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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 1
CHAPTER1
INTRODUCTION
1.1 Introduction
The increased requirements on supervision, control and performance in
modern power systems make power quality monitoring a common practice for
utilities. Studies of power quality phenomena have emerged as an important subject in
recent years due to renewed interest in improving the quality of the electric supply. As
sensitive electronic equipment continues to proliferate the studies of power quality
will be further emphasized. New tools are required to extract all relevant information
from the recordings in an automatic way.
It is well known that the main power quality deviations are caused by shortcircuits, harmonic distortions, notchings, voltage sags and swells, as well as transients
due to load
switching. In order do correct such problems, it is required, in general that, firstly,
they should be detected and identified. Nevertheless, whenever the disturbance lasts
for only for a few cycles, a simple observation of the waveform in a busbar may not
be enough to allow one to recognize that there is a problem in there or, more difficult
yet, to identify the sort of the problem.
Switching phenomena results in oscillatory transients in the electrical supply, for
example capacitors switching contributes considerably to power quality (PQ)
disturbances. In addition, high power non-linear loads add to the generation of current
and voltage harmonic components. Among the different voltage disturbances that can
produce the most noteworthy and critical power quality problems are voltage sags.
Short-term voltage drops (sags) can trip electrical drives or more sensitive equipment,
leading to interruptions of vital production. For these reasons, from the consumer
point of view, power quality issues turn out to be key factor for satisfying good
productivity. On other part, for electrical supply industry, the quality of power
delivered will be one of the distinguishing factors intended for ensuring customer
loyalty in the present competitive and deregulated market. International standards
define power quality as the physical characteristics of the electrical supply provided
under normal operating conditions that do not disrupt or upset the customer’s process
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 2
. As a result, power quality problems arise with the association of any deviation in
voltage, current or frequency resulting into an undesirable performance of customer’s
equipment. Though, it is important to notice that the quality of power supply implies
basically voltage quality and supply reliability PQ disturbances result in complete
interruption or force many applications to halt working. So PQ problems relate to the
basic system design, system maintenance issues, ensuring equipment protection
within customer facilities. The impact of PQ problems is aggregated through
proliferation of extremely sensitive computerized equipment. As the design of most
conventional equipments such as lights, constant speed motors and power systems are
based on the assumption that the voltage source are sinusoidal and the loads are
linear, so that the resulting waveforms are also sinusoidal. As demands on accuracy
have increased and nonlinear loads have become more common, this approximation is
now no longer valid. Consequently, power quality monitoring and classification has
become an essential service which many utilities perform for their customers. The
monitoring and analysis tools must be able to detect, identify, and localize the
disturbances on the supply lines and make proper system decisions. The whole
process should be completed before these cause widespread customer complaints;
equipments malfunction and even equipment failures. So fast and accurate
identification and classification of power quality events is extremely important at all
levels of the electrical power system and is a value for both power distributor and
power consumer. However, there is still further scope for research work to identify
and classify the power quality problems with very high accuracy so as to keep the
losses due to power quality problems at a minimum.
The wavelet transform is a mathematical tool like Fourier Transform in
analyzing a signal that decomposes a signal into different scales with different levels
of resolution. Santoso et al proposed wavelet transform technique for the detection
and localization of the actual power quality disturbances. They explored the potential
of wavelet transform as a new tool for automatically classifying power quality
disturbances. Heydt and Galli proposed wavelet techniques for the identification of
the power system transient signals. Fuzzy logic control technique has been discussed
by Hiyama et al to enhance power system stability using static VAR compensator.
The proposed control scheme is simple and suitable for on-line implementation using
a microcontroller. Santoso et al combined wavelet transform with Fourier transform
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for the characterization of the power quality events. The Fourier transform has been
used to characterize steady state phenomena, whereas the wavelet transform has been
applied to transient phenomena. A hybrid scheme using a Fourier linear combiner and
a fuzzy expert system for the classification of transient disturbance waveforms in a
power system has been presented by Dash et al. Olivier et al investigated the use of a
continuous wavelet transform to detect and analyze voltage sags and transients. They
developed an efficient and simple algorithm for detecting and measuring power
quality analysis. Thebasic unit of the architecture is the wavelet network which
combines the ability of the wavelet transform for analyzing non stationary signals
with the classification capability of artificial neural networks Styvaktakis et al
developed an expert system to classify different types of power system events and
offer useful information in terms of power quality. Huang et al presented a neuralfuzzy technology based classifier for the recognition of power quality disturbances.
The proposed recognition system provides a promising approach applicable in power
quality monitoring. Driesen and Belmans proposed further alternatives for power
quantification based on formulations and time frequency domain described by wavelet
bases. They used both the real and complex valued wavelets. He and Starzyk
proposed a novel approach for power quality disturbances classification based on
wavelet transform and self organizing learning array system. Wavelet transform has
been utilized here to extract feature vectors for various power quality disturbances
based on multi resolution analysis.
Owing to various reasons mentioned above an attempt has been made in the
present work to classify the most commonly occurring power quality disturbances
using wavelet analysis, Multi-resolution signal decomposition (MSD) using wavelet
transformation (WT) is used as a basis for feature vector for obtaining the training
and testing data.
1.2Literature survey
A.K. Chandel, G. Guleria, and R. Chandel [2] has explained about the various
power quality disturbances, and how they are classified using wavelet analysis. In the
pre-processing voltage signals are captured during a power quality problem. Due to
the absence of field results different power quality problems have been simulated in
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 4
the MATLAB/SIMULINK environment. The PQ data thus obtained matches the field
data. Subsequently, using the Wavelet toolbox of the MATLAB, multi signal
decomposition on the captured signals is performed. Depending on the selected
resolution levels, the PQ signal is decomposed into a number of wavelet levels. If the
resolution level is defined as n, after decomposing the signal, there will be one level
of approximation coefficients with n level of detail coefficients. The information
contained in the coefficients of details and approximations is very useful for further
processing
M. H. Bollen [1] has explained ,what is power quality, what is quality of supply,
and IEEE definitions for power quality. He explained about two types of power
quality problems .they are voltage sag and interruption. The causes for this problems
and their mitigation methods.
Resende, J.W., Chaves, M.L.R., Penna, C. [3] This paper presents an approach
that is able to provide the detection and location in time as well as the identification of
power quality problems present in both transient and steady-stable signals. The
method was
developed by using the discrete wavelet transform (DWT) analysis. The given signal
is decomposed through wavelet transform and any change on the smoothness of the
signal is detected at the finer wavelet transform resolution levels. Later, the energy
curve of the given signal is evaluated and a relationship between this energy curve
and the one of the corresponding fundamental component is established. The paper
shows that each
power quality disturbance has unique deviations from the pure sinusoidal waveform
and this is adopted to provide a reliable classification of the type of disturbance.
Sudipta Nath, Arindam Dey and Abhijit Chakrabarti[4] presented the features
that characterize power quality disturbances from recorded voltage waveforms using
wavelet transform. The discrete wavelet transform has been used to detect and
analyze power quality disturbances. The disturbances of interest include sag, swell,
outage and transient. A power system network has been simulated by Electromagnetic
Transients Program. Voltage waveforms at strategic points have been obtained for
analysis, which
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includes different power quality disturbances. Then wavelet has been chosen to
perform feature extraction. The outputs of the feature extraction are the wavelet
coefficients representing the power quality disturbance signal. Wavelet coefficients at
different levels reveal the time localizing information about the variation of the signal.
