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Detection & Localization of Turn To Turn Fault of A Transformer Using Wavelets.
Mr.Rohit Girase PG Student,
Electrical Engg.Dept SSGBCOET Bhusawal
[email protected]
Prof.Ajit P. Chaudhari Associate Professor Electrical Engineering Dept
SSGBCOET, Bhusawal [email protected]
Prof.Girish K Mahajan Associate Professor Electrical Engineering Dept
SSGBCOET, Bhusawal [email protected]
ABSTRACT
Transformers have become an important and efficient element of the power system. A fault or damage in the transformer windings will result in outage and heavy loss, as a result it needs to be monitored continuously. Due to the adaptation of various advanced techniques in monitoring and diagnostics of power system it has contributed a major hand in the research.
The most common fault in the transformer (or in any electrical machine in general), is turn to turn fault in windings of transformer, and it is a type of incipient fault which cannot be detected easily as the magnitude of fault current is very nominal. This dissertation presents an approach to simulated model of turn to turn fault and its detection in a transformer by analyzing the neutral current of transformer after subjecting it to a standard impulse wave and subsequently applying wavelet transform. The identification of faults by using frequency or time domain based method is difficult. The Wavelet transform is most suitable method providing excellent discriminative features in finding the location of the disturbances in transformer as it will work based on both time and frequency domain.
Keywords
Wavelet, Maximum Modulus Algorithm, Impulse Generator, Transformer.
1. INTRODUCTION
Fault location and distance estimation is very important issue in power system engineering in order to clear fault quickly and restore power supply as soon as possible with minimum interruption. This is necessary for reliable operation of power equipment and satisfaction of customer. In the past several techniques were applied for estimating fault location with different techniques such as, line impedance based numerical methods, travelling wave methods and Fourier analysis [1].
Nowadays, high frequency components instead of traditional method have been used [2]. Fourier transform were used to abstract fundamental frequency components but it has been shown that Fourier Transform based analysis sometimes do not perform time localisation of time varying signals with acceptable accuracy. Recently wavelet transform has been used extensively for estimating fault location accurately. The most important characteristic of wavelet transform is to analyze the waveform on time scale rather than in frequency domain.The faults occurring in a transformer are divided into two types: External and Internal faults. External faults occur outside the transformer and internal faults occur inside it.
There are different types of external faults like overvoltage, under voltage, over fluxing, external system short circuits and under frequency and some of the internal faults are winding turn-to-turn, turn-to-ground etc. From the last few years, a continuous improvement has occurred in power and is continuing. A transformer is most costly equipment of the
power system and it is a significant linkage between a generating body and the consumer as it steps up and steps down voltage and current for efficient transmission of power.
Due to its 24hrs duty transformer has the highest possibility to faults. Internal winding faults in transformers causes a huge damage in short time and sometime the fault may be rising slowly which could be vast after some period which is generally known as incipient fault. According to a survey 70%-80% of transformer failures are due to internal faults of which turn to turn fault in transformer winding is very hard to be detected as the magnitude of fault current is very less. But locating the fault is a necessary work for the efficient working of transformer and also to reduce the outage time. Now days many techniques have been developed for detecting these faults like: off-line techniques, high frequency analysis, Artificial Neural Networks (ANNs), Frequency Response Analysis (FRA), and winding transfer functions, online diagnostics techniques park vector approach, finite element analysis, discrete wavelet transforms and combination of above methods etc.Fig. 1 models the winding turn to turn fault in three-legged type transformer. A fault is shown on the R- Phase of the primary winding by connecting fault-impedance (Zf) across the short circuited turns. The cause of the fault is mostly due to the failure of the insulation of windings which causes a low resistance path for the current. It is leads to internal fault and can be detected by several methods in practice. [1]
The most important constructional element of transformer is insulation. Dielectric Strength is a measure of the electrical strength of a material as an insulator. Transformer under continuous operation confronts to thermal and electrical stresses may result into failure of transformer insulation. A fault in the power transformer may lead to the power outages and blackouts. For reliable operation of electrical power system it has become necessary to analyses the fault on the transformer. Impulse tests is used to validate withstand capacity of insulation material at high voltage [1]. When fault Occurs in the transformer the changes will be observed in neutral current characteristics. The fault in the Transformer winding can be diagnosed by analyzing and comparing the neutral current characteristics at Normal healthy condition and fault condition.
