42 A Novel Fault-Detection Technique

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 17, NO. 4, OCTOBER 2002

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A Novel Fault-Detection Technique of High-Impedance Arcing Faults in Transmission Lines Using the Wavelet Transform Chul-Hwan Kim, Member, IEEE, Hyun Kim, Young-Hun Ko, Sung-Hyun Byun, Raj K. Aggarwal, Senior Member, IEEE, and Allan T. Johns, Senior Member, IEEE

so in of the fact that apart from threatening the reliability Abstract\u2014This paper describes a novel fault-detect ioview n technique of high-impedance faults (HIFs) in high-voltage trans- of the electric power supply, these faults pose a risk of fires and mission lines using the wavelet transform. Recently, the wavelet endanger life through the possibility of electric shock. transform (WT) has been successfully applied in many fields. The Most conventional fault-detection techniques for HIF mainly technique is based on using the absolute sum value of coefficients involve processing information based on the feature extraction in multiresolution signal decomposition (MSD) based on the discrete wavelet transform (DWT). A fault indicator and fault of post-HIF current and voltage. Several researchers in recent criteria are then used to detect the HIF in the transmission line. years have presented results aimed at detecting HIF more effecIn order to discriminate between HIF and nonfault transient tively. Hitherto, the algorithms developed include the current phenomena, such as capacitor and line switching and arc furnace loads, the concept of duration time (i.e., the transient time period), ratio method [3], the high-frequency method [4], the off-harmonic current method [5], the neural network and Kalman filis presented. On the basis of extensive investigations, optimal mother wavelets for the detection of HIF are chosen. It is shown tering method [1], [6]\u2013[8]. S.J. Huang [9] has proposed an HIF that the technique developed is robust to fault type, fault inception detection technique [10], [11] for distribution systems, which angle, fault resistance, and fault location. The paper demonstrates uses a Morlet wavelet transform approach [12]. However, each a new concept and methodology in HIF in transmission lines. The performance of the proposed technique is tested under a variety of these techniques improves fault detection to a certain extent, but each has its drawbacks as well. Hitherto, a few techniques of fault conditions on a typical 154-kV Korean transmission-line system. (some available as commercial products) have been subjected Index Terms\u2014Fault

to quite extensive testing in order to ascertain their effective-

detection, high-impedance arcing fault, ness under different system and fault conditions. transmission lines, wavelet transform.

It is well known that conventional Fourier transform-based techniques (i.e., those which rely totally on spectrum analysis I. INTRODUCTION of Fourier transform) do not possess the inherent time information associated with fault initiation. The wavelet transform, on IGH-IMPEDANCE faults (HIFs) are, in general, difficult the other hand, is useful in analyzing the transient phenomena to detect through conventional protection such as distance associated with transmission-line faults and/or switching opor overcurrent relays. This is principally due to relay insensiUnlike Fourier analysis, it provides time information, tivity to the very low level fault currents and/or limitationserations. on has the attribute of very effectively realizing nonstationary sigother relay settings imposed by HIFs. This type of fault usually nals comprising of low- and high-frequency components (such occurs when a conductor touches the branches of a tree having a as those commonly encountered in power systems networks) high impedance or when a broken conductor touches the ground. through the use of a variable windows length of a signal [13]. In the case of an overcurrent relay, the low levels of current The advantages (particularly in terms of increased reliability associated with HIF are below the sensitivity settings of the and dependability) of a wavelet transform, which possesses relay. In the case of a distance relay, which relies on an estimation of impedance to fault based on the measured voltagestime and and frequency information unlike the Fourier transform, particularly in the detection of HIFs, are thus apparent, and currents, the accuracy of the estimation (particularly in terms oneby of these techniques is the subject of this paper. It should be of relay overreach/underreach) can be significantly affected the high-impedance fault [1], [2]. HIFs, albeit uncommon,noted must that although wavelet analysis is more complex than other signal-processing techniques, it is ideally suited for dealing nonetheless be accurately detected and removed. This is more with nonstationary signals such as those encountered under HIF arcing faults. This, in turn, enhances accuracy and reliManuscript received April 24, 1999; revised February 14, 2002. Thisability work in fault detection and the features can be applied to was supported by the Korea Ministry of Science and Technology and Korea affecting fault-location techniques [14]. Science and Engineering Foundation. This paper describes a new fault-detection technique which C.-H. Kim, H. Kim, Y.-H. Ko and S.-H. Byun are with the School of Electrical involves capturing the current signals generated in a transmisand Computer Engineering, Sungkyunkwan University, Suwon-city, 440-746, Korea and NPT Center, Korea (e-mail: [email protected]) sion line under HIFs. It is shown that the technique improves the R. K. Aggarwal and A. T. Johns are with the Department of Electronic and performance of HIF detection by employing the absolute sum Electrical Engineering, University of Bath, Bath BA2 7AY, U.K. value based on the DWT. The detection process is performed Digital Object Identifier 10.1109/TPWRD.2002.803780

