i

Table of Contents ACKNOWLEDGEMENT ............................................................................................................. vi

CHAPTER ONE ............................................................................................................................. 2

1.0 Testing and Measurement ..................................................................................................... 2

1.1 Wattmeters or Dynamometer ................................................................................................ 2

1.2 Measuring power in single phase circuit using wattmeter .................................................... 3

1.3 Methods for measuring a 3 phase power with wattmeter ..................................................... 3

1.4 Phase angle of three phase angle by 2-wattmeter ................................................................. 6

1.5 Errors in Wattmeter reading due to connections................................................................... 7

1.6 Other sources of errors in the wattmeter ............................................................................... 9

1.7 Specialized instrument for testing electrical installation .................................................... 10

1.8 Earth electrode resistance ................................................................................................... 13

1.9 Measuring Earth electrode resistance ................................................................................. 13

CHAPTER TWO .......................................................................................................................... 14

2.0 Transmission and Distribution of electric Power ................................................................ 14

2.1 Electric Power transmission ................................................................................................ 14

2.2 Advantages of using AC power in Transmission ............................................................... 15

2.3 Electric Distribution Plant................................................................................................... 15

2.4 Types of Electrical power Distribution System .................................................................. 18

2.5 Disadvantages of radial electrical power distribution ......................................................... 18

2.6 Advantages of a closed Ring Distribution System ............................................................. 19

2.7 Importance of Transformer in transmission of power ........................................................ 19

2.8 Importance of Transformer in Distribution of electrical power .......................................... 19

2.9 Three Phase AC Power Systems ........................................................................................ 20

2.10 Electrical power Distribution Switch Gear ....................................................................... 21

2.11 Types of Switch gear ........................................................................................................ 21

2.12 What is An Arc?................................................................................................................ 22

2.13 Arc in Circuit Breakers ..................................................................................................... 22

2.14 Methods of Arc Control in circuit breakers ...................................................................... 22

2.15 Fuse Advantages and disadvantages in electrical circuit .................................................. 24

ii

2.16 Fuse advantages ................................................................................................................ 24

2.17 Fuse Disadvantages ........................................................................................................... 25

2.18 Fusing factor ..................................................................................................................... 25

2.19 Limitations of a Fuse ........................................................................................................ 25

2.19 Relays ................................................................................................................................ 25

2.21 Operation Of A relay ........................................................................................................ 26

2.22 Advantages of relays ......................................................................................................... 26

2.23 Disadvantages of relays .................................................................................................... 26

2.24 Inverse definite minimum time (IDMT) protection relays ............................................... 27

2.25 Power factor ...................................................................................................................... 28

2.26 Power Triangle .................................................................................................................. 29

2.27 Disadvantages of low power factor in the system ........................................................... 30

2.28 Causes of low Power Factor ............................................................................................. 31

2.29 Methods for power factor improvement ........................................................................... 32

2.30 Calculating KVAR ratings and Capacitance ..................................................................... 35

2.31 Tables (Capacitor sizing in kVAr and Farads for PF correction) ..................................... 35

2.32 Converting Farads into KVAR and vice-versa ............................................................... 39

2.33 Factors affecting the choice of power cable ..................................................................... 43

2.35 Cable Insulation ................................................................................................................ 45

2.36 Advantages of materials used for cable conductors .......................................................... 45

2.37 Advantages Materials used for cable insulation ............................................................... 45

2.38 Dielectric Stress ................................................................................................................ 47

2.39 Methods of stress control in high voltage cable................................................................ 47

2.40 Principle of earthing power supply systems ..................................................................... 48

CHAPTER THREE ...................................................................................................................... 50

3.0 DC Machines ...................................................................................................................... 50

3.1 Electric Motors Mode ......................................................................................................... 50

3.2 Principle of operation of a simple D.C. motor .................................................................... 50

3.3 Generator Mode .................................................................................................................. 51

3.4 Principle of operation of a simple Generator ...................................................................... 51

3.5 DC machine construction .................................................................................................... 55

iii

3.6 Classification of DC Machine ............................................................................................. 56

3.7 EMF equation of a dc machine ........................................................................................... 57

3.8 D.C generators .................................................................................................................... 61

3.9 Types of D.C, generator and their characteristics ............................................................... 61

3.10 Generator Characteristics .................................................................................................. 63

3.11 Application of Separately excited field windings ............................................................. 64

3.12 Open circuit Characteristics .............................................................................................. 66

3.13 Load characteristics .......................................................................................................... 67

3.14 Application of a shunt wound DC generators ................................................................... 67

3.15 Load characteristics of DC generator ............................................................................... 68

3.16 Open circuit characteristics ............................................................................................... 68

3.17 Application of a series wound generators ......................................................................... 68

3.18 Characteristics Compound Wound Machines ................................................................... 71

3.19 Application of compound Generators ............................................................................... 71

3.20 Source of Losses in DC machines .................................................................................... 72

3.21 Efficiency of a DC generator ............................................................................................ 72

3.22 DC Motors ........................................................................................................................ 74

3.23 Back E.M.F ....................................................................................................................... 74

3.24 Torque of a DC Motor ...................................................................................................... 75

3.25 Types of DC motor and their characteristics .................................................................... 79

3.26 Characteristics of shunt wound DC motor ........................................................................ 80

3.27 Application of Shunt wound DC motors .......................................................................... 82

3.28 Characteristics of series DC wound Motor ....................................................................... 84

3.29 Characteristics of compound wound DC Motor ............................................................... 88

3.30 Application of compound DC wound Motor .................................................................... 88

3.31 The efficiency of a DC motor ........................................................................................... 88

3.32 DC motor starter ............................................................................................................... 93

3.33 The need for Motor Starter ............................................................................................... 94

3.34 Methods of varying the speed of a DC Motors ................................................................. 94

3.35 Armature Reaction and Commutation in DC Machines ................................................. 101

3.36 Commutation in DC Machine ......................................................................................... 101

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3.37 Armature Reaction .......................................................................................................... 101

3.38 Mains magnetic field of a machines ............................................................................... 102

3.39 Armature field ................................................................................................................. 103

3.40 Methods to neutralize armature reaction and commutation in DC Machines ................ 104

CHAPTER FOUR ....................................................................................................................... 111

4.0 Induction Motors ............................................................................................................... 111

4.1 Advantages of using a rotating magnetic field instead of stationary magnetic field ........ 111

4.2 Advantages of a Three Phase Induction Motors ............................................................... 111

4.3 Principle disadvantages of a three phase induction motor ................................................ 112

4.4 Classes of AC Machines ................................................................................................... 112

4.5 Three phase Induction Motor ............................................................................................ 112

4.6 Construction of a three phase induction motor ................................................................. 112

4.7 Squirrel cage rotor............................................................................................................. 113

4.8 Phase wound rotor............................................................................................................. 114

4.9 Production of a rotating magnetic field ............................................................................ 115

4.10 Principle of operation of a three-phase induction motor ................................................ 118

4.11 Synchronous speed of induction Motors......................................................................... 118

4.12 Slip in Induction Motor ................................................................................................... 121

4.13 Rotor e.m.f and Frequency.............................................................................................. 124

4.14 Rotor Impedance and current .......................................................................................... 127

4.15 Induction Motor losses and efficiency ............................................................................ 129

4.16 Torque equation For a induction Motor .......................................................................... 132

4.17 Relationship between, torque and rotor Power Factor .................................................... 137

4.18 Starting torque of three phase induction Motor .............................................................. 137

4.19 Starting torque of a squirrel cage rotor ........................................................................... 138

4.20 Starting torque of a slip ring motor (Phase wound Motor) ............................................. 138

4.21 Induction motor torque-speed characteristics ................................................................. 138

4.21 Speed torque characteristics of a three phase induction motors ..................................... 140

4.22 Squirrel cage induction motor characteristics ................................................................. 140

4.23 Wound –rotor induction motor characteristics ............................................................... 141

4.24 Starting methods for induction motor ............................................................................. 141

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4.25 Three Phase Synchronous Motor .................................................................................... 143

4.26 The advantages of the wound rotor motor compared with the cage type ....................... 143

4.27 Construction of three phase Synchronous Motor ............................................................ 143

Stator: Revolving Magnetic Field ....................................................................................... 143

4.28 Working of principle synchronous motor ....................................................................... 144

4.29 Main Features of Synchronous Motors ........................................................................... 144

4.30 Methods of Starting of Synchronous Motor ................................................................... 145

CHAPTER FIVE ........................................................................................................................ 146

5.0Transformers ...................................................................................................................... 146

5.1 Construction Of transformers ........................................................................................... 146

5.2 Categories of transformer basing on the construction ...................................................... 147

5.3 Elementary theory of ideal transformers........................................................................... 148

5.4 Transformer no-load phasor diagram ................................................................................ 152

5.5 Equivalent circuit of a transformer ................................................................................... 155

5.6 Transformer regulation ..................................................................................................... 158

5.7 Transformer Regulation .................................................................................................... 160

5.8 Transformer losses and efficiency .................................................................................... 163

5.9 Methods of Reducing eddy currents ................................................................................. 163

5.10 Maximum efficiency of Transformer .............................................................................. 167

5.11 Transformer Test ............................................................................................................. 168

5.12 Types of Transformer Tests ............................................................................................ 168

5.13 Why Transformer rating is in KVA? .............................................................................. 177

5.14 Autotransformers ............................................................................................................ 178

5.15 Advantages of Auto-transformer compared to double wound transformer .................... 178

5.16 Types of Autotransformers ............................................................................................. 178

Reference .................................................................................................................................... 180

vi

ACKNOWLEDGEMENT

I, Mr. Kifaru J. Malale, would like to thank God, my Almighty for giving me the power and

strength to prepare this Study guide. This study guide, is aimed for guiding students at NTA

Level 6 who pursue Diploma in Electrical & Electronics, on how to go through in order to cover

their syllabus for Electrical Power

Nevertheless, many thanks should go directly to all staff members (Both Academic and

Management Part), who truly, by one way or another advised me, in order to come up with a

good Study guide, that covers what is supposed under the syllabus

2

CHAPTER ONE

1.0 Testing and Measurement

1.1 Wattmeters or Dynamometer

The wattmeter is an instrument for measuring the electric power in watts of any given circuit.

The common instrument used to measure AC power is DYNAMOMETER wattmeter

It has been shown that, power in DC circuit is obtained by the following simple electrical

formula

( ) ( )P Current A xVoltage V

P IV watt

But power in AC circuit, can be calculated by the following formula

( ) ( ) cos

, , ,

cos

P current A xvoltage V x

Where phase angle between current and voltage

P IV

Structure of dynamometer wattmeter

Figure 1.1: Structure of Dynamometer

Wattmeter is a four terminal device that consists of a voltage and current measurement elements

The current coil, has low impedance, hence has a negligible voltage, while the voltage coil has

high impedance, hence it passes a negligible current

Current coil: responsible for measuring current

Voltage coil: Responsible for measuring voltage

3

AC power is given by

cos

cos

Power VoltagexCurrentx

Power VI

The wattmeter will display the average power, which is the product of the magnitude of the

voltmeter (V) and Ammeter (A) times the cosines of phase angle between the two (Voltage and

current)

1.2 Measuring power in single phase circuit using wattmeter

Figure bellows, shows a typical connection of a WATTMETER used for measuring Single phase

AC power supplied to a load

Figure 1.2: Wattmeter in single phase source

i. A current coil , which is connected in series with the load ,it is like an Ammeter

ii. A Voltage coil , which is connected in parallel with the load , it is like a voltmeter

Question: Electrical Power June 2014, Question 1 a)

1.3 Methods for measuring a 3 phase power with wattmeter

There are various methods which are used for measurement of a 3 phase power in a three

phase circuit basing on the numbers of wattmeter being used. We have the following

methods

a. Three wattmeters method

b. Two wattmeters methods

c. One wattmeters methods

a. measurement of a three phase power by three wattmeters

In this case, three wattmeters, each one connected to each of one phase line, it is clear

that each wattmeter will give reading, which correspond to power measured in a

single phase

4

Figure 1.3: Three wattmeter method

The resultant sum of all the readings of wattmeter will give the total power of the circuit.

Mathematically we can say that

1 2 3TP P P P

b. measurement of a three phase power by two wattmeters

In this method we have two types of connections

i. Star connection Loads

When the star connected load, the diagram is shown in below-

Figure 1.4: Two wattmeter Method

By two wattmeters method, we can see that the total power delivered to the above system, can be

given by the sum of the individual power of each wattmeter

5

1 2

1 1 1 3 2 2 2 3

1 1 3 2 2 3

1 1 1 3 2 2 2 3

1 1 2 2 3 1 2

1 2 3 1 2 3

1 1 2 2 3 3

1 1 2 2 3 3

, ( ), ( )

( ) ( )

( )

, 0, ,

( )

T

T

T

T

T

T

P P P

But P I V V P I V V

P I V V I V V

P I V I V I V I V

P I V I V V I I

But I I I I I I substitute above

P I V I V V I

P I V I V V I

ii. For a delta connected Loads

When the Delta connected load, the diagram is shown in below

Figure 1.5: Two wattmeter method in Delta circuit

By two wattmeters method, we can see that the total power delivered to the above system, can be

given by the sum of the individual power of each wattmeter

1 2

1 3 3 1 2 2 2 1

3 3 1 2 2 1

3 3 3 1 2 2 2 1

3 3 2 2 3 1 2 1

3 3 2 2 1 3 2

1 2 3 3 2 1

3 3 2 2 1 1

, ( ), ( )

( ) ( )

( )

, 0, ,

T

T

T

T

T

T

P P P

But P V I I P V I I

P V I I V I I

P V I V I V I V I

P V I V I V I V I

P V I V I I V V

But V V V V V V substitute above

P V I V I I V

6

1.4 Phase angle of three phase angle by 2-wattmeter

Consider the diagram below

Figure 1.6: Phase angle by 2 wattmeter method

In case of balanced 3 phase system, the power factor, can be proved as follows

Assuming the wattmeter W1 is lagging, and then we can say that , power displayed by the W1, is

given by

1 cos30cos sin30sinL L L LP V I V I

Assuming also the wattmeter W2 is leading, then we can say that , the power displayed by the

W2, is given by

2

2

cos(30 )

cos30cos sin30sin

L L

L L L L

P V I

P V I V I

1

1

2

2

1 2

1 2

cos(30 )

cos30cos sin 30sin

cos(30 )

cos30cos sin 30sin

( cos30cos sin 30sin ) ( cos30cos sin 30sin )

cos30cos sin 30sin cos30

L L

L L L L

L L

L L L L

L L L L L L L L

L L L L L L

P V I

P V I V I

P V I

P V I V I

P P V I V I V I V I

P P V I V I V I

1 2

1 2

cos sin 30sin

2 sin 30sin

sin ......................( )

L L

L L

L L

V I

P P V I

P P V I i

7

Again, proceed in the following manner

1 2

1 2

1 2

( cos30cos sin 30sin ) ( cos30cos sin 30sin )

2 cos30cos

3 cos ..................( )

L L L L L L L L

L L

L L

P P V I V I V I V I

P P V I

P P V I ii

Then take equation (i)/(ii)

1 2

1 2

1 2

1 2

1 2

1 2

1 2

1 2

1 1 2

1 2

sin

3 cos

sin

3 cos

tan

3

tan 3

tan 3

L L

L L

V I P P

P PV I

P P

P P

P P

P P

P P

P P

P P

P P

1.5 Errors in Wattmeter reading due to connections

There are two possible ways of connecting the Wattmeters in the single phase AC circuit

In these two methods, neither of them measures the correct power dissipated by the load in the

circuit. A wattmeter is supposed to indicate the power consumed by the load, but its actual

reading is slightly higher due to extra power losses that occur inside its own coils. Therefore,

amount of errors introduced; depend much on the type of connection

1. Pressure coil/voltage coil on the supply side

In this method, voltage coil is connected to the supply side, the voltage applied to the

pressure coil/voltage coil is higher than that of the load

Figure 1.7: Voltage coil on the supply side

8

Now, from above circuit connection

Voltage across pressure coil of the wattmeter is Vl

But V1 is the phasor sum of Load Voltage V, and voltage across current Coil V‘ (=Ir,

where r is the resistance of the current coil)

Hence, the total power reading of the wattmeter, for this type of connection, will be given

as

cosT lP V I

But from this equation, we can say that, the total power PT displayed by the wattmeter

2

, , , , , , ,

cos

, , , , , , , , ,

, tan , , ,

T

T

P Power in the load Power in the current coil

P IV I r

where

phase difference between V and I in the current coil

r small resis ce of the coil

2. Pressure coil/voltage coil on the load side

In this method, voltage coil is connected to the load side. Now, the current coil CC

carries extra current taken by the pressure coil

Figure 1.8: Voltage coil on the load side

The current through a current coil (CC), I1 is the phasor sum of load current I, and current

through voltage coil (VC), I‘, the power reading indicated by the wattmeter is given by

1 cosTP VI

Where,

1

1

, , , ,

, , , &

V load voltage

I current in the current coil

phase angle between V I

9

But form the phasor diagram, we can see that

1 cos cos 'I I I

1

2

cos ( cos ')

cos ', , '

cos

T

T

T

but

P VI V I I

VP VI VI but I

R

VP VI

R

TP Power in load power in voltage coil circuit

1.6 Other sources of errors in the wattmeter

a) Inductance of both voltage or current coils

This causes phasing effect of the voltage coil

This phasing effect can be reduced by introducing, the high non inductive resistance R

connected in series with the voltage coil

Figure 1.9: Inductance of both voltage and current coils

b) Errors due to some voltage drop inside the wattmeter instrument that leads to a little

increase in extra power displayed in the output of the instrument

Total power displayed = Power consumed inside instrument + power consumed across

the load under measurement

c) Errors due to small current taken by a voltage coil

10

1.7 Specialized instrument for testing electrical installation

For all low voltage electrical installation verification and condition reporting work, electrical

contractors and installers should, as a minimum, have the following range of test instruments

Continuity test instrument

Where the installation can be safely isolated from the supply, then the circuit. Protective

conductors and equipotential bonding conductors can be disconnected from the main earthing

terminal in order to verify their continuity

Where the installation cannot be isolated from the supply, the circuit protective conductors and

the equipotential bonding conductors must not be disconnected from the main earthing terminal,

as under fault conditions extraneous metalwork could become live. Under these circumstances a

combination of inspection, continuity testing and earth loop impedance testing should establish

the integrity of the circuit protective conductors

When testing the effectiveness of the main bonding conductors or supplementary bonds, the

resistance value between any service pipe or extraneous metalwork and the main earthing

terminal should not exceed 0.05 ohms

Insulation resistance test instrument

This is a test that can be carried out in whole installation, or in a single circuit. The test is

necessary to find out if there is likely to be any leakage through the insulated part of installation.

