Chapter 10 - Electrical Machine

ENT188

ELECTRICAL TECHNOLOGY

(Electrical Machine)

MUTUAL INDUCTANCE

INTRODUCTION TO TRANSFORMER

STEP-UP AND STEP-DOWN TRANSFORMER

LOADING THE SECONDARY WINDING

IDEAL TRANSFORMER

DC GENERATOR

DC MOTORS

INTRODUCTION TO MACHINE THEORY

Electrical Machine

MUTUAL INDUCTANCE

When a second coil is placed very close to the first coil so that the

changing magnetic lines of force cut through the second coil, the coils

are magnetically coupled and a voltage is induced.

When two coils are magnetically coupled, they provide electrical

isolation because there is no electrical connection between them,

only magnetic link.

MUTUAL INDUCTANCE

The amount of voltage induced in the second coil as a result of the

current in the first coil is dependent on the mutual inductance.

The mutual inductance is established by the inductance of each coil

(L1 and L2) and by the amount of coupling k between the two coils.

Mutual inductance is the ability of one inductor to induce a

voltage across a neighboring inductor, measured in Henrys (H).

To maximize coupling, the two coils are wound on the same core.

Coefficient of

Coupling

= the flux ( lines of force) produced by the primary linking of secondary

=the total flux produced by the primary

Coefficient coupling (k) is depends

on the physical closeness of the coils

and the type of core material that

they are wound. Also the construction

and shape of the core.

MUTUAL INDUCTANCE Formula for Mutual Inductance

Example 1

A transformer is a stationary electric machine which transfers electrical energy (power) from one voltage level to another voltage level.

Unlike in rotating machines, there is no electrical to mechanical energy conversion.

INTRODUCTION TO ELECTRICAL MACHINE

INTRODUCTION TO TRANSFORMER

The Basic Transformer

A basic transformer is an electrical device constructed of two coils of wire (windings) magnetically coupled to each other so that there is a mutual inductance for the transfer of power from one winding to the other.

A schematic of a transformer

INTRODUCTION TO TRANSFORMER

The source voltage is applied to the primary winding, and the

load is connected to the secondary winding.

The primary winding is the input winding, and the secondary

winding is the output winding.

There are three general categories of core material: air, ferrite,

and iron.

Schematic symbols based on type of core.

INTRODUCTION TO TRANSFORMER

The amount of magnetic coupling between the primary winding and

the secondary winding is set by the type of core material and by the

relative positions of the windings.

Transformers with cylindrical-

shaped cores.

Iron-core transformer construction with

multilayer windings.

INTRODUCTION TO TRANSFORMER Some common types of transformers.

Turns Ratio

Function of transformer stepping up or stepping down ac voltage

or currents

Planar transformer

Low-voltage transformer

Common type of small

transformers

Example 2

A transformer primary winding has 100 turns, and the secondary

winding has 400 turns. What is the turns ratio?

Solution:

INTRODUCTION TO TRANSFORMER

How does a transformer work? An AC current in the primary coil creates a changing magnetic

field in the iron core.

This changing magnetic field induces a current in the secondary coil as described by Faradays Law.

Primary voltage Iron core

INTRODUCTION TO TRANSFORMER

Direction of winding

The direction of the windings determines the polarity of the voltage

across the secondary winding (secondary voltage) with respect to the

voltage across the primary winding (primary voltage).

Phase dots indicate relative polarities of primary and secondary

voltages.

What is a step-up transformer?

STEP-UP AND STEP DOWN TRANSFORMERS

A transformer in which the secondary voltage is greater than the

primary voltage.

The amount that the voltage is stepped up depends on the turns

ratio.

1N

N

V

V

1

2

rms1

rms2

STEP-UP TRANSFORMERS

Applications

Power plants to increase the generated voltage and send it to high

voltage transmission lines.

To increase the voltage in order to get higher electrical field (TVs,

Radar and Microwaves,)

Example 3

The transformer in Figure has a turns ratio of 3. What is the voltage

across the secondary winding?

Solution:

Note that the turns ratio of 3 is indicated on the schematic as 1:3. meaning that

there are three secondary turns for each primary turn.

What is a step-down transformer?

