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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.
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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
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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
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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%
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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%
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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%
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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%
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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%
8/7/2019 example of thesis format
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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%
8/7/2019 example of thesis format
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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%