H

0885-8977/02$17.00 \u00a9 2002 IEEE

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By simple interchange of the variables , , and rearrangement of the DWT (1) gives (2)

Fig. 1.

Korean transmission system (154 kV) studied.

Upon closer observation of this equation, it can be noticed that there is a remarkable similarity to the convolution equation for the finite-impulse-response (FIR) digital filters, therefore (3) where is the impulse response of the FIR filter. By comparing (2) with (3), it is evident that the impulse response of the filter in the DWT equation is (4)

By selecting or ( ) and , the DWT can be implemented by using a multistage and its filter with the mother wavelet as the lowpass filter dual as the highpass filter. Also, downsampling the output of the lowpass filter by a factor of effectively scales the wavelet by a factor of 2 for the next stage, thereby simplifying the process of dilation. The implementation of the DWT with a filter bank is comFig. 2. Typical fault current waveform at relaying point (\u201ca\u201d-earth HIF, fault putationally efficient. The output of the highpass filter gives the at , 10 km, ). detailed version of the high-frequency component of the signal. Also, the low-frequency component is further split to get the through signal decomposition, thresholding of the wavelet other details of the input signal. By using this technique, any transform coefficients, and duration time. Threshold value is wavelet can be implemented [13]. determined by weighting the absolute sum value for one period in a moving window scheme and this forms the basis of a III. FAULT-DETECTION TECHNIQUE USING THE DWT sophisticated decision logic for the limitation of a trip decision. A. Typical Waveforms Through Wavelet Transform Realization The results presented in this paper relate to a typical 154-kV Korean transmission line, the faulted signals of which are Fig. 1 shows a typical 154-kV Korean Transmission System attained using the well known Electromagnetic Transients used in the simulation studies presented herein. It consists Program (EMTP) software. The simulation also includes an of a 26-km line length terminated in two sources of 240 and embodiment of a realistic nonlinear HIF model [15], [16].180 TheMVA at ends P and Q, respectively; the nominal power relay performance is then examined for HIF signals under a frequency is 60 Hz. The simulation of the power system has variety of different system and fault conditions encountered been carried out using the well known EMTP. Within the simin practice. ulation, an emulation of the nonlinear high-impedance arcing V

Z

=

3

0

0

\ue000

faults has also been embodied [16]. Fig. 2 typifies the actual current waveform (measured at end P but which has been scaled down through a CT) and is for an \u201ca\u201d-earth HIF at 10 km fr Analogous to the relationship between continuous Fourier , the distortion observed P and is for a fault near transform (FT) and discrete Fourier transform (DFT), theline-end conin the faulted \u201ca\u201d phase can be directly attributed to the h tinuous wavelet transform (CWT) has a digitally implementable complex and nonlinear characteristics of the HIF arc path. counterpart known as the DWT, and is defined as To aid the development of the fault-detection technique using the DWT, wavelet transform realization has been employed (1) which determines a coefficient of d1 (detail one) using different mother wavelets from an actual current waveform. The where is the mother wavelet, is the input signal, andmother wavelet considered is Daubechies (db)4, biorthogonal the scaling and translation parameters \u201c \u201d and (bior)3.1, \u201c coiflets \u201d (coif)4, are functions and symlets (sym)5. Fig. 3 depicts of integer parameter . The result is geometric scaling (i.e., the coefficient of d1 for different mother wavelets with the ) and translation by . DWT realization. The behavior of the DWT for this actual fault This scaling gives the DWT a logarithmic frequency coverage current waveform is illustrated in Fig. 3(a)\u2014(d) as expected. and this is in marked contrast to the uniform frequency coverage All of the coefficients of d1 increase on fault inception and of, for example, the short-time Fourier transform (STFT) [13]. there are small discernible differences in the DWT outputs II. DISCRETE WAVELET TRANSFORM

KIM et al.: HIGH-IMPEDANCE ARCING FAULTS IN TRANSMISSION LINES USING WAVELET TRANSFORM

Fig. 3.

