Transformer Fault Diagnosis Using DSP

This assignment explores fault diagnosis techniques applied to power transformers, focusing on the utilization of Digital Signal Processing (DSP). It delves into research papers that investigate methods such as Fuzzy Fault Tree Analysis and the application of FIR filters for identifying and classifying transformer faults. The assignment emphasizes the role of DSP in analyzing signals from transformers to detect anomalies indicative of potential issues.

ENS6126 Master of Engineering 1
Progress Report
Modern Transformer Protection
John Citizen
Student # 12345678
26 May 2099
Supervisor: Dr Jane Public

Abstract
The advancement in Modern Power System has gained a design of wide range of
Transformers With sizes of few KVA to several hundred of MVA. Huge Transformers
are used to step up a voltage of about 25KV to transmission level, such as 330KV.The
Transformers are availed in various sizes to step down the voltages from 330KV to
130KV and then its distributed in level of 33KV ,then its again stepped down for
domestic supply to 415V.The transformer has to be protected for reliable Power
System. The losses due to thermal stress and electrodynamics forces of the transformer
has to be decreased to make steady flow of supply. To ensure the supply magnetising
inrush current and fault current of transformer has be reduced. In this project the fault
and magnetising inrush current has been identified using wavelet transform and
continuous monitoring of the system will help to handle the fault current so it can be
reduced. The harmonics are formed by the non-linear devices placed in the power
system. These harmonics are the multiple integers of the fundamental frequency. These
Harmonics Frequencies are due to the voltage and current distortions. Distortions in
voltage and current will results problem in power quality. So approximation of
harmonics is most important for the efficiency of the system. The Quality of the system
has to be maintained as per the given standards and to protect the system from damages
due to loads. A filtering device has been used to filter the unwanted frequencies. This
device will allow only some specific frequencies and reduce the distortions. Therefore a
digital filter has been designed to reduce the harmonics and improve the quality of the
power in the system. This project is to explain the methods of protection of transformer
by reducing the fault current and magnetising inrush current using Wavelet Transform
and to reduce the harmonics in the power system using Digital Filter. There are various
types of digital filter has been used to improve the efficiency and reduce the distortions
to maintain the quality of the system. Digital Filters are basically classified in two types
depending upon the impulse response as IIR and FIR filters. The FIR filter have linear
Phase response and there won’t be any phase distortion and it will maintain the stability.
Therefore a Transformer protection methods has been given using Wavelet Transform
and FIR filter based algorithms and analysed using MATLAB.
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Table of Contents
List of Figures..........................................................................................................................iii
1. Introduction....................................................................................................................1
1.1 Introduction................................................................................................................1
1.2 Objectives....................................................................................................................2
1.3 Significance.................................................................................................................2
1.4 Report Organisation...................................................................................................3
2. Background.....................................................................................................................5
2.1 Literature Review.............................................................................................................5
2.2 Transformer losses...........................................................................................................9
2.3 Different current losses in transformer........................................................................10
2.4 Current Transformer Issues..........................................................................................14
3. Proposed Approach......................................................................................................17
3.1 Wavelet transform..........................................................................................................17
3. 2 Continuous wavelet transform.....................................................................................18
3.3. Wavelet based algorithm..............................................................................................19
3.4 Digital filters...................................................................................................................20
3.5 Infinite impulse response (IIR) filter............................................................................22
4. Preliminary Results and Discussions..........................................................................29
4.1 Wavelet based Algorithm Result.............................................................................29
5. Conclusion.....................................................................................................................35
References.............................................................................................................................37
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List of Figures
Figure 1 Magnetizing inrush current..........................................................................................11
Figure 2 Harmonic distortion.....................................................................................................13
Figure 3 Basic Circuit of Relay....................................................................................................15
Figure 4 Circuit to implement the Relay.....................................................................................16
Figure 5 Wavelet based algorithm flow chart............................................................................19
Figure 6 Digital filters.................................................................................................................20
Figure 7 Magnitude response for the filters...............................................................................21
Figure 8 Infinite impulse response (IIR) filter.............................................................................22
Figure 9 Structure of FIR Filter...................................................................................................25
Figure 10 Digital Filter Design Flow Chart..................................................................................26
Figure 11 Magnitude Response of the Filter..............................................................................27
Figure 12 Simulation Diagram of Transformer for Fault.............................................................29
Figure 13 the output Waveform for fault current......................................................................30
Figure 14 Output Waveform for inrush Current.........................................................................30
Figure 15 Output waveform of FIR Filter....................................................................................33
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1. Introduction
1.1 Introduction
Generally Transformers are considered as a most reliable unit, but there is a
chance of failure because of internal fault, due to stresses from external sources. Fuse
has been used for smaller distribution Transformer. Sometimes inverse definite
minimum time or instantaneous over current and Earth fault relays has been used for
Transformer Protection. For this type of protection downstream power system co-
ordination is necessary.so this could lead to time delay. Therefore this method cannot be
used for Large Power Distribution which could lead to unstable system and generate
more power losses.
A Device where the electrical energy from one circuit is transferred to another
by a magnetic field without changing the frequency, this is done by a transformer. At
this modern times it is essential to have transformers that have reduced loss and to
transmit electric power at a greater level. The life span of a transformer is reduced due
to the effect of overload that increases the temperature of the transformer. Filters are
used for reducing the loss of electric power in the transformers. The aim of the report is
to provide a transformer protection for the purpose of steady electrical flow by using
wavelet transform algorithm and algorithm based on filter. This project also explains the
current transformer issues and their restrain characteristics. By providing a continuous
the supply magnetizing inrush current and fault current of the transformer, it has been
reduced the fault current of the transformer. The required hardware for the
implementation of the reduced electrical losses is been given in this project. The
methods to protect the transformer through minimizing the fault current by using the
wavelet transformation algorithm and to reduce the harmonics by using the digital filter
will be explained in this project. The result of this implementation of the steady flow
electric power will be given in MATLAB, which is a programming language that
includes data visualization and creating user interface, also includes developing and
running algorithms. The report will provide the harmonic distortions, different varieties
of current in the transformer and external and internal short circuits. Various types of
digital filter has been used to progress the efficiency and to reduce the distortions to
maintain the quality of the system. Digital Filters are basically classified in two types
depending upon the impulse response as IIR and FIR filters. The FIR filter have linear
Phase response and there won’t be any phase distortion and it will maintain the stability.
Digital filters will be used for reducing the electric losses and the distortion are
protected.
