Experimental Investigations on Multi-end Fault Location System based on Current Traveling Waves

download Experimental Investigations on Multi-end Fault  Location System based on Current Traveling Waves

of 6

Transcript of Experimental Investigations on Multi-end Fault Location System based on Current Traveling Waves

  • 8/13/2019 Experimental Investigations on Multi-end Fault Location System based on Current Traveling Waves

    1/6

    Experimental Investigations on Multi-end FaultLocation System based on Current Traveling Waves

    A. Elhaffar, student member IEEE,N. I. Elkalashy, student member IEEE and M. Lehtonen.

    Abstract Traveling Waves Recorders (TWR) are used toaccurately find the location of different faults in transmissionnetworks. These recorders are installed at few substation buseswhere current traveling waves can be extracted. The recordedsignals time delay of the initial wave is recoded at each TWR. Inthis paper, the minimum travel time of the traveling wave hasbeen calculated considering Dijkstra algorithm to select thenearest TWR to the faulted line. The Wavelet Transform is usedto find the highest spectral energy of the frequency band of thetraveling wave signals. Thus, the Wavelet Transform enhancesthe traveling wave fault location. The current transformers (CT)are modeled and experimentally verified to represent thetraveling wave interaction with the CT. The secondary wiringfrom the CT secondary winding to TWR has also some effect onthe measured traveling wave signal which motivates practical

    issues associated with measuring the arrival times. Correctionfactors are derived to monitor high frequency current travelingwave signals. Validation of fault location is examined byATP/EMTP simulations for typical 400 kV power system faults.

    Keywords: Traveling waves, fault location, multi end method,

    single phase to ground fault, modal analysis, wavelet transform.

    I. INTRODUCTION

    ccuratly locating faults on high voltage transmission

    systems is very important for utilities to allow quick

    maintenance action of the repair crew. Fault location systems

    have been traditionally relied on the measurement of power

    frequency components. However, traveling wave faultlocation shows an increasing interest to researchers and

    utilities due to its accuracy [1]-[7].

    As the number of traveling wave recorders (TWR) are

    usually less than the number of buses, efficient methods are

    needed to find the fault from only the existing recording units

    [8]. Recently, traveling waves and the wavelet transform of

    the current transient are used to extract initial arrival times of

    fault initiated waves reflected from the fault point[9]-[11].

    In [8], a method was developed to estimate the fault area

    using several recorders scattered throughout the system by

    comparing a fault signature record with calculated fault

    signatures. This method is used in this presented paper

    considering few recording units installed at few monitored

    substations in the power system. The fault location is

    determined by accurately time-tagging the arrival of the

    traveling wave at these monitored substations and comparing

    the time difference to the total propagation time of the lines.

    The time reference signal can be attained using satellite from

    A. Elhaffar, N. I. Elkalashy and M. Lehtonen are with Power System & High Voltage Engineering,

    Department of Electrical and Communication Engineering, Helsinki University of Technology (TKK),

    P.O.Box 3000, FIN-02015 HUT, Finland, Tel. +358 9 4515484, Fax +358 9 460224, Finland.(email:

    [email protected], [email protected], [email protected]).

    the Global Positioning System (GPS). Fault distance

    calculation is, therefore, carried out using double end method

    and pre-selected two TWR signals.

    Conventional CTs are used to monitor the traveling wave

    transients. In this paper, effects of CT and split-core inductive

    couplers filtering current transformers on the recorded signals

    and therefore on the traveling wave fault locator performance

    are investigated. This investigation is carried out using the

    total transfer function of the whole fault locator measuring

    system. Then, a practical solution for fault location using few

    traveling wave current signals is studied taking into account

    CT and associated secondary system model. The signals are

    analyzed using wavelet transform. A method of selecting anoptimum mother wavelet and an optimum level according to

    signals energy content is presented. The minimum travel time

    of the current traveling wave signal traveling to the nearest

    TWR has been calculated using Dijkstra algorithm [12].

    Simulation results indicate good correlation between the

    estimated and actual fault locations for the studied network.