S. El Safty, and A. El-Zonkoly [8] a novel algorithm is presented to detect
the fault and identify its type using wavelet entropy energy. The main principle of
wavelet entropy is first presented. Then algorithm used in fault detection and
identification is
discussed. Simulation of the proposed system in order to obtain different current
signals for testing of the proposed technique has been done using PSCAD program.
1.3 Organization of the thesis
Chapter 1 explains about background and overview of power quality wavelet
analysis
Chapter 2 explains about power quality and power quality problems and their
mitigation methods
Chapter 3 explains about classification of loads
Chapter 4 explains about an overview of wavelet analysis
Chapter 5 explains about simulink results and conclusion
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CHAPTER 2
INTRODUCTION TO POWER QUALITY
2.1 POWER QUALITY:
International standards define power quality as the physical characteristics of
the electrical supply provided under normal operating conditions that do not disrupt or
upset the customer’s process.
Now days, power quality is a key issue for the producers, distributors
and consumers. The most common problems, like harmonics, short term voltage
variations (sags, swells and interruptions), long term voltage variations (under
voltages, over voltages and interruptions), transients, unbalance, frequency variations
and others, can cause several problems to the consumers which require high levels of
power quality for their industrial processes or home use. Power quality studies are the
necessary first step in order to determine what is wrong, so that measures can be taken
to solve the problems. Because many of the commercially available equipments are
either too expensive, or have too many limitations, it was decided to develop a new
low-cost power quality monitor that could be an alternative to the equipment in the
market.
The utility is most commonly perceived by the user as the source of power
quality and reliability problems. This is understandable because the effects of events
in the mains, like lightning or breaker clearing, are fairly noticeable in a facility’s
performance. However, these events represent a small percentage of total events,
although they may be true in some specific areas such as weak grids. The reality is
that a large percentage of problems are generated within a user’s own facility. Even
though it may seem unbelievable, the main source of power disturbances in a facility
is its own activity. Normal utilization of the facility and normal operation of its own
equipment, including turn-on and turn-off, may give rise to undesirable events which
affect the sensitive equipment within the facility if it has not been taken into account
in the design process. The increasing spread of information technology and
automation to practically every business and activity is mainly responsible. The
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increasing application of electronics to all kind of appliances makes possible real-time
communication and/or continuous operation. This improves facilities performance
levels through effective data and energy management.
But electronic devices are non-linear loads and they introduce more
disturbances into the same facility they are fed by. Therefore, facilities and sensible
equipment are becoming more vulnerable and dependent on both the quality and
continuity of the electric power supply because of their operation. Typical examples
of power quality problems are overloaded circuits and transformers, and unwanted
operation of protection caused by the presence of harmonics
. Therefore, power quality, reliability and availability must be considered as a
complete set from the design stage because they are closely related. Equipment is
designed for normal operation within a rated range of power supply values. Small
deviations from these values can result in increased losses, poor efficiency and
unpredictable operation. Large deviations can cause protective devices to trip or the
failure of a component. In addition, components always break down from time to time
because they have a limited lifetime. Thus, both power quality and reliability
influence the availability of any facility.
Availability is easier to estimate and quantify than reliability, so users are
more concerned about the former. Nevertheless, the way to increase the availability is
through power quality and reliability improvements. But high availability means
much more than high power quality and reliability. At first, it requires a proper design
to reduce failures or disturbances in the power supply. The reliability levels wanted or
needed for the equipment of a business or an activity are known at the outset. So, if
the reliability level must be higher than the one provided by the utility according to
power quality and availability standards, additional investment is needed in order to
achieve the expected power quality and availability for the facility.
2.2 QUALITY OF SUPPLY
According to the Council of European Regulators (CEER) Working Group on
Quality of Supply, the following definitions apply:
• Customer service.
• Continuity of supply (typically referred to as reliability in the USA).
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• Voltage quality (typically referred to as power quality in the USA).
2.2.1 Customer Service
Customer service typically relates to the nature and quality of the service
provided to electricity consumers. Customer service (referred to as commercial
quality in Europe) indicators are typically quantitative operational measures that are
used extensively in existing performance-based ratemaking (PBR) schemes
throughout the world. Some examples of customer service indicators utilized include:
• Customer satisfaction.
• Customer complaints.
• Customer meter and billing accuracy.
• Response to customer enquiries.
• Appointments met.
• Customer call/wait times.
• Time required for new service connections.
• Emergency/storm response.
• Safety/health.
• Estimating charges for work.
Although important in assessing the overall quality of supply, customer
service is not the focus of this research and will largely not be addressed in this
chapter. There is a variety of information and resources available to policy makers
and utilities regarding this component of the quality of supply, some of which are
referenced at the end of this chapter.
2.2.2 Continuity of Supply
Continuity of supply is characterized by the number and duration of
interruptions. Several indicators are used to evaluate the continuity of supply in
transmission and distribution networks. Regulation can aim to compensate customers
for very long supply interruptions, keep restoration times under control and create
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incentives to reduce the total number and duration of interruptions (and disincentives
to increase them). Different methods and accuracies of measuring interruptions and in
assigning liability for each of them create problems in regulating continuity of supply.
2.2.3 Voltage Quality
The third and final component of the quality of supply is voltage quality.
Voltage quality is the quantitative form of describing power quality and includes both
steady-state power quality variations and momentary disturbances that may impact
loads. Categories of voltage quality include:
Power frequency
Magnitude of the supply voltage
Harmonics and inter harmonics
Voltage unbalance
Flicker
Voltage sags and momentary interruptions (r.m.s. variations)
Transients
2.3 Power Quality Deterioration:
2.3.1 Voltage Dips
The main causes of voltage dips are: short-circuits in the supply network,
start-up of large loads, faulted grounding system and failures of the customer facilities
Fig 2.1 voltage dip
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 Sources of Voltage Dips
The primary source of voltage dips is the electrical short circuit occurring on
the power supply system.
The switching of large loads, starting of large motors connected to the end of a
long supply line
power fluctuations of great magnitude (particularly of reactive power) are
characteristic of some categories of loads and installations, such as variable
load and/or speed drives, arc furnaces, welding equipment, etc.,
2.3.2 Short Supply Interruptions
Short interruptions are typically associated with switchgear operation related
to the occurrence and termination of short circuits in the system or installations
connected to it .The operation of a circuit-breaker or fuse disconnects part of the
system from the source of energy. In the case of a radial circuit, this interrupts the
supply to all downstream parts of the system. In the case of a meshed network,
disconnections at more than one point are necessary in order to clear the fault. Electric
power users within the disconnected segment of network suffer an interruption of
supply.
Automatic reclosing sequences are often applied in the supply system. Their
purpose is to restore the circuit to normal operation with the minimum of delay in the
event that the fault proves to be a transient one. The reclosing operation may be
attempted several times (depending on the adopted practice of fault clearing) until
self-clearance of the fault, or the circuit-breaker remains in the open position if the
fault is a permanent one. Interruptions having duration up to 1 min (or, in the case of
some reclosing systems, up to 3 min) are classified typically as short interruptions.
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Fig.2.2 short supply interruptions: r.m.s voltage characteristics
Fig. 2.3 Short supply interruptions: voltage waveform
2.3.3 Long interruptions
The importance of labor costs increases, reaching some 20% on average. This
is twice as great as the equivalent figure for voltage dips and some 40% higher than
with short interruptions. In addition there are instances where some of the other cost
categories take on greater importance and these tend to be related to the long-term
economic consequences created by penalties (commercial or statutory), loss of brand
equity or the need for unanticipated business investment to regain lost sales/market
share.
