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A Simple Method for Evaluating Ground-Fault Current Transfer at the Transition Station of a Combined Overhead-Cable Line Stefano Mangione, Member, IEEE
Abstract—When a substation is fed by a combined overheadcable transmission line, a significant part of the ground fault current flows through cable sheaths and is discharged into the soil at the transition station where cables are connected to the overhead line. Such a phenomenon, known as “fault application transfer,” may result in high ground potentials at the transition station which may cause shocks and equipment damage. The scope of this paper is to present new analytic formulas which can be used for the direct calculation of the fault current transferred at the transition station and its ground potential rise as well as the substation earth current. The proposed formulas allow evaluating the influence of the main factors to the fault application transfer phenomenon and can be employed, at the preliminary design stage, to easily assess the most appropriate safety conditions to avoid dangerous effects. Index Terms—Fault application transfer, ground fault current distribution, grounding, safety conditions.
I. INTRODUCTION HEN a ground fault occurs at a substation, the fault current returns back to the supply station, in part, discharging into the soil from the substation grounding system, in part through different metallic return paths either directly or through other auxiliary ground electrodes [1]. The amount of the fault current diverted away from the substation ground grid depends primarily from the conductively and inductively coupled parameters of the various possible paths. In practice, a significant part of the fault current is diverted away from the substation grounding system by overhead ground wires or cable sheaths of feeding transmission lines, mutually coupled with the faulted phase conductor; while a smaller quantity is carried out by neutrals or other return paths of outgoing lines, which provide only a ground impedance in parallel with the substation ground grid [2]–[4]. In particular, if the substation is fed by a cable transmission line, a very large percentage of the fault current (up to 95% for cable line consisting of three single core cables) returns directly to the remote source via the cable sheaths, because of their strong inductive coupling with phase conductors [5]. Instead, in case of a substation fed by an overhead line, the return current flowing trough the ground wire, weakly inductively coupled with phase conductors, varies from 5–30% of the total fault current in dependence from
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Manuscript received November 7, 2006. Paper no. TPWRD-00686-2005. The author is with the Department of Electrical, Electronic and Telecommunication Engineering, Università degli Studi di Palermo, Palermo 90128, Italy (e-mail:
[email protected]). Digital Object Identifier 10.1109/TPWRD.2007.915895
number, size, material, and spacing from phase conductors of the ground wire and from towers’ footing resistance. When the substation is fed by a combined overhead-cable transmission line, a significant part of the ground fault current flows through the grounded cable sheaths and discharges into the soil at the transition station (TS), where cables are connected to the overhead line. This is due to the difference in coupling factors for cable and overhead lines, so that only a small portion of the return current carried by cable sheaths continues toward the remote source through the overhead ground wire; instead, a large portion of such current flows into the soil surrounding the TS ground electrode and continues toward the source through the earth. This phenomenon has been presented in literature for the first time and is called “fault application transfer” by Sobral et al. [6], referring to an actual transition station and to the shocks and equipment damages that have occurred there, as a consequence of high ground potentials caused by a fault to ground occurring at the receiving end substation. The phenomenon of the fault application transfer does not have any relation to the well-known potential transfer effect and it has not been yet extensively dealt with in literature. Reference [7] reports the results of a measurement campaign of the ground fault current distribution during a fault at a substation fed by a multicombined overhead-cable transmission line. As expected, measurements have shown that more than 25% of the fault current flows between each transition station’s ground electrode and the surrounding soil, yielding dangerous voltages which exceed allowable safety limits. In [8], the effects of the fault application transfer have been usefully utilized to design the substation ground grid in a dense urban area, as a suitable technical control of the substation ground potential rise (GPR), in order to ensure safety conditions, avoiding difficulties in grounding measurements. Two additional bare copper bonding wires, tied to the cable sheaths, have also been considered in the final design to better achieve the fixed objective. From the aforementioned, it is clear that the fault application transfer effects must be properly taken into account at the design stage of substations fed by a combined overhead-cable line, both for a more efficient and economic design of a substation grounding system as well as for safety concerns at the transition stations. Moreover, it should be considered that problems concerning ground fault transfer effects are expected to grow further in the future for a number of reasons: • the use of underground transmission cables in modern HV installations continuously increases due to technical and
