High-speed differential busbar protection usingwavelet-packet transform

M.E. Mohammed

Abstract: A novel wavelet-packet-transform- (WPT-) based differential busbar-protectiontechnique is presented. The paper uses the wavelet-packet- transform (WPT) method to extractfeatures from a fault-current signal. The WPT can decompose the fault signal into differentfrequency bands in the time domain. The differential signal is computed from the decomposedextracted signal. The WPT-based differential busbar-protection scheme solves several problems ofcurrent protective relays. The CT error and ratio-mismatch problems do not have any impact onthe proposed WPT-based scheme. ATP simulations are used to test and validate the proposedtechnique for model-power-system faults.

1 Introduction

Protection of substation busbars is almost universallyaccomplished by differential relaying. This method makesuse of Kirchhoff’s law that all currents entering or leaving apoint must sum vectorially to zero. This type of protectionis accomplished by balancing the current-transformer (CT)secondary current of all of the circuits connected to thebusbar and then bridging this balanced circuit with a relay-operating coil.

The principle of current-differential relaying is describedin Fig. 1. For an external fault, the current leaving thebusbar is equal to the sum of all of the currents entering thebusbar, and the total summation is zero. The same wouldbe true when considering load flow. On the other hand, foran internal fault, the sum of all of the currents entering thebusbar is equal to the total fault current.

The current transformers in the faulty circuit may be sobadly saturated by the total fault current that they will havevery large errors; the other CTs in circuits carrying only apart of the total current may not saturate so much and,hence, may be quite accurate. As a consequence, thedifferential relay may receive a very large current, and,unless the relay has a high enough pickup or a long enoughtime delay or both, it will operate undesirably and cause allbusbar breakers to be tripped.

However, The impact of CT error and ratio mismatch iscountered by using a practical percentage differentialcharacteristic (Fig. 1c) that reduces the sensitivity of therelay.

Numerical techniques in protective-relay design offer theopportunity to improve busbar-protection schemes andhence overall power-system availability and reliability [1, 2].Relatively few algorithms for protecting busbars have beenpublished using the differential current [3–10]. Sometechniques have not studied the effect of CT saturation.

The other techniques have introduced additional measures.Such solutions are not effective during early and severe CTsaturation. If the DC components will not saturate the CTsseverely, it is relatively simple to calculate the errorcharacteristics of the CTs and to find out how muchcurrent will flow in the differential relay. However, if theDC saturation is severe, as it usually is, the problem is muchmore difficult, particularly if instantaneous relaying isdesired [11].

Protection of busbars demands high-speed reliability andstability. Failure to trip on an internal fault, as well as falsetripping of a busbar during service, or in the event anexternal fault, can both have disastrous effects on thestability of the power system, and may even cause acomplete blackout [11].

A different approach to differential busbar protection,based on wavelet-packet transform (WPT) of faulttransients is presented in this paper. Wavelets are a newfamily of basis functions that satisfy certain mathematicalrequirements and are used in representing data and otherfunctions. The wavelet-packet method is a generalisation ofwavelet decomposition that offers a richer signal analysis.Wavelet packets provide a more precise estimation of theactual signal than the wavelet transform.

2 From wavelets to wavelet packets

In the orthogonal wavelet-decomposition procedure, thegeneric step splits the approximation coefficients into twoparts. After splitting, a vector of approximation coefficientsand a vector of detail coefficients are obtained, both at acoarser scale. The information lost between two successiveapproximations is captured in the detail coefficients. Thenext step consists of splitting the new approximation-coefficient vector; successive details are never reanalysed.

In the corresponding wavelet-packet situation, eachdetail-coefficient vector is also decomposed into two partsusing the same approach as in approximation-vectorsplitting. This offers the richest analysis: the completebinary tree is produced as shown in Fig. 2.