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2.3.4 Voltage fluctuations:
Voltage fluctuations are caused when loads draw currents having significant
sudden or periodic variations. The fluctuating current that is drawn from the supply
causes additional voltage drops in the power system leading to fluctuations in the
supply voltage. Loads that exhibit continuous rapid variations are thus the most likely
cause of voltage fluctuations. Examples of loads that may produce voltage
fluctuations in the supply include
Arc furnaces
Arc welders
Installations with frequent motor starts (air conditioner units, fans)
Motor drives with cyclic operation (mine hoists, rolling mills)
Equipment with excessive motor speed changes (wood chippers, car
shredders)
2.3.5 Harmonics:
A harmonic is defined as a component with a frequency that is an integer
multiple (the so called order of harmonic n) of the fundamental frequency (Figure
7.1). The harmonic number indicates the harm onic frequency: the first harmonic is
the fundamental frequency (50 or 60 Hz), the second harmonic is the component with
frequency two times the fundamental (100 or 120 Hz), and so on.
Fig.2.4 harmonics
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 Effects due to harmonics:
1.Thermal effects on transformers
2.Neutral conductor overloading
3.Over stressing of capacitor brands
4.Unexpected fuse operation
5.Abnormal operation of electronic relays
6.Telephonic interference
7.Thermal effects on rotating machines
8.Pulsating torque in rotating machines
 Sources of Current Harmonics
Among the sources of harmonic voltages and currents in power systems three
groups
of equipment can be distinguished:
magnetic core equipment, like transformers, electric motors, generators, etc.
arc furnaces, arc welders, high-pressure discharge lamps, etc.
electronic and power electronic equipment.
2.3.6 transient over voltages
Transient over voltages are brief, high-frequency increases voltage on AC mains.
Brodly speaking here are two different types of transient over voltages, low frequency
transients with frequency components in the few hundred hertz region typically
caused by capacitor switching, and high frequency transients with frequency
components in the few hundred kilo-hertz region typically caused by lighting and
inductive loads. low frequency transients are often called” capacitor switching
transients”, high frequency transients are often called “impulse” ,”spike”, or surge.
Fig 2.5 transient over voltages
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2.3.7 Voltage Sag
A decrease in voltage to between 10 % to 90% of nominal voltage for onehalf cycle to one minute .
Fig.2.6voltagesag
2.3.8 Under Voltage
Under voltage is a decrease in voltage below 90% of its nominal value for
more than one minute.
Fig.2.7 under voltage
2.3.9 Swell
A swell is the opposite of a sag an increase in voltage above 110% of nominal
voltage for one- half cycle to one minute.
Fig.2.8 voltage swell
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2.3.10 Flicker
Flicker is a low-frequency phenomenon in which the magnitude of voltage or
frequency changes, that is perceptible to human eye.
Flicker frequency of 8 to 10 hz.
Voltage variation of 0.3 to 0.4%.
2.3.11 Over Voltage:
Over voltage is an increase in voltage above 110% of nominal for more than one
minute.
Reasons of cause: - Load Rejection
Effects:
- Overheat of electronic equipments
Possible Solution: Power conditioner
Fig.2.9 over voltage
2.4 Cost of poor power quality:
While the consequences are not limited to electrical systems in non-residential
environments and can harm domestic systems and appliances as well as mainly
introducing electrical danger into the home, the residential sector is not addressed
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here. It is only by knowing what the cost consequences are that effective plans can be
drawn up to reduce or eliminate these unnecessary productivity and efficiency losses
and to design in solutions that make economic as well as operational sense.. The
economic impacts of power quality are usually divided into three broad categories:
 Direct economics impacts:
loss of production;
unrecoverable downtime and resources (e.g. raw material, labor,
capital);
process restart costs;
spoilage of (semi-)finished production;
equipment damage;
direct costs associated with human health and safety;
financial penalties incurred through non-fulfillment of contract;
environmental financial penalties;
utility costs associated with the interruption.
 Indirect economic impacts:
the costs to an organization of revenue/income being postponed;
the financial cost of loss of market share;
the cost of restoring brand equity.
 Social economic impacts:
uncomfortable building temperatures as related to reduction in efficient
working/health and safety;
personal injury or fear, also as related to reduction in efficiency and
health and safety;
evacuating neighboring residential buildings as an indirect social
impact in the event of failure of industrial safety, as it relates to the
additional costs incurred by an organization that has to carry out these
measures.
The harmonics category may be further subdivided to focus on particular
impacts that were treated as separate cases, defined as follows:
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Overstressing
insulation,
effects
on
electrical
equipment
including
transformers, capacitors , motors; the consequences of not measuring TRMS (True
Root Mean Square); additional losses.
Overheating of the neutral conductor (e.g. burn-off and subsequent disruption
or damage to electrical equipment).
Nuisance tripping of protective devices.
Malfunction of equipment control systems due to additional zero crossing. To
calculate the total cost of each PQ disturbance the following PQ cost
categories are to be considered for each disturbance category.
2.5 Other disturbances:
There have been no other major surveys or studies on costs of PQ phenomena
apart from the Leonardo PQ survey already mentioned above. Individual case studies,
however, do exist, which cover such phenomena as:
Inter harmonics
Unbalance
Problems with earthing and high-frequency phenomena
These are responsible for substantial PQ costs within particular sites and regions. The
approach here, however, is limited rather to analyzing historical events, recording the
consequences mainly in terms of damaged equipment and associated costs.
2.6. Over view of mitigation methods
To understand the various ways of mitigation, the mechanism leading to an
equipment trip needs to be understood. The underlying event of the equipment trip is
a short-circuit fault, a low-impedance connection between two or more phases, or
between one or more phases and ground. At the fault position the voltage drops to a
low value. The effect of short circuit at other positions in the system is an event of a
certain magnitude and duration at the interface between the equipment and the power
system. The short circuit fault will always causes a voltage sag for some customers.
If the fault takes place in a radial part of the system, the protection intervention
clearing the fault will also leads to an interruption.
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2.6.1 Reducing the number of short-circuit faults.
Reducing the number of short-circuit faults in a system not only reduces the sag
frequency but also the frequency of sustained interruptions. This is a very effective
way of improving the quality of supply and many customers suggest this as the
obvious solution when a voltage sag or a short interruption problem occurs. Some
examples of fault mitigation are
Replace overhead lines by underground cables
Use covered wires for overhead line
Implement a strict policy of tree trimming
Install additional shielding wires
Increase the insulation level
Increase maintenance and inspection frequencies
2.6.2 Reducing the fault-clearing time
Reducing the fault-clearing time does not reduce the number of events but only
their severity. Faster fault-clearing does also not affect the number of voltage sags but
it can significantly limit the sag duration. The ultimate reduction in fault clearing
time is achieved by using current limiting fuses. Current limiting fuses are able to
clear a fault with in one half-cycle, so that the duration of a voltage will rarely exceed
one cycle. The recently introduced static circuit breakers also gives a fault clearing
time within one half-cycle, but it is obviously much more expensive than a current
limiting fuse. Some options for the reduction of the fault clearing time in transmission
systems are
 In some cases faster circuit breakers could be of help.
 A certain reduction in grading margin is probably possible.
 Faster backup protection is one of the few effective means of reducing fault
clearing time in transmission systems.
