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REDUCING HARMONIC VOLTAGE AT INDUSTRIAL AREADISTRIBUTION NETWORK USING NETWORK CONFIGURATION

MANAGEMENT

by

MOHD SHAHED BIN LATIF

Thesis submitted in fulfillment of the requirementsfor the degree of

BEng. (Electrical & Electronic Engineering)

March 2008

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ACKNOWLEDGEMENTS

This research could not been completed and this thesis cannot be written

without the scholarship and resources provided by Tenaga Nasional Berhad.

Thanks to my supervisor, Dr. Ir. Syafruddin Masri, for the guidance and

encouragement during my study process. Also thanks to my colleagues at

Gelugor Power Station, Penang who always support and encourage me and,

the staff at Regional Control Centre, Bayan Lepas who provided me all the

information required for my research. And finally, thanks to my family, especially

my departed wife who offered moral support and endured this long process with

me.

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TABLE OF CONTENTS

PAGE

ACKNOWLEDGEMENTS iiTABLE OF CONTENTS iiiLIST OF TABLES viLIST OF FIGURES viiiLIST OF ABBREVIATION xABSTRAK xiABSTRACT xii

CHAPTER ONE : INTRODUCTION

1.1 Overview on Harmonic 11.2 Standards on Harmonic 31.3 Harmonic Mitigation 41.4 Time-Varying Harmonic 51.5 Industrial Area 61.6 Factors Contributing to Harmonic Fluctuation 71.7 Evaluating Harmonic Characteristic 81.8 Objective and Scope of Research 81.9 Methodology 91.10 Contribution of This Study 101.11 Overview of Thesis 11

CHAPTER TWO : LITERATURE SURVEY

2.1 Background 12

2.2 Basic on Harmonics 12

2.3 Harmonic Characteristic of Industrial Area 16

2.4 Harmonic Standards 192.5 Time Varying Harmonic 22

2.6 Harmonic Mitigation and Economic Consideration 242.7 Identifying Harmonic Source 26

CHAPTER THREE : SIMULATION AND ANALYSIS

3.1 Effect of Consumer Load Fluctuation Size 303.2 Effect of Consumer Location 313.3 Effect of Different Network Configuration 333.4 Effect of Network Total Load 333.5 Voltage Total Harmonic Distortion Calculation 343.6 Baseline for Comparison 36

3.7 Evaluating Probabilistic Aspect of Harmonic Voltage 383.8 Simulation on Effect of Consumer Load Fluctuation Size 40

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3.9 Simulation on Effect of Consumer Location in NetworkBranch

41

3.10 Simulation on Effect of Different Network Configuration 423.11 Simulation on Effect of Adding New Load 42

CHAPTER FOUR : TEST NETWORK, MODELING AND

PARAMETERS4.1 Industrial Area Distribution Network 434.2 Component Rated Values and Impedance Modeling 45

4.2.1 Transmission System 454.2.2 Transformer 474.2.3 Cables 48

4.2.4 Consumer Loads 504.2.5 Harmonic Source 51

4.3 Probability of Network Loading 524.4 Simulation Software 53

CHAPTER FIVE : SIMULATION RESULTS AND DISCUSSION

5.1 Rated Voltage Total Harmonic Distortion 585.2 Simulation I Results And Analysis 595.3 Simulation II Results And Analysis 625.4 Analysis of Distance of Disturbance on THDv Variation 635.5 Results and Analysis for Configuration B and C 65

5.6 Analysis for Different Branch Loading 695.7 Result of Adding New Linear Load 705.8 Discussions 71

CHAPTER SIX : CONCLUSIONS AND RECOMMENDATION

6.1 Conclusions 756.2 Recommendation for Future Study 77

REFERENCES 78

APPENDICESAppendix A - Table of Random Load LevelAppendix B - Results for Effect of Load Variability in Configuration AAppendix C - Results for Effect of Load Variability in Configuration A

at 2/3 Current Harmonic

Appendix D - Results for Effect of Load Variability in Configuration Aat 1/3 Current Harmonic

Appendix E - Load Variability Results for Configurations A, B and C

Appendix F - Difference in Network Branch Load and Difference InTHDv Between Configuration B and C

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LIST OF TABLES

PAGE

2.1 Harmonic Phase Sequence 15

2.2 Basis for harmonic current limits based on IEEE 519-1992

20

2.3 Current distortion limit for general distribution systems(120V through 69000V)

20

2.4 Voltage Distortion Limits 21

3.1 Load Variability Level 39

4.1 System Base Value 45

4.2 Transmission System Parameter 46

4.3 Cables Data 48

4.4 Consumer Plant Rated Load and Power Factor 50

4.5 Harmonic Current Spectrum 52

4.6 Probability of Network Loading 53

5.1 Configuration A Average THDv for Range of NetworkLoad Demand

60

5.2 Configuration A - Probability and Cumulative Probabilityof Ranged THDv

60

5.3 Variation of THDv Result for Total Tripping Of EachConsumer Load

62

5.4 THDv Variability Result for Total Tripping of Each

Consumer Based on Consumer Distance to PCC

64

5.5 Configuration B - Average THDv for Range of NetworkLoad Demand

66

5.6 Configuration B - Probability and Cumulative Probabilityof Ranged THDv

67

5.7 Configuration C - Average THDv for Range of NetworkLoad Demand

67

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5.8 Configuration C - Probability and Cumulative Probabilityof Ranged THDv

67

5.9 THDv at PCC as a Result of Adding New Load 70

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LIST OF FIGURES

PAGE

1.1Methodology flow chart

10

2.1 Harmonic Current and Voltage Distortion 13

2.2 A 33KV Industrial Area Distribution Network 17

2.3 Balanced harmonic characteristic at industrial areanetwork

18

2.4 Minimal levels of triplen and even current harmonic 18

2.5 Typical distribution network of an industrial area 19

2.6 Harmonic voltage fluctuation at an industrial areaincoming feeder

22

3.1 Factors affecting harmonic voltage fluctuation and factorswithin utilitys control

29

3.2 Effect of consumer distance from PCC 32

3.3 Process flowcharts for calculating total harmonic voltage

distortion (THDv) at PCC

35

3.4 A 33KV Test distribution network (Configuration A) 37

3.5 Network Configuration B 37

3.6 Network Configuration C 38

4.1 A 33KV test distribution network 444.2 Equivalent pi-circuit model for cables 48

4.3 Aggregate load model 51

4.4 Sample of component model programming usingspreadsheet

54

5.1 Harmonic voltage at each harmonic order forconfiguration A

58

5.2 Harmonic voltage Distortion characteristic for networkconfiguration A at maximum current harmonic and varyingconsumer loads

59

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5.3 Configuration A THDv pdf and cpf 61

5.4 Scatter plot for different level of current harmonic 62

5.5 Correlation between load fluctuation size and THDv

variability

63

5.6 Correlation between consumer load distance to PCC andTHDv variability range at PCC due to total tripping of eachload

64

5.7 Harmonic voltage level at each harmonic for configurationB and C using the same random load level data,simulation and calculation