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environmental reasons, so that combined overhead-cable transmission lines are becoming more frequent in current applications (e.g., to supply newly built substations in dense urban or suburban areas from a nearby existing overhead line); • an overhead-to-underground transition station occupies a very small area compared to a conventional substation and, in some cases, it consists simply of a dead-end steel pole structure (transition pole); then, its ground electrode, of relatively small size and high resistance, could be inadequate to maintain the GPR within safety limits in case of a fault application transfer, also considering the ever-increasing values of fault currents; • the practice of using additional bare copper bonding wires connected to cables sheath, although not strictly necessary for safety conditions at the receiving end substation, may magnify fault application transfer effects at the transition structure in case of a combined overhead-cable feeding line; • optical fibers for telecommunication systems are even more frequently located inside ground wires on high-voltage overhead transmission lines. The effects of fault application transfer on GPR at the transition structure and the closest towers, can expose workers to unsafe conditions during maintenance operations of optical ground wires on towers where the equipment boxes are located. Different methods for evaluating ground fault current distribution, in stations supplied by nonuniform lines or overhead lines combined with cables, have been presented in the literature [9]–[11]. Nevertheless, these methods and their applications focus on evaluating the earth current and the related GPR only at the faulted substation and not also at the transition station. In this paper, a simple but accurate method is presented to calculate, beside the substation earth current, the portion of the fault current transferred to the transition station during a fault to ground at a remote substation fed by a combined overhead-cable line. The method utilizes a compact equivalent model of a combined overhead-cable line, which takes into account all of the relevant parameters and uses simple equations derived from the application of Kirchhoff’s laws. Numerical applications show the efficiency of the proposed method and reveal the main factors influencing the fault application transfer phenomenon.
Fig. 1. Ground fault at a substation fed by a combined overhead-cable line.
current flowing in the cable sheaths discharges into the soil from the transition structure ground electrode ( ), returning to the supply source through the earth rather than through the overhead ground wire. In other words, the ground wire of the overhead line section acts as a “bottleneck” for the return current carried by the cable sheaths. At the design stage of the substation grounding system, the is the basis to make knowledge of the proper earth currents a safe and economically convenient grounding grid. Moreover, it should be of prime importance to also evaluate the amount of the fault current transferred to the transition structure , in order to make sure that local dangerous voltages do not exceed safety limits, thus preventing shock hazards due to fault application transfer effects. In the following, we assume that the total ground fault current at the substation is known from prior system studies. With reference to the notation used in the scheme of Fig. 1, the following relationships hold: (1) (2) In order to evaluate the return currents through the cable sheath and the overhead ground wire , it is necessary to properly model both the overhead and the cable line sections, taking into account all of the conductively and inductively coupled elements of the two sections as well as the proper boundary conditions. III. EQUIVALENT CIRCUITS
II. PROBLEM FORMULATION Consider a combined overhead-cable transmission line with the ground wire and cable sheaths grounded at both ends of each section, as schematically depicted in Fig. 1. In case of a phase-to-ground fault at the receiving end substation, the total fault current is, in part, injected into the soil through the local grounding grid ; in part, it returns to the remote source, first through the cable sheath ( ) and then through the overhead ground wire ( ) as the result of both galvanic connection and inductive coupling with the faulted conductor. Nevertheless, due to the difference in coupling and conductive factors for cable and overhead-line ground return paths, part of the fault
In this section, the equivalent circuits of both the overhead and cable line sections are first defined separately and then combined together to represent the whole system of Fig. 1. A. Cable Line Consider the cable line consisting of three coated single-core cables, regularly transposed with the metallic sheaths cross-bonded along the path and grounded only at both ends. In case of a ground fault at the supplied station, it can be assumed that the return current in Fig. 1 is divided equally between the three sheaths circuit flowing toward the remote source. This is undoubtedly true with the cables in trefoil formation, but it
MANGIONE: SIMPLE METHOD FOR EVALUATING GROUND-FAULT CURRENT TRANSFER
can be assumed to do so with little error also when the cables are laid flat [12]. Under such assumption, the cable line section in Fig. 1 can be represented by the single-line equivalent circuit depicted in Fig. 2, derived after some mathematical manipulations is the self of the equations system given in [13]; where impedance of cable sheaths, all operating in parallel with the models the common ground return, and the voltage source electromotive force’s (emf’s) induction upon the cable sheaths by the fault current flowing through the phase conductor, due to inductive coupling. The following relationships hold:
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Fig. 2. Equivalent circuit of a cable line during a ground fault.