A leakage could occur for various reasons. The voltage used in an insulation test of 230V ac is

500V which is more than double the voltage circuit

Cable insulation could deteriorate through aging of the cable. A low insulation resistance caused

by aging of the cable, is found where the rubber has been used as an insulator of the cable

Cables which are crushed by the floor boards, clipped on the edge or worn thin where pulled

through holes in joints next to other cable can give a very low reading when testing

The instrument used to test insulation is called an insulation resistance tester. To comply with the

requirements of safety and health executive, the instrument must be capable of delivering current

of 1mA when a voltage of 500V DC is applied to a resistance of 0.5MΩ. the table below, gives

the test voltages and minimum acceptable resistance

11

Circuit between 0V-

50V a.c

Circuit between 50V-

500V a.c

Circuit between

500V-1000Va.c

Required Test Voltage 250V DC 500V DC 1000V DC

Minimum Acceptable

Resistance

0.25MΩ 0.5MΩ 1MΩ

In 17th

Edition of

Wiring regulation

0.5MΩ 1MΩ 2MΩ

For Domestic Installation, the testing should be done immediately from the day the Installation

commences

Testing the Whole Installation

In new Domestic Installation, it is advised to carry out the insulation resistance test of the whole

installation before connecting the supply in the house by adopting the following safe procedures

i. Safe Isolation must be done before commencing the test

ii. Inform the occupants of the building that, testing is to be done

iii. Ensure that all protective devices are in place and they are switched ON

iv. Remove all lamps from fittings, where accessible

v. If the lamps are not accessible, open the switch controlling those lamps

Note:

Great care must be taken as during this test, 500V DC will be passed through cable, any

electrical equipment‘s which is left connected will be damaged

Loop impedance test instrument

This is used to test the earth fault loop impedance of the circuit

Earth fault loop impedance is the path followed by fault current when a low impedance

fault occurs between the phase conductor and earth, i.e. ―earth fault loop‖. Fault current is

driven round the loop by the supply voltage. The higher the impedance, the lower the fault

current will be and the longer it will take for the circuit protection to operate.

To make sure the protection operates fast enough; the loop impedance must be low. Every

circuit must be tested to make sure that the actual loop impedance does not exceed that

specified for the protective device concerned. It is recommended that the Ze test be done

first. This test, done at the distribution board, gives the loop impedance of the circuit,

excluding the installation.

The path followed by fault current as the result of a low impedance occurring between the

phase conductor and earthed metal is called the earth fault loop. Current is driven through the

loop impedance by the supply voltage.

12

Figure 1.10: Complete earth loop path

Loop impedance test instrument, allows current of up to 25 A to flow around the earth fault

loop . It measure the current flow, and by doing so, can calculate the resistance of the earth

fault loop. The values given are given in ohm

The maximum value accepted for earth fault loop impedance depend on the type of electrical

circuit components used like circuit breakers

Residual current device test instrument (Residual current device Tester RCD’s)

A residual-current device (RCD), or residual-current circuit breaker (RCCB) is an

electrical wiring device that disconnects a circuit whenever it detects that the electric current

is not balanced between the energized (line) conductor(s) and the return (neutral) conductor.

In normal circumstances, these two wires are expected to carry matching currents, and any

difference usually indicates a short circuit or other electrical anomaly is present. Even a small

leakage current can mean a risk of harm or death due to electric shock if the leaking electric

current passes through a human being; a current of around 30 mA (0.030 Amps) is

potentially sufficient to cause cardiac arrest or serious harm if it persists for more than a

small fraction of a second

RCDs are usually testable and resettable devices. Commonly they include a button that when

pressed safely creates a small leakage condition, and a switch that reconnects the conductors

13

when a fault condition has been cleared. Depending upon their design, some RCDs

disconnect both the energized and return conductors upon a fault, while others only

disconnect the energized conductor, and rely upon the return conductor being at ground

(earth) potential. The former are commonly known as "double pole" designs; the latter as

"single pole" designs. If the fault has left the return wire "floating", or not at its expected

ground potential for any reason, then a single pole RCD model will leave this conductor still

connected to the circuit when it detects the fault.

1.8 Earth electrode resistance

Earthing of electrical systems is essential for the correct functioning and the protecting of life

and equipment in the event of faults. The earth electrode (connection of the earthing system to

the ground) is an essential part of any system.

The estimation of electrode resistance and functioning during the design stage ensures workable

solutions are proposed, enhances the operation and potentially reduces the cost of any

installation.

The earth Electrode resistance should always be as low as possible in order to provide a good

protection of equipment in the event of electric faults

1.9 Measuring Earth electrode resistance

The approximate resistance R of the electrode in ohms:

where L = length of conductor in meters

ρ = resistivity of the soil in ohm-meters (see ―Influence of the type of soil‖ )

14

CHAPTER TWO

2.0 Transmission and Distribution of electric Power

2.1 Electric Power transmission

Is a process in the delivery of electricity to consumers and also the bulk transfer of electric

power. Electric power can be transmitted through overhead power cables or power line,

supported over high towers

Power lines are overhead wires supported by high towers that transmit electric energy from

power supplies or plants. The centre strands of power lines are made of steel to give them

strength and the outer strands are made of aluminum because of its lightness and ability to carry

current. The wires are insulated from the towers by porcelain insulators to prevent the loss of

electric energy

A.C. power transmission is the distribution of power using alternating current.

Generation

Electricity is produced, or generated, by the turning of turbines. In most power plants, these

turbines are turned by pressurized steam. The steam is created by the burning of coal or other

fossil fuels in massive boilers. In the case of hydroelectricity, the force of rushing water turns the

turbines.

Transmission

once the turbines generate the electricity, its voltage is significantly increased by passing it

through step-up transformers. Then the electricity is routed onto a network of high-voltage

transmission lines capable of efficiently transporting electricity over long distances.

Distribution

At the electric distribution substation that serves your home, the electricity is removed from the

transmission system and passed through step-down transformers that lower the voltage. The

electricity is then transferred onto your local electric co-op's network of distribution lines and

delivered to your home. There, the electricity's voltage is lowered again by a distribution

transformer and passed through your electric meter into your home's network of electric wires

and outlets.

15

2.2 Advantages of using AC power in Transmission

A.C. voltages have the advantage of increasing and decreasing in value more readily than that of

the (D.C).

Transmission efficiency is improved by increasing the voltage using a step up transformer which

reduces the current in the conductors while keeping the power transmitted nearly equal to the

power input. The reduced current flowing through the conductor reduces the losses in the

conductor

In alternating current systems, energy loss across power lines is reduced because transformers

make it possible to raise the A.C. voltage to very high values. These high voltages allow the

same level of electric power made available at a lower current. This results in less power loss,

smaller transmission cables and higher efficiency. In addition to stepping up or raise the voltage

for long distance transmission, transformers also step-down or lower the voltage to the

requirements of the load

2.3 Electric Distribution Plant

Refers to that all part of electric power system between the bulk power sources and consumers

services switches.

The distribution plant occupies an important place in any electric power system. Briefly,

its function is to take electric power from the bulk power source or sources and distribute

or deliver it to the consumers

It can be divided into two main parts.

Transmission System

Distribution System

Furthermore, AC power supply Network, can be divided into five elements, as shown

below

1. Generating Station

2. Primary transmission

3. Secondary transmission

4. Primary Distribution

5. Secondary Distribution

Following is detail of the above sections

i. Generating Station: The place where electric power produced by parallel connected three phase

alternators/generators is called Generating Station. The Ordinary generating voltage may be

11kV, 11.5 kV 12kV or 13kV. But economically, it is good to step up the produced voltage

from (11kV, 11.5kV Or 12 kV) to 132kV, 220kV or 500kV or greater (in some countries,

up to 1500kV) by Step up transformer (power Transformer).

16

ii. Primary Transmission: The electric supply (in 132kV, 220 kV, 500kV or greater, depending on the country) is

transmitted to load center by three phase wire overhead transmission system.

Load Centre: refers to that part of the city where consumers with large electrical power

requirements can be found

iii. Secondary transmission: Area far from city which has connected with receiving station by line is called Secondary

transmission. At receiving station, the level of voltage reduced by step-down transformers

up to 132kV, 66 or 33 kV, and Electric power is transmitted by three phase three wire

overhead system to different sub stations. So this is a Secondary Transmission.

iv. Primary Distribution: At a substation, the level of secondary transmission voltage (132kV, 66 or 33 kV) reduced

to 11kV by step down transforms.

generally, electric supply is given to those heavy consumer which demands is 11 kV, from

these lines which carries 11 kV ( in three phase three wire overhead system) and they make

a separate substation to control and utilize this power. Consider the following diagram

Figure 2.1: Big consumers (factories), connected to Electrical power supply system

in other cases, for heavier consumer (at large scale) their demand is about 132 kV or 33

kV. they take electric supply from secondary transmission or primary distribution ( in 132

kV, 66kV or 33kV) and then step down the level of voltage by step-down transformers in

their own substation for utilization ( i.e. for electric traction etc).

v. Secondary Distribution: Electric power is given by (from Primary distribution line i.e.11kV) to distribution

substation. This substation is located near by consumers areas where the level of voltage

reduced by step down transformers to 440V.

These transformers called Distribution transformers, three phase four wire system). So there

is 400 Volts (Three Phase Supply System) between any two phases and 230 Volts (Single

Phase Supply) between a neutral and phase (live) wires. Residential load (i.e. Fans, Lights,

and TV etc.) may be connected between any one phase and neutral wires, while three phase

load may be connected directly to the three phase lines.

17

To understand this explanation, consider the diagram below that shows how domestic house and

three phase load are connected directly through secondary distribution

Figure 2.2 : Domestic Houses connected to AC power

SINGLE LINE PHASE DIAGRAM OF A TYPICAL THREE PHASE POWER SYSTEM

FROM GENERATOR TO CONSUMERS

Figure 2.3: Single line phase diagram of 3 phase power from generation to consumer

18

2.4 Types of Electrical power Distribution System

a) Radial Electrical power distribution

In this system, separate feeders radiate from single substation and feed the single

distributors at one end only. Figure below, shows a single line diagram of a radial system

for ac distribution. The radial system is employed only when power is generated at low

voltage, and substation is located at the centre of the load

Figure 2.4 Radial Electrical Power Distributions

This is a simplest distribution circuit and has lowest initial cost, however it suffers from

the following drawbacks

2.5 Disadvantages of radial electrical power distribution

i. The end of the distributors, nearest to the feeding point (feeder) will be heavily

loaded

ii. The consumers are dependent on a single feeder and a single distributor.

Therefore any faults on the feeder or distributors, cuts off the supply to the

consumers who are on the side of the fault away from the substation

iii. The consumers at the distant end of the distributor would be subjected to a serious

voltage fluctuations, when the load on the distributor changes

b) Closed Ring Electrical Power supply distribution

In this system, the primaries of the distribution transformers form a loop. This loop

circuit starts from the substation bus bars (feeder), makes the loop throughout the area to

be served and returns to the substation. Consider the diagram below

Figure 2.5: Closed Ring Electrical Power Supply distribution

19

Figure above, shows a single line diagram of a closed Ring distribution system,, where a

substation supplies through a closed feeder LMNOPQRS. The distributors, are tapped

from different points M,O and Q of the feeder through distribution transformers

2.6 Advantages of a closed Ring Distribution System

i. There are less voltage fluctuation at consumers terminals

ii. The system is very reliable, as each distributor is fed via two feeders. In the event

of faults on any section of the feeder , the continuity of supply will be maintained

c) Open Ring Electrical power distribution system

It provides the isolating switch or circuit breakers (Normally opened ), as a link for AC

supply

To provide high electrical power supply reliability, two substations are used, and this

substation will be fed from two sources. The customers substation is normally supplied

from a single end , in case of loss of supply from the one source end , for example due to

component failures, the normally opened point can be closed to restore supply after the

faulty portion of the component is isolated

2.7 Importance of Transformer in transmission of power

Transmission efficiency is improved by increasing the voltage using a step up transformer which

reduces the current in the conductors while keeping the power transmitted nearly equal to the

power input. The reduced current flowing through the conductor reduces the losses in the

conductor

In alternating current systems, energy loss across power lines is reduced because transformers

make it possible to raise the A.C. voltage to very high values. These high voltages allow the

same level of electric power made available at a lower current. This results in less power loss,

smaller transmission cables and higher efficiency. In addition to stepping up or raise the voltage

for long distance transmission

2.8 Importance of Transformer in Distribution of electrical power

Transformers are very important in distribution network, because their function is to step down

voltage from higher transmission voltage to lower levels so that it can be used by the end

consumers

These transformers are commonly known as DISTRIBUTION TRANSFOMERS, consider the

diagram below, where the transformers, step down voltage form 11KV to 400V/240V suitable to

be used by the end consumers

20

Figure 2.6: Distribution Transformer

2.9 Three Phase AC Power Systems

In three phase systems, they can further be categorized in two groups

a) Three wires, three phase systems (3 wires, three phase systems)

If large amount power, to be transmitted and the demand is constant on all phases, three

phase three wire system would be more preferable and economical, hence generally in

transmission of high power (HV AC),it is used and fed to delta connected primary to step

down.

Figure 2.7: Three wires-three phase AC systems

b) Four wires, three phase systems (4 wires, three phase systems)

Generally on power distribution side three phase four wire system is more preferable, yet

if the load is industrial loading (balanced mainly by induction motor/furnace etc.) three

phase three wire is used. In three phase four wire system, with domestic unbalanced load,

as unbalanced current get path through neutral, the phase/line voltage applied to

appliances remains as per requirement, and hence the better performance is obtained

21

Figure 2.8: Four wires-three phase AC systems

2.10 Electrical power Distribution Switch Gear

In an electric power system, switchgear is the combination of electrical disconnects switches,

fuses or circuit breakers used to control, protect and isolate electrical equipment. to maintain the

security levels at all distribution units and sub stations, it is critical to install safety devices and

mechanisms. While there are many mechanisms that help in safeguarding electrical connections

at residential and industrial areas, switchgear is one of the most popular ones due to its various

functions and features.

2.11 Types of Switch gear

Oil Switch

This is a switch, Oil-filled equipment allowed arc energy to be contained and safely controlled

Circuit breakers

In switchgear systems ‗power circuit breakers‘ can be used, these breakers allow for high

voltages to be utilized, as well as enabling breakers and other parts to be withdrawn or replaced

while the system is still live.

Electrical isolators/ Disconnectors

Isolator is a mechanical switch which isolates a part of circuit from system as when required.

Electrical isolators separate a part of the system from rest for safe maintenance works. Circuit

breaker always trip the circuit but open contacts of breaker cannot be visible physically from

outside of the breaker and that is why it is recommended not to touch any electrical circuit just

by switching off the circuit breaker. So for better safety there must be some arrangement so that

one can see open condition of the section of the circuit before touching it

22

Switch fuse/ Fuse Cutout

In electrical distribution, a fuse cutout or cut-out fuse is a combination of a fuse and a switch,

used in primary overhead feeder lines and taps to protect distribution transformers from current

surges and overloads. An overcurrent caused by a fault in the transformer or customer circuit will

cause the fuse to melt, disconnecting the transformer from the line. It can also be opened

manually by utility linemen standing on the ground and using a long insulating stick called a "hot

stick".

2.12 What is An Arc?

During opening of current carrying contacts in a circuit breaker the medium in between opening

contacts become highly ionized through which the interrupting current gets low resistive path

and continues to flow through this path even the contacts are physically separated. During the

flowing of current from one contact to other the path becomes so heated that it glows. This is

called arc.

