Objectives

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.  

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. 

Significance

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.

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.

Power transformer can electrically segregate the circuits.

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.

Power transformer can also be used to avoid DC current passing starting from one circuit to another circuit.

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.

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

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. 

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.

Report Organisation

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 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  

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 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.  

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.

Background of the Project

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. 

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. 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.

Proposed Approach

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 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.

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.

Preliminary Results and Discussions

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.

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.

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.  

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.

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.

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.

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. 

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. 

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.

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. 

Conclusion

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 

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.

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.

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.

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. 

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. 

Hardware

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.  

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 .

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.

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 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.                        

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, 

Both the wavelet components are high frequency components. The main lobe of the spectrum is change to the high frequency range.

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 

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.

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. 

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.

Magnitude response considerations, There are 4 types of ideal filters. They are

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. 

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 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.

• Digital filters will have high accuracy.
• Digital filters are linear phase filters.
• In digital filters flexible and adaptive filtering is done.
• 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.

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.  

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.

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.

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. 

• 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.

• 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.

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 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

It specifies the type of the filter, Phase difference, Tolerance, Amplitude and Sampling Frequency.

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.

It is a process of converting Transfer Function into a required Filter structure.

It is a process of Quantization of the co-efficient of the filter and inputs for the process of filtering.

It is a process of doing software or hardware model of the filter for performing the filter operations.

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 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

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.

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 

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. 

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 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.

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.

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. 

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 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. 

References 

Ahmad Rizal Sultan, A., & Mustafa, M. (2011). Ground Fault Currents in Unit Generator Transformer at Various Voltage and Transformer Configurations. Indian Journal Of Applied Research, 3(5), 224-227. https://dx.doi.org/10.15373/2249555x/may2013/69

BANASZAK, S. (2017). Frequency Response Patterns of Transformer Windings with Mechanical Faults. PRZEGL?D ELEKTROTECHNICZNY, 1(4), 119-122. https://dx.doi.org/10.15199/48.2017.04.29

Barlik, R., Nowak, M., Grzejszczak, P., & Zdanowski, M. (2016). Estimation of power losses in a high-frequency planar transformer using a thermal camera. Archives Of Electrical Engineering, 65(3). https://dx.doi.org/10.1515/aee-2016-0044

bin Ahmad Khiar, M., Talib, M., bin Ab Ghani, S., & bin Sutan Chairul, I. (2015). Transformer Fault Classification from Polarization Current Measurement Results by Using Statistical Technique. Applied Mechanics And Materials, 754-755, 654-658. https://dx.doi.org/10.4028/www.scientific.net/amm.754-755.654

Bouderbala, R., & Bentarzi, H. (2014). A New Differential Relay Framework for Power Transformer. Applied Mechanics And Materials, 492, 426-430. https://dx.doi.org/10.4028/www.scientific.net/amm.492.426

Christopoulos, C., & Wright, A. (2010). Electrical power system protection. Dordrecht, The Netherlands: Kluwer.

Corsi, S. Voltage Control and Protection in Electrical Power Systems.

Cui, H. (2013). Faults Diagnosis of Converter Transformer Based on the Vibration Method. Advanced Materials Research, 712-715, 2101-2106. https://dx.doi.org/10.4028/www.scientific.net/amr.712-715.2101

Del Vecchio, R. (2010). Transformer design principles. Boca Raton, FL: CRC Press.

Digital Filters and Signal Processing. (2012).

Distribution Transformer Losses Calculation Based on TSFEM. (2015). International Journal Of Computing, Communication And Instrumentation Engineering, 2(2). https://dx.doi.org/10.15242/ijccie.ae1115005

Fan, J., & Zhang, Z. (2011). Speeding up Fault Simulation using Parallel Fault Simulation. Procedia Engineering, 15, 1817-1821. https://dx.doi.org/10.1016/j.proeng.2011.08.338

Fernandez-Vazquez, A., & Dolecek, G. (2014). Generalized Chebyshev Filters for the Design of IIR Filters and Filter Banks. Circuits, Systems, And Signal Processing, 33(7), 2237-2250. https://dx.doi.org/10.1007/s00034-014-9742-4

Georgilakis, P. (2011). Environmental cost of distribution transformer losses. Applied Energy, 88(9), 3146-3155. https://dx.doi.org/10.1016/j.apenergy.2010.12.021

Gers, J., & Holmes, E. (2011). Protection of electricity distribution networks. London: The Institution of Engineering and Technology.