65

5.8 Scatter plot of THDv for the three different configuration at

random load level

66

5.9 Configuration B THDv pdf and cpf 68

5.10 Configuration C THDv pdf and cpf 68

5.11 Correlation between difference in branches total load anddifference in configuration B and C THDv

69

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LIST OF ABBREVIATION

ASD Adjustable speed drives

BK Breaker

Cpf Cumulative probability function

CIGRE International Congress of Large Power Systems

IEC International Electrotechnical Commission

IEEE Institute of Electrical and Electronics Engineers

IEEE PES IEEE Power Engineering Society

ISC Short Circuit Current

IL Load Current

LPC Large Power Consumer

MS Microsoft

MVA Mega Volt Ampere

NOP Normally open position

Pdf Probability density function

PCC Point of Common Coupling

SCC Short Circuit Current

SCR Short Circuit Ratio

SHI Shunt Harmonic Impedance

THD Total Harmonic Distortion

THDv Voltage Total Harmonic Distortion

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MENGURANGKAN VOLTAN HARMONIK DI RANGKAIAN PEMBAHAGIANKAWASAN INDUSTRI MENGGUNAKAN PENGURUSAN KONFIGURASI

RANGKAIAN

ABSTRAK

Syarikat pembekal elektrik diperlukan untuk mengekalkan tahap voltan

harmonik di dalam sistem di bawah batas piawaian. Namun, voltan harmonik

berubah mengikut masa dan disebabkan oleh naik turun tahap arus harmonik

dan perubahan impedans rangkaian. Mengurangkan harmonik menggunakan

kaedah sedia ada adalah mahal untuk pembekal tenaga dan memerlukan

pertimbangan ekonomi. Pemerhatian dan analisa ke atas rangkaian

pembahagian kawasan industri menunjukkan perubahan pada impedans

rangkaian disebabkan oleh perubahan beban pelanggan dan perubahan

konfigurasi rangkaian boleh menyebabkan perubahan ketara terhadap kadar

voltan total harmonic distortion (THD) pada point of common coupling (PCC).

Simulasi terhadap rangkaian pembahagian ujian, menganalisa faktor seperti

saiz perubahan beban pelanggan dan lokasi beban sepanjang rangkaian, dapat

mengurangkan perubahan maksima voltan THD sebanyak 21.7% dari satu

pelanggan. Mengubah konfigurasi rangkaian dapat mengurangkan voltan THD

sebanyak 10.6% sementara menambah 5MVA beban tambahan mengurangkan

voltan THD sebanyak 3.5%. Jumlah pengurangan adalah bermakna

memandangkan caranya yang mudah dengan kos yang minima menjadikannya

sesuai untuk pembekal tenaga atau pelanggan gunakan sebagai cara

tambahan menghalang voltan harmonik daripada melebihi had piawaian atau

memperbaiki bentuk gelombang voltan.

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REDUCING HARMONIC VOLTAGE AT INDUSTRIAL AREA DISTRIBUTIONNETWORK USING NETWORK CONFIGURATION MANAGEMENT

ABSTRACT

Electric utility company is required to maintain harmonic voltage level in the

system below the standards limit. However, harmonic voltage is time variant

and is caused by fluctuation of current harmonic level and changes in network

impedance. Mitigating harmonic using existing methods is costly for utility and

requires economic consideration. Observation and analysis on an industrial

area distribution network shows that network impedance fluctuation caused by

consumer loads variability and changing network configuration can significantly

change voltage total harmonic distortion (THD) level at point of common

coupling (PCC). Simulation on a test distribution network, analyzing factors

such as size of fluctuating consumer load and location of load along radial

network, is able to reduce maximum voltage THD variability from a single load

up to 21.7%. Changing network configuration can achieve voltage THD

reduction up to 10.6% while adding 5MVA additional load into the network

reduced voltage THD up to 3.5%. Amount of reduction is significant considering

the methods simplicity and with minimum cost which makes it feasible for utility

or consumer to use as an additional method to prevent harmonic voltage from

exceeding the standards limit or to improve voltage waveform.

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CHAPTER ONE

INTRODUCTION

Demand for quality power supply is becoming a major issue for

consumer, especially large power consumer (LPC) such as industrial

community. Electric utility company is expected to comply with power quality

standards. One of power quality index is related to harmonic distortion. Unlike

other power quality indexes such as transient, sag and swell which occur

intermittently, harmonic distortion exist continuously in electrical network. This

chapter describes issues regarding harmonic distortion at an industrial area

distribution network from utilitys perspective.

1.1Overview on Harmonic

Harmonics in electrical power system is becoming a major concern for electric

utility company and consumers. It is produced by power electronics and other

equipments which are called non-linear loads. Examples of nonlinear loads are

computers, fluorescent lamp and television in residential while variable speed

drives, inverters and arc furnaces are mostly common in industrial areas.

Increasing numbers of these loads in electrical system for the purpose of, such

as improving energy efficiency, has caused an increase in harmonics pollution.

These loads draw non-sinusoidal current from the system. The waveform is

normally periodic according to supply frequency which is either 50Hz or 60Hz

depending on the country.

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Effect of high level of voltage or current harmonics can cause transformer

heating, nuisance tripping of fuse, circuit breaker and protective devices, 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 transformers

inductance.

All triplen 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 triplen harmonic from entering utility distribution system.

However, triplen harmonic current flows in neutral conductor and are three

times in magnitude.

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1.2 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 Electrotechnical Commission (IEC), produced a standard, IEC

61000-3-6, which also provides guidelines 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 (Halpin, 2005). 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

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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.

1.3 Harmonic Mitigation

Several methods of mitigating harmonics have been developed over the

years. The most common method is using filter, either passive or active.

Passive filter block certain harmonic bandwidth while active filter injects current

into the system to cancel the current harmonic waveforms. Both methods have

their advantages and disadvantages, for example, advantage of passive filter is

easy to design and active filter can monitor many frequencies simultaneously

while disadvantage of passive filter is bulky in size and active filter is costly

(Izhar et. al., 2003). Harmonic filters are useful and practical to be implemented

by consumer near the proximity of the non-linear load at the low voltage system.

Another method which is normally used by consumers is using phase

cancellation method using twelve pulse converters instead of six pulse

converters.

Similar application using filters for utility at higher voltage level such as

distribution network requires extensive economic consideration. This is due to

the size and cost of the equipment while most of harmonic pollutant is caused

by consumer. There is little study on a feasible and cost effective means for

utility to mitigate harmonic, especially harmonic voltage. A study was conducted

on method using shunt harmonic impedance (Ryckaert et. al., 2004 ) which can

act like a central damper to reduce harmonic at distribution network. This

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method is considered to be less expensive compared to active filter. The

method uses power electronic to emulate resistive behavior for harmonic.

However, the method is still under further study. Currently, all harmonic

mitigation techniques involve equipment required to be installed on the system.

