rajput, “Alternating Current Machines”, Laxmi
Publication (P) Ltd.
[7] A. F. Puchstein, T. C. Lloyd, A. G. Conrad, “Alternating Current
Machines”, Asia Publishing House.

2. Theories Related to the
Electrical Machine
Angular Velocity (ω): Angular velocity (or speed) is
the rate of change in angular position with respect to
time.
It is assumed to be positive if the rotation is in a
clockwise direction.
Angular velocity defined by the following equation:
rad/sec
dt
dθ
ω = where, θ is angular position.
If we use the subscript m for the mechanical quantity
then let
θm: angular position in rad.
ωm: angular velocity (or speed) in rad./sec
fm: angular velocity (or speed) in rev./sec
Nm: angular velocity (or speed) in rev./m
The measures of shaft speed are related to each other
by the following equations: mmmm fNf 60;2/ == πω
The relation of mechanical angular potion (θm) with the
electrical angular position (θe) is given by: me P θθ )2/(=
where P is number of magnetic pole.
Torque (T): The torque of an object is defined as the
product of the force applied to the object and the smallest
distance between the line of the action of the force and the
object’s axis of rotation.
If r is a vector pointing from the axis of rotation to the
point of application of the force, and if F is the applied
force, then the torque can be described as follows:
θ
θ
sin
)sin)((
distance)pendicularforce)(per(
FrT
rFT
T
=
=
=
Where θ is the angle between the
vector r and the vector F.

3. Work (W): For linear motion, work is defined as the
application of a force through a distance.
In equation form:
constant]isforceapplied[if
joules
FrW
FdrW
=
= ∫
For rotational motion, work is defined as the
application of a torque through an angle.
In equation form:
constant]istorqueapplied[if
joules
θ
θ
TW
TdW
=
= ∫
Power (P): Power is the rate of doing work, or the
increase in work per unit time.
The equation for the power is:
wattorjoules/sec
dt
dW
P =
watt
)(
ω
θθ
T
dt
d
T
dt
Td
P ===
watt
)(
Fv
dt
dr
F
dt
Frd
P ===
For linear motion with constant applied force:
For rotational motion with constant applied torque:
Magnetic Field Around Current
Carrying Conductor
In Fig. 1.2, the solid circle shows the cross-sectional
view of a round conductor.
It is seen from Fig. 1.2 (a) that the direction of magnetic
field is clockwise direction when the conductor carries a
current in inward direction.
It is seen from Fig. 1.2
(b) that the direction of
magnetic field is
anticlockwise direction
when the conductor
carries a current in
outward direction.
When two parallel conductors
carry opposite (inward and
outward) current, the resultant
flux flows through in the middle of
those conductor.
When two parallel conductors carry same (inward and
inward or outward and outward) current, the resultant
flux flows through in the outside of those conductor.

4. Right Hand Cork Screw Rule
The direction of the magnetic field set up by a
carrying conductor is in the same direction as that of
the rotation of a right-handed cork screw, so that the
screw moves in the direction as that of the current
flow.
Right-hand cork-screw
rule is used to obtain
the direction of current
flow when a magnetic
field sets up around a
conductor.
Direction of
magnetic field
Direction of
current flow
Right Hand Grip Rule
When the current carrying conductor is gripped by
right-hand with sufficient insulation in such a way that
the thumb points toward the direction of current flow,
and the direction of other four fingers which grip the
conductor indicates the direction of magnetic field.
Direction
of current
Direction of
magnetic field
Right-hand grip rule is used
to obtain the direction of
magnetic field when a
conductor is carrying current.
Electromagnet
Fig. 1.5 shows a current carrying solenoid.
A solenoid is a piece of iron wound a coil.
A battery B is connected to the solenoid and it causes
current I to flow through it.
The current in the conductor at the top flows in the
outward direction.
Therefore, they set up
magnetic field in the
anticlockwise direction.
The conductor at the bottom
carries the current inward
and hence they set up flux in
the clockwise direction.
NS NS
In the result, the magnetic flux set by the solenoid now
looks similar to those available around the permanent
magnet.
By changing the current direction the direction of flux
can be changed.
Thus in an electromagnet,
the magnitude and the
direction of the magnetic
field can be controlled.