Hamming, R. (2013). Digital Filters. Dover Publications.

Hashemnia, N., Abu-Siada, A., & Islam, S. (2015). Improved power transformer winding fault detection using FRA diagnostics – part 1: axial displacement simulation. IEEE Transactions On Dielectrics And Electrical Insulation, 22(1), 556-563. https://dx.doi.org/10.1109/tdei.2014.004591

Himbele, J., Kojima, H., Hayakawa, N., Hanai, M., & Okubo, H. (2012). Current Limitation and Recovery Function for Superconducting Fault Current Limiting Transformer (SFCLT). Physics Procedia, 36, 841-844. https://dx.doi.org/10.1016/j.phpro.2012.06.137

IEEE guide for transformer loss measurement. (2010). New York.

J & P Transformer Book. (2011).

Jena, P., & Pradhan, A. (2015). Reducing current transformer saturation effect in phasor measurement unit. International Transactions On Electrical Energy Systems, 26(7), 1397-1407. https://dx.doi.org/10.1002/etep.2152

Jiménez, L., & Verde, C. (2012). Multi-Fault Discrimination with Fault Model and Periodic Residual. IFAC Proceedings Volumes, 45(20), 49-54. https://dx.doi.org/10.3182/20120829-3-mx-2028.00087

Jovanovic-Dolecek, G. (2013). Random signals and processes primer with MATLAB. New York, NY: Springer.

Kim, H. (2012). Advances in Technology and Management. Berlin, Heidelberg: Springer Berlin Heidelberg.

KOMARZYNIEC, G. (2015). Increase in losses in a superconducting transformer due to inrush current. PRZEGL?D ELEKTROTECHNICZNY, 1(4), 38-41. https://dx.doi.org/10.15199/48.2015.04.09

Komatsu, W., Ama, N., & Matakas Junior, L. (2015). Digital Control for PLLs Based on Moving Average Filter: Analysis and Design in Discrete Domain. Eletrônica De Potência, 20(3), 293-299. https://dx.doi.org/10.18618/rep.2015.3.2547

KOOCHAKI, A., & KOUHSARI, S. (2010). Detailed Simulation of Transformer Internal Fault in Power System by Diakoptical Concept. Advances In Electrical And Computer Engineering, 10(3), 48-54. https://dx.doi.org/10.4316/aece.2010.03008

Kovacevic, B., Banjac, Z., & Milosavljevic, M. (2013). Adaptive Digital Filters. Berlin: Springer.

KRSTIVOJEVIC, J., & DJURIC, M. (2016). A new algorithm for avoiding maloperation of transformer restricted earth fault protection caused by the transformer magnetizing inrush current and current transformer saturation. TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES, 24, 5025-5042. https://dx.doi.org/10.3906/elk-1409-92

Li, N., & Zhou, R. (2011). Rolling Element Bearing Fault Detection Using Redundant Second Generation Wavelet Packet Transform. Advanced Materials Research, 199-200, 931-935. https://dx.doi.org/10.4028/www.scientific.net/amr.199-200.931

Liu, Z., Xu, X., Abdelsalam, H., & Makram, E. (2015). Power System Harmonics Study for Unbalanced Microgrid System with PV Sources and Nonlinear Loads. Journal Of Power And Energy Engineering, 03(05), 43-55. https://dx.doi.org/10.4236/jpee.2015.35004

Lo?pez, C. (2014). MATLABOptimization Techniques. Berkeley, CA: Apress.

Malathi, V. (2007). Support Vector Machine for Discrimination Between Fault and Magnetizing Inrush Current in Power Transformer. Journal Of Computer Science, 3(11), 894-897. https://dx.doi.org/10.3844/jcssp.2007.894.897

Maya P., shree, S., Roopasree K., & Soman, K. (2015). Discrimination of Internal Fault Current and Inrush Current in a Power Transformer Using Empirical Wavelet Transform. Procedia Technology, 21, 514-519. https://dx.doi.org/10.1016/j.protcy.2015.10.038

Maya P., shree, S., Roopasree K., & Soman, K. (2015). Discrimination of Internal Fault Current and Inrush Current in a Power Transformer Using Empirical Wavelet Transform. Procedia Technology, 21, 514-519. https://dx.doi.org/10.1016/j.protcy.2015.10.038