There is yet a study on using other factors which can affects harmonic voltage

distortion such as network impedance. Optimizing network impedance to

mitigate harmonic can be cost effective for utility to apply. Because of mitigating

harmonic is expensive, many utility company have resorted in imposing penalty

to consumer for injecting current harmonic above the standard steady state limit

into the system. This process requires method on determining harmonic

contribution by the consumers (Li, et. al., 2004) and the equipment need to be

installed at all consumers feeder which is very costly.

1.4 Time-Varying Harmonic

Many recent studies on harmonic limit focus on development of time

varying limit and probabilistic aspects of harmonics in power system (Baghzouz,

2005). This includes the probabilistic modeling of power system (Carbone, et.

al., 2000) and probabilistic aspects of harmonic impedance (Testa, et. al.,

2002). In order to comply with time varying harmonic limits, prediction of the

systems time varying harmonic characteristic is crucial. Simulation is still the

best method of assessment but calculation based on steady state design value

does not reflect the actual fluctuation of harmonic. This is due to the fact that

current harmonic and network impedance changes over time. Therefore it is

imperative for utility to be able to predict the time varying characteristic of

harmonic voltage of a distribution network at PCC based on the varying factors

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within distribution system, especially factor that within its influence where they

can be controlled or managed. The factors which can contribute to harmonic

voltage fluctuation will be discussed in detail in section 1.6.

1.5 Industrial Area

Setting up of an industrial area or industrial zone has become a common

practice in many countries where all industrial plant is located within a certain

geographical area. There are many reasons for the set up such as economic

consideration, safety issues and environmental concern. The development of

industrial area has also caused a unique electrical distribution system with

unique electrical characteristic, power quality and system stability requirements.

Due to the strict requirements from consumer to utility, consumers are provided

with redundant incoming feeders and the distribution network is supplied by

several sources from transmission system. The network is also operated by

extensive network control system to provide stable and reliable supply to

consumers.

Utility monitors power supply quality of an industrial area at the

incoming feeder after the step down transformer from transmission system. For

harmonic monitoring, this point is the point of common coupling. The reason for

choosing the point is to ensure harmonic pollution from the industrial area is not

being transmitted into transmission system and vice versa, and to ensure

harmonic pollution from one branch does not affect another branches

connected on the feeder. Harmonic level on the feeder is the best indication of

harmonic quality in the network.

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1.6 Factors Contributing to Harmonic Fluctuation

Analysis into factors contributing to harmonic voltage fluctuation at

industrial area shows that changes in non-linear loads, network configuration

and number of linear loads within the network are the main factors. However,

utility has no control over the number and operational of non-linear load within

industrial plant which caused changes in production of current harmonic. The

only factors within utilitys control are configuration of the network and number

of consumer plants in the network. These two factors affect the network

impedance. Looking in detail into network components, network total

impedance comprises of transmission system impedance, step down

transformer impedance, cable impedance and consumers plant network

impedance.

Transmission system network impedance looking from the low voltage

side of a step down transformer varies slightly over time because of the

impedance of a step down transformer dominates and does not vary much.

Cables impedance is also constant and can be assume steady. However,

number of consumer plant in the network and their load demand changes over

time depending on plant operation and unforeseen tripping. Overall network

configuration can also change due to switching process. These two factors,

consumer load variability and network configuration changes, are the main

factors which utility can use to mitigate harmonic voltage.

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1.7 Evaluating Harmonic Characteristic

In order to determine the effect of the above factors on harmonic voltage,

network harmonic characteristic is important as a baseline for comparison. The

characteristic must be able to indicate the effect of time varying nature of

harmonic. Since major contribution of harmonic voltage is the fluctuation of load

impedance under normal operation, development of harmonic characteristic of a

network due to load variability is crucial. There is currently no specific method

been developed to determine or predicting harmonic characteristic of a certain

network, other than frequency scan for resonance analysis which only

applicable for steady state analysis. For this study, since utility is able to

determine the statistical loading pattern of a network, the probability of loading

can be used to develop and estimate the probabilistic aspect of harmonic.

1.8 Objectives and Scope of Research

The objectives of this study were to determine methods for utility to

reduce harmonic voltage in meeting standards steady state limit of 5% voltage

THD and time varying limit of 95th percentile voltage THD within steady state

limit at PCC. The second objective is to determine methods of reducing

harmonic voltage with little or no cost. The study focused on distribution network

for industrial area which has the capability of switching into other configuration

since the network normally has different possible sources, backup and

redundant feeders to ensure reliability of the supply system. Action plan for this

study were as follows:

1. To determine whether varying consumer load increases harmonic

voltage.

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2. To determine amount of changes in harmonic voltage due to size

of varying consumer load.

3. To determine amount of change in harmonic voltage due to

location of varying consumer load.

4. To determine changes in harmonic voltage due to switching

network configuration.

5. To determine changes in harmonic voltage due to adding

consumer load into existing network.

1.9 Methodology

In order to achieve the objectives, the following protocol had been set up.

Select and gather data on industrial area distribution

network configuration and components

Decide method on modeling of equipment for harmonic

analysis and method of simulation

Model the selected industrial area distribution network

Simulate identified factors affecting harmonic voltage

Analyze data using statistical technique and compare with

calculation based on design values

Conclude the research, suggest and recommend mitigating

action

Base on protocol and action plan a flow diagram of research

methodology was drawn and shown in Figure 1.1.

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Figure 1.1 Methodology flow chart

1.10 Contribution of This Study

The outcome of this study is important to utility in controlling harmonic

voltage and improving power quality without huge investment in mitigating

equipment. Components which are affected by harmonic voltage will have

longer life and cost of maintenance is reduced. Consumers will also benefit from

the method since utility is able to provide better power quality. System design

engineers can use the method in planning of electrical system and control

engineers will be able to use the method in controlling harmonic voltage.

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1.11 Overview of Thesis

This thesis discusses and analyzes harmonic voltage distortion at a utility

distribution network supplying to industries due to changes in consumer load

and network configuration. The analysis determines the condition which can

reduce total harmonic voltage distortion THDv at point of common coupling.

Recommendation to reduce harmonic voltage distortion was proposed which

can be integrated into the network control system.

The content in Chapter 2 provides reader with the applicable standards

for harmonic, harmonic mitigation, probabilistic aspects of harmonic, economic

consideration and effect of network impedance on harmonic. Reviews from past

studies by researchers related to those issues were presented.

Chapter 3 discusses the method of simulation and the process flow of the

simulation. Each factors contributing to the changes to harmonic voltage at PCC

were taken into consideration for simulation. Method of calculations and

analysis were also presented in this chapter.

Chapter 4 contains information on test distribution network system

together with component data and test values that were used for analysis.

Methods for modeling and calculation of each component in the network were

described in details.

Chapter 5 exhibits the simulation results and analysis together with

discussion of the overall situation. A conclusion of the thesis was presented in

Chapter 6 which includes recommendation for future studies.

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CHAPTER TWO

LITERATURE SURVEY

2.1Background

The studies required broad knowledge of the issues regarding harmonic

in power system, the standard limit and requirements, modeling and simulation,

issues related to utility and consumers especially at an industrial area, and

result from studies by other researchers. All this information is necessary to

address the changes and dynamic of harmonic voltage at an industrial area.

