paths (ground wire, towers, and substation grounding electrodes) of the ground fault current to its sources (the power system). The algorithm takes into account ...
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 4, OCTOBER 2003
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A Digital Fault-Location Algorithm Taking Into Account the Imaginary Part of the Grounding Impedance at the Fault Place Ljubivoje M. Popovic´, Senior Member, IEEE
Abstract—The paper presents a new digital fault location algorithm developed for the determination of the location of the transmission line faults. The calculations for the estimation of the fault location are performed using one-terminal voltage and current data of the transmission line. The development of the algorithm is based on the detailed consideration of all the return paths (ground wire, towers, and substation grounding electrodes) of the ground fault current to its sources (the power system). The algorithm takes into account all of the factors important for the accuracy of the estimation (i.e., fault impedance, fault current component supplied from the opposite end of the line, and the prefault current). Also, the imaginary part of the fault impedance is not ignored as is the case with the previously published methods. The proposed algorithm was tested using simulated current data. Sample test results are also included. Index Terms—Fault impedance, fault location, transmission line.
I. INTRODUCTION
A
N increased-accuracy estimation of the location of faults occurring on transmission lines is of a great importance for fast repair and reinforcement of damaged and weak points in each power system as a whole. It gives us as a final result a more cost-effective maintenance and exploitation of the power system. However, a problem is that in practice it is often not possible to provide all of the data necessary for exact determination of the fault location. Most of the relevant data about the fault are available only at the transmission line terminals. Thus, some important data (e.g., the value of the fault impedance) that would enable simple and correct detection of the fault place remains unknown. Because of these practical limitations, the development of fault locators has a long history and a number of location methods (algorithms) have already been proposed and utilized. Especially in the last several years, many digital fault location algorithms have been presented. According to the data on which they are based, the digital fault location algorithms can be classified in two categories. The first category is founded on the data from only one terminal of a transmission line [1]–[3], while the second one includes the data measured at the other terminal of the line. However, two-terminal data are not widely available (it is necessary to provide long-distance data transfer).
Manuscript received April 26, 2002; revised July 9, 2002. The author is with the JP “Elektroprivreda Srbije,” Belgrade 11000, Yugoslavia. Digital Object Identifier 10.1109/TPWRD.2003.817800
The methods described in [1] and [2] are based on the use of the voltage and current data measured at a single terminal of the transmission line. These methods are developed for the transmission lines with power sources at both terminals (fault current is supplied from both terminals). In these cases, the problem is that the part of the fault current flowing from the opposite line end is unknown quantity, but contributes to the fault current through the fault place. This current influences the measured quantities (voltage and current), and thus, instead of the real, an apparent impedance is measured. Takagi et al. [1] and Eriksson et al. [2] each in a different way manage to solve this problem, but not without certain approximations. The approximation in [1] is that the currents from both of the terminals have the same phase difference for any power system configuration. This approximation is overcome in [2] by means of the impedance on the opposite-side power source. However, it is difficult to acquire the accurate value of the power source impedance, because it varies depending on the configuration of the power network connected to the line. Besides that, both of the methods were developed with an assumption that the fault impedance is purely resistive. It may be said that both of these methods compensate the mentioned lack of necessary data, but either not completely, or not without approximations. This paper is a logical continuation of the former publications [6], [7] and belongs to the methods that calculate the distance to the fault place by using fundamental frequency voltage and current from one terminal of the transmission line. The proposed algorithm is focused on a single phase-to-ground fault, a type of fault that occupies about 90% of all of the transmission line faults (e.g., [9]). Finally, the proposed algorithm significantly compensates the deficiency of the data on the relevant factors—the fault impedance and the fault current coming from the opposite line end. This is done by analyzing the ground fault current return paths and by using the fact that the ratio between the real and the imaginary part of the fault impedance varies along the whole line length in a very narrow range of values. The influence of the ratio between the total fault current and the fault current measured at one of the line ends is also separately considered. II. BASIC PROBLEM Let us assume that we have two parts of a power system with directly grounded neutral points and connected by a single circuit line. For a single phase-to-ground fault occurring anywhere along the line, the electrical circuits established during the fault may be schematically presented as in Fig. 1.
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Fig. 1. Faulted power system.