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1.2 Objectives
The objective of the project is to reduce the loss due to thermal stress and
electrodynamics forces of the transformer and to maintain a steady flow of electric
current, to maintain the quality of the system and to protect the reliable power system of
the transformer. It also aims at reducing problems related to power quality by
decreasing the distortions in the current. To reduces the higher voltage electricity into
lower voltage systems that is used by the end users.
1.3 Significance
1. In a distribution system a better regulation of voltage is been produced by the
transformer that acts as a booster to it. The transmission of power occur in
higher rate that is not economical, the voltage level is been enhanced by the
transformers by producing a voltage with greater level at a very low loss. The
power transformers assist in maintaining the power quality and control and
simplifies the electrical networks.
2. The transformer that is generated in electrical power is a cost effective
transformer with a low voltage level, if this low voltage power is transmitted in
in the receiving end it results in a greater linear circuit that causes the line losses.
The increase in the voltage power causes the reduction in the ohmic.
3. Power transformer can electrically segregate the circuits.
4. Power transformer can decrease or increase the capacitor’s value, a resistance or
an inductor in an AC circuit. Power transformer thus perform as an impedance
transferring device.
5. Power transformer can also be used to avoid DC current passing starting from
one circuit to another circuit.
6. Each single show gadget or recording gadget can be perused in the wire lengths
between the distinctive channels for get to, not caused by wire length going
between accuracy.4mA to zero level, to decide the open circuit or sensor is
harmed (0mA state) is extremely helpful, in the simple expansion of two-line
outlet surge and lightning assurance gadgets, is helpful for safe mine blast.
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7. The capacitive protection of the beneficiary causes obstruction on the blunder,
both for 4 ~ 20mA wire circle, the recipient protection is normally 250
(specimen Uout = 1 ~ 5V) that protection sufficiently little to create huge
mistakes, in this manner, can permit the link length longer than the voltage
telemetry framework further
8. In the present source yield protection is sufficiently expansive, the attractive
field sensor coupled to the wire the voltage circle won't have a huge effect, on
the grounds that the obstruction caused by the current is little, as a rule utilizing
turned combine can decrease the impedance resistance. Less defenseless to
parasitic thermocouples and weight drop along the wire protection and
temperature float of the transmission line can be extremely economical contorted
match wire better.
1.4 Report Organisation
This report contains five topics namely introduction, Background of the project,
proposed approach, preliminary results and discussions and conclusion, which are
arranged as below
Introduction provides a general description about the Power transformers the
magnetic field that is changed by the transformers is given. The objective of the report
and its significance of implementation of the transformer is been explained. The
objective is gives as to provide a steady flow of electric power. The aim of the report is
given as to provide a transformer protection for the purpose of steady electrical flow by
using wavelet transform algorithm and algorithm based on filter. The main theme of the
project is given in the introduction part. A description about the MATLAB and the
definition of the filters is given.
The Background topics presents the clear vision about the project background. This
explains about the transformer losses, different current losses in the transformer and
current transformer issues. This topic also includes the literature review related to the
journals Modern Protection of Three-Phase and Spare Transformer Banks by Michael
Thompson, Faridul Katha Basha, and Craig Holt, article about Transformers Fault
Detection Using Wavelet Transform by Y. Najafi Sarem, E. Hashemzadeh, and M.A.
Layegh , a journal about Simulation Of Transformer For Fault Discrimination Using
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Wavelet Transform & neural Network by Laxminarayan Sonwani, Dr. Dharmendra
Kumar Singh and Durga Sharma and journal about A Review Of Design Digital Filter For
Harmonics Reduction In Power System by Prashant Nagare, Dr. Sachin Pable, Dr. A.K.
Kureshi. In transformer losses explanation is given about Copper loss, Dielectric loss
and Radiation and induction loss. The Different current losses in transformer topic
explains about the hysteresis loss eddy current loss and a graph that shows the inrush
current is caused when application of source voltage to a reenergized transformer gives
rise to sudden increase in current is been explained. The hardware that are required to
implement the relay is been given and a figure of basic circuit of the relay is given and a
figure Circuit to implement the Relay is also provided
The topic Proposed Approach addresses the wavelet transform, continuous wavelet
transform, wavelet based algorithm, digital filters and Infinite impulse response filter.
Preliminary Results and Discussions describe the Wavelet based Algorithm Result and
figures of Simulation Diagram of Transformer for Fault, the output Waveform for fault
current, Output Waveform for inrush Current and Output waveform of FIR Filter. FIR
Based Algorithm is also been explained
Conclusion gives the summary of the project.
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2. Background
2.1 Literature Review
As per (Sonwani, Kumar Singh & Sharma, 2015), the Fault discrimination of the
transformer is simulated by using neural network and wavelet transform. The simulation
of power transformer fault discrimination is done by using Mat lab. The wavelet
transform is used to identifying the non-stationary signals like magnetizing fault current
and inrush current. The wavelet transform process is almost equal to the Fourier
transform. It provides the decomposition of signal in the function form. It has the ability
to abstract information since transient signal in both frequency and time domain.The
artificial neural network is utilized for detecting the discrimination of fault current and
inrush current. It is powerful tool. It is used at artificial intelligence. The artificial neural
network has the ability to detect & automate the knowledge, has been proposed for
discrimination. The neural network is used for protecting the power transformer. To
reduce the maintainability and damage of the power system, the protective relays are
used. Because it has ability to separate the faulty part from the good part. It has the
interconnection between artificial neurons. It leads to the simulation of nervous system
in the human brain. For the discrimination process of power system, the input data is
imported to artificial neural network, but it is not possible. Because the dimension of
wavelet is too huge. The convergence of artificial neural network is difficult due to the
result of importing huge input data. To reduce the dimension of input, the spectral
energy wavelet signal is planned with (∆t) time length. The output is produced at three
phases. So the data window is separated into three. The methodology of this project is to
plan & demonstrating a power system at MATLABthrough Simulink library. The
received output signal is imported to the wavelet transform with the help of wavelet
toolbox. This is done at MATLAB. The signal of wavelet decomposition is provided the
approximate coefficients of signals also it provided the detailed coefficient of signal. By
using this signal the fault current is classified. The fault current may be internal fault
current or inrush current. It is detected by using neural network toolbox. The featured
data is mined after wavelet analysis. It is given to the neural network. Because it is used
to provide the more accurate and reliable information. By using this data, one could
reduce the number of neuron present at the middle layer. It is needed for simple neural
network architecture. For identifying the discriminating fault of power system, the
neural network Input, Output and Hidden layer is used. The discrimination fault of
power system is detected using wavelet transformer and neural network.
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As per (Nagare & Pable, 2016), the harmonics of power system is reduced using a
designed digital filter. The non-linear devices are created the harmonics in the power
system. The Power system quality damages are occurred due to the harmonics. Because
the harmonics created the distorted voltage and current. The limitation of harmonics is
very important to maintain the efficiency of the power system quality. Harmonics is the
sinusoidal components. It is a repetitive waveform. It contains the frequencies. The
filter is used to reject the unwanted frequencies. The Electric arc furnaces, Magnetic
Circuits and Power Electronics are sources for generating harmonics. These three are
nonlinear devices. The consequence of harmonics is explained in that paper.to decrease
the harmonics effect in the filter by using filter, one could know the magnitude and
phase of the harmonics. Because it is necessary to design the filter. To evaluate the
harmonics, multiple algorithms are used. The algorithms are mostly depending on the
Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) method. The
digital filter is designed to control the harmonic problems and increase power quality by
distributing electrical power to the system. The many filters are used to reduce the
harmonic in the power system and increase the power system quality. The IIR and FIR
filters are discussed to reduce the harmonics. The FIR and IIR filters are designed for
reducing the harmonic distortion in the power system. These two filters are basic digital
filters. The IIR filters are most often used for harmonic distortion. Because it is
implemented with less coefficients. The transfer function of the FIR and IIR filter
impulse response is provided. The structure of the FIR filter is viewed. The design
procedure for the FIR filter is provided as the flowchart. The FIR and IIR filter
differentiation also provided. Many types of windows are used for design and analysis
the filter and spectral. The mathematical equations for these windows are provided. The