The following sections include brief knowledge of harmonics and reviews

on papers related to relevant harmonic standards and requirements, mitigation,

probabilistic aspects, cost of mitigation and effect of harmonic impedance

variability. The review focus on studies related to harmonic in power system

with regards to relation between utility and consumers. The reviews also

pointed out the differences and similarities between previous studies and this

research.

2.2 Basic on Harmonics

IEEE PES Winter Meeting 1998 provides basic harmonic theory which

according to Fourier theorem, periodic non-sinusoidal or complex voltage

(Figure 2.1) or current waveforms can be represented by the sum of a series of

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multiple frequency terms of varying magnitudes and phases as shown in

equation (2.1).

++= )]cos([)( 0 nn qtnaatf (2.1)

where: na is the magnitude of the nth harmonic frequency

oa is the d.c. component

nq is the phase angle of the nth harmonic frequency

is the fundamental frequency

n =1,2,3,

Harmonic is measured using total harmonic distortion (THD) which is

also known as distortion factor and can be applied to current and voltage. It is a

26

Figure 2.1 Harmonic Current and Voltage Distortiona) Non-linear load draws non-sinusoidal current from the system.b) Resulting voltage distortion due to non-sinusoidal current

Non-linear current

Supply

voltage

(a)(b)

V

time

Distorted

Voltage

waveform

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square-root of sum of all harmonic magnitudes over the fundamental. Equation

(2.2) shows the calculation for voltage total harmonic distortion (THDv).

1

2

2

V

V

THDn

n

V

==

(2.2)

where: 1V is the magnitude of fundamental frequency voltage

nV is the magnitude of nth harmonic frequency voltage

For a balanced three-phase network with three-phase non-linear loads,

harmonic current or voltage has phase sequences. Equations (2.3) until (2.7)

describe the equation for each phase for the first three harmonics.

)3sin()2sin()sin()( 332211 +++++= tItItIti oooa (2.3)

)3

63sin()

3

42sin()

3

2sin()( 332211

+++++= tItItIti

ooob (2.4)

)3

63sin()

3

42sin()

3

2sin()( 332211

++++++++= tItItIti

oooc (2.5)

where: nI is the nth current harmonic magnitude

o is the fundamental frequency

n is the nth harmonic phase angle

n = 1,2,3

Equation (2.4) and (2.5) can also be described as follows:

)03sin()322sin()

32sin()( 332211 ++++++= tItItIti ooob (2.6)

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)03sin()3

22sin()

3

2sin()( 332211 +++++++=

tItItIti

oooc (2.7)

Current magnitude of all phases for all harmonic frequencies is equal for

a balanced system. Looking at equations (2.3), (2.6) and (2.7), the first

harmonic or the fundamental is positive sequence since ib(t) lags ia(t) by 120o

and ic(t) leads ia(t) by 120o. The second harmonic is negative sequence since

and ib(t) leads ia(t) by 120o and ic(t) lags ia(t) by 120

o. The third harmonic is zero

sequence since ib(t) and ic(t) are in phase with ia(t). The sequence pattern for

each harmonic order is shown in Table 2.1.

Table 2.1Harmonic Phase Sequence

Harmonic Phase Sequence

1 +

2 -

3 0

4 +

5 -

6 0

7 +

8 -

9 0

10 +

11 -

12 0

13 +

14 -15 0

CHAPTER SIX

CONCLUSIONS AND RECOMMENDATIONS

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6.1 Conclusions

This study has succeeded in developing methods to reduce harmonic

voltage at industrial area. The simulations have showed a reduction of 10.6%

voltage THD by switching configuration at design condition and 3.5% voltage

THD by switching in additional 5MVA load into the network. The simulation also

produced reduction of time varying 95th percentile level from between 3.5% and

4.0% to between 3.0% and 3.5% which was about 10% reduction.

The main purpose of this research was to obtain methods for utility to

mitigate harmonic voltage at the point of common coupling using minimum cost

by looking at load and network management. The study did not only address

steady state limit but also include time varying characteristic of harmonic. Focus

was made on optimizing harmonic impedance of an industrial area distribution

network in order to reduce the effect of impedance variability on voltage THD.

Consumer load variability has been determined as the main contribution to time

varying harmonic voltage in the system. Based on the study, several factors

have been identified which could be manipulated to reduce the effect such as

consumer load fluctuation size, consumer load location within the network

relative to PCC, difference network configuration and introduction of additional

load into the system. The test distribution network was described in detail

including components data and modeling required for harmonic analysis.

Methods of simulation to observe the effect of the various factors had also been

explained.

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Based on the results, it is concluded that the following mitigating actions

can be an alternative means available for utility company to use in managing

and complying with standards requirement on harmonic voltage distortion

especially at industrial area distribution network. These methods are able to

reduce the effect of load variability on harmonic voltage and also reduce the

level of harmonic voltage level at PCC. Depending on the availability of

switching facilities of the network, one or combination of the following criteria

can be performed to change network configuration:

1. Switching the network by locating large consumer plant or large

fluctuating load to the end of network branch and locating smaller load or

less fluctuating load closer to PCC to reduce the effect of consumer load

variability on THDv.

2. Increase load demand of the sub network by switching other linear load

into the network.

3. Combining two short branches into a longer branch by switching the

branch with lower total load demand to the end of the other branch which

has higher load demand.

These actions could be incorporated into the automated network

distributed control system together with other power quality control scheme and

during planning or designing of a new system. The amount of reduction was

significant, whether comparing with steady state limit or time-varying limit, since

the implementation cost is trivial where it uses existing switching facilities of the

network system.

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6.2 Recommendation for Future Study

The research was performed with assumption that there is only one

current harmonic source from a single consumer in the system while others are

linear loads. It is important to note that changing network configuration with

several harmonic sources in the system can change the location of other

harmonic source. Further study is required to determine the effect of changing

current harmonic source location in the system on harmonic voltage which

includes impedance variability of the network. Software on handling simulation

of several harmonic sources with randomly varying load can be developed to

assist utility and consumer in analyzing and estimating the probability of the

system in complying with harmonic standards.