2.13 Arc in Circuit Breakers

Whenever, on load current contacts of circuit breaker open there is an arc in circuit breaker,

established between the separating contacts. As long as this arc is sustained in between the

contacts the current through the circuit breaker will not be interrupted finally as because arc is

itself a conductive path of electricity. For total interruption of current the circuit breaker it is

essential to quench the arc as quick as possible. The main designing criteria of a circuit breaker is

to provide appropriate technology of arc quenching in circuit breaker to fulfill quick and safe

current interruption.

2.14 Methods of Arc Control in circuit breakers

Arc in a circuit breakers can be controlled or extinguished by two main ways

Oil Circuit Breaker

Mineral oil has better insulating property than air. In oil circuit breaker the fixed contact and

moving contact are immerged inside the insulating oil. Whenever there is a separation of current

carrying contacts in the oil, the arc in circuit breaker is initialized at the moment of separation of

contacts, and due to this arc the oil is vaporized and decomposed in mostly hydrogen gas and

ultimately creates a hydrogen bubble around the arc. This highly compressed gas bubble around

the arc prevents re-striking of the arc after current reaches zero crossing of the cycle. The oil

circuit breaker is the one of the oldest type of circuit breakers.

Air circuit breakers

This type of circuit breakers, is those kind of circuit breaker which operates in air at atmospheric

pressure. After development of oil circuit breaker, the medium voltage air circuit breaker (ACB)

is replaced completely by oil circuit breaker in different countries. But in countries like France

and Italy, ACBs are still preferable choice up to voltage 15 KV.

23

Working Principle of Air Circuit Breaker

The working principle of this breaker is rather different from those in any other types of circuit

breakers. The main aim of all kind of circuit breaker is to prevent the reestablishment of arcing

after current zero by creating a situation where in the contact gap will withstand the system

recovery voltage. The air circuit breaker does the same but in different manner. For

interrupting arc it creates an arc voltage in excess of the supply voltage. Arc voltage is defined as

the minimum voltage required maintaining the arc. This circuit breaker increases the arc voltage

by mainly three different ways,

1. It may increase the arc voltage by cooling the arc plasma. As the temperature of arc

plasma is decreased, the mobility of the particle in arc plasma is reduced, hence more

voltage gradient is required to maintain the arc.

2. It may increase the arc voltage by lengthening the arc path. As the length of arc path is

increased, the resistance of the path is increased, and hence to maintain the same arc

current more voltage is required to be applied across the arc path. That means arc voltage

is increased.

3. Splitting up the arc into a number of series arcs also increases the arc voltage.

The first objective is usually achieved by forcing the arc into contact with as large an area as

possible of insulating material. Every air circuit breaker is fitted with a chamber surrounding the

contact. This chamber is called 'arc chute'. The arc is driven into it. If inside of the arc chute is

suitably shaped, and if the arc can be made conform to the shape, the arc chute wall will help to

achieve cooling. This type of arc chute should be made from some kind of refractory material.

High temperature plastics reinforced with glass fiber and ceramics are preferable materials for

making arc chute.

The second objective that is lengthening the arc path, is achieved concurrently with fist

objective. If the inner walls of the arc chute is shaped in such a way that the arc is not only

forced into close proximity with it but also driven into a serpentine channel projected on the arc

chute wall. The lengthening of the arc path increases the arc resistance.

Vacuum Circuit Breaker

A vacuum circuit breaker is such kind of circuit breaker where the arc quenching takes place in

vacuum. The technology is suitable for mainly medium voltage application. For higher voltage

vacuum technology has been developed but not commercially viable. The operation of opening

and closing of current carrying contacts and associated arc interruption take place in a vacuum

chamber in the breaker which is called vacuum interrupter. The vacuum interrupter consists of a

steel arc chamber in the centre symmetrically arranged ceramic insulators. The vacuum pressure

inside a vacuum interrupter is normally maintained at 10 - 6

bar.

The main aim of any circuit breaker is to quench arc during current zero crossing, by establishing

high dielectric strength in between the contacts so that reestablishment of arc after current zero

24

becomes impossible. The dielectric strength of vacuum is eight times greater than that of air and

four times greater than that of SF6 gas.

This high dielectric strength makes it possible to quench a vacuum arc within very small contact

gap. For short contact gap, low contact mass and no compression of medium the drive energy

required in vacuum circuit breaker is minimum. When two face to face contact areas are just

being separated to each other, they do not be separated instantly, contact area on the contact face

is being reduced and ultimately comes to a point and then they are finally de-touched. Although

this happens in a fraction of micro second but it is the fact.

At this instant of de-touching of contacts in a vacuum, the current through the contacts

concentrated on that last contact point on the contact surface and makes a hot spot. As it is

vacuum, the metal on the contact surface is easily vaporized due to that hot spot and create a

conducting media for arc path. Then the arc will be initiated and continued until the next current

zero.

2.15 Fuse Advantages and disadvantages in electrical circuit

Fuse is the cheapest protection device in electrical circuit against short circuits and overloading

of circuits. Fuse is a metal wire or thin metal strip which has the property of low melting point

which is inserted into the electrical circuit as protective device.

Fuse provides protection against excessive currents which can flow in circuit during short

circuits. Under normal working condition the current flowing through the circuit is within safe

limits but when fault occurs such as short circuit occurs or when loads more than circuit capacity

is connected to it, current exceeds the limiting value results in fuse wire gets heated up, melts

and break the current. Thus fuse protects the machine or

2.16 Fuse advantages

Fuse is cheapest type of protection in an electrical circuit

Fuse needs zero maintenance

Operation of fuse is simple and no complexity is involved

Fuse has the ability to interrupt enormous short circuit current without producing noise,

flame, gas or smoke

The operation time of fuse can be made much smaller than operation of circuit breaker. It

is the primary protection device against short circuits

It affords current limiting effect under short-circuit conditions

Fuse inverse time current characteristic has the ability to use for over-load protection

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2.17 Fuse Disadvantages

During short circuit or overload once fuse blows off replacing of fuse takes time. During

this period the circuit lost power

When fuses are connected in series it is difficult to discriminate the fuse unless the fuse

has significant size difference

2.18 Fusing factor

Fusing factor is ratio of minimum fusing current to the current rating of the fuse element.

Fusing Factor = minimum fusing current / current rating of fuse

2.19 Limitations of a Fuse

Advantage of fuse based protection is its simplicity and cheapness. However, with fuses it is

difficult to control the time to trip. This creates difficulty in primary-backup coordination

activity. Also, once a fuse melts, unless it is replaced, the equipment cannot be energized again.

Thus, it is not possible to have remote operation. This motivates development of an overcurrent

relay

2.19 Relays

A relay is automatic device which senses an abnormal condition of electrical circuit and closes

its contacts. These contacts in turns close and complete the circuit breaker trip coil circuit hence

make the circuit breaker tripped for disconnecting the faulty portion of the electrical circuit from

rest of the healthy circuit.

In Electromagnetic relays operating current flows through the coil. When this operating current

increases, coil energizes the electromagnet. When the operating current becomes large, the

magnetic field produced by electromagnet is high such that this magnetic field pulls the armature

or plunger making the trip circuit contacts to close. Some of the advantages, disadvantages and

applications of electromagnetic relays are explained below

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2.21 Operation Of A relay

Consider the diagram below

Figure 2.9: Relay system

All relays contain a sensing unit, the electric coil, which is powered by AC or DC current. When

the applied current or voltage exceeds a threshold value, the coil activates the armature, which

operates either to close the open contacts or to open the closed contacts. When a power is

supplied to the coil, it generates a magnetic force that actuates the switch mechanism. The

magnetic force is, in effect, relaying the action from one circuit to another. The first circuit is

called the control circuit; the second is called the load circuit.

2.22 Advantages of relays

Relays can switch AC and DC, transistors can only switch DC.

Relays can switch high voltages, transistors cannot.

Relays are a better choice for switching large current >5A

Relays can switch many contacts at once

2.23 Disadvantages of relays

Relays are bulkier than transistors for switching small currents.

Relays cannot switch rapidly (except reed relays), transistors can switch many times per

second.

Relays use more power due to the current flowing through their coil.

Relays require more current than many ICs can provide so a low power transistor may be

needed to switch the current for the relay's coil

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2.24 Inverse definite minimum time (IDMT) protection relays

Under Electrical Protection In this type of relays, the time of operation depends upon the

magnitude of actuating quantity. If the magnitude of actuating quantity is very high, the relay

operation is very fast. In other words, the relay operating time that is time delay in the relay is

inversely proportional to the magnitude of actuating quantity. The general characteristics of an

inverse time relay are shown in figure below.

Figure 2.10: IDMT protection relay

Here, in the graph it is clear that, when, actuating quantity is OA, the operating time of the relay

is OA', when actuating quantity is OB, the relay operating time is OB' and when actuating

quantity is OC, the relay operating quantity is OC'.

In the graph above, it is also observed that, when actuating quantity is less than OA, the relay

operating time becomes infinity that means for actuating quantity less than OA, the relay does

not at all actuate. This minimum value of actuating quantity for which a relay initiates its

operation is known as pick up value of actuating quantity. Here it is denoted as OA.

It is also seen from the graph that, when actuating quantity approaches to infinity along x axis the

operating time does not approach to zero. The curve approaches to an approximately constant

operating time. This is approximately minimum time required to operate the relay.

The inverse time relay, where the actuating quantity is current, is known as inverse current relay.

In this type of relay, the inverse time is achieved by attaching some mechanical accessories in

the relay.

Inverse time delay is achieved in induction disc relay by providing a permanent magnet in such a

way, that, when disc rotates, it cuts the flux of permanent magnet. Due to this, current is induced

28

in the disc which slows down the movement of the disc. A solenoid relay can be made inverse

time relay, by providing a piston and a oil dash-pot. A piston, attached to the moving iron

plunger, is immersed in oil in a dash-pot. When the solenoid relay is actuated, the piston moves

upwards along with iron plunger.

Viscosity of oil slows the upward movement of plunger. The speed of this upward movement

against gravity also depends upon how strongly the solenoid attracts the iron plunger. This

attraction force of the solenoid depends upon the magnitude of actuating current. Hence, time of

operation of relay is inversely proportional to actuating current.

2.25 Power factor

Power factor, may be defined as the cosine of a phase angle between current and voltage

represented on a phasor diagram.

Power factor = cos

If the circuit is inductive in nature, the current lags behind the applied voltage and the power

factor is referred to as lagging. Consider the phasor diagram below

Figure 2.11: Phasor diagram of an Inductive device

The components cosI is known as wattful component or active component, where the

component sinI is called, wattless or reactive component

Active component is the measure of power factor

However, in a capacitive circuit, current leads the voltage, and the power factor is said to be

leading

Most of loads used in industries such as , induction motors, arc lamps, transformer , are inductive

in nature, and hence have low lagging power factor. The low lagging power factor is highly

undesirable as it cause many disadvantages on the system. Current ―I‖ is inversely proportional

to CosФ i.e. Power Factor. In other words, When Power Factor increases, Current Decreases,

and when Power Factor decreases, Current Increases.

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2.26 Power Triangle

The analysis of power factor can also be made in terms of power drawn by the AC circuit. If

each side of the previous triangle, is multiplied by voltage V, then we obtain power triangle

AOB, shown below

Figure 2.12: Power triangle

The following points may be noted in the power triangle

The apparent power in an AC circuit has two components, active and reactive power at

right angle to each other

30

Now, In case of Low Power Factor, Current will be increased, and this high current will cause to

the following disadvantages.

2.27 Disadvantages of low power factor in the system

1.) Large Line Losses (Copper Losses):

We know that Line Losses is directly proportional to the squire of Current ―I2‖

Power Loss = I2xR i.e., the larger the current, the greater the line losses i.e. I>>Line Losses

In other words,

Power Loss = I2xR = 1/CosФ

2 ….. Refer to Equation ―I ∝ 1/CosФ‖….… (1)

Thus, if Power factor = 0.8, then losses on this power factor =1/CosФ2 = 1/ 0.8

2 = 1.56 times will

be greater than losses on Unity power factor.

2.) Large kVA rating and Size of Electrical Equipment’s:

As we know that almost all Electrical Machinery (Transformer, Alternator, Switchgears etc)

rated in kVA. But, it is clear from the following formula that Power factor is inversely

proportional to the kVA i.e.

CosФ = kW / kVA

Therefore, The Lower the Power factor, the larger the kVA rating of Machines also, the larger

the kVA rating of Machines, The larger the Size of Machines and The Larger the size of

Machines, The Larger the Cost of machines.

3.) Greater Conductor Size and Cost:

In case of low power factor, current will be increased, thus, to transmit this high current, we need

the larger size of conductor. Also, the cost of large size of conductor will be increased.

4.) Poor Voltage Regulation and Large Voltage Drop:

Voltage Drop = V = IZ.

Now in case of Low Power factor, Current will be increased. So the Larger the current, the

Larger the Voltage Drop.

Also Voltage Regulation = V.R = (VNo Load – VFull Load)/ VFull Load

In case of Low Power Factor (lagging Power factor) there would be large voltage drop which

cause low voltage regulation. Therefore, keeping Voltage drop in the particular limit, we need to

install Extra regulation equipment i.e. Voltage regulators.

31

5.) Low Efficiency:

In case of low Power Factor, there would be large voltage drop and large line losses and this will

cause the system or equipment efficiency too low. For instant, due to low power factor, there

would be large line losses; therefore, alternator needs high excitation, thus, generation efficiency

would be low.

6.) Penalty from Electric Power Supply Company on Low Power factor

Electrical Power supply Company imposes a penalty of power factor below 0.95 lagging in

Electric power bill. So you must improve Pf above 0.95.

2.28 Causes of low Power Factor

Low power factor is undesirable form economic point of view. Normally the power factor of the

whole load on the supply system is lower than 0.8. The following are the causes of low power

factor

i. Most of the AC motor are of induction type (single phase or three phase), which have a

low lagging power factor. These motors works at extremely low power factor on light

load (0.2 to 0.3) and rises to 0.8 to 0.9 at full load

ii. Arc lamp, electric discharge lamps and industrial heating furnaces operates at low

lagging power factor\

iii. The load on the power system is varying, being high during morning and evening and

low at other times. During low load period, supply voltage is increased, which increases

the magnetizing current. This result in decreasing power factor

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2.29 Methods for power factor improvement

The following devices and equipment‘s are used for Power Factor Improvement.

1. Static Capacitor

We know that most of the industries and power system loads are inductive that take

lagging current which decrease the system power factor (See Disadvantages of Low

Power factor) . For Power factor improvement purpose, Static capacitors are connected in

parallel with those devices which work on low power factor.

Figure 2.13: Static capacitor

These static capacitors provide leading current which neutralize (totally or approximately) the

lagging inductive component of load current (i.e. leading component neutralize or eliminate the

lagging component of load current) thus power factor of the load circuit is improved. These

capacitors are installed in Vicinity of large inductive load e.g Induction motors and transformers

etc, and improve the load circuit power factor to improve the system or devises efficiency.

n above, a Capacitor (C) has been connected in parallel with load. Now a current (Ic) is flowing

through Capacitor which lead 90° from the supply voltage ( Note that Capacitor provides leading

Current i.e., In a pure capacitive circuit, Current leading 90° from the supply Voltage, in other

words, Voltage are 90° lagging from Current). The load current is (I). The Vectors combination

of (I) and (Ic) is (I‘) which is lagging from voltage at θ2 as shown in fig above.

It can be seen from fig above that angle of θ2 < θ1 i.e. angle of θ2 is less than from angle of θ2.

Therefore Cosθ2 is less than from Cosθ1 (Cosθ2> Cosθ1). Hence the load power factor is

improved by capacitor.

Also note that after the power factor improvement, the circuit current would be less than from

the low power factor circuit current. Also, before and after the power factor improvement, the

active component of current would be same in that circuit because capacitor eliminates only the

re-active component of current. Also, the Active power (in Watts) would be same after and

before power factor improvement.

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Advantages:

Capacitor bank offers several advantages over other methods of power factor

improvement.

Losses are low in static capacitors

There is no moving part, therefore need low maintenance

It can work in normal air conditions (i.e. ordinary atmospheric conditions)

Do not require a foundation for installation

They are lightweight so it is can be easy to installed

Disadvantages:

The age of static capacitor bank is less (8 – 10 years)

With changing load, we have to ON or OFF the capacitor bank, which causes switching

surges on the system

If the rated voltage increases, then it causes damage it

Once the capacitors spoiled, then repairing is costly

2. Synchronous Condenser

When a Synchronous motor operates at No-Load and over-exited then it‘s called a

synchronous Condenser. Whenever a Synchronous motor is over-exited then it provides

leading current and works like a capacitor. When a synchronous condenser is connected

across supply voltage (in parallel) then it draws leading current and partially eliminates

the re-active component and this way, power factor is improved. Generally, synchronous

condenser is used to improve the power factor in large industries.

Consider the diagram below

Figure 2.14 : Improving power factor synchronous condenser

34

Advantages:

Long life (almost 25 years)

High Reliability

Step-less adjustment of power factor.

No generation of harmonics of maintenance

The faults can be removed easily

It‘s not affected by harmonics.

Require Low maintenance (only periodic bearing greasing is necessary)

Disadvantages:

It is expensive (maintenance cost is also high) and therefore mostly used by large power

users.

