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Discrimination of Internal Fault Current and Inrush Current in a Power Transformer Using Empirical Wavelet Transform

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Procedia Technology 21 ( 2015 ) 514 – 519

ScienceDirect

2212-0173 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of Amrita School of Engineering, Amrita Vishwa Vidyapeetham University doi: 10.1016/j.protcy.2015.10.038

SMART GRID Technologies, August 6-8, 2015

Discrimination of Internal Fault Current and Inrush Current in a

Power Transformer using Empirical Wavelet Transform

Maya.P

a*

, S.Vidya shree

b

, Roopasree.K

c

, K.P.Soman

d

aAssistant professor(Sr. Gr), Dept. of Electrical and Electronics Engineering b,cStudents, Amrita Vishwa Vidyapeetham, Coimbatore, India d Professor, Dept.of Computational Engineering and Networks, Amrita Vishwa Vidyapeetham Coimbatore, India

Abstract

Transformers are crucial equipment in a power system, which require reliable solutions for their protection to ensure smooth operation. Identification between internal fault current and in rush current is a challenging problem in the design of transformer protection relay. Transformers are often tripped when inrush current flows in the system causing problems in operation and maintenance in addition to the customer disturbance. Conventional identification methods have limitations in providing accurate solution to this problem. This work investigates the scope of a classification method based on EWT and SVM in distinguishing internal fault current and inrush current in a power transformer. Validation of this method is done using generated synthetic data from MATLAB/SIMULINK. Feature extraction of the generated data is done using EWT algorithm. These features are used for training SVM. Later, accuracy of classification is checked using test vectors. Different kernel functions for SVM are also tested for improved accuracy.

© 2015 The Authors. Published by Elsevier Ltd.

Peer-review under responsibility of Amrita School of Engineering, Amrita Vishwa Vidyapeetham University. Keywords: inrush current; internal fault current; EWT; SVM; kernel function; MATLAB/SIMULINK.

1. Introduction

Inrush current is a transient over current occurring due to part-cycle saturation of the magnetic core of the transformer at the time of excitation. Inrush current may flow due to various reasons. Energizing inrush current occurs when the system voltage is reapplied on the transformer that has been de-energized. Energizing some other transformer connected to the same network leads to the flow of sympathetic inrush current in the transformer.

* Corresponding author. Tel.: +91-9003344703

E-mail address:pk_maya@cb.amrita.edu

© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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A short circuit on the system reduces the system voltage resulting in recovery inrush current on transformer voltage being restored. Inrush currents may also arise due to out-of-phase synchronization of any nearby generator connected to that transformer. This causes unbalance in the current loop of the differential relay causing unwanted tripping[1],[2].A method to distinguish between internal fault currents (for which the relay should trip) and inrush current (for which relay should not trip) is of importance for ensuring disturbance free operation of power transformer. Effects of inrush currents on power transformer protection relay are well explained in [3],[4].

Existing methods provide solution to this problem by distinguishing both the types of currents by taking the ratio of second harmonics to the fundamental of the current waveform. It is based on the assumption that the magnitude of second harmonic present in the inrush current is more in comparison to the magnitude of second harmonic in internal fault current. But due to the improvement in magnetic property of transformer core material, the level of second harmonics inrush has been reduced .Also in some severe faults; the level of second harmonic component is higher than that in inrush currents. Other sources of second harmonics can also be saturation of CTs, parallel capacitances or disconnected transformers [3].

In [5], S.R.Praraskar, M.A.Beg and G.M.Dhole worked on an approach based on artificial neural network which is used to discriminate between inrush current and the internal fault current in the transformer. Further in [6], discussion is done on controlling the instant of energising to eliminate the transformer inrush current. Classification of inrush and internal fault current using wavelet transform is discussed in [7] by G.J.Raju. In [8], a classification methodology based on empirical mode decomposition is applied to this problem and results were not satisfactory. In [10] SVM classifier has been used to analyse the power supply quality. In this paper an alternate method is proposed where EWT [9] is used along with SVM [11]to discriminate between inrush and internal fault currents in power transformer. Synthetic data for validating this method are generated using MATLAB/SIMULINK .Methodology and results are described in subsequent sections of this paper.

2. EWT and SVM 2.1 EWT

A wavelet is a mathematical function used to divide a given function or continuous signal in time domain into different frequency components and study each component. The wavelet transform is used to represent the given function in terms of wavelets. In wavelet analysis signal to be analysed is multiplied with the wavelet function and for each segment generated the transform is computed. The width of the wavelet function changes with each spectral component. The wavelets adjust the time width to frequency so that the high frequency wavelets are narrow and the low frequency wavelets are broader. Assuming real signals and ߱ א [0,ߨሿ and the Fourier support [0,ߨሿ to be

segmented into N segments. ߱n is denoted as the limits between each segment, and each segment is given by ٿ ൌ݊

[߱n-1 ,߱n]. Therefore ڂܰ݊ൌͳٿ ൌ݊ [0, ߨ]. Nomenclature

CT Current Transformer

EWT Empirical Wavelet Transform SVM Support Vector Machine ߮ොn(߱) Empirical wavelets

