FREQUENCY VARIATIONS MEASUREMENT TECHNIQUES IN POWER
QUALITY MONITORING
TERENCE WOOD
A project report submitted in partial fulfillment of the
requirements for the award of the degree of
Master of Engineering (Electrical-Power)
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
MAY 2008
iii
To my beloved fiancée
iv
ACKNOWLEDGEMENTS
In preparing this thesis, I was in contact with various people who whether
directly or indirectly contributed in making this project successful and enhancing my
knowledge and understanding. In particular, I would like to thank my supervisor
Associate Professor Dr. Mohd Wazir Mustafa for his guidance and support.
My fiancée should also be recognized for her continuous motivation and help
on various occasions.
v
ABSTRACT
Power quality is a term used to describe electric power that motivates an
electrical load and the load's ability to function properly with that electric power.
Without the proper power, an electrical device load may malfunction, fail
prematurely or not operate at all. There are many ways in which electric power can
be of poor quality and many more causes of such poor quality power. The aim of
this thesis is to study measurement techniques available in monitoring power system
frequency particularly using the Least Square Error (LSE) method and neural
network approach (ADALINE).
The algorithms for the various measurement
methods in this thesis were implemented using MATLAB. Results concluded that
the neural network approach (ADALINE) is much better for frequency
approximation although the LES algorithm provides an easier measurement method.
The LES technique was found to be not accurate in the presence of noise and
harmonics. Further studies could be done on recursive LES which may compensate
the drawbacks of non-recursive LES algorithm which was studied in this work.
vi
ABSTRAK
Kualiti kuasa membawa maksud kuasa elektrik yang membolehkan muatan
elektrik berfungsi dengan sempurna. Tanpa kuasa elektrik, muatan elektrik mungkin
tidak akan befungsi dengan sempurna, rosak sebelum tamat tempoh hayatnya atau
langsung tidak dapat beroperasi. Terdapat banyak sebab yang menyebabkan kualiti
kuasa eletrik menjadi rendah. Tujuan utama tesis ini adalah untuk mengkaji kaedahkaedah menentukan frekuensi sistem kuasa terutamanya menggunakan teknik Least
Square Error (LSE) dan neural network approach (ADALINE). Algoritma untuk
kaedah tersebut telah dilaksanakan menggunakan MATLAB.
Keputusan yang
diperolehi menunjukkan bahawa neural network approach (ADALINE) lebih sesuai
unuk menganggarkan frekuensi meskipun kaedah LES lebih mudah diukur. Kaedah
LES didapati kurang tepat disebabakan mudah terganggu dengan kebisingan dan
harmonik. Kajian seterusnya dapat dilakukan terhadap recursive LES yang mungkin
dapat mengatasi kelemahan dalam non-recursive LES yang telah digunakan dalam
kerja ini.
vii
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
TITLE PAGE
i
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xi
LIST OF ABBREVIATIONS
xiii
LIST OF APPENDICES
xiv
INTRODUCTION
1
1.1 Introduction
1
1.2 Problem Statement
2
1.3 Objectives
3
1.4 Scope of Work
3
1.5 Thesis Organization
4
POWER QUALITY ISSUES
5
2.1 Introduction
5
2.2 Effects of Power Quality to Industrial Users
6
2.3 Common Power Quality Problems
7
2.3.1 Transients
9
viii
3
2.3.2 Voltage Sag and Momentary Interruptions
10
2.3.3 Harmonic Distortion
11
2.3.4 Voltage Fluctuation
13
2.3.5 Power Quality Variation
14
2.4 Identifying Power Quality Problems
15
2.5 Possible Solutions to Power Quality
17
2.6 Summary
19
FREQUENCY VARIATION IN POWER QUALITY
20
3.1 Introduction
20
3.2 The Need for Digital Techniques
23
3.3 Power Quality Monitoring Digital Techniques
23
3.4 Power Quality Monitoring under the Effect of Harmonics 25
4
3.5 Power Quality Monitoring under the Effect of Noise
26
3.6 Least Error Square (LES)
27
3.7 New Numeric Method
31
3.7.1 Direct and Iterative Method
32
3.7.2 Generation and Propagation
33
3.7.3 Interpolation, Extrapolation and Regression
36
3.7.4 Optimization
36
3.8 Adaptive Linear Neuron (ADALINE)
37
3.9 MATLAB
41
3.10 Sumary
42
FREQUENCY MEASUREMENT ALGORITHM
44
4.1 Introduction
44
4.2 Implementation
45
4.3 Least Error Square (LES) Technique for Frequency
Variation
45
4.4 Method of Investigation for ADALINE
46
4.5 Flow Chart of Work Flow Implementation
47
4.6 Summary
50
ix
5
RESULTS AND DISCUSSION
51
5.1 Introduction
51
5.2 Least Error Square (LES) Method
52
5.2.1 Least Error Square (LES) Without any Distortion
52
5.2.2 Least Error Square (LES) With Presence of
54
Harmonics
5.2.3 Least Error Square (LES) With Presence of Noise
6
54
55
5.3 Numerical Technique
56
5.4 Adaptive Linear Network (ADALINE)
57
5.5 Comparison between Various Measurement Techniques
60
5.6 Summary
61
CONCLUSION AND RECOMMENDATIONS
62
6.1 Conclusion
62
6.2 Recommendations
63
REFERENCES
Appendices A-E
64
67-79
x
LIST OF TABLES
TABLE NO .
3.1
TITLE
Babylonian Method vs. Method X
PAGE
35
xi
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
2.1
Voltage Sag Waveform
10
2.2
Voltage Flicker caused by Arc Furnace Operation
14
3.1
A Circuit Representing a Simple Power System
21
3.2
Basic Components in Modern Power Quality Monitoring
System
24
3.3
Data Acquisition Subsystem Basic Components
24
3.4
Effect of Harmonic Distortion to Voltage Signal
26
3.5
Noise and Frequency Variation Effects on Voltage Signal
27
3.6
Discrete-Time LTI System
28
3.7
Sampling of Voltage Signal
31
3.8
Learning inside a Single Layer ADALINE
37
3.9
Adaptive Linear Network (ADALINE)
39
4.1(a)
Flow Chart of Work
48
4.1(b)
Flow Chart of Work
49
5.1
Effect of Variation of Frequency to Estimated Frequency
Using LES Algorithm
5.2
Effect of Harmonics Magnitude Change to the Measured Frequency
using LES algorithm
5.3
53
54
Error of Frequency Deviations Corresponding to the
Change in its Signal-to-Noise Ratio
55
5.4
The Training of the Network to Minimize the Error
57
5.5
Training of the Network to Measure Frequency when there is
Variation of 0.5 Hz.
5.6
58
Training of the Network for Variation of 3.0 Hz in Frequency 59
xii
5.7
The Effect of Variation of Frequency to the Frequency
Measured using ADALINE
60
xiii
LIST OF ABBREVIATIONS
AC
-
Actuating Current
ADALINE
-
Adaptive Linear Neuron
ADC
-
Analogue-to Digital Converter
DAS
-
Data Acquisition Subsystem
DC
-
Direct Current
DFT
-
Discrete Fourier Transform
LES
-
Least Error Square
LMS
-
Least Mean Square
MATLAB
-
Matrix Laboratory
PCC
-
Points of Common Coupling
PQ
-
Power Quality
xiv
LIST OF APPENDICES
APPENDIX
A
TITLE
MATLAB Code for Least Error Square Frequency
Estimation Analysis
B
72
MATLAB Code for Numerical Method Frequency
Estimation Analysis
E
69
MATLAB Code for Least Error Square Frequency
Estimation with Noise Analysis
D
67
MATLAB Code for Least Error Square Frequency
Estimation with Harmonics Analysis
C
PAGE
74
MATLAB Code for ADALINE Network Frequency
Estimation Analysis
76
CHAPTER 1
INTRODUCTION
1.1
Introduction
Power quality is the electrical power that enables an electrical load to
function. The electric power industry is in the business of electricity generation (AC
power), electric power transmission and ultimately electricity distribution to a point
often located near the electricity meter of the end user of the electric power. The
electricity then moves through the distribution and wiring system of the end user
until it reaches the load. The complexity of the system to move electric energy from
the point of production to the point of consumption combined with variations in
weather, electricity demand and other factors provide many opportunities for the
quality of power delivered to be compromised.
While "power quality" is a convenient term for many, it is actually the quality
of the voltage, rather than power or electric current that is the actual topic described
by the term. Power is simply the flow of energy and the current demanded by a load
is largely uncontrollable.