An auxiliary device has to be used for this operation because synchronous motor has no

self-starting torque

It produces noise

3. Phase Advancer

Phase advancer is a simple AC exciter which is connected on the main shaft of the motor and

operates with the motor‘s rotor circuit for power factor improvement. Phase advancer is used to

improve the power factor of induction motor in industries. As the stator windings of induction

motor takes lagging current 90° out of phase with Voltage, therefore the power factor of

induction motor is low. If the exciting ampere-turns are excited by external AC source, then

there would be no effect of exciting current on stator windings. Therefore the power factor of

induction motor will be improved. This process is done by Phase advancer.

Advantages:

Lagging kVAR (Reactive component of Power or reactive power) drawn by the motor is

sufficiently reduced because the exciting ampere turns are supplied at slip frequency (fs).

The phase advancer can be easily used where the use of synchronous motors is

Unacceptable

Disadvantage:

Using Phase advancer is not economical for motors below 200 H.P. (about 150kW)

35

2.30 Calculating KVAR ratings and Capacitance

Consider the following Examples.

Example: 1

A 3 Phase, 5 kW Induction Motor has a P.F (Power factor) of 0.75 lagging. What size of

Capacitor in kVAR is required to improve the P.F (Power Factor) to 0.90?

Solution #1 (By Simple Table Method)

Motor Input = 5kW

From Table, Multiplier to improve PF from 0.75 to 0.90 is .398

Required Capacitor kVAR to improve P.F from 0.75 to 0.90

Required Capacitor kVAR = kW x Table 1 Multiplier of 0.75 and 0.90

= 5kW x .398

= 1.99 kVAR

And Rating of Capacitors connected in each Phase

1.99/3 = 0.663 kVAR

Solution # 2 (Classical Calculation Method)

Motor input = P = 5 kW

Original P.F = Cosθ1 = 0.75

Final P.F = Cosθ2 = 0.90

θ1 = Cos-1

= (0.75) = 41°.41; Tan θ1 = Tan (41°.41) = 0.8819

θ2 = Cos-1

= (0.90) = 25°.84; Tan θ2 = Tan (25°.50) = 0.4843

Required Capacitor kVAR to improve P.F from 0.75 to 0.90

Required Capacitor kVAR = P (Tan θ1 – Tan θ2)

= 5kW (0.8819 – 0.4843)

= 1.99 kVAR

And Rating of Capacitors connected in each Phase

1.99/3 = 0.663 kVAR

2.31 Tables (Capacitor sizing in kVAr and Farads for PF correction)

The following tables have been prepared to simplify kVAR calculation for power factor

improvement. The size of capacitor in kVAR is the kW multiplied by factor in table to improve

from existing power factor to proposed power factor. Check the others Examples below.

36

37

38

Example 2:

An Alternator is supplying a load of 650 kW at a P.F (Power factor) of 0.65. What size of

Capacitor in kVAR is required to raise the P.F (Power Factor) to unity (1)? And how many

more kW can the alternator supply for the same kVA loading when P.F improved.

Solution #1 (By Simple Table Method)

Supplying kW = 650 kW

From Table 1, Multiplier to improve PF from 0.65 to unity (1) is 1.169

Required Capacitor kVAR to improve P.F from 0.65 to unity (1)

Required Capacitor kVAR = kW x Table 1 Multiplier of 65 and 100

= 650kW x 1.169

= 759.85 kVAR

We know that P.F = Cosθ = kW/kVA . . .or

kVA = kW / Cosθ

= 650/0.65 = 1000 kVA

When Power Factor is raised to unity (1)

No of kW = kVA x Cosθ

= 1000 x 1 = 1000kW

Hence increased Power supplied by Alternator

1000kW – 650kW = 350kW

Solution # 2 (Classical Calculation Method)

Supplying kW = 650 kW

Original P.F = Cosθ1 = 0.65

Final P.F = Cosθ2 = 1

θ1 = Cos-1

= (0.65) = 49°.45; Tan θ1 = Tan (41°.24) = 1.169

θ2 = Cos-1

= (1) = 0°; Tan θ2 = Tan (0°) = 0

Required Capacitor kVAR to improve P.F from 0.75 to 0.90

Required Capacitor kVAR = P (Tan θ1 – Tan θ2)

= 650kW (1.169– 0)

= 759.85 kVAR

39

2.32 Converting Farads into KVAR and vice-versa

Example: 3

A Single phase 400V, 50Hz, motor takes a supply current of 50A at a P.F (Power factor) of 0.6.

The motor power factor has to be improved to 0.9 by connecting a capacitor in parallel with it.

Calculate the required capacity of Capacitor in both kVAR and Farads.

Solution.:

(1) To find the required capacity of Capacitance in kVAR to improve P.F from 0.6 to 0.9

(Two Methods)

Solution #1 (By Simple Table Method)

Motor Input = P = V x I x Cosθ

= 400V x 50A x 0.6

= 12kW

From Table, Multiplier to improve PF from 0.60 to 0.90 is 0.849

Required Capacitor kVAR to improve P.F from 0.60 to 0.90

Required Capacitor kVAR = kW x Table Multiplier of 0.60 and 0.90

= 12kW x 0.849

= 10.188 kVAR

Solution # 2 (Classical Calculation Method)

Motor Input = P = V x I x Cosθ

= 400V x 50A x 0.6

= 12kW

Actual P.F = Cosθ1 = 0..6

Required P.F = Cosθ2 = 0.90

θ1 = Cos-1

= (0.60) = 53°.13; Tan θ1 = Tan (53°.13) = 1.3333

θ2 = Cos-1

= (0.90) = 25°.84; Tan θ2 = Tan (25°.50) = 0.4843

Required Capacitor kVAR to improve P.F from 0.60 to 0.90

Required Capacitor kVAR = P (Tan θ1 – Tan θ2)

= 5kW (1.3333– 0.4843)

= 10.188 kVAR

40

(2) To find the required capacity of Capacitance in Farads to improve P.F from 0.6 to 0.9

(Two Methods)

Solution #1 (Using a Simple Formula)

We have already calculated the required Capacity of Capacitor in kVAR, so we can easily

convert it into Farads by using this simple formula

Required Capacity of Capacitor in Farads/Microfarads

C = kVAR / (2 π f V2) in microfarad

Putting the Values in the above formula

= (10.188kVAR) / (2 x π x 50 x 4002)

= 2.0268 x 10-4

= 202.7 x 10-6

= 202.7μF

Solution # 2 (Simple Calculation Method)

kVAR = 10.188 … (i)

We know that;

IC = V/ XC

Whereas XC = 1 / 2 π F C

IC = V / (1 / 2 π F C)

IC = V 2 F C

= (400) x 2π x (50) x C

IC = 125663.7 x C

And,

kVAR = (V x IC) / 1000 … [kVAR =( V x I)/ 1000 ]

= 400 x 125663.7 x C

IC = 50265.48 x C … (ii)

Equating Equation (i) & (ii), we get,

50265.48 x C = 10.188C

C = 10.188 / 50265.48

C = 2.0268 x 10-4

C = 202.7 x 10-6

C = 202.7μF

41

Example 4

What value of Capacitance must be connected in parallel with a load drawing 1kW at 70%

lagging power factor from a 208V, 60Hz Source in order to raise the overall power factor

to 91%.

Solution:

You can use either Table method or Simple Calculation method to find the required value of

Capacitance in Farads or kVAR to improve Power factor from 0.71 to 0.97. So I used table

method in this case.

P = 1000W

Actual Power factor = Cosθ1 = 0.71

Desired Power factor = Cosθ2 = 0.97

From Table, Multiplier to improve PF from 0.71 to 0.97 is 0.783

Required Capacitor kVAR to improve P.F from 0.71 to 0.97

Required Capacitor kVAR = kW x Table Multiplier of 0.71 and 0.97

= 1kW x 0.783

=783 VAR (required Capacitance Value in kVAR)

Current in the Capacitor =

IC = QC / V

= 783 / 208

= 3.76A

And

XC = V / IC

= 208 / 3.76 = 55.25Ω

C = 1/ (2 π f XC)

C = 1 (2 π x 60 x 55.25)

C = 48 μF (required Capacitance Value in Farads)

Good to Know:

Important formulas which is used for Power factor improvement calculation as well as

used in the above calculation

Power in Watts kW = kVA x Cosθ

kW = HP x 0.746 or (HP x 0.746) / Efficiency … (HP = Motor Power)

kW = √ ( kVA2– kVAR

2)

kW = P = VI Cosθ … (Single Phase)

kW = P =√3x V x I Cosθ … (Three Phase)

Apparent Power in VA kVA= √(kW

2+ kVAR

2)

kVA = kW/ Cosθ

42

Reactive Power in VA kVAR= √(kVA

2– kW

2)

kVAR = C x (2 π f V2)

Power factor (from 0.1 to 1) Power Factor = Cosθ = P / V I … (Single Phase)

Power Factor = Cosθ = P / (√3x V x I) … (Three Phase)

Power Factor = Cosθ = kW / kVA … (Both Single Phase & Three Phase)

Power Factor = Cosθ = R/Z … (Resistance / Impedance)

XC = 1/ (2 π f C) … (XC = Capacitive reactance)

IC = V/ XC … (I = V / R)

Required Capacity of Capacitor in Farads/Microfarads

C = kVAR / (2 π f V2) in microfarad

Required Capacity of Capacitor in kVAR

kVAR = C x (2 π f V2)

43

2.33 Factors affecting the choice of power cable

The electrical power distribution networks for industrial systems, normally rely on cable feeders

to distribute the necessary power to the various industrial processes. Some overheads are used

but this normally only for the longer length and higher voltage circuits.

The distance involved, and the general configuration of the plant set the method of installation of

the cable that can be used. Cables can either be installed in cable trays, in concrete or metallic

ducts or can be buried directly in the soil

The main factors that influence the selection of the cable to be employed in any applications are

the cable sizes, whether single or three core cables. The type and size of the cables are selected

basing on four main criteria.

The maximum loading of the feeder

This refers to the maximum voltage rate designed on the specific cable; this also can be

influenced by the type of a cable and the method of installation and the ambient temperature

In any particular industrial system, it is convenient to use small number of different cable

sizes possible to ease installation and reduce spare holding

Maximum voltage drop that can be allowed

Conductor size also influences cable impedance and hence the voltage drop along the feeder

due to load current being taken. It is therefore necessary to check that drop of voltage along

the cable route doesn‘t exceed the design criteria for the network or operating voltages ranges

of the equipment being fed

Fault current to which the cable is exposed

In addition to the continuous current rating of the cable, cables have also a corresponding

short time rating. This is rarely a bases for the sizing of the larger cables, but it must always

be checked, When setting the protection or choosing feeder fusing, to ensure that the

protection adequately protects the cable during the faults

Level of insulation of the cable

In north America, it is customary to design cables for three different overvoltage rating, for

each operating voltage, dependent on the type of neutral grounding system used

For solidly grounded system, where a health phase voltage rise during ground faults is

minimum, a basic cable known as 100% insulation class is used

44

For high resistance grounded system (HR) or for ungrounded systems, where the health

phase voltage rise can reach the full phase to phase voltage, a phase rated voltage cable

known as a 173% class is available

There is also an intermediate class , for use in condition where an intermediate limited

grounding current is allowed. This class is known as 133%

2.34 Cable shielding

It is important for optimum cable design, to control the stress levels in the various layers of

insulation applied in the cable to limit external fields, particularly for higher application

voltages. Internal and external shielding, is used to control these internals stresses

Inner Shield

It consists of semiconducting material, applied over the conductor circumference, to even out

the conductors contours. This shield prevents dielectrics filed lines from being distorted by

the shape of the outer strands of the conductor and eliminates the peak stresses near the

conductor

Figure 2.15: Cable shielding

45

Outer shield

This forms the outer layer of insulation grading and is connected to the grounding to fix the

voltage gradient across the insulation. It also minimizes the effects of the outside electric

field, also it confined electric field inside the cable

2.35 Cable Insulation

When selecting a cable, This should base on service life, dielectric characteristics, resistance

to flame, mechanical strength and flexibility, temperature capability , moisture resistance and

the type of location where the cable has to be installed

2.36 Advantages of materials used for cable conductors

The table below summarizes the pros and cons of copper and aluminum as conductor

materials:

2.37 Advantages Materials used for cable insulation

Thermoplastic compounds are materials that go soft when heated and harden when cooled:

PVC (Polyvinyl Chloride) – is the most commonly used thermoplastic insulator for cables. It is

cheap, durable and widely available. However, the chlorine in PVC (a halogen) causes the

production of thick, toxic, black smoke when burnt and can be a health hazard in areas where

low smoke and toxicity are required (e.g. confined areas such as tunnels). Normal operating

temperatures are typically between 75C and 105C (depending on PVC type). Temperature limit

is 160C (<300mm2) and 140C (>300mm2).

PE (Polyethylene) – is part of a class of polymers called polyolefin. Polyethylene has lower

dielectric losses than PVC and is sensitive to moisture under voltage stress (i.e. for high voltages

only).

46

Thermosetting

Thermosetting compounds are polymer resins that are irreversibly cured (e.g. by heat in the

vulcanization process) to form a plastic or rubber:

XLPE (Cross-Linked Polyethylene) – has different polyethylene chains linked together (―cross-

linking‖) which helps prevent the polymer from melting or separating at elevated temperatures.

Therefore XLPE is useful for higher temperature applications. XLPE has higher dielectric losses

than PE, but has better ageing characteristics and resistance to water treeing. Normal operating

temperatures are typically between 90C and 110C. Temperature limit is 250C.

EPR (Ethylene Propylene Rubber) – is a copolymer of ethylene and propylene, and commonly

called an ―elastomer‖. EPR is more flexible than PE and XLPE, but has higher dielectric losses

than both. Normal operating temperatures are typically between 90C and 110C. Temperature

limit is 250C.

The table below summarizes advantages and disadvantages of material used for cable insulation

47

2.38 Dielectric Stress

Dielectric stress is the electrostatic force divided by the area.

A high-voltage cable (HV cable) is a cable used for electric power transmission at high voltage.

A cable includes a conductor and insulation, and is suitable for being run underground or

underwater. This is in contrast to a conductor, which does not have insulation.

High-voltage cables of differing types have a variety of applications in instruments, ignition

systems, and AC and DC power transmission. In all applications, the insulation of the cable must

not deteriorate due to the high-voltage stress, ozone produced by electric discharges in air, or

tracking. The cable system must prevent contact of the high-voltage conductor with other objects

or persons, and must contain and control leakage current. Cable joints and terminals must be

designed to control the high-voltage stress to prevent breakdown of the insulation. Often a high-

voltage cable will have a metallic shield layer over the insulation, connected to the ground and

designed to equalize the dielectric stress on the insulation layer.

2.39 Methods of stress control in high voltage cable

There are basically two methods to control effects of dielectric stress

Grading method

AC cables are designed to be suitable for specific design voltages, which is called the "Voltage

Grade" (or "Voltage Designation", "Voltage Class" or "Voltage Rating") of the cable. The

voltage grade is commonly expressed in the following form: U0 /U

Where U0 is the power frequency voltage between phase and earth (V rms)

U is the power frequency voltage between two phase conductors (V rms)

Inter sheath grading

Inter sheath Grading is a method of creating uniform voltage gradient across the insulation by

means of separating the insulation into two or more layers by thin conductive strips. These strips

are kept at different voltage levels through the secondary of a transformer. This ensures that all

parts of the insulation are exposed to relatively the same stress.

Inter sheath Grading is a method of ensuring that the voltage gradient across the insulation of a

cable does not become so steep as to cause the failure of the insulation. The insulation of a cable

is subjected to constant electrostatic stress. This electrical stress is dependent on the voltage of

the conductor. The electrostatic stress needs to be uniform across the insulation. Uneven

electrostatic stresses can result in failure of the insulation.

48

2.40 Principle of earthing power supply systems

Suitable power supply systems, according to the type of connection to the earth, are required.

The type of connection to the earth must be selected carefully for the medium or low voltage

network, as it has major impact on the expense required for protective measures

In TN systems, in the event of short circuit, to an exposed conductive part, a considerable part of

the single-pole short-circuits current is not fed back to the power source via a connection to earth

but via the protective conductor.

TN system: In the TN system, one operating line is directly earthed; the exposed conductive

parts in the electrical installation are connected to this earthed point via protective conductors.

Dependent on the arrangement of the protective (PE) and neutral (N) conductors. The following

are the types of TN system

a) TN-S system:

This is probably the most usual earthing system in the UK, with the Electricity Supply

Company providing an earth terminal at the incoming mains position. This earth terminal

is connected by the supply protective conductor (PE) back to the star point (neutral) of

the secondary winding of the supply transformer, which is also connected at that point to

an earth electrode. The earth conductor usually takes the form of the armour and sheath

(if applicable) of the underground supply cable. The system is shown diagrammatically

Figure 2.16: TN –S Systems

b) TN-C system

This installation is unusual, because combined neutral and earth wiring is used in both the

supply and within the installation itself. Where used, the installation will usually be the

earthed concentric system, which can only be installed under the special conditions

Figure 2.17: TN-C system

49

c) TN-C-S system

In a part of the system, the functions of the neutral and protective conductor are combined in

one conductor (PEN).