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2.6.3 Changing the power system
By implementing changes in the supply system, the severity of the event can be
reduced. But the costs become very high, especially for the transmission and sub
transmission voltage levels. Some mitigation methods especially directed toward
voltage sags are
 Install a generator the sensitive load the generators will keep the voltage up
during a sag due to a remote fault
 Split buses or substations in the supply path to limit the number of feeders in
the exposed area.
 Install current limiting coils at strategic paces in the system to increase the
‘clearing distance” to the fault.
 Feed the bus with the sensitive equipment from two or more substations. The
best mitigation effect is by feeding from two different transmission
substations.
2.6.4 installing mitigation equipment
The most commonly applied method of mitigation is the installation ofaditional
equipment at the system-equipment interface. The popularity of mitigation equipment
is explained by it being the only place where the customer has control over the
situation.
Voltage- source converter: most modern voltage-sag mitigation methods at the
system-equipment interface contain a so called voltage source converter. A voltage
source converter is a power electronic device which can generate a sinusoidal voltage
at any required frequency, magnitude, and phase angle. In voltage mitigation it is used
to temporarily replace the supply voltage or to generate the part of the supply voltage
which is missing.
Series voltage controllers-DVR: The series voltage controller consists of a voltage
source converter in series with the supply voltage. The dynamic voltage
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restorer(DVR) is commonly used instead of series voltage controller. The amount of
energy storage depends on the power delivered by the converter and on the maximum
duration of a sag. The controller is typically designed for certain maximum sag
duration and a certain minimum sag voltage.
combined shunt and series controllers: The series controller cannot mitigate any
interruptions and that it is normally not designed to mitigate very deep sags(much
below 50% of remaining voltage). A series-connected converter injects the missing
voltage, and a shunt-connected converter takes a current from the supply. The power
taken by the shunt controller must be equal to the power injected by the series
controller. The change in stored energy in the capacitor is determined by the
difference between the power injected by the series converter and the power taken
from the supply by the shunt converter.
Back up sources-SMESS.BESS: One of the main disadvantage of a series controller
is that it can not operate during an interruption. A shunt controller operates during an
interruption, but its storage requirements are higher. Various forms of energy storage
have been proposed. A so called “ super conducting magnetic energy storage
(SMESS)” stores electrical energy in a super conducting coil. A BESS or “battery
storage system uses a large battery bank to store the energy.
Cascade connected voltage controllers-UPS: The main device used to mitigate
voltage sags and interruptions at the interface is the so-called “ uninterruptible power
supply (UPS)” the popularity of the UPS is based on its low costs and easy use.
Motor-generator set: motor generator sets are often depicted as noisy and as needing
much maintenance. But industrial environments noisy equipment and maintenance on
rotating machines are rather normal. Large battery blocks also require maintenance,
expertise on which is much less available.
2.6.5 improving equipment immunity
Improvement of equipment immunity is probably the most effective solution against
equipment trips due to voltage sags. But it is often not suitable as a short time
solution.
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The immunity of consumer electronics, computers, and control equipment can be
significantly improved by connecting more capacitance to the internal dc bus.
Single-phase low power equipment can also be improved by using a more
sophisticated dc/dc converter
The main source of concern are adjustable-speed drives.
2.7. Summary
This chapter has explained about the power quality, and the quality of supply. In
addition to this the various power quality problems are also studied, they are like
capacitor switching, sag, swell, interruption etc. The mitigating methods for various
power quality problems are studied.
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CHAPTER 3
3. CLASSIFICATION OF LOADS
3.1 Introduction
Unbalanced operating conditions in an electric power system are caused
mainly by the operation of unbalanced loads. Most low-voltage loads and certain
medium-voltage ones, e.g. an electric traction motors, are single-phase appliances.
Operation of such equipment in the three-phase system results in unbalanced load
currents. Consequently, unsymmetrical voltage drops in individual phases of the
supply system are produced, thus voltage at nodes of the network becomes
unbalanced.
Three-phase loads which may introduce unbalance in the power system are arc
furnaces. The disturbance results from different impedances of high-current paths of
the furnace and not equal phase loads being the effect of the physical nature of the
melting process, i.e. variations in the arc impedance.
As arc furnaces are the devices of relatively large power (tens or even
hundreds of MVA), the furnace load unbalance may result in significant voltage
unbalance in the supply system.
The sources of unbalance can also be three-phase components of the
transmission system, in particular overhead lines. Due to different tower geometries
the conductors of
individual phases are not simultaneously at the same location as each other and to
earth. Following this, the line has different values of phase parameters, and also the
values of a voltage loss in individual phases are different.
Effects:
The negative-sequence and zero-sequence currents flowing in an electric
power system result in
• Additional losses of power and energy;
• Additional heating, the consequence of which is the limitation of line transmission
capability for positive-sequence currents;
• Voltage unbalance at nodes of the network. Voltage unbalance adversely affects the
operation of loads. Asynchronous motors, synchronous generators and rectifiers are
the most sensitive loads in this respect.
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3.2 Classification
3.2.1 Linear Loads
Linear loads are those in which voltage and current signals follow one another
very closely, such as the voltage drop that develops across a resistance, which
varies as a direct function of the current that passes through it.
Linear loads can be classified as follows:
 Resistive Elements
Incandescent Lighting
Electric Heaters
 Inductive Elements
Induction motors
Current limiting reactors
Induction generators
Damping reactors used to attenuate harmonics
Turning reactors in harmonic filters
 Capacitive Elements
Power factor correction capacitor banks
Underground cables
Insulated cables
Capacitors used in harmonic filters
3.2.2Non-Linear loads
Non linear loads are loads in which the current waveform does not resemble
the applied voltage waveform due to a number of reasons, for example the use of
electronic switches that conduct load current only during a fraction of the power
frequency period
 Power Electronics
Power converters
Variable frequency drives
DC motor controllers
Cycloconverters
Cranes
Elevators
Steel mills
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Power supplies
UPS
Battery Chargers
 ARC devices
Fluorescent lighting
ARC furnaces
Welding machines
3.2.3. Other Loads
Unbalance can also affect the operation of other three-phase loads,
changing the electric power, exploitative characteristics and their service life.
Moreover, voltage unbalance associated with a change in voltage magnitude has an
effect on the operation of single-phase loads. Some of them may be under the
influence of a supply voltage that is too high or too low. Disturbances in the
functioning of control systems can also occur, resulting in disturbing and even in
interrupting the operation of equipment.
Harmonics have always been present in power systems. Recently, due to
the widespread use of power electronic systems resulting in an increase in their
magnitude, they have become a key issue in installations. Harmonic disturbances
come generally from equipment with a non-linear voltage/current characteristic.
Nowadays a large part of industrial, commercial and domestic loads is non-linear,
making the distortion level on the low-voltage (but not only) supply network a serious
concern. Linear loads are comparatively rare today: the only examples which can be
considered as common are undimmed filament bulbs and unregulated heaters.
Non-linear loads represent a large percentage of the total loads. Under these
conditions, total harmonic distortion (THD) may become very high and therefore
dangerous for the system. Harmonic distortion can be considered as a sort of pollution
of the electric system which can cause problems if the sum of the harmonic currents
exceeds certain limits. Knowledge of electromagnetic disturbances associated with
this phenomenon is still developing; for this reason harmonics are currently an issue
of great interest.
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CHAPTER 4
4. WAVELET ANALYSIS
4.1 Introduction
Wavelet theory is the mathematics associated with building a model for nonstationary signal, with a set of components that are small waves, called wavelets.