(3) with being the mutual impedance between the cable sheaths and the phase conductors with common ground return. and can be evaluated by means Both the impedances of Carson’s theory [14], once the soil resistivity and cable sheaths characteristics are assigned (i.e., material, size, spacing between phase conductors, etc.). B. Overhead Line in Fig. 1, in part, returns to the remote The return current source through the ground wire and, in part, discharges into the soil through the transmission-line tower structures. Apart from the characteristics of the ground wire (i.e., number, material, depends also on the size, spacing from phase conductors), towers footing resistance, whose value is not constant along the line but varies with the soil resistivity of the sites where the towers are located. However, it is a common practice at the design stage to adopt an approximate value, corresponding to the estimated average value. If tower footing resistance and span are assumed constant along the line, the overhead line section in Fig. 1 can be represented by means of a ladder circuit model composed by a chain of identical circuits as the number of spans [15]. However, is of inif only the evaluation of the overall return current terest and not the distribution of the fault current along the entire line, the overhead line section of Fig. 1 can be represented by the compact equivalent scheme depicted in Fig. 3, obtained by using the decoupling technique and the reduction method described in [16] and [17], respectively. The current source (4) models the fault current component flowing through the ground wire due to its inductive coupling with the phase conductors, with being the mutual impedances of the overhead ground wire and the phase conductors and as the self impedance of the overhead ground wire. Both of the impedances and are per span and for ground return and can be evaluated by means of Carson’s theory [14], once the soil resistivity and ground wire conductor characteristics are assigned.
Fig. 3. Compact equivalent circuit of an overhead line during a ground fault.
The equivalent -circuit in Fig. 3 models the ground wire of the line self-impedances and towers footing resistance spans; its parameters are given by the following expressions [17]: (5) (6) where
is the total number of spans and
is defined as (7)
represents the equivaIn the aforementioned equations, lent impedance of the ground wire and its connections to ground, through the towers footing resistances, of an infinite line. Its expression is [18] (8)
C. Combined Overhead-Cable Line Combining the schemes of Figs. 2 and 3 and including the resistance to ground of grounding systems at the ends of each line section, the equivalent circuit shown in Fig. 4 is obtained for a combined overhead-cable line during a fault to ground at the receiving-end substation. In practice, referring to an actual overhead transmission line, the value of the impedance , defined by (5), is much greater compared to the other impedances in the scheme; hence, the current flowing through is very small and can be neglected with a little error. With this assumption, the compact equivalent model shown in Fig. 5 can be derived. The following expressions for the earth current at the faulted substation and the fault current transferred to the TS can be
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Fig. 4. Compact equivalent circuit of a combined overhead-cable line supplying a phase-to-ground fault.
Fig. 5. Compact equivalent model.
easily obtained, applying Kirchhoff’s voltage and current laws to the scheme of Fig. 5, after some mathematical manipulations: (9) (10) where (11) and parameters and are the reduction factor of cable sheaths and ground wire, respectively, defined as (12) (13) The GPR at the transition station can then be obtained as (14)
IV. NUMERICAL RESULTS Some numerical applications are presented in order to validate the proposed method and to quantify the effects of the fault application transfer phenomenon. With this in mind, only the influence of the main factors is considered: line length, TS ground resistance, and the type of material used for the overhead ground wire. Let us assume that the combined overhead-cable line, which supplies the receiving-end substation in Fig. 1, is a 110-kV line.
Fig. 6. Substation earth current against cable line length.
