Applying wavelet entropy principle in fault classification

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    t uscur. The wavelet entropies of such decompositions are analyzed reaching a suc-ultti

    ower system plays a great roler systeuit breeformthorouoning,Many rfaultsnticatransfh trans

    system was used to identify the fault.In this paper, a much simpler algorithm is introduced to detect

    and identify the transmission line fault and also determine thephases involved in the fault.

    In this paper a novel algorithm is presented to detect the faultand identify its type using wavelet entropy energy. The main prin-

    proposed system in order to obtain different current signals for

    ltering the signal by a high-pass lter. The band width of thesetwo lters is equal. After each level of decomposition, the samplingfrequency is reduced by half. Then recursively decompose the low-pass lter outputs (approximations) to produce the components ofthe next stage [68].

    Given a discrete signal x(n), being fast transformed at instant kand scale j, it has a high-frequency component coefcient Dj(k) anda low-frequency component coefcient Aj(k). The frequency bandof the information contained in signal components Dj(k) andAj(k), obtained by reconstruction are as follows [5].

    * Corresponding author. Address: Electrical Engineering and Control Department,Arab Academy for Science and Technology, Miami, Alexandria, P.O.1029, Egypt.Tel.: +20 35778640.

    Electrical Power and Energy Systems 31 (2009) 604607

    Contents lists availab

    Electrical Power an

    .e lE-mail address: (A. El-Zonkoly).energy entropy in association with neural-fuzzy inference systemis used for fault classication [3]. The wavelet entropy principlehas been used in different applications in power system [4,5].

    In [68], wavelet entropy when used in feature pickup, neuralnetwork and fuzzy system was used to identify the fault. Wavelettransform generated time-frequency parameters and waveletentropy generated characteristic vector. These characteristics wereput into neural network to detect the fault transient then a fuzzy

    wavelet transform of transient signal is expressed by multi-resolu-tion decomposition fast algorithm which utilizes the orthogonalwavelet bases to decompose the signal to components under dif-ferent scales. It is equal to recursively ltering the signal with ahigh-pass and low-pass lter pair. The approximations are thehigh-scale, low-frequency components of the signal produced byltering the signal by a low-pass lter. The details are thelow-scale, high-frequency components of the signal produced byThe importance of protection of pin the successful operation of powecessful decision for tripping of circon for a long time. The transient wavresulting during the fault has beenthe novel methods for signal conditiused in analyzing such waveforms.networks in identication of type ofanalysis for fault detection and ideanalyzing fault signal using wavelettain many useful data. Based on suc0142-0615/$ - see front matter 2009 Elsevier Ltd. Adoi:10.1016/j.ijepes.2009.06.003m. The rapid and suc-aker has been focuseds of current and voltageghly discussed. Due todifferent methods wereesearchers used neural[1] others used wavelettion [2]. The results oformation method con-formation, the wavelet

    testing of the proposed technique has been done using PSCAD pro-gram. At the end, results for testing of the proposed technique arepresented.

    2. Principles of wavelet entropy

    Transient signals have some characteristics such as high-fre-quency and instant break. Wavelet transform is capable of reveal-ing aspects of data that other signal analysis techniques miss and itsatises the analysis need of electric transient signals. Usually,1. Introduction ciple of wavelet entropy is rst presented. Then algorithm used infault detection and identication is discussed. Simulation of theApplying wavelet entropy principle in fa

    S. El Safty, A. El-Zonkoly *

    Arab Academy for Science and Technology, Miami, Alexandria, P.O.1029, Egypt

    a r t i c l e i n f o

    Article history:Received 8 June 2008Received in revised form 25 May 2009Accepted 7 June 2009

    Keywords:Fault classicationWavelet transformWavelet entropy

    a b s t r a c t

    The ability to detect and claprocedure is required to bbeen implemented using wpower system is carried oucurrent waveforms. Theseapproximation and detailscessful methodology for faand proven successful iden

    journal homepage: wwwll rights reserved.classication. The suggested approach is tested using different fault typescation for the type of fault.