5. Hysteresis Loop
When a ferromagnetic material is magnetized in one direction, it will
not relax back to zero magnetization when the imposed magnetizing
field is removed.
It must be driven back to zero by a field in the opposite direction.
If an alternating magnetic
field is applied to the
material, its magnetization
will trace out a loop called a
hysteresis loop.
The lack of retraceability of
the magnetization curve is
the property called
hysteresis.
Residual Magnetism: A
property of magnetic
material by which magnetic
materials retain a certain
amount of magnetization
after the magnetizing force
has been removed.
Faraday’s Laws
In order to have a voltage induced in a conductor the
following elements are required:
1. A conductor,
2. Lines of magnetic flux, and
3. Motion that produces cutting of the magnetic flux.
Faraday’s First Law: Whenever flux linking a
conductor coil changes, an emf is induced in the coil.
Faraday’s Second Law: The amount of emf induced
in a conducting coil is proportional to the rate of change
in flux linked by the coil.
Lenz’s Law
When a conductor is moved through a magnetic field a voltage is
induced in the conductor.
If the circuit is closed, the induced voltage will cause a current flow.
The magnetic filed produced by the current will always oppose the
motion of conductor.
This is known as Lenz’s law.
Thus Lenz’s Law can be stated that the direction of the induced emf
due to electromagnetic induction is such that the current set up by it
tends to oppose the change which cause the induced emf.
In all cases of electromagnetic induction, an induced voltage will
cause a current to flow in a closed circuit in such a direction that its
magnetic effect will oppose the change that produces it.
EMF: The force that establishes the
flow of charge (or current) in a
system due to the application of a
difference in potential.

6. The Faraday’s laws and Lanz’s Law put together can be expressed by
the following equation (1):
)1(volt
dt
dNe Φ−=
Where,e is the induced emf,
N is the number of turns in the coil,
dΦ is the change in flux, and
dt is the time taken for the change to occur.
Example: A coil of 1000 turns is linking a flux of 0.01 Wb. The flux
is reversed in an interval of 0.1 s. Calculate the average value of the
induced emf in the coil.
Solution: N=1000, Φ1=0.01 Wb, Φ2=-0.01 Wb, dt=0.1s and eav=?
dΦ=(Φ2-Φ1)=-0.01-0.01=-0.02 Wb
V200
1.0
02.01000av =−×−=∴ e
Voltage Induced in a Conductor
When a conductor moves in a magnetic field, the expression of
induced voltage can be written as follows: voltssinθvlBE=
where B= flux density, wb/m2; l= length of that part of conductor that
actually cuts flux, m; v= speed of conductor, m/s, θ= angle between
lines of flux and direction of motion of conductor.
From above equation it is seen that BE∞ vE∞lE∞
The induced voltage E is maximum when θ=90o.
The direction of induced voltage is obtained by using Fleming’s
Right-hand Rule.
Flux density is given by: A
B φ=
Where, φ = flux lines, wb; A= Area of cross-section of iron through
which flux passes through.
Fleming’s Right-Hand Rule
When a conductor moves in a magnetic field, the direction (or the
polarity) of the induced voltage can be obtained by using the
Fleming’s right-hand rule.
Thus, Fleming’s Right hand rule is used for generator to find out the
direction of induced emf (or voltage).
Extend the thumb, index finger, and
middle finger of the right hand so
they are at right angle to each other.
With the index finger pointing in the
direction of the lines of flux (from
north to south) and the thumb
pointing in the direction of motion of
the conductor, the middle finger
will point in the direction of that
current will flow in the conductor.
Force Exerted on a Conductor
When a current carrying conductor is located in a magnetic field, a
force is exerted on the conductor.
The expression of exerted force by the Biot-Savart-Law can be
written as follows:
(N)snewton'sinθlIBF =
where B= flux density, wb/m2; l= length of that part of conductor that
actually cuts flux, m; I= current in the conductor, amp, θ= angle
between the conductor and flux density vector.
From above equation it is seen that BF∞ IF∞lF∞
The exerted force F is maximum when θ=90o.
The direction of exerted force is obtained by using Fleming’s Left-
hand Rule.