The underground cable section consists of a trefoil formation of coated single-core cables with the following characteristics: 50 mm copper sheath, geometric mean radius of the sheath of 0.0434 m, and geometric mean distance (GMD) between phase conductors of 0.25 m. The overhead line section is first considered with a steel ground wire over its entire length, then better conducting materials are taken into consideration; the relevant ground wires characteristics are given in Table V. For all of the studied cases, the GMD between the ground wire and phase conductors was 8.21 m, while the average span length and towers’ footing resistance were assumed to be 200 m and 10 , respectively. Moreover, the overhead line section has been considered to be 10 km long. This is because, in practice, the effect of the overhead line length on the fault current distribution does not change with lengths of more than 15–20 spans. The other relevant data are: specific soil resistance along both line section 50 m, substation ground resistance ( ) 0.1 , source ground resistance ( ) 0.5 . For a better interpretation of the results, currents are expressed in per-unit absolute values as a part of the total substation fault current, as is supposedly known. A. Effects of Cable Line Length and TS Ground Resistance The curves illustrated in Figs. 6 and 7 obtained using (9) and (10) yield the substation earth current and the TS transferred current, respectively, as a function of the cable line length for different values of the TS ground resistance . It can be observed that the distribution of the fault current between the substation grid and the TS electrode is dramatically affected by the length of the cable line section. For example, , when km, the percentage of the assuming fault current dissipating from the substation ground system is 79% and from the TS electrode, it is 19%, while when km, they are 37% and 46%, respectively. Moreover, as can be seen, the TS ground resistance influences the current dissipating from the TS ground electrode more than the substation earth current. The higher the TS ground resistance is, the lower the return current is injected at the TS. Nevertheless, a high value of does not imply better safety conditions at the transition structure in terms of ground potentials. This is shown in Fig. 8, where the GPR at the TS calculated using (14)
MANGIONE: SIMPLE METHOD FOR EVALUATING GROUND-FAULT CURRENT TRANSFER
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TABLE II EFFECT OF GROUND WIRE ON THE TS TRANSFERRED CURRENT, I
TABLE III COMPARISON OF CALCULATION RESULTS OF I , FOR A NONUNIFORM GROUND WIRE WITH DIFFERENT NUMBERS OF TERMINAL SPANS AND VALUES OF R Fig. 7. Fault current transferred to the TS against the cable line length.
TABLE IV COMPARISON OF CALCULATION RESULTS OF I , FOR NONUNIFORM GROUND WIRE WITH A DIFFERENT NUMBER OF TERMINAL SPANS AND VALUES OF R
Fig. 8. Ground potential rise at the transition station against cable line length.
TABLE I EFFECT OF GROUND WIRE ON THE SUBSTATION EARTH CURRENT, I
In practice, for the case examined here, in order to obtain similar effects on the earth current reduction at both the faulted and the transition stations, it should be sufficient to apply the better conducting ground wire in a maximum of 15–20 terminal spans as shown in the next subsection. C. Method Validation
is reported, as a function of the cable line length ferent values of .
and for dif-
B. Effects of Ground Wire Material The effect of the type of material used for the overhead ground wire is presented in Tables I and II, where values of and obtained with aluminium/steel and copper/steel ground wires, when km, are compared with those obtained with the steel conductor. As can be seen, good conducting ground wires considerably reduce both the substation earth current and the TS transferred current; however, the benefits obtained on the latter are much greater. Furthermore, the higher the TS ground resistance is, the more the decrement of both currents is. Note that the values in Tables I and II are obtained by means of (9) and (10), respectively, considering the overhead ground wire uniform over its entire length. Nevertheless, similar values should be obtained if the better conducting ground wire is used only in a limited number of the line’s receiving end spans [10].
According to the aforementioned discussion, consider now the overhead line section with the steel ground wire over its entire length, saved at a certain number of receiving end spans, where the copper/steel conductor is used. By applying the proposed method, based on the compact model of Fig. 5, calculations are made considering only the better conducting ground wire as it was installed over the entire line length ( ). Tables III and IV compare, for different numbers of terminal spans with copper/steel conductor, the results obtained in such a manner with those obtained by a computer program which employs a more rigorous method [19], based mainly on the overhead line complete circuit model and the solution technique presented in [15]. As can be seen, the maximum error in values of currents and in all of the studied cases is negligibly small; less than 4% in cases of 15 terminal spans with better conducting ground wires and about 1% in cases of 20 terminal spans. V. CONCLUSION The compact equivalent model of a combined overhead-cable line presented in this paper allows deriving relatively simple
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TABLE V OVERHEAD GROUND WIRE SIZE AND TYPE
expressions for a quick and correct evaluation of the fault current distribution between the faulted substation and the transition station. Numerical results show that in practical cases, a great portion of the fault current that appears at a remote receiving-end substation could involve the transition station, depending mainly on its ground resistance value and on the type of material used for the overhead ground wire. In this situation, the local ground electrode at the transition station, generally small and with high resistance, could be inadequate to maintain the GPR within safety limits. The proposed formulae can be employed at the design stage to easily assess safety conditions and enhancements at the transition station, which can be achieved by using different ground wire materials, also when a nonuniform overhead ground wire is used . The accuracy of the proposed compact model is demonstrated by comparing the obtained results with those obtained from the more rigorous method based on the complete circuit model. REFERENCES [1] IEEE Guide for Safety in AC Substation Grounding, IEEE Std. 80, 2000. [2] D. L. Garret, J. G. Myers, and S. G. Patel, “Determination of maximum substation system fault current using graphical analysis,” IEEE Trans. Power Del., vol. PWRD-2, no. 2, pp. 725–732, Apr. 1987. [3] A. P. Meliopoulos, R. P. Webb, and E. B. Joy, “Computation of maximum earth current in substation switchyards,” IEEE Trans. Power App. Syst., vol. PAS-102, no. 9, pp. 3131–3139, Sep. 1983. [4] J. M. Nahman, V. B. Djordjevic, and D. D. Salamon, “Grounding effects of HV and MV underground cables associated with urban distribution substation,” IEEE Trans. Power Del., vol. 17, no. 1, pp. 111–116, Jan. 2002. [5] L. M. Popovic´, “Determination of the reduction factor for feeding cable lines consisting of three single-core cables,” IEEE Trans. Power Del., vol. 18, no. 3, pp. 736–743, Jul. 2003. [6] S. T. Sobral, J. O. Barbosa, and V. S. Costa, “Ground potential rise characteristics of urban step-down substations fed by power cables – A practical example,” IEEE Trans. Power Del., vol. 3, no. 2, pp. 1564–1572, Apr. 1988.