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Coefficient of d1 under \u201ca\u201d-earth HIF using DWT (a) db4 mother wavelet. (b) sym5 mother wavelet. (c) bior3.1 mother wavelet (d) co

for the four different mother wavelets that are considered. 2) theclassificationabilitybetween thefaultedphaseandthe The performance of the DWT realization was evaluated under healthy phase. different fault types, fault inception angle, and fault location, In order to select the most suitable mother wavelet, the and some of the results will be shown. It should be mentioned maximum sum value (this is over a 1-cycle period at power that due to a limitation of space, only the coefficient associated frequency) of d1 coefficients based on wavelet analysis is with \u201ca\u201d-earth HIF at 10 km is shown. adopted for this work. Consider, for example, the waveforms shown in Fig. 4 which illustrate the maximum sum value of d1 coefficients of the three-phase current signals (as measured at B. Selection of Mother Wavelet for HIF Detection the relaying point) for an \u201ca\u201d-earth HIF at a distance every km from end P in Fig. 1. First of all, considering Fig. 4(a) (this As a second step in fault-detection technique, selection of the is based on the db4 mother wavelet), it is clearly evident that mother wavelet is essential to enhance the performance of HIF the maximum sum value of d1 coefficients is significantly detection technique to extract the useful information rapidly. larger for the faulted \u201ca\u201d-phase than for the two healthy For the technique considered here, this process leads to an acphases \u201cb\u201d and \u201cc.\u201d This is also true when emp curate classification between the faulted phase and the healthy and bior3.1 mother wavelets [as evident from Fig. 4(b) and phase in the first instance, thereby significantly improving the 4(c)], although the levels are somewhat smaller in the case performance and speed of the HIF detection process. As menof the former. However, when employing the coif4 mother tioned in the foregoing section, the mother wavelets considered wavelet, although there is a discernible difference between the are db4, bior3.1, coif4, and sym5. For comparison of the perforlevels attained for the faulted \u201ca\u201d phase and the two health mances attained using different mother wavelets, two conditions phases, in comparison to the previous three mother wavelets are compared as follows. considered, they are significantly lower. Also, equally important 1) a significant magnitude of d1 coefficient for detecting the is that the differences in magnitudes between the faulted and fault; healthy phases in the case of coif4 is much smaller than the

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Fig. 4. Variation in the maximum sum value of d1 coefficients for three-phase current signals (a) db4 mother wavelet (b) sym5 mother wavelet (c) bior3. wavelet (d) coif4 mother wavelet.

corresponding other types of mother wavelets as apparent sample from number that signifies the duration time for which a the graphs shown in Fig. 4, and this is true for all fault positions. transient event (such as HIF) has to persist continuously. This Thus, with regard to the selection of the mother wavelet, the is to discriminate between HIF and nonfault transient events simple criterion adopted herein is based on the magnitudes such of as capacitor and line switching, arc furnace loads, etc. As the summated coefficients d1 and the differences in magnitudes can be seen, when is greater than or equal to FC, the between the faulted and healthy phases. In this respect, after value of FI is incremented and as soon as it attains the level , a series of studies employing the foregoing d1 coefficients this indicates an internal fault and a trip signal is initiated. As distribution approach, the db4 and sym5 are appropriateshown for in Fig. 5, the absolute sum value is based on detection of HIF in transmission line. The db4 mother wavelet summating the d1 coefficients over a 1-cycle period and the is chosen for this study. sampling rate employed is 3840 Hz (i.e., 64 samples/cycle at 60 Hz). The summated values associated the three phases are C. Fault-Detection Algorithm compared with a preset threshold level FC. The whole process is based on a moving window approach where the 1-cycle Fig. 5 shows the fault-detection procedure of the proposed technique, where FI is a counter that signifies the samplewindow is moved continuously by one sample. It is apparent from the foregoing decision logic that the number (and, therefore, the time period) for which useful information through DWT realization under HIF persists. criteria for the protection relay to initiate a trip signal is must stay above the threshold level FC such is the sum value of the detailed output (d1 component) for a that continuously for samples (after fault inception). In this 1-cycle period and is represented as an absolute value, fault respect, an extensive series of studies has revealed that in criterion (FC) is the signal magnitude threshold as the lower that is used to detect the HIF, and is the order to maintain relay stability for external faults (i.e., faults limit of


Fig. 5.

