EXPERIMENTAL STUDY AND COMPARATIVE

ANALYSIS OF TRANSFORMER HARMONIC

BEHAVIOUR UNDER LINEAR AND NONLINEAR

LOAD CONDITIONS

A THESIS SUBMITTED TO THE

GRADUATE SCHOOL OF APPLIED SCIENCES

OF

NEAR EAST UNIVERSITY

By

AHMED AL BARRAWI

In Partial Fulfillment of the Requirements for the Degree of

Master of Science

In

Electrical and Electronic Engineering

NICOSIA 2012

ii

ACKNOWLEDGMENTS

I am indebted to my supervisor Assoc. Prof. Dr. Özgür C. Özerdem for his total support and

belief in me in the course of this work. His humane and kind disposition assisted in no small

measure to the successful completion of this thesis.

I am grateful to Prof. Dr. Senol Bektas and Mr. Samet Biricik for the never failing support,

encouragement and assistance especially with the Latex end of the thesis and would also like to

thank Mr. Mohammed Kmail, Mr. Yousef Kassem who introduced me to the world of soft

computing,

iii

Dedicated to my family who have supported me through it all.

iv

ABSTRACT

This study aims of effecting of harmonic currents on the power losses of three phase transformer.

Harmonics are considered of the most issues of power quality problems due to the spread of

harmonic producing loads and the different effects on the electrical and electronic elements.

Using of non-linear loads in power systems is increasing, and this has become a power quality

problem for both electric companies and customers. Non-linear loads not only increase the

distribution transformer operational costs, it cause which an increase in losses as well also create

additional heating in power system components.

Hence, this study covers the basic losses in transformers mainly due to the non-linear loads,

analysis of the total transformer losses. In conventional loss-analysis, harmonic distortion is not

taken into consideration; even though it is of consequence in applications where high harmonic

power is observed.

The analysis of the transformer losses under linear and non-linear loads is conducted. The results

of experiment were tabulated and discussed.

Keywords: Transformer Losses; Harmonic; Sinusoidal Sources; Nonlinear Load.

v

CONTENTS

ACKNOWLEDGMENTS ii

ABSTRACT iv

CONTENTS V

LIST OF TABLES viii

LIST OF FIGURES ix

LIST OF SYMPOLS xi

USED ABBREVIATIONS xiii

CHAPTER 1 1

INTRODUCTION 1

1.1 Project Objective 2

1.2 Thesis Outline 3

CHAPTER 2 4

Transformers 4

2.1 History 4

2.2 Transformer 5

2.3 Transformer terminology 6

2.4 Transformer cores 7

2.5 Transformer classification 8

2.6 Insulation between windings 9

2.7 Single phase transformer 10

2.8 Three-phase transformer 11

2.8.1 Three Phase Transformers Introduction 11

2.8.2 Three Phase Transformer Construction 11

2.8.3 Delta Connections 12

2.8.4 Wye Connections 13

2.9 Applications and Types of Transformers 14

2.10 Ideal transformer 16

2.11 Autotransformer 17

2.12 Transformer Losses 17

2.13 Transformer losses 18

vi

2.13.1 Transformer Losses And The AC Winding Resistance 18

2.14 The Open-Circuit Test 20

2.15 The Short-circuit Test 22

CHAPTER 3 24

Harmonic 24

3.1 Harmonic history 24

3.2 Total Harmonic Distortion (THD) 25

3.3 Harmonics phenomenon 26

3.4 Effect of power system harmonics on transformers 26

3.5 The efficiency 27

3.6 Power factor 27

3.7 Source of Harmonic 27

3.8 Harmonics from Fast Switching of Power Electronic Devices 28

3.9 Effects of Harmonic Distortion 29

3.10 Effects of Harmonics on Rotating Machines 30

3.11 Effects of Harmonics on Transformers 30

3.12 Harmonic from Conventional Sources 32

3.13 Effects of Harmonics on Lines and Cables 32

3.14 Standards on Harmonic 32

3.15 Harmonic Analysis 33

3.16 Three Phase Non- Linear Load 36

CHAPTER 4 38

SINGLE PHASE TRANSFORMER 38

4.1 EXPERMENT SINGLE PHASE TRANSFORMER 38

4.2 Single Phase Transformer Open and Short Circuit Test Results 38

4.3 Power Analysis under Cases of Linear and Nonlinear Load Conditions 39

Chapter 5 42

EXPERIMENTS AND RESULTS THREE PHASE TRANSFORMER 42

5.1 Equipments 42

5.2 The Y-Y Connection in Three-Phase Systems 42

vii

5.2.1 Advantages of the Y-Y Connection 43

5.3 Identification of Transformer parameters 44

5.3.1 Open circuit 45

5.3.1.1 Primary 45

5.3.1.2 Secondary 45

5.3.2 Short circuit experiment 48

5.3.2.1 Primary 48

5 .3.2.2 Secondary Current 49

5.4 Transformer Data 53

5.5 Experiments Linear Load Condition 54

5.6 Experiments Nonlinear inductive load Condition 58

5.7 Experiments Nonlinear Capacitive Loads Condition 62

5.8 Transformer losses and efficiency (Practical) 66

5.9 Transformer losses and efficiency (Theoretical) 66

5.10 Error between the theoretical and practical values 66

Linear and Nonlinear load Condition, current harmonic 67

5.11 Transformer losses and efficiency using MATLAB 67

5.12 MATLAB/SIMULINK 68

5.13 Linear Load Condition using MATLAB 72

5.14 Nonlinear inductive load Condition using MATLAB 73

5.15 Nonlinear Capacitive Loads Condition using MATLAB 74

CONCLUSIONS 81

REFERENCES 83

viii

LIST OF TABLES

4.12 Open-Circuit single phase transformer 38

4.13 Short-Circuit single phase transformer 38

4.14 Transformer Data single phase transformer 39

4.15 Linear Load Condition (single phase transformer) 39

4.16 Inductive Nonlinear Load Condition (single phase transformer) 40

4.17 Capacitive Nonlinear Load Condition (single phase transformer) 40

5.1 open circuit parameters (Primary) 45

5.2 open circuit parameters (Secondary) 45

5.3 short circuit parameters (Primary) 48

5.4 Transformer Data 54

5.5 Linear Load Condition 57

5.6 Inductive Nonlinear Load Condition 61

5.7 Capacitive Nonlinear Load Condition 65

5.8 Transformer losses and efficiency (Practical) 66

5.9 Transformer losses and efficiency (Theoretical) 66

5.10 Error between the theoretical and practical values 66

5.11 Linear and nonlinear load Condition, current harmonic 67

5.11 Linear Load Condition using MATLAB 67

5.12 Inductive Nonlinear Load Condition using MATLAB 67

5.13 Capacitive Nonlinear Load Condition using MATLAB 68

5.14 Transformer losses and efficiency using MATLAB 68

ix

LIST OF FIGURES

2.1 Faraday's experiment with induction between coils of wire 4

2.2 The elementary transformer 6

2.3 Assembly of transformer-core laminations 7

2.4 Epoxycast step-down transformer Assembly 8

2.5 Eypoxycast high- voltage transformer in a NEMA enclosure 8

2.6 Core and Shell forms with Windings 10

2.7 Simplified Single-Phase Transformer 10

2.8 Wye-Delta connection 12

2.9 Delta-Wye connection 12

2.10 Delta connection 13

2.11 Wye connection 13

2.12 A variable autotransformer 17

2.13 Transformer loss classifications 18

2.14 The approximate equivalent circuit of a two-winding transformer under open-circuit test 21

2.15 Approximated equivalent circuit of the transformer in short circuit case 23

3.1 sine wave 34

3.2 Fundamental with two harmonics 35

3.3 three phase bridge diode rectifier 36

3.4 input line current and voltage wave form 37

4.1 Linear load V, I waveforms and harmonic (single phase transformer) 39

4.2 Inductive Nonlinear Load Condition(single phase transformer) 40

4.3 Capacitive Nonlinear Load Condition (single phase transformer) 41

5.1 Y-Y transformer connections 43

5.2 Y-Y Connection with the primary neutral brought out 43

5.3 Connection for transformer open–circuit test 44

5.4 Connection for transformer short–circuit test 48

5.5 Linear Load Condition 54

5.6 Linear load V, I waveforms and harmonic 55

5.7 Nonlinear inductive load Condition 58

x

5.8 Nonlinear load V, I waveforms and harmonic 59

5.9 Nonlinear load, current harmonic (primary) 59

5.10 Nonlinear load, current harmonic (secondary) 60

5.11 Nonlinear Capacitive load 62

5.12 Nonlinear load V, I waveforms and harmonic 63

5.13 Nonlinear load, current harmonic (primary) 63

5.14 Nonlinear load, current harmonic (secondary) 64

5.15 MATLAB/SIMULINK 69

5.16 linear load current (secondary) 72

5.17 linear load voltage (secondary) 72

5.18 : linear load harmonic (secondary) 72

5.19 Nonlinear load voltage for inductor (secondary) 73

5.20 Nonlinear load current for inductor (secondary) 73

5.21 Nonlinear load harmonic for inductor (secondary) 73

5.22 Nonlinear load voltage for capacitor (primary) 74

5.23 Nonlinear load current for capacitor (primary) 74

5.24 Nonlinear load harmonic for capacitor (primary) 74

5.25 Nonlinear load current for capacitor (secondary) 75

5.26 Nonlinear load voltage for capacitor (secondary) 75

5.27 Nonlinear load harmonic for capacitor (secondary) 75

5.28 Three Phase Bridge Rectifier 77

5.29 Arrangement of Experimental Set-up (three phases) 78

xi

LIST OF SYMBOLS

∅B magnetic flux

∅ Angular frequency

d∅m electromotive force

μ Efficiency of the transformer

ε magnitude of the EMF in volts

η efficiency

a Transformation ratio

f frequency

Ih Magnitude of each harmonic current

Ioc current open circuit

Ip Current on the primary side

IS Current on the secondary side

Isc current short circuit

N number of turns

PdC losses due to load current and dc winding resistance

PEC winding eddy losses

P. F Power factor

PLL load loss

PNL no-load loss

Poc power open circuit

POSL other stray losses in clamps

Psc power short circuit

PSL stray loss

PT total loss

Qoc reactive power open circuit

xii

Rc Iron losses resistance

Rep Equivalent resistance of the primary.

RP Primary winding resistance

RS Secondary winding resistance

SOC apparent power open circuit

SSC apparent power short circuit

Vh Magnitude of each harmonic voltage

Voc voltage open circuit

Vp Primary voltage

VS Secondary voltage

Vsc voltage short circuit

Xep equivalent inductance of the primary

Xm Magnetizing reactance

Zep equivalent impedance of the primary

xiii

USED ABBREVIATIONS

RMS root mean square

SCR silicon controlled rectifiers

EMF electric and magnetic fields

H V high voltage

L V low voltage

P. F Power factor

THD total harmonic distortion

1

CHAPTER 1

INTRODUCTION

Harmonics and distortion in power system current and voltage waveforms have been present for

decades. However, today the number of harmonic producing devices is increasing rapidly. These

loads use diodes, silicon controlled rectifiers (SCR), power transistors, etc. Due to their

tremendous advantages in efficiency and controllability, power electronic loads are nowadays

significant in industrial and domestic applications, and can be found at all power levels, from

low-voltage appliances to high voltage converters. One result of this is a significant increase in

the level of harmonics and distortion in power system networks.