On the basis of the quantities measurable on the left line terminal (voltage and current ), it is necessary to determine the fault point or in other words to find out the distance to the fault point ( ). If we assume for a moment that the fault impedance is negligible, the line impedance to the fault point will be very easy to determine. As this impedance is proportional to the distance , the determination of the fault position will be also easy. However, under practical conditions, the fault impedance is not negligible and represents a very complex function of the distance to the fault location [7], [8]. As a consequence of this fact, at the fault place a potential appears with a value proportional to the ) for a certain value of the impedance total fault current ( . Since the fault current from the opposite end of the line contributes to the creation of this potential, the microprocessor-based relay DFL sees an apparent impedance that is somewhat larger ). This increase introduces a than the real impedance ( deviation in the measurement data ( and ) that we will use for the fault distance determination. The deviation is more pronounced when the relative share of the current in the total fault current is larger. The prefault (load) current has a similar influence on the measured quantities. This current is not separately presented in the given circuit, but it is clear that this current represents the difference between the current through the faulted phase conductor and the current through the fault place . The above discussion can be summarized into the following. For a more accurate estimation of the fault location, it is necessary to eliminate the influence of the unknown (not available by measurement) quantities on the data obtained by measurement. This certainly means that our investigation should be focused on the unknown but relevant factors. In the circuit shown represents only one part of the in Fig. 1, the fault impedance loop impedance measured at the relay location, or in the local station. However, in practice, this is an equivalent impedance of a very complex and spontaneously formed electrical circuit. Because of that, it is certain that more information about the fault impedance can be obtained only through a detailed investigation of this circuit. During a ground fault, a transmission line represents a very complicated electrical circuit with a large number of conductively and inductively coupled elements. Towers of transmission lines are grounded through the footing electrodes and mutually connected by a ground wire(s). At the place of the faulted tower, the ground fault current leaves the phase conductor. Its flow to the feeding sources continues through many different paths. Due to inductive coupling between the phase conductors and the ground wire(s), a part of this current circulates exclusively through metal paths (in the line, through the ground
Fig. 2.
Three-phase transmission line with a ground fault.
wire(s) and in the station, through the grounding connections.) The remaining part of the fault current returns conductively to the power system, through the earth via ground wire(s), through a large number of towers and through the grounding grid of all substations with grounded neutral point(s).
III. APPARENT IMPEDANCE FOR THE RETURN PATHS GROUND-FAULT CURRENT
OF
We will start our consideration by assuming that the substations at the line terminals are the only substations with grounded neutral point(s) in the whole power system. This means that returns to the power system the total ground fault current only through the grounded neutral point(s) of these substations (A and B in Fig. 2). The real physical model of the transmission line under the conditions of a ground fault at an arbitrary tower is schematically presented in Fig. 2. The notation used in this circuit has the following meaning: part of the current flowing left (right) from the fault place; impedance of the grounding system of the substation A (B) which does not include the grounding effects of the ground wire(s) of the line under consideration; self impedance of the ground wire(s), per span; mutual impedance between the ground wire(s) and the faulted phase conductor, per span; average tower footing resistance; number of spans to the fault location, counted from the substation A; overall number of spans; remote ground. By forming the presented transmission line model, the following approximations and idealizations of the real physical model were used. • phase and ground wire(s) impedances and their mutual impedances are identical to the values calculated on the basis of infinite transmission lines; • towers footing resistances are mutually equal and any mutual interference to their own ground current is neglected; • impedances of the ground wire(s) between the two towers are mutually equal. and can be either calculated by using The impedances formulae based on Carson’s theory of the ground fault current return path (e.g., [6]) or measured.
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Fig. 5. Auxiliary equivalent circuit.
Fig. 3.
The parameter is the current distribution factor at any node, assuming that the number of the nodes is infinite. This parameter is determined by
Return paths of ground fault current.
(5) represents the input impedance of the The impedance uniform ladder circuit with an infinite number of nodes. This impedance is given by (6) Fig. 4.
All-conductive couplings on the ground-fault current return paths.