Ngaopitakkul, A., & Jettanasen, C. (2014). A discrete wavelet transform approach to discriminating among inrush current, external fault, and internal fault in power transformer using low-frequency components differential current only. IEEJ Transactions On Electrical And Electronic Engineering, 9(3), 302-314. https://dx.doi.org/10.1002/tee.21971

Ngaopitakkul, A., & Jettanasen, C. (2014). A discrete wavelet transform approach to discriminating among inrush current, external fault, and internal fault in power transformer using low-frequency components differential current only. IEEJ Transactions On Electrical And Electronic Engineering, 9(3), 302-314. https://dx.doi.org/10.1002/tee.21971

Numerical methods in engineering: theories with MATLAB, Fortran, C and Pascal programs. (2011). Choice Reviews Online, 49(01), 49-0331-49-0331. https://dx.doi.org/10.5860/choice.49-0331

Ojima, H., Nonomura, K., Zhou, L., Shimizu, J., & Onuki, T. (2012). Research on Digital Filters for Si Wafer Surface Profile Measurement – Design of Filters by Total Variation. Advanced Materials Research, 565, 656-661. https://dx.doi.org/10.4028/www.scientific.net/amr.565.656

Ozgonenel, O., & Karagol, S. (2014). Transformer differential protection using wavelet transform. Electric Power Systems Research, 114, 60-67. https://dx.doi.org/10.1016/j.epsr.2014.04.008

MATLABSIMULINK BASED DIGITAL PROTECTION OF TRANSFORMER. International Journal Of Research In Engineering And Technology, 03(02), 484-488. https://dx.doi.org/10.15623/ijret.2014.0302084

Paraskar, S., Beg, M., & Dhole, G. (2012). Discrimination between inrush and fault condition in transformer: a probabilistic neural network approach. International Journal Of Computational Systems Engineering, 1(1), 50. https://dx.doi.org/10.1504/ijcsyse.2012.044743

Paraskar, S., Beg, M., & Dhole, G. (2012). Discrimination between inrush and fault condition in transformer: a probabilistic neural network approach. International Journal Of Computational Systems Engineering, 1(1), 50. https://dx.doi.org/10.1504/ijcsyse.2012.044743

Peng, F. (2015). Study on Transformer Fault Diagnosis Based on Dynamic Fault Tree. Journal Of Electrical And Electronic Engineering, 3(5), 133. https://dx.doi.org/10.11648/j.jeee.20150305.16

Pe?rez Lo?pez, C. (2014). MATLABgraphical programming. [Berkeley, Calif.]: Apress.

Power Transformer Control by Neuro Fuzzy Controller and Haar Wavelet Transform. (2016). International Journal Of Science And Research (IJSR), 5(4), 947-951. https://dx.doi.org/10.21275/v5i4.nov162736

Pre?ve?, C. (2010). Protection of Electrical Networks. New York, NY: John Wiley & Sons.

Rao, B., Zou, Q., Zhong, T., & Liu, Q. (2013). The Simulation Study of Shunt Active Power Filter in the Power System Harmonics Restraint. Applied Mechanics And Materials, 457-458, 661-666. https://dx.doi.org/10.4028/www.scientific.net/amm.457-458.661

Ren, S., Zhao, X., & Zhang, W. (2012). Design and Realization of FIR Digital Filter Based on MATLAB. Advanced Materials Research, 490-495, 1867-1870. https://dx.doi.org/10.4028/www.scientific.net/amr.490-495.1867

Ren, S., Zhao, X., & Zhang, W. (2012). Design and Realization of FIR Digital Filter Based on MATLAB. Advanced Materials Research, 490-495, 1867-1870. https://dx.doi.org/10.4028/www.scientific.net/amr.490-495.1867

Retrieved 20 October 2017, from Bonneville Power Administration. (2002). Alternative Transient Programs: ATP/EMTP. Retrieved from: https://www.emtp.rog/.