31


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REFERENCES

Baghzouz,Y.; An overview on Probabilistic Aspects of Harmonics in PowerSystems, IEEE Power Engineering Society General Meeting, 2005 Vol. 3, pp.2394 2396, 2005

Carbone, R.; Castaldo, D.; Langella, R.; Testa, A.; Probabilistic modeling ofindustrial systems for voltage distortion analyses, Ninth International

Conference on Harmonics and Quality of Power, 2000,Volume 2, 1-4 Oct. 2000 Page(s):608 - 613 vol.2

Halpin, S.M.; Comparison of IEEE and IEC Harmonic Standards, IEEE PowerEngineering Society General Meeting, 2005, Vol. 3, Page(s) 2214-2216

IEEE std. 519-1992 IEEE Recommended Practices and Requirements forHarmonic Control in Electrical Power Systems

IEEE PES Winter meeting 1998, Tutorial on Harmonic Modeling and Simulation,Available: http://www.ee.ualberta.ca/pwrsysIEEE/download.html24/12/2005

Izhar, M.; Hadzer, S.M.;Masri, S.; Idris, S.; A Study of The FundamentalPrinciples to Power System Harmonic, Proceedings on National Power andEnergy Conference, 2003, Page(s) 223 - 231

Li, C.; Xu, W.; Tayjasanant, T.; A critical impedance-based method for

identifying harmonic sources, IEEE Transactions on Power Delivery, Volume19, Issue 2, April 2004 Page(s):671 678

Ryckaert, W.R.A.; Ghijselen, J.A.L.; Melkebeek, J.A.A.; Desmet, J.J.M.;Driesen, J.; The influence on harmonic propagation of the resistive shuntharmonic impedance location along a distribution feeder and the influence ofdistributed capacitors, 11th International Conference on Harmonics and Qualityof Power, 2004. 12-15 Sept. 2004 Page(s):129 135

32
http://www.ee.ualberta.ca/pwrsysIEEE/download.htmlhttp://www.ee.ualberta.ca/pwrsysIEEE/download.html


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Testa, A.; Castaldo, D.; Langella, R.; Probabilistic aspects of harmonicimpedances, Power Engineering Society Winter Meeting, 2002. IEEE Volume2, 27-31 Jan. 2002 Page(s):1076 - 1081 vol.2

Wakileh, George J.; Power Systems Harmonics, Fundamentals, Analysis andFilter Design, Springer, 2001 Page(s) 275 286

Xu, W.; Liu, X.; Liu, Y.; An investigation on the validity of power-directionmethod for harmonic source determination, IEEE Transactions on PowerDelivery, Volume 18, Issue 1, Jan 2003 Page(s):214 219

Xu, W.; Component Modeling Issues for Power Quality AssessmentIEEE Power Engineering Review, November 2001 Page(s): 12 15

33


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APPENDIX A

Table of Random Load Level

Load1

Load2

Load3

Load4

Load5

Load6

Load7

Load8

Load9

Load10

15% 55% 33% 0% 0% 0% 0% 15% 66% 105%33% 0% 33% 0% 33% 105% 66% 15% 66% 0%0% 15% 105% 85% 33% 85% 0% 85% 105% 0%85% 15% 15% 105% 105% 105% 0% 55% 85% 105%15% 66% 15% 15% 15% 33% 0% 0% 33% 15%55% 33% 85% 0% 15% 15% 85% 33% 66% 105%0% 85% 105% 55% 55% 33% 85% 55% 85% 15%0% 0% 66% 105% 0% 15% 15% 85% 85% 33%85% 55% 85% 0% 0% 33% 105% 55% 33% 15%

105% 105% 33% 0% 33% 0% 33% 55% 33% 66%0% 105% 66% 55% 105% 0% 0% 85% 105% 15%15% 33% 66% 105% 66% 15% 33% 15% 55% 85%33% 55% 85% 105% 85% 85% 0% 105% 15% 85%15% 0% 15% 55% 55% 0% 15% 85% 66% 33%85% 66% 66% 85% 15% 85% 55% 33% 105% 85%66% 105% 66% 0% 105% 33% 105% 33% 55% 66%15% 85% 0% 66% 15% 0% 33% 55% 66% 55%15% 105% 15% 55% 55% 15% 0% 85% 85% 105%66% 15% 55% 15% 85% 55% 66% 15% 33% 33%

105% 85% 15% 33% 0% 105% 33% 66% 55% 0%0% 15% 0% 0% 66% 85% 0% 33% 66% 15%55% 66% 105% 105% 0% 33% 85% 15% 0% 66%85% 55% 66% 85% 0% 0% 66% 55% 105% 33%15% 55% 66% 66% 105% 55% 66% 0% 105% 33%105% 66% 105% 0% 55% 66% 55% 55% 0% 66%85% 105% 15% 85% 0% 33% 0% 66% 15% 33%15% 55% 85% 55% 15% 105% 55% 55% 33% 85%85% 55% 33% 66% 85% 85% 85% 55% 15% 55%15% 55% 0% 15% 33% 105% 85% 66% 66% 85%33% 55% 105% 55% 15% 33% 55% 66% 0% 0%

0% 105% 85% 55% 15% 66% 85% 15% 105% 33%105% 105% 66% 15% 15% 66% 15% 85% 66% 66%0% 33% 66% 0% 66% 85% 33% 15% 0% 33%15% 0% 0% 85% 105% 105% 85% 33% 0% 0%0% 66% 66% 0% 66% 66% 105% 85% 85% 33%66% 33% 33% 66% 0% 66% 33% 55% 33% 0%85% 85% 66% 85% 0% 0% 33% 33% 105% 55%85% 15% 55% 55% 55% 15% 15% 33% 33% 85%


34/44

Table of Random Load Level continued

Load1

Load2

Load3

Load4

Load5

Load6

Load7

Load8

Load9

Load10

0% 66% 105% 33% 15% 105% 33% 0% 85% 0%0% 0% 33% 85% 33% 15% 55% 33% 0% 0%

66% 66% 33% 66% 15% 33% 33% 0% 66% 55%105% 85% 0% 15% 15% 66% 33% 15% 33% 85%55% 66% 55% 66% 15% 15% 0% 0% 55% 85%105% 105% 85% 85% 55% 55% 0% 105% 0% 0%15% 0% 15% 33% 33% 55% 85% 85% 105% 15%85% 33% 66% 85% 0% 0% 105% 15% 66% 66%66% 55% 15% 55% 55% 85% 0% 66% 33% 15%85% 85% 85% 85% 0% 105% 66% 66% 15% 85%66% 15% 0% 85% 66% 33% 15% 33% 33% 33%15% 66% 105% 33% 105% 105% 33% 15% 15% 33%66% 105% 33% 66% 105% 33% 33% 55% 33% 0%

105% 15% 66% 105% 15% 105% 66% 85% 0% 33%15% 0% 55% 15% 105% 15% 66% 0% 15% 66%66% 33% 85% 33% 15% 66% 55% 85% 55% 66%105% 33% 66% 33% 0% 105% 55% 15% 0% 85%15% 15% 0% 66% 0% 85% 55% 85% 33% 85%15% 0% 0% 66% 55% 15% 66% 85% 105% 55%105% 85% 55% 0% 15% 85% 0% 33% 0% 85%55% 33% 33% 15% 55% 0% 55% 33% 33% 33%66% 0% 33% 0% 33% 33% 66% 0% 66% 66%105% 105% 0% 105% 66% 15% 15% 85% 33% 66%

15% 66% 55% 85% 85% 15% 105% 66% 0% 15%66% 66% 33% 66% 105% 33% 85% 0% 33% 55%85% 33% 66% 85% 55% 55% 15% 66% 0% 105%85% 33% 33% 85% 15% 105% 0% 33% 15% 33%85% 55% 105% 15% 85% 66% 66% 85% 33% 85%0% 33% 105% 33% 66% 66% 15% 55% 33% 66%85% 15% 15% 15% 105% 33% 66% 33% 105% 55%105% 33% 15% 105% 33% 66% 66% 55% 33% 15%15% 105% 0% 15% 105% 105% 66% 66% 85% 66%0% 66% 15% 33% 105% 0% 85% 85% 0% 15%15% 85% 105% 66% 15% 33% 0% 33% 0% 33%