In order to simplify the problem, we will consider only the elements representing the ground fault current return paths, as shown in Fig. 3. In this circuit, the influence of the inductive coupling between the ground wire and the phase conductors is separately presented (e.g., [6]). The induced current and the corresponding so-called reduction factor of the line are determined by (1) (2)
However, in our case, the problem is such that it cannot be solved by direct application of these equations. Before that, the real electrical circuit shown in the previous figure should be modified. By using the superposition principle, the equivalent circuit shown in Fig. 3 can be substituted (with regards to the potentials ) by the equivalent circuit appearing in the points presented in Fig. 5. represents the grounding impedance of The impedance the transmission line ground wire(s) seen from the point toward the station B. Its value depends on the fault place. In pracon the value tical conditions, the influence of the impedance is so small that it can be neglected ( of the impedance ). On the basis of this approximation and by using (4), we get
(3) Since a transmission line is usually transposed, the value of the reduction factor varies from tower to tower. These variations are limited between the values corresponding to the closest and the farthest position of phase conductor with respect to the ground wire(s). Since we are interested only in the potential differences between the points and 0 (or and ), the equivalent circuit represented in Fig. 3 can be reduced to the circuit presented in Fig. 4. Looking from the fault point F, we discern two uniform lumped-parameter ladder circuits with a finite number of elements. In the general case, the voltage and the current at the input end ( and ) and the voltage and the current at the output end ( and ) according to [6] are related by
(7) After the described modification, we have a circuit convenient for the application of the general equations of the uniform ladder circuit. According to the equivalent circuit in Fig. 5, the potential in is given by the point 0 created only by the current source (8) On the basis of (8) and the (4), the potential at the point created by the current sources is given by (9) or, with certain approximations
(4)
(10)
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By using an analogous procedure, the potential at the point created by the current sources is given by (11) represents the grounding impedance where the impedance of the transmission line ground wire at the fault place. Using (8) and , this impedance is given and assuming that by
(12) is defined by using the general When the potential equations of uniform ladder circuit (4), the potential can be expressed as
narrow range of values [6] and can be determined by precalculation, or by premeasurement. When the line is untransposed, this factor has the same value along the whole line length, but different for each of the phase conductors because of their different space positions in relation to the ground wire. The variations of the effective value of the impedance along the line length are considered in [7] and [8], while in this paper, a quantitative analysis of the real and the imaginary part of this impedance is performed. On the basis of these considerations, the imaginary part is not negligible in comparison to the real part (contrary to the assumption used in the previously published algorithms, for example, in [1]–[3], [5]). As a conclusion it can be said that the potential at the fault (Fig. 1) depends on the factors , , and . Their place values depend on the fault place and cannot be determined if the fault place is an unknown quantity.
(13) IV. ALGORITHM DERIVATION By using the superposition principle, the real potentials at the points 0 and are determined by (14) (15) Finally, we can express the voltage drop on the ground-fault current return paths as (16) In practical conditions, the relations between the considered and ) that potenquantities are such ( , and can be disregarded. Thus, tials we can write (17) At the same time, it means that instead of the impedance of all of the ground fault current return paths, it is sufficient to (or ). consider only impedance When we have the expression (17), the apparent impedance for the ground fault current return paths according to Fig. 2 is given by (18) where (19) The coefficient represents a complex number with an imaginary part that can be disregarded in many practical situations. Its value along the line length varies in a very wide range of realistically possible values. On the basis of (19), it is interesting (load current) to note that the effects of the currents and (from A to B, or opdepend on the direction of the current posite) and accordingly may cancel or supplement each other. The current represents the measured component of the fault current, but includes the load current as well. Many of the quantitative analyses already performed show that the reduction factor represents a complex number with a negligible imaginary part. Its value varies along the line in a very
According to the circuit shown in Fig. 1, the measured voltage is the sum of the voltage drop in the line to the fault point and the fault point potential . By dividing the measured voltage with the measured current , according to (18), we obtain (20) The notation used in the above equation has the following meaning. impedance determined on the basis of the measured and ( ); quantities relative distance to the faulted tower expressed in the relation to the total line length; line impedance determined [in accordance to (e.g., [7]) by the following expression]: (21) The notation in (21) has the following meaning: positive-sequence impedance for the total line length; zero-sequence impedance for the total line length. and represent the parameters of the The impedances line that can be obtained by measurement in the moment immediately before putting the line in operation. Thus, it can be said that the impedance is an a priori known quantity. However, is often afthe value of the imaginary part of the impedance fected by the changeable soil resistivity along the line and it can be different for different sections of the same line. Because of that, in practical situations, this impedance can be only approximately taken as a linear function of the line length. By separating the complex (20) into its real and imaginary part, we obtain the following two equations: (22) (23) By dividing (22) with the real part of the impedance and (23) with the imaginary part of the same impedance ( ), we obtain (24)