Informally, a wavelet is a short- term duration wave. These functions have been
proposed in connection with the analysis of signals, primarily transients in a wide
range of applications.
A wavelet is a waveform of effectively limited duration that has an average
value of zero. It gives a tool for the analysis of transient, non-stationary or time
varying phenomena.
The basic concept in wavelet transform is to select an appropriate wavelet
function “mother wavelet” and then perform analysis using shifted and dilated
versions of this wavelet. Wavelet can be chosen with very desirable frequency and
time characteristics.
According to Fourier theory, signal can be expressed as a sum of possibly
infinite series of sines and cosines. This sum is referred to as Fourier expansion. The
big disadvantage of Fourier expansion is, it has only frequency resolution and no time
resolution. This means it determines all the frequencies present in the signal but it
does not tell at what time they are present. To overcome this problem Wavelet
transform is proposed. It provides time and frequency information simultaneously,
hence giving a time frequency representation of the signal.
In the wavelet analysis, the use of a fully scalable modulated window solves
the signal-cutting problem. The window is shifted along the signal and for every
position the spectrum is calculated. Then this process is repeated many times with a
slightly shorter (or longer) window for every new cycle. In the end, the result will be a
collection of time representation of the signal, all with different resolutions.
The basis functions used in Fourier analysis, sine waves and cosine waves, are
precisely located in frequency information of a signal calculated by the classical
Fourier transform is an average over the entire time duration of the signal. Thus, if
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there is a local transient over some small interval of time in the total duration of the
signal, the transient will contribute to the Fourier transform but its location on the
time axis will be lost. Although the short –time Fourier transform overcomes the time
location problem to a large extent, it does not provide multiple resolutions in time and
frequency, which is an important characteristic for analyzing
transient signal containing both high and low frequency components.
Wavelet analysis overcomes the limitations of Fourier methods by employing
analyzing functions that are local both in time and frequency. Unlike Fourier analysis,
which uses one basis function, wavelet analysis uses a number of basis functions of a
rather wide functional form. The wavelet functions are generated in the form of
translation and dilation of fixed function. The basis wavelet is termed as a mother
wavelet. The basic difference is, Short time Fourier transform uses a single analysis
window where as wavelet transform uses short windows at high frequencies at high
frequencies and long windows at low frequencies. The basis functions in WT employ
time compression or dilation rather than a variation in time frequency of the signal.
4.2 Capabilities Of Wavelet Analysis:
One major advantage afforded by wavelets is the ability to perform
local analysis — that is, to analyze a localized area of a larger signal. Consider
a sinusoidal signal with a small discontinuity — one so tiny as to be barely
visible. Such a signal easily could be generated in the real world, perhaps by a
power fluctuation or a noisy switch.
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Fig 4.1 fourier coefficients and wavelet coefficients
Wavelet analysis is capable of revealing aspects of data that other signal
analysis techniques miss, aspects like trends, breakdown points, discontinuities in
higher derivatives, and self-similarity. Furthermore, because it affords a different
view of data than those presented by traditional techniques, wavelet analysis can often
compress or de-noise a signal without appreciable degradation. Indeed, in their brief
history within the signal processing field, wavelets have already proven themselves to
be an indispensable addition to the analyst’s collection of tools and continue to enjoy
a burgeoning popularity today.
4.3.Wavelet Analysis
Now that we know some situations when wavelet analysis is useful, it is
worthwhile asking “What is wavelet analysis?” and even more fundamentally, “What
is a wavelet?” A wavelet is a waveform of effectively limited duration that has an
average value of zero. Compare wavelets with sine waves, which are the basis of
Fourier analysis. Sinusoids do not have limited duration — they extend from minus to
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plus infinity. And where sinusoids are smooth and predictable, wavelets tend to be
irregular and asymmetric.
Fig.4.2 sine wave and wavelet
Fourier analysis consists of breaking up a signal into sine waves of various
frequencies. Similarly, wavelet analysis is the breaking up of a signal into shifted and
scaled versions of the original (or mother) wavelet. Just looking at pictures of
wavelets and sine waves, you can see intuitively that signals with sharp changes might
be better analyzed with an irregular wavelet than with a smooth sinusoid, just as some
foods are better handled with a fork than a spoon. It also makes sense that local
features can be described better with wavelets that have local extent. Fourier analysis
consists of breaking up a signal into sine waves of various frequencies. Similarly,
wavelet analysis is the breaking up of a signal into shifted and scaled versions of the
original (or mother) wavelet. Just looking at pictures of wavelets and sine waves, you
can see intuitively that signals with sharp changes might be better analyzed with an
irregular wavelet than with a smooth sinusoid, just as some foods are better handled
with a fork than a spoon. It also makes sense that local features can be described
better with wavelets that have local extent.
Thus far, we’ve discussed only one-dimensional data, which encompasses most
ordinary signals. However, wavelet analysis can be applied to two-dimensional data
(images) and, in principle, to higher dimensional data. This toolbox uses only oneand two-dimensional analysis techniques.
4.3.1 scaling:
The parameter scale (or dilation) in the wavelet analysis is similar to the scale
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used in maps. As in the case of maps, high scales correspond to a non-detailed global
view (of the signal), and low scales correspond to a detailed view. Similarly, in terms
of frequency, low frequencies (high scales) correspond to a global information of a
signal (that usually spans the entire signal), whereas high frequencies (low scale)
correspond to a detailed information of a hidden pattern in the signal.
Fortunately in practical applications, low scales (high frequencies) do not last
for the entire duration of the signal, unlike those shown in the figure, but they usually
appear from time to time as short bursts, or spikes.
Scaling, as a mathematical operation, either dilates or compresses a signal.
Larger scales correspond to dilated (or stretched out) signals and small scales
correspond to compressed signals. All of the signals given in the figure are the dilated
and compressed versions of the same function. In the figures shown, a = 0.25 is the
smallest scale anda=l
is the largest scale.
However, in the definition of the wavelet transform, the scaling term is used in
denominator, and therefore, the opposite of the above statement holds, i.e., scales a>1
dilates the signals whereas scales a<1, compresses the signal. This interpretation of
scale will be used throughout this text. It is clear from the figure that scale factor, a is
inversely related to the frequency of the signal.
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Fig4.3.wavelet and sine wave at different frequencies
4.4 Classification of wavelets
We can classify wavelets into two classes: (a) orthogonal and (b)
biorthogonal. Based on the application, either of them can be used.
(a)Features of orthogonal wavelet filter banks
The coefficients of orthogonal filters are real numbers. The filters are of
the same length and are not symmetric. The low pass filter, G0 and the high pass filter,
H0 are related to each other by
H0 (z) = z
-N
-1
G0 (-z )
The two filters are alternated flip of each other. The alternating flip automatically
gives double-shift orthogonality between the lowpass and highpass filters [1], i.e., the
scalar product of the filters, for a shift by two is zero. i.e.,
ΣG[k] H[k-2l] = 0,
where k,lЄZ [4]. Filters that satisfy equation 2.4 are known as Conjugate Mirror
Filters (CMF). Perfect reconstruction is possible with alternating flip.
Also, for perfect reconstruction, the synthesis filters are identical to the
analysis filters except for a time reversal. Orthogonal filters offer a high number of
vanishing moments. This property is useful in many signal and image processing
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applications. They have regular structure which leads to easy implementation and
scalable architecture.