2
In recent years, power quality has become an important issue and is receiving
increasing attention by utility, facility and consulting engineers. Today’s modern
commercial and industrial facilities are installed with many electronics equipment
and devices such as digital computer, power electronics devices and automated
equipment that are sensitive to many types of power disturbances.
Power
disturbances such as the harmonics currents injected to the system arising within
customer facilities have increased significantly due to the increasing use of energy
efficient equipment [1]. Examples of these equipments are switch-mode power
supplies, inverters for variables speed drives, etc. Therefore, the monitoring and data
collection activities for power quality study have to be conducted at the users’
premises in order to locate the source of disturbances.
1.2
Problem Statement
This work deals with the power quality problems caused by frequency
variation. A frequency variation involves a change in frequency from the normally
stable utility frequency of 50 or 60 Hz, depending on the geographic location. This
may be caused by erratic operation of emergency generators or unstable frequency
power sources. For sensitive equipment, the results can be data loss, program failure,
equipment lock-up or complete shut down. To minimize frequency measurement
errors, a very accurate measurement technique needs to be implemented on the
related system to monitor the power quality. The challenge is to obtain a robust
measurement technique that can precisely capture the true system distortion even in
the presence of fast frequency variations, harmonics and noise [2]. From the results
obtained, a suitable solution such as voltage regulators and power conditioners can
be designed.
3
1.3
Objectives
The ultimate goals of this thesis are :
i.
To study issues related to power quality and possible solutions.
ii.
To study and evaluate various frequency variation measurement techniques
and its application.
iii.
To model, develop and test the effectiveness of frequency variation.
measurement techniques available namely the Least Error Square, numerical,
and ADALINE methods.
iv.
To analyze and compare the performance of the three techniques studied.
v.
To enhance the techniques used for future improvement and possible
industrial application.
1.4
Scope of Work
Power quality monitoring involves several factors such as voltage, current
and frequency effects on the overall power quality. The scope of work for this
project only concentrates on power frequency variations measurement techniques.
This project incorporates the software implementation where various
frequencies and their effects on power quality are studied for LES, numerical and
ADALINE techniques. The development done for the software section involves
simulations and analysis of the results obtained using the MATLAB software.
4
As this project focuses solely on software implementation, nevertheless a
brief literature research of a possible hardware implementation is also included in
Chapter 3.
1.5
Thesis Organization
The body of this report consists of six chapters. After this introductory
Chapter 1, the following Chapter 2 will discuss in detail on power quality issues, its
applications and challenges. Chapter 3 will elaborate on the frequency variation
measurement techniques for power quality monitoring studied for this scope of work
particularly the LES, numerical and ADALINE methods. Each method will cover
the application using digital technique, the effects of harmonics and noise.
Chapter 4 will present the detailed equations and mathematical algorithms
and parameters used for LES, numerical and ADALINE techniques. The equations
used are inclusive of the basic measurement without distortion, measurement under
the effect of noise and measurement under the effect of harmonics. The subsequent
Chapter 5 presents the graphic MATLAB results for each equation or algorithm
generated in the previous chapter. The results and comparisons are also discussed.
Chapter 6 is the final chapter which consists of the conclusion and
recommendations of this study. The last sector of this thesis includes the references
used and appendices on the MATBLAB source codes for each algorithm mentioned
in Chapter 4 and Chapter 5.
CHAPTER 2
POWER QUALITY ISSUES
2.1
Introduction
Power Quality (PQ) has become increasingly important for industrial and
commercial electric power customers, particularly as today’s manufacturing and
control processes rely on computerized equipment which is sensitive to power
system interruptions and disturbances. Power Quality is simply the characteristic of
the energy or electrical supply by the utility such as Tenaga Nasional Berhad (TNB)
which might affect the load (electrical equipments that are connected for an electrical
supply) or vise versa [1].
Power quality issues have in recent years received an increasing attention
both by the end users and utilities alike. This chapter aims to elaborate power quality
issues and the impact it may have to the users and utilities as utilities are bound in
most cases to a pre-determined quality supply agreement.
6
2.2
Effects of Power Quality to Industrial Users
Electrical power is perhaps the most essential raw material used by commerce
and industry today. It is an unusual commodity because it is required as a continuous
flow - it cannot be conveniently stored in quantity - and it cannot be subject to
quality assurance checks before it is used. It is, in fact, the epitome of the ‘Just in
Time’ philosophy in which components are delivered to a production line at the point
and time of use by a trusted and approved supplier with no requirement for ‘goods
in’ inspection. Thus, it is necessary for end customer to have good control of the
onwards supply component specification.
The reliability of the supply must be known and the resilience of the process
to variations must be understood. In reality, of course, electricity is very different
from any other product – it is generated far from the point of use, is fed to the grid
together with the output of many other generators and arrives at the point of use via
several transformers and many kilometres of overhead and possibly underground
cabling. Where the industry has been privatized, these network assets will be owned,
managed and maintained by a number of different organizations.
Assuring the
quality of delivered power at the point of use is no easy task – and there is no way
that sub-standard electricity can be withdrawn from the supply chain or rejected by
the customer.
From the consumers’ point of view the problem is even more difficult. There
are some limited statistics available on the quality of delivered power, but the
acceptable quality level as perceived by the supplier (and the industry regulator) may
be very different from that required, or perhaps desired, by the consumer. The most
obvious power defects are complete interruption (which may last from a few seconds
to several hours) and voltage dips or sags where the voltage drops to a lower value
for a short duration. Naturally, long power interruptions are a problem for all users,
but many operations are very sensitive to even very short interruptions. Examples of
sensitive operation are [2] :
7
i.
Continuous process operations, where short interruptions can disrupt the
synchronisation of the machinery and result in large volumes of semiprocessed product. A typical example is the paper making industry where the
clean-up operation is long and expensive.
ii.
Multi-stage batch operations, where an interruption during one process can
destroy the value of previous operations. An example of this type is the
semiconductor industry, where the production of a wafer requires a few
dozen processes over several days and the failure of a single process is
catastrophic.
iii.
Data processing, where the value of the transaction is high but the cost of
processing is low, such as share and foreign exchange dealing. The inability
to trade can result in large losses that far exceed the cost of the operation
These are examples of the most sensitive industries, but it is surprising how
many apparently mundane operations have quite critical power supply requirements.
Examples include large retail units with computerized point of sale and stock control
equipment and manufacturing plant with distributed control.
2.3
Common Power Quality Problems
So, what do we mean by ‘power quality’? A perfect power supply would be
one that is always available, always within voltage and frequency tolerances, and has
a pure noise free sinusoidal wave shape.[3] Just how much deviation from perfection
can be tolerated depends on the user’s application, the type of equipment installed
and his view of his requirements.
8
Power quality defects – the deviations from perfection – fall into six
categories:
i.
Voltage Fluctuation (flicker)
ii.
Harmonic Distortion
iii.
Power Frequency Variation
iv.
Under or Over voltage
v.
Voltage Dips (or sags) and Surges
vi.
Transients
Each of these power quality problems has a different cause. Some problems
are a result of the shared infrastructure. For example, a fault on the network may
cause a dip that will affect some customers and the higher the level of the fault, the
greater the number affected, or a problem on one customer’s site may cause a
transient that affects all other customers on the same subsystem. Other problems,
such as harmonics, arise within the customer’s own installation and may or may not
propagate onto the network and so affect other customers. Harmonic problems can
be dealt with by a combination of good design practice and well proven reduction
equipment [4].
Electricity utilities argue that critical users must bear the costs of ensuring
supply quality themselves rather than expect the supply industry to provide a very
high reliability supply to every customer everywhere on the network [1]. Such a
guaranteed quality supply would require a very substantial investment in additional
network assets for the benefit of relatively few customers (in numerical, not
consumption, terms) and would be uneconomic. It is also doubtful whether it would
be technically feasible within the current social and legal framework in which any
customer is normally entitled to be connected to the supply and utility providers have
the right to excavate roadways with the risk of cable damage. It is therefore a
growing trend that critical industry consumer take steps to ensure that the quality of
power delivered to his process is good enough, with the clear implication that this
9
quality level may well be higher than that delivered to the plant by the utilities.
Section 2.4 will discuss in general individual problem and the available solutions.
2.3.1
Transients
AC and DC drives, along with other electronic loads, can be very sensitive to
transient voltages. The tolerance levels of these devices are often less than other
loads such as standard motors. A major concern for transient voltages occurs with
possible magnification of utility capacitor switching transients at low-voltage
capacitor locations on customer power systems.