66% 55% 0% 85% 55% 33% 85% 33% 33% 0%105% 0% 105% 33% 85% 105% 33% 85% 15% 85%105% 33% 55% 105% 105% 66% 85% 105% 85% 0%0% 15% 15% 55% 105% 55% 15% 85% 66% 55%33% 0% 105% 55% 33% 33% 85% 66% 0% 66%105% 105% 85% 105% 33% 55% 0% 0% 33% 85%55% 55% 55% 105% 55% 15% 33% 0% 66% 66%


35/44

Table of Random Load Level continued

Load1

Load2

Load3

Load4

Load5

Load6

Load7

Load8

Load9

Load10

0% 85% 33% 55% 0% 55% 0% 105% 15% 15%0% 85% 15% 33% 0% 85% 105% 105% 105% 105%

33% 33% 55% 66% 15% 0% 55% 105% 55% 85%85% 0% 15% 55% 85% 85% 0% 105% 105% 15%85% 66% 0% 55% 0% 66% 0% 15% 105% 33%66% 85% 0% 55% 85% 55% 0% 85% 0% 66%33% 85% 85% 15% 55% 15% 85% 0% 33% 55%15% 15% 15% 15% 66% 85% 66% 55% 66% 0%0% 66% 66% 15% 85% 105% 85% 105% 66% 33%85% 85% 0% 55% 66% 105% 66% 0% 105% 15%105% 55% 105% 33% 85% 33% 33% 33% 0% 0%105% 66% 85% 66% 55% 85% 55% 85% 33% 55%33% 66% 66% 66% 33% 105% 55% 15% 55% 0%

105% 33% 15% 85% 33% 33% 15% 0% 66% 15%105% 55% 15% 66% 33% 33% 66% 105% 85% 85%66% 55% 85% 55% 15% 33% 15% 105% 105% 85%85% 55% 66% 55% 85% 66% 105% 66% 85% 33%105% 55% 33% 66% 105% 15% 33% 33% 85% 105%66% 55% 66% 55% 0% 85% 85% 85% 33% 85%66% 55% 85% 55% 55% 33% 33% 15% 33% 55%105% 0% 85% 85% 55% 15% 85% 66% 105% 15%


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APPENDIX B

Results for Effect of Load Variability in Configuration A

No.TotalMVA

THDvNo.

TotalMVA

THDvNo.

TotalMVA

THDv

1 22.25 5.23% 41 34.72 4.42% 81 51.66 3.71%2 30.51 4.61% 42 37.50 4.27% 82 40.86 4.13%3 42.90 4.04% 43 32.40 4.57% 83 48.70 3.79%4 57.08 3.49% 44 51.03 3.71% 84 34.95 4.42%5 16.79 5.61% 45 37.51 4.27% 85 42.64 4.03%6 39.92 4.16% 46 41.51 4.08% 86 37.50 4.28%7 46.97 3.87% 47 38.56 4.21% 87 34.84 4.39%8 32.37 4.56% 48 55.35 3.54% 88 53.60 3.62%9 39.29 4.17% 49 32.20 4.53% 89 49.08 3.77%

10 38.92 4.22% 50 44.61 3.95% 90 42.06 4.05%11 45.03 3.98% 51 45.38 3.93% 91 58.46 3.44%

12 38.90 4.22% 52 50.35 3.70% 92 40.96 4.10%13 54.69 3.58% 53 29.83 4.66% 93 33.40 4.48%14 28.84 4.75% 54 46.79 3.86% 94 54.20 3.59%15 55.29 3.56% 55 41.27 4.07% 95 51.04 3.72%16 53.45 3.62% 56 35.89 4.34% 96 59.55 3.41%17 30.92 4.65% 57 38.50 4.23% 97 53.14 3.64%18 43.43 4.04% 58 38.99 4.19% 98 50.64 3.71%19 37.95 4.22% 59 29.38 4.70% 99 40.07 4.15%20 42.62 4.03% 60 30.36 4.63% 100 52.10 3.66%21 24.84 4.98% 61 49.69 3.76%

22 41.74 4.07% 62 42.30 4.04%23 44.65 3.97% 63 45.24 3.92%24 46.89 3.87% 64 47.05 3.84%25 49.01 3.76% 65 36.74 4.28%26 35.85 4.36% 66 58.04 3.46%27 45.37 3.92% 67 39.41 4.18%28 52.69 3.62% 68 45.59 3.91%29 43.65 3.99% 69 44.44 3.93%30 34.65 4.41% 70 53.27 3.63%31 44.90 3.96% 71 34.89 4.39%32 50.80 3.72% 72 30.74 4.65%

33 28.38 4.74% 73 37.39 4.25%34 37.26 4.23% 74 56.50 3.49%35 48.36 3.81% 75 64.22 3.27%36 32.45 4.51% 76 40.03 4.15%37 43.71 4.02% 77 39.35 4.16%38 37.23 4.28% 78 48.84 3.80%39 36.05 4.35% 79 40.49 4.15%40 20.78 5.24% 80 30.04 4.68%


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APPENDIX C

Results for Effect of Load Variability in Configuration A at 2/3 Current Harmonic

No.TotalMVA

THDvNo.

TotalMVA

THDvNo.

TotalMVA

THDv

1 22.25 3.51% 41 34.72 2.94% 81 51.66 2.45%2 30.51 3.09% 42 37.50 2.92% 82 40.86 2.74%3 42.90 2.66% 43 32.40 3.04% 83 48.70 2.57%4 57.08 2.33% 44 51.03 2.51% 84 34.95 2.98%5 16.79 3.74% 45 37.51 2.83% 85 42.64 2.72%6 39.92 2.80% 46 41.51 2.69% 86 37.50 2.84%7 46.97 2.54% 47 38.56 2.84% 87 34.84 2.92%8 32.37 2.97% 48 55.35 2.36% 88 53.60 2.41%9 39.29 2.83% 49 32.20 3.01% 89 49.08 2.52%

10 38.92 2.91% 50 44.61 2.62% 90 42.06 2.76%11 45.03 2.64% 51 45.38 2.63% 91 58.46 2.32%

12 38.90 2.74% 52 50.35 2.47% 92 40.96 2.70%13 54.69 2.37% 53 29.83 3.08% 93 33.40 3.00%14 28.84 3.15% 54 46.79 2.61% 94 54.20 2.43%15 55.29 2.37% 55 41.27 2.76% 95 51.04 2.51%16 53.45 2.43% 56 35.89 2.86% 96 59.55 2.28%17 30.92 3.06% 57 38.50 2.79% 97 53.14 2.45%18 43.43 2.69% 58 38.99 2.90% 98 50.64 2.48%19 37.95 2.84% 59 29.38 3.16% 99 40.07 2.77%20 42.62 2.75% 60 30.36 3.13% 100 52.10 2.45%21 24.84 3.34% 61 49.69 2.53%