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Block diagram of fault-detection technique.

Fig. 7. Variation in the sum value for “a”-earth HIF at 10 km from end P (a) fault inception angle 90 (b) fault inception angle 0 .

and are 0.085 and 128, respectively. The setting values of these thresholds are dependent on the system environments. Note that the latter corresponds to a two-cycle period at power frequency. IV. SIMULATION RESULTS In this section, some typical results illustrate the performance of the protection technique being developed. It should be noted that although not shown herein, responses/limitations due to CTs, relay hardware (such as current interface module comprising anti-aliasing filters and analog-to-digital converters), etc. have been taken into account in the simulation so that the relay performance attained pertains closely to that expected in reality. Fault Fig. 6. Variation in the sum value for “a”-earth HIF as a functionA. of Single-Phase-Earth fault distance (a) fault inception angle 90 (b) fault inception angle 0 . Fig. 6 depicts the absolute sum value of d1 associated with the

three-phase currents (measured at end P of the system shown behind busbar P and beyond busbar Q in Fig. 1) and also in Fig. 1) using the db4 mother wavelet; the graphs shown in Fig. restrain under no-fault conditions, the optimal settings for6(a) FC and 6(b) are for an “a”-phase-earth HIF, as a function

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Fig. 9. Variation in the sum value for “a”- “b” earth HIF at 10 km from end P (a) fault inception angle 90 (b) fault inception angle 0 .

Fig. 7 shows the behavior of absolute sum value of d1 for one particular fault position (i.e., 10 km from end P, as a funcFig. 8. Variation in the sum value for “a”- “b” earth HIF as a function of fault tion of time, the graphs also depict the moving-window regime distance (a) fault inception angle 90 (b) fault inception angle 0 . adopted). It is apparent that for both fault inception angles considered, the faulted “a” phase stays above the set threshold level of fault distance and are for fault inception anglesand of ( ) for more than two cycles; this corresponds to a , respectively. As expected, the magnitudes of the faulted sample number of approximately 192 and is well above the set “a” phase are much higher than the healthy phases and this is of level . The protective relay will thus initiate a trip true for both fault inception angles considered. Also important, signal. For comparison purposes, the healthy phase currents “b” although the magnitudes reduce in size as the fault moves away and “c” are also shown and, as expected, their magnitudes are from end P, the very significant difference between the faulted . well below the threshold level and healthy phases is retained for an appreciable time period. It should be mentioned that in all HIF cases, the fault impedance B. Double-Phase-Earth Fault has been represented by a realistic nonlinear arc model, but Fig. 8 typifies the variations in the absolute sum values of the for reference purposes only, this can be considered as approxicoefficients d1 for a double-phase-earth HIF fault. The graphs mately equivalent to about 300 .


Fig. 11.

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Coefficient of d1 under arc furnace phenomenon.