߰ሺ߱ሻ Empirical wavelets ࣱ݂߳(n,t) Wavelet transforms Class C1 Class for inrush current Class C2 Class for fault current TP True positive FP False positive

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Fig.1. Division of the Fourier axis [9]

Let Tn be the transition phase (shaded area in Fig.1) around each ɘn with a width of 2τn. Therefore the empirical

scaling function and the empirical wavelets, ɔෝ(ɘ) and ɗ෡(ɘ) respectively is given by

߮ොn(߱) = ە ۖ ۔ ۖ ۓ ͳǡ ݂݅ȁ߱ȁ ൑ ߱ െ τ …‘• ቆߨ ʹߚ ൬ ͳ ʹτሺȁ߱ȁ െ ߱ ൅ τሻ൰ቇ ߱ ൅ ɒሺͳሻሺͳሻ Ͳǡ݋ݐ݄݁ݎݓ݅ݏ݁ ǡ ݂݅߱ െ τ ൑ ȁ߱ȁ ൑ (1) ߰ሺ߱ሻ෣ = ە ۖ ۖ ۔ ۖ ۖ ۓ ͳǡ ݂݅߱ ൅ τȁ߱ȁ ൑ ߱ ൅ ͳ െ τ ൅ ͳ …‘• ቆߨ ʹߚ ൬ ͳ ʹτ൅ͳ൫ȁ߱ȁ െ ሺ߱ ൅ ͳሻ ൅ ሺτ ൅ ͳሻ൯൰ቇ •‹ ቆߨ ʹߚ ൬ ͳ ʹτሺȁ߱ȁ െ ߱ ൅ τሻ൰ቇ ݂݅߱ െ τ ൑ ȁ߱ȁ ൑ ߱ ൅ τ Ͳǡ݋ݐ݄݁ݎݓ݅ݏ݁ (2)

The above expressions are obtained by considering the method used in construction of Littlewood-Paley and Meyer’s wavelets; and for all n൐0. By choosing the value of τn to be proportional to ɘn, that is τn= ɀɘn, where

0൏ ɀ ൏ ͳ, the expressions (1) and (2) can be further simplified.

Empirical wavelet transforms technique, which has been recently introduced, is used to address the classification problem under consideration.EWT algorithm is detailed below.

x Fast Fourier transform of the signal is computed.

x Along the frequency axis, wherever the amplitude is high, signal is divided by taking support boundaries between two consecutive maxima of the signal.

x After dividing the signal into portions, wavelet transform is computed.

x The empirical wavelet transform is defined Jerome Gilles [9] as डࣕ

(n, t). The detail coefficients are given

by inner products with empirical wavelets as: ࣱ݂߳(n,t)= <f, ߰n> = ׬ ݂ሺ߬ሻ ߰nሺ߬ െ ݐሻd߬

=(݂መ(߱) ߰ሺ෢ ߱ሻ)ǤƼ (3) The approximation coefficients by inner product with scaling function are given by:

ࣱ݂߳(0,t)= <f, ߮1> = ׬ ݂ሺ߬ሻ ߮1ሺ߬ െ ݐሻd߬

= (݂መ(߱) ߮ͳሺ෢ ߱ሻ)ǤƼ (4)

Where ߰෠n(߱) and ߮ොn(߱) are given by (1) and (2).

After the above mentioned step, components are passed through filters. Different filters are available for this purpose. Here, Meyer’s filter is used. After filtering the portions, the signal can be reconstructed by the expression: f(t) = ࣱ݂߳(0,t)*߮1(t) + σܰ݊ൌͳࣱ݂߳ሺǡ –ሻ*߰n(t) (5)

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2.2 SVM

Support vector machines are supervised learning methods used for classification and regression analysis. In this a model is built by training a set of examples for different classes. A new sample’s class can be predicted based on the training. If there are two classes the classification involves the choosing of a hyper plane which can best divide both the classes. The division into classes is done using margins and feature expansion. For computational feasibility of feature expansion kernel functions are required. Kernel functions are class of algorithms for pattern analysis. Pattern analysis involves studying different types of relations in datasets. For many algorithms the raw data is required to be transformed into feature vector. Kernel functions operate in high dimensional implicit feature space without computing the coordinates of the data in that space, but rather simply computing the inner products between the images of all pairs of data in the feature space.These two classes here are inrush current and fault current.

3. System Description

Two classes of data are required for the validation of the proposed algorithm. First class C1, should contain waveforms of inrush currents and second class, C2 should contain waveforms of internal fault currents, both occurring at different circumstances in a power system. Fig.2 shows the sample power system simulated in MATLAB/SIMULINK platform for data synthesis. Two power transformers T1 and T2 are considered. A generator is connected to T1 through a transmission line.T1 and T2 are connected by another transmission line. Transformer T2 supplies a load. The length of transmission line from source to T1 is 1km and that between the transformers is 20km.Specifications of the components used are given in Appendix.