STEP-UP AND STEP DOWN TRANSFORMERS

A transformer in which the secondary voltage is less than the primary

voltage.

The amount by which the voltage is stepped down depends on the

turns ratio.

1N

N

V

V

1

2

rms1

rms2

STEP DOWN TRANSFORMERS

Electrical distribution networks (to reduce the voltage from medium

voltage (10,000 V 30 000 V) to low voltage (110 V 208 V) for

different customers).

Applications

Distribution Transformers used by Hydro companies to deliver the electric energy

STEP DOWN TRANSFORMERS

To reduce plug voltage (110 V) to lower voltages in electronic.

Equipments/ circuits such as radio, phone, laptop, adaptors,

Applications

Example 4

The transformer in Figure has a turns ratio of 0.2, What is the

secondary voltage?

Solution:

LOADING THE SECONDARY WINDING

When a resistive load is connected to the secondary winding of a

transformer, the relationship of the load (secondary) current and the

current in the primary circuit is determined by the turns ratio.

Thus, for a step-up transformer, in which n is greater than 1, the

secondary current is less than the primary current.

For a step-down transformer, n is less than 1, and Isec is greater than

Ipri When the secondary voltage is greater than the primary voltage, the

secondary current is lower than the primary current and vice versa.

Example 5 The two transformers in Figure have loaded secondary windings. If the

primary current is 100 mA in each case. what is the load current?

SOLUTION

IDEAL TRANSFORMER

Ideal transformer is one with perfect coupling (k=1).

Ideal transformer is a unity-coupled, lossless transformer in which

the primary and secondary coils have infinite self inductances.

Iron core transformers are close approximation to ideal transformer.

These are used in power systems and electronics.

Ideal Transformer Circuit Symbol for Ideal Transformers

IDEAL TRANSFORMER

Relating primary and secondary quantities in an ideal transformer.

The turns ratio or transformation ratio:

nI

I

N

N

V

V

2

1

1

2

1

2

1. A transformer primary winding has 100 turns, and the secondary

winding has winding 400 turns. What is the turns ratio?

n = Nsec / Npri = 400/100 = 4

2. A certain transformer has a turn ratio of 10. If Npri = 500, what is

Nsec?

n = 10, Npri = 500

Nsec = n X Npri = 10 X 500 = 5000

Example 5

For an ideal transformer , the complex power (VA) in the primary winding is equal to the secondary:

P1 = V1I1 = V2I2 = P2

where, P1= power in the primary winding

P2=power in secondary winding

(This shows that the complex power supplied to the primary is

delivered to the secondary without loss, since ideal transformer is

lossless).

IDEAL TRANSFORMER

Transformer Efficiency

The efficiency () of the transformer is measure of the percentage

of the input power that delivered to the output.

100% P

P

in

out

DC GENERATOR

Simplified dc generator. Consist of:

A single loop of wire rotates in a permanent magnetic field

Commutator split-ring arrangement, connected at each end

of the loop.

Brushes the fixed contacts that connects wire to external

circuit.

DC GENERATOR

DC GENERATOR

When driven by an external mechanical force the wire loop rotates

through the magnetic field and cuts through the flux lines at varying

angles.

End view of wire loop cutting through the magnetic field.

At position A the loop of wire is effectively moving parallel with the

magnetic field the rate at which it is cutting through the magnetic

flux lines is zero.

DC GENERATOR

As the loop moves from position A to position B the loop cuts

through the flux lines at an increasing rate.

At position B, it is moving effectively perpendicular to the magnetic

field and thus is cutting through a maximum number of lines.

As the loop rotates from position B to position C, the rate at which it

cuts the flux lines decreases to minimum (zero) at C.

From position C to position D, the rate at which the loop cuts the flux

lines increase to a maximum at D and then back to a minimum again at

A.

End view of wire loop cutting through the magnetic field.

DC GENERATOR

Recall from Faradays law:

1. When a wire moves through a magnetic field, a voltage is

induced.

2. According to Faradays Law amount of induced voltage is

proportional to the number of loops turns in the wire and the

rate at which it is moving with respect to the magnetic field.

3. The angle at which the wire moves with respect to the magnetic

flux lines determines the amount of induced voltage because

the rate at which the wire cuts through the flux lines depends

on the angle of motion.