Transient disturbances are high frequency events with durations much less
than one cycle of the supply [5]. Causes include switching or lightning strikes on the
network and switching of reactive loads on the consumer’s site or on sites on the
same circuit. Transients can have magnitudes of several thousand volts and so can
cause serious damage to both the installation and the equipment connected to it.
Electricity suppliers and telecommunications companies go to some effort to ensure
that their incoming connections do not allow damaging transients to propagate into
the customers’ premises.
Nevertheless, non-damaging transients can still cause
severe disruption due to data corruption. The generation and influence of transients
is greatly reduced and the efficacy of suppression techniques greatly enhanced where
a good high integrity earthing system has been provided. Such an earthing system
will have multiple ground connections and multiple paths to earth from any point, so
ensuring high integrity and low impedance over a wide frequency band.
10
2.3.2
Voltage Sags and Momentary Interruptions
Voltage sag is widely recognized as one of the most important power quality
disturbances [1]. These can be caused by the utility or by customer loads. When
sourced from the utility, they are most commonly caused by faults on the distribution
system. Voltage sag (Figure 2.1) is a short reduction in rms voltage from nominal
voltage, happened in a short duration, about 10ms to seconds [8], can be single or
three phase . Depending on the design of the distribution system, a ground fault on
one phase can cause a simultaneous swell on another phase . The IEC 61000-4-30
defines the voltage sag (dip) as a temporary reduction of the voltage at a point of the
electrical system below a threshold [3]. According to IEEE Standard 1159-1995,
defines voltage sags as an rms variation with a magnitude between 10% and 90% of
nominal voltage and duration between 0.5 cycles and one minute [4].
Figure 2.1 : Voltage Sag Waveform
Voltage sag normally happens at the feeder adjacent to an unhealthy feeder.
This unhealthy feeder are caused by two factors which are short circuits due to faults
in power system networks and starting motor which draw very high lagging current.
Both of these factors are the main factor creating voltage sag as power quality
problem in power system.
11
Increased sensitivity of power electronic equipment such as programmable
logic controller (PLC), adjustable speed drive (ASD), coupled with the high
likelihood of voltage sags and interruptions, has resulted in these being the most
visible power quality events. Adjustable-speed drives, computers, office equipment,
programmable controllers, and induction heating furnaces can be extremely sensitive
to these events. Typically, sags occur when there are temporary faults on the utility
power system, resulting in a reduction in the voltage level [1]. Equipment sensitivity
to these events is important because nuisance tripping of sensitive industrial loads
can cause equipment downtime, reduce productivity, and hurt your bottom line.
There are many ways in order to mitigate voltage sag problem. One of them
is minimizing short circuits caused by utility directly which can be done such as with
avoid feeder or cable overloading by correct configuration planning.
Another
alternative is using the flexible ac technology (FACTS) devices which have been
used widely in power system nowadays because of the reliability to maintain power
quality condition including voltage sag [7]. There are many devices have been
created with purpose to enhance power quality such as Dynamic Voltage Restorer
(DVR), Distribution Static Compensator (D-STATCOM) and Uninterruptible Power
Supply (UPS). All of these devices are also known as custom power devices.
2.3.3
Harmonics Distortion
Harmonics are distortions in the AC waveform. These distortions are caused
by loads on the electrical system that use the electrical power at a different frequency
than the fundamental 50 or 60 Hz [8]. Adjustable-speed and dc drives, along with
switch-mode power supplies, cause harmonic currents due to their nonlinear
characteristics.
These harmonic currents can combine with system frequency
response characteristics to cause harmonic voltage distortion. This distortion can
cause control malfunction, capacitor failures, motor and transformer overheating, and
12
increased system losses. These problems are compounded by the use of capacitor
banks, which can cause resonance conditions magnifying the harmonic distortion
levels. These banks are normally installed for power factor correction purposes, as
well as to free up transformer capacity.
While the majority of voltage dips and interruptions originate in the
transmission and distribution system and are the responsibility of the supplier,
harmonic problems are almost always the responsibility of the consumer. It is
harmonic currents that cause problems in installations and when these currents flow
back into the supply impedance at the point of common coupling, a harmonic voltage
is developed.
This voltage distortion, or at least some components of it, are
distributed around the system and are combined with the background harmonic
voltage distortion present in any transmission system (due to the non-linearity of
transformers for example) [7].
In general harmonics cause magnetic portions of the electrical system to
overheat. Such as transformers, line reactors, magnetic relays and power factor
capacitors. The affect of harmonics on loads varies a great deal and is dependent on
the load itself.
Most loads are not affected by moderate levels of harmonics.
Exceptions to this are loads that perform electrical measurements in the frequency
domain of the harmonics. By limiting the harmonic current consumers are permitted
to draw, the level of voltage distortion on the supply is kept within acceptable limits.
Most national limits are based on the IEEE's Std. 519 [5] which specifies strict
current distortion limits that can prove difficult to comply with. Other standards
available are the UK electrical supply industry standard, (currently G5/4) which
originated as G5/1. This planning standard established arbitrary voltage distortion
limits.
Determining the source of harmonic distortion can be difficult and this often
leads to consumers blaming the supplier for the problem. In fact, it is unusual for
13
harmonic problems within an installation to arise from external causes – the cause is
almost always due to the equipment on site and the installation practice used [1].
2.3.4
Voltage Fluctuation
Voltage fluctuations are systematic variations of the voltage envelope or a
series of random voltage changes, the magnitude of which does not normally exceed
the voltage ranges specified by ANSI C84.1 of 0.9 pu to 1.1 pu [2]. IEC 555-3
defines various types of voltage fluctuations [2]. For this project, the discussion here
to IEC 555-3 Type (d) voltage fluctuations, which are characterized as a series of
random or continuous voltage fluctuations.
Loads which can exhibit continuous, rapid variations in the load current
magnitude can cause voltage variations that are often referred to as flicker [5]. The
term flicker is derived from the impact of the voltage fluctuation on lamps such that
they are perceived to flicker by the human eye. To be technically correct, voltage
fluctuation is an electromagnetic phenomenon while flicker is an undesirable result
of the voltage fluctuation in some loads. However, the two terms are often linked
together in standards. Therefore, the common term voltage flicker is used to describe
such voltage fluctuations.
An example of a voltage waveform which produces
flicker is shown in Figure 2.2 [6].
14
Figure 2.2 : Voltage Flicker caused by Arc Furnace Operation
This is caused by an arc furnace, one of the most common causes of voltage
fluctuations on utility transmission and distribution systems [1]. The flicker signal is
defined by its rms magnitude expressed as a percent of the fundamental. Voltage
flicker is measured with respect to the sensitivity of the human eye. Typically,
magnitudes as low as 0.5% can result in perceptible lamp flicker if the frequencies
are in the range of 6-8 Hz [4].
2.3.5
Power Frequency Variation
Power Frequency Variations are defined as the deviation of the power system
fundamental frequency from it specified nominal value (e.g. 50 Hz or 60 Hz). The
power system frequency is directly related to the rotational speed of the generators
supplying the system [8]. There are slight variations in frequency as the dynamic
balance between load and generation changes. The size of the frequency shift and its
duration depends on the load characteristics and the response of the generation
15
control system to load changes. Frequency variations that go outside of accepted
limits for normal steady state operation of the power system can be caused by faults
on the bulk power transmission system, a large block of load being disconnected, or
a large source of generation going off-line [6].
On modern interconnected power systems, significant frequency variations
are rare. Frequency variations of consequence are much more likely to occur for
loads that are supplied by a generator isolated from the utility system. In such cases,
governor response to abrupt load changes may not be adequate to regulate within the
narrow bandwidth required by frequency- sensitive equipment.
Voltage notching can sometimes be mistaken for frequency deviation. The
notches may come sufficiently close to zero to cause errors in instruments and
control systems that rely on zero crossings to derive frequency or time.
2.4
Identifying Power Quality Problems
Power quality monitoring has become an important issue for electric utilities
and their customers. Customers, in particular, have become less tolerant of power
quality disturbances because these disturbances degrade the performance and
efficiency of customer loads, especially power electronic loads and semiconductor
manufacturing plants. In order to improve the quality of power, PQ monitoring has
become essential and with the advances in signal analysis, new methodologies are
being considered. It requires specialty, measurement equipment to measure, record
and diagnosis harmonic problems. Because most equipment does not specify what
level of power quality is required.