Figure 2.18: TN-C-S system

d) TT system:

This arrangement covers installations not provided with an earth terminal by the

Electricity Supply Company. Thus it is the method employed by most (usually rural)

installations fed by an overhead supply. Neutral and earth (protective) conductors must

be kept quite separate throughout the installation, with the final earth terminal connected

to an earth electrode by means of an earthing conductor.

Figure 2.19: TT system

Effective earth connection is sometimes difficult. Because of this, socket outlet circuits

must be protected by a residual current device (RCD) with an operating current of 30 mA

50

CHAPTER THREE

3.0 DC Machines

DC machines are the electromechanical converters, which work form a dc source and generate

mechanical power, or convert mechanical power into a DC power. DC Machines, can be

operated mainly in two Modes, Electric Motor Modes, and Generator Mode

3.1 Electric Motors Mode

When the input to an electrical machine is electrical energy, (seen as Applying a voltage to the

electrical terminals of the machine), and the Output is mechanical energy, (seen as a rotating

shaft), the machine is called an electric motor.

3.2 Principle of operation of a simple D.C. motor

A rectangular coil which is free to rotate about a fixed axis is shown placed

Inside a magnetic field produced by permanent magnets as seen in Figure below. A direct current

is fed into the coil via carbon brushes bearing on a commutator, which consists of a metal ring

split into two halves separated by insulation.

Figure 3.1: Principle Operation Of a DC motor

When current flows in the coil a magnetic field is set up around the coil which interacts with

the magnetic field produced by the magnets. This causes a force F to be exerted on the current-

carrying conductor which, by Fleming‘s left-hand rule, is downwards between points A and B

and upward between C and D for the current direction shown above. This causes a torque and

the coil rotates anticlockwise. When the coil has turned through 90° from the position shown

in Figure above, the brushes connected to the positive and negative terminals of the supply

make contact with different halves of the commutator ring, thus reversing the direction of the

current flow in the conductor.

51

If the current is not reversed and the coil rotates past this position the forces acting on it

change direction and it rotates in the opposite direction thus never making more than half a

revolution.

The current direction is reversed every time the coil swings through the vertical position and

thus the coil rotates anti-clockwise for as long as the current flows. This is the principle of

operation of a D.C. motor which is thus a device that takes in electrical energy and converts it

into mechanical energy.

3.3 Generator Mode

When the input to an electrical machine is mechanical energy, (seen as, say, a diesel motor,

coupled to the machine by a shaft), and the output is electrical energy, (seen as a voltage

appearing at the electrical terminals of the machine), the machine is called a generator. Thus, a

generator converts mechanical energy to electrical energy.

There are two types of generators, one is ac generator and other is dc generator. Whatever may

be the types of generators, it always converts mechanical power to electrical power. An Ac

generator produces alternating power. A DC generator produces direct power. Both of these

generators produce electrical power, based on same fundamental principle of Faraday's law of

electromagnetic induction.

According to this law, when a conductor moves in a magnetic field it cuts magnetic lines force,

due to which an EMF is induced in the conductor. The magnitude of this induced EMF depends

upon the rate of change of flux (magnetic line force) linkage with the conductor. This EMF will

cause an current to flow if the conductor circuit is closed.

3.4 Principle of operation of a simple Generator

In the figure below, a single loop of conductor of rectangular shape is placed between two

opposite poles of magnet.

Let's us consider, the rectangular loop of conductor is ABCD which rotates inside the magnetic

field about its own axis ab. When the loop rotates from its vertical position to its horizontal

position, it cuts the flux lines of the field. As during this movement two sides, i.e. AB and CD of

the loop cut the flux lines there will be an EMF induced in these both of the sides (AB & BC) of

the loop.

52

Figure 3.2: Principle operation of generator

As the loop is closed there will be a current circulating through the loop. The direction of the

current can be determined by Fleming‘s right hand Rule. This rule says that is you stretch thumb,

index finger and middle finger of your right hand perpendicular to each other, then thumbs

indicates the direction of motion of the conductor, index finger indicates the direction of

magnetic field i.e. N - pole to S - pole, and middle finger indicates the direction of flow of

current through the conductor.

Now if we apply this right hand rule, we will see at this horizontal position of the loop, current

will flow from point A to B and on the other side of the loop current will flow from point C to D.

Figure 3.3: Rotating Rectangular coil in a Generator

Now if we allow the loop to move further, it will come again to its vertical position, but now

upper side of the loop will be CD and lower side will be AB (just opposite of the previous

vertical position). At this position the tangential motion of the sides of the loop is parallel to the

flux lines of the field. Hence there will be no question of flux cutting and consequently there will

be no current in the loop. Observe the figure below

53

Figure 3.4: Generator rotating

If the loop rotates further, it comes to again in horizontal position. But now, said AB side of the

loop comes in front of N pole and CD comes in front of S pole, i.e. just opposite to the previous

horizontal position as shown in the figure below

.

Figure 3.5: Generator rotating

Now the loop is opened and connects it with a split ring as shown in the figure below. Split ring

are made out of a conducting cylinder which cuts into two halves or segments insulated from

each other. The external load terminals are connected with two carbon brushes which are rest on

these split slip ring segments.

54

Figure 3.6 : DC Generator

It is seen that in the first half of the revolution current flows always along ABLMCD i.e. brush

no 1 in contact with segment a. In the next half revolution, in the figure the direction of the

induced current in the coil is reversed. But at the same time the position of the segments a and b

are also reversed which results that brush no 1 comes in touch with that segment b. Hence, the

current in the load resistance again flows from L to M. The wave from of the current through the

load circuit is as shown in the figure. This current is unidirectional.

Figure below, shows the Waveforms of the EMF voltage against angle

Figure 3.7: DC production In Generator

55

3.5 DC machine construction

The basic parts of any D.C. machine are shown in Figure below,

Figure 3.8: DC machine construction

DC machines, comprises of the following main parts

a. a stationary part called the stator having,

i. a steel ring called the yoke, to which are attached

ii. the magnetic poles, around which are the

iii. field windings, i.e. many turns of a conductor wound round the pole core; current passing

through this conductor creates an electromagnet,

b. a rotating part called the armature mounted in bearings housed in

The stator and having,

i. a laminated cylinder of iron or steel called the core, on which

Teeth are cut to house the

ii. armature winding, i.e. a single or multi-loop conductor system and

iii. the commutator

Armature windings can be divided into two groups, depending on how the wires are joined to the

commutator. These are called wave windings and lap windings.

a. In wave windings there are two paths in parallel irrespective of the number of poles,

each path supplying half the total current output. Wave wound generators produce high

voltage, low current outputs.

b. In lap windings there are as many paths in parallel as the machine has poles. The total

current output divides equally between them. Lap wound generators produce high

current, low voltage output.

56

3.6 Classification of DC Machine

Figure 3.9: Classification of DC Machine

D.C machines are classified according to the method of their field excitation. These

groupings are:. There are two basic DC machines

i. Separately-excited DC machines, where the field winding is connected to a source of

supply other than the armature of its own machine.

ii. Self-excited DC Machines, where the field winding receives its supply from the

armature of its own machine, and which are sub-divided into

a) Shunt wound DC machines

b) Series Wound DC Machines

c) Compound wound DC machine

a) Shunt wound DC machines

When the field winding of a D.C. machine is connected in parallel with the armature, as

shown in Figure below, the machine is said to be shunt wound.

Figure 3.10: Shut wound DC motor

57

b) Series Wound DC Machines

If the field winding is connected in series with the armature, as shown in Figure below,

then the machine is said to be series wound.

Figure 3.11: Series Wound DC motor

c) Compound wound DC machine

Compound wound machine has a combination of series and shunt windings

Depending on whether the electrical machine is series wound, shunt wound or compound

wound, it behaves differently when a load is applied. The behavior of a DC machine

under various conditions is shown by means of graphs, called characteristic curves or just

characteristics. The characteristics shown in the following sections are theoretical, since

they neglect the effects of armature reaction.

3.7 EMF equation of a dc machine

Let z= be number of armature conductors

Let φ= be useful flux per pole, in Webbers

p= number of pairs of poles

n= armature speed in rev/sec

The e.m.f. generated by the armature is equal to the e.m.f. generated by one of the

parallel paths. Each conductor passes 2p poles per revolution and

Total flux cut per revolution is given by = 2p φ Wb

Hence flux cut by one conductor per second =2pφn Wb

so the average EMF E generated per conductor is given by =2pφn Wb

Let c be a number of parallel paths through the winding between positive and negative

brushes

c=2 for a wave winding

c=2p for a lap winding

The number of conductors in series in each path is given by z

c

The total e.m.f. between brushes is given by

2 p nzE

c

Remember this (tuponz)

Where this formula can be expressed in different format as shown below

58

2,

2 , 2 tan

2

p nz zE N number of turns

c c

E p nN but k pn cons t

E pn N

E k N

Where K=constant

N=number of turns/conductors per parallel path

Φ=flux per pole

59

60

+

61

3.8 D.C generators

3.9 Types of D.C, generator and their characteristics

D.C generators are classified according to the method of their field excitation. These

groupings are:

i. Separately-excited DC Generator, where the field winding is connected to a source of

supply other than the armature of its own machine.

ii. Self-excited DC Generators, where the field winding receives its supply from the

armature of its own machine, and which are sub-divided into (a) shunt, (b) series, and (c)

compound wound generators

i. Separately-excited generator

A typical separately-excited generator circuit is shown in Figure below,

Figure 3.12: Separately Excited generator

62

When a load is connected across the armature terminals, a load current Ia

Will flow. The terminal voltage V will fall from its open-circuit E.M.F E

Due to a volt drop caused by current flowing through the armature resistance, shown as

Ra

a)

63

3.10 Generator Characteristics

The two principal generator characteristics

a) the open-circuit characteristic

Are the generated voltage/field current characteristics. A typical separately-excited

generator open-circuit characteristic is shown in Figure below

Figure 3.13: Open Circuit Characteristics

64

b) the load characteristic

the terminal voltage/load current characteristic. A typical load

Characteristics shown in Figure below

Figure 3.14: The load characteristics

3.11 Application of Separately excited field windings

A separately-excited generator is used only in special cases, such as when a wide

variation in terminal p.d. is required, or when exact control of the field current is

necessary. Its disadvantage lies in requiring a separate source of direct current.

ii. Self-excited DC Generators,

a) Shunt-wound generator

In a shunt wound generator the field winding is connected in parallel with the armature as

shown in Figure below. The field winding has a relatively high resistance and therefore

the current carried is only a fraction of the armature current.

Figure 3.15 : Self Excited DC generator

65

a) Consider the circuit below

66

3.12 Open circuit Characteristics

The generated EMF, E, is proportional ωφ, hence at constant speed, since, ω=2πn, Eαφ. Also the

flux φ is proportional, to field current If until magnetic saturation of the iron circuit of the

generator occurs. Hence the open circuit characteristic is as shown below

Figure 3.16: Open circuit Characteristics

67

3.13 Load characteristics

As the load current on a generator having constant field current and running at constant speed

increases, the value of armature current increases, hence the armature volt drop, IaRa increases

The generated voltage E is larger than the terminal voltage V and the voltage equation for the

armature circuit is given below

Since E is constant decreases with increasing load. The load characteristic is as shown in Figure

below

In practice, the fall in voltage is about 10% between no-load and full-load for many DC shunt-

wound generators. The shunt-wound generator is the type most used in practice, but the load

current must be limited to a value that is well below the maximum value. This then avoids

excessive variation of the terminal voltage.

Figure 3.17: Load Characteristics

3.14 Application of a shunt wound DC generators

Typical applications are with battery charging and motor car generators.

b) Series Wound Generators

In the series-wound generator the field winding is connected in series with the armature

as shown in Figure, below

Figure 3.18: Series Wound DC Generator

68

The generated voltage equation is given by

E V IaRa

or

V E IaRa

3.15 Load characteristics of DC generator

The load characteristic is the terminal voltage/current characteristic. The generated EMF E, is

proportional to φω, and at constant speed( ω=2πn is also constant). Thus E is proportional to φ,

Eαφ. A typical load characteristic for a series generator is shown in Figure, below

Figure 3.19 : Load Characteristics of a DC generator

3.16 Open circuit characteristics

In a series-wound generator, the field winding is in series with the armature and it is not possible

to have a value of field current when the terminals are open circuited, thus it is not possible to

obtain an open circuit characteristic.

3.17 Application of a series wound generators

Series-wound generators are rarely used in practice, but can be used as a ‗booster‘ on DC

transmission lines.

69

c) Compound-wound generator

In the compound-wound generator two methods of connection are used, both having a

mixture of shunt and series windings, designed to combine the advantages of each. Figure

below shows what is termed a long shunt compound generator

Figure 3.20: Long shunt compound DC generator

And also, Figure below shows a short-shunt compound generator

Figure 3.21: Short shunt compound DC Generator

70

Consider the circuit below

71

3.18 Characteristics Compound Wound Machines

In cumulative-compound machines the magnetic flux produced by the series and shunt fields are

additive. Included in this group are over-compounded, level-compounded and under-

compounded machines—the degree of compounding obtained depending on the number of

turns of wire on the series winding.

A large number of series winding turns results in an over-compounded characteristic, as shown

in Figure below, in which the full-load terminal voltage exceeds the no-load voltage. A level-

compound machine gives a full-load terminal voltage which is equal to the no-load voltage, as

shown in same Figure

Figure 3.22: Characteristics of compound Wound generator

An under-compounded machine gives a full-load terminal voltage which is less than the no-load

voltage, as shown in Figure above. However even this latter characteristic is a little better than

that for a shunt generator alone.

3.19 Application of compound Generators

Compound-wound generators are used in electric arc welding, with lighting sets and with marine

equipment.

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3.20 Source of Losses in DC machines

As stated earlier, a generator is a machine for converting mechanical energy into electrical

energy and a motor is a machine for converting electrical energy into mechanical energy. When

such conversions take place, certain losses occur which are dissipated in the form of heat.

The principal losses of machines are

i. Copper loss, due to I2 R heat losses in the armature and field windings.

ii. Iron (or core) loss, due to hysteresis and eddy-current losses in the armature. This loss

can be reduced by constructing the armature of silicon steel laminations having a high

resistivity and low hysteresis loss. At constant speed, the iron loss is assumed constant.

iii. Friction and windage losses, due to bearing and brush contact friction and losses due to

air resistance against moving parts (called windage). At constant speed, these losses are

assumed to be constant.

iv. Brush contact loss between the brushes and commutator. This loss is approximately

proportional to the load current. The total losses of a machine can be quite significant and

operating efficiencies of between 80% and 90% are common.

3.21 Efficiency of a DC generator

The efficiency of an electrical machine is the ratio of the output power to the input power and is

usually expressed as a percentage. The Greek letter, ‗ɳ‘ (eta) is used to signify efficiency and

since the units are power/power, then efficiency has no units. Thus

If the total resistance of the armature circuit (including brush contact resistance) is Ra, then the

total loss in the armature circuit is I2aRa. If the terminal voltage is V and the current in the shunt

circuit is If, then the loss in the shunt circuit is If V.

If the sum of the iron, friction and windage losses is C then the total losses is given by:

If the output current is I, then the output power is VI

73

The efficiency of a generator is a maximum when the load is such that

The circuit is shown in Figure below

74

3.22 DC Motors

The construction of a DC motor is the same as a DC generator. The only difference is that in a

generator the generated e.m.f. is greater than the terminal voltage, whereas in a motor the

generated e.m.f. is less than the terminal voltage.

DC motors are often used in power stations to drive emergency standby pump systems which

come into operation to protect essential equipment and plant should the normal AC supplies or

pumps fail.

3.23 Back E.M.F

When a DC motor rotates, an e.m.f. is induced in the armature conductors. By Lenz‘s law this

induced E.M.F E opposes the supply voltage V and is called aback E.M.F and the supply

voltage, V is given by:

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3.24 Torque of a DC Motor

From equation above, for a DC Motor, the supply voltage V is given by

Multiplying each term by current Ia gives:

76

77

78

79

3.25 Types of DC motor and their characteristics

a) Shunt-wound motor

In the shunt wound motor the field winding is in parallel with the armature across the

supply as shown in Figure below

Figure 3.23: Shunt wound DC motor

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3.26 Characteristics of shunt wound DC motor

The two principal characteristics are found here

i. the torque/armature current

The theoretical torque/armature current characteristic can be derived from the

expression below

For a shunt wound motor, the field winding is connected in parallel with the

Armature circuit and thus the applied voltage give a constant field

Current, i.e. a shunt-wound motor is a constant flux machine.