DC GENERATOR

Operation of Basic DC Generator

1. Assume that the loop is in its instantaneous horizontal position, so

the induced voltage is zero.

2. As the loop continues in its rotation, the induced voltage builds up

to a maximum at position B. as shown in part (a) of the figure.

3. Then, as the loop continues from B to C, the voltage decreases to

zero at position C, as shown in part (b).

DC GENERATOR

During the second half of the revolution ,the brushes switch to

opposite commutator sections, so the polarity of the voltage remains

the same across the output.

Thus, as the loop rotates from position C to position D and then back

to position A, the voltage increases from zero at C to a maximum at D

and back to zero at A.

DC GENERATOR

Induced voltage over three rotations of the wire loop in the dc generator.

The induced voltage for a two-loop generator. There is much less variation in the induced voltage.

When more wire loops are added, the voltage induced across each loop are combined across the output resulting a smoother dc voltage

DC GENERATOR

Operation of Basic DC Generator

DC MACHINE

The direct current (dc) machine can be used as a motor or as a

generator.

DC Machine is most often used for a motor.

The major advantages of dc machines are the easy speed and

torque regulation.

However, their application is limited to mills, mines and trains.

As examples, trolleys and underground subway cars may use dc

motors.

In the past, automobiles were equipped with dc dynamos to

charge their batteries.

DC MOTOR

Direct current (DC) motors convert the electrical energy

into mechanical motion.

They drive devices such as hoists, fan, pumps, punch-presses

and cars.

These devices may have a definite torque-speed characteristic

(such as a pump or fan ) or a highly variable one ( such as hoist

or automobile).

38

Fundamental characteristics of DC

Motors

N

S

Stator

Coils

N

SS

N

Rotor

Stator

S

N

S

N

N

S

End view Time 0

N

S

Stator

Coils

N

S NRotor

Stator

S

N

S

N

N

S

S

End view Time 0+

Shifting magnetic field in rotor causes rotor to be forced to turn

39

Nature of commutation Power is applied to armature

windings

From V+

Through the +brush

Through the commutator contacts

Through the armature (rotor) winding

Through the brush

To V-

Rotation of the armature moves the commutator, switching the armature winding connections

Stator may be permanent or electromagnet

Rotor

V-

V+Brush

Assembly

S

S

N

N

N

Stator

Stator

Comutator

V-

V+

LP11 40

Armature of a DC Motor

Figure : Cutaway view of a dc motor.

DC Machines Construction

DC Machines Construction

Motor Ratings

Some motor are rated by the torque they can

provide, others are rated by the power they are

produce.

Torque and power are different physical

parameters. If one is known, the other can be

obtained. Torque tend to rotate the object. In dc motors, torque is

proportional to the amount of flux and to the armature current.

AIKT T = Torque (newton-meter) (N-m)

K = constant

= magnetic flux (weber @ Wb)

IA = armature current ( Amperes)

Motor Rating

Power is defined as the rate of doing work.

The equation to determine the power from

torque is given by:

TsP 105.0 P = Power in watts

T = Torque in newton-meter (N-m)

s = speed of motor

The torque-speed characteristic of the motor must be adapted to

the type of the load it has to drive.

DC motors are classified based on the connection between field

coil and armature coil.

i) Series wound motor

ii) Shunt wound motor

iii) Compound wound motor

iv) Separate wound motor Shunt motors

Types of Motors

12/3/2002 BAE 4353 46

DC motor wiring topologies P

erc

en

t o

f ra

ted

Sp

ee

d

Percent of Rated Torque

120

Series

Com

pound

Shunt100

80

60

40

20

0

400300200100

0

Sh

un

t F

ield

Series Field

Sh

un

t F

ield

Series Field

Shunt

Series

Compound

Torque Speed Characteristic

In shunt motor, armature and filed windings are connected parallel and at same voltage.

Field winding resistance is higher compared to armature winding. High torque characteristics for wide range of speed.

Torque can be increased by increasing current in the motor. Generally field resistance is changed to achieve this. Starting torque is 1.5 times of rated torque.

To reverse the direction of the rotor, armature or field polarity is to be reversed.

DC Shunt Motor

DC Shunt Motor

Armature and field windings are connected in series. The current is same in both the windings.