16
Though the power quality issues is subjectively dependent on the facilities,
specific issues have to be looked into to determine a specific solutions such as [8] :
i.
Harmonic analysis
ii.
Utility capacitor switching activities
iii.
Voltage variation analysis
iv.
Power factor correction
Consultants also use a wide range of techniques and tools to find, study, and
correct power quality problems.
Monitoring and field measurements are a key
element in the problem-solving process.
A combination of fixed and portable
monitoring instruments is normally used to detect and analyze disturbances on both
the utility and customer end, as well as at key process points and other locations.
This monitoring helps to locate where problems are occurring, and determine their
potential cause(s) and solution(s).
Computer simulations are also used to model the power system and key
connection points - utility service entrance, major systems, and backup systems.
These simulations can help to perform analyses to determine power system
vulnerability and identify potential problems, as well as possible solutions. Models
are verified against the measurement results.
The wide range of corrective measures available will be briefly discussed in the
following section, including providing a range of cost-effective options for
mitigation such as [8] :
i.
Harmonic filters
ii.
Capacitors
iii.
Surge arrestors or protectors
iv.
Increased line insulation
v.
Uninterruptible power supplies (UPS)
17
vi.
Superconducting Magnetic Energy Storage (SMES)
vii.
Backup generation
In this research, time-frequency analysis techniques namely LES, ADALINE,
and Neural Network approach are studies in obtaining the time-frequency features of
power quality disturbances. The Neural network approach features combined with
fuzzy rule-based classifier and simple pattern recognition technique is found to be
effective in detection and classification of various power quality disturbances under
noise as well as under harmonic distortion.
2.5
Possible Solutions to Power Quality
There are a variety of engineering solutions available to eliminate or reduce
the effects of supply quality problems and it is a very active area of innovation and
development. As such, one need to be aware of the range of solutions available and
the relative merits and costs.
Users are faced with the need to make design investment decisions about the
type and quantity of additional plant required to achieve the quality of supply
required. Unfortunately, some vital information is missing – the extent and severity
of power quality problems likely to be experienced in any particular location is
largely unknown. Because there are so few published statistics it is very difficult for
consumers to quantify the cost of failure and justify the cost of preventative measures
[1].
The issue of short interruptions and voltage dips highlights the difference in
perspective between supplier and customer. They are by definition short term events
18
so that unless there is a permanent monitor installed the very existence of the event is
difficult to prove. It is even more difficult to attribute a business loss to a particular
event. The electricity supply industry tends to value an interruption in terms of the
cost of the electricity that was not supplied as a result, while the consumer values it
in terms of the revenue lost as a consequence of the break in production. Electricity
is relatively cheap and the supply interruption relatively short, while lost production
can be very valuable (as in the case of semiconductors) and the downtime very long
to allow for clean up (as in the paper making industry). The two parties therefore
have completely different views of the importance of voltage dips and on the level of
investment in reduction equipment that is justified.
Longer interruptions – power cuts – are usually thought of as being caused by
the supplier but can also be caused by the failure of on-site equipment, conductors
and connections. Careful design using high resilience techniques can minimise the
effects. The objective is to identify single points of failure and eliminate them by
providing redundant equipment or alternative supply paths so that operation can
continue despite a single failure [7]. Systems designed in this way are easier to
maintain and are better maintained as a result. It is important that maintenance
procedures are developed at an early stage as part of the resilient design concept.
Standby generation and UPS systems, required to cover short and longer term power
cuts are essential elements of a resilient system.
Power quality problems present designers with many questions, perhaps the
greatest of which is, ‘How good is good enough?’. This question is impossible to
answer. While it is relatively simple to quantify the behavior of a particular piece of
equipment to voltage dips, determining the likely incidence of voltage dips at a
particular location on the supply system is rather more difficult; it will change over
time as new consumers are added and assets replaced. It is extremely difficult to
collect any meaningful data on the sensitivity of equipment to harmonic voltage
distortion, and even on the harmonic current distortion caused by equipment. The
real question is one of compatibility between the equipment and the supply [8].
19
There are some international standards available that set limits of voltage
variation and harmonic voltage distortion below which equipment should function
without error. Similarly, there are standard limits for voltage deviation and harmonic
voltage distortion of the supply. Ideally, there should be a guard band – a safety
margin between the two [8].
2.6
Summary
To overcome the negative impact of poor power quality on equipment and
businesses, suitable power quality equipment can be invested. Identifying the right
solution remains the first step.
Many power quality problems are easily identified once a good description of
the problems is obtained. Unfortunately, the tensions caused by power problems
often result in vague or overly dramatic descriptions of the problem. A power
quality audit can help determine the causes of your problems and provide a welldesigned plan to correct them [4]. The power quality audit checks the facility's
wiring and grounding to ensure that it is adequate for your applications and up to
code. The auditor normally will check the quality of the AC voltage itself, and
consider the impact of the utility's power system.
Many businesses and organizations rely on computer systems and other
electrical equipment to carry out mission-critical functions, but they aren't
safeguarding against the dangers of an unreliable power supply. It is time utilities as
well as businesses engage in more proactive approach to power quality treats by
engaging in power quality analysis.
CHAPTER 3
FREQUENCY VARIATION IN POWER QUALITY
3.1`
Introduction
Power frequency variations and the effects of its variations are defined as the
deviation of the power system fundamental frequency from its specified nominal
value which is usually 50 Hz or 60 Hz. In Malaysia, the nominal power frequency is
50 Hz [1].
Power system frequency is directly related to the rotational speed of the
generators supplying the system. There are slight variations in the frequency as the
dynamic balance between the load and generation changes.
The size of the
frequency shift and its duration depends on the load characteristics and the response
of the generation control system to load changes. Frequency variations that go
beyond acceptable limits for normal steady-state operation of the power system can
be caused by faults on the bulk power transmission system, a large block of load
being disconnected, or a large source of generation going offline [3].
21
Figure 3.1 shows the circuit of a simple power system. Based on the circuit,
a comprehensive formula [9] is developed to show the correlation between power
and frequency.
Figure 3.1: A circuit representing a simple power system
From the model above, considering an RL-circuit the impedence could be derived as
(3.2). Hence the corresponding line current is given (3.3).
(3.1)
(3.2)
(3.3)
(3.4)
(3.5)
(3.6)
By considering the phase angle (3.4), the line power is described as (3.6)
22
(3.7)
(3.8)
(3.9)
From the formula derivation, it can be seen that if frequency decreases, power
consumed by the load increases and vice versa. For a small variation in frequency,
there will be large change in power consumed by the load. Hence, this will cause
dysfunctions of the consumer’s equipment.
3.2
The Need for Digital Techniques
Variations in frequency must be monitored accurately for optimum operation
of power systems. Variations in frequency are an indication of unexpected fault or
transient disturbances, starting motor, heavy load, transformer inrush current etc.
Permissible variation in frequency must be within the limit of +/- 3Hz only
[6]. Beyond the permissible value, frequency relays will take care of the system such
as trip the system and power will not be supplied beyond the limit.
23
Consumers and electric provider companies have agreed with the permissible
value of frequency.
If that limit is exceeded, this might cause failure to the
equipment. Reliable frequency measurement is a prerequisite for effective power
control, load-shedding, load restoration and generator protection.
With the
advancement in microprocessor technology, monitoring power system frequency is
becoming more accurate.
Such digital techniques for programming the
microprocessor frequency relays are Discrete Fourier Transform (DFT), Least Error
Square (LES) technique, recursive Least Error Square, Kalman filtering, extended
complex Kalman filtering, recursive Newton type algorithm, numerical technique
and many more.
3.3
Power Quality Monitoring using Digital Techniques
Power quality monitoring involves the capturing and processing of voltage
and current signals at various points of the power system. The signals to be captured
are normally of high voltage and current levels and thus require large transformation
ratios before they can be processed by the instruments. The voltage at which the
signals are measured is at 110V or 120V and 5A or 1A for current signals [5].
Basically, power quality monitoring system consists of [5] :
i.
Input signal conditioning and data acquisition subsystem
ii.
Digital processing and storing subsystem
iii.
Display and user interface subsystem.
Figure 3.2 illustrates the basic components in a modern power quality
monitoring system [8]. Its function is the conversion of the analogue signals into
digital format. This digitization simplifies the design of analogue circuits and
provides better flexibility for altering the algorithm to be used in processing data
samples.