This thesis deals with the effects of power system harmonics on power system transformers. The

main target is transformer units.

The transformer designed to operate at rated frequency has had its loads gradually replaced with

non-linear loads that inject harmonic currents. These harmonic currents will increase losses.

additional heating losses, shorter insulation lifetime, higher temperature and insulation stress,

reduced power factor, lower productivity, efficiency, capacity and lack of system performance.

Such conditions require either transformer de-rating to return to the normal life expectancy or

upgrading with a larger and more economical unit. Therefore the need for investigating the

harmonic problems is obvious.

Examples of linear loads are induction motor, heaters and incandescent lamps. But the rapid

increase in the electronics device technology such as diode, thyristers, etc cause industrial loads

to become non-linear. These components are called solid state electronic or non-linear loads.

Harmonic distortion is a form of pollution in the electric system that can cause problems if the

sum of the harmonic currents increases above certain limits. All power electronic converters used

in different types of electronic systems can increase harmonic disturbances by injecting harmonic

currents directly into the grid. A non-linear load is created when the load current is not

proportional to the instantaneous voltage. Non-linear currents are non sinusoidal, even when the

source voltage is a clean sine wave. The principle is that the harmonic components are added to

the fundamental current [1].

2

Increases in harmonic distortion component of a transformer will result in additional heating

losses, shorter insulation lifetime, higher temperature and insulation stress, reduced power factor,

lower productivity, efficiency, capacity and lack of system performance of the plant [2]

The percentage of total harmonic distortion (%THD) can be defined in two different ways, as a

percentage of the fundamental component (the IEEE definition of THD) or as a percentage of the

RMS (used by the Canadian Standards Association and the IEC) [3]

There are three effects that result in increased transformer heating when the load current includes

harmonic components.

1. RMS current: If the transformer is sized only for the KVA requirements of the load, harmonic

currents may result in the transformer RMS current being higher than its capacity.

2. Eddy-current losses: These are induced currents in a transformer caused by the magnetic

fluxes.

3. Core losses: The increase in nonlinear core losses in the presence of harmonics will be

dependent under the effect of the harmonics on the applied voltage and design of the transformer

core [4].

The same project was held as a research for the case of single phase transformer with linear and

non-linear loads by Assoc. Prof. Dr. Özgür Cemal Özerdem and Mr. Samet Biricik in 11 May

2011 [24].

1.1 Project Objective

The objective of this thesis is to obtain an analysis of the power transformer harmonics in the

case of the use of linear and non-linear loads, and the analysis of the losses of the power

transformers under these conditions of linear and non-linear loads.

The methodology used in the research base on analysis and experimentation approach. The

important aspects in the study of harmonic minimization for three phase three wires power

system distribution are given

3

1.2 Thesis Outline

Chapter 2 covers a literature review of transformers. The main topics discussed here are

transformer types, transformer connection, isolation of transformers, identifying transformer

parameters.

Chapter 3 provides a quantitative discussion of harmonics. Definition of harmonics, Sources of

harmonics, and effects of harmonics on the different power and communication systems.

Chapters 4 and 5 present the experiment results in the case of linear and non-linear loads. In the

first case resistive and inductive loads were used. While in the case of non-linear load a three

phase bridge rectifier with inductive and capacitive loads were used. The results of the

experiment were tabulated and discussed in this chapter. A comparison between the obtained

results in our work and those published in [24] which were obtained by Assoc. Prof. Dr. Özgür

Cemal Özerdem and Mr. Samet Biricik in 11 May 2011

4

CHAPTER 2

TRANSFORMERS

2.1 History

The phenomenon of electromagnetic induction was discovered independently by Michael Faraday and

Joseph Henry in 1831. However, Faraday was the first to publish the results of his experiments and thus

receive credit for the discovery.[5] The relationship between electromotive force (EMF) or "voltage" and

magnetic flux was formalized in an equation now referred to as "Faraday's law of induction":

ε = d∅B

dt 2.1

Where ε is the magnitude of the EMF in volts and ∅B is the magnetic flux through the circuit (in

Weber’s) [6].

Faraday performed the first experiments on induction between coils of wire, including winding a

pair of coils around an iron ring, thus creating the first steroidal closed-core transformer. [7]

Figure 2.1 Faraday's experiment with induction between coils of wire. [8]

5

2.2 Transformer

A transformer is a static device that transfers electrical energy from one circuit to another by

electromagnetic induction without the change in frequency. The transformer, which can link

circuits with different voltages, has been instrumental in enabling universal use of the alternating

current system for transmission and distribution of electrical energy. Various components of

power system, generators, transmission lines, distribution networks, and finally the loads can be

operated at their most suited voltage levels. As the transmission voltages are increased to higher

levels in some part of the power system, transformers again play a key role in interconnection of

systems at different voltage levels. Transformers occupy prominent positions in the power

system, being the vital links between generating stations and points of utilization.

The transformer is an electromagnetic conversion device in which electrical energy received by

primary winding is first converted into magnetic energy which is reconverted back into a useful

electrical energy in other circuits (secondary winding, tertiary winding, etc.). Thus, the primary

and secondary windings are not connected electrically, but coupled magnetically. A transformer

is termed as either a step-up or step-down transformer depending upon whether the secondary

voltage is higher or lower than the primary voltage, respectively. Transformers can be used to

either step-up or step-down voltage depending upon the need and application; hence their

windings are referred as high-voltage/low-voltage or high-tension/low-tension windings in place

of primary/secondary windings. [9] [10]

Voltage transformer consists essentially of three parts: the primary coil which carries the

alternating current from the supply lines, the core of magnetic material in which is produced an

alternating magnetic flux, and the secondary coil in which is generated an electromotive force

(emf) by the change of magnetism in the core which it surrounds. Sometimes the transformer

may have only one winding, which will serve the dual purpose of primary and secondary coils

[11].

The high-tension winding is composed of many turns of relatively fine copper wire, well

insulated to withstand the voltage impressed on it. The low-tension winding is composed of

relatively few turns of heavy copper wire capable of carrying considerable current at a low

voltage.

6

2.3 Transformer terminology

The primary winding is the winding of the transformer which is connected to the source of

power. It may be either the high- or the low voltage winding, depending upon the application of

the transformer.

Figure 2.2 The elementary transformer [11]

The secondary winding is the winding of the transformer which delivers power to the load. It

may be either the high- or the low-voltage winding, depending upon the application of the

transformer.

The core is the magnetic circuit upon which the windings are wound. The high-tension winding

is the one which is rated for the higher voltage. The low-tension winding is the one which is

rated for the lower voltage.

There are three types of transformers depending on the relation between primary and secondary

voltages: the step-up transformer is a voltage transformer so connected that the delivered voltage

is greater than the supplied voltage. The step-down transformer is one so connected that the

delivered voltage is less than that supplied; the actual transformer may be the same in one case as

in the other, the terms step up and step-down relating merely to the application of the apparatus.

The safety transformer is a transformer where the delivered voltage is equal to the absorbed

voltage. This transformer is used to insulate the primary side from the secondary side for safety

purposes.

7

2.4 Transformer cores

Until recently, all transformer cores were made up of stacks of sheet-steel punching firmly

clamped together. One method of assembly and clamping of the sheets is shown in Fig. 2.3.

Sometimes the laminations are coated with a thin varnish to reduce eddy-current losses. When

the laminations are not coated with varnish, a sheet of insulating paper is inserted between

laminations at regular intervals.

A new type of core construction consists of a continuous strip of silicon steel which is

wound in a tight spiral around the insulated coils and firmly held by spot welding at the end.

This type of construction reduces the cost of manufacture and reduces the power loss in the core

due to eddy currents. [11]

Figure 2.3 Assembly of transformer-core laminations.[11]

8

.

2.5 Transformer classification:

Transformers are classified according to many aspects, the type of insulation, the cooling

method, the number of phases, the method of mounting, purpose and service. We can distinguish

the next classifications:

1. According to method of cooling

a. Self air cooled (dry type)

b. Air-blast–cooled (dry type)

c. Liquid-immersed, self-cooled

d. Oil-immersed, combination self-cooled and air-blast

e. Oil-immersed, water-cooled

f. Oil-immersed, forced-oil–cooled

g. Oil-immersed, combination self-cooled and water-cooled

2. According to insulation between windings

a. Windings insulated from each other

b. Autotransformers

3. According to number of phases

a. Single-phase.

9

b. Poly-phase.

4. According to method of mounting

a. Pole and platform

b. Subway

c. Vault

d. Special

5. According to purpose

a. Constant-voltage

b. Variable-voltage

c. Current

d. Constant-current

6. According to service

a. Large power

b. Distribution

c. Small power

d. Sign lighting

e. Control and signaling

f. Gaseous-discharge lamp transformers

g. Bell ringing

h. Instrument

i. Constant-current

j. Series transformers for street lighting

2.6 Insulation between windings

The great majority of transformers are constructed with two or more windings which are

electrically insulated from each other. In some cases a single winding is employed, parts of the

winding functioning as both primary and secondary. These transformers are called

autotransformers. They are frequently used when the voltage ratio is small. Autotransformers

10

should never be used for high voltage ratios, as the low-voltage winding is not insulated from the

high-voltage one, so that in case of trouble it would be dangerous to both life and equipment.

2.7 Single phase transformer

There are two basic core designs for single-phase transformer: core form and shell form.

Figure 2.6 Core and Shell forms with Windings [12]

Due to insulation requirements, the low voltage (LV) winding normally appears closest to the

core, while the high voltage (HV) winding appears outside. The windings are usually referred to

as primary and secondary winding(s) as denoted by the P and S.

In the shell form, the flux generated in the core by the windings splits equally in both "legs" of

the core. Winding configurations may vary with core design and include concentric windings,

pancake windings and assemblies on separate legs. A commonly used equivalent circuit for a

single-phase model is shown below:

Figure 2.7 Simplified Single-Phase Transformer [12]

11

This model is sufficient to model the short circuit behavior of a single-phase transformer. It

includes the winding resistance and leakage as well as the core losses so it is widely used for all

core and winding configurations of the single-phase two-winding variety [12]

2.8 Three-phase transformer

2.8.1 Three Phase Transformers Introduction

Three phase transformers are used throughout industry to change values of three phase voltage

and current. Since three phase power is the most common way in which power is produced,

transmitted, and used, an understanding of how three phase transformer connections are made is

essential. In this section it will discuss different types of three phase transformers connections,

and present examples of how values of voltage and current for these connections are computed

2.8.2 Three Phase Transformer Construction

A three phase transformer is constructed by winding three single phase transformers on a single

core. These transformers are put into an enclosure which is then filled with dielectric oil. The

dielectric oil performs several functions. Since it is a dielectric, a nonconductor of electricity, it

provides electrical insulation between the windings and the case. It is also used to help provide

cooling and to prevent the formation of moisture, which can deteriorate the winding insulation.

Three-Phase Transformer Connections:

There are only 4 possible transformer combinations:

1. Delta to Delta - use: industrial applications

2. Delta to Wye - use : most common; commercial and industrial

3. Wye to Delta - use : high voltage transmissions

4. Wye to Wye - use : rare, don't use causes harmonics and balancing problems.

Three-phase transformers are connected in delta or wye configurations. A wye-delta transformer

has its primary winding connected in a wye and its secondary winding connected in a delta (see

12

figure 2.8). A delta-wye transformer has its primary winding connected in delta and its secondary

winding connected in a wye (see figure 2.9).