7. Fleming’s Left-Hand Rule
When a current carrying conductor moves in a magnetic field, the
direction (or the polarity) of the produced force can be obtained by
using the Fleming’s left-hand rule.
Thus, Fleming’s Right hand rule is used for Motor to find out the
direction of produced force.
Extend the thumb, index finger, and
middle finger of the left hand so they
are at right angle to each other.
The index finger is used to indicate
the direction of flux from the north
pole to south pole. The middle
finger points in the direction of the
current, and the thumb points in the
direction of force on the conductor.
Machine: A piece of equipment with moving parts that is
designed to do a particular job is called machine.
Example: Dynamo
Dynamo: A dynamo converts electrical energy to
mechanical energy or mechanical energy to electrical
energy.
Generator : A generator is a dynamo in as much as it
converts the mechanical energy imparted to it in the rotation
of the coils into electrical energy that is supplied to the
electrical load.
Motor: A motor is a dynamo in as much as it converts
electrical energy imparted to it in the rotation of the shaft
into mechanical energy that is supplied to the load.
Principle of Generator Action
Consider a conductor of active length l meters placed in a uniform
magnetic field with an average flux density B tesla (wb/m2) as shown
in Fig. 1.1.
The uniform magnetic field is provided by two
magnetic poles, north pole (N) at the top and
south pole (S) at the bottom.
Direction of the magnetic field is from north
pole to south pole.
Therefore magnetic field shown in Fig. 1.1 is
from top to bottom.
The conductor is initially placed at the point A.
The active length mentioned here differs from
the physical length of the conductor as it is only
the portion of the conductor which is linked with
the magnetic field.
Now mechanical force F is applied to the conductor such that the
conductor move from left to right with a velocity of v m/s in a
direction perpendicular to the magnetic field.
Due to the force, the conductor moves from point A to B covering a
distance of d meters in t seconds.
During this movement, the flux linking the conductor changes and
hence according to Faraday’s law, an emf is induced in the one turn of
conductor which is given by
N=1 and dΦ=B×l×d. )01.1(volt1 Blv
t
dlB
dt
d
Ne =
××
=
Φ
=
Equation (1.01) holds good only when the conductor
moves at an angle 90o with respect to the magnetic
field.
In case if the conductor moves at an angle θ degrees
with respect to magnetic field the eqn. (1.01) has to be
modified as given below
(1.02)voltsinθBlve =

8. Lenz’s law gives direction of emf induced and hence the current set up
by the emf.
The current direction will be in the inward direction to that the current
carrying conductor sets up another magnetic field in the clockwise
direction.
To the right of the conductor, the direction of the magnetic field set up
by the current is in the same direction as that of the uniform magnetic
field giving a resistive force to the movement.
It is known as backward force or magnetic drag on the conductor.
It is against this drag action on the conductor that the prime mover
(device which help to move the conductor) has to work. The work done
in overcoming this opposition is converted into electrical energy.
In this set up, the input energy is a mechanical energy i.e. force given
to the conductor and output energy is an electrical energy with voltage
and current.
Hence this process helps us to understand how a mechanical energy is
converted into an electrical energy which from the basic principle of all
types of generator action.
Principle of Motor Action
All rotating machines which perform operation can be operated in the
reverse mode also namely motor operation. All DC motors and AC
asynchronous motors work on the same principle.
When a current carrying conductor is placed in a uniform magnetic
field, a force is developed in the conductor.
Fig. 1.2(a) indicates the direction of uniform magnetic field set up by
two magnetic poles.
When a current
carrying conductor is
placed in the space
between the poles, as
indicated in Fig.
1.2(b), the magnetic
field is set up by the
inward current in
clockwise direction.
Fig. 1.2(c) shows the resultant of the two magnetic fields.
To the right of the conductor, as both fields are in the same direction,
field strength is more and bent around the conductor.
Where as on the left of the conductor, since both fields are opposite,
the field strength is less.
If the conductor is allowed to move it moves from right to left due to
this force.
The amount of force developed by a current conductor is given by
(1.03)NBIlF =
The force in a direction perpendicular to both
the current and the main field.
Fleming’s left-hand rule helps us to find the
direction of force.
As the conductor is moved (rotated) inside a
magnetic field, an emf is produced in the
conductor.
The direction of this induced emf as found by
Fleming’s Right-Hand Rule.
The induced emf oppose the supply voltage in the conductor.
So, this induced is known as back emf or counter emf.
The applied voltage has to be forced current through the conductor
against this back emf.
The electric work done in overcoming this opposition is converted into
mechanical energy developed in the conductor.
Here, the input energy is electrical energy which is the current given to
the conductor by a source voltage.
Output energy is a
mechanical energy which is
the movement of the
conductor due to the force
experienced by it.
The energy conversion from
electrical to mechanical or
vice-versa takes place via the
magnetic field provided by
the field system.