The objective of WPA is to create a binary treedecomposition of the signal into a set of energy levels,called ‘octave’ windows [12] where the frequencydomain has been divided logarithmically [13]. During the

The author is with Electrical Engineering Department, Faculty of Engineering,Helwan University, Cairo, Egypt

E-mail: islammmm2002@hotmail.com

r IEE, 2005

IEE Proceedings online no. 20045162

doi:10.1049/ip-gtd:20045162

Paper first received 3rd September 2004 and in final revised form 29thMay 2005

IEE Proc.-Gener. Transm. Distrib., Vol. 152, No. 6, November 2005 927

segmentation, each scale retains the dominant signalfeatures while minimising the wavelet-coefficient amplitudeof their representation. Because the wavelet-packet coeffi-cients contain information about the energy-magnitudecontribution for each discrete feature in terms of scale,frequency and position, this provides a robust method offeature and singularity detection. It is notable thatdetermination of the singularity spectrum of fractalfunctions by wavelet analysis provides a microscopicstatistical description of the scaling behaviour in terms ofdifferent energy functions. Convolving the signal (subsam-pling) at each iteration by keeping only every second point

makes the expansion into the wavelet-packet best-basisfinite [14]. Each transformation into the next level is anenergy-conservation process, and the total energy isconsidered to be the sum of all the individual energiesmapping out the feature fluctuations. The input signal canalso be rebuilt via up-sampling and summing the combina-tion of coefficients. By choosing a set of mother-and-fatherwavelet functions a quadrature mirror filter (QMF) withknown oscillation index, one can decompose an input signalto create a wavelet-packet table.

3 Wavelet-packet transform

Wavelet packets are a particular linear combination ofwavelets. They form bases that retain many of theorthogonality, smoothness and location properties of theirparent wavelets [15]. The coefficients in the linear combina-tions are computed by a recursive algorithm, with the resultthat expansions in wavelet-packet bases have low computa-tional complexity.

Recently, the wavelet-packet transform has been pro-posed as a significant new tool in signal analysis andprocessing. Wavelet transform is a good solution in thefrequency and time domains, synchronously, and canextract more information in the time domain at differentfrequency bands. The wavelet-packet transform has beenused for on-line monitoring of the process. It can captureimportant features of the fault-current signal that aresensitive to the CT saturation. The wavelet-packet trans-form can decompose the current signal into differentcomponents in different time windows and frequencybands; the components, hence, can be considered as featuresof the original signal.

In order to decompose a current signal, which is an one-dimensional discrete-time signal, a simple and fast methodis required for computation of wavelet-transform coeffi-cients of the signal. Reference [16] defines the one-dimensional discrete wavelet transform in terms of aquadrature-mirror-filter (QMF) pair {h(m)} and {g(m)}given as follows:

cj f ðtÞ½ � ¼ hðtÞ � cj�1½f ðtÞ� ð1Þ

dj f ðtÞ½ � ¼ gðtÞ � cj�1½f ðtÞ� ð2Þ

where c0 f ðtÞ½ � ¼ f ðtÞ represents the original signal andcorresponds to the subspace V0 in the continuous time, and

restraint current

c

ratio mismatch

CT error

margin

trip zone

diffe

rent

ial c

urre

nt

b

If

I1 I2 I3

I4I5I6

If

I1 I2 I3

I4I5I6

a

Fig. 1 Busbar differential-relay principlea External fault and load flowb Internal faultc Percentage differential-relay characteristic

current signalA(0)

A(1)

DDD(3)ADD(3)DAD(3)AAD(3)DDA(3)ADA(3)DAA(3)AAA(3)

DD(2)AD(2)DA(1)AA(2)

D(1)

Fig. 2 Wavelet packet-decomposition tree at level 3

928 IEE Proc.-Gener. Transm. Distrib., Vol. 152, No. 6, November 2005

fdj f ðtÞ½ �g; j ¼ 1; 2; . . . are the wavelet coefficients. Set

Hf�g ¼X

k

hðk � 2tÞ ð3Þ

Gf�g ¼X

k

gðk � 2tÞ ð4Þ

then (1) and (2) can be written as

cj½f ðtÞ� ¼ Hfcj�1½f ðtÞ�g ð5Þ

dj½f ðtÞ� ¼ Gfcj�1½f ðtÞ�g ð6ÞDWT only is the approximation cj�1½f ðtÞ� but not thedetail signal dj�1½f ðtÞ�. The Wavelet-packet transform doesnot omit the detail signal; therefore, the wavelet-packettransform is

cj½f ðtÞ� ¼ Hfcj�1½f ðtÞ�g þ Gfdj�1½f ðtÞ�g ð7Þ

dj½f ðtÞ� ¼ Gfcj�1½f ðtÞ�g þ Hfdj�1½f ðtÞ�g ð8ÞLet Qi

jðtÞ be the ith packet on jth resolution; then the

recursive algorithm can also compute the wavelet-packettransform, and is

Q10ðtÞ ¼ f ðtÞ

Q2i�1j ðtÞ ¼HQi

j�1ðtÞQ2i

j ðtÞ ¼GQij�1ðtÞ

ð9Þ

where t¼ 1, 2, y, 2J-I, i¼ 1, 2, y, 2j, j¼ 1, 2, y, J,J¼ log2N, N being data length.