Very high starting torque compared to shunt motors and very high speed at no load.

Series motor can fail on sudden removal of load and this condition is called run-away. Parabolic variation between speed and torque and nearly constant power output over a wide range.

Reversing the supply voltage has no effect on the direction of motor rotation because both field direction and armature current directions are changed.

DC Series Motor

DC Series Motor

It is a combination of shunt and series motor. Contain two coils one in series and another in parallel. Maximum speed is limited, but the speed regulation is not as good as shunt motor.

DC Compound Motor

1. DC motor control is achieved by changing the armature current or field current.

2. Control system is added in the low power part of the system. For example field coil of shunt motor.

3. In a series motor, control resistor is put parallel to field coil to control current in it.

4. To understand how these changes will effect the output detail study on DC motor operation is required.

DC Motor Control

Braking: DC motor can be stopped by switching off the power supply and let it coast. Large motors may take lot of time due to large inertia.

Electromechanical braking is used for quick slow down. In this case the stator is kept energized and it is used as generator.

It means that the output of the rotor is given to resistor or fed back to the power supply. It is very effective at high

speeds. Another method is armature current direction is changed and it is switched off when it comes to halt.

DC Motor Control

DC Motor Control

Motor efficiency

Comparison of a DC generator and a DC motor:

DC Generator DC Motor

No source is connected to the commutator circuit

A DC source is connected to the commutator circuit, producing current through the wire loop.

External mechanical energy is used to rotate the loop to produce an induced voltage

External electrical energy is used to rotate the loop to produce a mechanical rotation.

DC Generator Vs DC Motor

INTRODUCTION TO MACHINE THEORY

In electrical machine, electrical energy is used to

drive machines.

All electrical machines operate on a common set

of principles operate either in alternating

current or direct current.

CONTENTS

Basic Principles:

CONVERSION PROCESS IN A MACHINE

MAGNETIC FIELD ENERGY

ANALYSIS OF FORCE OF ALIGNMENT

DIVISION OF CONVERTED ENERGY AND

POWER

Introduction

All electrical machine operate on a common set

of principles.

The most simple electrical machine involve with

linear movement (e.g. relay and contactor).

Rotating machine (e.g. motors)

Conversion Process In A Machine

An electromagnetic machine is one that links an

electrical energy system to another energy

system by providing a reversible mean of energy

flow in its magnetic field.

The coupling between two system is called

mutual link.

The energy transferred from one to another

system is temporarily stored in the field.

Conversion Process In A Machine

Energy conversion:

Mechanical to electrical energy (generator)

Electrical to mechanical energy (motor)

An electromagnetic system can develop a

mechanical force in two ways:

By alignment

By interaction

The force of alignment

The figure show two poles situated opposite

one to another.

A flux pass through the surfaces are said to be

magnetized surface.

They are attracted towards one another.

The force of alignment act in any direction will

increase the magnetic energy stored in the

arrangement.

It will try to bring the poles together since this

decreases the reluctance of the air gap in

magnetic circuit and hence will increase the

flux and the energy stored.

Force of attraction

Force of Attraction

The force of alignment

The poles are not situated opposite one to

another.

The resultant force tries to achieve greater

stored magnetic energy by two component

action:

By attraction of the poles toward one another as

before.

By aligning poles laterally

If the poles move laterally, the cross-section

area of air gap is increased and the reluctance

is reduced.

Both action attempt to align the poles to

point of maximum stored energy.

Lateral Force of Alignment

Lateral force of alignment

Application of force of alignment

Electromagnetic relay demonstrate the force of

alignment giving rise to linear motion.

The force of alignment can also be used to produce the

rotary motion.

i. When the coil is energized, a flux set

up in the relay core and their air gap.

ii. The surface adjacent to the air gap

become magnetized and are attracted. (

pulling the armature plate in the

direction indicated in a figure given).

i. The rotor experiences a torque due to the

magnetized rotor and pole surfaces attempting to

align themselves.

ii. Torque occurs in any rotating machine.

Alignment torque

The force of interaction

Advantage : simplicity in its application

Many application involving the force of

interaction to give rise the rotary motion include

synchronous and induction machines.