Figure 2.8 Wye-Delta connections [13]

Figure 2.9 Delta-Wye connections [13]

2.8.3 Delta Connections

A delta system is a good short-distance distribution system. It is used for neighborhood and small

commercial loads close to the supplying substation. Only one voltage is available between any

two wires in a delta system. The delta system can be illustrated by a simple triangle. A wire from

each point of the triangle would represent a three-phase, three-wire delta system. The voltage

would be the same between any two wires (see figure 2.10).

13

Figure 2.10 Delta connection [ 13]

2.8.4 Wye Connections

In a wye system the voltage between any two wires will always give the same amount of voltage

on a three phase system. However, the voltage between any one of the phase conductors (X1,

X2, X3) and the neutral (X0) will be less than the power conductors (see figure 2.11) [12].

Figure 2.11 Wye connections [13]

14

2.9 Applications and Types of Transformers

Before invention of transformers, in initial days of electrical industry, power was distributed as

direct current at low voltage. The voltage drop in lines limited the use of electricity to only urban

areas where consumers were served with distribution circuits of small length. All the electrical

equipment had to be designed for the same voltage. Development of the first transformer around

1885 dramatically changed transmission and distribution systems. The alternating current (AC)

power generated at a low voltage could be stepped up for the transmission purpose to higher

voltage and lower current, reducing voltage drops and transmission losses. Use of transformers

made it possible to transmit the power economically hundreds of kilometers away from the

generating station. Step-down transformers then reduced the voltage at the receiving stations for

distribution of power at various standardized voltage levels for its use by the consumers.

Transformers have made AC systems quite flexible because the various parts and equipment of

the power system can be operated at economical voltage levels by use of transformers with

suitable voltage ratio [11].

Transformers can be classified depending on their application as follow:

a. Generator transformers: generator transformer is one of the most important and critical

components of the power system. Power generated at a generating station (usually at a

voltage in the range of 11 to 25 kV) is stepped up by a generator transformer to a higher

voltage (220, 345, 400 or 765 kV) for transmission.

b. Unit auxiliary transformers: These are step-down transformers with primary connected to

generator output directly. The secondary voltage is of the order of 6.9 kV for supplying to

various auxiliary equipments in the generating station.

c. Station transformers: These transformers are required to supply auxiliary equipment

during setting up of the generating station and subsequently during each start-up

operation. The rating of these transformers is small, and their primary is connected to

high voltage.

d. Interconnecting transformers: These are normally autotransformers used to interconnect

two grids/systems operating at two different system voltages. They are normally located

in the transmission system between the generator transformer and receiving end

transformer.

15

e. Receiving station transformer: These are basically step-down transformers reducing

transmission/sub-transmission voltage to primary feeder level. Some of these may be

directly supplying an industrial plant. Loads on these transformers vary over wider limits,

and their losses are expensive. The farther the location of transformers from the

generating station, the higher the cost of supplying the losses.

f. Distribution transformers: Using distribution transformers, the primary feeder voltage is

reduced to actual utilization voltage (~415 or 460 V) for domestic/industrial use. A great

variety of transformers fall into this category due to many different arrangements and

connections. Load on these transformers varies widely, and they are often overloaded. A

lower value of no-load loss is desirable to improve all-day efficiency. Hence, the no-load

loss is usually capitalized with a high rate at the tendering stage. Since very little

supervision is possible, users expect the least maintenance on these transformers. The

cost of supplying losses and reactive power is highest for these transformers.

g. Phase shifting transformers: These are used to control power flow over transmission lines

by varying the phase angle between input and output voltages of the transformer.

Through a proper tap change, the output voltage can be made to either lead or lag the

input voltage. The amount of phase shift required directly affects the rating and size of

the transformer. Presently, there are two types of design: single-core and two-core design.

Single-core design is used for small phase shifts and lower MVA/voltage ratings. Two-

core design is normally used for bulk power transfer with large ratings of phase shifting

transformers. It consists of two transformers, one associated with the line terminals and

other with the tap changer.

h. Earthing or grounding transformers: These are used to get a neutral point that facilitates

grounding and detection of earth faults in an ungrounded part of a network (e.g., the delta

connected systems). The windings are usually connected in the zigzag manner, which

helps in eliminating third harmonic voltages in the lines. These transformers have the

advantage that they are not affected by a DC magnetization.

i. Transformers for rectifier and inverter circuits: These are otherwise normal transformers

except for the special design and manufacturing features to take into account the

harmonic effects. Due to extra harmonic losses, operating flux density.

16

2.10 Ideal transformer

A transformer works on the principle of electromagnetic induction, according to which a voltage

is induced in a coil if it links a changing flux. a single-phase transformer consisting of two

windings, wound on a magnetic core and linked by a mutual flux Transformer is in no-load

condition with primary connected to a source of sinusoidal voltage of frequency f Hz. Primary

winding draws a small excitation current, i0 (instantaneous value), from the source to set up the

mutual flux in the core. All the flux is assumed to be contained in the core (no leakage). The

windings 1 and 2 have N1 and N2 turns respectively. The instantaneous value of induced

electromotive force in the winding 1 due to the mutual flux is:

e1 = N1

d∅m

dt 2.2

Equation 2.2 is as per the circuit viewpoint; there is flux viewpoint also, in which induced

voltage (counter electromotive force) is represented as:

e2 = N2

d∅m

dt 2.3

If the winding is assumed to have zero winding resistance,

𝑉1=𝑒1

Since 𝑉1 (instantaneous value of the applied voltage) is sinusoidal varying, the flux must also be

sinusoidal in nature varying with frequency f.

17

2.11 Autotransformer

Figure 2.12 A variable autotransformer [14]

In an autotransformer portions of the same winding act as both the primary and secondary. The

winding has at least three taps where electrical connections are made. An autotransformer can be

smaller, lighter and cheaper than a standard dual-winding transformer however the

autotransformer does not provide electrical isolation.

Autotransformers are often used to step up or down between voltages in the 110-117-120 volt

range and voltages in the 220-230-240 volt range, e.g., to output either 110 or 120V (with taps)

from 230V input, allowing equipment from a 100 or 120V region to be used in a 230V region.

A variable autotransformer is made by exposing part of the winding coils and making the

secondary connection through a sliding brush, giving a variable turns ratio. [15]Such a device is

often referred to by the trademark name variac.

2.12 Transformer Losses

Stray losses can be particularly high in power transformers with large ratings. Transformer

designers today are challenged by high loss evaluation, high reliability requirements, and low

cost and weight requirements, for which they need advanced techniques and tools that lead to

optimum design and product performance improvements. Among the most important of these

calculations and techniques are those for winding eddy losses, stray losses in other structural

18

parts and, in general, potential regions of excessive heating. All of these can be determined by

the strength of the electromagnetic leakage field of the transformer winding. This chapter

reviews transformer losses. It also presents transformer winding eddy current losses from the

point of view of their estimation. Such information is important for winding hot spot calculation.

2.13 Transformer losses

Transformer losses are generally classified into no load or core losses and load losses

as shown in Fig 2.13.

Figure 2.13 Transformer loss classifications [8]

2.13.1 Transformer Losses and the AC Winding Resistance

In ANSI/IEEE C57.110-1986 [16], transformer losses are categorized as: no-load loss (excitation

loss); load loss (impedance loss); and total loss (the sum of no-load loss and load loss). Load loss

is subdivided into 𝐼2𝑅 loss and “stray loss.” [15].

𝑃𝑡𝑜𝑡𝑎𝑙 = 𝑃𝑛𝑜 𝑙𝑜𝑎𝑑 + 𝑃𝑙𝑜𝑎𝑑 2.4

𝑃𝑡𝑜𝑡𝑎𝑙 =𝑃𝑛𝑜 𝑙𝑜𝑎𝑑 + (𝐼2𝑅 + 𝑃𝑠𝑡𝑎𝑟𝑦 ) 2.5

Where 𝑃𝑡𝑜𝑡𝑎𝑙 is the total loss,𝑃𝑛𝑜−𝑙𝑜𝑎𝑑 is the no-load loss, 𝑃𝑙𝑜𝑎𝑑 is the load loss and the

𝑃𝑠𝑡𝑎𝑟𝑦 is the stray loss.

19

“Stray Loss” is the loss caused by stray electromagnetic flux in the windings, core, core clamps,

magnetic shields, enclosure or tank walls, etc. Thus, the stray loss can be subdivided into

winding stray loss and stray loss in components other than the windings (POSL).

This can be expressed in equation form:

𝑃𝑇 = 𝑃𝑁𝐿 + 𝑃𝐿𝐿 𝑊 2.6

Where

𝑃𝑁𝐿 are the no load losses

𝑃𝐿𝐿 are the load losses.

𝑃𝑇 are the total losses.

𝑃𝑁𝐿 are the losses due to the voltage excitation of the core. 𝑃𝐿𝐿 is, in accordance with convention,

subdivided into 𝑃𝑑𝐶 losses ( 𝐼2 𝑅𝑑𝑐 ) and stray losses caused by electromagnetic fields in the

windings, core clamps, magnetic shields, enclosure or tank walls, etc. 𝑃𝑑𝐶 is calculated by

measuring the dc resistance of the winding and multiplying it by the square of the load current.

The stray losses can be further divided into winding eddy losses and structural part stray losses.

Winding eddy losses consist of eddy current losses and circulating current losses, which are all

considered to be winding eddy current losses. Other stray losses are due to losses in structures

other than windings, such as clamps, tank or enclosure walls, etc.; this can be expressed as:

𝑃𝐿𝐿 = 𝑃𝑑𝐶 + 𝑃𝐸𝐶 + 𝑃𝑂𝑆𝐿 𝑊 2.7

Where

𝑃𝑑𝐶 are the losses due to load current and dc winding resistance

𝑃𝐸𝐶 are the winding eddy losses.

𝑃𝑂𝑆𝐿 are other stray losses in clamps, tanks, etc

The total stray losses 𝑃𝐶𝐿 are determined by subtracting 𝑃𝑑𝐶 from the load losses measured

during the impedance test, i.e.:

20

𝑃𝑆𝐿 = 𝑃𝐸𝐶 + 𝑃𝐸𝐶 + 𝑃𝑂𝑆𝐿 = 𝑃𝐿𝐿 − 𝑃𝑑𝐶 𝑊 2.8

There is no test method to distinguish the winding eddy losses from the stray losses that occur in

structural parts.

2.14 The Open-Circuit Test

As the name implies, one winding of the transformer is left open while the other is excited by

applying the rated voltage. The frequency of the applied voltage must be the rated frequency of

the transformer. Although it does not matter which side of the transformer is excited, it is safer to

conduct the test on the low-voltage side. Another justification for performing the test on the low-

voltage side is the availability of the low-voltage source in any test facility. If we assume that the

power loss under no load in the low-voltage winding is negligible, then the corresponding

approximate equivalent circuit as viewed from the low-voltage side is given in Figure 2.14. From

the approximate equivalent of the transformer as referred to the low-voltage side (Figure 2.14), it

is evident that the source supplies the excitation current under no load. One component of the

excitation current is responsible for the core loss, whereas the other is responsible to establish the

required flux in the magnetic core. In order to measure these values exactly, the source voltage

must be adjusted carefully to its rated value. Since the only power loss in Figure 2.14 is the core

loss, the wattmeter measures the core loss in the transformer.