Fig No 1. Schematic of winding turn to turn fault
684 1.1 Introduction to Transformer Inter-
Turn Winding Faults
During operation of transformer, the electrical windings and the magnetic core get subjected to a variety of mechanical forces [3], such as:-
Expansion and contraction due to thermal cycling
Mechanical vibrations
Localized hot spots due to magnetic flux and current
Excessive heating due to overloading and/or inefficient cooling
Impact forces due to through-fault current
2. FAULT DETECTION TECHNIQUES
Transformer manufacturers and operators over the years have employed different tests and Methods to detect inter-turn winding faults in transformers .Contemporary researchers have also been involved in rigorous research to come up with more efficient and sensitive inter-turn Winding faults detection schemes. Brief descriptions of the various techniques for inter-turn Winding fault diagnosis is provided below:
2.1. Methods in Practice
There are numerous methods to detect fault in the transformers which can be divided into two major groups:
One is the electrical-based methods other is oil-based techniques [2]. The oil based method include basically the Dissolved Gas Analysis (DGA) method [3], in which various IEC codes have been developed. These IEC codes interpret the DGA results from data directly. Some of the criteria used are Doernenburg, EEC and CSUS ratios modified Rogers, Rogers etc. Fuzzy logic, neural networks have been some of the Artificial intelligence techniques which have been developed in the last few years which have been an efficient method for detecting faults. The electric-based methods generally evaluate the power transformer by means of the differential relaying technique and impulse testing [4]. The identification of the faults at an early stage can decrease the loss and necessary actions can be taken at right time and at the same time if the fault localization is done then the fault clearing time would be less and can be taken to service after a very less outage time. Incipient faults are generally characterized by low level arcing due to the deterioration of electrical insulation of the turns of the transformer. From many years the Impulse test has become a quality test done on power transformers to test their insulation reliability. In this impulse test a standard lightning impulse is applied to one terminal of the transformer winding and the other terminal is grounded and then full and reduced impulse voltages are applied and the neutral currents of the transformer are observed in both the cases. Then by analyzing the output neutral current waveform the presence of fault can be detected. The magnitude and wave shape of the input current are a function of the surge characteristics of the tested winding and its damage affect the feature of the wave. The characteristics of the internal incipient fault current are low amplitude, are of short duration and rapidly decaying signals.
From this point of view and to make the tests more competent, more information must be acquired from each test. Other methods include Transfer function method, FFT [5][6], ANN, Fuzzy methods etc.
2.2 Conventional Techniques
• Magnetic Balance Test
• Buchholz Relay operation
• Dissolved Gas Analysis (DGA)
• No-load test
2.3 Modern Techniques
• Park’s Vector Approach
• Artificial Neural Networks (ANN)
• Frequency Response Analysis (FRA)
• Wavelet Transform
3. WAVELET TRANSFORM
Today wavelet transform have been used for the analysis of various signals and helps in finding the Information from the signals. The wavelet transform (WT) helps to study the transient phenomena Associated with the transformer winding faults. Generally the basis function used in standard Fourier analysis techniques localize the signal in frequency itself but the wavelet transform localize Both in frequency and time.
This property helps in detection of the time of occurrence of a fault in The winding of the transformer. Wavelet provides higher precision frequency resolution for long Duration for low frequency signals as well as higher precision time resolution for short-duration High-frequency signals.
Overcoming the loopholes of the Fourier transform Short time Fourier Transform (STFT) was developed which represents the signal both in frequency and time but had The disadvantage of fixed window due which there was resolution problems for the signal. In Comparison to STFT [7], wavelets was developed which has an adjustable window that Automatically adjusts to give the most appropriate resolution.
In addition to above noise Suppression characteristic of the WT makes it more dynamic as it makes possible to de-noise the Contaminated. It is a real or complex value continuous time function φ(t) that can be defined with The following properties: The function when integrated results to zero.
(1) It is square integrable i.e it has finite energy
(2)
Or it satisfies the admissibility condition, the function Ψ (t) is called a mother wavelet or wavelet if It satisfies the first two properties. The admissibility condition is useful in formulating a simple Inverse wavelet transform whereas the first two properties suffice to describe the continuous Wavelet transforms. Property 1 hints about the wavy or oscillatory nature of the function while Property 2 hints that f the energy of φ (t) is confined to a finite duration. Thus, in contrast to a Sinusoidal function as used for Fourier transform, it is a small wave’ or a wavelet. The two Properties
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are satisfied easily and there is infinity of functions that qualify as mother wavelets. The Wavelets may be supported compactly or may be of an infinite duration. Wavelet transform is a mathematical tool for the analysis of a signal. It is the extension of Fourier analysis and can determine the exact time at which a particular frequency occurs in a signal.