depicts the behavior of the “a”-phase absolute sum value for an “a”-earth fault for faults just behind the busbar P and beyond the remote busbar Q. It is apparent that although the levels of the signals are quite high, they are nonetheless , thereby restraining well below the threshold level the relay from asserting a trip decision. This is the case for voltage maximum and voltage minimum faults. Although not shown here, this is also true in the case of double-phase-earth HIF faults. It should be mentioned that when considering the behavior of the aforementioned signals under nonfault transient conditions, such as capacitor and line switching, arc furnace loads, etc. (these signals are not shown in this paper), although the can momenmagnitudes of the absolute sum value . In some cases, tarily exceed the threshold level importantly, an extensive series of studies has revealed that in all cases, the levels are significant for a much shorter period ( 1 cycle) compared to a fault situation. This effectively means that Fig. 10. Variation in the sum value for “a”-earth external faults the (a) decision fault logic as described in Section III-C would inhibit inception angle 90 (b) fault inception angle 0 . relay operation in the case of the former. shown are for two fault inception angles, one near voltage maxD. to Nonfault Transient Events imum of the “a”-phase [Fig. 8(a)] and the other is in relation voltage zero of the “a”-phase [Fig. 8(b)]. Here again, there is Inathe development of any new fault-detection technique, large difference in magnitudes between the faulted phases and such as the type described in this paper, it is important to ensure the healthy phase and, as expected, both of the faulted phases that it is secure under nonfault events such as capacitor and line (“a” and “b” involved in the fault) attain high levels. switching, arc furnace loads, etc. In this respect, it should be When considering the dynamic behavior of the absolute sum noted that for this fault detector, the parameter ‘ ’ (comprising value as a function of time, for one particular fault poof 128 samples) within the decision logic plays a crucial role in sition (which is 10 km from end P in Fig. 1), Fig. 9 portrays charmaintaining the fault detector’s security. acteristics which are very much in line with what is expected The HIF detector presented herein was extensively tested (i.e., both the faulted phases “a” and “b” stay well above theunder set many nonfault transient events. As an example, Fig. 11 ) for an appreciable time after fault inception level depicts the behavior of coefficient d1 (with DWT realization) to and the healthy phase stays well below the threshold throughout arc furnace phenomenon. As can be seen, its magnitude is quite the period of interest. large when the load is switched in but decreases rapidly within a short duration of time thereafter. With regard to the absolute C. Relay Performance Under External Faults sum value of d1, it is apparent from Fig. 12 that although its As mentioned before, it is vitally important for the designed magnitude exceeds the preset threshold level ( ) for protection to be stable under external fault conditions.both Fig.the 10 “b” and “c” phases, this is only momentary, certainly

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[3] R. E. Lee and M. T. Bishop, “Performance testing of the ratio ground relay on a four-wire distribution feeder,” IEEE Trans. Power App. Syst., vol. 102, pp. 2943–2949, Sept. 1983. [4] B. M. Aucoin and B. D. Russell, “Detection of distribution high impedance faults using burst noise signals near 60 Hz,” IEEE Trans. Power Delivery, vol. 2, pp. 342–348, Apr. 1987. [5] D. I. Jeerings and J. R. Linders, “A practical protective relay for downconductor faults,” IEEE Trans. Power Delivery, vol. 6, pp. 565–574, Apr. 1991. [6] A. A. Girgis, W. Chang, and E. B. Makram, “Analysis of high-impedance fault generated signals using a Kalman filtering approach,” IEEE Trans. Power Delivery, vol. 5, pp. 1714–1722, Oct. 1990. [7] S. Ebron, S. L. Lubkeman, and M. White, “A neural network approach to the detection of incipient faults on power distribution feeders,” IEEE Trans. Power Delivery, vol. 5, pp. 905–912, Apr. 1990. [8] E. A. Mohamed and N. D. Rao, “Artificial neural network based fault diagnostic system for electric power distribution feeders,” Elect. Power Syst. Res., vol. 35, no. 1, pp. 1–10, 1995. [9] S. J. Huang and C. T. Hsieh, “High impedance fault detection utilizing a Morlet wavelet transform approach,” IEEE Trans. Power Delivery, vol. 14, pp. 1401–1410, Oct. 1999. [10] A. E. Emanuel and E. M. Gulachenski, “High impedance fault arcing on sandy soil in 15 kV distribution feeders: Contributions to the evaluation Fig. 12. Variation in the sum for arc furnace loads. of the low frequency spectrum,” IEEE Trans. Power Delivery, vol. 5, pp. 676–686, Apr. 1990. [11] D. C. T. Wai and X. Yibin, “A novel technique for high impedance fault identification,” IEEE Trans. Power Delivery, vol. 13, pp. 738–744, July for a much short period than samples, thus ensuring 1998. the stability of the fault detector. [12] O. Chaari, M. Meunier, and F. Brouaye, “Wavelets: A new tool for the resonant grounded power distribution systems relaying,” IEEE Trans. Power Delivery, vol. 11, pp. 1301–1308, July 1996. V. CONCLUSION [13] G. Strang and T. Q. Nguyen, Wavelets and Filter Banks. Cambridge, MA: Wellesley-Cambridge, 1996. This paper has presented a novel technique for transmis-[14] F. H. Magnago and A. Abur, “Fault location using wavelets,” IEEE sion-line fault detection under high-impedance Earth faults Trans. Power Delivery, vol. 13, pp. 1475–1480, Oct. 1998. [15] V. L. Buchholz, M. Nagpal, J. B. Neilson, and W. Zarecki, “High using the discrete wavelet transform for which a near optimal impedance fault detection device tester,” IEEE Trans. Power Delivery, vol. 11, pp. 184–190, Jan. 1996. mother wavelet (suitable for a vast majority of different samples [16] A. T. Johns, R. K. Aggarwal, and Y. H. Song, “Improved techniques for and fault conditions) has been selected after an extensive series modeling fault arcs on faulted EHV transmission systems,” Proc. Inst. of studies. The DWT-based technique presented herein has Elect. Eng. Gener. Transm. Distr., vol. 144, no. 2, pp. 148–154, 1994.