24
Data
Acquisition
Subsystem
Analog
Signal
Digital
Signal
processing
or PC
Digital
Samples
Display
User
Interface
Digital
Processing
and Storage
Figure 3.2 : Basic components in modern power quality monitoring system
The basic components performing a Data Acquisition Subsystem (DAS) are
presented in Figure 3.3 [9]. In DAS, voltage and current is reduced to instrument’s
processing values by the transducers. Then, analog multiplexer will select a signal
from one of a number of input channels and transfer it to its output channel, thereby
permitting the transmission of several signals in a serial manner over a single
communication channel. Further, the signals are sampled and hold the sampled
value until the next sample is taken. By using an Analog to Digital Converter
(ADC), analog samples are converted to digital values. These values are the input
for PC or signal processing devices for characterizing the power quality problems.
Figure 3.3: Data acquisition subsystem basic components
Algorithm studied in this project is applied at this stage. It is necessary to
estimate the fundamental frequency voltage and current phases efficiently and
accurately in the presence of transients and waveform distortions. Also, higher level
complexity in processing is required to obtain the complete frequency spectrum of
periodic and no periodic voltage and current waveforms. Traditionally, this has been
25
achieved exclusively by Fourier techniques but more recently by alternative
techniques like wavelet, neural network and fuzzy logic.
In an existing power system, the waveforms to be monitored can be obtained
from measurements at points of common coupling (PCC) and their frequency
components are then derived [10]. For active power conditioning, essential to some
industrial processes, the information is derived directly from the waveforms in real
time.
The same applied to disturbance detections to obtain the magnitude and
duration of the event.
3.4
Power Quality Monitoring Under the Effect of Harmonics
IEC 61000-2-1 defines harmonics as sinusoidal voltages and currents having
frequencies that are whole multiples of the frequency at which the system is designed
to operate, for example 50Hz or 60Hz [8]. Harmonics currents are generated to a
small extent and at low distortion level by generation, transmission and distribution
equipment and to a larger extent by the industrial and domestic loads. Examples of
devices producing harmonics are saturation of transformer core during energization,
phase-angle control and uncontrolled rectification, static power converter, induction
furnaces and arc furnaces and many more.
Normally permissible harmonics magnitude is 5% to 10%. Figure 3.4 is the
graph showing the effect of harmonics distortion to power signal in a system.
26
Figure 3.4: Effect of harmonic distortion to voltage signal
Thus, the frequency measurement is taken using the distorted signal by the
technique studied and the performance of the measurement is evaluated.
3.5
Power Quality Monitoring Under the Effect of Noise
Noise is defined as unwanted signals with broadband spectral content lower
than 200 kHz superimposed upon the power system voltage or current in phase
conductors or found on neutral conductors or single lines [11]. Power electronics
devices, control circuits, arcing equipments, loads with solid-state rectifiers and
switching power supplies may causer noise in power systems. Improper grounding
27
that fails to conduct noise away from power system often exacerbates noise
problems.
Noise disturbs electronics devices such as microcomputer and programmable
controllers. Since noise can cause dysfunction of equipments, hence, examples for
measurements of frequency deviations under the effect of noise is presented so as to
test the performance of the digital technique used. Figure 3.5 shows the voltage
signal with variation in frequency when there is noise.
Figure 3.5 : Noise and frequency variation effects on voltage signal
3.6
Least Error Square (LES)
Field data is often accompanied by noise. Even though all control parameters
which are the independent variables remain constant, the resultant outcomes which
are the dependent variables vary. A process of quantitatively estimating the trend of
28
the outcomes, also known as regression or curve fitting, therefore becomes
necessary.
The curve fitting process fits equations of approximating curves to the raw
field data. Nevertheless, for a given set of data, the fitting curves of a given type are
generally not unique. Thus, a curve with a minimal deviation from all data points is
desired. This best-fitting curve can be obtained by the method of least squares.
The method of least squares assumes that the best-fit curve of a given type is
the curve that has the minimal sum of the deviations squared (least square error)
from a given set of data. Suppose that the data points are
where
fitting curve
,
, ...,
is the independent variable and
is the dependent variable. The
has the deviation (error)
from each data point, i.e.,
,
, ...,
. According to the method
of least squares [10], the best fitting curve has the property that [10]:
(3.10)
The Least Error Square (LES) estimation method can be used to estimate the
system h[m] by minimizing the squared error between estimation and detection as
shown in Figure 3.6 [7].
.
Figure 3.6 : Discrete-Time LTI System
The generalized equation for the output of the system shown in Figure 3.6 is [11] :
29
(3.11)
and this can be re-written in the matrix form [8] :
,
,
(3.12)
(3.13)
The data matrix D has a Toeplitz structure, which has constant diagonal entries. The
system output error, e, can be calculated with the equation [8] :
.
(3.14)
where y is the desired output of the system.
This equation is used to estimate the squared error using equation [11] :
.
(3.15)
Substituting (3.14) into (3.15), the squared error S can be expanded to [11] :
.
( 3.16)
Since the squared error S is a scalar component, (3.16) can be differentiated with
respect to h [11].
(3.17)
30
Then the filter component h can be solved in terms of input data matrix D and
desired output y as [11] :
.
(3.18)
However, in the above case, when estimating h, if y is not known, it is best to assume
that
= y[n], which will minimize the error from Equation 2.6, along with the
error for the estimated filter h,
. Thus Equation 3.15 can be rewritten for
.
as [11] :
(3.19)
Equation 3.12 can alternatively be written in another matrix form [9] as given
below to show the relationship between the values and the output for the sampling of
the voltage signal.
In Matrix form [9],
(3.20)
Where,
Matrix Y = Measured Signal, V(t)
Matrix A = [ sin ω 0t tcos ω 0t -tsin ω 0t ]
Matrix X =
Taking 4 samples [10] :
31
(3.21)
Figure 3.7 : Sampling of Voltage Signal
3.7
New Numeric Method
Numerical analysis is the study of algorithms for the problems of continuous
mathematics as distinguished from discrete mathematics.
Numerical analysis
continues the long tradition of practical mathematical calculations.
Numerical analysis naturally finds applications in all fields of engineering
and the physical sciences, but in the 21st century, the life sciences and even the arts
have adopted elements of scientific computations. Ordinary differential equations
appear in the movement of heavenly bodies such as planets, stars and galaxies;
32
optimization occurs in portfolio management; numerical linear algebra is essential to
quantitative psychology; stochastic differential equations and Markov chains are
essential in simulating living cells for medicine and biology.
Before the advent of modern computers numerical methods often depended
on hand interpolation in large printed tables. Nowadays these tables have fallen into
disuse, because computers can calculate the required functions. The interpolation
algorithms nevertheless may be used as part of the software for solving differential
equations and the like [12].
Much like the Babylonian approximation to, modern numerical analysis does
not seek exact answers, because exact answers are impossible to obtain in practice.
Instead, much of numerical analysis is concerned with obtaining approximate
solutions while maintaining reasonable bounds on errors [12].
3.7.1
Direct and Iterative Methods
Direct methods compute the solution to a problem in a finite number of steps.
These methods would give the precise answer if they were performed in infinite
precision arithmetic. Examples include Gaussian elimination, the QR factorization
method for solving systems of linear equations, and the simplex method of linear
programming. In practice, finite precision is used and the result is an approximation
of the true solution (assuming stability) [17].
In contrast to direct methods, iterative methods are not expected to terminate
in a number of steps.
Starting from an initial guess, iterative methods form
successive approximations that converge to the exact solution only in the limit. A
33
convergence criterion is specified in order to decide when a sufficiently accurate
solution has hopefully been found [17]. Even in infinite precision arithmetic these
methods would not reach the solution in finitely many steps in general [18].
Examples include Newton's method, the bisection method, and Jacobi iteration. In
computational matrix algebra, iterative methods are generally needed for large
problems.
Iterative methods are more common than direct methods in numerical
analysis. Some methods are direct in principle but are usually used as though they
were not, for example GMRES and the conjugate gradient method [18]. For these
methods the number of steps needed to obtain the exact solution is so large that an
approximation is accepted in the same manner as for an iterative method.
3.7.2
Generation and Propagation of Errors
The study of errors forms an important part of numerical analysis. There are
several ways in which error can be introduced in the solution of the problem.
a) Round-off
Round-off errors arise because it is impossible to represent all real numbers
exactly on a finite-state machine which is what all practical digital computers are.
34
b) Truncation and Discretization Error
Truncation errors are committed when an iterative method is terminated and
the approximate solution differs from the exact solution. Similarly, discretization
induces a discretization error because the solution of the discrete problem does not
coincide with the solution of the continuous problem [16]. For instance, in the
iteration in the sidebar to compute the solution of 3x3 + 4 = 28, after 10 or so
iterations, we conclude that the root is roughly 1.99. We therefore have a truncation
error of 0.01.