    2009 Elsevier Ltd. All rights reserved.t classication

    y the type of fault plays a great role in the protection of power system. Thisecise with no time consumption. In this paper detection of fault type haselet analysis together with wavelet entropy principle. The simulation ofing PSCAD/EMTDC. Different types of faults were studied obtaining variousrent waveforms were decomposed using wavelet analysis into different

    le at ScienceDirect

    d Energy Systems

    sevier .com/locate / i jepes

  • Djk : 2j1fs; 2jfsAjk : 0; 2j1fs

    (j 1;2; :::;m 1

    Where, fs is the sampling frequency.The original signal sequence x(n) can be represented by the sum

    of all components as follows [5].

    xn D1n A1n D1n D2n A2n


    Djn AJn 2

    Various wavelet entropy measures were dened in [6]. In thispaper, the non-normalized Shannon entropy will be used. The def-inition of non-normalized Shannon entropy is as follows [9].

    Ej Xk

    Ejk log Ejk 3

    Where Ejk is the wavelet energy spectrum at scale j and instant kand it is dened as follows.

    Ejk jDjkj2 4

    3. Proposed algorithm

    During fault, the amplitude and frequency of the test signal willchange signicantly as the system change from normal state tofault. The Shannon entropy will change accordingly. It becomesincapable of dealing with some abnormal signals while waveletcan. Wavelet combined entropy can make full use of localized fea-ture at time-frequency domains. Wavelet analysis deals with un-steady signal while information entropy expresses information ofthe signal. That is why wavelet entropy can analyze fault signalsmore efciently.

    The proposed algorithm detects if there is a fault or the systemis under normal conditions. It also determines the type of fault if itis a single line to ground (SLG) fault, line-to-line (LL) fault, doubleline to ground (DLG) fault or a three line to ground (3LG) fault. Fi-nally, the algorithm selects the phases involved in the fault.

    The algorithm is applied in two steps. In the rst step the fault isdetected and identied and in the second step the faulted phasesare determined. The three phase current signals (ia, ib and ic)and the ground current (ig = ia + ib + ic) are inputs to the proposedalgorithm.

    The ow chart of the detection and identication part is shownin Fig. 1, while the ow chart of the phase selection part is shownin Fig. 2.

    Input the three phase current signals and calculate the ground current

    Perform DWT to the four current signals

    Calculate the entropies of the wavelet coefficients of the four currents

    Calculate the sum of absolute entropies of the wavelet coefficients of each current

    (suma , sumb , sumc , sumg)

    sumg = 0

    The max. value of




    Arrange the entropies sums such that,max1 = max (suma , sumb , sumc)min1 = min (suma , sumb , sumc)

    max2 = the remaining sum (intermediate value)

    Determine the phase with entropies sum equal to max1

    Determine the phase with entropies sum equal to max2

    S.E. Safty, A. El-Zonkoly / Electrical Power and Energy Systems 31 (2009) 604607 605entropies sum of three phase currents >


    No Fault


    L-L FaultNo

    sumg > min1

    3LG Fault

    sumg < max2

    DLG FaultSLG Fault




    NoPhase selection algorithm

    Fig. 1. Flow chart of fault detection and identication algorithm.Is the fault a SLG fault?


    The phase involved is ph1 and ground

    It is a 3LG fault



    Is the fault a L-L fault?

    The phases involved are ph1 and ph2



    Is the fault a DLG fault?

    The phases involved are ph1, ph2 and ground



    Fig. 2. Flow chart of phase selection algorithm.

    GS GR TLFig. 3. Power System Model.

  • er an1







    606 S.E. Safty, A. El-Zonkoly / Electrical Pow4. System simulation

    The system simulated is composed of two generators withtransmission line between them as shown in Fig. 3. The 400 kVtransmission line model adapts the frequency-dependent modelof the PSCAD software. The transmission line parameters are asfollows: positive sequence impedance Z1 = 0.02473 + j0.2872X/km, zero sequence impedance Zo = 0.2245 + j1.02X/km, positivesequence capacitance C1 = 0.0132 lF/km, zero sequence capaci-tance Co = 0.009 lF/km, and the bus-bar-to-ground capacitance1 lF. Different types of faults at different locations along thetransmission line are performed. The obtained results are usedfor implementation of the proposed technique and then for test-ing its validity.

    Fig. 4 shows the current waveform for single line to ground faultat phase A at the middle of the transmission line.

    0 0.05 0.1 0.1-1



    Fig. 4. Three phase curr

    0 0.05 0.1 0.15-5




    0 0.05 0.1 0.15-5


    5 x 10-4 Detail (Le

    0 0.05 0.1 0.15-2


    2 x 10-3

    Time (s

    Detail (Le

    Fig. 5. Approximate and DetIaIbIc

    d Energy Systems 31 (2009) 6046075. Test results

    The current signals obtained from system simulation areopened with MATLAB, the ground current is calculated. Using thewavelet toolbox, the current signals are decomposed using 2 levelHaar wavelet. Several wavelet families were examined and it wasnoticed that it makes no difference in the values of the entropiessums.