ROMANIUK, F. (2016). Comparative assessment of digital filters for microprocessorbased relay protection. PRZEGL?D ELEKTROTECHNICZNY, 1(7), 130-133. https://dx.doi.org/10.15199/48.2016.07.28

Sanchez, S., Richardeau, F., & Risaletto, D. (2017). Design and fault-operation analysis of a modular cyclic cascade inter-cell transformer (ICT) for parallel multicell converters. Mathematics And Computers In Simulation, 131, 190-199. https://dx.doi.org/10.1016/j.matcom.2016.01.004

Shah, A., & Bhalja, B. (2016). Fault discrimination scheme for power transformer using random forest technique. IET Generation, Transmission & Distribution, 10(6), 1431-1439. https://dx.doi.org/10.1049/iet-gtd.2015.0955

Song, H., Zhao, F., & He, D. (2012). Simulation Study on Internal Fault of Transformer. Physics Procedia, 25, 459-464. https://dx.doi.org/10.1016/j.phpro.2012.03.111

Su, Q. (2013). Electromagnetic transients in transformer and rotating machine windings. Hershey, PA: Engineering Science Reference.

Subramanian, S., Mathur, B., & Henry, J. (2010). Wavelet Packet Transform and Support Vector Machine Based Discrimination of Power Transformer Inrush Current from Internal Fault Currents. Modern Applied Science, 4(5). https://dx.doi.org/10.5539/mas.v4n5p67

Suh, J., & Kim, Y. (2014). Accelerating MATLABwith GPU computing. Amsterdam: Morgan Kaufmann/Elsevier.

To Reduce Magnetic Inrush Current by Point Wave Switching Method. (2016). International Journal Of Science And Research (IJSR), 5(2), 782-784. https://dx.doi.org/10.21275/v5i2.nov161123

Transformer Differential Protection Using Wavelet Packet Transform. (2015). International Journal Of Science And Research (IJSR), 4(12), 907-913. https://dx.doi.org/10.21275/v4i12.09111502

Tseng, H., & Chen, J. (2012). Voltage compensation-type inrush current limiter for reducing power transformer inrush current. IET Electric Power Applications, 6(2), 101. https://dx.doi.org/10.1049/iet-epa.2011.0151

Tyagi, S., Pandey, D., & Kumar, V. (2011). Fuzzy Fault Tree Analysis for Fault Diagnosis of Cannula Fault in Power Transformer. Applied Mathematics, 02(11), 1346-1355. https://dx.doi.org/10.4236/am.2011.211188

Wang, Y. (2013). The Influence of Exciting Inrush Current of Transformer Differential Protection. Applied Mechanics And Materials, 397-400, 1935-1938. https://dx.doi.org/10.4028/www.scientific.net/amm.397-400.1935

Wen, H., & Li, S. (2011). DSP-Based FIR Filter Design and Circular Buffer Implementation. Advanced Materials Research, 403-408, 1755-1758. https://dx.doi.org/10.4028/www.scientific.net/amr.403-408.1755

Wiak, S. (2015). Special issue on Electromagnetic Fields in Electrical Engineering. Bradford: Emerald Group Publishing Limited.

Xu, Y. (2013). Intelligent fault diagnosis of house transformer simulation system in hydro-electricity factory by fuzzy reasoning. International Journal Of Internet Manufacturing And Services, 3(2), 87. https://dx.doi.org/10.1504/ijims.2013.058709

YANG, C., & MA, Y. (2010). New fast algorithm in DSP FIR filter design. Journal Of Computer Applications, 29(12), 3221-3223. https://dx.doi.org/10.3724/sp.j.1087.2009.03221

Yang, H. (2014). Research on Three-Phase Calibration Method of HV Three-Phase Combined Transformer and its Implementation. Applied Mechanics And Materials, 568-570, 1191-1195. https://dx.doi.org/10.4028/www.scientific.net/amm.568-570.1191

Zahoor, S., & Naseem, S. (2017). Design and implementation of an efficient FIR digital filter. Cogent Engineering, 4(1). https://dx.doi.org/10.1080/23311916.2017.1323373

Zeng, F., Liu, Q., & Shi, C. (2013). The Discrimination of Inrush Current from Internal Fault of Power Transformer based on EMD. Energy And Power Engineering, 05(04), 1425-1428. https://dx.doi.org/10.4236/epe.2013.54b270

Ziegler, G. (2012). Numerical differential protection. Erlangen: Publicis Pub.

???????, ?. (2011). Computer generator based upon MatLab. Electronics And Control Systems, 1(27). https://dx.doi.org/10.18372/1990-5548.27.259