Once an error is generated, it will generally propagate through the
calculation. For instance, we have already noted that the operation + on a calculator
or a computer is inexact. It follows that a calculation of the type a+b+c+d+e is even
more inexact [16].
c) Numerical Stability and Well Posedness
This leads to the notion of numerical stability: an algorithm is numerically
stable if an error, once it is generated, does not grow too much during the calculation.
This is only possible if the problem is well-conditioned, meaning that the solution
changes by only a small amount if the problem data are changed by a small amount.
Indeed, if a problem is ill-conditioned, then any error in the data will grow a lot [15].
However, an algorithm that solves a well-conditioned problem may or may
not be numerically stable. An art of numerical analysis is to find a stable algorithm
for solving a well-posed mathematical problem. For instance, computing the square
root of 2 (which is roughly 1.41421) is a well-posed problem. Many algorithms
solve this problem by starting with an initial approximation x1 to , for instance
x1=1.4, and then computing improved guesses x2, x3, etc... One such method is the
35
famous Babylonian method [14], which is given by xk+1 = xk/2 + 1/xk. Another
iteration, which we will call Method X, is given by[14] xk + 1 = (xk2−2)2 + xk. We
have calculated a few iterations of each scheme in Table 3.1, with initial guesses x1 =
1.4 and x1 = 1.42.
Table 3.1 : Babylonian Method vs Method X
Babylonian
Babylonian
Method X
Method X
x1 = 1.4
x1 = 1.42
x1 = 1.4
x1 = 1.42
x2 = 1.4142857...
x2 = 1.41422535...
x2 = 1.4016
x2 = 1.42026896
x3 = 1.414213564... x3 = 1.41421356242... x3 = 1.4028614...
...
x3 = 1.42056...
...
x1000000 = 1.41421... x28 = 7280.2284...
Observe that the Babylonian method converges fast regardless of the initial
guess, whereas Method X converges extremely slowly with initial guess 1.4 and
diverges for initial guess 1.42. Hence, the Babylonian method is numerically stable,
while Method X is numerically unstable [14].
36
3.7.3
Interpolation, Extrapolation and Regression
Interpolation solves the following problem: given the value of some unknown
function at a number of points, what value does that function have at some other
point between the given points? A very simple method is to use linear interpolation,
which assumes that the unknown function is linear between every pair of successive
points. This can be generalized to polynomial interpolation, which is sometimes
more accurate but suffers from Runge's phenomenon. Other interpolation methods
use localized functions like splines or wavelets [13].
Extrapolation is very similar to interpolation, except that now we want to find
the value of the unknown function at a point which is outside the given points.
Regression is also similar, but it takes into account that the data is imprecise.
Given some points, and a measurement of the value of some function at these points
(with an error), we want to determine the unknown function. The least squaresmethod is one popular way to achieve this.
3.7.4
Optimization
Optimization problems ask for the point at which a given function is
maximized or minimized. Often, the point also has to satisfy some constraints.
The field of optimization is further split in several subfields, depending on the
form of the objective function and the constraint. For instance, linear programming
37
deals with the case that both the objective function and the constraints are linear. A
famous method in linear programming is the simplex method [12].
The method of Lagrange multipliers can be used to reduce optimization
problems with constraints to unconstrained optimization problems.
3.8
Adaptive Linear Neuron (ADALINE)
ADALINE (Adaptive Linear Neuron or later Adaptive Linear Element) is a
single layer neural network. It was developed by Professor Bernard Widrow and his
graduate student Ted Hoff at Stanford University in 1960.
It is based on the
McCulloch-Pitts neuron. It consists of a weight, a bias and a summation function as
shown in Figure 3.8 [15].
Figure 3.8 : Learning inside a single layer ADALINE
38
ADALINE is a single layer neural network with multiple nodes where each
node accepts multiple inputs and generates one output.
Given the following
variables [16] :
i.
x is the input vector
ii.
w is the weight vector
iii.
n is the number of nodes
iv.
θ some constant
v.
y is the output
then we find that the output is. If we further assume that [16]
i.
xn + 1 = 1
(3.22)
ii.
wn + 1 = θ
(3.23)
then the output reduces to the dot product of x and w
Let us assume [16]:
i.
η is the learning rate (some constant)
ii.
d is the desired output
iii.
is the actual output
then the weights are updated as follows. The ADALINE converges to the least
squares error which is E = (d − o)2 [15]
One of the most important aspect of ADALINE is the learning capability
whereby synaptic or connection weights are adaptively changed according to an
adaptive algorithm [15]. In other words, the key to learning in artificial neural
networks is adjusting the synaptic weights so that the desired outputs are produced
when the appropriate inputs are applied.
39
ADALINE is one of the simplest models of the artificial neuron with learning
capabilities. Referring to Figure3.9, the desired response dk is an auxiliary input
which is only used during the training (learning) process [15].
The output xk
produces a weighted sum of the input signals. The synaptic weights are essentially
continuously variable and may take positive or negative values. The output signal xk
is compared with the desired espoused input signal dk and the difference is the error
signal ek. Hence, the output signal provides the least-squares match to the desired
response input signal over the time.
Figure 3.9 : Adaptive Linear Network (ADALINE)
The input to the system is multiplied with the corresponding weights and
summed up at the summing junction. The summation of the weighted input is given
by [17]:
x(k) = (y(m+2) *w(1))+(y(m +1) *w(2))+(y(m) *w(3))
(3.24)
Then, the output xk then compared with the desired response dk and the difference ek
of the two quantities is taken. The error along with the next set of sample input is
then fed to the adaptation or learning algorithm. For the program I developed, the
value of dk is 0 [17].
ek = dk − xk
(3.25)
40
From the error obtained, the weights are updated using the following formula [18]:
(3.26)
The learning algorithm determines how the network synaptic weights are to
be modified so that the difference between the output of the network xk and the
desired response dk is made as small as possible. Equation (3.26) is known as the
LMS algorithm for updating weights of the adaptive linear combiner [18]. Based on
new calculated weights, the process will repeat until the error is minimized. When
error becomes very small, the value of the frequency deviation can be calculated.
To derive the equation for obtaining the value of the frequency, consider the
basic signal equation below [19]:
y = Asin(ω.t +φ )
(3.27)
For three consecutive signals [19],
y(k)= Asin(ωkΔt + φ)
(3.28)
y(k+1)= Asin(ω(k + 1)Δt + φ)
(3.29)
y(k+2)= Asin(ω(k + 2)Δt + φ)
(3.30)
Expanding the equation [19] :
y(k+2)= Asin(ω.kΔt + 2ω.t+φ) − 2cosω.Δt.y(k +1)
=Asin(ω.kΔt + φ ) cos 2ω.Δt + Acos(ω.kΔt + φ )sin 2ω.Δt)
= −2cosω.Δt{Asin(ω.kΔt + φ ).cosω.Δt + Acos(ω.kΔt + φ ).sinω.Δt}
= −2cos2 ω.Δt.Asin(ωkΔt + φ ) − 2cosω.Δt.Acos(ω.kΔt + φ )sinω.Δt(3.31)
Hence, for the summation of weighted inputs [19],
y(k + 2) − 2cos .T .y(k +1) + y(k) = 0 s ω
(3.32)
41
where s w 2cos .T 2 = − ω is the weight for the second input
(3.33)
y(k+ 2)- 2cos .Ts .y(k+1) + y(k)
= Asin(ω.kΔt + φ ).cos 2ω.Δt + Acos(ω.kΔt + φ ).sin 2ω.Δt) − sin2ω.Δt.A.cos(ω.kΔt+φ
) − (1+ cos 2ω.Δt)Asin(ω.kΔt + φ ) + Asin(ω.kΔt+φ )
= Asin(ω.kΔt + φ ) cos 2ω.Δt − cos 2ω.Δt.Asin(ω.kΔt+φ ) − Asin(ω.kΔt + φ ) +
Asin(ω.kΔt+φ )=0
(3.34)
From (3.34), the value of ω obtained consists of ωo + Δω. Thus, frequency
deviation can be obtained by subtracting the fundamental frequency from the value
of frequency obtained [19].
3.9
MATLAB
MATLAB is a high-performance language for technical computing.
It
integrates computation, visualization, and programming in an easy-to-use
environment where problems and solutions are expressed in familiar mathematical
notation. Typical uses include [8] :
i.