    Fig. 5 shows the detailed and approximation of the line toground fault obtained from the MATLAB wavelet toolbox.

    Table 1 shows the sums of wavelet coefcients entropies of thefour currents.

    The proposed algorithm successfully detected and identied thefault at each case. As an example on how the algorithm works letus consider a line-to-line fault. As shown in Table 1, the value ofsum g in case of LL fault and in case of no fault is equal to 0 but

    5 0.2 0.25 0.3(sec)

    ents for AG fault.

    0.2 0.25 0.3


    0.2 0.25 0.3

    vel 1)

    0.2 0.25 0.3ec)

    vel 2)

    ails for phase A current.

  • the entropies sums of the three phase currents in case of LL faultis much higher than that in case of no fault. That is how the thresh-old in the ow chart in Fig. 1 is determined. It is also noticed that incase of AB fault, sum a and sum b are higher than sum c. This wayphases involved in the fault were selected.

    6. Conclusion

    The transient current waveform during the fault has beendecomposed using wavelet transform. A novel technique com-posed of measuring the wavelet entropy of the decomposed wave-

    forms was used for dening both the type of fault and the faultedphase. The proposed technique has been tested using differentfault types and all the cases were successfully dened.


    [1] Kezunovic M, Rikalo I. Detect and classify faults using neural nets. IEEE ComputAppl Power 1996;9:427.

    [2] Wilkinson WA, Cox MD. Discrete wavelet analysis of power system transients.IEEE Trans Power Syst 1996;11:203844.

    [3] Zhang Bin, He Zhengyou, Qian Qingquan. Application of wavelet entropy andadaptive nerve-fuzzy inference to fault classication. In: Proceedings of theinternational conference on power system technology; 2006.

    [4] He Zhengyou, Cai Yumei, Qian Qingquan. A study of wavelet entropy theory andits applications in power system. In: Proceedings of the internationalconference on intelligent mechatronics and automation, China, August 2004.

    [5] Li Zhimin, Li Weixing, Liu Ruiye. Applications of entropy principles in powersystem: a survey. IEEE/PES Transmission and Distribution conference andExhibition, China; 2005.

    [6] Zheng-you H, Xiaoqing C, Guoming L. Wavelet entropy denition and itsapplication for transmission line fault detection and identication (Part I:Denition and methodology). In: Proceedings of the international conference onpower system technology; 2006.

    [7] Zheng-you H, Xiaoqing C, Guoming L. Wavelet entropy denition and itsapplication for transmission line fault detection and identication (Part II: Faultdetection in transmission line). In: Proceedings of the international conferenceon power system technology; 2006.

    [8] Zheng-you H, Xiaoqing C, Guoming L. Wavelet entropy denition and itsapplication for transmission line fault detection and identication (Part III:Transmission line faults transients identication). In: Proceedings of theinternational conference on power system technology; 2006.

    [9] MATLAB reference manual. The Mathworks Inc.; 2002.

    Table 1The wavelet entropies sums of the three phase and ground currents under differentsystem conditions.

    Fault Type Sum a Sum b Sum c Sum g

    AB 6.0354e + 005 4.4352e + 005 6.9734e + 003 0BC 6.8788e + 003 3.6524e + 005 2.1949e + 005 0CA 5.6659e + 005 6.8709e + 003 7.4036e + 005 0AG 3.0057e + 005 7.2072e + 003 6.9623e + 003 3.0357e + 005BG 6.9279e + 003 1.2962e + 005 7.3106e + 003 1.3231e + 005CG 7.2180e + 003 6.9223e + 003 1.9457e + 005 1.9764e + 005ABG 7.4752e + 005 3.7257e + 005 7.1938e + 003 7.7568e + 004BCG 7.1099e + 003 3.1790e + 005 2.7062e + 005 1.6280e + 005CAG 6.6925e + 005 7.4527e + 003 6.8548e + 005 5.7053e + 004No fault 6.9072e + 003 6.8789e + 003 6.9634e + 003 0

    S.E. Safty, A. El-Zonkoly / Electrical Power and Energy Systems 31 (2009) 604607 607

    Applying wavelet entropy principle in fault classificationIntroductionPrinciples of wavelet entropyProposed algorithmSystem simulationTest resultsConclusionReferences


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