a number of distinct advantages over other traditional HIF detection techniques. For example, it is robust to a variation in different system and Chul-Hwan Kim (M’97) was born in Korea on January 10, 1961. He fault conditions and is predominantly dependent upon thereceived non- the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering from Sungkyunkwan University, Korea, in 1982, 1984, and 1990, respectively. linear behavior of the HIF; it is stable for external faults and has Currently, he is Professor in the School of Electrical and Computer the ability to discriminate clearly between internal faultsEngineering and at Sungkyunkwan University, Korea. He was a Visiting Academic nonfault transient events such as capacitor and line switching, in the University of Bath, U.K., in 1996, 1998, and 1999. In 1990, he became a Full-Time Lecturer at Cheju National University, Cheju, Korea. His arc furnace loads, etc; it has the inherent attribute of distinresearch interests include power system protection, artificial intelligence, the guishing between the faulted phase(s) and healthy phase(s) and modeling/protection of underground cable, and EMTP software. this is a significant advantage for transmission systems in which single-pole tripping is employed, and which therefore requires phase selection. The technique developed is based on current Hyun Kim was born in Korea on October 4, 1972. He received the B.Sc. and signals only and, therefore, requires the use of current transM.Sc. degrees in electrical engineering from Sungkyunkwan University, Korea, in 1997 and 1999, respectively. formers (CTs) only. Currently, he is involved with condition monitoring in a nuclear power plant Work is now in progress to extend the research for at Woori Technology, Inc., where he has been since March 1999. ultra-high–voltage transmission systems comprising of long lines and for fault detection/fault location in low-voltage distribution lines. The outcome of the research will be reported Young-Hun Ko was born in Korea on July 7, 1975. He received the B.Sc. and in due course. M.Sc. degrees in electrical engineering from Sungkyunkwan University, Korea, REFERENCES

in 1998 and 2000, respectively. Currently, he is a Researcher of product R&D center in Daewoo Telecom.

[1] A. F. Sultan, G. W. Swift, and D. J. Fedirchuk, “Detection of high Byun was born in Korea on February 11, 1973. He received the impedance arcing faults using a multi-layer perceptron,” IEEESung-Hyun Trans. Power Delivery, vol. 7, pp. 1871–1877, Oct. 1992. B.Sc. and M.Sc. degrees in electrical engineering from Sungkyunkwan Univer[2] B. D. Russel, C. L. Benner, and A. V. Mamishev, “Analysis of high sity, Korea, in 1996 and 1998, respectively. Currently, he works in power system protection and control at the Korea impedance fault using fractal techniques,” IEEE Trans. Power Syst., vol. 11, pp. 435–440, Feb. 1996. Power Exchange (KPX), Seoul.


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Raj Aggarwal (SM’91) received the B.Sc. and Ph.D degrees in electrical engiAllan T. Johns (SM’88) received the B.Sc. and Ph.D. degrees from the Univer-

neering from the University of Liverpool, U.K., in 1970 and 1973, respectively. sity of Bath, U.K. In 1982, he was awarded the degree of D.Sc. for an original and substantial contribution to knowledge of electrical engineering. Currently, he is a Professor and Head of the Power and Energy Systems Group Currently, he is Emeritus Professor in the Electrical Engineering Department at the University of Bath, U.K. His main areas of research interests are power system modeling and the application of digital techniques and artificial at intellithe University of Bath, U.K. Dr. Johns is is a fellow of the IEE U.K. gence, protection and control, and power quality issues. Dr. Aggarwal is a fellow of the IEE U.K.

42 A Novel Fault-Detection Technique

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