Math and computation
ii.
Algorithm development
iii.
Modeling, simulation, and prototyping
iv.
Data analysis, exploration, and visualization
v.
Scientific and engineering graphics
vi.
Application development, including Graphical User Interface building
MATLAB is an interactive system whose basic data element is an array that does
not require dimensioning [17]. This allows you to solve many technical computing
problems, especially those with matrix and vector formulations, in a fraction of the
42
time it would take to write a program in a scalar non-interactive language such as C
or Fortran.
The name MATLAB stands for matrix laboratory. MATLAB was originally
written to provide easy access to matrix software developed by the LINPACK and
EISPACK projects, which together represent the state-of-the-art in software for
matrix computation [8].
MATLAB has evolved over a period of years with input from many users. In
university environments, it is the standard instructional tool for introductory and
advanced courses in mathematics, engineering, and science. In industry, MATLAB
is the tool of choice for high-productivity research, development, and analysis.
MATLAB features a family of application-specific solutions called
toolboxes. Very important to most users of MATLAB, toolboxes allow you to learn
and apply specialized technology.
Toolboxes are comprehensive collections of
MATLAB functions (M-files) that extend the MATLAB environment to solve
particular classes of problems [8]. Areas in which toolboxes are available include
signal processing, control systems, neural networks, fuzzy logic, wavelets,
simulation, and many others.
3.10
Summary
In short, this chapter focuses on the details of each frequency measurement
technique studied.
It provides the history of LES, numerical and ADALINE
techniques. Diagrams, derivations and formulas used for each method are also
included.
43
A short description is also made on the tool for implementing this frequency
measurement which is the MATLAB software.
Possible applications for each
method used are also included in brief in this chapter.
The application of each algorithms described in this chapter is only the basic
algorithms. The full set of data and parameters which will be incorporated into the
respective formulas are explained in detail in the subsequent chapter.
CHAPTER 4
FREQUENCY MEASUREMENT ALGORITHM
4.1
Introduction
In this chapter, the three methods which is in this scope of work will be
implemented; LES, numerical and ADALINE. The implementation methods will be
discussed to determine the most suitable frequency measurement techniques in
power systems applications where frequency is to be estimated over a wide range
such as generator protection. The recommended techniques used should have the
characteristic of being precise especially during harsh variation conditions.
The related models and equations or algorithms used for each LES, numerical
and ADALINE methods were represented earlier in Chapter 3. Implementation will
be conducted in MATLAB. The objective of measuring using MATLAB is to
determine the accuracy of the frequency measurement through analysis of the
measurement’s error at various frequencies.
The calculated and graphical results of each algorithm used for the three
methods will be presented in the subsequent Chapter.
45
4.2
Implementation
From the techniques studied, a program in MATLAB environment using the
related algorithm is developed. Least Error Square (LES), a well-known and easier
implementation methodology is used first. From the simulation of the technique
including in the presence of noise and harmonics, the variation of frequency is
calculated. Based on the measurement, errors are calculated and the performance of
the system is evaluated. Furthermore, a neural network approach is used to minimize
the error. The simulation is also done in MATLAB environment using Adaptive
Linear Network (ADALINE). From there, the variation in frequency is calculated as
the error approaching zero.
4.3
LES Technique
From LES algorithm in Chapter 3, a MATLAB program is developed to
calculate the variation in frequency. To test the program, the voltage signal of
magnitude 1.5 and frequency 50 Hz with variations of 3Hz and phase shift of π /6 is
created and input to the algorithm as the Y matrix. The input signal is quantized into
n samples for the simulation. Samples are digitized into 20. The equation for the
power system voltage used is in equation 4.1[11].
V (n ) = 1.5*sin(314*n* 0.001 + 2*π*3*0.001*n+π/6)
(4.1)
Then, the algorithm is tested for voltage signal in the presence of harmonics
and noise. Signals with various magnitudes are tested. For harmonics, voltage
signal with 5th harmonics and 7th harmonics is used to measure the frequency
variations. Then, the magnitudes of the harmonics voltage are varied and the error
for each variation is calculated and plot with respect to its harmonics magnitude.
46
Equation for voltage signal that contains harmonics is as in equation 4.2 [11].
(4.2)
where for 7th harmonics component, the phase shift is +π/3 and for 5th harmonics c
component, the phase shift is –π/6, and h v is the magnitude of the harmonics voltage
that is to be varied.
Furthermore, the measurement of frequency under the effect of noise is done
by creating a random noise from MATLAB function. The function used is “randn”
function with the magnitude of the noise is specified by the user. By varying the
magnitude of noise in dB, the error resulting from calculation of frequency deviation
using LES algorithm is determined and the performance of the technique is analyzed.
4.4
Method of Investigation for ADALINE
A study of the Artificial Neural Network (ANN) was conducted to have a full
understanding. This was the first step before it could be applied to the basic Linear
Network for frequency measurement. The ultimate aim was to have the measured
frequency similar to the fundamental frequency.
Development of the algorithm took into account one of the following two
situations:
47
1. The measured frequency is equal to the fundamental frequency inputs. This
means that the error is “0” and the measured frequency is equal to the input
frequency.
2. The measured frequency is not equal to the fundamental frequency input.
This means that the calculated frequency is not the fundamental frequency of
the signal. Hence there exists an error. And the error will be calculated by
subtracting the measured frequency to the input frequency.
In order to
achieve situation A the iteration procedure could be computed as follows
:[10]
(i) Design t he error along with the next set of sample input to be then
fed to the adaptation or learning algorithm.
(ii) Using the ANN’s LMS computation, the sypnaptic weights is
updated.
Synaptic weight should be determined appropriately.
(iii) Based on new calculated weights, the process will repeat until the error is
minimized. When error becomes very small, the value of the frequency
deviation can be calculated.
A program written based on the algorithm developed was computed in the following
iteration until the desired maximum error was achieved. Graphical representation
was analyzed to determine its performance.
4.5
Flow Chart of Work Flow Implementation
Figure 4.1 shows the flow chart for the entire work implementation of this
thesis which incorporates the initial study, selection of measurement method,
generation of source codes for each method, results and discussion.
48
Literature Study
• PQ Monitoring
• PQ Issues
• Frequency Variation Measurement in PQ
Selection of Frequency Measurement Techniques
• LES
• Numerical
• ADALINE
Frequency Measurement
LES without Distortion
• MATLAB algorithm generation
• Error calculation
LES with Presence of Harmonics
• MATLAB algorithm generation
• Error calculation
LES with Presence of Noise
• MATLAB algorithm generation
• Error calculation
A
Figure 4.1(a) : Flow Chart of Work
49
Numerical without Distortion
• MATLAB algorithm generation
• Error calculation
Numerical with Noise and Frequency Variation
• MATLAB algorithm generation
• Error calculation
ADALINE with Small Frequency Variation
• MATLAB algorithm generation
• Error calculation
ADALINE with Large Frequency Variation
• MATLAB algorithm generation
• Error calculation
Comparison of Results between the Various Techniques
Conclusion and Recommendations
Figure 4.1(b) : Flow Chart of Work
50
4.6
Summary
Basically, this chapter explains in detail the step-by-step approach used to
implement the frequency measurement for LES, numerical and ADALINE
techniques. The details include the algorithms and other relevant parameter such as
sampling size and frequency variation size which were incorporated in the MATLAB
source codes. Explanation was also provided on the errors which were expected
from each method.
CHAPTER 5
RESULTS & DISCUSSION
5.1
Introduction
In Chapter 4, the methodology for implementation of the frequency variation
calculation and its errors was explained together with the algorithm and parameter
values. In this chapter, the graph generated from the MATLAB source codes is
presented for each method and each error from the related algorithm is calculated.
From the graphs and calculations obtained, the pros and cons of each method
in frequency measurement can be determined. Hence the most suitable method can
be deduced from the overall results.
Nevertheless, the suitability on which method is the best for implementation
would greatly depend on the power system it is utilized. That sector is not covered in
this scope of work and hence will not be discussed.
52
5.2
Least Error Square (LES) Method
The LES method is used to simulate a regular distortion free signal. The
desired variation of frequency is determined by the user and included in the program.
The program then calculates the deduced error for the related frequency variation.
The LES method is next used to simulate frequency with the presence of
harmonics. The related harmonics and the range of frequency will be determined by
the user. The program then calculates the effect of error on the corresponding
harmonics magnitude as well as the estimated frequency with regard to time.