given windows are Hanning, Bartlett, Hamming, Kaiser, rectangular and Blackman
window. The harmonics problem in the electrical system design pollutes the power.
This paper is helpful to find out which loads are accountable for great level of alteration
and to identify their distortion level. The harmonic measurements results are helpful to
find out the quality of electric power. This paper provides the information to reduce the
harmonics and to increase the quality of electric power.
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According to the author (Sarem, 2012), the transmission and generator applications
are done by using spare and three phase transformer. The modern protection technology
is used in spare and three phase transformer banks. This technology is used for reduce
the complexity of wiring, detect the faulted equipment and provide automatic, easy
reconfiguration to facilitate the transmission facility to service. Here transmission and
generator applications use this Three-single-phase-and-spare transformer banks. This
bank is used to increase the fault tolerance by the single phase transformer which
replaces the fault one and produces speed repair of the critical path. For speeding up the
critical path modern protection method is used. This method involves precise intimation
of the fault in the transformer. For this purpose TOOLS configuration is used. In this
paper two major applications are analysed. They are the transmission substation
autotransformer and the sub transmission grid and the generator step up transformer.
Here the configuration is done in three ways. In the first one the fault transformer is
eliminated and the spare one is replaced. In second way of configuring, normal in
service transformers are replaced by the spare one. In the third configuration spare
transformer does not exist, for reconfiguring the banks high and low side phases are
used. There are some basic functions for the protection of the transformer which
includes ampere turns (AT) matched about the magnetic circuits. Closed magnetic
circuits are present in the single phase transformers. AT expressions are expressed
individually for each phase of the transformer for calculating the amount of current
flowing in the winding. Next is the fault protection of the winding, which will be tough
to spot the faults. In this we have two types of faults. They are turn-to-turn faults and
turn-to-ground faults. It has a high amount of short circuit current flowing and wastes
energy at the point of fault. Under this fault protection immediate protection of pressure
is used. In order to prevent the pressure relay is used. This relay find out the increase in
pressure created by the energy in the turns of the circuit. This provides the positive
intimation. Another protection is transformer restricted earth fault. This is used for
finding out the fault produced in the windings of the terminal. Two main elements are
used for this protection, one is current polarized direct element and the other is high
impedance differential element. Another protection method is negative sequence
differential protection, in this method sequence is negative because of the higher
sensitivity to all the faults. This method is not that much used for the single phase
transformer since this is very tough to be applied. This paper explains about the
conventions of the diagram and the compensation. Here autotransformer protection is
discussed. The transformer is protected in the bulk electric power substation application.
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This has two sides of bank that is high side is in ring bus, breaker-and-a-half bus, or
double-bus double-breaker arrangement and low side has a single breaker. Here bus
unloading is made and sometimes territory loading is done. Under this protection of
fault many schemes are used and implemented. Another method for protection is GSU
transformer that protects the single phase transformer in power generating station. Here
high side is taken as ring bus that is double breaker and low side is the single breaker.
Here many types of relay and their uses are explained. In programmable relays the
unconventional uses are simplified by the user configurable matrix. For achieving the
protection many relays are used in this paper. Modern system used in this paper
improves the sensitivity.
As per (Thompson, Basha & Holt, 2016), the protection of the transformers using
the wavelet transform by introducing the differential current signals. This method
detects the various types of faults in the circuit. This method is used for the single phase
transformer but not applied for the three-phase. The concept of inrush current is used
here. This paper provides the new method for shielding the transformer by means of
electrical signal. The inrush current is magnetized by removing the magnetic flux, even
after the transformer is cut from the foundation flux is remains in the field. When
voltage is applied to primary winding, after the transformer is electrified the initial
current occurs and this is called the magnetizing of inrush current. This inrush current
emerge high forces between windings and dependent elements. Stimulation is made and
extraction process is done. For the purpose of simulation MATLABsoftware is used in
this power process. Here simulation of power network is done by getting the
information from the line diagrams of the network used. After the simulation work is
over, pre-processing is done. The simulated information are pre-processed for the
training. This process involves passing difference in the current and sampling the
frequency using the sampling frequency. This result is used for the harmonics
extraction. Low pass filter is used in this method to reduce the high frequency and
eliminate the unwanted frequencies. The frequency higher than the Nyquist frequency is
eliminated. In the extraction of harmonics inrush current is used for the demonstration
purpose. Here the signal is converted from each period and is examined for the basic
frequency content. Two methods are used for protecting the transformer. They are in
general electric method and Westinghouse method. Signal energy is one of the factor for
the protection of transformer. Here signal energy is derived by using the parsval’s
theorem for wavelet transform. By giving certain conditions and values for the formula
we get the signal energy. An algorithm is used for the protection. A protection
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algorithm is designed for the transformers, which protects the transformer from the
fault. In order to detect the fault, threshold of above 40% is given and the window
samples of around 60 samples replaced to 30 samples. This algorithm is used in phases
of the circuit. The algorithm is designed in such a way that all the parameters are used in
proper way. Particular specifications are given for designing the algorithm. Result of
simulation is obtained by observing the performance of the fault detection algorithm.
From the inrush current analysis the fault detection is obtained. Results related to relays
are provided. The tables and graph which shows the faults of various kinds are listed.
This algorithm is same as that of the ANFIS method. The difference in the current of the
various phases are shown in the graph.
2.2 Transformer losses
In a transmission line a loss of current or voltage of a transmitted wave through
the circuit is called the transmission loss. Transmission lines are called as rf lines. This
loss is defined by decrease in the amount of energy when the wave spreads from the
source. There are several types of transmission losses. They are copper loss, dielectric
loss, and radiation and induction losses.
Copper loss
This type of loss is produced due to the skin effect. In the transmission lines
conductor resistance is nor equal to zero, therefore when any current flows through this
line some amount of energy released in the usage of heat. This losses will be reduced by
increasing the transmission line by coating with silver. Because silver is good conductor
than the copper all the current will flow through the silver and it remains as a care for
the copper layer.
Dielectric loss
This loss occurs when dielectric between the conductors are affected by heating
effect. This heat generated is dissipated over the environment. This type of loss can be
avoided by using polyethylene as the dielectric medium.
Radiation and induction loss
This is caused by the field present around the conductors. When electromagnetic
filed cuts through any metals around the conductor induction loss occurs. When
magnetic lines that does not reach the conductor when cycle changes, the radiation loss
occurs.
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2.3 Different current losses in transformer
In a transformer loss of current is classified into iron losses which consist of
eddy current loss and hysteresis loss. Iron loss is due to the alternating flux present in
the core.
Hysteresis loss
This type of loss is produced when ferromagnetic material is used and when
only small amount of energy is allowed inside the circuit. Here the transformer core is
exposed to a magnetic force and separate cycle of electromagnetic force of hysteresis
loop will be sketched. Hysteresis loss can be reduced by using the hysteresis loop which
has less area.
Eddy current loss
This loss is produced when core is of conductor type and produces circulating
current so the voltage will be induced by changing the flux. This eddy current loss is
related with the magnetic flux of the transformer. This loss can be decreased by
increasing the resistance of the transformer core.
Magnetizing inrush current
Magnetization of inrush current occurs when a transformer is linked with any
alternating current source, no load transformer is switched that produces the inrush
current by the ammeter. This inrush current will be more than the full load current and
no load current. This current generally occurs when transformer is switched on.
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Figure 1 Magnetizing inrush current
This inrush current is caused when application of source voltage to a reenergized
transformer gives rise to sudden increase in current. The normal range of inrush current
will be around 5 percent of the rated value. When the power transformer is switched on
the range of inrush current is from 10 times the full load value. For the distribution
transformers range will be between 25-50 times the full loads current.