4 Signal analysis during CT Saturation

The current busbar-protection techniques depend onmonitoring the current magnitude for identifying the busbarfaults. When the CT saturates, the magnetising impedanceis assumed to go to zero and the secondary current also goesto zero at that time. The effect on relay performance willdepend on the type of relay being used. However, the faultcurrent is information-rich during CT saturation. Theproposed technique is based on extraction features of thecurrent signal during the CT saturation (zero current value).From a mathematical point of view, the extraction featurescan be considered as signal compression. Wavelet-packettransform is represented as a compressed-signal method.Therefore, it is ideal to use the wavelet packets as theextracted features [17]. From the above, each wavelet-packet transform represents certain information about thesignal in a specific time–frequency window. Figure 3 showsthe decomposition results of current signal during CTsaturation. A wavelet-packet table for a sampled currentsignal with 20kHz is used. The QMF filter was a two-dimensional wavelet function. Level 0 is equivalent to theoriginal current signal and resolution levels 1–3 are plottedbelow. For each level, the left-most block has oscillationwhich is the ‘approximation’ or blurred signal created fromthe lowpass father wavelet which convolves the signal bykeeping only every second point. The right-most block hasoscillation and contains the high-frequency coefficientcreated from the high-pass mother wavelet. Figure 3represents the constituent parts of the current signal atfrequency bands [0, 2.5], [2.5, 5],y, [17.5, 20] kHz, respec-tively. These decomposition results of the current signalprovide more information such as the time-domainconstituent part at the frequency band. The average valuesof the constituent parts of the current signal at everyfrequency band can represent the energy level of the currentsignal in the frequency band. In the fault tests during CTsaturation, a total of 225 cases were simulated. Different

decomposition parameters (levels and packets) are tested.Results concluded that the same goal of analysis at level 3or more and different packets (from 2 to 4) can be obtained.

5 WPT-based differential busbar scheme

The proposed technique is based on a feature signalextracted from the original current value using the WPTmethod. The proposed technique uses the differential-relayprinciple for the extracted signals rather than the currentvalues. The original measured line currents (entering orleaving the busbar) utilise (9) to fulfill WPT. The results offeature extraction from wavelet coefficients correspondingto the line currents are computed at a certain frequencyband (level-3, packet 4 and d2 wavelet function). The resultis computed from (9) as Q7

3ðtÞ ¼ HQ42ðtÞ. According to the

differential-relay principle, the differential-coefficient signalSDCðkÞ is computed as

SDCðkÞ ¼Xm

L¼1Q7

3ðkÞL ð10Þ

where m indicates the total number of lines connected to thebus, k is the most recent sample after fault occurrence. SDCðkÞ represents the instantaneous sum of the waveletcoefficients decomposed from the original current signalsusing the WPT.

The accumulated value of the constituent parts of theSDC can represent the energy level of the SDC in thefrequency band as

tripðkÞ ¼ tripðk � 1Þ þ SDCðkÞ ð11ÞThe criterion for the protection relay to initiate a trip signalis such that Trip(k) must stay above a threshold level(THR) continuously for a number of samples (threesamples after fault inception). In this respect, an extensiveseries of studies has revealed that, in order to maintain relaystability for external faults (i.e. faults out side the bus zone),the THR is 0.125. The setting of the value of this thresholdis dependent on the system environment.

6 Simulation model

The model shown in Fig. 4 has been simulated. Thesubstation includes a 230kV busbar. Data for verifying theproposed technique was generated by modelling the selected

la

level 0

level 1

level 2

level 3

Fig. 3 Decomposition results of current signal by wavelet-packettransformations

IEE Proc.-Gener. Transm. Distrib., Vol. 152, No. 6, November 2005 929

system by using the alternative transient program (ATP)[18]. The transmission-line parameters are given in [19, 20].Each source was modelled as three separate generators withan equivalent circuit in which positive sequence can becalculated from the fault level. Type 98 element is used forCT saturation. The current/voltage points are converted tocurrent/flux points using the ATP supporting routine. The10C800 (1200:5, Rs¼ zero) CT is used for the case studiespresented here. The l/i curve with a saturation point (1A,3.53Vs) is used with the CT model. A sampling frequencyof 20kHz for a system operating at a frequency 50Hz isused in this study.