    II. CURRENT TRANSFORMER MODELING

    In this section, the CT modeling is presented. The

    modeling is carried out with the aid of experimental results

    measured at Helsinki University of Technology (TKK). The

    CT used in this measurement was a hair-pin type 110 kV,

    200/5 CT with three secondary windings as shown in Fig. 1.The CT modeling is divided into two parts; the low and high

    frequency models. The low frequency model parameters of the

    CT are calculated from open and short circuit tests of the CT

    at power frequency. The inductance of secondary windings

    dominates the impedance at a low frequency and the stray

    capacitances have negligible effects. Open circuit tests were

    only measured from the secondary side while the short circuit

    tests were measured from both primary and secondary sides.

    Towards high frequency transfer function modeling of the

    CT, an impulse current signal was injected in the primary

    winding and the output secondary current was measured using

    a low inductance shunt resistor (0.4905 ). The signals aredigitally recorded using a digitizer. The digital recorded

    signals are transformed using Fourier Transform to obtain the

    frequency spectra from which the desired transfer functions

    are calculated. The shunt capacitances representing the

    capacitances of the transformer windings can no longer be

    ignored. These parasitic secondary capacitances have a great

    influence on the output current. Open and short circuit

    impulse tests are also carried out for the abovementioned CT

    to find high frequency model parameters [13]. Fig. 2 shows

    secondary winding 1 spectrum during the open circuit test.

    A

  • 8/13/2019 Experimental Investigations on Multi-end Fault Location System based on Current Traveling Waves

    2/6

    Figure 1 CT High Frequency equivalent circuit.

    103

    104

    105

    1060

    2

    4

    6

    8

    x 104 S1 Winding Impedance

    Zs

    1[Ohms]

    Frequnecy [ Hz]

    103

    104

    105

    106

    -100

    0

    100

    S1 Winding Impedance Angle

    Phi[deg]

    Frequnecy [ Hz] Fig. 2 Open circuit test from secondary winding 1.

    The frequency response measurements were carried out

    using standard 1.2/50 s low impulse voltage signals for opencircuit tests and non-standard 2.2/6 s current signals for shortcircuit test. The first resonance frequency is found for each

    secondary winding from its corresponding spectrum. Then,

    the secondary winding shunt capacitances Cs1, Cs2and Cs3can

    be calculated. Consequently, from these tests, a frequency

    dependent correction factors can be obtained based on the

    calculated parameters of the CT as in:

    n

    n

    n

    nn

    Zc

    Zs

    Zm

    ZsCFs ++= 1 (1)

    whereZcnis the capacitance of secondary winding and n is the

    secondary winding number 1, 2 and 3.

    Split-core current transformers are connected directly to thesecondary of the relaying CTs for isolating high frequency

    signals. They are also tested and their transfer function

    calculated using the system identification tool box of

    MATLAB[14].Obviously the Box-Jenkins model gives good

    results as shown in Fig. 3. From impulse current

    measurements, the overall transfer function was plotted

    against the frequency. Therefore, the resonance frequency

    values for the CT, wiring and coupler was located and

    recorded. The overall transfer function bode plot is shown in

    Fig. 4. Considering the interaction between the ATP/EMTP

    simulated network and the transient analysis control system

    (TACS) function, the transfer function of the measuring

    system of the CT, secondary wiring and split-core inductive

    couplers are inserted in the ATP/EMTP transmission line 110

    kV model in addition to the secondary wiring cable from the

    CT to the TWR as shown in Fig. 5 [15], [16].

    0 1 2 3 4 5 6 7 8

    x 10-6

    -2

    -1.5

    -1

    -0.5

    0

    0.5

    1

    1.5

    2 x 10

    -3

    y1

    Coupler Measured and Simulated Models Output

    Measured Output Current

    Box-Jenkins Model Fit: 71.22%

    PEM Fit: 51.7%

    Fig. 3 Inductive coupler model comparison

    10

    -5

    10

    0

    10

    510

    -8

    10-6

    10-4

    Amplitude

    Overall Transfer function of CT and coupler

    10-5

    100

    105

    -400

    -200

    0

    200

    Phase(degrees)

    Frequency (rad/s) Fig. 4 Overall transfer function of both CT and inductive coupler

    110kV 110kV

    Wave-imp

    B1

    Wave-imp

    G(s)

    G(s)

    G(s)

    Transfer function: CT and Line Couplers

    Fig. 5 Simulated 110 kV transmission Line with CT Transfer Function and

    secondary Wiring

  • 8/13/2019 Experimental Investigations on Multi-end Fault Location System based on Current Traveling Waves

    3/6

    III. SIGNAL PROCESSING

    A. Wavelet Analysis

    The main problems that came across by using current

    traveling waves are that they have no direction and are noisy.