External system short circuits
Generally short circuit is the circuit where the current flowing will be in
improper direction having very less electrical impedance. There will not be any normal
connection between the nodes. The short circuit damage can be reduced by using fuses,
circuit breakers or some other protection circuits. The circuit in which the connection
between the nodes having similar voltage.
Internal short circuits
In the internal short circuit of the battery, the materials of electrodes are
interconnected that provides high amount of local current. This internal short circuit can
be occurred in any battery. For example in the lithium battery internal short circuit is
caused by dendrite development.
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Harmonic distortion
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Harmonics means the combination of all the fundamental frequencies which is
represented in sinusoidal waveform. The measure of power in the harmonics signal is
called the harmonic distortion
Figure 2 Harmonic distortion
Harmonic distortion is produced due to the components such as diodes,
transistors, motors, switches, etc. total harmonics distortion is the total amount of
measure of waveform in distortion. This can be calculated by taking sample sets, using
Fourier transform to get the frequency transform and then all the power is added and
divided by the power in fundamental frequency.
Effect of Harmonic distortion
Harmonic distortion is mostly affects the devices such as capacitors,
transformers and motors. It has harmful properties on electrical components. These
distortion will increase the current in power system and cause greater temperatures. This
distortion cause losses in core.
Reduction of harmonic distortion
This distortion can be decreased by using some methods. They are reduced by using
DC choke, line reactor, twelve pulse converter, twelve pulse distributor, harmonic trap
filters, broadband filters, active filters, and clean power.
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2.4 Current Transformer Issues
The differential relay performance is related on the accuracy of the Current
Transformers producing the primary current on the secondary side. In some cases the
current transformers primary ratings in low voltage and high voltage side doesn’t match
the rated value of current in the Power Transformer. Because of this a Current
Transformer difference occurs, which causes a small false differential current. Which
could even cause an amount of differential current which could operate even the
differential relay. This false current in the current transformer will cause some serious
problems while in operation. The next problem which occurs while transformer is in
prefect operation is the saturation problem that happens in one or more current
Transformer in different levels. When the transformers are in operation a false
differential current occurs in the relay, it could cause some unwanted operations. The
Dc Component in the transformer provide the worst case of operation while this Current
Transformer is in saturation.
Different Kinds of High and Medium Voltage Networks process the signals from
the Transformers in many cases there are current Transformers and the relay works
when the differential current is high to correct the operations in the circuit. These relays
are used to detect the defects in the short circuit current. These relay are important to
detect the false current and for protective function of the circuit .It also determine the
characteristics of the current transformer.
Hardware to Implement Digital Relay
There are different types of protection circuit as the energy requirements of our day
today life has increased. Due to Increase in the population in the world the requirement
of the power also increased. The basic problem in transmission of power and
distribution is the loses and the faults that happens in the Transformer. The fault causes
major problems in the transformers for that many Protective devices are used to
decrease the faults in the transformers the main protective device is the relay. The Relay
in the circuit is utilised to identify the faults in the circuit. The relay are used as switches
for ON/OFF condition depending on the flow of fault current in the circuit with
electromagnetic induction. The relay consumes less power compared to circuit breaks
and Isolators.
The Relays used in Electrical power systems are shown in the figure
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Figure 3 Basic Circuit of Relay
The important part of the relay is the sensing unit which is the electrical coil, when
the current flows in the circuit if it goes to the value higher than the threshold limit then
the relay get closed the open contact to protect the circuit from the damage. The switch
is activated using the magnetic force. When the coil gets energized it sends the
information to the circuit breaker its breaks the circuit till the fault has been cleared. The
relay present near the Transformer compares the current or voltages from the
transformer and sends the signal to the circuit breaker to break or close the circuit.
There are many types of the relays based on the construction they are
1. Electromechanical
2. Static
3. Numerical
In the Electromechanical relays have some mechanical parts and critical to design
with electrical circuits. The static Relays are used for the basic electrical circuits. The
electronic switches has been used as the relays diodes SCR thyristor are used. In
Numerical relays are used in digital methods it has been programmed with
microcontroller and generally used in digital circuits.
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Figure 4 Circuit to implement the Relay
The Static Relays has been used for the circuit with opto oscillator to design a
hardware to implement the relay operation since the electrical circuit has been used.
Triac have been used as relay in the circuit. The circuit is designed with a transformer,
the transformer is then connected to a bridge Rectifier it converts the ac signal to Dc
signal and then it’s passed to a voltage regulator. The voltage regulator makes the
current to flow in a constant voltage of 5V as per the requirements. This voltage is
applied to a micro controller for operating the micro controller it load the code in the
device the random pulses are given to the micro controller, these pulses are amplified
using the transistors and then the output is given to the opto-isolator which drives the
Triac that act as a switch to on and off condition. The opto-isolator generally conducts
in zero crossing voltage which means even at peak supply of voltage the switch will
turn ON only at zero crossing current and voltages. The ZVS make the lossless switch
which is the main characteristics of the opto isolator and its improves the life of the
Microcontroller.
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3. Proposed Approach
3.1 Wavelet transform
The function of the Wavelet transform is same as the Fourier transform. But it
has the completely different merit function. It is the infinite set of various transforms. In
general the wavelet transform is expressed by using this expression,
Wavelet transform is very good for signal processing and compression. In this
wavelet 2types of wavelets there.
1. Discrete wavelet transform:
Discrete wavelet returns data vector as same as in the input set of data.
The most of the values in that set was may be zero. So that we can decompose very
efficiently the original signal. It uses the discrete set of the wavelets scales. The main
difference between these 2 sets is the discrete wavelet decompose the signal into
mutually orthogonal set of values. The wavelet is constructed by using the scaling
function,
The discrete wavelet transform is mainly used for de noise the noise signal. Also in
this transform the noise variance obtained in the independent way. Which is the unique
function in this wavelet transform. The wavelet transform is developed alternative to the
short time Fourier transform. To understand the wavelet transform in detail lets take a 3
values or set of values which are in the range of 0-250 hertz,250-500hertz,500-
1000hertz.Here the all signals are indicating the same type but everyone in different
frequency bands. By doing some experiments by using these signals we can concluded
that we can’t know that what frequency exist at what time period. Instead of that we can
only know that what range of frequency exist in what time intervals.
If we increase the number of coefficients and the wavelets becomes smoother.
Different kind of wavelets are used for different purposes. Haar wavelet is one of the
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important wavelet among them .Here we can take only less number of coefficients in
the wavelet and we can perform the inverse transform or any kind of operation on that
coefficients.by using this function we can find the threshold value for the scales.
By using this expression we can remove the coefficient values which are below the
threshold level.
3. 2 Continuous wavelet transform
The continuous wavelet transform is based on arbitrary scales or it is almost
arbitrary wavelet. The wavelets are used in this form is not orthogonal wavelets also the
data obtained by this are highly correlated. When the transform is applied to the small
wavelet forms the translations should be equal to data sampling. This is the one of the
important limitation of the continuous wavelet transform. The discrete time continuous
wavelet transform is the method which is used in real time applications compared to
other transforms.
The working principle of the continuous wavelet transform is more or less same as
the working principle of the discrete wavelet transform. In this wavelet we are
computing the convolution of the signal within the scaled form of the wavelet. For using
this format we can obtain array which has the length of N. Here the N is the
corresponding value to the number of the input samples. By using the M arbitrary
values we can obtain N x M samples at the output. The algorithm that we used for this
process is based on this principle. The choice of the wavelet transform that have to be
used for the particular process is most important thing in the signal processing.
The main features of the continuous wavelet transform is same for the different
situations we can’t change the features. We can obtain the samples in the continuous
wavelet transform by using this expression,
19