The core-loss component of the excitation current is in phase with the applied voltage while the

magnetizing current lags the applied voltage by 90 degree. If 𝑉𝑂𝐶is the rated voltage applied on

the low-voltage side, I𝑂𝐶 is the excitation current as measured by the ammeter, and 𝑃𝑂𝐶 is the

power recorded by the wattmeter, then the apparent power at no-load is at a lagging power-factor

angle of

21

+

-

Figure 2.14 The approximate equivalent circuit of a two-winding transformer under open-circuit

test. [10]

𝑆𝑂𝑐 = 𝑉𝑂𝑐𝐼𝑂𝑐 2.9

∅𝑂𝑐 = cos−1 𝑃𝑂𝑐

𝑆𝑂𝑐 2.10

The core-loss and magnetizing currents are

𝐼𝑐 = 𝐼𝑂𝑐 cos ∅𝑂𝑐 2.11

and

𝐼𝑐 = 𝐼𝑂𝑐 sin ∅𝑂𝑐 2.12

Thus, the core-loss resistance and the magnetizing reactance as viewed from the low-voltage side

are

𝑅𝑐 =𝑉𝑂𝑐

𝐼𝑐=

𝑉𝑂𝐶2

𝑃𝑂𝑐 2.13

And

𝑋𝑚 =𝑉𝑂𝑐

𝐼𝑚=

𝑉𝑂𝐶2

𝑄𝑂𝑐 2.14

Where

𝑄𝑂𝑐 = 𝑆𝑂𝐶2 − 𝑃𝑂𝐶

2 2.15

22

2.15 The Short-circuit Test

This test is designed to determine the winding resistances and leakage reactances. The short-

circuit test is conducted by placing a short circuit across one winding and exciting the other from

an alternating-voltage source of the frequency at which the transformer is rated. The applied

voltage is carefully adjusted so that each winding carries a rated current. The rated current in

each winding ensures a proper simulation of the leakage flux pattern associated with that

winding. Since the short circuit constrains the power output to be zero, the power input to the

transformer is low. The low power input at the rated current implies that the applied voltage is a

small fraction of the rated voltage. Therefore, extreme care must be exercised in performing this

test. Once again, it does not really matter on which side this test is performed.

However, the measurement of the rated current suggests that, for safety purposes, the test be

performed on the high-voltage side.

Since the applied voltage is a small fraction of the rated voltage, both the core loss and the

magnetizing currents are so small that they can be neglected. In other words, the core loss is

practically zero and the magnetizing reactance is almost infinite. The approximate equivalent

circuit of the transformer as viewed from the high-voltage side is given in Figure 2.15. In this

case, the wattmeter records the copper loss at full load.

If 𝑉𝑆𝐶 , 𝐼𝑆𝐶and 𝑝𝑠𝑐are the readings on the voltmeter, ammeter, and wattmeter,

Then

𝑅𝑒𝑝 =𝑃𝑆𝑐

𝐼𝑆𝐶2 2.16

Is the total resistance of the two windings as referred to the high-voltage side. The magnitude of

the impedance as referred to the high-voltage side is

𝑍𝑒𝑝 =𝑉𝑆𝑐

𝐼𝑆𝑐 2.17

Therefore, the total leakage reactance of the two windings as referred to the high voltage side is

23

𝑋𝑒𝑝 = 𝑍𝑒𝐻2 − 𝑅𝑒𝐻

2 2.18

If we define the a-ratio as

𝑎 =𝑁𝑠

𝑁𝑝 2.19

Figure 2.15 Approximated equivalent circuit of the transformer in short circuit case [12]

Where 𝑅𝑝 is the resistance of the high-voltage winding, 𝑅𝑠 is the resistance of the low-voltage

winding, , 𝑋𝑝 is the leakage reactance of the high-voltage winding, and , 𝑋𝑠 is the leakage

reactance of the low-voltage winding.

If the transformer is available, we can measure, 𝑅𝑝 and, 𝑅𝑠and verify Eq. 2.18

However, there is no simple way to separate the two leakage reactances. The same is also true

for the winding resistances if the transformer is unavailable. If we have to segregate the

resistances, we will assume that the transformer has been designed in such a way that the power

loss on the high-voltage side is equal to the power loss on the low-voltage side. This is called the

optimum design criterion and under this criterion [12].

𝐼𝑝2𝑅𝑝 = 𝐼𝑠

2𝑅𝑠 2.20

Which yields?

𝑅𝑝 = 𝑎2𝑅𝑠 = 0.5𝑅𝑒𝑝 2.21

Similarly, we can assume that

𝑋p = 𝑎2𝑋𝑠 = 0.5𝑋𝑒𝑝 2.22

24

CHAPTER 3

HARMONIC

3.1 Harmonic history

Before the twentieth century, the predominant use of electricity for business and industry was

power motors, lights and heating devices. These uses have little effect on the fundamental

frequency. They are called linear loads, because the current rises and falls in proportion to the

voltage wave.

In recent years, few industries use devices such as rectifiers or converters, power supplies and

other devices to improve product quality [16]. All of these make the current sinusoidal waveform

distorted, because the current flow is not directly proportional to the voltage. These loads are

called non-linear loads. Non-linear loads cause waveforms that are multiples of the fundamental

frequency sine wave to be superimposed on the base waveform. These multiples are called

harmonics, like the frequency of the second harmonic is two times the fundamental; the third

harmonic is three times the fundamental. The combination of the sine wave with all the

harmonics creates a new non sinusoidal wave of entirely different shape is called harmonic

distortion [16].

Ideally, all power utilities should provide their customers with a quality supply which has

constant magnitude and frequency of sinusoidal voltage. Unfortunately, it is a hard task to

maintain this quality supply for constant magnitude and frequency of sinusoidal voltage. In

reality the supply waveforms always get distorted resulting in supply or not purely sine wave due

to nonlinear load [17].

Harmonics are usually defined as sinusoids of any frequency other than the AC power system

fundamental frequency. There are two types of harmonics that can be encountered in a power

system [IEEE Std. 100-1988].

i. Synchronous harmonics

ii. Asynchronous harmonics

25

Synchronous harmonics are sinusoids with frequencies which are multiples of the fundamental

frequency. The multiplication factor is often referred to as the harmonic number. The

synchronous harmonics can be subdivided into two categories.

i. Sub-harmonic when the harmonic number is less than one

ii. Super-harmonic when the harmonic number is greater than one

For example, the line current contains both sub-harmonic and super-harmonic such as

cycloconverters and line commutated three phase thyristor based rectifiers. These waveforms are

considered as distortion [16]

Asynchronous harmonics are those sinusoids which do not maintain a frequency relationship

with the fundamental frequency sinusoid. These sinusoids never exhibit a constant harmonic

number and similarly do not maintain a stationary phase relationship with the fundamental

frequency sinusoid.

3.2 Total Harmonic Distortion (THD)

The total harmonic distortion of a signal is a measurement of the harmonic distortion present. It

is defined as the ratio of the sum of the powers of all harmonic components to the power of the

fundamental frequency. Harmonic distortion is caused by the introduction of waveforms at

frequencies in multiplies of the fundamental. THD is a measurement of the sum value of the

waveform that is distorted.

%𝑇𝐻𝐷 = 𝑥𝑖

2∞𝑖=2

𝑋1 ( .1) 3.1

The THD is a very useful quantity for many applications. It is the most commonly used

harmonic index. However, it has the limitation that, it is not a good indicator of voltage stress

within a capacitor because that is related to the peak value of voltage waveform. Electric motors

are the most popular loads which are situated between these two categories.

26

3.3 Harmonics phenomenon

The presence of harmonics phenomenon was characterized in beginning of 1800th by a famous

mathematician Jean Baptiste Joseph Fourier. Harmonics are multiples of the fundamental

frequency which is 50Hz for European and many Asian countries and 60Hz in for instance USA,

Canada and other neighboring countries. Harmonics occur mainly due to loads with non-linear

characteristics. This results in distorting the applied line current or voltage of the system. The

higher order harmonics can be filtered out; the lower order harmonic are usually present and

these harmonics have a notable impact on transformers especially when the transformers are

under load condition. The total harmonic content THD ( Total Harmonic Distortion), of the

current or voltage can be calculated as can be seen from eq3.2 and 3.3

%THDV = 𝑉𝑛 2∞

ℎ=2

𝑉1 3.2

%THDI = 𝐼𝑛 2∞

ℎ=2

𝐼1 3.3

Where, 𝑉𝑛 represents the voltage harmonics and 𝐼𝑛 the current harmonic contents of the system.

According to Swedish Standard EN 50160 [19]. The total harmonic distortion should be

maximum 8%, which must be said to be a very high value.

3.4 Effect of power system harmonics on transformers

Transformer losses are classified into load and no-load losses. No-load losses are those losses in

a transformer whenever the transformer is energized. No-load losses include, eddy current losses,

magnetic hysteresis, winding resistance to exciting current, and the losses of dielectric materials.

Load losses are those losses that exist with the loading of transformers. Load losses vary with the

square of the load current and the dc resistance in the windings (𝐼2𝑅 losses), core clamps, the

loss due to leakage fluxes in the windings, parallel winding strands and other parts. For

distribution transformers, the major source of load losses is the 𝐼2𝑅 losses in the windings.[19]

27

3.5 The efficiency:

)( )(

2

2

1

2

cui PlossescupperPlossesironP

P

P

P

PowerInput

powerOutput

3.4

3.6 Power factor

For a sinusoidal signal, the power factor is given by the ratio between the active and the apparent

power. Electrical equipments, parameters are normally given under nominal voltage and current.

A low power factor can indicate bad use of these equipments.

𝑃. 𝐹 =𝑃

𝑆=

𝑃

𝑃2+𝑄2 ( .2) 3.5

Where, Q is the reactive power.

In the case where there is harmonics, a supplementary power called the deformed power D

appears. This power can be given by the relation

D = 𝑆2 + 𝑃2 + 𝑄2 3.6

3.7 Source of Harmonic

The main source of the harmonics is any non-linear loads that produce the voltage harmonics and

current harmonics. This occurs because the resistance of the device is not a constant. The

resistance in fact, changes during each sine wave. So, non linear device is one in which the

current is not proportional to the applied voltage.