Rotary Machine illustrate force of interaction

By passing a current through the coil, it experiences

a force on each of the coil sides resulting in a torque

about the axis rotation.

Alignment torque

Method Analysis of Machine

Performance

There are two possible approaches to analysing the energy conversion. i. The so-called classical approach.

The operation of machine can be predicted from study of the machine losses.

This classical approach can be use in order to analyze the characteristic of AC Synchronous Machine, Induction Motor, DC Motor, and in motor selection and efficiency.

Disadvantage It deals almost exclusively with machine operating under steady state

conditions, thus transient response conditions are virtually ignore

( i.e. when it is accelerating and decelerating.)

The losses of each machine are different. It follows that each type of machine requires to be separately analysed.

Method Analysis of Machine

Performance

ii. The generalized-machine approach.

This approach depends on a full analysis of the coupling field as observed from terminals of the machine windings.

The losses are recognized as necessary digressions from the main line of the analysis.

The coupling field is described in term of mutual inductance.

The measured quantities are voltage, current, power, frequency, torque and rotational speed, from which may be derived the resistance and inductance values for the coils.

It is possible to analyze to performance both under steady state and transient conditions.

Air Gap on Magnetic circuit

Let us consider the effects that an

air gap has on magnetic circuit.

The spreading of the flux line

outside the common area of core

for the air gap known as fringing.

Ignore the fringing effect and

assume the flux distribution to be

as in Figure (b).

g

g

gA

B

bygiven is gapair theofdensity Flux

Where;

g = core Ag = Acore

In most practical applications, the permeability

of air is taken to be equal to that of free space.

Magnetizing force of the air gap determined by

o

g

g

BH

Air Gap on Magnetic circuit

Magnetic Field Energy

The energy in magnetic field is given by

Energy storage

However, there are a number of way in which the inductance can be expressed.

These expressions can be substituted in the energy relation to give

Where;

= magnetic flux linkage, electric flux

= magnetic flux

F= force

i = Current

2

2

1Liw f

l

AN

S

N

ii

NL r

022

SFiw f2

1

2

1

2

1

All of these expressions for the energy

depend on the flux and the m.m.f being

directly proportional, i.e. the inductance is

constant.

Magnetic Field Energy

In the case of an air gap, the B/H characteristic

is straight, the energy stored given by

Fw

lBHw

l

BHw

f

f

f

2

1

A x 2

1

length andA area sectional-cross a has gapair theif

gapair of x volume2

1

Wf

B

H

The stored energy density is thus given by

o

f

Bw

2

2

Simple analysis of force of

alignment

Consider the force alignment between 2 poles of

the magnetic circuit.

Let there be a flux in the air gap and let there be

no fringing of the flux.

The uniform flux density in the air gap is given

by

CSA

A

Flux

And force F

x

AB

The poles separated by a small distance dx. There is

mechanical experience by poles and the work done is given

by

Assume the magnetic core is ideal ( infinity permeability and

no m.m.f to create a magnetic field in it)

The air gap has been increase by a volume A.dx

Since the flux density is constant, energy density must remain

unchanged.

Therefore, the increase in the stored energy

Simple analysis of force of

alignment

dxB

dWo

f A.x 2

2

dxFdWm .

Simple analysis of force of

alignment

Since the system is ideal and the motion has

takes slowly form one point to another, this

energy must be due to the input of mechanical

energy

o

ABF

2

2

dxAB

dxFo

.2

.2

fm dWdW

Force of magnetic field

Example 5

An electromagnetic is made using a horseshoe core as shown in Fig.36.14. the

core has an effective length of 600 mm and a cross-sectional area of 500 mm2.

A rectangular block of steel is held by the electromagnets force of alignment

and a force of 20 N is required to free it. The magnetic circuit through the

block is 200 mm long and the effective cross-sectional area is again 500 mm2.

the relative permeability of both core and block is 700. if the magnetic is

energized by a coil of 100 turns, estimate the coil current.

20 N

1. Principles of Electric Circuits; Conventional Current version, 8th Edition, Pearson, Floyd.

2. Fundamental of Electric Circuits. 2nd Edition, McGrawHill, Alexander & Sadiku.

3. Electrical Machines, Drives, And Power System, 6th Edition, Pearson Prientice Hall, Wildi.

Further reading