Both the wavelet components are high frequency components. The main lobe of the
spectrum is change to the high frequency range.
3.3. Wavelet based algorithm
For analysing a signal in any component the wavelet and the Fourier transform
both of them are used. Comparing to the Fourier transform the wavelet transform
components are exhibit the frequency characteristics as well as time component
characteristics. Whereas the Fourier components only exhibit time components. The
wavelet based algorithm defines the methods to predict the loses in the transformer or
similar type of component. The algorithm includes following steps
Figure 5 Wavelet based algorithm flow chart
Here the signal energy is calculated as same as in the Fourier transform. Here also
we use the parsval’s theorem to calculate the signal energy. In this algorithm we using
time frequency mapping which is nothing but a level is divided into 21 quadratic levels.
Here the mother wavelet signal is consist of breaking signal of the scaled values.
Therefore the energy can be obtained by summing and squaring the functions in both of
the sides. To design a protection algorithm the pre-processing values of the CT current
from anti-aliasing filter to the high frequency ranges. The algorithm is based on the
threshold chosen which is 50% and the samples that have taken for the experiment that
is 64 samples. And also the 32 samples are added to the algorithm for each of the time
regarding to the wavelet transform these kind of functions are defined.
20

3.4 Digital filters
In general the process of changing the relative amplitude and frequency of any
signal is referred to as filtering. Filters are commonly used in signal processing and
communication systems in applications such as channel equalization, noise reduction,
radar, audio processing, video processing, biomedical signal processing, and analysis of
economic and financial data. A filter is a mathematical model used for modifying the
signal. Digital filter is a filter which is used in digital signal processing. There are two
main purpose of digital filter. They are signal separation and signal restoration. Signal
separation is done when any signal is interrupted with noise or disturbance. Signal
restoration takes place when any signal is distorted. Compared to analog filters digital
filters are better in their performance. Digital filter can attain more than 1000 times
better performance than analog filters.
Figure 6 Digital filters
Filters input and output are represented in time domain because the signals are
produced only by sampling at regular time intervals. The primary functions of filters are
1. Signal is confined into prearranged band frequency as high-pass, low-pass,
and band-pass filters.
2. Signal can be decomposed into more than three sub bands.
3. The frequency spectrum of the signal can be changed similar to telephone
channel equalization and audio graphic equalizers.
4. System modelling can be made, that is the input and output relationship can
be modelled.
Filter analysis
First order filters coefficients are willingly interpretable, as the rates of decay of
exponentials. The interpretation of the coefficients are tough for higher-order filters.
Polynomial analysis is done to develop an easier interpretation of the transfer function.
Digital filter specification
Magnitude response considerations, There are 4 types of ideal filters. They are
21