Some examples of common sources of power distribution system harmonics cause serious

problems are:

1. Fluorescent lighting

2. Computer switch mode power supplies

3. Static VAR compensators

28

4. Variable frequency motor drives (VFD)

5. DC-DC converters

6. Inverters

7. Television power supplies

3.8 Harmonics from Fast Switching of Power Electronic Devices

Nowadays, due to the applications advanced technologies in industrial sectors such as power

semiconductor systems which are designed using phase controlled or uncontrolled rectifiers,

inverters, AC voltage controllers, cycloconverter and converters

In single phase full wave controlled rectifiers the harmonic generated are more significant at

lower frequency compared with higher frequency. Meanwhile, the three phase controlled

rectifiers is used for high power with large Mega Volt Ampere (MVA) rating it produces large

harmonics currents on 3rd, 5th, 7th, 9th, 11th, 13th, 15th, 17th and 19th harmonics. Others

applications of thyristor controlled rectifiers such as [17]:

i. To control the acceleration and deceleration of electric engine can cause current

distortion including order 3rd, 5th and 7th harmonic currents is directly injected into

utility.

ii. To control the speed of portable hand tool driver. The 3rd harmonics is dominant

harmonic which contributed to the power distribution systems

iii. To establish a voltage level in providing the gate current to turn on and off the thyristor

for home and industry applications such as light dimmer and induction motor. The 3rd

harmonics is dominant harmonic into power distribution system

iv. To control mine winders, draglines, electrical shoves, electrochemical and metallurgical

plants. It founds that the almost harmonic current is 5th, 7th and 11th harmonics. It’s rare

to find the 3rd, 9th, or 15th harmonics.

v. To control variable speed motor drives. Effects from this phenomenon will be served the

main contributor harmonic distortion in supply system is 3rd, 5th and 7th harmonic

currents

29

vi. To vary the AC voltage controller for lighting control, variable transformer by using taps

changing, heather, industrial heating and induction motor. By controlling the phase delay

of the thyristor the load currents are varied within desired limits. This result will effect in

distorted input current and simultaneously significant harmonic current such as 3rd, 5th,

7th, 9th and 11th is generated and injected into the supply system.

3.9 Effects of Harmonic Distortion

The effect of current distortion on power distribution systems can be serious, primarily because

of the increased current flowing in the system. In other words, because the harmonic current

doesn't deliver any power, its presence simply uses up system capacity and reduces the number

of loads that can be powered. Harmonic current occur in a facility’s electrical system can cause

equipment malfunction, data distortion, transformer and motor insulation failure, overheating of

neutral buses, tripping of circuit breakers, and solid-state component breakdown [3], high current

in neutral conductor and distorted voltage waveform. Capacitors are sensitive to harmonic

voltage while transformers are sensitive to current harmonics. There are many researches which

study the effect of harmonics which affects both utility and consumers. Greater concerns have

been expressed by industries which have equipment or processes that are sensitive to distortion

on the supply voltage which affect their plant operation and productivity. Resonance is another

problem related to harmonics. It occurs when harmonic current produced by non-linear load

interacts with system impedance to produce high harmonic voltage. Two types of resonance can

occur in the system, either series resonance or parallel resonance, depending on the structure of

the network. This problem is most common in industrial plant due to the interaction of series of

power factor correction capacitors and transformer’s inductance. All tripled harmonics (odd

multiples of three i.e. 3, 9, 15 …) is zero sequence and cannot flow in a balanced three-wire

systems or loads.

Therefore, the delta-wye-grounded transformer at the entrance of industrial plant can block the

triple harmonic from entering utility distribution system [20].

30

Harmonic currents also increase heat losses in transformers and wiring. Since transformer

impedance is frequency dependent, increasing with harmonic number, the impedance at the 5th

harmonic is five times that of the fundamental frequency. So each ampere of 5th harmonic

current causes five times as much heating as an ampere of fundamental current. More

specifically, the effects of the harmonics can be observed in many sections of electrical

equipment and a lot machines and motors. These effects can be described in more details as

follows [16].

3.10 Effects of Harmonics on Rotating Machines

For both the synchronous and the induction machines, the main problems of the harmonics are

increasing on the iron and copper losses, and heating by result of the high current caused by

harmonics as a result reducing the efficiency. The harmonics can be a one reason as an

introduction of oscillating motor torque. Also, the high current can cause high noise level in

these machines.

3.11 Effects of Harmonics on Transformers

Transformers are designed to deliver the required power to the connected loads with minimum

losses at fundamental frequency. Harmonic distortion of the current, in particular, as well as the

voltage will contribute significantly to additional heating. There are three effects that result in

increased transformer heating when the load current includes harmonic components:

1. RMS current. If the transformer is sized only for the KVA requirements of the load,

harmonic currents may result in the transformer RMS current being higher than its

capacity. The increased total RMS current results increase conductor losses.

The %THD is a ratio of the root-mean-square (RMS) value of the harmonic current to the RMS

value of the fundamental.

%THD = 𝐼ℎ 2∞

ℎ=1

𝐼1 3.7

31

It is a measure of the additional harmonic current contribution to the total RMS current.

Both of the above methods are limited because frequency characteristics of the transformer are

not considered

2. Eddy-current losses. These are induced currents in the transformer caused by the

magnetic fluxes. These induced currents flow in the windings, in the core, and in the

other connecting bodies subjected to the magnetic field of the transformer and cause

additional heating. This component of the transformer losses increases with the square of

the frequency of the current causing the eddy current. Therefore, this becomes a very

important component of transformer losses for harmonic heating.

3. Core losses. The increase in core losses in the presence of the harmonics will be

dependent on the effect of the harmonics on the applied voltage and the design of the

transformer core. Increasing the voltage distortion may increase the eddy currents in the

core laminations. The net impact that this will have depends on the thickness of the core

laminations and the quality of the core steel. The increase in these losses due to

harmonics is generally not as critical as the previous two.

3.12 Harmonic from Conventional Sources

Over the past decade, some electric power facility such as electrical rotating machine,

transformer and reactor will be injected harmonic current into power distribution system. Effect

from this the electric current drawn by these devices is non sinusoidal which contain a lot of

harmonics. Therefore, this harmonics current can produce problems such as vibration and

overheated to that device respectively

3.13 Effects of Harmonics on Lines and Cables

The main problems associated with harmonics are: increased losses and heating, serious damages

in the dielectric for capacitor banks and cables, appearance of the corona (the amount of the

32

ionization of the air around the conductor or the transmission line) due to higher peak voltages

and corrosion in aluminum cables due to DC current.

3.14 Standards on Harmonic

Institute of Electrical and Electronics Engineers (IEEE) has come out with standards and

guidelines regarding harmonics. One of the standards, IEEE

Standard 519-1992, provides comprehensive recommended guidelines on investigation,

assessment and measurement of harmonics in power system.

The standard includes steady state limits on current harmonic and harmonic voltages at all

system voltage levels. The limit was set for a steady state operation and for worst case scenario.

Another international standards and conformity assessment body,

International Electro technical Commission (IEC), produced a standard, IEC 61000-3-6, which

also provides guide lines to address harmonics issue with sets of steady state limits. Both

standards are in common where the limits were derived based on a basic principle of insuring

voltage quality and shared responsibility between utility and customer. Both lay the

responsibility on consumer to limit the penetration of current harmonic into power system while

utility company is responsible to limit harmonic voltage at point of common coupling (PCC).

According to IEEE definition, point of common coupling is a point anywhere in the entire

system where utility and consumer can have access for direct measurement and the indices is

meaningful to both.

Example of steady state harmonic voltage limit from IEEE Std. 519-1992 at PCC for medium

voltage level (< 69 kV) is 5% THD and 3% individual voltage distortion. In reality, harmonic is

time-variant and it changes over time due to several factors. Both standards recognize this

condition and allow the limits to be exceeded for short duration. IEC has provided a set of time-

varying limits based on percentile over a period of time i.e. 95th and 99th for very short time (3

second) and short time (10 minute) aggregate measurements.[20]

33

3.15 Harmonic Analysis

Harmonics current are created by non-linear loads that generate non-sinusoidal current on

distribution power system. However, because of the increased popularity of electronic and other

non-linear loads, the current waveform quite often became distorted. To understand the distortion

phenomena, it is necessary to analyze the distorted waveform by a process called harmonic

analysis. It allows us to express the distorted waveform as a sum of dc component, fundamental

sine wave of the distorted waveform and a series of pure sine waves.

These sine waves have different magnitudes and their frequencies are integer multiple of the

fundamental distorted waveform. In this chapter provides a quantities discussion of harmonics

analysis. Distorted waveform, effective value, Total Harmonics Distortion (THD), effect of

harmonic for power and power factor are analyzed and presented using Fourier series.

Characteristic of symmetrical component and their relation with sequence of harmonic on three

phase distribution system

Harmonics are usually defined as periodic steady state distortions of voltage and current

waveforms in power system. The purpose of this chapter is to present basic harmonic theory.

Initially, the Fourier Series and analysis method that can be used to interpret waveform

phenomenon are reviewed. The general harmonics theory, the definitions of harmonic quantities,

harmonic indices in common use, and power system response are then described [16].

The typical definition for a harmonic is “a sinusoidal component of a periodic wave or quantity

having a frequency that is an integral multiple of the fundamental frequency” [21]. Some

references refer to “clean” or “pure” power as those without any harmonics.

But such clean waveforms typically only exist in a laboratory. Harmonics have been around for a

long time and will continue to do so. In fact, musicians have been aware of such since the

invention of the first string or woodwind instrument. Harmonics (called “overtones” in music)

are responsible for what makes a trumpet sound like a trumpet, and a clarinet like a clarinet.

Electrical generators try to produce electric power where the voltage waveform has only one

frequency associated with it, the fundamental frequency. In the North America, this frequency is

60 Hz, or cycles per second. In European countries and other parts of the world, this frequency is

usually 50 Hz. Aircraft often uses 400 Hz as the fundamental frequency. At 60 Hz, this means

34

that sixty times a second, the voltage waveform increases to a maximum positive value, then

decreases to zero, further decreasing to a maximum negative value, and then back to zero.

The rate at which these changes occur is the trigonometric function called a sine wave, as shown

in figure 1. This function occurs in many natural phenomena, such as the speed of a pendulum as

it swings back and forth, or the way a string on a violin vibrates when plucked.

Figure 3.1: sine wave [21]

The frequencies of the harmonics are different, depending on the fundamental frequency. For

example, the 2nd harmonic on a 60 Hz system is 2*60 or 120 Hz. At 50Hz, the second harmonic

is 2* 50 or 100Hz. 300Hz is the 5th harmonic in a 60 Hz system or the 6th harmonic in a 50 Hz

system.

Figure 3.2 shows how a signal with two harmonics would appear on an oscilloscope-type

Display, which some power quality analyzers provide.

35

Figure 3.2 Fundamental with two harmonics [23]

In order to be able to analyze complex signals that have many different frequencies present, a

number of mathematical methods were developed. One of the more popular is called the Fourier

Transform. However, duplicating the mathematical steps required in a microprocessor or

computer-based instrument is quite difficult. So more compatible processes, called the FFT for

Fast Fourier Transform, or DFT for Discrete

Fourier Transform, are used. These methods only work properly if the signal is composed of

only the fundamental and harmonic frequencies in a certain frequency range (called the Nyquist

frequency, which is one-half of the sampling frequency). The frequency values must not change

during the measurement period. Failure of these rules to be maintained can result in mis-

information.

For example, if a voltage waveform is comprised of 60 Hz and 200 Hz signals, the FFT cannot

directly see the 200 Hz. It only knows 60, 120, 180, and 240, which are often called “bins”. The

result would be that the energy of the 200 Hz signal would appear partially in the 180Hz bin, and

partially in the 240 Hz bin. An FFT-based processer could show a voltage value of 115V at 60

Hz, 18 V at the 3rd harmonic, and 12 V at the

4th harmonic, when it really should have been 30 V at 200 Hz.

36

These in-between frequencies are called “interharmonics”. There is also a special category of

interharmonics, which are frequency values less than the fundamental frequency value, called

sub-harmonics. For example, the process of melting metal in an electric arc furnace can result

large currents that are comprised of the fundamental,

interharmonic, and subharmonic frequencies being drawn from the electric power grid.