    Recently, it was shown that the wavelet transform of the

    modal components of the fault initiated traveling waves is

    used to estimate the location of the fault [10].

    The wavelet transforms of the modal current componentsare obtained yielding the corresponding wavelet coefficients

    in selected levels. The potential benefits of applying digital

    wavelet transform (DWT) for analyzing traveling waves

    transients have been well-recognized because of its inherent

    time and frequency localization characteristics [17]. DWT

    offers an alternative to windowed (Short-Time) Fourier

    (STFT) analysis where a uniform window is used for all

    frequencies. This problem has been solved in DWT by

    employing short windows at high frequencies and long

    windows at low frequencies. The windowing is performed in

    practice by scaling and translating a Mother Wavelet (t).

    The continuous wavelet transform (CWT) is initiallyshown in equation (8).

    +

    = dttx

    a

    bt

    abaCWT )().(

    1),(

    (2)

    The mother wavelet )(t is a band pass filter which should

    satisfy some conditions: It should be short and satisfies the

    relation:

    +

    = 0)( dtt (3)

    a1 is a coefficient used in order to have the same "energy"

    in each analyzing wavelet.

    In practice discrete wavelet transform DWT is used

    instead of CWT. The two parameters aand bare discretized.

    For a signal x(t), its DWT with respect to a discrete mother

    wavelet (t)can be represented by

    [ ] [ ] =

    k a

    bnkx

    anmxDWT )(

    1,, (4)

    The b gives the time position of the wavelet, while the

    parameter acontrols its frequency.

    DWT of a sampled signal is calculated by choosing a= a0m,

    and b= nb0a0m. Toward better efficiency of computations, a0

    and b0 are set to 2 and 1 respectively resulting in a binarydilation of 2

    mand dyadic translation of 2

    mn[18]. The dyadic

    DWT analysis is the most popular implementation of DWT,

    which is used in most applications. The discrete basis function

    of the dyadic DWT is given by:

    020

    0

    ( , )

    m m

    m

    x a nn m a

    a

    =

    (5)

    The wavelet coefficients that represent the fault traveling

    wave signal are:

    0 0 1 2[ ........ 1]TWC c d d d dj= (6)

    wherejrepresents the total number of resolution levels.

    For carrying out wavelet analysis, first, a suitable mother

    wavelet must be chosen, which plays a significant role in a

    fault-location scheme. In this work, an optimum mother

    wavelet is selected based on the highest energy content and

    based on its ability to reconstruct the original signal with

    minimum errors [19],[20].

    B. Optimum Wavelet FunctionDifferent wavelets can be used to decompose the fault

    transient signal and extract the feature vector. A comparison

    between three different groups of orthogonal wavelets was

    carried out. These wavelets used in the comparison were: db2,

    db4, db6, db8, db10, db20, db30, db40, sym4, sym8, sym10,

    coi1..5, bior2.4, bior3.3, and bior3.7. The criterion for

    selecting the proper wavelet, to be used in feature extraction,

    is based on its ability to reconstruct the original signal with

    minimum errors. The norm of the error is used as a

    discriminator. For selecting the proper details level, the energy

    content at different resolution levels is calculated and the

    highest one is selected. Fig. 6 shows the details energy at sixlevels for a fault at 112.2 km from OL substation for a pre-

    selected mother wavelet.

    The problem now arises from which level of the sub-band

    components should be used in DWT analysis procedure. The

    main reason is at fault location, there is one level at which the

    calculation of the fault distance is more accurate than other

    levels. If the used scaling function and the wavelets form an

    orthonormal basis, the Parseval's theorem relates the energy of

    the fault traveling wave signal to the energy in each of the

    expansion components and their wavelet coefficients.

    Therefore, the energy of the fault traveling wave signal will be

    partitioned at different resolution levels according to the

    transmission line transients [21].

    22 2

    0

    ( ) ( ) ( )jk j k

    x t dt c k d k

    = = =

    = + (7)where, djis thejlevel wavelet coefficient and cjis thej level

    scaling coefficient.