7 Simulation results

The system shown in Fig. 4 was subjected to various faultsevents. ATP program was used to generate data to test theperformance of the proposed technique. The resultsobtained from the tests are given here. Simulated wave-forms of the currents provided by unsaturated andsaturated CTs are also given. The proposed approach wastested by computing the ‘Trip’ value of single-phase-to-earth, two-phase-to-earth, phase-to-phase and balancedthree-phase faults. The performance of the proposedtechnique was evaluated for different types of internal andexternal faults, source impedance and fault resistance.Fault-inception angles were examined over the entire cycle.The effect of sampling rate ranging from 5 and 200kHz wasapplied. The effect of severe and early CT saturation wasalso provided. Finally, there are a total of 1750 cases for

0.3

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, p.u

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1000 10 20 30 40 50 60 70 80 90

b

0.03

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0

WC-lct 2WC-lct 3

WC-lct 1

Fig. 5 Waveforms of saturated and unsaturated current transfor-mersa Line currentsb WC signalsc DCS signald Trip signal

F3

F1

F2

ct2

ct3

ct1

T-line 1190km

zone-1

T-line 2155km

T-line 4200km

T-line 3190km

Fig. 4 Model for simulation studies

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WC-lct 1WC-lct 2WC-lct 3

Fig. 6 Waveforms and WPT in case of ratio mismatch

930 IEE Proc.-Gener. Transm. Distrib., Vol. 152, No. 6, November 2005

investigation. Different wavelet-packet functions weretested. Other resolution packets (from 2 to 4) were alsotested. The selection of other available wavelet packetfunctions and resolution packets could achieve the samegoal.

7.1 Impact of CT saturation and ratiomismatchFigure 5a shows the waveforms of the fault currents (ict1,ict2 and ict3) provided by saturated CT3 and an externalfault located at F2. Figure 5b shows the wavelet coefficientsWC of the current signals at level 3, packet 4 and d2 waveletfunction. Figure 5c shows the corresponding differential-coefficient signal SDC. The SDC signal carries richerinformation during CT saturation. Figure 5d shows thetrip signal (Trip) that indicates the final response of therelay. This plot shows that the trip signal seen by the relaylies between positive and negative threshold boundaries(0.125). This led to the decision that the fault was outsidethe busbar-protection zone.

The errors in transformation of the CTs may differ fromeach other, thus leading to a significant differential currentwhen there is normal load flow, or an external fault. In anycase, even with some adjustments, there remains someresidual ratio mismatch, which leads to a small differentialcurrent during normal conditions. This is one of theshortcomings of current differential relays based on currentmagnitude.

The proposed approach is used to monitor various eventsof fault-generated features as time varies, rather than

monitoring the current values. The approach describedpresents both frequency and time information simulta-neously. The Trip signal has features that are directly relatedto frequency changes rather than current magnitude. Thisleads to the fact that the CT-error and ratio-mismatchproblems do not affect on the fault decision made by therelay. The impact of the ratio mismatch on the proposedtechnique is provided.

Figure 6 shows the waveforms of the fault currents for anexternal fault located at F2 without CT saturation. Achange in the CT3 ratio is taken to give +20% error. Thischange gives a different current magnitude. The computedSDC value does not depend on the current magnitude (seeFig. 6c). Consequently, the Trip value is not affected in anysignificant manner by this error. The CT ratio mismatchtherefore does not affect the performance of the technique.

7.2 Test resultsThe performance of the proposed technique was evaluatedfor different types of internal and external faults:

(i) Internal fault: A three-phase-to-earth fault in the bus-protection zone at F1 zone-1 was simulated. The perfor-mance of the algorithm is shown in Fig. 7. The computedTrip signal moves as a function of the samples. The Tripsignal has a value greater than the threshold boundary thatindicates the fault is in the protection zone of the busbar(zone 1). Immediately after three samples, the trip

0.2

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0

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S, p

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0 10 20 30 40 50 60 70 80 90 100c

0.30.20.1

0−0.1−0.2

trip

, p.u

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0 10 20 30 40 50 60 70 80 90 100

samples

d

line

curr

ents

, p.u

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lct 2lct 3

lct 1

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0

−0.1

−0.2

WC

, p.u

.