(b)Features of biorthogonal wavelet filter banks
In the case of the biorthogonal wavelet filters, the low pass and the
high pass filters do not have the same length. The low pass filter is always symmetric,
while the high pass filter could be either symmetric or anti-symmetric. The
coefficients of the filters are either real numbers or integers.
For perfect reconstruction, biorthogonal filter bank has all odd length or all even
length filters. The two analysis filters can be symmetric with odd length or one
symmetric and the other antisymmetric with even length. Also, the two sets of
analysis and synthesis filters must be dual. The linear phase biorthogonal filters are
the most popular filters for data compression applications.
4.4.1 Wavelet families:
There are a number of basis functions that can be used as the mother
wavelet for Wavelet Transformation. Since the mother wavelet produces all wavelet
functions used in the transformation through translation and scaling, it determines the
characteristics of the resulting Wavelet Transform. Therefore, the details of the
particular application should be taken into account and the appropriate mother
wavelet should be chosen in order to use the Wavelet Transform effectively.
Figure 4.4 Wavelet families (a) Haar (b) Daubechies4 (c) Coiflet1 (d) Symlet2 (e)
Meyer (f) Morlet (g) Mexican Hat.
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Figure 4.4 illustrates some of the commonly used wavelet functions.
Haar wavelet is one of the oldest and simplest wavelet. Therefore, any discussion of
wavelets starts with the Haar wavelet. Daubechies wavelets are the most popular
wavelets. They represent the foundations of wavelet signal processing and are used in
numerous applications. These are also called Maxflat wavelets as their frequency
responses have maximum flatness at frequencies 0 and π. This is a very desirable
property in some applications. The Haar, Daubechies, Symlets and Coiflets are
compactly supported orthogonal wavelets. These wavelets along with Meyer wavelets
are capable of perfect reconstruction. The Meyer, Morlet and Mexican Hat wavelets
are symmetric in shape. The wavelets are chosen based on their shape and their ability
to analyze the signal in a particular application.
Haar:
Any discussion of wavelets begins with Haar wavelet, the first and simplest.
Haar wavelet is discontinuous, and resembles a step function. It represents the same
wavelet as Daubechies db1.
Biorthogonal:
This family of wavelets exhibits the property of linear phase, which is needed
for signal and image reconstruction. By using two wavelets, one for decomposition
(on the left side) and the other for reconstruction (on the right side) instead of the
same single one, interesting properties are derived.
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Fig:4.5different types of Biorthogonal wavelets
Symlets:
The symlets are nearly symmetrical wavelets proposed by
Daubechies as modifications to the db family. The properties of the two wavelet
families are similar.
Fig 4.6 different types of Symlets wavelets
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Morlet:
This wavelet has no scaling function, but is explicit.
Fig 4.7 Morelet wavelet
Mexican Hat: This wavelet has no scaling function and is derived from a function
that is proportional to the second derivative function of the Gaussian probability
density function.
Fig 4.8 Maxican Hat wavelet
Other Real Wavelets
Some other real wavelets are available in the toolbox:
Reverse Biorthogonal
Gaussian derivatives family
FIR based approximation of the Meyer wavelet
Complex Wavelets
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Some complex wavelet families are available in the toolbox:
Gaussian derivatives
Morlet
Frequency B-Spline
Shannon
4.5 THE DISCRETE WAVELET TRANSFORM
The transform of a signal is just another form of representing the
signal. It does not change the information content present in the signal. The Wavelet
Transform provides a time-frequency representation of the signal. It was developed to
overcome the short coming of the Short Time Fourier Transform (STFT), which can
also be used to analyze non-stationary signals. While STFT gives a constant
resolution at all frequencies, the Wavelet Transform uses multi-resolution technique
by which different frequencies are analyzed with different resolutions.
A wave is an oscillating function of time or space and is periodic. In
contrast, wavelets are localized waves. They have their energy concentrated in time or
space and are suited to analysis of transient signals. While Fourier Transform and
STFT use waves to analyze signals, the Wavelet Transform uses wavelets of finite
energy
The wavelet analysis is done similar to the STFT analysis. The signal to be
analyzed is multiplied with a wavelet function just as it is multiplied with a window
function in STFT, and then the transform is computed for each segment generated.
However, unlike STFT, in Wavelet Transform, the width of the wavelet function
changes with each spectral component. The Wavelet Transform, at high frequencies,
gives good time resolution and poor frequency resolution, while at low frequencies,
the Wavelet Transform gives good frequency resolution and poor time resolution.
4.5.1 The Continuous Wavelet Transform and the Wavelet Series
The Continuous Wavelet Transform (CWT) is provided by equation 2.1,
where x(t) is the signal to be analyzed. ψ(t) is the mother wavelet or the basis
function. All the wavelet functions used in the transformation are derived from the
mother wavelet through translation (shifting) and scaling (dilation or compression).
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The mother wavelet used to generate all the basis functions is designed based on some
desired characteristics associated with that function. The translation parameter τ
relates to the location of the wavelet function as it is shifted through the signal. Thus,
it corresponds to the time information in the Wavelet Transform. The scale parameter
s is defined as |1/frequency| and corresponds to frequency information. Scaling either
dilates (expands) or compresses a signal. Large scales (low frequencies) dilate the
signal and provide detailed information hidden in the signal, while small scales (high
frequencies) compress the signal and provide global information about the signal.
Notice that the Wavelet Transform merely performs the convolution operation of the
signal and the basis function. The above analysis becomes very useful as in most
practical applications, high frequencies (low scales) do not last for a long duration,
but instead, appear as short bursts, while low frequencies (high scales) usually last for
entire duration of the signal. The Wavelet Series is obtained by discretizing CWT.
This aids in computation of CWT using computers and is obtained by sampling the
time-scale plane. The sampling rate can be changed accordingly with scale change
without violating the Nyquist criterion. Nyquist criterion states that, the minimum
sampling rate that allows reconstruction of the original signal is 2ω radians, where ω
is the highest frequency in the signal. Therefore, as the scale goes higher (lower
frequencies), the sampling rate can be decreased thus reducing the number of
computations.
4.5.2 The Discrete Wavelet Transform
The Wavelet Series is just a sampled version of CWT and its
computation may consume significant amount of time and resources, depending on
the resolution required. The Discrete Wavelet Transform (DWT), which is based on
sub-band coding is found to yield a fast computation of Wavelet Transform. It is easy
to implement and reduces the computation time and resources required.
The foundations of DWT go back to 1976 when techniques to decompose
discrete time signals were devised [5]. Similar work was done in speech signal coding
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which was named as sub-band coding. In 1983, a technique similar to sub-band
coding was developed which was named pyramidal coding. Later many
improvements were made to these coding schemes which resulted in efficient multiresolution analysis schemes.
In CWT, the signals are analyzed using a set of basis functions which relate to each
other by simple scaling and translation. In the case of DWT, a time-scale
representation of the digital signal is obtained using digital filtering techniques. The
signal to be analyzed is passed through filters with different cutoff frequencies at
different scales.
4.5.3 DWT and Filter Banks:
4.5.3.1 Multi-Resolution Analysis using Filter Banks
Filters are one of the most widely used signal processing functions.
Wavelets can be realized by iteration of filters with rescaling. The resolution of the
signal, which is a measure of the amount of detail information in the signal, is
determined by the filtering operations, and the scale is determined by up sampling and
down sampling (sub sampling) operations[5].