    With the energy in the expansion domain is partitioned in

    time by kand in scale by j. This means that the energy of the

    distorted signal can be partitioned in terms of the expansion

    coefficients [21]. The above method was implemented in a

    MATLAB program using the current details of the fault line

    signal as the absolute sum value of the current signal details

    squared computed in a discrete form, as in:2

    1

    ( ) ( )

    N

    j

    k

    DE k d k

    =

    = (8)whereDE(k)is the details energy detector in discrete samples.

    j is considered as the scale number, and k is the index of

    wavelet details coefficients. Fig. 6 indicates that high-

    frequency current was more powerful in the fault signal at the

    fist level, and the signal energy was distributed over the whole

    analyzed resolution levels with different magnitude [19].

  • 8/13/2019 Experimental Investigations on Multi-end Fault Location System based on Current Traveling Waves

    4/6

    1 2 3 4 5 60

    1

    2

    3

    4

    5

    6x 10

    6

    Levels

    DetailsEnergy

    Fig. 6. OL current traveling wave wavelets transform details energy

    0 20 40 60 80 100 120 140 160-2

    -1.5

    -1

    -0.5

    0

    0.5

    1

    Fault Distance [km]

    Error

    %

    Percentage Error

    Fig. 7 Error analysis of single end method

    IV. FAULT LOCATION PROBLEM FORMULATION

    Traveling wave methods for transmission lines fault

    location have been reported since a long time. Subsequentdevelopments had employed high-speed digital recording

    technology to capture the traveling wave transients created by

    faults. It is well known that when a fault occurs in overhead

    transmission lines systems, the abrupt changes in voltage and

    current at the point of the fault generate high frequency

    electromagnetic travelling waves which propagate along the

    transmission line in both directions away from the fault point.

    If the times of arrival of the travelling waves in the two ends

    of the transmission line can be measured precisely, the fault

    location then can be determined by comparing the difference

    between these two arrival times of the first initial traveling

    wave signal.By modal transform, a three-phase system can be

    represented by an earth mode and two aerial modes. Each

    mode has a particular velocity and characteristic impedance.

    In this paper, the aerial mode 1 signal is used in the fault

    distance estimation. The modal components are obtained by:

    ),(),(

    ),(),(

    txITtxI

    txUTtxU

    mi

    mv

    =

    =

    (9)

    (10)

    where Tv and Ti are voltage and current transformation

    matrices, U and I are phase voltage and current components,

    Um and Im are modal voltage and current components

    respectively. for transposed lines to transform the transient

    current signals Ia, Iband Icinto their modal components using

    Clarks transformation as follows [22],[23]:

    1

    2

    3

    1 1 11

    2 1 13

    0 3 3

    a

    b

    c

    I I

    I I

    II

    =

    (11)

    where I1 is the ground mode current, I2 and I3are known asaerial mode current components for transposed lines.

    In single-ended fault location method, the signals reflected

    from the fault points as well as from the remote end busbars

    imposes more difficulties in finding the arrival times of the

    recorded signals especially for faults at the second half of a

    transmission line. The time difference between the ground and

    Ariel mode wavelet coefficients (dt0) is compared with that of

    the time difference produced by a fault located at the middle

    of the line (dtm) [11]. If dt0dtm, then the fault will be locatedin the first half of the line and the fault distance x will be:

    2

    dtv

    x

    = (12)where x is the distance to the fault, td=(t2 t1)

    which is the

    time difference between two consecutive peaks of the

    optimum wavelet transform detail coefficients of the recorded

    currents at the terminal bus and v is the wave propagation

    velocity of the aerial mode.

    For a fault between the midpoint and remote end bus, some

    reflections from remote end will arrived at the sending station

    before the first reflection from the fault point. The time

    difference between the ground and arial mode wavelet

    coefficients is greater than that of the time difference

    produced by a fault located at the middle of the line (dt0> dtm).Then the fault will be located in the second half of the line and

    the fault distance x will be calculated using:

    2 1x - (t -t )2

    vL= (13)

    where L is the line length and t2-t1 is the time difference

    between two consecutive peaks of wavelet coefficients of the

    aerial mode current signal. These signals are processed using

    MATLAB [18]. Current signal was acquired at a sampling

    rate of 1.25 MHz and so frequencies up to 625 kHz were

    considered and the faults are simulated on the OL-KA line

    using ATP/EMTP program.