Shifting (in time) of the peaks of the neutral current waveform of three-phase transformers between reduced and full voltage impulse tests have been employed as a tool for detecting winding inter-turn faults in using the Shannon and Morlet wavelets respectively. In the inherent noise component in the neutral current signal was isolated effectively from the original signal using a biorthogonal wavelet and the signals were reconstructed after de-noising. This improved the performance of the fault detection scheme. A shift in the neutral current peak from 6.45 μsec to 6.6 μsec under the influence of a winding fault was reported in . Further research has been done in , using the wavelet transforms coefficients to distinguish a winding inter-turn fault from the magnetizing inrush current phenomena. However, the shifting in the current peaks in time domain is generally very minimal and incipient winding faults can easily get unnoticed.
3.1 Continuous Wavelet Transforms
The Continuous wavelet transform (CWT) of a given function f (t) will be as follows:-
(3) Where α is the scaling (dilation) parameter and β is time shift constants, and Ψ is the wavelet Function the CWT offers both time and frequency localization which was not in the case of FFT. The segment of the function f ( t ) that affects the value of W(a, b) is that part of the function f (t) That coincides with the interval over which Ψab (t) = Ψ[(t- b)/a]
has the part of its energy. The Frequency selectivity of the CWT can be modeled as a group of linear, time-invariant filters Whose impulse responses are dilations of the mother wavelet with respect to the time axis. This Follows from the fact that the cross-correlation operation on the two signals can be represented as a convolution and the CWT was seen to be a cross correlation in b parameterized by a scale factor
• Denoting the convolution of two signals h(t) and z(t) by
(4) We have,
(5) Thus for a given α the wavelet transform W(α, β) is the output of a filter with impulse response Ψ*α,0( -β) and input f ( β ) . We have a set of filters which are dilated by the scale factor of α. Choosing of the wavelet function (mother wavelet) is adaptable provided that it satisfies the admissibility conditions [8]. While in actual any admissible wavelet can be used for analysis, we have chosen Daubechies4 [9] wavelet as the mother wavelet in the analysis of transformer’s turn to turn fault.
3.2. Discrete Wavelet Transform
The wavelet multi resolution analysis is a new and powerful method of signal analysis and is well suited to travelling wave signals. Wavelets can provide multiple resolutions in both time and frequency domains. The windowing of wavelet transform is adjusted automatically for low and high- frequencies i.e., it uses long time intervals for low frequency components and short time intervals for high frequency components. Wavelet analysis is based on the decomposition of a signal into „scales‟ using wavelet analyzing function called „mother wavelet‟. The temporal analysis is performed with a contracted, high frequency version of the „mother wavelet‟, while the frequency analysis is performed with a dilated, low frequency version of the „mother wavelet‟.
Wavelets are functions that satisfy the requirements of both time and frequency localization. The necessary and sufficient condition for wavelets is that it must be oscillatory, must decay quickly to zero and must have an average value of zero.
In addition, for the discrete wavelet transform considered here, the wavelets are orthogonal to each other. Wavelet has a digitally implementable counterpart called the discrete wavelet transform (DWT). The generated waveforms are analyzed with wavelet multi resolution analysis to extract sub- band information from the simulated transients. Daubechies wavelets are commonly used in the analysis of travelling waves. They were found to be closely matched to the processed signal, which is of utmost importance in wavelet applications. Daubechies wavelets are more localized i.e., compactly supported in time and hence are good for short and fast transient analysis and provide almost perfect reconstruction. However, there are some other wavelets show a good correlation with the transient signals and may be used in the analysis. Several wavelets have been used in this thesis.