1. Linear filters versus nonlinear filters.
2. Time-invariant filters versus time-varying filters.
3. Adaptive filters versus non-adaptive filters.
4. Recursive versus non-recursive filters.
5. Direct-form, cascade-form, parallel-form and lattice structures.
The magnitude response for the filters are given below
Figure 7 Magnitude response for the filters
Linear time invariant filters (LTI)
This is the type of filter whose output is the, linear combination of the input signal
samples and their coefficients does not vary with respect to time. The filter coefficients
and the frequency response remains constant and does not vary with time. Linear time
invariant filters are classified into two. They are finite impulse response (FIR) and
infinite impulse response (IIR).
Recursive and Non-recursive filters
Recursive filter is a type of filter in which the feedback is from output to input and
gets output by previous output samples and past and present input samples.
Non-recursive filter is a type of filter where it has no feedback and has output from
present and past input samples.
Advantages of digital filters
 Digital filters will have high accuracy.
 Digital filters are linear phase filters.
 In digital filters flexible and adaptive filtering is done.
22

 The design and simulation process of the digital filters are easy to be done.
 The working out of the digital filters can be finished within the sampling period.
The sampling period is the period which allows only limited time operation.
 High performance analog digital converter, digital to analog converter and
digital signal processing are essential.
All the linear filters will have an impulse response, a step response and a frequency
response.
3.5 Infinite impulse response (IIR) filter
This is the infinite digital filter with infinite impulse response. This IIR filter has
feedback which is otherwise called as the recursive part of the filter. Hence it is called
as the recursive digital filter. IIR filter has better accuracy then FIR filter. This IIR filter
can be used in linear time invariant systems. It has nonlinear phase response and phase
distortion. This filter is stable but nor every time. IIR filters are sometimes selected over
FIR filters since an IIR filter can achieve a much sharper transition region roll-off than
an FIR filter of the same order.
Figure 8 Infinite impulse response (IIR) filter
IIR difference equation is given by
23