0 10 20 30 40 50 60 70 80 90 100

b

WC-lct 2WC-lct 3

WC-lct 1

Fig. 7 Waveforms and WPT of three-phase-to-earth fault at F1

(zone 1)

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trip

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0 10 20 30 40 50 60 70 80 90 100d

samples

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curr

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lct 2lct 1

lct 3

WC

, p.u

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−0.05

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0.05

0

1000 10 20 30 40 50 60 70 80 90

b

WC-lct 2WC-lct 1

WC-lct 3

3

2

1

0

−1

−2

−3

DC

S, p

.u.

×10−1

0 10 20 30 40 50 60 70 80 90 100c

Fig. 8 Waveforms and WPT of single-phase-to-earth fault at F2

out of protection zone

IEE Proc.-Gener. Transm. Distrib., Vol. 152, No. 6, November 2005 931

confirmed that the fault was in the bus-protection zone. Ittook the algorithm 1.2ms to make the final decision.

(ii) External fault: A wide variation of external faultboundaries and fault resistance was investigated. For thepower system shown in Fig. 4, consider a single phase-to-earth fault outside the bus-protection zone F2. The relaycomputed the Trip value. The results are shown in Fig. 8.Figure 8 shows that the Trip signal has a value less than thethreshold boundary. This led to the final decision that thefault was outside the bus-protection zone.

(iii) Busbar fault out of zone 1: The effect of CT2 saturationand bus-2 fault at zone 2 is also investigated. A 3LG fault inthe second zone is located. Figure 9 shows the computedTrip value before and after saturation. The case showssaturation late in CT2. The Trip signal seen by the relay liesinside the threshold boundaries.

(iv) Early and severe CT saturation: The secondary currentcan be quite distorted relative to the primary current. Ifconditions are severe enough, it is possible that thedistortion may be even worse and that saturation can startto occur even sooner. Such early and severe saturation cancause problems in the busbar differential circuit. Somecurrent relays detect the fault before saturation, but this isnot possible in this case. The others require very highsettings that may not be sensitive to detection of minimumbusbar faults.

The proposed technique can also be used to detect anddiscriminate successfully early and severely CT saturations.For an early and severely saturation, the current goes to

zero almost immediately after fault inception. To analysethis concern, a phase-A to phase-B fault outside the busbar–protection zone at F3 was examined. Figure 10 shows thewaveforms of the fault currents and the correspondingperformance of the Trip signal. The Trip signal movesdirectly with a positive value which is less than the thresholdboundary, thus recognising that the fault is out of thebusbar zone.(v) Effect of high path resistance: The fault resistancereduces the magnitude of the transient waves, but thewavelet-packet transform-based transient detection has highsensitivity to signal variation. The small transient signal canbe detected. To analyse this, a three-line-to-earth in the bus-protection zone at F1 with a fault resistance equal to 250Owas simulated. The performance of the technique is shownin Fig. 11. The impact of increased fault resistance is to slowthe rise of the Trip signal, thus delaying the action ofcrossing the threshold boundary. It took the algorithm5.2ms to make the final decision. Various values of earthfaults were also tested through fault resistances up to 350Oand the results indicated that the trip time was 6ms afterfault inception.

8 Conclusions

The principle and application of the wavelet-packet-trans-form-based differential busbar protection is analysed anddiscussed in this paper. Several features were derived fromwavelet-packet transforms, and the optimal featuressensitive to the fault current during CT saturation. The

1.010

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WC-lct 1

Fig. 9 Waveforms and WPT of three-phase-to-earth fault onbusbar 2 (zone 2) out of protection zone

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Fig. 10 Waveforms and WPT during early and severe current-transformer saturation for an external fault located at F3

932 IEE Proc.-Gener. Transm. Distrib., Vol. 152, No. 6, November 2005

technique is stable during CT saturation and is not affectedby CT error and ratio mismatch. The technique is alsosensitive in the event of high fault resistance, which is mostlikely on busbars. The tripping time is recorded within 6ms

for all types of fault. The feature extraction with wavelet-packet transform can be implemented in real time sincewavelet-packet transform requires only a small amount ofcomputation.

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Fig. 11 Waveforms and WPT of three-phase-to-earth fault at F1

(zone 1) and 250O fault resistance

IEE Proc.-Gener. Transm. Distrib., Vol. 152, No. 6, November 2005 933