Due to the unique feature of providing multiple resolution in both time and frequency by wavelets, the sub-band information can be extracted from the original signal. When applied to faults, these sub-band information are seen to provide useful signatures of transmission line faults, so that the fault location can be done more accurately. By randomly shifting the point of fault on the transmission line, a number of simulations are carried out employing the MATLAB. The generated time domain signals for each case are transferred to the modal domain using Clark‟s transformation. Then, the aerial mode signal is analyzed using wavelet transform. From the Different decomposed levels, only one level is considered for the analysis. This level has the highest energy level output and the dominant frequency of the transient. Waveforms associated with the travelling waves are typically non-periodic signals that contain localized high frequency oscillations superimposed on the power frequency and its harmonics. DFT was found to be not adequate for decomposing and detecting these kinds of signals because it does not provide any time information. On the other hand, the STFT takes the time dependency of the signal spectrum into account. However, the time-frequency plane cannot give both accurate time and frequency localizations. The Wavelet transform allows time localization of different frequency components of a given signal like the STFT but its transformation functions called wavelets which adjust their time widths to their frequency in such a way that higher frequency wavelets will be narrow and lower frequency ones will be broader. Wavelet’s time frequency resolution provides a useful tool for decomposing and analyzing fault transient signal.
3.3 Daubechies wavelet
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Daubechies wavelet is based on the work of Ingrid Daubechies. It consists of a family of orthogonal Wavelets defining a discrete wavelet transform and is represented by maximal number of disappearing Moments for some given support. With each and every wavelet type of the class, there exists a scaling Function (called the father wavelet) which produces an orthogonal multi resolution analysis. Generally The Daubechies wavelet is having the highest number (A) of disappearing moments for given width 2A - 1.They have two methods of naming, DN - the length or number of taps and dbA - the number of disappearing moments. So, D4 and db2 represent the same wavelet transform. Of the 2A−1 outcomes of the algebraic equation for the moment and orthogonally condition, only one result is chosen whose scaling filter has external phase. Daubechies wavelets help in solving a vast range of problems, e.g. Self-similarity property of a signal or signal discontinuities or fractal problems etc. Daubechies orthogonal wavelets D2-D20 or db1-db10 are generally used.
The N number of coefficients is represented by the index number. Each wavelet consists of a number of zero moments which equals to half the number of coefficients. For example, D2 (the Haar wavelet) has one disappearing moment, D4 has two, etc. The wavelets ability to represent polynomial behavior or information in a signal is limited by the number of disappearing moments. For example D2 with one moment easily solves polynomials of one coefficient or constant signal components. D4 solves polynomials with two coefficients, i.e.
constant and linear signal components and D6 encodes 3- polynomials, i.e. constant, linear and quadratic signal components. The D4 scaling coefficients are [1+sqrt(3), 3+sqrt(3), 3- sqrt(3), 1-sqrt(3)]/4sqrt(2). In each step the data input is applied to the above four scaling functions. Similarly there are four wavelet function coefficients. Generally daubechies wavelet is used as it has high computational head and more complex. There is a greater overlap between iterations in Daubechies D4 transform steps.
4. MODELING SIMULATION &
RESULT ANALYSIS
4.1 Description of Impulse Generator
In high voltage engineering, an impulse voltage is generally defined as a unidirectional voltage which attains quickly the required peak value and then declines to zero instantly. A full impulse Wave generator produces the complete waveshape without flashover or puncture and on the other Hand a chopped wave generator makes flash-over leading to rapid fall of voltage. The lightning Waveform is generally shown as a unidirectional impulse of double exponential in shape i.e. it can be shown as the variation of two equal magnitude exponentially decaying waveforms. In this project Double exponential waveform is generated using the circuit given below in fig. 3 and the equation of The impulse wave shape is
(6)
Fig No 2 Standard 1.2-50μsec impulse wave
Where a depends on the rate of rise and b depends on the decay of the pulse. For a specified value of a and b impulse voltage generated has a rise time of 1.2μsec (T1) and a tail of 50μsec (T2). The Capacitor C1 is charged from an external source initially.
Fig No 3 Impulse Generator Circuit
Fig No 4 Laplace transform of impulse generator circuit
After Laplace transform of this circuit we can find the equation of output voltage as
It can be seen from the equation that the output waveform is in double exponential form. For a 1/50μs. it can be derived that α= 0.0139 and β= 6.1when t is in μs. For the standard 1.2/50μs IEC Waveform,α= 0.0143 and β= 4.87 the values of the capacitors were chosen with respect to the Applied voltages and frequency; C1=5000pf and C2=1000pf and the values of resistances were Approximated as R1=333Ώ and R2=20Ώ.