IIR filter design
Steps for designing
 First step is to select the prototype for the analog filter family. It can be
Butterworth filter or chebychev type one or two or elliptic filter.
 Select any one transformation method that is either impulse invariant method or
bilinear transformation method.
 The digital filter specifications should be transformed to analog filter
specifications.
 Analog filter must be designed
 Again transform the analog to digital filter.
 At last frequency transformation is performed.
There are 2 methods of designing IIR filter. They are impulse invariant method and
bilinear transformation method.
Impulse invariant method
In this method the digital filter impulse response and the analog filter impulse
response are made equal at a sampling period. Here aliasing occurs if the prototype
analog signal is changed back into digital signal. In order to reduce the distortion
produced the specifications on the digital filter is tightened. But this leads to many
iterations before the filter is introduced.
Bilinear transformation method
In this method aliasing is reduced and eliminated by one to one correspondence
between the sampling frequencies. This bilinear method eliminated the aliasing by
bringing back the analog filter from digital filter.
IIR filter can be designed by mapping analog filter to digital filter. The bilinear
transformation is particularly flexible. This filter provides similar magnitude response
with fewer coefficients, or lower side lobes for same number of coefficients.
24

Advantages of IIR filter
 This is an efficient type filter.
 The implementation of the IIR filter is very easy.
 In this filter the characteristics of filtering is achieved by using only limited
calculations and a smaller amount of memory.
 This filter provides better approximation for the analog methods in digital
applications.
 IIR filter is mainly used in digital signal processing and in audio applications
such as speakers and for the sound processing purposes.
Disadvantages of IIR filter
 IIR filter are more prone to complications of finite-length arithmetic, such as
noise generated by calculations, and limit cycles.
 IIR filter is slower to implement using fixed-point arithmetic.
 IIR filter does not have advantages of FIR filters for multirole applications.
 IIR filter design is difficult and it is a nonlinear phase.
Since the IIR filter is nonlinear and the design process is difficult we go for FIR
filter called the finite impulse response which is linear and stable.
FIR Filters
The Transfer Function of the FIR Filter is given below
The impulse response is given as
The FIR filter design has following specifications windowing function, Frequency
Sampling, Minimising the maximum error and MSE.
The FIR Filter Structure is shown below
25

Figure 9 Structure of FIR Filter
The Filter consists of the multiplier, delay units and adder blocks.
The digital filter can be designed using the following steps:
1. Filter Requirements
2. Filter Co-efficient Calculation
3. Realization
4. Analysing of Finite Word Length
5. Implementation
Filter Requirements
It specifies the type of the filter, Phase difference, Tolerance, Amplitude and
Sampling Frequency.
Filter Co-efficient Calculation
The Filter Co-efficient is calculated using window or Frequency sampling
Method. The Co-efficient H(z) is calculated as it satisfies the required specifications of
the filter.
26

Realization
It is a process of converting Transfer Function into a required Filter structure.
Analysing of Finite Word Length
It is a process of Quantization of the co-efficient of the filter and inputs for the
process of filtering.
Implementation
It is a process of doing software or hardware model of the filter for performing
the filter operations.
Figure 10 Digital Filter Design Flow Chart
FIR Filter Based Algorithm
FIR Based on Frequency Transformation Technique
This method the sub filter and the Pro-type filter has been used, the number of sub
filters in the network are cascaded and form a sub block. The sub filter and the co
27

efficient of the filter are added depending on the pro-type filter. The pro-type filter of
the length 2N has been used, the Magnitude response of the filter is given below
Figure 11 Magnitude Response of the Filter
The Frequency Response is denoted as
The Zero Phase Term is given as
The Transfer Function can be expressed as
The Magnitude Response is denoted as
By varying the variables in the expression Fir filter is designed to reduce the
harmonic distortions in the waveform.
Thus the program has been written depending on the expression first the value has
been initialised and then the expression for the sub filter and the data needed has been
programmed. Depending upon these values the prototype filter has been designed in the
given expression and the basic building blocks of the filter is formed.
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4. Preliminary Results and Discussions
4.1 Wavelet based Algorithm Result
The MATLAB/Simulink Model tool has been used to design the Transformer fault
Current
A 250KVA, 50Hz three phase two winding transformer is connected to a 25KV
source
Simulation diagram of a transformer for fault has been given
Figure 12 Simulation Diagram of Transformer for Fault
In this Simulation diagram when a ground fault happens in the transformer, then
the value of the normal current is converted to fault current. The Three phase fault is
used in the circuit to display the fault current. The Scope5 is used to display the fault
current whereas the Scope8 is used to display inrush current. The values of the fault
currents have been noticed instantly and actually instead of taking some theoretical
values and reducing the errors in the transformer the real values are taken so the co-
efficient for the neural model will be reduced since the real values are taken for
decreasing the losses in the transformer. The Magnetizing Inrush current and the fault
current readings are used in neural network model and the loses get decreased.
29