Fig. 2. Single line diagram of the sample power system

Internal fault current waveforms are generated by creating faults like winding to ground fault in the secondary of transformer T1. Energizing inrush current is simulated by closing first circuit breaker after a time delay keeping the second one open. Simulation of sympathetic inrush is done by closing the second circuit breaker after a time delay with first circuit breaker kept closed. Recovery inrush current waveform is also simulated in a similar way.Various combinations of signals are generated based on different instances at which the two power transformers are energized.

4. Result and Discussion

The classification results obtained can be summarized as a confusion matrix which is a specific table layout that allows visualization of the performances of a supervised learning algorithm in a table format [11].Table 1 shows a typical confusion matrix for a two class classification.

Table 1. A typical confusion matrix

C1 C2

C1 True positive False positive C2 False negative True negative

Each column represents the instances in predicted class and each row represents the instances in an actual class. The diagonal elements, true positive and true negative represent the number of correctly classified signals in each of

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the classes. Whereas the off diagonal elements-false positive and false negative- represent the number of misclassified elements in each class. To find accuracy of classification,

ƒ……—”ƒ…› ൌ א–”—‡ ’‘•‹–‹˜‡ ൅א–”—‡ ‡‰ƒ–‹˜‡

–‘–ƒŽ ‘ ‘ˆ ’‘’—Žƒ–‹‘ (6) TP is the proportion of positive cases that were correctly identified. FP is the proportion of negatives cases that were incorrectly classified.

Where true positive signals correspond to actual signals that were correctly classified as C1, true negative corresponds to all the remaining signals that were classified as C2. Total population corresponds to total signals that were given for testing.

A confusion matrix contains information about actual and predicted classifications done by a classification system. Performance of such systems is commonly evaluated using the data in the matrix.

A confusion matrix of size 2×2 for representing the result of this work for various kernel functions is shown in Table 2.

Table 2. Confusion matrix obtained from proposed methodology

User Defined kernel function Class C1 C2 C1 3 0 C2 3 0 Accuracy 50% Linear kernel function Class C1 C2 C1 3 0 C2 2 1 Accuracy 66.7% Polynomial kernel function Class C1 C2 C1 3 0 C2 0 3 Accuracy 100% Radial Basis Kernel function Class C1 C2 C1 3 0 C2 0 3 Accuracy 100% 5. Conclusion

This paper summarizes a work done based on EWT and SVM for distinguishing between inrush current and internal fault current in a power transformer. Better accuracy of EWT makes it useful in extracting feature vector. Resulting feature vectors are used for training SVM. Classification results gives good accuracy between two classes C1 and C2.Accuracy is improved by choosing appropriate kernel functions. From the result, it is observed that polynomial kernel function and radial basis kernel function gives 100% accuracy in classification. This work can be extended to design a control circuit for differential relay for protection of power transformer. It can be also used to classify faults occurring in electric machines, power quality disturbances, control for active filters.

Appendix

Specification

Generator-G1: 3phase, 11kV, 50Hz, 25MVA;

Transformer-T1: Y-∆, 11/(66/√3)kV,1MVA,R=0.002,L=0.08 ( in pu) Transformer-T2:

Y-∆, (66/√3)/11kV, 1MVA,R=0.002,L=0.08(in pu) Transmission Line:

from G1 to T1 1 km, 0.5Ω, 6.7mH from T2 to load 20km, 0.5Ω,6.4mH Circuit breakers CB1 and CB2: Breaker resistance= 0.001Ω

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References

[1] Y.G.Paithankar, Fundamentals of Power System Protection,page 86-88,PHI Learning Pvt. Ltd., 2010 . [2] Sunil .S.Rao, Switchgear protection and power system, page 604,13th edition Khanna publications,2000.

[3] Li-Chang, Chih-Wen Liu, Shih-EnChien, Ching-Shan Chen, The Effect of Inrush Current on Transformer Protection, NAPS 2006. 38th North American,p. 449 – 456.

[4] R.M.Holmukhe, K.D.Deshpande, Power Transformer Inrush Currents and its Effect on Protective Relays, International Conference on sunrise technologies (ICOST 2011) , January 2011 .

[5] S.R.Praraskar, M.A.Beg, G.M.Dhole, Discrimination Between Inrush and Fault in Transformer: ANN Approach, International Journal of Advancements in Technology, vol.2, no.2, April 2011.

[6] J.H.Brunke, K.J.Frohlich, Elimination of Transformer Inrush Currents By Controlled Switching .IEEE transactions on power delivery, vol. 16, NO. 2, April 2001 p. 281-285.

[7] G.J.Raju, Discrimination Between Internal Faults and Inrush Currents In Power Transformers Using The Wavelet Transform, International Journal of Advancements in Technology,Vol 2, No 2,April 2011.

[8] FanyuanZeng, QianjinLiu, Chao Shi The Discrimination of Inrush current from Internal fault of power transformer based on EMD ,Energy and power engineering, p. 1425-1428,5,2013

[9] Jerome Gilles, Empirical Wavelet Transform,IEEE Transaction on Signal Processing, Vol.61, no.16, 15 August 2013, p.3999-4010. [10] Jiaqi Li, M.V.Chilukuri, Power Supply Quality Analysis using S-Transform and SVM Classifier, Journal of Power and Energy Engineering,

no.2,2014, p.438-447.

References

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