Electrical Power and Energy Systems 31 (2009) 604–607

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Applying wavelet entropy principle in fault classification

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 classificationWavelet transformWavelet entropy

0142-0615/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.ijepes.2009.06.003

* Corresponding author. Address: Electrical EngineeArab Academy for Science and Technology, Miami,Tel.: +20 35778640.

E-mail address: amanyelz@yahoo.com (A. El-Zonk

a b s t r a c t

The ability to detect and classify the type of fault plays a great role in the protection of power system. Thisprocedure is required to be precise with no time consumption. In this paper detection of fault type hasbeen implemented using wavelet analysis together with wavelet entropy principle. The simulation ofpower system is carried out using PSCAD/EMTDC. Different types of faults were studied obtaining variouscurrent waveforms. These current waveforms were decomposed using wavelet analysis into differentapproximation and details. The wavelet entropies of such decompositions are analyzed reaching a suc-cessful methodology for fault classification. The suggested approach is tested using different fault typesand proven successful identification for the type of fault.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

The importance of protection of power system plays a great rolein the successful operation of power system. The rapid and suc-cessful decision for tripping of circuit breaker has been focusedon for a long time. The transient waveforms of current and voltageresulting during the fault has been thoroughly discussed. Due tothe novel methods for signal conditioning, different methods wereused in analyzing such waveforms. Many researchers used neuralnetworks in identification of type of faults [1] others used waveletanalysis for fault detection and identification [2]. The results ofanalyzing fault signal using wavelet transformation method con-tain many useful data. Based on such transformation, the waveletenergy entropy in association with neural-fuzzy inference systemis used for fault classification [3]. The wavelet entropy principlehas been used in different applications in power system [4,5].

In [6–8], 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 fuzzysystem was used to identify the fault.

In this paper, a much simpler algorithm is introduced to detectand 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-

ll rights reserved.

ring and Control Department,Alexandria, P.O.1029, Egypt.

oly).

ciple of wavelet entropy is first presented. Then algorithm used infault detection and identification is discussed. Simulation of theproposed system in order to obtain different current signals fortesting 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 itsatisfies the analysis need of electric transient signals. Usually,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 filtering the signal with ahigh-pass and low-pass filter pair. The approximations are thehigh-scale, low-frequency components of the signal produced byfiltering the signal by a low-pass filter. The details are thelow-scale, high-frequency components of the signal produced byfiltering the signal by a high-pass filter. The band width of thesetwo filters is equal. After each level of decomposition, the samplingfrequency is reduced by half. Then recursively decompose the low-pass filter outputs (approximations) to produce the components ofthe next stage [6–8].

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

S.E. Safty, A. El-Zonkoly / Electrical Power and Energy Systems 31 (2009) 604–607 605

DjðkÞ : ½2�ðjþ1Þfs; 2�jfs�AjðkÞ : ½0; 2�ðjþ1Þfs�

(ðj ¼ 1;2; :::;mÞ ð1Þ

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

of all components as follows [5].

xðnÞ ¼ D1ðnÞ þ A1ðnÞ ¼ D1ðnÞ þ D2ðnÞ þ A2ðnÞ

¼XJ

j¼1

DjðnÞ þ AJðnÞ ð2Þ

Various wavelet entropy measures were defined 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 ¼ �X

k

Ejk log Ejk ð3Þ

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

Ejk ¼ jDjðkÞj2 ð4Þ

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 entropies sum of three

phase currents > Threshold

No Fault

End

L-L Fault

Yes

Yes

No

No

sumg > min1

3LG Fault

sumg < max2

DLG Fault

SLG Fault

Phase selection algorithm

Yes

Yes

No

No

Fig. 1. Flow chart of fault detection and identification algorithm.

3. Proposed algorithm

During fault, the amplitude and frequency of the test signal willchange significantly 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 efficiently.

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 (L–L) 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 first step the fault isdetected and identified 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 flow chart of the detection and identification part is shownin Fig. 1, while the flow chart of the phase selection part is shownin Fig. 2.

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

Is the fault a SLG fault?

End

The phase involved is ph1 and ground

It is a 3LG fault

Yes

No

Is the fault a L-L fault?

The phases involved are ph1 and ph2

Yes

No

Is the fault a DLG fault?

The phases involved are ph1, ph2 and ground

Yes

No

Fig. 2. Flow chart of phase selection algorithm.

GS GR

TL

Fig. 3. Power System Model.

0 0.05 0.1 0.15 0.2 0.25 0.3-1

0

1

2

3

4

5

Time (sec)

Current(kA)

IaIbIc

Fig. 4. Three phase currents for A–G fault.

0 0.05 0.1 0.15 0.2 0.25 0.3-5

0

5

10Approximate

0 0.05 0.1 0.15 0.2 0.25 0.3-5

0

5 x 10-4 Detail (Level 1)

0 0.05 0.1 0.15 0.2 0.25 0.3-2

0

2 x 10-3

Time (sec)

Detail (Level 2)

Fig. 5. Approximate and Details for phase A current.

606 S.E. Safty, A. El-Zonkoly / Electrical Power and Energy Systems 31 (2009) 604–607

4. 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 + j0.2872 X/km, zero sequence impedance Zo = 0.2245 + j1.02 X/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.

5. 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 coefficients entropies of thefour currents.

The proposed algorithm successfully detected and identified 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 L–L fault and in case of no fault is equal to 0 but

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) 604–607 607

the entropies sums of the three phase currents in case of L–L faultis much higher than that in case of no fault. That is how the thresh-old in the flow 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 defining both the type of fault and the faultedphase. The proposed technique has been tested using differentfault types and all the cases were successfully defined.

References

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