Since Φ is constant, it follows that

and the characteristic is as shown in Figure below

Figure 3.24: Torque Armature current characteristics

81

ii. Speed/armature current relationships

The armature circuit of a DC motor has resistance due to the armature winding

and brushes, Ra ohms, and when armature current Ia is flowing through it, there

is a voltage drop of IaRa volts. Consider the graph below

Figure 3.25: Speed Armature current characteristics

So, when the Motor is rotated, the EMF E , generated is given by the following

equation

Also, even though the machine is a motor, because conductors are rotating in a

magnetic field, a voltage, is generated by the armature conductors

But ω=2πn

Therefore, from the above equations, we can conclude that

For a shunt motor, Φ, and Ra are constants, hence as armature

Current Ia increases, IaRa increases and V-IaRa decreases, and

The speed is proportional to a quantity which is decreasing and is

as shown in Figure above

As the load on the shaft of the motor increases, Ia increases and the speed drops

slightly. In practice, the speed falls by about 10% between no-load and full-load

on many DC shunt-wound motors

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3.27 Application of Shunt wound DC motors

Due to this relatively small drop in speed, the DC shunt-wound motor is taken as basically being

a constant-speed machine and may be used for driving lathes, lines of shafts, fans, conveyor

belts, pumps, compressors, drilling machines

Since torque is proportional to armature current, (see a above), the Theoretical speed/torque

characteristic is as shown in Figure 3.25

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b) Series-wound DC motor

In the series-wound motor the field winding is in series with the armature across the

supply as shown in Figure below

Figure 3.26: Series –wound DC motor

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3.28 Characteristics of series DC wound Motor

In a series motor, the armature current flows in the field winding and is equal to the supply

current, I

There are also two graphs/ characteristics here

i. The torque/current characteristic.

It has been shown that torque

Since the armature and field currents are the same current, I, in a series machine,

Then

This is Over a limited range, before magnetic saturation of the Magnetic circuit

of the motor is reached, (i.e., the linear portion of the B–H curve for the yoke,

poles, air gap, brushes and armature in series).

Thus

After magnetic saturation, Φ almost becomes a constant and TαI. Thus the

theoretical torque/current characteristic is as shown in Figure below

Figure 3.27: Torque current characteristics

ii. The speed/current characteristic

It has been shown in equation above that

In a series motor Ia= I and below the magnetic saturation level, ΦαI. Thus

Where R is the combined resistance of the series field and armature circuit. Since

IR is small compared with V, then an approximate relationship for the speed is

since

Vis constant. Hence the theoretical speed/current characteristic is as shown in

Figure below

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Figure 3.28: Speed current characteristics

The high speed at small values of current indicates that this type of motor must

not be run on very light loads and invariably, such motors are permanently

coupled to their loads.

The theoretical speed/torque characteristic may be derived from (i) and (ii)

above by obtaining the torque and speed for various values of current and

plotting the co-ordinates on the speed/torque characteristics. A typical

speed/torque characteristic is shown in Figure below

Figure 3.29: Speed –Torque characteristics

86

a) Generated e.m.f., E, at initial load ,is given by

87

c) Compound wound DC Motor

There are two types of compound wound motor:

i. Cumulative compound,

In which the series winding is so connected that the field due to it assists that due to the

shunt winding.

ii. Differential compound,

In which the series winding is so connected that the field due to it opposes that due to the

shunt winding.

Further compound wound DC motors; can be subdivided into following groups

i. Long-shunt compound motor

Figure 3.30: Long –shunt compound motor

ii. short-shunt compound motor

Figure 3.31: Short-shunt compound motor

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3.29 Characteristics of compound wound DC Motor

A compound-wound motor has both a series and a shunt field winding, (i.e. one winding in series

and one in parallel with the armature), and is usually wound to have a characteristic similar in

shape to a series wound motor

A limited amount of shunt winding is present to restrict the no-load speed to a safe value.

However, by varying the number of turns on the series and shunt windings and the directions of

the magnetic fields produced by these windings (assisting or opposing), families of

characteristics may be obtained to suit almost all applications.

Typical compound motor torque and speed characteristics are shown in Figure below

Figure 3.32: Characteristics of compound wound DC Motor

3.30 Application of compound DC wound Motor

Generally, compound-wound motors are used for heavy duties, particularly in applications where

sudden heavy load may occur such as for driving plunger pumps, presses, geared lifts,

conveyors, hoists and so on.

3.31 The efficiency of a DC motor

It has been stated that, the efficiency of a DC machine is given by:

89

The circuit, can be drawn as shown below

90

The circuit can be redrawn as shown below

91

But efficiency, is given by the following formula

92

93

3.32 DC motor starter

Is a special a device containing a variable resistance connected in series to the armature winding

so as to limit the starting current of dc motor to a desired optimum value taking into

consideration the safety aspect of the motor.

If a DC motor whose armature is stationary is switched directly to its supply voltage, it is likely

that the fuses protecting the motor will burn out.

This is because the armature resistance is small, frequently being less than one ohm. Thus,

additional resistance must be added to the armature circuit at the instant of closing the switch to

start the motor.

As the speed of the motor increases, the armature conductors are cutting flux and a generated

voltage, acting in opposition to the applied voltage, is produced, which limits the flow of

armature current. Thus the value of the additional armature resistance can then be reduced.

When at normal running speed, the generated e.m.f. is such that no additional resistance is

required in the armature circuit. To achieve this varying resistance in the armature circuit on

starting, a DC motor starter is used

Consider the diagram below that shows a DC motor starter

Figure 3.33: DC motor Starter

The starting handle is moved slowly in a clockwise direction to start the motor. For a shunt-

wound motor, the field winding is connected to stud 1 or to L via a sliding contact on the starting

handle, to give maximum field current, hence maximum flux, hence maximum torque on

starting, since Tα ΦIa

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3.33 The need for Motor Starter

Motor starter helps to limit starting current of a DC motor, since motor has a very high starting

current that has the potential of damaging the internal circuit of the armature winding of dc

motor if not restricted to some limited value.

3.34 Methods of varying the speed of a DC Motors

To vary speed of a DC motors, depend very much on the type of DC motors

i. Shunt-wound motors

It has been shown that, The speed of a shunt-wound DC motor, n, is proportional

to

i.e.

nα (V-IaRa)/Φ

The speed is varied either by varying the value of flux, Φ, or by varying the value

of Ra

The former (Ra) is achieved by using a variable resistor called the shunt field

regulator in series with the field winding, as shown in Figure below

Figure 3.34: applying shunt filed regulator

As the value of resistance of the shunt field regulator is increased, the value of the field current,

If is decreased. This results in a decrease in the value of flux, and hence an increase in the speed,

since

Thus only speeds above that given without a shunt field regulator can be obtained by this

method.

Speeds below those given by

95

are obtained by increasing the resistance in the armature circuit, as shown in Figure below

Figure 3.35: Increasing armature resistance

Since resistor R is in series with the armature resistance Ra therefore, the equation is changed to

In this case, it carries the full armature current and results in a large power loss in large motors

where a considerable speed reduction is required for long periods.

These methods of speed control are demonstrated in the following worked problem

96

a) With reference to Figure below

97

ii. Series Wound DC motors

Variation in speed of series-wound motors is achieved using either

(a) Field resistance or (b) armature resistance techniques.

a) Field resistance

Remember this equation derived earlier

The speed of a DC series-wound motor is given by:

Where k is a constant, Vis the terminal voltage, R is the combined

Resistance of the armature and series field (Ra +Rf ) and Φ is the flux.

Thus, a reduction in flux results in an increase in speed. This is achieved by

putting a variable resistance in parallel with the field winding and reducing the

field current, and hence fluxes, for a given value of supply current

A circuit diagram of this arrangement is shown in Figure below

Figure 3.36; Variable resistor in series wound Motor

A variable resistor connected in parallel with the series-wound field to control

speed is called a diverter. Speeds above those given with no diverter are obtained

by this method.

This scenario can be further demonstrated using the following example

98

99

b) Armature resistance techniques.

Speeds below normal are obtained by connecting a variable resistor in series with the

field winding and armature circuit, as shown in Figure below. This effectively increases

the value of R in the equation

And thus reduces the speed. Since the additional resistor carries the full supply current, a

large power loss is associated with large motors in which a considerable speed reduction

is required for long periods.

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With reference to the figure below at 800rev/min

101

3.35 Armature Reaction and Commutation in DC Machines

3.36 Commutation in DC Machine

is the process in which generated alternating current in the armature winding of a dc machine is

converted into direct current after going through the commutator and the stationary brushes.

The voltage generated in the armature, placed in a rotating magnetic field, of a DC generator is

alternating in nature.

Commutation is the positioning of the DC generator brushes so that the commutator segments

change brushes at the same time the armature current changes direction. More simply stated,

commutation is the mechanical conversion from AC to DC at the brushes of a DC machine, as

shown in Figure below

Figure 3.37: Commutation Process

In order to achieve sparkless commutation, the brushes must lie along M.N.A.

3.37 Armature Reaction

Is the phenomena where by armature flux react in opposite to the main flux (Field flux)

In a DC Machines, the purpose of field winding is to produce magnetic field (Called main flux)

whereas the purpose of armature winding is to carry armature Current.

Although the armature winding is not provided for the purpose of producing a magnetic field,

nevertheless the current in the armature winding will also produce magnetic flux (called

armature flux)

The armature flux distorts and weakens the main flux from field winding, posing problems for

the proper operation of the DC Machines

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3.38 Mains magnetic field of a machines

Main field of a machine is obtained only when excited machine, say a generator is operated at

NO load condition. This filed is represented by an arrow , which indicates the direction of

magnetic flux form the north pole to south pole as shown in figure below

Figure 3.38: Main Magnetic field in DC Machine

In the figure above, there is a symmetrical distribution of flux with respect to the

polar axis, which is a line joining the centers of North Pole (N) and South Pole (S)

Magnetic neutral axis or Plane (MNA) coincidence with geometrical neutral axis

or plane (GNA)

Magnetic neutral axis may be defined as the axis along which no e.m.f is

produced in the armature conductors because they then move parallel to the

conductors

It may also be defined as the axis which is perpendicular to the flux passing

through the armature

Brushes are always placed along MNA. Hence, MNA is also called the axis of

commutation because reversal of a current in the armature conductor , takes place

across this axis

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3.39 Armature field

A load is now connected to the excited machine, and of course current flow exist. Consider the

figure below that shows the armature rotating in magnetic file. The direction of the armature

conductors, may be determined from Fleming right hand rule, and the direction of the magnetic

field around each conductors may be determined from Right hand grip rule

Figure 3.39: Armature Magnetic field in DC Machine

When current flows in a conductor, magnetic fields are set up around as shown above. When

several conductors are placed together, the flux from each conductor is combined to form a

resultant flux. Note the direction of resultant flux. The flux from the conductors on the left side

of the armature and the flux from the conductors on the right side of the armature, causes the

resultant flux on the centre of the armature, that is downward in the direction

This resultant flux can be represented by an arrows indicated, noting that arrows passes

through both top and bottom brushes

The armature magnetic field has two effects on the Field winding magnetic field

i. It demagnetises or weakens the main magnetic field

ii. It cross magnetizes or distort it

104

Now there are two fluxes inside the machine, one produced by the main filed poles of the

machine, and the other by the current in the armature coil. These two fluxes now combine to

form a new resultant flux shown in figure below

Figure 3.40: Armature reaction in DC Machines

This new resultant flux, is not in the same direction as the original main field flux, but runs from

the tip of the poles across the armature to the tip of the other pole

The armature conductors are now cutting this new resultant flux. The brushes are now supposed

to be located at the point of minimum flux, which of course are at right angles to the direction of

flux.

Since the brushes were originally at right angles to the direction of flux produced by the main

filed poles, they are certainly not at right angles to the direction of the new resultant flux

With the brushes in their present location (At right angle to the main flux poles), they will be

short circuiting the coils in which there is voltage induced, there by producing a sparking at the

brushes, causes the brushes to wear and other

3.40 Methods to neutralize armature reaction and commutation in DC Machines

If magnetic neutral axis or plane is shifted in the direction of rotation, commutation is seriously

affected because sparking will occur at brushes unless they are shifted to the new magnetic

neutral plane

Furthermore the brushes must be shifted back and forth continuously as the load changes,

because effects of armature reaction depend upon the value of the armature current. In practice

repeated brush shifting would of course be almost objectionable as the sparking that it attempts

to correct

This has led to several corrective methods that counteract in part or completely the detrimental

effects of armature reaction as follows

105

a) By increasing the length of the air gap

The equivalent gap is usually made longer under the pole tips than elsewhere or by using

the punchings as shown below

This is accomplished either by cutting off, or chamfering the pole tips

The use of the long air gap, make the air gap reluctance (resistance), to become high.

This would requires a strong m.m.f (magnetomotive force) in order to force the flux to

pass across the air gap

On account of the greater equivalent air gap length under the pole tips, the influence of

the armature m.m.f in shifting the main filed is greatly minimized

b) By providing the machine with a compensating winding

Compensating winding is placed in slots of the poles of the machines as shown in figure

below. And is usually connected in series with the armature winding in such a way that at

any point in the air gap, the current will be flowing in opposite direction to the current in

the armature winding.

In this case, if the compensating winding has the same m.m.f as the armature m.m.f, the

m.m.f of the armature will be completely neutralized. Hence overall armature reaction

will be neutralized

c) By reducing the cross sectional area of the pole pieces

When the cross sectional area of the pole pieces is reduced, it becomes highly saturated

and offer large reluctance to the cross field

106

d) By using commutating pole

Commutating pole is small auxiliary pole, mounted on the frame between the pole. These

poles must be wound in such a way that, their actions opposes that of the cross field

Further Problems in DC machines

107

108

109

110

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CHAPTER FOUR

4.0 Induction Motors

As general rule, conversion of electrical power to Mechanical power take place in rotating part

called ROTOR of an electric motor.

In D.C Motor, the electric current is usually conducted directly to the armature (Rotating part),

through brushes and commutator. In this case D.C Motors are called CONDUCTION MOTOR.

However, In A.C motor, the rotating Part (ROTOR), doesn‘t receive electric current by

conduction, rather it receives by INDUCTION, That‘s why A.C motors are referred to as

INDUCTION Motors

In a DC machines, conductors on a rotating armature pass through a stationary magnetic field

In a three-phase induction motor, the magnetic field rotates and this has the advantage that no

external electrical connections to the rotor need be made. Its name is derived from the fact that

the current in the rotor is induced by the magnetic field instead of being supplied through

electrical connections to the supply.

4.1 Advantages of using a rotating magnetic field instead of stationary magnetic field

i. The motor is cheap and robust

ii. Motor is explosion proof, due to the absence of a commutator or slip-rings and brushes

with their associated sparking

iii. Motor requires little or no skilled maintenance

iv. The motor has self-starting properties when switched to a supply with no additional

expenditure on auxiliary equipment

4.2 Advantages of a Three Phase Induction Motors

i. It has simple and extremely rugged , almost Unbreakable construction (Especially,

squirrel cage Type)

ii. Its cost is low, and it is very reliable Motor

iii. It has sufficient very high efficient. In normal running condition, no brushes are needed,

hence frictional loss is reduced. It has a reasonable good power factor

iv. It requires minimum maintenance

v. It start up from rest, and needs no extra starting motor, and has not to be synchronized

112

4.3 Principle disadvantages of a three phase induction motor

i. Its speed cannot be easily varied without affecting efficiency

ii. Just like DC motor, its speed decreases with increasing in load

iii. Starting torque is somewhat inferior to that of a DC motor

4.4 Classes of AC Machines

There are basically two major classes of AC electrical machines,

a) Synchronous Machines

b) Induction machines

4.5 Three phase Induction Motor

Three phase induction motor as this type of motor does not require any starting device or

we can say they are self-starting induction motor.

Basically there are two types of 3 phases Induction Motor –

1. Squirrel cage induction motor

2. Phase Wound induction motor (slip-ring induction motor).

Both types have similar constructed rotor, but they differ in construction of rotor. This is

explained further

4.6 Construction of a three phase induction motor

Just like any other motor, a 3 phase induction motor also consists of a stator and a rotor

Stator

The stator of a three-phase induction motor is the stationary part corresponding to the yoke of

a DC machine. It is made up of number of stampings, which are slotted to receive the

windings It is wound to give a 2-pole, 4-pole, 6-pole, rotating magnetic field, depending on

the rotor speed required. The number of poles is determined from the required speed. For

greater speed, lesser number of poles is used and vice versa.

Starter carries 3 phase winding, and is fed from a 3 phase supply

113

Consider the diagrams below

Figure 4.1 : Stator

When stator windings are supplied with 3 phase ac supply, they produce alternating flux

which revolves with synchronous speed given by 120

s

fN

p , where P= number of poles

produced in a rotating magnetic field , P=2n, where n= number of stator slots/pole/phase, f=

frequency of the AC supply

Rotor

The rotor, corresponding to the armature of a DC machine, is built up of laminated iron, to

reduce eddy currents. As described earlier, rotor of a 3 phase induction motor can be of

either two types, squirrel cage rotor and phase wound rotor (or simply - wound rotor).

4.7 Squirrel cage rotor

Most of the induction motors (up to 90%) are of squirrel cage type. Squirrel cage type rotor

has very simple and almost indestructible construction. This type of rotor consists of a

cylindrical laminated core, having parallel slots on it. Consider the diagram below

Figure 4.2 : Squirrel Cage Rotor

These parallel slots carry rotor conductors. In this type of rotor, heavy bars of copper,

aluminum or alloys are used as rotor conductors instead of wires. One bar is placed in each

slots, rather the bar are inserted from the end when semi-closed slots are used. The rotor bars

114

are blazed or electrically welded or bolted to two heavy and stout short-circuiting end rings

thus giving us what is so pictured as squirrel cage rotor

It should be noted that, rotor bars are permanently short circuited on themselves; hence it

is not possible to add any external resistance in series with the rotor for starting purpose

Rotor slots are slightly skewed to achieve following advantages

1. It reduces locking tendency of the rotor, i.e. the tendency of rotor teeth to remain under

stator teeth due to magnetic attraction.

