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”, LaxmiPublication (P) Ltd.

[7] A. F. Puchstein, T. C. Lloyd, A. G. Conrad, “Alternating Current Machines”, Asia Publishing House.

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/secdtdθω = 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:

θθ

sin)sin)((

distance)pendicularforce)(per(

FrTrFT

T

===

Where θ is the angle between the vector r and the vector F.

Work (W): For linear motion, work is defined as the application of a force through a distance.

In equation form:

constant]isforceapplied[ifjoules

FrWFdrW

=

= ∫

For rotational motion, work is defined as the application of a torque through an angle.

In equation form:

constant]istorqueapplied[ifjoules

θθ

TWTdW

=

= ∫

Power (P): Power is the rate of doing work, or the increase in work per unit time.

The equation for the power is:

wattorjoules/secdt

dWP =

watt)( ωθθ TdtdT

dtTdP ===

watt)( FvdtdrF

dtFrdP ===

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.

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.

ElectromagnetFig. 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.

Hysteresis LoopWhen 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 LawWhen 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 emfdue 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.

The Faraday’s laws and Lanz’s Law put together can be expressed by the following equation (1):

)1(voltdtdNe 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

V2001.002.01000av =−×−=∴ e

Voltage Induced in a ConductorWhen 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: AB 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 thumbpointing in the direction of motion of the conductor, the middle fingerwill point in the direction of that current will flow in the conductor.

Force Exerted on a ConductorWhen 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.

Fleming’s Left-Hand Rule

When a current carrying conductor moves in a magnetic field, thedirection (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 ActionConsider 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 andhence according to Faraday’s law, an emf is induced in the one turn of conductor which is given byN=1 and dΦ=B×l×d. )01.1(volt1 Blv

tdlB

dtdNe =

××=

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 =

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 ActionAll 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.