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(25) and represent rough esIn this system of equations, timates of the fault distance obtained by using the known and and by ignoring the fault impedance ( ). The estimates based on the real and on the imaginary part are mu) since according to the quantitative tually different ( analysis [e.g., [7] the real and the imaginary parts of the impedin general case are not mutually proportional ances and )]. ( The only exception is the case of a fault at the end of the is negligible ( line, because only then the impedance ). Also, because the ratio between and changes from tower to tower, it is realistic to assume that the in a general case proportion does not exist. is unknown and The product of the quantities , , and each of these quantities seen separately is unknown. However, the real and the imaginary part of this product are mutually connected by
(a)
(26) where (27) phase angle of the line reduction factor ; phase angle of the coefficient , separately considered in Part VI; phase angle of the impedance , separately considered in Part V (may be obtained by measurement). The relations (24), (25), and (26) form a closed system of equations that enables the estimation of the desired distance . It is determined by the following expression: (28) The effects of numerous line and system parameters considered in Part III, including the arc resistance [5], are expressed only through , , and . Regarding the identification of this fault type, it is important to mention the following. When a ground fault occurs, the transmission line zero-sequence voltage and current can be picked up at the monitoring point. They will not appear in the power system when a nonground fault (phase-to-phase or three-phase) occurs. Therefore, a fault is regarded as nonground if the signal of zero-sequence voltage does not appear at the monitoring point when a fault occurs. Expressed in another way: if the condition is satisfied for a one phase conductor, we have a single phase-to-ground fault on the line. If this condition is simultaneously satisfied for two phase conductors, we have a double phase-to-ground fault on the line. V. QUANTITATIVE ANALYSIS OF THE PARTS OF FAULT IMPEDANCE In the aim to get a general impression about the relationship between the real and the imaginary part of the fault impedance
(b) Fig. 6. Ratio R =X as a function of the fault place along the line with a steel g. wire. a) short line; b) long line.
, we will consider 110-kV transmission lines of different lengths and equipped with ground wire, in one case steel and in the other ACSR 95/55 . Assuming that 50 the average span length is 250 m, the value of the ground wire self-impedance is ; • in the first case, . • in the second case, Also, we will assume that we have line cases with different towers footing resistance (10, 20, 40, and 80 ). On the basis of the given data and the expression (12), the results obtained are presented in [6]and for the absolute values of impedance [7], while the results obtained for the values of the ratio between and are presented here, in Figs. 6 and 7. On the basis of the given results, it is interesting to note the and is practically not sensifollowing. The ratio between tive to the variations in the value of the towers footing resistance. This is a very important observation for practical applications of the given algorithm since in the practical conditions, the value of the towers footing resistance may vary in a relatively wide range, depending on the year season, the kind of the soil, and the aging of the material in the soil. Also, it is important to note that the imaginary part of the fault impedance is not negligible in comparison with the real part, especially in the case of an
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(a)
(b) Fig. 7. Ratio R =X as a function of the fault place along the line with an ACSR g. wire. a) short line; b) long line.
ACSR ground wire. This certainly puts in question the approximation used in the earlier methods [1]–[3], [5] that are based on . the assumption Some earlier quantitative analyzes (e.g., [10]) have showed that the mutual differences in the values of the towers footing resistances or the span lengths along the line encountered in practice have no significant influence on the effective value of the impedance . Based on the results presented here (Figs. 6 and 7), it is possible to conclude that these differences, even if they are extremely large, have only a negligible influence on the value of the angle . Owing to this fact, we can treat the as an a priori known quantity that is constant along the angle whole line length. We can obtain its value for a particular line by performing a measurement at only one tower that is located approximately in the middle of the short line (shorter than the double active line length [6]). For long lines, this tower can be freely chosen among all towers whose distance from each of the two line terminals is larger than one active line length [6]. This certainly does not exclude a more detailed consideration in any particular case if deemed necessary (e.g., large differences in the values of towers footing resistances along the line). Because of the so-called “end effects” (Figs. 6 and 7) exas well as in the case of pressed in the case of the angle the effective value of the impedance [6], in this way we do a relatively rough approximation. However, the influence of this
Fig. 8. Variation of the angle ' along a 5-km line.