Figure 13 the output Waveform for fault current
Figure 14 Output Waveform for inrush Current.
In MATLAB the circuit can be constructed using Simulink Model using sim
cape elements, the elements have been selected in Simulink library in sim cape with sim
30

power systems .This has been mainly used for three phase network with the transformer
the fault has been detected using three phase fault and it has been given to current
converter and displayed using Scope.
Using this waveform the actual fault and inrush current data can be taken and it
can be rectified since the actually value are taken compare to approximate data so the
values can be simplified using neural network tools.
The circuit has been constructed using MATLAB tool in Simulink model the elements
required for the circuit will be selected and it will be placed in the workspace. The
elements needed in this model is a three phase source of 25KV and three phase
Transformer are taken. Later after that a three phase fault has been included near
transformer to identify the fault for each phase a current convertor has been given to
converted the voltage signal to current and the output can be viewed using Scope .For
each phase a Scope has been connected and the output wave is viewed. The Three Phase
switch breaker is used to open and close of the switch, the scope connected to view the
inrush and fault current .After giving connections in the circuit, the given circuit is
executed using the run button in the simulation model, the output will be continuous
since the continuous power GUI has been given. The output is viewed continuously so
the fault in the transformers can be taken continuously when the transformer is running
so the faults can be rectified instantaneously.
FIR Based Algorithm
The FIR filter has been formed depending on Frequency Transformation Method
using repeated building blocks of sub filters. The bandwidth and frequency has been
optimum using multipliers blocks in this type of filters. The MATLABcoding for the
filter s given below. In MATLAB the coding has to be written by opening a script file
and it should be saved a .m file and the file has to be complied and run .The plot will be
displayed after running the file. The program has been written based on fir filter
formulae, the values of the variables are stated and depending upon this the program has
be written and it’s executed.
31

%*********** Initialise input of the filter ****************
L_g=31;
wl=0.01*pi;
L_p=14; Om_L=0.2237*pi;
%************** Subfilter parameters**********************
wH=pi-wl;
dG = (1/2) - (1/2)*sin(Om_L/2);
vd = (( 1 - sin(Om_L/2) )/2) + sin(Om_L/2);
g = firpm(L_g-1,[wl/pi wH/pi],[vd vd],'hilbert');
%*************Prototype filters parameters*****************
[p]=firpm(L_p-1,[Om_L/pi 1],[1 1],'hilbert');
%***************BASIC BUILDING BLOCK H1********************
r1=2*conv(g,g);
delay=[zeros(1,L_g-1) 1 zeros(1,L_g-1)];
h1=r1+delay;
%************** COEFFICIENTS FROM CHEBYSHEV POLYNOMIAL
**************
N = L_p/2
for mm=1:N; d(mm)=2*(p((N+1)-mm)); end
D(N)=2*d(N);
for Mm=fliplr([3:N]); D(Mm-1)=(2*d(Mm-1))+(D(Mm)); D(1)=d(1)+((1/2)*D(2));
end
tt=0;
for nn=fliplr([0:N-1]); tk=ChebyshevPoly(nn); T(nn+1,:)=[zeros(1,tt) tk'] ;
32

tt=tt+1;
end
ll=sum((D'*[ones(1,N)]).*T);
alpha=fliplr(ll);
%**************OVERALL FILTER **************
upper_branch = g; lower_branch = g*alpha(1); h = lower_branch;
for ii=1:N-1;
upper_branch = conv(upper_branch,h1);
lower_branch = conv(h, [zeros(1,L_g-1) 1 zeros(1,L_g-1)]);
h=lower_branch + alpha(ii+1)*upper_branch;%Overall Hilbert transformer
end
[H w]=freqz(h,1,1000);
figure
plot(w/pi,abs(H))
The output has been given below
Figure 15 Output waveform of FIR Filter
33

The frequency co efficient has been reduced nearly to 75% so this frequency
transformation design is better compare to other methods. The ripples in the waveform
has been decreased. Thus a transformer has been protected from the harmonics
distortions and from other circumstances.
34

5. Conclusion
In this Project, the importance of the Transformer in electrical supply and how the
transformer has been used in various fields is explained. The losses in the transformer is
elaborated clearly, the various losses in the transformer and the ways it can be reduced.
There are various types of protection circuit due to the energy requirements of our day
today life has increased. Due to Increase in the population in the world the requirement
of the power also increased. So the Power Distribution and transmission plays a major
role in our life. The transformer plays a vital role in the power distribution to maintain
the steady flow of electricity. These transformer while used in small power distribution
it doesn’t cause major losses so its cost effective but while used industrial application it
cause huge losses which could even damage the human life. In the small power
distribution system the loss can be rectified easily the process become difficult while the
large power system is used. The transformer issues in the circuit has been discussed.
The Relay is the one of the protective device used to the circuit if the fault current
occurs. The various relays has be explained and losses of the transformer has been given
in detail. The operation that could happen in the circuit because of the false differential
current has elaborated .This false current causes serious damage so it’s rectified using a
relay circuit .different types of the relays has been discussed and the used of the static
relay to the circuit has been justified. Since the static relay uses electronic devices
which could been connected to a micro controller and the circuit is briefly explained.
The working of the circuit and purpose of the microcontroller has been given with
opto coupler circuit which gives zero varying voltage used to make the operation in the
relay. The circuit using the static relay has been explained to reduce the faults and the
wavelet transform methods is used to find out the fault and Inrush currents which causes
the major issue in the Transformer. The wavelet transform algorithm is used to find the
errors in the transformer and the various distortions are reduced using the FIR filter. The
reason for using wavelet transform and its advantages are given briefly since it uses
frequency domain the wavelet has been used and the nature of the algorithms is
discussed. The reason for using Digital Filters and their basic models of filters IIR and
FIR filters, and the concept why the FIR filter has been used in this transformer is given
in detail. The magnitude response of the FIR filter is done by given the specifications to
the filter using frequency transformation technique. The advantages of the frequency
transformation technique is given. The waveforms of the circuit to visualize the fault
and inrush current is done. The filter has been designed to reduce the harmonics and
35

their magnetic response is shown in the graph. These two algorithms have been
discussed and the losses in the transformer are rectified for the protection of the
transformer.
6.
36

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