The DWT is computed by successive lowpass and highpass filtering of the discrete
time-domain signal as shown in figure 2.2. This is called the Mallat algorithm or
Mallat-tree decomposition. Its significance is in the manner it connects the
continuous-time multi resolution to discrete-time filters. In the figure, the signal is
denoted by the sequence x[n], where n is an integer. The low pass filter is denoted by
G0 while the high pass filter is denoted by H0. At each level, the high pass filter
produces detail information, d[n], while the low pass filter associated with scaling
function produces coarse approximations, a[n].
Fig. 4.9 Three-level wavelet decomposition tree.
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At each decomposition level, the half band filters produce signals spanning
only half the frequency band. This doubles the frequency resolution as the uncertainty in
frequency is reduced by half. In accordance with Nyquist’s rule if the original signal has
a highest frequency of ω, which requires a sampling frequency of 2ω radians, then it
now has a highest frequency of ω/2 radians. It can now be sampled at a frequency of
ω radians thus discarding half the samples with no loss of information. This
decimation by 2 halves the time resolution as the entire signal is now represented by
only half the number of samples. Thus, while the half band low pass filtering removes
half of the frequencies and thus halves the resolution, the decimation by 2 doubles the
scale.
With this approach, the time resolution becomes arbitrarily good at high
frequencies, while the frequency resolution becomes arbitrarily good at low
frequencies. The time-frequency plane is thus resolved as shown in figure 1.1(d) of
Chapter 1. The filtering and decimation process is continued until the desired level is
reached. The maximum number of levels depends on the length of the signal. The
DWT of the original signal is then obtained by concatenating all the coefficients, a[n]
and d[n], starting from the last level of decomposition.
Fig. 4.10 Three-level wavelet reconstruction tree.
Figure 2.3 shows the reconstruction of the original signal from the
wavelet coefficients. Basically, the reconstruction is the reverse process of
decomposition. The approximation and detail coefficients at every level are up sampled
by two, passed through the low pass and high pass synthesis filters and then added. This
process is continued through the same number of levels as in the decomposition process
to obtained the original signal. The Mallat algorithm works equally well if the analysis
filters, G and H , are exchanged with the synthesis filters, G .
0
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4.6.3.2 Conditions for Perfect Reconstruction
In most Wavelet Transform applications, it is required that the original signal be
synthesized from the wavelet coefficients. To achieve perfect reconstruction the
analysis and synthesis filters have to satisfy certain conditions. Let G0(z) and G1(z) be
the low pass analysis and synthesis filters, respectively and H0(z) and H1(z) the high
pass analysis and synthesis filters respectively. Then the filters have to satisfy the
following two conditions as given in [4] :
G0 (-z) G1 (z) + H0 (-z). H1 (z) = 0
G0 (z) G1 (z) + H0 (z). H1 (z) = 2z
-d
The first condition implies that the reconstruction is aliasing-free and the second
condition implies that the amplitude distortion has amplitude of one. It can be
observed that the perfect reconstruction condition does not change if we switch the
analysis and synthesis filters.
There are a number of filters which satisfy these conditions. But not all of them give
accurate Wavelet Transforms, especially when the filter coefficients are quantized.
The accuracy of the Wavelet Transform can be determined after reconstruction by
calculating the Signal to Noise Ratio (SNR) of the signal. Some applications like
pattern recognition do not need reconstruction, and in such applications, the above
conditions need not apply.
4.6 Applications :
There is a wide range of applications for Wavelet Transforms. They are
applied in different fields ranging from signal processing to biometrics, and the list is
still growing. One of the prominent applications is in the FBI fingerprint compression
standard. Wavelet Transforms are used to compress the fingerprint pictures for
storage in their data bank. The previously chosen Discrete Cosine Transform (DCT)
did not perform well at high compression ratios. It produced severe blocking effects
which made it impossible to follow the ridge lines in the fingerprints after
reconstruction. This did not happen with Wavelet Transform due to its property of
retaining the details present in the data.
In DWT, the most prominent information in the signal appears in high amplitudes and
the less prominent information appears in very low amplitudes. Data compression can
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be achieved by discarding these low amplitudes. The wavelet transforms enables high
compression ratios with good quality of reconstruction. At present, the application of
wavelets for image compression is one the hottest areas of research. Recently, the
Wavelet Transforms have been chosen for the JPEG 2000 compression standard.
Fig.4.11 Signal processing application using Wavelet Transform.
Figure 4.11 shows the general steps followed in a signal processing
application. Processing may involve compression, encoding, denoising etc. The
processed signal is either stored or transmitted. For most compression applications,
processing involves quantization and entropy coding to yield a compressed image.
During this process, all the wavelet coefficients that are below a chosen threshold are
discarded. These discarded coefficients are replaced with zeros during reconstruction
at the other end. To reconstruct the signal, the entropy coding is decoded, then
quantized and then finally Inverse Wavelet Transformed.
Wavelets also have numerous applications in digital communications.
Orthogonal Frequency Division Multiplexing (OFDM) is one of them. Wavelets are
used in biomedical imaging. For example, the ECG signals, measured from the heart,
are analyzed using wavelets or compressed for storage. The popularity of Wavelet
Transform is growing because of its ability to reduce distortion in the reconstructed
signal while retaining all the significant features present in the signal.
4.7 Summary
This chapter has explained brief discussion about the wavelet analysis, this analysis
shows the comparison between the sine wave and wavelet wave form. Different types
of wavelet families and their related waveforms are also studied. The applications of
wavelet analysis is also studied in brief.
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CHAPTER 5
TEST SYSTEM AND SIMULATION RESULTS
5.1 Introduction to MATLAB
The MATLAB is a high performance language for technical computing integrates
computation, visualization, and programming in an easy –to- use environment where
problems and solutions are expressed in familiar mathematical notation. MATLAB software
can provide solution for you in technical computing, some of the common applications of
MATLAB and the types of add-on, application-specific solutions that are available in
MATLAB toolbox.
The MATLAB documentation is organized into these main topics
Graphics: Tools and techniques for plotting graph annotation, printing and programming with
handle graphics.
Desktop tools and development environment: start up and shutdown, the desktop and other
tools that help you use and become more productive with MATLAB.
Mathematics: Mathematical operations
Data analysis: Data analysis, including data fitting, Fourier analysis, and time series tools.
Programming fundamentals: the MATLAB language and how to develop MATLAB
applications
MATLAB classes and Object-Oriented programming: Designing and implementing
MATLAB classes.
3-D visualization: Visualizing surface and volume data, transparency, and viewing and
lighting techniques
Creating graphical user interfaces: GUI-building tools and how to write callback functions
External interface: MEX-files, the MATLAB engine, and interfacing to sun Microsystems
java software, COM, and the serial port
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 42
5.2 POWER SYSTEM NETWORK
In this work, we consider single source feeding to 0.8 MW and 0.4 MVAR load
through a transmission line of 200 Km length at 5 kV. Here the test system have been
simulated for normal loading condition, sag, swell and interruption. The MATLAB test
system shown in fig.5.
Fig.5.1network used for creating various PQ problems
5.2.1 SPECIFICATION OF TEST SYSTEM
Rating of the source voltage is 5 k.v and 50 Hertz
The length of the transmission line is 100 K.M
The ratings of the transmission line parameters
Resistance is 2.568 ohm
Inductance is 20 Mh
Capacitance is 0.86 Micro farad
Total length of the transmission system used is 200 K.M.