2. increases the effective transformation ratio between stator and rotor

3. increases rotor resistance due to increased length of the rotor conductor

This type of rotor has no external connection which means that slip rings and brushes are not

needed. The squirrel-cage motor is cheap, reliable and efficient.

A cross-sectional view of a three-phase induction motor is shown in Figure below

Figure 4.3: Cross sectional view of three phase induction motor

Figure above contains 4 conductors per phase, where R=red, Y=yellow=Blue, s=start,

F=finish

4.8 Phase wound rotor

Phase wound rotor is wound with 3 phase, double layer, distributed winding. The number of

poles of rotor is kept same to the number of poles of the stator. The rotor is always wound 3

phase even if the stator is wound two phase.

115

The windings may be internally connected in star or delta and the other three winding terminals

are brought out and connected to three insulated slip rings, mounted on the shaft, with the

brushes resting on them

These three brushes are further externally connected to 3 phase star or delta connected rheostat.

Consider the diagram below

Figure 4.4 : Phase Wound Rotor

This arrangement is done to introduce an external resistance in rotor circuit for starting

purposes and for changing the speed / torque characteristics.

When motor is running at its rated speed, slip rings are automatically short circuited by means of

a metal collar which is pushed along the shaft and connects all the rings together

Next the brushes are automatically lifted up from the slip rings to reduce the frictional losses and

the wear and tear hence it is seen that under normal running condition, the wound rotor is short

circuited on itself just like the squirrel cage rotor

The principle of operation is the same for both the squirrel cage and the wound rotor machines.

4.9 Production of a rotating magnetic field

When a three-phase supply is connected to symmetrical three-phase windings, the currents

flowing in the windings produce a magnetic field. This magnetic field is constant in magnitude

and rotates at constant speed as shown below, and is called the synchronous speed.

With reference to Figure below, the windings are represented by three single-loop conductors,

one for each phase, marked RS , RF , YS , YF and BS , BF , the S and F signifying start and finish

116

Figure 4.5: Production of Rotating Magnetic Field

In practice, each phase winding comprises many turns and is distributed around the stator; the

single-loop approach is for clarity only.

When the stator windings are connected to a three-phase supply, the current flowing in each

winding varies with time and is as shown in Figure below

Figure 4.6: Rotating Magnetic field

If the value of current in a winding is positive, the assumption is made that it flows from start to

finish of the winding, i.e., if it is the red phase, current flows from RS to RF, i.e. away from the

viewer in RS and towards the viewer in RF

When the value of current is negative, the assumption is made that it flows from finish to start,

i.e. towards the viewer in an ‗S‘ winding and away from the viewer in an ‗F‘ winding.

At time, sayt1, shown in Figure above, the current flowing in the red phase is a maximum

positive value. At the same time, t1, the currents flowing in the yellow and blue phases are both

0.5 times the maximum value and are negative.

The current distribution in the stator windings is therefore as shown in Figure below, in which

current flows away from the viewer, (shown as ‗x‘ mark enclosed in a circle) in RS, since it is

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positive, but towards the viewer (shown as ‗dot‘ mark enclosed in a circle) in YS and BS, since

these are negative.

Figure 4.7: Rotating Magnetic field

The resulting magnetic field is as shown below, due to the ‗solenoid‘ action and application of

the corkscrew rule (Right hand grip rule)

A short time later at timet2, the current flowing in the red phase has fallen to about 0.87 times its

maximum value and is positive, the current in the yellow phase is zero and the current in the blue

phase is about 0.87 times its maximum value and is negative. Hence the currents and resultant

magnetic field are as shown in Figure below

Figure 4.8: Rotating magnetic field

At time t3, the currents in the red and yellow phases are 0.5 of their maximum values and the

current in the blue phase is a maximum negative value. The currents and resultant magnetic field

are as shown below

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Figure 4.9: Rotating Magnetic field

4.10 Principle of operation of a three-phase induction motor

When a three-phase supply is connected to the stator windings, a rotating magnetic field is

produced. As the magnetic flux cuts a bar on the rotor, an e.m.f. is induced in it and since it is

joined, via the end conducting rings, to another bar one pole pitch away, current flows in the

bars. The magnetic field associated with this current flowing in the bars interacts with the

Rotating magnetic field and a force is produced, tending to turn the rotor in the same direction as

the rotating magnetic field, see the figure below

Figure 4.10: Operation of a three phase induction Motor

Similar forces are applied to all the conductors on the rotor, so that a torque is produced causing

the rotor to rotate.

4.11 Synchronous speed of induction Motors

The synchronous speed of an AC motor is the speed of the stator's magnetic field rotation

The rotating magnetic field produced by three phase windings could have been produced by

rotating a permanent magnet‘s north and south pole at synchronous speed. (Shown as N and S at

the ends of the flux phasors) Consider the diagram below

119

Figure 4.11: 2 poles Induction Motor

For this reason, an induction motor using three phase windings only is called a 2-pole induction

motor. Since it contains only N-pole and S-pole of a magnet

If six windings displaced from one another by 60° are used, as shown in Figure below, It can be

seen that for six windings on the stator, the magnetic flux produced is the same as that produced

by rotating two permanent magnet north poles and two permanent magnet south poles at

synchronous speed

This is called a 4-pole system and an induction motor using six phase Windings is called a 4-pole

induction motor. By increasing the number of phase windings the number of poles can be

increased to any even number.

Figure 4.12: 4 poles Induction motor

120

By drawing the current and resultant magnetic field diagrams at various time values, it may be

shown that one cycle of the supply current to the stator windings causes the magnetic field to

move through half a revolution.

In general, if f is the frequency of the currents in the stator windings and the stator is

wound to be equivalent to p pairs of poles, the speed of revolution of the rotating magnetic

field, i.e., the synchronous speed, nS is given by:

120

min

,

sec

S

S

f revnp

where

p total number of poles

Another formula

f revnp

f frequency of current in Hz

p pair of poles

121

4.12 Slip in Induction Motor

Slip may be fined as the deviation or difference in speed between the rotor speed and the

synchronous speed of the rotating magnetic field

The force exerted by the rotor bars causes the rotor to turn in the direction of the rotating

magnetic field. As the rotor speed increases, the rate at which the rotating magnetic field cuts the

rotor bars is less and the frequency of the induced e.m.f.‘s in the rotor bars is less.

If the rotor runs at the same speed as the rotating magnetic field, no e.m.f. are induced in the

rotor, hence there is no force on them and no torque on the rotor. Thus the rotor slows down.

For this reason the rotor can never run at synchronous speed.

Slip speed

May be defined as, The difference between the rotor speed, nr , and the synchronous speed, ns.

When there is no load on the rotor, the resistive forces due to windage and bearing friction are

small and the rotor runs very nearly at synchronous speed. As the rotor is loaded, the speed falls

and this causes an increase in the frequency of the induced e.m.f.‘s in the rotor bars and hence

the rotor current, force and torque increase.

The difference between the rotor speed, nr , and the synchronous speed, ns, is called the slip

speed, i.e.

122

123

124

4.13 Rotor e.m.f and Frequency

Rotor e.m.f.

When an induction motor is stationary, the stator and rotor windings form the equivalent of a

transformer as shown below

Figure 4.13: Equivalent circuit of a rotor

The rotor e.m.f. at standstill is given by

125

When an induction motor is running, the induced e.m.f. in the rotor is less since the relative

movement between conductors and the rotating field is less. Hence induced e.m.f. is proportional

to this movement, hence it must be proportional to the slip, s

Rotor frequency.

The rotor e.m.f. is induced by an alternating flux and the rate at which the flux passes the

conductors is the slip speed. Thus the frequency of the rotor e.m.f. is given by:

Frequency of a rotor current

When the rotor is stationary, the frequency of the rotor current is the same as the supply

frequency. But when the rotor starts revolving, then the frequency depend upon the relative

speed or sleep speed, Let the frequency of the rotor current be f‘ , then we can say that

126

'

'

'

120....................

120............................

, /

'

s r

s

s r

s

fn n i

P

fn ii

P

divide i ii

n n f

n f

fs

f

f sf

127

4.14 Rotor Impedance and current

Rotor resistance

The rotor resistance R2 is unaffected by frequency or slip, and hence remains constant.

Equivalent circuit of the rotor when running

Rotor reactance

Rotor reactance varies with the frequency of the rotor current.

Rotor impedance

128

Rotor current

From the figures above of the rotor circuit

Rotor copper loss

129

4.15 Induction Motor losses and efficiency

Figure below summarizes losses in induction motors,

Figure 4.14: Different losses in Induction motor

130

131

132

4.16 Torque equation For a induction Motor

Under normal conditions, the supply voltage is usually constant, hence equation above becomes:

133

Remember this equation already derived

previously

134

135

136

137

4.17 Relationship between, torque and rotor Power Factor

It has been shown that, in case of DC motor, the torque Ta is propotional to the product of

armature current and flux per pole IaΦ (Ta α IaΦ ). Similarly in the case of induction motor, the

torque is also propotional to the product of rotor current (armature) and flux pole. However there

is one more factor that has to be considered, i.e. the power factor of the rotor. Therefore

T α ΦIrCosφ or T= K ΦIrCosφ, where k is constant

Where Ir =rotor current at stand stiil,φ= angle between rotor current and rotor EMF

Form this expression T= K ΦIrCosφ we can conclude that

When the phase angle φ increases, cos φ decreases, hence torque will also decrease.

Conclusively, Torques is directly propotional to the power factor

4.18 Starting torque of three phase induction Motor

Starting torque is the torque developed by the motor at the instant of starting. In some cases, it is

greater than the normal running torque. Where in some other cases is somewhat less

Let E2 = EMF per phase of a rotor, at stand still

R2 = Rotor resistance per phase

X2 = Rotor reactance per phase at standstill

Z2 = Rotor impedance per phase at stand still= 2 2 2Z R X

2 2 2

2 22

2 22 2 2

2 22

2 22 2 2

cos

Z R X

E EI

Z R X

R RPower factor

Z R X

But standstill torque, starting torque is given by = 1 2 2 2cosT k E I

1 2 2 2

2 21 2

2 2

2 2 2 2

2

1 2 2

2 2

2 2

cosT k E I

E RT k E x x

R X R X

k E RT

R X

138

1

3,

2 s

but kn

ns is synchronous speed in rps

4.19 Starting torque of a squirrel cage rotor

The resistance of a squirrel cage motor is fixed, and small as compared to its reactance, which is

very large especially at the start, because at stand still, the frequency of the rotor current is equal

to the supply frequency

In this case, the starting current I2 of the rotor , though very large in magnitude lags by a very

large angle behind E2 , with the resultant that the starting torque is very poor. The starting

torque is about 1.5 times full load torque though the starting current I2 is about 5-7 times

full loads current. Hence squirrel cage Motor is not usefully where the motor has to start

against heavy loads

4.20 Starting torque of a slip ring motor (Phase wound Motor)

Starting torque of this motor is increased by improving its power factor by adding external

resistance, in the rotor circuit from the star connected rheostat, the rheostat resistance being

progressively cut out as the motor gathers speed

Additional external resistance, however increases the rotor impedance, and so reduces the rotor

current. At first the effect of improved power factor predominates the current decreasing effect

of impedance,; hence starting torque is increased

But after certain point, the effect of increased impedance, predominates the effect of improved

power factor and so the torque start decreasing

4.21 Induction motor torque-speed characteristics

From Problem 10, parts (c) and (g), it is seen that the normal starting torque may be less than the

full load torque. Also, from Problem 10, parts (e) and (f), it is seen that the speed at which

maximum torque occurs is determined by the value of the rotor resistance. At synchronous

Speed, slips s=0 and torque is zero. From these observations, the torque speed and torque-slip

characteristics of an induction motor are as shown in Figure below

139

Figure 4.15: Induction Motor Torque speed characteristics

The rotor resistance of an induction motor is usually small compared with its reactance, so that

maximum torque occurs at a high speed, typically about 80% of synchronous speed.

Curve P, in Figure above, is a typical characteristic for an induction motor. The curve P cuts the

full-load torque line at point X, showing that at full load the slip is about 4–5%.

The normal operating conditions are between 0 and X, thus it can be seen that for normal

operation the speed variation with load is quite small — the induction motor is an almost

constant speed machine.

If maximum torque is required at starting then a high resistance rotor is necessary, which gives

characteristic Q in Figure above

However, as can be seen, the motor has a full load slip of over 30%, which results in a drop in

efficiency. Also such a motor has a large speed variation with variations of load. Curves R and S

of Figure above are characteristics for values of rotor resistances between those of P and Q.

Better starting torque than for curve P is obtained, but with lower efficiency and with speed

variations under operating conditions.

140

4.21 Speed torque characteristics of a three phase induction motors

Redrawing the speed-torque characteristic between 0 and X gives the characteristic shown in

Figure below, which is similar to a DC shunt motor

4.22 Squirrel cage induction motor characteristics

This would normally follow characteristic P. This type of machine is highly efficient and about

constant-speed under normal running conditions. However it has a poor starting torque and must

be started off-load or very lightly loaded. Consider the graph below

Figure 4.16: Squirrel cage induction motor characteristics

141

Also, on starting, the current can be four or five times the normal full, load current, due to the

motor acting like a transformer with secondary short circuited

4.23 Wound –rotor induction motor characteristics

A wound-rotor induction motor would follow characteristic P when the slip-rings are short-

circuited, which is the normal running condition. However, the slip-rings allow for the addition

of resistance to the rotor circuit externally and, as a result, for starting, the motor can have a

characteristic similar to curve Q shown in the previous figure and the high starting current

experienced by the cage induction motor can be overcome.

In general, for three-phase induction motors, the power factor is usually between about 0.8 and

0.9 lagging, and the full load efficiency is usually about 80–90%.

From equation below, it is seen that torque is proportional to the square of the supply voltage.

Any voltage variations therefore would seriously affect the induction motor performance

4.24 Starting methods for induction motor

Squirrel-cage rotor

i. Direct-on-line starting

With this method, starting current is high and may cause interference with supplies to other

consumers.

ii. Auto transformer starting

With this method, an auto transformer is used to reduce the stator voltage, E1, and thus the

starting current, see the figure below

142

However, the starting torque is seriously reduced, because Torque is propotional to the square of

a voltage, therefore the voltage is reduced only sufficiently to give the required reduction of the

starting current. A typical arrangement is shown in Figure below

Figure 4.17 :Starting induction motor by Auto transformer

A double-throw switch connects the auto transformer in circuit for starting, and when the motor

is up to speed the switch is moved to the run position which connects the supply directly to the

motor.

iii. Star-delta starting

With this method, for starting, the connections to the stator phase winding are star-connected, so

that the voltage across each phase winding is 1/ 3 (i.e. 0.577) of the line voltage. For running,

the windings are switched to delta-connection. A typical arrangement is shown in Figure below

This method of starting is less expensive than by auto transformer.

Figure 4.18 : Starting induction Motor by star delta

143

4.25 Three Phase Synchronous Motor

As the name suggests Synchronous motors are capable of running at constant speed irrespective

of the load acting on them. Unlike induction motors where speed of the motor depends upon the

torque acting on them, synchronous motors have got constant speed-torque characteristics.

Synchronous motors have got higher efficiency (electrical to mechanical power conversion ratio)

than its counterparts. Its efficiency ranges from 90 – 92%.

4.26 The advantages of the wound rotor motor compared with the cage type

i. Have a much higher starting torque

ii. have a much lower starting current

iii. Have a means of varying speed by use of external rotor resistance.

4.27 Construction of three phase Synchronous Motor

The construction of a synchronous motor (with salient pole rotor) is as shown in the figure

below Just like any other motor; it consists of a stator and a rotor.

Stator: Revolving Magnetic Field

The stator core is constructed with thin silicon lamination and insulated by a surface coating, to

minimize the eddy current and hysteresis losses. The stator has axial slots inside, in which

three phase stator winding is placed. The stator is wound with a three phase winding for a

specific number of poles equal to the rotor poles.

The field coil of stator is excited by a 3 phase AC supply. This will produce a revolving

magnetic field (RMF), which rotates at synchronous speed.

Figure 4.19: Stator for synchronous Motor

144

Rotor: Constant Magnetic field

Rotor is excited by a D.C power supply, magnetic field produced around the rotor coil by DC

excitation is shown above. It is clear that the rotor acts like a permanent magnet due to such

magnetic field. Alternatively rotor can also be made of permanent magnet.

The rotor in synchronous motors is mostly of salient pole type. DC supply is given to the rotor

winding via slip-rings. The direct current excites the rotor winding and creates electromagnetic

poles. In some cases permanent magnets can also be used. The figure above illustrates the

construction of a synchronous motor very briefly.