These levels can be quite high during the melt-down phase, and usually affect the voltage

waveform. [22].

3.16 Three Phase Non- Linear Load

In fact, the non linear load is the source of the harmonic. A three phase electrical power system

distribution has high capacity non-linear load such as converter for electric motor control use to

power drive in industries, factories, power supply and direct current transmission system. In

general, this nonlinear load base on three phase bridge diode rectifier, also known as the six

pulse bridge because it is six pulses per cycle on the DC output. It is shown in Figure (3.3).

load

Figure 3.3 three phase bridge diode rectifier

To assume that three phase bridge diode rectifier is ideal, therefore no ripple of instantaneous

output current. The input current of three phase bridge rectifier is square wave perform. It is

shown in Figure (3.4).

37

Figure 3.4 input line current and voltage wave form [8]

These rectifiers are mainly used in DC power supplies. Most the above configuration

circuit is used to convert AC supply to DC supply. This DC supply is used for internally circuits.

Both single phase and three phase diode rectifiers injects large amounts of harmonic currents into

the utility system. It means that this is the major contributors of harmonic in the supply system.

The single and three phase inverters are commonly used to convert DC to AC power at

some desired output voltage and frequency. The output voltage, current and frequency of inverter

can be controlled by control strategies of inverters.[8]

38

CHAPTER 4

SINGLE PHASE TRANSFORMER

4.1 EXPERMENT SINGLE PHASE TRANSFORMER

In the table (4.2, 4.3 and 4.4) which was published in 11 May 2011 by Assoc. Prof. Dr. Özgür

Cemal Özerdem and Mr. Samet Biricik the experiment was held on single phase transformer

under the same conditions of linear and non linear loads. From the tables (4.1) and tables (5.8,

5.9, 5.10 and 5.14) we find that the results match well for the resistive and inductive loads while

a small deviation was seen in the case of the capacitive load. This deviation is due mostly to the

difference in transformers and the grid conditions (load on the grid).

4.2 Single Phase Transformer Open and Short Circuit Test Results

Open-Circuit Test Results

Tables 4.1: Open-Circuit (single phase transformer)

Voltage (V 380 V

Current (A) 0.221 A

Power (W) 31.6 W

Short-Circuit Test Results

Tables 4.2: Short-Circuit (single phase transformer)

Voltage (V) 28 V

Current (A) 5.41 A

Power (W) 147 W

39

Parameter Value

Tables 4.3: Transformer Data (single phase transformer)

S (VA) 1500

𝑉𝑝 (V) 380

𝑉s (V) 105

𝑁𝑝 (Turn) 872

𝑁𝑆 (Turn) 241

𝑅𝑝 (Ω) 2.51

𝑋𝑝 (Ω) 0.62

𝑅𝑆 (Ω) 191.5

𝑋𝑆 (Ω) 47.3

𝑅C (KΩ) 60.28

𝑋𝑚 (KΩ) 24.2

A 3.62

4.3 Power Analysis under Cases of Linear and Nonlinear Load Conditions

(single phase transformer)

Tables 4.4: Linear Load Condition (single phase transformer)

NO 𝑝𝑖𝑛 𝑝𝑜𝑢𝑡 𝑝𝑙𝑜𝑠𝑠 efficiency 𝑉𝑖𝑛 𝑉𝑜𝑢𝑡 𝐼𝑖𝑛 𝐼𝑜𝑢𝑡 𝑇𝐻𝐷𝑖 cos 𝜃 PF

1 406 375 33 92 380 106.9 1.07 3.51 4.2 1 1

2 677 640 37 95 380 105.8 1.78 6.05 3.9 1 1

3 828 787 41 95 380 105.3 2.18 7.47 4.0 1 1

Figure 4.1: Linear load V, I waveforms and harmonic (single phase transformer)

40

As can be seen in Fig. 4.1, the load current is purely sinusoidal and in phase with the voltage.

The THD of the load current is 4.0%. The efficiency of the transformer was calculated as 95%

during the linear load feeding.

Tables 4.5: Inductive Nonlinear Load Condition (single phase transformer)

NO 𝑝𝑖𝑛 𝑝𝑜𝑢𝑡 𝑝𝑙𝑜𝑠𝑠 efficiency 𝑉𝑖𝑛 𝑉𝑜𝑢𝑡 𝐼𝑖𝑛 𝐼𝑜𝑢𝑡 𝑇𝐻𝐷𝑖 cos 𝜃 PF

1 408 372 36 91 380 106.7 1.15 3.63 21.8 0.98 0.95

2 705 649 56 92 380 105.0 1.96 6.52 26.6 0.98 0.94

3 875 804 71 92 380 104.9 2.47 8.20 28.5 0.98 0.93

Tables 4.2: Inductive Nonlinear Load Condition (single phase transformer)

The voltage and current waveforms of the harmonic polluting load is given in Fig. 4.2. In this

case, the load current contains a significant amount of harmonics. The magnitudes of the

harmonic spectrum of the load currents are given in Table 4.5. The THD of the load currents are

21.8%, 26.6% and 28.5%, which are increased the losses about 3% according to the linear load.

In this case, the efficiency of the transformer was calculated as 92%.

Tables 4.6: Capacitive Nonlinear Load Condition (single phase transformer)

NO 𝑝𝑖𝑛 𝑝𝑜𝑢𝑡 𝑝𝑙𝑜𝑠𝑠 efficiency 𝑉𝑖𝑛 𝑉𝑜𝑢𝑡 𝐼𝑖𝑛 𝐼𝑜𝑢𝑡 𝑇𝐻𝐷𝑖 cos 𝜃 PF

1 434 385 37 89 380 106.6 1.74 5.95 78.8 1 0.51

2 710 632 50 89 380 105.8 2.68 9.22 75.7 1 0.64

3 921 820 69 89 380 105.3 3.26 11.35 71.7 0.99 0.67

41

Tables 4.3: Capacitive Nonlinear Load Condition (single phase transformer)

The voltage and current waveforms of the harmonics polluting load is given in Fig. 4.3. The load

current contains a significant amount of harmonics.

The magnitudes of the harmonic spectrum of the load currents are given in Table 4.6. The THD

of the load currents are 78.8%, 75.9% and 71.7%, which are increased the losses about 6%

according to the inductive type nonlinear load. In this case, the efficiency of the transformer was

calculated as 89%.

42

CHAPTER 5

EXPERIMENTS AND RESULTS THREE PHASE TRANSFORMER

Our experiment was established to determine the harmonics and losses cause by the harmonics in

three phase transformer. The transformer was a three phase transformer 415/47 with power of 8

KVA under 50 HZ.

5.1 Equipments

We used in this experiment the next equipments.

1. Three variac to control voltage

2. Fuses to ensure the security during the experiment

3. Resistor elements, capacitors, inductors

4. Three phase bridge rectifier

5. Power quality analyses

There is many types of connection of the transformer (Y-Y, Δ- Δ, Y- Δ, Δ-Y).

In our experiment we used the Y-Y connection for the next reasons.

5.2 The Y-Y Connection in Three-Phase Systems

The most obvious way of transforming voltages and currents in a three-phase electrical system is

to operate each phase as a separate single-phase system.

This requires a four-wire system comprised of three phase wires plus a common neutral wire that

is shared among the three phases. Each phase is transformed through a set of primary and

secondary windings connected phase-to-neutral.

This is commonly referred to as the Y-Y connection, as illustrated in Figure 5.1. The left-hand

part of Figure 5.1 shows the physical winding connections as three separate two-winding

transformers. Both the primary and secondary windings of each of these transformers are

connected between one phases.

43

A A

B B

C C

N N FIGURE 5.1: Y-Y transformer connections

N

i

i

i

i

FIGURE 5.2: Y-Y Connection with the primary neutral brought out.

5.2.1 Advantages of the Y-Y Connection

Although care must be exercised when using the Y-Y connection, this connection has certain

inherent and important advantages over other three-phase transformer connections.

44

1. The primary and secondary circuits are in phase; i.e., there are no phase angle

displacements introduced by the Y-Y connection. This is an important advantage when

transformers are used to interconnect systems of different voltages in a cascading manner

2. Since the phase-to-neutral voltage is only 57.7% of the phase-to-phase voltage, the

windings of a Y-Y transformer require fewer turns to produce the same level of excitation

in the core compared to windings connected across the phases.

3. If the neutral end of a Y-connected winding is grounded, then there is an opportunity to

use reduced levels of insulation at the neutral end of the winding. A winding that is

connected across the phases requires full insulation throughout the winding.

5.3 Identification of Transformer parameters

After discussing the connection of transformer we are going at the first stage to define the

parameters of the transformer. The equivalent circuit of our phase of the transformer is shown in

the next figure.

Figure 5.3: Connection for transformer open–circuit test.

45

5.3.1 Open circuit

In this experiment the secondary is in open circuit and the primary is under normal voltage.

In this experiment it is clear that the power consumed by the primary is used in the

magnetization and as losses in the core of the transformer. The next parameter must be measured

in this experiment.

VOC , IOC and POC

The next table summarizes the result of this experiment.

5.3.1.1 Primary:

Table 5.1: open circuit parameters (Primary)

5.3.1.2 Secondary

Table 5.2: open circuit parameters (Secondary)

USA USB USA

27.61V 27.22V 27.15V

We can notice that the current in the primary phases are aboutly equals in the secondary there is

no current which the secondary voltage are:

POC = RPIOC2 + RCIOC

2 5.1

POC = RPIOC2 + RIR 5.2

POC ≈ RIR 5.3

POC = VOC IOC cos ∅OC = RIR 5.4

UR 241.5V IR 1.48A S1 358VA P1 131W

US 243.4 V IS 1.02A S2 249VA P2 45W

UT 242.9 V IT 1.538A S3 374VA P3 5W

46

POC = VOC IOC = RCIOC2 5.5

RC = VOC

IOC =

VOC2

RIR 5.6

VRC = VXM 5.7

RC = IOC cos ∅OC = XM IOC sin ∅OC 5.8

RIR ∶ power for losses IOC ∶ Active current

XM = RC IOC cos ∅OC

IOC sin ∅OC 5.9

cos ∅OC = POC

VOC IOC =

W

AV 5.10

SOC = VOC IOC QOC = SOC2 − POC

2

RC = VOC

2

POC XM =

VOC2

QOC

Using the next formulas we can calculate the core losses and magnetization parameters as

follow.

Phase R:

RC = VOC

IOC =

416 .7

3

IOC ∗ P

S

= 416.7

3∗ 1.516∗2

375

= 28939Ω

OR

RC = VOC

2

POC =

416 .7

3

2 = 28939Ω

XM = VOC

2

QOC =

416 .7

3

2

SOC2 − POC

2 = 154.34Ω

47

Phase S:

RC = VOC

IOC =

419 .2

3

IOC ∗ P

S

= 419.2

3∗1.052∗33

246

= 1715Ω

OR

RC = VOC

2

POC =

419 .2

3

33 = 1715Ω

XM = VOC

2

QOC =

419 .2

3

2

SOC2 − POC

2 = 240Ω

Phase T:

RC = VOC

IOC =

418 .4

3

IOC ∗ P

S

= 418.4

3∗1.55∗142

374

= 410.3Ω

OR

RC = VOC

2

POC =

418 .4

3

142 = 410.3Ω

XM = VOC

2

QOC =

418 .4

3

2

SOC2 − POC

2 = 168Ω

48

5.3.2 Short circuit experiment

In this experiment the secondary phases of the transformer are short circuit and the primary

voltage is reduced. From this experiment the equivalent resistor and inductors of the primary and

secondary can be determined as shown in the next figure.