The rating of RL load connected to this transmission line is 0.8 M. and 0.4 Mvar
The one by one added loads for this transmission line are
0.34 M.W,0.16 Mvar
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 43
0.18 M.W, 0.06 Mvar
0.3 M.W, 0.14 Mvar
Parallel RC load is 0.06 M.W, 0.6 Mvar
0.36 M.W, 0.17 Mvar
0.38 M.W, 0.19 Mvar
Breaker resistance 0.01 Ohm
Snumbber resistance 1M Ohm
These are the specifications used to simulate the test system using MATLAB SIMULINK.
SIMULATION
The above network had simulated in MATLAB using simulink blocks with the given
specifications mentioned above.
Case 1:
For the normal condition simulated load voltage and currents are presented.
Fig .5.2 normal voltage
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 44
Case 2:
After applying the load at breaker 1 the obtained distorted signal (Sag in voltage
magnitude) is shown below
Fig 5.3 Sag voltage
To get the voltage sag by adding a RL Load of 0.3 MW& 0.16 Mvar at breaker 1. For
sag magnitude levels varies from 10% to 90% with different duration of time with a base
value of voltage (1 p.u).
Case 3:
After applying the parallel RC load (0.06 MW, 0.6 Mvar) at breaker 6 the obtained
load voltage waveform is shown in fig 5.4
Fig.5.4 voltage for swell
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 45
For voltage swell magnitude of PQ disturbance varies from 110% to 180% with
different duration of time.
Case4: To make the load end ded short circuit by closing the breaker 8, the obtained load
voltage waveform is shown in Fig5.5. .
Fig 5.5 voltage for interruption
Because of shot circuit at load the load voltage becomes zero. So we obtained the interruption
during the time 0.2 to 0.6 seconds.
5.3 wavelet decomposition
In the pre-processing voltage signals are captured during a power quality problem.
Due to the absence of field results different power quality problems have been simulated in
the MATLAB/SIMULINK environment. The PQ data thus obtained matches the field data.
Subsequently, using the Wavelet toolbox of the MATLAB, multi signal decomposition on the
captured signals is performed. Depending on the selected resolution levels, the PQ signal is
decomposed into a number of wavelet levels. If the resolution level is defined as n, after
decomposing the signal, there will be one level of approximation coefficients with n level of
detail coefficients. The information contained in the coefficients of details and
approximations is very useful for further processing.
5.3.1 Procedure of power quality problem
Various possible PQ disturbances viz. sag, swell, and interruption are classified using
Wavelet analysis.
Network is shown in Fig.5.1 is used for simulation as well as for
visualizing disturbances in MATLAB/SIMULINK. After obtaining the disturbances data with
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 46
wide range of parameters variation, MSD wavelet analysis is applied on the PQ signal for
extracting the useful information relating the event.
Thereafter, Parseval’s energy theorem is used to determine the energy of the PQ
signal corresponding to each detailed level. Parseval theorem relates the energy of the
distorted signal to the energy in each of the expansion components and their wavelet
coefficients. This means that energy of the PQ signal can be partitioned in terms of the
expansion coefficients as per equation 5.1.

2
N
2
N
f ( n) =
 c j (n) +  d j (n)
n 1
n 1
j
N
2
(5.1)
j 1 n 1
Where, f(n)is the time domain signal under analysis
N is the total number of samples of the signal
N
 f ( n)
2
=total energy of the signal
n 1
2
N
c
n 1
j
(n) =total energy connected in the level ‘j’ of the
approximated version of the signal
j
2
N
 d
j 1 n 1
j
( n)
is the total energy connected in the detailed
version of the signal from levels 1 to j
In the present work the signal is decomposed in 6 levels using db-3. The average
energies, Ej up to sixth level of detailed signals are determined. These six energy values
contain the information of energy distribution of particular PQ signal.
Thereafter normalization of these energy values is carried out. Normalization is done
to extract the useful information of the PQ problem in a better way for classification. Further
this enhances the information embedded in lower energy levels. The normalized Shannon
entropy will be used. The definition of normalized Shannon entropy is as follows
EJ  k E jk log E jk
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 47
Where Ejk is the wavelet energy spectrum at scale j and instant k and it as follows is defined
EJK  DJ (k )
2
5.3
Equations (5.2) and (5.3) are used for normalization of the extracted energy values.
where j has values from 1, 2, ……6
Ej= Energy at each level
In order to make the information easy to handle scaling of the energy values is done
by scaling factor ‘ k ’ so as to make the system efficient and consuming less memory in
computation.
5.3.2 Wavelet tool box main menu
Fig 5.6 wavelet toolbox main menu
5.3.3 Decomposition levels for each power quality disturbance
The simulation results of load voltage signal have been loaded to wavelet menu and
decomposed using db-3 with 6 levels. The decomposed signals are presented in fig.5.7 .
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 48
Fig 5.7 decomposition levels for normal voltage
The simulation results of load voltage signal have been loaded to wavelet menu and
decomposed using db-3 with 6 levels. The decomposed signals are presented in Fig5.8
Fig5.8 decomposition levels for sag voltage
The simulation results of load voltage signal have been loaded to wavelet menu and
decomposed using db-3 with 6 levels. The decomposed signals are presented in fig 5.9
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 49
Fig5.9 decomposition levels for voltage swell
The simulation results of load voltage signal have been loaded to wavelet menu and
decomposed using db-3 with 6 levels. The decomposed signals are presented in fig 5.10
Fig 5.10 decomposition levels for voltage interruption
5.3.4 Wavelet entropy table for different power quality disturbances
From the results of wavelet decomposed values, we find the entropy using shaman
formula and normalized. Finally finding energy levels of each signal and based on energy
values, made the classifying the various power quality problems.
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 50
Condition
o
e
a. load=0.6MW
32.7628
114.3192
b. load=0.7MW
26.9059
88.5833
c. load=0.8MW
15.1958
41.3481
d. load=0.9MW
24.8938
80.0242
e. load=1MW
18.1092
52.4517
1.normal
2.sag
a.0.2-0.4
17.6076
b.0.2-0.6
15.9491
50.5044
44.1535
c.0.2-0.8
17.1694
48.4581
d. 2 breakers
17.228
e. 3 breakers
14.2696
f.5 breakers
12.8830
49.0337
37.9306
32.9297
3.swell
a.0.2-0.4
25.8427
84.0410
b. 0.2-0.6
27.8535
92.3534
c. 0.2-0.8
35.1693
125.5135
a.0.2-0.4
14.6258
39.2514
b. 0.2-0.6
10.5068
24.7122
c. 0.2-0.8
7.5918
15.2129
4. interruption
Table 5.1 wavelet entropy for different power quality problems
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 51
6. CONCLUSION
In this work, the literature work carried out for various power quality disturbances for
classification of power quality problems. We carried out the MATLAB SIMULINK,
simulation and observed the power quality problems. Further analysis of power quality
problems using wavelet analysis, by calculating the entropy and energy levels for various
faults. Based on entropy and energy values it is to discriminate various power quality
problems.
Multi resolution signal decomposition using wavelet transformation is used as a basis for
feature vector for obtaining the training and testing data for ANN. The integration of wavelet
transform with ANN classifies various power quality problems with over 90% accuracy. This
is the extension for this thesis.
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 52
7. REFERENCES
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CLASSIFICATION OF POWER QUALITY PROBLEMS USING WAVELET BASED ARTIFICIAL NEURAL NETWORK| 53
[11] Thomas E. Grebe, PE Electrotek Concepts, Inc, “ CAPACITOR SWITCHING
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