4.28 Working of principle synchronous motor

Synchronous motor is a doubly excited machine i.e. two electrical inputs are provided to it. It‘s

stator winding which consists of a 3 phase winding is provided with 3 phase supply and rotor is

provided with DC supply. The 3 phase stator winding carrying 3 phase currents produces 3 phase

rotating magnetic flux. The rotor carrying DC supply also produces a constant flux

When a 3 phase electric conductors are placed in a certain geometrical positions (In certain angle

from one another) there is an electrical field generate. Now the rotating magnetic field rotates at

a certain speed, that speed is called synchronous speed. Now if an electromagnet (rotor magnetic

field ) is present in this rotating magnetic field, the electromagnet is magnetically locked with

this rotating magnetic field and rotates with same speed of rotating field. Synchronous motors is

called so because the speed of the rotor of this motor is same as the rotating magnetic field

It is basically a fixed speed motor because it has only one speed, which is synchronous speed and

therefore no intermediate speed is there or in other words it‘s in synchronism with the supply

frequency. Synchronous speed is given by

4.29 Main Features of Synchronous Motors

Synchronous motors are inherently not self-starting. They require some external means to bring

their speed close to synchronous speed to before they are synchronized.

At a particular instant rotor and stator poles might be of same polarity (N-N or S-S) causing

repulsive force on rotor and the very next second it will be N-S causing attractive force. But due

to inertia of the rotor, it is unable to rotate in any direction due to attractive or repulsive force and

remain in standstill condition. Hence it is not self-starting.

145

To overcome this inertia, rotor is initially fed some mechanical input which rotates it in

same direction as magnetic field to a speed very close to synchronous speed. After some

time magnetic locking occurs and the synchronous motor rotates in synchronism with the

frequency.

1. The speed of operation of is in synchronism with the supply frequency and hence for

constant supply frequency they behave as constant speed motor irrespective of load

condition

2. This motor has the unique characteristics of operating under any electrical power factor.

This makes it being used in electrical power factor improvement.

3. The only way to change its speed is to change its supply frequency. (As Ns = 120f / P)

4.30 Methods of Starting of Synchronous Motor

Synchronous motors are mechanically coupled with another motor. It could be either 3 phase

induction motor or DC shunt motor. DC excitation is not fed initially. It is rotated at speed very

close to its synchronous speed and after that DC excitation is given. After some time when

magnetic locking takes place supply to the external motor is cut off.

Damper winding : In case, synchronous motor is of salient pole type, additional winding is

placed in rotor pole face. Initially when rotor is standstill, relative speed between damper

winding and rotating air gap flux in large and an e.m.f is induced in it which produces the

required starting torque. As speed approaches synchronous speed, e.m.f and torque is reduced

and finally when magnetic locking takes place, torque also reduces to zero. Hence in this case

synchronous is first run as three phase induction motor using additional winding and finally it is

synchronized with the frequency

146

CHAPTER FIVE

5.0Transformers

A transformer is a device which uses the phenomenon of mutual induction, to change the values

of alternating voltages and currents. In fact, one of the main advantages of AC transmission and

distribution is the ease with which an alternating voltage can be increased or decreased by

transformers. Losses in transformers are generally low and thus efficiency is high. Being static

they have a long life and are very stable.

A transformer is represented in Figure below as consisting of two electrical circuits linked by a

common ferromagnetic core. One coil is termed the primary winding which is connected to the

supply of electricity, and the other the secondary winding, which may be connected to a load. A

circuit diagram symbol for a transformer is shown in Figure b.

Figure 5.1 : Transformer Construction

5.1 Construction Of transformers

Simple element of transformer consists of two coils, having mutual inductance, and the

laminated steel core. The two coils are insulated from each other, and the steel core. Other

necessary parts are

Suitable containers for the assembled core and windings

Suitable medium or material for insulating the core and its windings form its container

Suitable bushings , either of porcelain , oiled field or capacitor type for insulating and

bringing out the terminals of winding from the tank

Transformer Core

Transformer core, is constructed of transformer sheet steel laminations assembled to provide a

continuous magnetic path , with a minimum of air gap included. The steel used is of high silicon

content

147

Eddy current in transformer is minimized by the use of laminated steel sheet, being insulated

from each other by a light coat of core plate vanish or by an oxide layer on the surface

5.2 Categories of transformer basing on the construction

Constructionally, transformers are of two general categories, distinguished form each other ,

merely by the manner in which primary and secondary coil are placed around the laminated core

i. Core type transformers

In this type, the windings surround the considerable part of the core

Figure 5.2: Core type Transformer

ii. Shell type transformers

In this type, the core surrounds the considerable part of the winding coil

Figure 5.3 : Shell type Transformer

Shell type transformers are mostly applied in high voltage transformers

148

5.3 Elementary theory of ideal transformers

Consider an ideal transformers (lossless transformers), Whose primary winding is connected to

sinusoidal voltage V1 , with primary number of turns N1 and It draws primary current I1 .

Figure 5.4 : Structure of transformer

The secondary winding being connected to the Load, with secondary voltage of V2, secondary

current flowing I2 and number of turns in the secondary winding be N2 .

As you can see above, voltage applied in the primary windings, is an alternative voltage, whose

magnitude changes with time, generating magnetic field, that results to magnetic flux Φ, these

magnetic flux also will be changing with respect to time, as the flux travel through iron core to

the secondary winding (indicated as dashed line). When they reach secondary windings, it also

cuts the secondary winding, these results into production of an induced EMF in the secondary

which is propotional to the number of turns

Experimentally, it can be shown that, the induced EMF in both winding (primary and

secondary), is propotional to the number of turns I.e.

149

1 1

1 1

2 2

2 2

1 1

2 2

1 1

2 2

, ,

............................................( )

, ,

.........................................( )

, /

p p

s s

primary winding

V N or V N

V kN i

Secondary winding

V N or V N

V kN ii

Divide i ii

V kN

V kN

V N

V N

Note that N1 /N2 is called turns ratio

V1 /V2 =voltage ratio

Since we have assumed that the Transformer is ideal, i.e. Has no Loss, then we can say

that

Input power=output Power

1 1 2 2

1 2

2 1

V I V I

V I

V I

But Remember that

1 1

2 2

1 1 2

2 2 1

,V N

thereforeV N

V N I

V N I

Generally we can say that

p p s

s s p

V N I

V N I

This equation, is called equation of an Ideal transformer

150

151

152

5.4 Transformer no-load phasor diagram

The core flux is common to both primary and secondary windings in a transformer and is thus

taken as the reference phasor in a phasor diagram. On no-load the primary winding takes a small

no-load current I0 and since, with losses neglected, the primary winding is a pure inductor, this

current lags the applied voltage V1 by 90°. Consider the phasor diagram below

Figure 5.5: Transformer no-load phasor diagram

153

In the phasor diagram assuming no losses, shown in Figure above, current I0 produces the

flux and is drawn in phase with the flux. The primary induced e.m.f. E1 is in phase

opposition to V1 (by Lenz‘s law) and is shown 180° out of phase with V1 and equal in

magnitude.

The secondary induced e.m.f. is shown for a 2:1 turns ratio transformer.

A no-load phasor diagram for a practical transformer is shown in Figure below If current

flows then losses will occur. When losses are considered then the no-load current I0 is the

phasor sum of two components

i. IM , the magnetizing component, in phase with the flux,

ii. IC , the core loss component (supplying the hysteresis and eddy current losses)

No-load current,

154

The no-load phasor diagram is shown in Figure Below

155

5.5 Equivalent circuit of a transformer

Figure below shows an equivalent circuit of a transformer. R1 and R2 represent the resistances of

the primary and secondary windings and X1 and X2 represent the reactance‘s of the primary and

secondary windings, due to leakage flux.

Figure 5.6 : Equivalent circuit of a transformer

156

The core losses due to hysteresis and eddy currents are allowed for by resistance R which

takes a current Ic, the core loss component of the primary current. Reactance X takes the

magnetizing component IM.

In a simplified equivalent circuit shown in Figure below, R and X are omitted since the

no-load current I0 is normally only about 3–5% of the full load primary current. It is

often convenient to assume that all of the resistance and reactance as being on one side of

the transformer. Resistance R2 in Figure below can be replaced by inserting an additional

resistance R‘ 2 in the primary circuit such that the power absorbed

Figure 5.7 : Simplified equivalent circuit of a transformer

By similar reasoning, the equivalent reactance in the primary circuit is given by

The equivalent impedance Ze of the primary and secondary windings referred to the

primary is given by

157

The simplified equivalent circuit of a transformer is shown below

Solution

a) from equivalent circuit resistance given by

158

b) From equivalent circuit reactance‘s given by

c) From equivalent circuit impedances given by

d) Also from equation already shown above

5.6 Transformer regulation

When the secondary winding of the transformer is loaded, the Secondary voltage VS falls .When

Power factor of the transformer decreases, this voltage (Secondary voltage), increases. This

tendency of a secondary voltage VS to change when either secondary winding is loaded or when

the power factor of the transformer changes is called TRANSFOMER REGULATION

TRANSFOMER REGULATION: Is the tendency of a secondary voltage VS to change when

either secondary winding is loaded or when the power factor of the transformer changes.

Mathematically transformer Regulation may be defined as

2 2

2

Re 100%E V

gulation xE

Where E2 is the secondary voltage before connecting loadV2 is the secondary voltage after

connecting the load

159

Example 1:

The 5KVA, 200/400V, single phase transformer has a secondary terminal voltage of 387.6V

when loaded. Determine the regulation of the transformer

Solution

2 22 2

2

Re 100%, , 400 , 387.6

400 387.6Re 100%

400

12.4Re 100%

400

Re 3.1%

E Vgulation x Where E V V V

E

gulation x

gulation x

gulation

Example 2:

The open circuit voltage of a transformer is 240V.If the percentage regulation of the transformer

is 2.5%.determine the load Voltage at which the Transformer operates

Solution

2

2 2

2

2

2

2

2

2

2

2

Re 100%

Re 2.5%, 240 , ?

2402.5% 100%

240

2402.5

100 240

2400.025

240

240 6

240 6

234

E Vgulation x

E

g E V V

Vx

V

V

V

V

V V

160

5.7 Transformer Regulation

As the transformer is loaded, the secondary terminal voltage falls (for a lagging power factor).

Hence to keep output voltage constant, primary voltage must be increased. The rise in primary

voltage required to maintain rated output voltage from no load to full load at a given power

factor expressed as a percentage of the rated primary voltage, gives the regulation of the

transformer

Suppose, primary voltage has to be raised from its rated value V1 to V‘1 then

1 1

1

'% 100

V Vreg x

V

161

162

163

5.8 Transformer losses and efficiency

There are broadly two sources of losses in transformers on load, these being copper losses and

iron losses.

a) Copper losses are variable and result in a heating of the conductors, due to the fact that

they possess resistance. If R1 and R2 are the primary and secondary winding resistances

then the total copper loss is given by

b) Iron losses are constant for a given value of frequency and flux density and are of two

types — hysteresis loss and eddy current loss.

i. Hysteresis loss is the heating of the core as a result of the internal molecular

structure reversals which occur as the magnetic flux alternates. The loss is

proportional to the area of the hysteresis loop and thus low loss nickel iron alloys

are used for the core since their hysteresis loops have small areas

ii. Eddy current loss is the heating of the core due to e.m.f.‘s being induced not

only in the transformer windings but also in the core. These induced e.m.f.‘s set

up circulating currents, called eddy currents. Owing to the low resistance of the

core, eddy currents can be quite considerable and can cause a large power loss

and excessive heating of the core.

5.9 Methods of Reducing eddy currents

Eddy current losses can be reduced by increasing the resistivity of the core material or,

more usually,

By laminating the core (i.e., splitting it into layers or leaves) when very thin layers of

insulating material can be inserted between each pair of laminations. This increases the

resistance of the eddy current path, and reduces the value of the eddy current.

And is usually expressed as a percentage. It is not uncommon for power transformers to have

efficiencies of between 95% and 98%.

164

165

166

167

5.10 Maximum efficiency of Transformer

It may be shown that the efficiency of a transformer is a maximum when the variable copper loss

given by

Is equal to the constant iron losses.

168

5.11 Transformer Test

Transformer Test is very important in determining four main parameters of the transformer ,

These parameters are equivalent resistance of the transformers R01 referred to as primary or

secondary resistance R02 , the equivalent leakage reactance X01 as also referred to as primary or

secondary reactance X02 ,The core loss conductance G0 or resistance R0 and the magnetizing

susceptance B0 or reactance X0 .

5.12 Types of Transformer Tests

i. Open circuit tests

ii. Short circuit Test

These Tests are very economical and convenient because they furnish they information required

without actually loading the transformer

i. Open circuit or no load tests

The purpose of this test is to determine no load loss or core Loss and no load I0 , which is helpful

in finding X0 and R0 .Consider the figure below

Figure 5.8 : Open circuit or No load test

One winding of the transformer whichever is convenient , but usually high voltage winding is

left opened and the other is connected to its supply of normal voltage and frequency

169

A wattmeter W, voltmeter V, and an Ammeter A, are connected in the low voltage winding i.e.

primary winding in this case .

With normal voltage applied to the primary , normal flux will be set up in the core, hence normal

iron losses will occur which are recorded by the wattmeter . As the primary no load current I0 as

measured by an Ammeter, is small , usually 2 to 10% of the rated load current , copper losses is

negligibly small in primary and NIL in secondary (Because of open circuit). Hence Wattmeter

reading represent practically the core loss under no load condition

It should be noted that since I0 is itself very small , the pressure coils of the wattmeter and the

voltmeter are connected such that the current in them doesn‘t pass through the current coil of the

wattmeter

Sometimes high resistance voltmeter is connected across the secondary. The reading of the

voltmeter gives induced EMF in the secondary winding. This helps to find the Transformation

ratio K

The no vector diagram is shown in the figure below

If W, is the Wattmeter reading then we can say that

Or since, the current is practically all exciting current, when the transformer is on no load

170

And as the voltage drop in primary leakage impedance is small , hence the exciting admittance

Y0 of the transformer is given by

ii. Short circuit Test or Impedance Test

This is an economical Method of determining the following

Equivalent impedance (Z01 and Z02 ), leakage Reactance (X01 and X02 ), and Total

resistance (R01 and R02 ) of the transformers as referred to the winding in which

the measuring instrument are placed

171

Copper loss at full load at any desired load. This loss is used to calculate

efficiency of the transformer

Knowing Z01 and Z02 , the total voltage drop in the transformer as referred to

primary or secondary can be calculated and hence Regulation of the transformer

determined

In this test, one winding usually , the low voltage winding, is solidly short circuited

by a thick conductor (Or through an Ammeter which may serve the additional

purpose of indicating the rated load current ) , as shown in figure below

Figure 5.9 : Short circuit Test

A low Voltage Usually (5 to 10 % of the normal primary voltage) at a correct frequency (though

copper losses is not essential ), is applied to the primary and is cautiously increased till full load

current are flowing both in primary and secondary (as indicated by the respective ammeters)

Since, in this test, the applied voltage is a small percentage of the normal voltage, the mutual flux

Φ produced is also in small percentage of its normal value. Hence core losses are very small,

with the result that the wattmeter readings represent the full load copper loss or I2R loss for the

whole transformer, i.e. both primary copper loss and secondary copper loss.

172

The equivalent circuit of the transformer under short circuit condition is shown in figure below

Figure 5.10 : Equivalent circuit of a transformer

If VSC is the voltage required to circulate the rated load current then 01

1

SCVZ

I

The figure below, shows the equivalent circuit vector diagram for the short circuit test.

It is obvious that, the entire voltage VSC is consumed in the impedance drop of the two winding

173

If R1 can be measured, then knowing R01 , we can find 2 01 1'R R R , the impedance triangle can

then be divided into appropriate equivalent triangles for primary and secondary as shown in the

previous figure (b)

174

As shown in the figure below, these values refers to the primary, i.e. low voltage side

Form S.C test

It may be noted that, in this test, instrument have been placed in the secondary , i.e. high voltage

winding, where the low voltage winding , i.e. primary winding, has been shorted, Now as shown

below

175

176

Use the approximate equivalent circuit of the figure shown below

Figure 5.11: equivalent circuit diagram

Then, we have

As seen in figure below

177

5.13 Why Transformer rating is in KVA?

As seen, copper loss of the transformer, depends on current and iron loss on voltage. Hence total

transformer loss depends on Volt-Ampere (VA) and not on phase angle between voltage and

current, i.e. it is independent of load power-factor. That is why rating of transformer is in KVA

instead of KW

178

5.14 Autotransformers

It is a transformer with only one winding. Part of this being common to both primary and

secondary. Obviously form this transformer, primary winding and secondary windings are not

electrically isolated from each other as in the case for a 2 winding transformer

But its theory of operation is the same as that of a 2 winding transformer

5.15 Advantages of Auto-transformer compared to double wound transformer

Because of only one winding, then it uses less copper and its cheaper

It is used where the transformation ration differs from unity

5.16 Types of Autotransformers

Basically there are two type of Autotransformers

Step down Autotransformer

The figure below show construction of a step down Autotransformer

Figure 5.12 : Step down Transformer

As shown above, AB is a primary winding with N1 turns, and BC is a secondary windings

with N2 turns

179

Step Up Autotransformer

Figure 5.13: Step Up transformer

Neglecting the Iron losses and no load current, it can be shown that

180

Reference

1) Theraja A.K and Theraja B.L. (2005). ‗A text book of electrical technology‘, Volume II, S

Chand.

2) Theraja A.K and Theraja B.L.(2004). ‗Electrical Power Transmission and distribution‘,

Volume III, S Chand

3) Theraja A.K and Theraja B.L.(2002). ‗A text book of electrical technology‘, Volume I, S

Chand

4) John B. (2003).‘Electrical circuit theory and technology’, Second Edition, Great Britain.