Figure 5.4: Connection for transformer short–circuit test

The result of this experiment is shown in the next table:

5.3.2.1 Primary:

Tables 5.3: short circuit parameters (Primary)

UR 21.41V IR 9.18A S1 196.5VA P1 186.7W

US 21.06 V IS 10.27A S2 216VA P2 203W

UT 21.17V IT 10.17A S3 215.3VA P3 206.6W

cos ∅1 cos ∅2 cos ∅3

0.95 0.94 0.96

49

5.3.2.2 Secondary Current:

I = 82 A.

We can see that the primary voltage was 21V because we reduced it in order to avoid the passage

of high current in the transformer.

The next formulas explained the steps to calculateX1, X2, R1 and R2

PJ = RPIPSC2 + RS ISSC

2 5.11

PPSC = VPSC IPSC cos ∅PSC 5.12

PPSC = RPIPSC2 + RS ISSC

2 5.13

PPSC = RS ISSC2 4.14

RS = PPSC

ISSC2 5.15

QPSC = VPSC IPSC sin ∅PSC 5.16

QPSC = LfP ω IPSC2 + LfS ω ISSC

2 5.17

XS = QPSC

ISSC2 XS =

mVPSC

ISSC

2

− RS 5.18

m = NP

NS =

VP

VS =

IS

IP 5.19

ω= 2πf 5.20

ZSC = VSC

ISC PF = cos ∅OC =

POC

VOC IOC Q = cos−1 POC

VOC IOC

ZSC = VSC

ISC RSC =

PSC

ISC2 XS = ZSC

2 − RSC2

RSC = ZSC cos ∅SC XS = ZSC sin ∅SC

50

After the calculation of the parameters we found these results:

Phase R :

a= 415

47 = 8.82

RR = P

I2 =

186.7

9.18 2 = 2.21Ω

ZR = V

I = 2.33Ω

XR = ZR2 − RR

2 = 0.73Ω

RR = R1 + a2R2

XR = X1 + a2X2

R1 = a2R2 = 0.5RR

R2 = 1

2∗

RR

a2 =

1

2 ∗

2.21

8.822 = 0.014Ω

R1 = a2R2 = 8.822 * 0.014 = 1.089Ω

X1 = a2X2 = 0.5XR

X2 = 1

2∗

XR

a2 =

1

2 ∗

0.73

8.822 =4.69*𝟏𝟎−𝟑Ω

X1 = a2X2 = 8.822 *4.69*10−3 = 0.36Ω

Phase S :

a= 415

47 = 8.82

RS = P

I2 =

203

10.27 2 = 1.92Ω

51

ZS = V

I = 2.05Ω

XS = ZS2 − RS

2 = 0.718Ω

RS = R1 + a2R2

XS = X1 + a2X2

R1 = a2R2 = 0.5RS

R2 = 1

2∗

RS

a2 =

1

2 ∗

1.92

8.822 = 0.0123Ω

R1 = a2R2 = 8.822 * 0.0123 = 0.96Ω

X1 = a2X2 = 0.5XS

X2 = 1

2∗

XS

a2 =

1

2 ∗

0.718

8.822 =4.61*𝟏𝟎−𝟑Ω

X1 = a2X2 = 8.822 *4.61*10−3 = 0.359Ω

Phase T :

a= 415

47 = 8.82

RT = P

I2 =

206.6

10.17 2 = 1.99Ω

ZT = V

I = 2.08Ω

XT = ZT2 − RT

2 = 0.605Ω

RT = R1 + a2R2

52

XT = X1 + a2X2

R1 = a2R2 = 0.5RT

R2 = 1

2∗

RT

a2 =

1

2 ∗

1.99

8.822 = 0.0127Ω

R1 = a2R2 = 8.822 * 0.0127=0.995 Ω

X1 = a2X2 = 0.5XS

X2 = 1

2∗

XS

a2 =

1

2 ∗

0.605

8.822 =3.888*𝟏𝟎−𝟑Ω

X1 = a2X2 = 8.822 *3.888*10−3 = 0.3025Ω

53

5.4 Transformer Data

Tables 5.4: Transformer Data

Parameter Value

R S T

RP Ω

1.089 0.96 0.99

XP Ω

0.36 0.359 0.305

𝑅𝑆 Ω

0.014 0.0123 0.0127

XS Ω

4.69*10−3 4.61*10−3 3.88*10−3

𝑅𝐶 Ω

28939 1715 410

𝑋𝑀 Ω

154.34 240 168

S (VA) 8K

𝑉𝑃 (V) 415

𝑉𝑆 (V) 47

A 8.82

54

5.5 Experiments Linear Load Condition

Firstly we connected resistive linear load with the transformer as shown in fig 5.5 and used the

digital signal analyzer to Secord and measure the current, voltage, power, power factor and

distortion factor of the voltage and current of the transformer. The value of resistive load was

gradually decreased and the same measurements were taken to verify the obtained results and to

examine the transformer losses under different resistive load in order to verify the accuracy of

the obtained results.

a

b

cPower quality

Analyzer

Transformer

Figure 5.5: Linear Load Condition

Fig5.6 shows the voltage and current wave forms with the harmonic spectrum of load current.

As seen in fig 5.6 the load current is purely sinusoidal and in phase with the voltage. Table 5.5

shows the obtained results in the case of resistive liner load.

55

Figure 5.6: Linear load V, I waveforms and harmonic

Is clear from table 5.5 that power factor in the secondary of the transformer is one and the

reactive power consumption.

56

These are no reactive power consumption. After the calculation of power losses in the

transformer by subtracting the output power from the input power for each phase we can and

compare these power losses with the transformer losses determined earlier.

Ploss = Pin − Pout 5.21

We can notice that the losses in the case of resistive liner load as about the same as in open

circuit experiment which means that the linear resistive load doesn’t cause any extra losses for

the transformer.

As it is clear from the transformer efficiency results we can see that the efficiency of the

transformer was 26% in the case of low power consumption and reached the value of 89% at

about 50% of the rating of transformer. The efficiency is due to the fact that consumed power

was small if compared with the power nailed for the magnetization of the transformer core and

the iron losses.

The THD of load current was less than 3% in this experiment.

57

Tables 5.5: Linear Load Condition

58

5.6 Experiments Nonlinear inductive load Condition

In this case a nonlinear load was connected to the transformer in order to verify the effect of

nonlinear loads on the harmonic spectrum of current and voltage and the effect of harmonic

current on the transformer efficiency and losses the nonlinear.

In the case shown in fig 5.7 it is composed of three phase diode rectifier with RL load. The load

was increased gradually.

Figure 5.7: Nonlinear inductive load Condition

The results of this experiment are tabulated in table 5.6 the THD value of the load currents is

between 24 and 30.8.

These values of THD are due to the use of nonlinear loads which injects harmonic currents into

the source side. The power factor was decreased from one to about 95% in this case due to

existence of inductive load which consume reactive power. Fig 5.8 shows the wave forms of

current and voltage with the harmonic spectrum of the current.

59

Figure 5.8: Nonlinear load V, I waveforms and harmonic

Nonlinear load, current harmonic (primary):

Figure 5.9: Nonlinear load, current harmonic (primary)

60

Nonlinear load, current harmonic (secondary):

Figure 5.10: Nonlinear load, current harmonic (secondary)

The losses in the transformer were increased due to existence of harmonics.

The loses of transformer in the case of harmonics are given below

Ploss = PNL − PFL 5.22

𝑃𝑐𝑢 = 𝐼𝑙2(𝑅𝑆+

𝑅𝑃

𝑎2 ) + 𝐼𝑙ℎ2𝑛=∞

𝑛=2 (𝑅𝑆 + 𝑅𝑃

𝑎2 ) 5.23

The efficiency of the transformer was 92.5% at 39% of the transformer power .

61

Tables 5.6: Inductive Nonlinear Load Condition

62

5.7 Experiments Nonlinear Capacitive Loads Condition

In this case a capacitive load was connected to recitatives as shown in figure 5.11 the results

measured and tabulated in table 5.7

Figure 5.11: Nonlinear Capacitive load

These values of THD are due to the use of nonlinear loads which injects harmonic currents into

the source side. The power factor was decreased from one to about 95% in this case due to

existence of inductive load which consume reactive power. Fig 5.12 shows the wave forms of

current and voltage with the harmonic spectrum of the current.

The losses in the transformer were increased due to existence of harmonics.

The loses of transformer in the case of harmonics are given below

Ploss = PNL − PFL 5.24

𝑃𝑐𝑢 = 𝐼𝑙2(𝑅𝑆+

𝑅𝑃

𝑎2 ) + 𝐼𝑙ℎ

2𝑛=∞𝑛=2 (𝑅𝑆+

𝑅𝑃

𝑎2 ) 5.25

From the above equation, it can be concluded that the copper losses are related to the harmonics

order.

In the following section, linear and nonlinear load measurement tests were done over transformer

The efficiency of the transformer was 92% at 37% of the transformer power.

63

In figure 5.10 we can see that the slope of the current wave from is totally distorted and the THD

of current wave forms arrive the value of 79%

Figure 5.12: Nonlinear load V, I waveforms and harmonic

Nonlinear load, current harmonic (primary):

Figure 5.13: Nonlinear load, current harmonic (primary)

64

Nonlinear load, current harmonic (secondary):

Figure 5.14: Nonlinear load, current harmonic (secondary)

From the table of results we can see that the capacitive non linear loads increasing the THD

transformer current the value of THD arrive the value of 79%.