4.2 Description of Equivalent Transformer
In this project the transformer winding is modeled as a ladder network. It has 4 components:Series inductance, ground capacitance, series capacitance and series resistance. [12][13].
The equivalent circuit consists of Cs, Cg and Ls, where, Cs: Series capacitance.
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Cg: Ground capacitance.
Ls: Series inductance.
RS: Series resistance.
Table No 1 shows a conceptual review of possible relationships of transformer parameters and Fault type [7].
Fig No 5 Equivalent transformer model
Table No 1 Relationship of Transformer model parameters change to fault type
Parameterss Faults
Ls Breakdown ,Short circuit and
disk deformation
Cg Moisture ingress buckling
due to large mechanical forces , disc movement and loss of clamping pressure
Cs Aging of Insulation
4.3 Model of Transformer Winding
The approximate high voltage transformer winding is represented by capacitance (Cs), shunt Capacitance (Cg), self-inductance (Ls), lumped resistance (r), which frames a ladder. The Fig. 6 Shows the mathematical model of transformer winding used for impulse voltage test. Total ground Capacitance is given by Cg [8]
Cg = C1 + C2 F C1 is capacitance between the high-voltage (HV) winding and the grounded low-voltage (LV) Winding on the same limb and C2 is capacitance between the HV winding of the side limb and the Grounded transformer tank.
Fig No 6 Equivalent circuit of transformer winding for impulse voltage test.
4.3 Practical Implementation of Modified Fault Detection Scheme
A standard impulse voltage which has a raise time of 1.2μs and a tail time of 50μs is applied to one of the limb of transformer winding. In this project simply 10 turns of a transformer is taken and fault is created at different locations by shorting the respective inductance and resistance of two consecutive turns. The measured neutral current is analyzed using the wavelet transform technique for different turn to turn fault in different sections. The neutral current signal obtained after applying the impulse voltage to a winding having turn to turn fault is shown in figure represents the wave shape of the neutral current for a transformer with no fault and turn to turn fault at different locations. So we can view that due to turn to turn fault the amplitude of the neutral current increases in comparison to no fault condition and with the change in the location in the fault location the wave shape shifts accordingly. Shifting in the peak may be related to the change in winding inductance and capacitance causing corresponding change in resonant frequency of the coil. But with this the position of fault is not easily comprehendible. So with simple time domain analysis the fault location cannot be located.The neutral current is sampled at 50μs of time and of the 86712 samples in the workspace. We took first 10000 samples from which we took only 500 samples i.e 1 sample from every 20 samples as the signal is very large to analyses.
Then we applied daubechies wavelet 4th level transform [14].
Fig.No.6 Recorded Neutral Current For Different Turn To Turn Fault Condition.
Fig 4.6 Recorded neutral current for different turn to turn fault condition
In this dissertation the wavelet maximum modulus algorithm [15] is used. The d4 wavelet coefficients were used for the maximum modulus algorithm for different location of turn to turn fault and we can visualize that with the change in location of turn to turn fault the maximum peak also changes accordingly. Also we can interpret that as the faults are moved away from the source the maximum modulus peaks become closer to each other in comparison to the peaks for the faults near the source.
4.6 Simulink Model of Transformer in Various conditions
Model has simulated in MATLAB Simulink software and obtained result in various conditions
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Fig.No 7 Simulink Model Under Healthy Condition
Fig.No.8 Simulink result of Transformer under Healthy Condition
Fig.No.9 Simulink model of Transformer under turn to turn fault condition
Fig.No 10 Simulink result of Transformer under turn to turn fault condition
Fig.No 11 Simulink model of Transformer inter turn fault condition
Fig.No 12 Simulink result of Transformer inter turn fault condition
CONCLUSION
This paper presents new technique for fault detection and location in power transformers by using neutral current of transformer winding. The neutral current of healthy winding and inter turn faults at different locations are analyzed by wavelet transform method. In the current work, an equivalent circuit of transformer primary winding was taken and applied with impulse voltage of IEC standard of 1.2/50μs and the resultant neutral current were studied by using daubechies
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wavelet level 4 and the resulting d4 coefficients were used for maximum modulus analysis. As the position of fault was changed from source side towards load side the peak moved accordingly. Hence the results indicate that in power transformer faults can be identified and analyzed more proficiently by using wavelet transform technique.
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