Fig. 9. Variation of the angle ' along a 50-km line.
approximation on the accuracy of the algorithm (28) is small because of the fact that when approaching to a line end the efand with it the difference between and fective value of (28) becomes smaller and smaller. Thus, it can be said that the effects of variations of the effective value and the phase angle almost completely cancel each other and of the impedance practically have not any influence on the accuracy of (28). VI. QUANTITATIVE ANALYSIS OF THE PHASE ANGLE OF COEFFICIENT In accordance to (27) and (28), one more parameter should be considered along the whole line length. The results of the calculations based on the data given in Section VII for the case are shown in Figs. 8 and 9. It of steel g. wire and is should be said about the adopted value of that the angle practically independent on the value of if this value is within the range of practically possible values. obtained under the Dashed lines denote the phase angle assumption that the measurements are performed in the substation B as well. For a better insight, the lines are divided into two sections. One of them satisfies the condition and the other satisfies . According to (19), the same and , conditions may also be expressed as respectively. It can be seen from the presented figures that the value of varies in very narrow limits along the line that satisfies the
POPOVIC´: A DIGITAL FAULT-LOCATION ALGORITHM TAKING INTO ACCOUNT THE IMAGINARY PART OF THE GROUNDING IMPEDANCE
condition . For the 5-km line, these limits are approx, while for the 50 km line they are 0.4 imately 1.5 and and . However, at the other section, where , its absolute value rapidly increases when approaching to the station B. According to the given diagrams, the absolute values of are significantly smaller on this section. the angle For the same terminal conditions, the length of the section satis longer if the line is isfying the mentioned condition longer. Also, this section is longer if the belonging network (A) is stronger in comparison to the network at the opposite line end (B). However, to determine this section, it is obviously necessary to measure and record the data at both of the line ends. This is why the following question arises: are there in practice the lines for which we a priori know that the condition is satisfied always and on the whole length? Such lines exist in power systems and they are the so-called radial lines, serving as a connection between the transmission and the distribution networks. According to the previous analysis for this type of line, can be disregarded so that instead of (27) we can the angle use the following approximation:
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TABLE I SHORT LINE WITH STEEL GROUND WIRE
TABLE II LONG LINE WITH STEEL GROUND WIRE
(29) Based on the given quantitative analysis, we determine the can be treated as an a priori conditions under which the angle known quantity (19). These conditions simultaneously define the scope of the application of the developed algorithm. Because of the certain approximations when determining the and due to the inaccuracy of measurements, the distance cannot be exactly determined. Thus, the faulted tower should be found among the towers that are nearest to the fault place determined by expression (28). VII. TESTING ALGORITHM The new algorithm for single phase-to ground faults was tested using computer simulations. The faults were simulated in a 110-kV network as shown in Fig. 1. The results of the numerical simulations are used as inputs for the calculation algorithm presented here. Afterwards, the outputs of the algorithms were compared. The network parameters for Fig. 1 are , , ; • network A: , , . • network B: Line data , • phase conductor: ; • total line length: 5 km and 50 km; • average span length: 250 m. a) Steel ground wire • self-impedance of steel ground wire: ; • reduction factor of the steel ground wire: . b) ACSR ground wire • self-impedance of ACSR ground wire: ; • reduction factor of the ACSR ground wire: .