22 41.74 2.66% 62 42.30 2.63%23 44.65 2.64% 63 45.24 2.59%24 46.89 2.53% 64 47.05 2.58%25 49.01 2.58% 65 36.74 2.87%26 35.85 2.93% 66 58.04 2.35%27 45.37 2.59% 67 39.41 2.78%28 52.69 2.42% 68 45.59 2.64%29 43.65 2.66% 69 44.44 2.62%30 34.65 2.92% 70 53.27 2.42%31 44.90 2.59% 71 34.89 2.90%32 50.80 2.56% 72 30.74 3.07%

33 28.38 3.15% 73 37.39 2.81%34 37.26 2.76% 74 56.50 2.38%35 48.36 2.54% 75 64.22 2.19%36 32.45 3.02% 76 40.03 2.75%37 43.71 2.68% 77 39.35 2.75%38 37.23 2.89% 78 48.84 2.54%39 36.05 2.87% 79 40.49 2.72%40 20.78 3.38% 80 30.04 3.11%


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APPENDIX D

Results for Effect of Load Variability in Configuration A at 1/3 Current Harmonic

No.TotalMVA

THDvNo.

TotalMVA

THDvNo.

TotalMVA

THDv

1 22.25 1.76% 41 34.72 1.47% 81 51.66 1.23%2 30.51 1.55% 42 37.50 1.46% 82 40.86 1.37%3 42.90 1.33% 43 32.40 1.52% 83 48.70 1.29%4 57.08 1.17% 44 51.03 1.26% 84 34.95 1.49%5 16.79 1.87% 45 37.51 1.42% 85 42.64 1.36%6 39.92 1.40% 46 41.51 1.35% 86 37.50 1.42%7 46.97 1.27% 47 38.56 1.42% 87 34.84 1.46%8 32.37 1.48% 48 55.35 1.18% 88 53.60 1.20%9 39.29 1.42% 49 32.20 1.51% 89 49.08 1.26%

10 38.92 1.45% 50 44.61 1.31% 90 42.06 1.38%11 45.03 1.32% 51 45.38 1.31% 91 58.46 1.16%

12 38.90 1.37% 52 50.35 1.24% 92 40.96 1.35%13 54.69 1.19% 53 29.83 1.54% 93 33.40 1.50%14 28.84 1.58% 54 46.79 1.30% 94 54.20 1.21%15 55.29 1.19% 55 41.27 1.38% 95 51.04 1.26%16 53.45 1.22% 56 35.89 1.43% 96 59.55 1.14%17 30.92 1.53% 57 38.50 1.39% 97 53.14 1.22%18 43.43 1.34% 58 38.99 1.45% 98 50.64 1.24%19 37.95 1.42% 59 29.38 1.58% 99 40.07 1.39%20 42.62 1.38% 60 30.36 1.56% 100 52.10 1.22%21 24.84 1.67% 61 49.69 1.26%

22 41.74 1.33% 62 42.30 1.32%23 44.65 1.32% 63 45.24 1.29%24 46.89 1.27% 64 47.05 1.29%25 49.01 1.29% 65 36.74 1.44%26 35.85 1.47% 66 58.04 1.17%27 45.37 1.29% 67 39.41 1.39%28 52.69 1.21% 68 45.59 1.32%29 43.65 1.33% 69 44.44 1.31%30 34.65 1.46% 70 53.27 1.21%31 44.90 1.29% 71 34.89 1.45%32 50.80 1.28% 72 30.74 1.53%

33 28.38 1.58% 73 37.39 1.40%34 37.26 1.38% 74 56.50 1.19%35 48.36 1.27% 75 64.22 1.09%36 32.45 1.51% 76 40.03 1.37%37 43.71 1.34% 77 39.35 1.38%38 37.23 1.44% 78 48.84 1.27%39 36.05 1.43% 79 40.49 1.36%40 20.78 1.69% 80 30.04 1.55%


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APPENDIX E

Load Variability Results for Configurations A, B and C

TotalMVA

ConfigurationA

THDv

ConfigurationB

THDv

ConfigurationC

THDv22.25 5.23% 4.99% 4.96%30.51 4.61% 4.24% 4.24%42.90 4.04% 3.63% 3.70%57.08 3.49% 3.16% 3.17%16.79 5.61% 5.35% 5.37%39.92 4.16% 3.83% 3.82%46.97 3.87% 3.53% 3.55%32.37 4.56% 4.24% 4.22%39.29 4.17% 3.80% 3.85%38.92 4.22% 3.87% 3.92%

45.03 3.98% 3.65% 3.67%38.90 4.22% 3.88% 3.89%54.69 3.58% 3.23% 3.26%28.84 4.75% 4.43% 4.41%55.29 3.56% 3.22% 3.25%53.45 3.62% 3.27% 3.31%30.92 4.65% 4.34% 4.33%43.43 4.04% 3.73% 3.71%37.95 4.22% 3.85% 3.89%42.62 4.03% 3.65% 3.71%

24.84 4.98% 4.65% 4.64%41.74 4.07% 3.70% 3.76%44.65 3.97% 3.62% 3.66%46.89 3.87% 3.52% 3.54%49.01 3.76% 3.39% 3.47%35.85 4.36% 4.00% 4.07%45.37 3.92% 3.57% 3.57%52.69 3.62% 3.25% 3.31%43.65 3.99% 3.65% 3.61%34.65 4.41% 4.03% 4.09%44.90 3.96% 3.62% 3.63%

50.80 3.72% 3.37% 3.42%28.38 4.74% 4.38% 4.40%37.26 4.23% 3.84% 3.87%48.36 3.81% 3.47% 3.46%32.45 4.51% 4.14% 4.19%43.71 4.02% 3.68% 3.73%37.23 4.28% 3.93% 3.97%36.05 4.35% 4.00% 4.03%


40/44

THDv Simulation Results for Three Different Configurations continued

TotalMVA

ConfigurationA

THDv

ConfigurationB

THDv

ConfigurationC

THDv

20.78 5.24% 4.90% 4.92%

34.72 4.42% 4.08% 4.11%37.50 4.27% 3.90% 3.95%32.40 4.57% 4.24% 4.27%51.03 3.71% 3.32% 3.44%37.51 4.27% 3.93% 3.89%41.51 4.08% 3.73% 3.76%38.56 4.21% 3.84% 3.89%55.35 3.54% 3.18% 3.24%32.20 4.53% 4.17% 4.21%44.61 3.95% 3.57% 3.63%45.38 3.93% 3.55% 3.64%

50.35 3.70% 3.32% 3.38%29.83 4.66% 4.31% 4.31%46.79 3.86% 3.51% 3.52%41.27 4.07% 3.68% 3.74%35.89 4.34% 4.00% 3.95%38.50 4.23% 3.91% 3.86%38.99 4.19% 3.82% 3.89%29.38 4.70% 4.35% 4.38%30.36 4.63% 4.29% 4.29%49.69 3.76% 3.40% 3.47%