Finally, a third LES method is used to simulate frequency variation with the
presence of noise. The noise is introduced through the program to distort the original
LES algorithm. The program then calculates the error in relation to its Signal-to
Noise Ratio (SNR).
5.2.1
Least Error Square Without any Distortion
A program in MATLAB was developed using the LES equation explained in
Chapter 3. The MATBLAB source codes are attached in Appendix A. From the
simulation, the variation of frequency obtained through the program calculation is
2.6102 Hz.
Hence the error can be calculated by :
error = desired – obtained
error = 3 – 2.6102
53
% error =
3 − 2.6102
X 100% = 12.98 %
3
The program was further modified for various values of frequency variation
ranging from 1 Hz to 3 Hz with increment of 0.2 Hz. The measured frequency and
error from the measurement is shown in Figure 5.1.
From Figure 5.1, it can be seen that as the frequency deviation from the
nominal power frequency increases, the error also increases. Hence, Least Error
Square technique is not very suitable for larger variations of frequency.
Figure 5.1 : Effect of Variation of Frequency to Estimated Frequency using LES
Algorithm
54
5.2.2
Least Error Square with Presence of Harmonics
A subsequent program was developed using the LES technique but the source
codes were modified to include the presence of harmonics. The MATLAB source
codes are attached in Appendix B.
From the simulation, the variations of frequency corresponding to its 7th
harmonics magnitude are calculated. The measurements are taken for 20 different
harmonics magnitudes which vary from 0.01 p.u to 0.2 p.u. Figure5.2 shows the
effect of harmonics magnitude change to the measured frequency using Least Error
Square Method.
Figure 5.2 : Effect of Harmonics Magnitude Change to the Measured Frequency
using LES algorithm.
55
From the data obtained, it can be deduced that for the 7th harmonics
magnitude in the range of 0.12 p.u to 0.2 p.u., the error is converging to 0. Else, the
error becomes large and the estimated frequencies are inaccurate.
5.2.3
Least Error Square with Presence of Noise
A third program for simulation of the LES algorithm is created with
modifications to include the presence of noise. The related MATLAB source codes
are attached in Appendix C. The results of the error from the desired value of
frequency deviations corresponding to change in its Signal-to-Noise ratio is shown in
Figure 5.3.
Figure 5.3 : Error of Frequency Deviations Corresponding to the Change in its
Signal-to-Noise Ratio
56
From Figure 5.3, it shows that as the magnitude of the noise increases, such
as there is decrement in Signal-to-Noise ratio, the error fluctuates to larger values. It
can be concluded that the Least Error Square algorithm is suitable for measurement
of frequency under the effect of noise with of Signal-to-Noise Ratio (SNR) with a
range greater than 30 dB or approximately 0.33 p.u. in magnitude.
5.3
Numerical Technique
A program was developed using the Numerical technique as attached in
Appendix E. The program did not incorporate any disturbance in the signal. The
result of the simulation without any disturbance in the signal voltage is 50.4153 Hz.
Hence the error can be calculated as :
%error =
50 − 50.4153
X 100%
50
= 1.98 %
Next the program was modified to include random noise and variation in
frequency of 0.5 Hz. The calculation results obtained from the simulation was
54.5241 Hz. Therefore the error can be calculated as:
%error =
50.5 − 54.524
X 100%
50.5
= 7.92 %
It can be concluded that the using the Numerical technique, the error
increases rapidly as the variations on frequency from the nominal power frequency
increases.
5.4
Adaptive Linear Network (ADALINE)
57
A program was developed using the basic ADALINE concept as detailed in
Chapter 3. The relevant MATLAB source codes can be found in Appendix F. From
the simulation, the training of the network can be seen from the Figure 5.4 :
Figure 5.4: The training of the network to minimize the error
From Figure 5.4, the error vs. iterations results above, it can be seen that the
weights are adjusted as the number of iterations increases. The nature of adjustment
of weights is such that the errors are minimized or converged to 0.
Figure 5.5 shows the estimated frequencies obtained from the ADALINE
simulation program. The program used 0.5 Hz as the frequency variation.
58
Figure 5.5 : Training of the network to measure frequency when there is variation of
0.5 Hz.
The calculated results of simulation for variation of frequency of 0.5 Hz to 0.5126
Hz is as :
% error =
| 0.5 − 0.5126 |
X 100%
0 .5
= 2.52 %
A similar program is developed using the same source codes but with the
variation of frequency at 3.0 Hz instead. The training of the related network is
illustrated in Figure 5.6 :
59
Figure 5.6 : Training of the network for variation of 3.0 Hz in frequency
The final value of frequency obtained is 52.7299 Hz. Hence the measured
variation on frequency is 2.7299 Hz.
% error =
| 3 − 2.7299 |
X 100%
3
=9%
The error for frequency estimated for the range on variation for 0.5Hz to 2.5
Hz is calculated and shown in Figure 5.7.
60
Figure 5.7 : The effect of variation of frequency to the frequency measure using
ADALINE
From the graphs plotted, it can be concluded that as the variation from
nominal value becomes larger, then the error of estimation is larger.
5.5
Comparison between Various Measurement Techniques
From the results of the simulation obtained, it can be seen that LES is the
easier method to be implemented in measuring power system frequency deviations.
The computations involved in the technique are straightforward and does not involve
lengthy equations. However, it still suffers from inaccuracies in the measurements.
Nevertheless, the method is still one of the popular techniques implemented for
microprocessor based-relaying.
61
Numerical method provides fast evaluation of power system frequency.
However, the major drawback of this technique is that it is very inaccurate in the
presence of noise.
ADALINE is a neural network approach to measure the power system
frequency as the error is minimized. This method provides good approximation with
less percentage of error even with the presence of noise in the signal.
5.6
Summary
This chapter presents the results for each method and the detailed error
calculations obtained. From the analysis of the results, it can be concluded that bets
method suited to this frequency variation measurement is ADALINE as it has the
least percentage of error even with distortions.
CHAPTER 6
CONCLUSION AND RECOMMENDATIONS
6.1
Conclusion
In conclusion, this research is basically about the study of power quality
measurement techniques developed for microprocessor-based relaying. Three main
methods which are LES, numerical and ADALINE for measuring the frequency were
discussed.
The performance of each algorithm under the effect of noise and
harmonics were also evaluated. Moreover, a neural network was also presented to
measure the frequency and minimize the error.
It has been shown that neural network approach is better for frequency
approximation. Even though LES algorithm provides easier method for frequency
measurement, the technique is not very accurate in the presence of noise and
harmonics.
However, recursive LES may compensate the drawbacks of non-
recursive LES algorithm.
\
63
6.2
Recommendations
Through simulation results, it was proven that the ADALINE has managed to
reduce errors.
However, this algorithm is adversely affected by presence of
harmonics at non-nominal frequencies and, therefore, the use of pre- and post-filters
could be studied in future works. We may expect this to result in a slower response.
An iterative technique for frequency estimation might provide more precise
estimates and should require modest computations.
The proposed technique is
capable of estimating frequency over a wide operating range.
The developed
technique should then tested using voltage signals obtained from a dynamic
frequency source.
The technique for estimating power system frequency is explained in the
previous section.
Future studies in ADALINE should also include practical
considerations for implementing the proposed technique. The estimation process
may require design of new orthogonal filters at every iteration. Design of filters
requires considerable amount of computations. These computations may not be
completed within one sampling interval which is available for performing
calculations. Therefore, the filters should be designed off-line and their coefficients
stored for use in estimating the frequency.
The iterative procedure for estimating frequency is terminated when the
estimated frequency obtained is equal to the fundamental frequency assumed for
designing the orthogonal filters. However, in practice, a margin should be allowed to
account for errors arising from truncations during calculations, data acquisition etc.
Number of iterations which can be performed in one sampling interval will be
limited by the capability of the digital processor.
64
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67
APPENDIX A
MATLAB CODE FOR LEAST SQUARE ERROR FREQUENCY
ESTIMATION ANALYSIS
68
69
APPENDIX B
MATLAB CODE FOR LEAST SQUARE ERROR FREQUENCY
ESTIMATION WITH HARMONICS ANALYSIS
70
71
72
APPENDIX C
MATLAB CODE FOR LEAST SQUARE ERROR FREQUENCY
ESTIMATION WITH NOISE ANALYSIS
73
74
APPENDIX D
MATLAB CODE FOR NUMERICAL METHOD FREQUENCY
ESTIMATION ANALYSIS
75
76
APPENDIX E
MATLAB CODE FOR ADALINE NETWORK FREQUECY ESTIMATION
ANALYSIS
77
78
79