    In single end method, usually it is difficult to find the exactfault location if the fault inception angle or the fault resistance

    changes. The auto-correlation of the details for each level

    gives good fault distance estimation [24]. The fault location

    percentage error using autocorrelation of the wavelet details

    has shown good results as shown in Fig 7. Due to the

    difficulties in finding the second peak signal, single end

    traveling wave fault location method has high errors when

    applied to meshed networks. The reason is the multipath

    reflections from different discontinuities. Utilities prefer

    multi-end fault location with few recording units.

  • 8/13/2019 Experimental Investigations on Multi-end Fault Location System based on Current Traveling Waves

    5/6

    V. MULTI END MEHOD

    Fig. 8 illustrates the single line diagram of a 400 kV

    transmission network simulated using ATP/EMTP [15], in

    which the processing is created by preprocessor program

    ATPDraw [16]. A small part of 400kV FinGrid network has

    been simulated and a fault scenario similar to that disturbances

    occurs on 29.6.2002 13:12:54 (GMT) between OL-KA

    substations at a distance 112.2km from OL substation. The

    TWR recorders that recorded the fault signals are YL, AJ, ES,OL recorders. The minimum path for the traveling wave has

    been calculated from Bus OL though OL-KA line to BUS AJ.

    The fault is then calculated using two end method using the

    OL and AJ recordings. Traveling wave velocities can be

    determined based on the type and configuration of lines using

    line/cable constant (LCC) program of ATP/EMTP[15].

    The power lines studied are part of the 400 kV Finnish

    EHV transmission system. The relevant lines and location of

    the current transducers are shown in Fig. 8. This system has

    been modeled using ATP/EMTP with measurements at three

    substations: OL, AJ and ES.

    If the times of arrival of the traveling waves in the chosentwo TWR units can be measured precisely, the fault location

    then can be determined by comparing the difference between

    these two arrival times. However, two main aspects which

    affect the accuracy directly and significantly need to be

    considered. One is the data synchronized sampling and the

    other is arrival time detection. The former can be obtained

    easily by using the Global Positioning System (GPS) which

    can provide time synchronization up to maximum 1 s

    accuracy over a wide area; the latter can be fulfilled by using

    wavelet analysis which has already been successfully applied

    in various fields in electrical engineering [19].

    A MatLab program has been developed to estimate the

    fault location from the first peak arrivals at three TWR units.

    The minimum path for the traveling wave between the closest

    two TWR units to the fault has been calculated using Dijkstra

    Algorithm [12]. The maximum value of the first recorded

    signals are selected as the two TWR candidates for fault

    location Then, the fault distance is calculated by the double-

    end method using the chosen TWR signals. For example: If a

    single earth fault occurs at OL-KA line, and the best two

    TWR candidates are OL and AJ recorders, the fault location

    can be calculated as follows:

    [OL-AJ] OL AJ

    OL

    line lengths + (T1 -T1 ).FL =

    2

    v

    (14)

    VI. RESULTS

    The proposed approach has been tested under different system

    circuit configurations, under different system and fault

    conditions. The minimum path for the traveling wave has been

    calculated using Dijkstra Algorithm. The fault is then

    calculated using double end method using the best two fault

    traveling wave signals as shown in Fig 9.

    AJ

    UL

    OLKA

    ES

    RA

    TM

    TWR

    TWR

    TWR

    HYYL

    TWR

    HU

    KR

    Fig. 8. Test transmission system single line diagram.

    0 0.5 1 1.5 2

    x 10-3

    -300

    -200

    -100

    0

    100

    200

    300

    Time [%mu s]

    OptimumD

    etailsCurrentLevel[A]

    AJ Recoder Signal

    OL Recoder Signal

    Fig. 9. The optimum details level of two TWR at AJ and OL buses.

    TABLEI SIMULATION RESULTS FOR ASINGLE-PHASE EARTH FAULTS

    Actual Location from OLFaulted

    Line % km

    Estimated Location

    from OL

    Error %

    OL-KA 20 % 32.6 32.6540 -0.1656

    OL-KA 50 % 81.5 81.6586 -0.1946

    OL-KA 80 % 130.4 130.4298 -0.0229

    UL-ES 20 % 97.2 96.9032 0.3053

    UL-ES 50 % 172.5 172.6376 -0.1096

    UL-ES 80 % 50.2 49.5104 -0.2783

    This method is sensitive to the travelling wave propagation

    velocity which can be calculated using the LCC program.