[7] J. Waes, M. Riet, F. Provoost, and S. Cobben, “Measurement of the current distribution near a substation during a single phase to ground fault,” presented at the CIRED 17th Int. Conf. on Electricity Distribution, Barcelona, Spain, 2003. [8] J. E. T. Villas, D. Mukhedkar, V. R. Fernandes, and A. C. Magalhaes, “Ground grid design of a transition station system – A typical example of fault transfer,” IEEE Trans. Power Del., vol. 5, no. 1, pp. 124–129, Jan. 1990. [9] L. M. Popovic, “Practical method for evaluating ground fault current distribution in station supplied by an unhomogeneous line,” IEEE Trans. Power Del., vol. 12, no. 2, pp. 722–727, Apr. 1997. [10] J. Nahman, “Compact models of nonuniform lines for earthing-system analysis,” in Proc. Inst. Elect. Eng., Gen. Transm. Distrib., Jun. 2001, vol. 148, pp. 579–582. [11] L. M. Popovic, “Reduction factor of feeding lines that have a cable and overhead section,” presented at the CIRED 17th Int. Conf. on Electricity Distribution, Barcelona, Spain, 2003. [12] IEEE Guide for the Application of Sheath-Bonding Methods for SingleConductor Cables and the Calculation of Induced Voltages and Currents in Cable Sheaths, IEEE Std. 575, 1988. [13] A Guide for Assessing the Rise of Earth Potential at Substation Sites Elect. Assoc. Eng. Recommendation, 1986, S.34. [14] C. F. Wagner and R. D. Evans, Symmetrical Components. New York: McGraw-Hill, 1933. [15] R. Verna and D. Mukhedkar, “Ground fault current distribution in substation, towers and ground wire,” IEEE Trans. Power App. Syst., vol. PAS-98, no. 3, pp. 724–730, May 1979. [16] S. T. Sobral, V. S. Costa, M. S. Campos, and D. Mukhedkar, “Dimensioning of nearby substations interconnected ground system,” IEEE Trans. Power Del., vol. 3, no. 2, pp. 1605–1614, Apr. 1988. [17] L. M. Popovic, “Practical method for evaluating ground fault current distribution in station towers and ground wire,” IEEE Trans. Power Del., vol. 13, no. 1, pp. 123–128, Jan. 1998. [18] J. Endrenyi, “Analysis of transmission tower potentials during ground faults,” IEEE Trans. Power App. Syst., vol. PAS-86, no. 10, pp. 1274–1283, Oct. 1967. [19] P. Buccheri, S. Mangione, R. Miceli, E. Finocchiaro, and G. Nicola, “Drenaggio della corrente di guasto a terra da parte di funi di guardia e guaine metalliche di cavi,” (in Italian) L’Energia Elettr., vol. 70, pp. 323–331, Jul./Aug. 1993.
Stefano Mangione (M’06) was born in Raffadali, Italy, on January 23, 1955. He received the electrical engineering degree from the Faculty of Engineering, University of Palermo, Palermo, Italy. Currently, he is a Full Professor of Electrical Power Systems at the University of Palermo. He was a Researcher with the University of Palermo in 1981 and from 1992 to 1994, he was an Associate Professor at the University of Cagliari, Cagliari, Italy. His main research interests include grounding systems and electrical safety in high-voltage substations, voltage stability, and distribution automation.