65

Tables 5.7: Capacitive Nonlinear Load Condition

66

5.8 Transformer losses and efficiency (Practical)

Tables 5.8: Transformer losses and efficiency (Practical)

Linear Load Inductive Nonlinear Load Capacitive Nonlinear Load

NO I 𝑃𝑙𝑜𝑠𝑠 efficiency I 𝑃𝑙𝑜𝑠𝑠 efficiency I 𝑃𝑙𝑜𝑠𝑠 Efficiency

1 5.5 156 79 5.4 183 72.18 8 142.9 73.76

2 15.5 171 88.6 14.4 198 85.54 13.5 160 84.60

3 23 250 89 23.3 199 90 24.7 188 89.82

4 33.5 323 88 31.2 184 92 33.8 201 91.8

5 42 354 90 38.9 244 92.35 37.9 230 92.66

mean 250.8 86 201.6 86.414 184.4 88.72

5.9 Transformer losses and efficiency (Theoretical)

Tables 5.9: Transformer losses and efficiency (Theoretical)

Linear Load Inductive Nonlinear Load Capacitive Nonlinear Load

NO I 𝑃𝑙𝑜𝑠𝑠 efficiency(%) I 𝑃𝑙𝑜𝑠𝑠 efficiency(%) I 𝑃𝑙𝑜𝑠𝑠 efficiency(%)

1 5.5 165.7 72.35 5.4 188.78 68.733 8 215.4 68.5

2 15.5 193.8 85.19 14.4 192 85.44 13.5 181.16 81.14

3 23 220.5 88.05 23.3 215.84 89.23 24.7 210 88.63

4 33.5 239 90.91 31.2 228.34 91.20 33.8 238.5 90.93

5 42 301 91.91 38.9 249.6 92.09 37.9 242.7 91.16

mean 224 85.682 213.4 85.1 217.55 84.08

5.10 Error between the theoretical and practical values

Tables 5.10: Error between the theoretical and practical values

Linear Load error Inductive Nonlinear Load

error

Capacitive Nonlinear Load

error

NO I 𝑃𝑙𝑜𝑠𝑠 Efficiency(%) I 𝑃𝑙𝑜𝑠𝑠 Efficiency(%) I 𝑃𝑙𝑜𝑠𝑠 efficiency(%)

1 5.5 5.8 5.04 5.4 3.061 5.01 8 10.105 7.3

2 15.5 11.76 2.12 14.4 3.065 0.11 13.5 8.2 4.2

3 23 13.37 1.07 23.3 7.80 0.862 24.7 10.6 1.13

4 33.5 35.14 3.2 31.2 19.3 0.877 33.8 11.6 0.99

5 42 17.6 2.07 38.9 2.2 0.47 37.9 5.7 1.6

mean 16.7 2.57

7.10 1.46 13.72 3.044

67

5.11 Linear and nonlinear load Condition, current harmonic

Tables 5.11: Linear and nonlinear load Condition, current harmonic

Linear Load

Condition

Nonlinear inductive load

Condition

Nonlinear Capacitive load Condition

Harmoni

c Order Ih /I1 Harmonic

Order Ih /I1 Difference % Harmonic

Order Ih /I1 Difference %

3 0.03A 3 0.15A 0.7 3 0.83A 5.6

5 0.17A 5 3.71A 19.9 5 9.41A 64.9

7 0.13A 7 2.24A 11.9 7 6.12A 42.3

9 0.01A 9 - - 9 0.41A 2.8

11 - 11 1.38A 7.7 11 0.37A 2.6

13 0.15A 13 1.22A 6.2 13 0.95A 6.1

5.12 Transformer losses and efficiency using MATLAB

The transformer and non linear load models were designed using MATLAB/SIMULINK with

the real transformer and load parameters. All the results were obtained from the model and

tabulated in table (5.11).

Tables 5.12: Linear Load Condition using MATLAB

R I

THD

5 5.2 429.8 414.5 15.3 96.4 108 - -

1.8 14.5 1160 1137 23 98.3 161.3 - -

1.13 23 1823 1787 36 98 252.3 - -

0.81 32 2510 2452 58 97.6 391.2 - -

0.66 38.5 3045 2966 79 97.4 532 - -

Tables 5.13: Inductive Nonlinear Load Condition using MATLAB

R I

THD

9.3 5.14 403.7 388 15.2 96.2 150.7 42.9 26.8

3 15.38 1169 1145 24 97.9 361 197 23.8

1.8 24 1858 1819 39 97.9 637 367.8 21.5

1.3 33.4 2468 2408 60 97.5 940 528 19.9

1.07 39 2909 2829 80 97.2 1190 648.6 18.8

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Tables 5.14: Capacitive Nonlinear Load Condition using MATLAB

R I

THD

10 5.3 376.7 361.7 15 96 183 76 55.05

3.2 14.8 1093 1070 23 97 390 232 32.4

1.9 23.8 1752 1715 37 97 658 403 26.66

1.4 32 2289 2235 54 97.3 919 549 23.6

1.1 38.8 2810 2735 75 97.7 1206 687 21.36

Tables 5.15: Transformer losses and efficiency using MATLAB

Linear Load Inductive Nonlinear Load Capacitive Nonlinear Load

NO I 𝑃𝑙𝑜𝑠𝑠 efficiency I 𝑃𝑙𝑜𝑠𝑠 efficiency I 𝑃𝑙𝑜𝑠𝑠 Efficiency

1 5.2 15.3 96.4 5.4 15.2 96.2 5.3 15 96

2 14.5 23 98 15.3 24 97.9 14 23 97.8

3 23 36 98 24 39 97.9 24 37 97.88

4 32 58 97.6 33 60 97.5 32 54 97.7

5 39 79 97.4 38.9 80 97.2 38 75 97.3

mean 42.26 43.6 40.8

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5.13 MATLAB/SIMULINK

Figure 5.15: MATLAB/SIMULINK

70

Different elements of the program:

1-Three phase AC voltage source: The AC Voltage Source block implements an ideal AC

voltage source

2-Three phase VI measurement: Used to measure three-phase voltages and currents in a

circuit. When connected in series with three-phase elements, it returns the three phase-to-ground

or phase-to-phase voltages and the three line currents.

3-Three-phase linear transformer: Implements three single-phase, two-winding linear

transformers where all the twelve winding connectors are accessible. The block can be used in

place of the Three-Phase Transformer (Two Windings) block to implement a three-phase

transformer when primary and secondary are not necessarily connected in Y or Delta.

4-grid impedance: Three phase RL elements used to represent the internal resistance and

inductance of cables or transformers in grid.

5- Diode: The diode is a semiconductor device that is controlled by its own voltage

𝑉𝑎𝑘 and current 𝐼𝑎𝑘 . When a diode is forward biased (𝑉𝑎𝑘 > 0), it starts to conduct with a small

forward voltage 𝑉𝑓 across it. It turns off when the current flow into the device becomes 0. When

the diode is reverse biased (𝑉𝑎𝑘 < 0), it stays in the off state.

anode cathodeA K+ -

6- Resistance: dc load

7- Inductor: Resistance in series with inductor in rectifier

8- Capacitor: in parallel with the load to smooth output voltage

71

9- The Voltage Measurement block: measures the instantaneous voltage between two electric

nodes. In this program it is used to measure the output voltage of the diode rectifier.

10- The Scope block displays its input with respect to simulation time: The Scope block can

have multiple axes (one per port) and all axes have a common time range with independent y-

axes. The Scope block allows you to adjust the amount of time and the range of input values

displayed. You can move and resize the Scope window and you can modify the Scope's

parameter values during the simulation.

11- THD calculation block: this block is used to calculate the Fourier Transform of a signal and

the total harmonic distortion, its output is the THD.

12- Three phase active and reactive power it is used to calculate the active and reactive power

when provided with three phase voltage and current.

13- RMS value calculation block: used to calculate the RMS value of a given signal. In the

program it is used to determine the RMS value of the load current.

14- Bridge rectifier: implements 6 diodes to construct a three phase bridge rectifier which is

used to convert the AC electric power and current to DC power

72

5.14 Linear Load Condition using MATLAB

Figure 5.16: linear load current (secondary)

Figure 5.17: linear load voltage (secondary)

Figure 5.18: linear load harmonic (secondary)

73

5.15 Nonlinear inductive load Condition using MATLAB

Figure 5.19: Nonlinear load voltage for inductor (secondary)

Figure 5.20: Nonlinear load current for inductor (secondary)

Figure 5.21: Nonlinear load harmonic for inductor (secondary)

74

5.16 Nonlinear Capacitive Loads Condition using MATLAB

Figure 5.22: Nonlinear load voltage for capacitor (primary)

Figure 5.23: Nonlinear load current for capacitor (primary)

Figure 5.24: Nonlinear load harmonic for capacitor (primary)

75

Figure 5.25: Nonlinear load current for capacitor (primary)

Figure 5.26: Nonlinear load voltage for capacitor (primary)

Figure 5.27: Nonlinear load harmonic for capacitor (secondary)

76

The theoretical losses in this experiment were calculated and it has been found that the error was

not too much but there is still a small error due to the existence of some factors that were not

taken in consideration. We can notice also that the error in the cause of non linear load was more

important due to the harmonics. From the tables we can notice that there is difference between

the theoretical values for the power, the efficiency, and the losses of the transformer. We have

taken many reading for the linear and non linear loads cases with the transformer. The theoretical

calculations have been done dependent on the theory explained in chapter II and compared with

the practical values. The comparison has been done for similar current values for the three load

types (linear, inductive non linear and capacitive non linear). The efficiency error between the

theoretical and practical results was calculated and tabulated in table (3). From this table we can

notice that the efficiency error is bigger in the case of the non linear load than in the linear load.

That is due to the existent of current harmonic with different levels in the case of the non linear

loads. These harmonics cause extra power losses in the core of the transformer and in the

primary and secondary circuits. These losses are difficult to be taken in consideration in the

theoretical calculations. In the linear load case we can notice that the error between the theory

and the experimental results is small and that error can be explained by many sources of error

such as the errors in the measurement devices, the errors in the identification of the transformer

parameters which is due to the changing conditions of the experiment; such as the grid voltage

which can be affected by the number of users connected to the grid at the moment of conducting

the experiment. The transformer conditions such as temperature can also affect the results of the

experiment.

The model of the transformer and the linear and non linear load were built in MATLAB

simulation environment. The results were printed and it showed that the increase of harmonics

causes an increase in the transformer losses. The results obtained in MATLAB shows better

performance than those in experiment due to the fact that MATLAB deals with mathematic

formulas without considering the environment in which the experiment has been conducted.

77

Figure 4.28: Three Phase Bridge Rectifier

78

79

80

Figures 4.29: Arrangement of Experimental Set-up (three phases)

81

CONCLUSIONS

This thesis focused on the study of harmonics and their effects on the power losses and reactive

power consumption in power transformers. The analysis of three phase transformer and its

equivalent circuit was applied using the conventional methods. The study of theoretical losses in

the case of linear load based on the equivalent circuit parameters was investigated. Another

analysis based on the same equivalent circuit with non-linear loads and harmonic currents was

also established in order to be compared with the linear ones.

A study of harmonics and their effects in power and communication systems was also

established. The harmonic analysis of experimentally obtained currents was applied using digital

signal analyzer. Three cases of linear and non-linear loads with resistive, inductive, and

capacitive elements were studied. The experimental results obtained in laboratory were discussed

and compared with the theoretical results.

A MATLAB model was developed. From the experiments as the theoretical analysis and

MATLAB model the increase of the harmonic contents of the electric current causes increase in

the transformer losses. The model of the transformer with linear and non linear load was built

and the results were compared with the experimental results. These losses are due mainly to the

inductances of the equivalent circuit of the transformer which increase with the harmonic order.

The harmonic contents in the case of capacitive load with diode rectifier were increased

compared to the case of inductive and resistive load. By consequence the losses of the

transformer were increased by comparison to the inductive and resistive loads.

This study proves that nonlinear loads cause a severe power quality problem for the power

systems especially for the secondary side of the three phase transformers. There is need to find

efficient solutions for the harmonics in order to decrease the losses of transformers. It focuses on

an important problem which is related strongly to the power quality and the losses caused by the

degradation of power quality. It encourages the research on new efficient solutions for harmonic

problems. Strategies for attenuating harmonics, from cheap to more expensive, include passive

harmonic filters consisting of linear capacitors and inductors to prevent harmonics from flowing

into the power supply, isolation transformers, harmonic mitigating transformers (HMTs), and

active filters.

82

Future work

This work can be considered as an introduction for the study of harmonic elimination methods to

reduce the losses of transformers due to harmonic currents. Future work includes the study of the

use of special design transformers and the investigation in passive and active power filters for

harmonics canceling and reactive power compensation.

83

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