42.30 4.04% 3.67% 3.71%45.24 3.92% 3.54% 3.60%47.05 3.84% 3.48% 3.53%36.74 4.28% 3.90% 3.97%58.04 3.46% 3.11% 3.15%39.41 4.18% 3.84% 3.84%45.59 3.91% 3.56% 3.57%44.44 3.93% 3.55% 3.62%53.27 3.63% 3.30% 3.29%34.89 4.39% 4.03% 4.05%30.74 4.65% 4.30% 4.36%

37.39 4.25% 3.88% 3.93%56.50 3.49% 3.14% 3.19%64.22 3.27% 2.93% 2.99%40.03 4.15% 3.82% 3.80%39.35 4.16% 3.80% 3.81%48.84 3.80% 3.43% 3.53%40.49 4.15% 3.79% 3.84%30.04 4.68% 4.34% 4.35%


41/44

THDv Simulation Results for Three Different Configurations continued

TotalMVA

ConfigurationA

THDv

ConfigurationB

THDv

ConfigurationC

THDv

51.66 3.71% 3.40% 3.32%

40.86 4.13% 3.80% 3.78%48.70 3.79% 3.43% 3.45%34.95 4.42% 4.07% 4.11%42.64 4.03% 3.67% 3.71%37.50 4.28% 3.92% 3.96%34.84 4.39% 4.02% 4.02%53.60 3.62% 3.28% 3.27%49.08 3.77% 3.40% 3.46%42.06 4.05% 3.66% 3.78%58.46 3.44% 3.08% 3.15%40.96 4.10% 3.73% 3.78%

33.40 4.48% 4.11% 4.18%54.20 3.59% 3.26% 3.27%51.04 3.72% 3.40% 3.40%59.55 3.41% 3.07% 3.11%53.14 3.64% 3.29% 3.33%50.64 3.71% 3.36% 3.37%40.07 4.15% 3.79% 3.85%52.10 3.66% 3.31% 3.35%


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APPENDIX F

Difference in Network Branch Load and Difference In THDv BetweenConfiguration B and C

Branch 1

Branch 2(MVA)

Configuration

BTHDv

Configuration

CTHDv

Difference in

THDv

-5.87 4.99% 4.96% 0.02%-12.36 4.24% 4.24% 0.00%-5.35 3.63% 3.70% -0.07%-0.58 3.16% 3.17% -0.02%3.47 5.35% 5.37% -0.02%-7.92 3.83% 3.82% 0.01%1.28 3.53% 3.55% -0.02%-7.11 4.24% 4.22% 0.02%-1.29 3.80% 3.85% -0.05%

8.67 3.87% 3.92% -0.06%9.98 3.65% 3.67% -0.02%7.37 3.88% 3.89% -0.01%5.14 3.23% 3.26% -0.03%-4.89 4.43% 4.41% 0.02%-3.78 3.22% 3.25% -0.03%6.40 3.27% 3.31% -0.05%-3.08 4.34% 4.33% 0.01%-3.73 3.73% 3.71% 0.02%4.74 3.85% 3.89% -0.04%

-2.90 3.65% 3.71% -0.07%-9.39 4.65% 4.64% 0.01%10.11 3.70% 3.76% -0.06%2.22 3.62% 3.66% -0.04%5.01 3.52% 3.54% -0.02%8.64 3.39% 3.47% -0.08%

10.35 4.00% 4.07% -0.07%-9.97 3.57% 3.57% 0.00%3.24 3.25% 3.31% -0.05%

-23.85 3.65% 3.61% 0.04%7.37 4.03% 4.09% -0.06%

-4.85 3.62% 3.63% -0.01%0.57 3.37% 3.42% -0.05%0.33 4.38% 4.40% -0.02%-1.51 3.84% 3.87% -0.03%-14.70 3.47% 3.46% 0.02%-0.44 4.14% 4.19% -0.04%7.66 3.68% 3.73% -0.05%8.68 3.93% 3.97% -0.04%-1.73 4.00% 4.03% -0.03%


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Difference in Network Branch Load and Difference In THDv BetweenConfiguration B and C... continued

TotalMVA

ConfigurationB

THDv

ConfigurationC

THDv

Difference inTHDv

3.01 4.90% 4.92% -0.01%5.24 4.08% 4.11% -0.04%0.31 3.90% 3.95% -0.04%9.00 4.24% 4.27% -0.03%

21.18 3.32% 3.44% -0.12%-21.04 3.93% 3.89% 0.04%2.06 3.73% 3.76% -0.03%3.34 3.84% 3.89% -0.05%-0.95 3.18% 3.24% -0.05%7.69 4.17% 4.21% -0.04%

10.56 3.57% 3.63% -0.06%

18.43 3.55% 3.64% -0.09%0.12 3.32% 3.38% -0.07%4.93 4.31% 4.31% -0.01%-8.08 3.51% 3.52% -0.01%-1.19 3.68% 3.74% -0.05%-21.55 4.00% 3.95% 0.04%-15.41 3.91% 3.86% 0.05%5.52 3.82% 3.89% -0.07%4.41 4.35% 4.38% -0.03%-5.94 4.29% 4.29% 0.00%

13.92 3.40% 3.47% -0.07%8.16 3.67% 3.71% -0.04%12.72 3.54% 3.60% -0.06%7.51 3.48% 3.53% -0.05%4.55 3.90% 3.97% -0.06%2.27 3.11% 3.15% -0.04%0.16 3.84% 3.84% -0.01%-1.69 3.56% 3.57% -0.01%4.17 3.55% 3.62% -0.07%

-11.57 3.30% 3.29% 0.01%3.04 4.03% 4.05% -0.01%

13.91 4.30% 4.36% -0.06%6.30 3.88% 3.93% -0.05%1.87 3.14% 3.19% -0.05%5.19 2.93% 2.99% -0.06%-6.68 3.82% 3.80% 0.02%-1.98 3.80% 3.81% -0.01%21.76 3.43% 3.53% -0.10%12.71 3.79% 3.84% -0.04%


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Difference in Network Branch Load and Difference In THDv BetweenConfiguration B and C continued

TotalMVA

ConfigurationB

THDv

ConfigurationC

THDv

Difference inTHDv

-4.31 4.34% 4.35% -0.01%-31.89 3.40% 3.32% 0.07%-8.60 3.80% 3.78% 0.02%-5.45 3.43% 3.45% -0.02%-1.20 4.07% 4.11% -0.03%7.35 3.67% 3.71% -0.05%8.22 3.92% 3.96% -0.04%

-12.04 4.02% 4.02% 0.01%-14.04 3.28% 3.27% 0.01%0.72 3.40% 3.46% -0.05%

24.57 3.66% 3.78% -0.12%

5.23 3.08% 3.15% -0.07%1.61 3.73% 3.78% -0.05%

12.40 4.11% 4.18% -0.07%-7.76 3.26% 3.27% -0.01%-5.95 3.40% 3.40% 0.00%0.11 3.07% 3.11% -0.04%

10.59 3.29% 3.33% -0.04%-11.59 3.36% 3.37% -0.01%13.02 3.79% 3.85% -0.06%4.36 3.31% 3.35% -0.05%

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