    Using a ground resistivity of 2300 .m and the data of table Ifor a horizontal transmission line configuration, the

    propagation speed was found to be 29177.4 km/s. At least,

    two recordings are needed for an accurate fault location in a

    meshed network. Simulation studies show that for earth faults,

    errors are symmetric along the transmission line except that

    when fault inception angle is too small or fault location is tooclose to the line terminals.

    VII. CONCLUSIONS

    The experimental results reveal that CTs can be used for

    monitoring high frequency current signals over a useful range

    suitable for traveling wave based fault locators.

    This paper presents a fault location procedure for multi end

    transmission line network using current transient signals from.

    For single end method, the wavelet transform of the current

  • 8/13/2019 Experimental Investigations on Multi-end Fault Location System based on Current Traveling Waves

    6/6

    transient is used to extract arrival times of fault traveling

    waves reflected from the fault point. Simulation results

    indicate good correlation between the estimated and actual

    fault locations for the studied transmission line. The maximum

    of the squared value of auto-correlation function of optimum

    level detail of the wavelet coefficients enhances the fault

    location accuracy. A detailed investigation of the capabilities

    of the DWT to identify, detect and localize signal disturbances

    expressing power system transients and fault conditions. Aproposed DWT implementation algorithm using an optimum

    mother wavelet has been introduced, examined, and validated.

    The investigation results show that the DWT can detect the

    band of traveling wave signals and localize them in time.

    For multi end method, the minimum path for the traveling

    wave has been calculated; it will be automatically done by

    Dijkstra Algorithm. The fault is then calculated using two end

    method using the appropriate fault recordings from the nearest

    TWR recorders.

    VIII. REFERENCES

    [1] T. W. Stringfeild, D.J. Mahart and R.F.Stevens, Fault Location

    Methods for Overhead Lines, AIEE Transactions, pp. 157-160, August

    1957.

    [2] F. S. Caralho and S. Carneiro,Detection of Fault Induced Transients in

    E.H.V. Transmission Lines for the Development of a Fault Locator,

    International Conference on Power Systems Transients- IPST 2003.

    [3] Y. G. Paithankar and M. T. Sant, A new algorithm for relaying and

    fault location based on auto-correlation of travelling waves ,

    Electric Power Systems Research, Volume 8, Issue 2, March 1985,

    Pages 179-185.

    [4] Rajendra S, McLaren PG. Traveling-wave techniques applied to

    protection of teed circuits: Principle of traveling wave techniques ,

    IEEE Trans PAS, 1985, 104, Page(s): 3544-3550.

    [5] Rajendra S, McLaren PG. Traveling wave techniques applied to the

    protection of teed circuits: Multi phase/multi circuit system. IEEE Trans

    PAS 1985; 104, Page(s): 3551-3557.[6] Christopoulos C, Thomas D, Wright A. Scheme, based on travelling-

    waves, for the protection of major transmission lines. IEEE Proc C 1988,

    pp.63-73.

    [7] Aurangzeb, M.; Crossley, P.A.; Gale, P.; Fault location using the high

    frequency travelling waves measured at a single location on a

    transmission line , Developments in Power System Protection, 2001,

    Seventh International Conference on (IEE), 9-12 April 2001

    Page(s): 403 406.

    [8] Z. Galijasevic and A. Abur,'Fault Area Estimation via Intelligent

    Processing of Fault-Induced Transients', IEEE TRANSACTIONS ON

    POWER SYSTEMS, VOL. 18, NO. 4, NOVEMBER 2003, pp. 1241-

    1247.

    [9] Robertson, D. C.; Camps, O. I.; Mayer, J. S. & Gish, W. B.: Wavelets

    and electromagnetic power system transients, IEEE Transactions on

    Power Delivery, Volume: 11 Issue: 2 , April 1996, Page(s): 1050 -1058.[10] A. Abur and F. H. Magnago, Fault location using wavelets , IEEE

    Trans Power Delivery 1998; 13, Page(s): 1475-1480.

    [11] A. Abur and F. H. Magnago, Use of time delays between modal

    components in wavelet based fault location , International Journal of

    Electrical Power & Energy Systems, Volume 22, Issue 6, August 2000,

    Pages: 397-403.