For the given data and for various cases regarding the type of the ground wire, line length, towers footing resistance, and different distances of the simulated ground fault, the results of calculations are presented in Tables I–IV. represents the relative distance of the In the given tables, simulated fault. In all of the considered cases, the high accuracy (the faulted tower is most often one of the two nearest) is obtained for the . A cerfaults at the sections satisfying the condition tain inaccuracy appears for the faults on the distant sections, . If all other relevant parameters retain the when same values, this inaccuracy caused by the approximation (29) is larger if the line is longer. For the faults on the section where is not satisfied (or when ), the condition more accurate results are obtained by using data available at the opposite line end (B). It is easy to show that the accuracy is higher for the same line lengths if the network A is stronger (or the network B weaker) than in the considered numerical example. When the network A is significantly stronger than the network B, the accuracy is . almost equal to the one on the section satisfying is satisfied for a fault anywhere If the condition along the line, the locator has a high accuracy [not demonstrated in earlier publications (e.g., [1] and [2])] along the whole line length. This condition is satisfied in the case of the radial lines serving as a connection between the transmission and the distribution networks. Here, the station A represents a source station and the load current has always the same direction (from A
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TABLE III SHORT LINE WITH ACSR GROUND WIRE
mission line, connecting the transmission and the distribution networks. With a somewhat lower accuracy, the algorithm can be used for the lines connecting a strong and a weak network. The algorithm is based on one-terminal data. The main advantages of the algorithm in comparison to the previously published methods are achieved by taking into account the imaginary part of the ground fault impedance at the fault place. REFERENCES
TABLE IV LONG LINE WITH ACSR GROUND WIRE
to B) reducing the value of the angle and increasing the accuracy of the algorithm. According to this, the value of this current is not necessary. Because of that, the presented algorithm is mainly dedicated to this kind of line. is not satisfied on In the cases when the condition the whole line length (in the considered examples, from to B and from to B for the short and the long lines, respectively), a higher accuracy can be achieved by the two here described locators placed at the both line ends and exchanging the data about the effective value of the fault currents measured and ). This is another techat the two different line ends ( nical solution and merits a special consideration and a separate paper.
[1] T. Takagi, Y. Yamakoshi, M. Yamaura, R. Kondov, and T. Matsushima, “Development of a new type fault locator using one-terminal voltage and current data,” IEEE Trans. Power App. Syst., vol. PAS-101, pp. 2892–2898, Aug. 1982. [2] L. Eriksson, M. M. Saha, and G. D. Rockefeller, “An accurate fault locator with compensation for apparent reactance in the fault resistance resulting from remote-end infeed,” IEEE Trans. Power App. Syst., vol. PAS-104, pp. 424–436, Feb. 1985. [3] K. Srinivasan and A. St-Jacques, “A new fault location algorithm for radial transmission lines with loads,” IEEE Trans. Power Delivery, vol. 4, pp. 1676–1682, July 1989. [4] W. Peterson, D. Novosel, D. Hort, T. W. Cease, and J. Schneider, “Tapping IED data to find transmission faults,” IEEE Comput. Appl. Power, vol. 12, pp. 36–42, Apr. 1999. [5] Z. M. Radojevic´, V. V. Terzija, and M. B. Djuric´, “Numerical algorithm for overhead lines arcing faults detection and distance and directional protection,” IEEE. Trans. Power Delivery, vol. 15, pp. 31–37, Jan. 2000. [6] L. M. Popovic´, “Practical method for evaluating ground fault current distribution in station, towers and ground wire,” IEEE Trans. Power Delivery, vol. 13, pp. 123–128, Jan. 1998. [7] L. M. Popovic´ and Z. M. Radojevic´, “Digital fault-location algorithm including grounding impedance at fault place,” Proc. Inst. Elect. Eng.–Gen. Transm. Dist., vol. 148, no. 4, pp. 291–295, July 2001. [8] L. M. Popovic´, “Analytical expression for voltage drops on return paths of ground-fault current when faults occur in transmission line,” in Proc. IEEE Power Eng. Soc. Summer Meeting, June 15–19, 2001, Paper #01SM046. [9] T. Funamashi, H. Otoguro, Y. Mizuma, L. Dube, M. Kizilicay, and A. Ametani, “Influence of fault arc characteristics on the accuracy of digital fault locators,” IEEE Trans. Power Delivery, vol. 2, pp. 195–199, Apr. 2001. [10] L. M. Popovic´, “The effect of partial compensation of the unfavorable influence of increased soil resistivity in long earthing conductors,” in Proc. CIGRÉ Symp., Brussels, Belgium, June 1985.
Ljubivoje M. Popovic´ (SM’91) was born in Markovac, Serbia, Yugoslavia, on February 24, 1944. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Belgrade, Yugoslavia, in 1969, 1983, and 1991, respectively. He has been a leading research engineer in the field of grounding problems and short circuit currents for the last 20 years. He has worked on the design of different power system installations in “Elektrodistribu-
VIII. CONCLUSIONS The paper presents a novel and highly accurate fault location algorithm for the single phase-to-ground faults on a trans-
cija – Beograd.”