    [12] E. W.Dijkstra, A note on two problems in connection with graphs,

    Numer. Math., vol. 1, pp. 269-271, 1959

    [13] D. A. Douglass, Current transformer accuracy with asymmetric and

    high frequency fault current, IEEE Trans-PAS, Vol. 100, No. 3, March

    1981.

    [14] L.Ljung, System Identification Toolbox users Guide for use with

    Matlab.

    [15] Alternative Transient Program, RuleBook, 1987.

    [16] Prikler, L. and Hoildalen, H. ATPDraw users' manual, SINTEF Energy

    Research AS, Norway, TR F5680, ISBN 82-594-2344-8, August 2002

    [17] Daubechies I. Ten lectures on wavelets , SIAM; 1992.

    [18] M. Misiti, Y. Misiti, G. Oppenheim and J. Poggi, Wavelet toolbox user's

    guide. Version 2. , The math works.

    [19] A. M. Gaouda, M. M. A. Salama, M. R. Sultan, and A. Y. Chikhani,

    'Application of Multiresolution Signal Decomposition for Monitoring

    Short-Duration Variations in Distribution Systems', IEEE Transactions

    on Power Delivery, Vol. 15, No. 2, April 2000,pp. 478-485.

    [20]N. Elkalashy et al, 'Impact of High Resistance Arcing FaultCharacteristics on Behavior of Dwt-Based Detection in MV Networks',

    Int'l conf. on Electrical and Control Technologies 3-4 May 2007,

    Kaunas, Lithuania.

    [21] C. Sidney Burrus, Ramesh A. Gopinath and Haitao Guo.Introduction to

    Wavelets and Wavelet Transform, Prentice Hall, New Jersey (1997).

    [22] L. M. Wedepohl, Application of matrix methods to the solution of

    travelling wave phenomena in polyphase systems, Proc. IEE, vol. 110,

    no. 12, pp. 2200-2212, Dec. 1963.

    [23] E. Clarke, Circuit Analysis of AC Power Systems, Symmetrical and

    Related Components, Wiley, NewYork, 1943.

    [24] Liang, J.; Elangovan, S; Devotta, J.B.X. "Application of Wavelet

    Transform in Travelling Wave Protection" International Journal of

    Electrical Power and Energy Systems, Vol. 22, 2000, 8, pp. 537-542.

    IX. BIOGRAPHIESAbdelsalam Elhaffar (S03) He received the

    B.Sc. (1989) and M.Sc. degrees in electrical

    engineering (1999) from Garyounis University,

    Libya. His worked as a protection engineer,

    General Electricity Company of Libya, and as a

    assistant lecturer at Engineering faculty, Gar-

    Younis university. Currently, he is working

    towards the Ph.D. degree at Power Systems and

    High Voltage Engineering, Helsinki University of

    Technology (TKK), Finland. His research interests

    are: transmission line fault location, power system protection studies. E-mail:

    [email protected])

    Nagy I. Elkalashy (S06) was born in Quesna,

    Egypt on August 4, 1974. He received the B.Sc.(with first class honors) and M.Sc degrees from the

    Electrical Engineering Department, Faculty of

    Engineering, Shebin El-Kom, Menoufiya University

    in 1997 and 2002, respectively. Currently, he is

    working towards the Ph.D. degree at Power Systems

    and High Voltage Engineering, Helsinki University

    of Technology (TKK), Finland under joint

    supervision with Menoufiya University. His research

    interests are high impedance fault detection, power system transient studies

    including AI, EMTP simulation, and switchgear. (E-mail:

    [email protected]).

    Matti Lehtonen (1959) was with VTT

    Energy, Espoo, Finland from 1987 to 2003, and

    since 1999 has been a professor at the HelsinkiUniversity of Technology, where he is now head

    of Power Systems and High Voltage Engineering.

    He received both his Masters and Licentiate

    degrees in Electrical Engineering from Helsinki

    University of Technology in 1984 and 1989

    respectively and the Doctor of Technology

    degree from Tampere University of Technology

    in 1992. His main activities include power system

    planning, earth fault problems, harmonic related

    issues and applications of information technology in distribution systems and

    distribution energy management. (Helsinki University of Technology, Power

    Systems and High Voltage Engineering, e-mail: [email protected])