maximum substation grounding system fault current, at selecting the ground wire capable of ... During ground faults in power systems, large currents and raised.
IEEE Transactions o n Power Delivery, Vol. 13, No. 1, January 1998
123
PRACTICAL METHOD FOR EVALUATING GROUND FAULT CURRENT DISTRIBUTION IN STATION, TOWERS AND GROUND WIRE Ljubivoje M.PopoviC, Senior Member, IEEE JP "Elektroprivreda Srbije", Belgrade, Yugoslavia Abstract: The paper presents an original analytical procedure which enqbles a quick and, for practical purposes sufficiently accurate evaluation of the significant parts of the ground fault current, for a fault at any of the towers of a transmission l i e of an arbitrary number of spans. The advantages of the method are the simplicity and accuracy of the formulae for solving uniform ladder circuits of any size (from one up to an infinite number of pis) and any terminal conditions. The formulae are obtained by applying the "general equations of the line represented by discrete parameters" on a specific electrical circuit formed by a transmission line ground wire during ground faults. The presented method is suitable for analyses aimed at evaluating the maximum substation grounding system fault current, at selecting the ground wire capable of withstanding the fault currents and at the prediction of step and touch voltages near transmission towers. INTRODUCTION During ground faults in power systems, large currents and raised potentials appear at places where they do not exist in normal operating conditions. In order to economically and securely protect against undesired consequences, such as loss of a human life, bumdown of transmission ground wires and the damage to sensitive telecommunications equipment entering power stations, it is necessary to evaluate as precisely as possible the value and distribution of the ground fault current in worst fault conditions. The problem here lies in the fact that the distribution of the ground fault current and the critical fault location cannot be evaluated in all caSes by using simple rules Under certain conditions, the prediction of the maximum current flowing between the grounding system and surrounding carth cannot be performed without including in the analysis the faults on a transmission line [7,8,9,14] In current engineering practice the parts of the ground fault current is analyzed for two important additional reasons. The first is the selection of the size of the ground wire capable of withstanding the anticipated fault current [6,11,12], while the other is the evaluation of the potential rise of the faulted tower [3,5] Extensive work has been undertaken, especially in the last two decades, to model transmission networks for ground fault current analysis. The advantages and drawbacks of the great number of developed methods and procedures have been presented in detail in [12], so that here we shall only point out that in their development and improvement two tendencies can be clearly distinguished On one hand, an effort is made to make these methods more convenient in applications [2,3,9,10,14] due to the great number of cases that have to be analysed. On the other hand, the authors try to improve the procedure further by including new, less important factors, but which, in some especially complex and unfavorable conditions, can contribute to an economically and technically acceptable solution [7,8,13] More accurate methods have been developed by using special matrix techniques. However, theoretical and practical considerations have shown that the relative error propagation can be a problem when solving a large complex matrix. Ways of overcoming this problem have been observed in an exact and simple solution for uniform ladder circuits 181. Since the late 1960's many authors (Endrenyi, Poter, Finsh, Johnson, Sebo, Fesonen, Dawalibi, Mukhedhar, etc.) have presented methods for the solution of ladder circuits. The approach generally used by these authors
PE-019-MD-0-02-1997 A paper recommended and approved by the IEEE Substations Committee of the IEEE Power Engmeenng Soclety for publication in the IEEE Transactions on Power Delivery. Manuscnpt submitted December I O , 1993; made avalable for pnnting February 20. 1997
was to represent the lumped parameter ladder circuit by an equivalent distributed parameter ladder circuit and to solve it by differential equations. However, the process gives satisfactory results only when the line and the line sections presented in this manner are sufficiently long [12] Recently, by using Kirchoff s laws, the principle of superposition and the summation of geometric series, equations were derived which take lnto consideration the discrete nature of the lumped parameter ladder circuits [8,14]. However, the procedure is not finalized, so that the solutions are valid only for certain specific cases from the point of view of possible terminal conditions. Finally, by deriving the "general equations of the line represented by discrete parameters" [IS], it can be said that the problem of lumped parameter ladder circuits is definitively solved On the basis of the above mentioned equations, the paper derives relatively simple formulae for the manipulation of lumped parameter ladder circuits of any size and any terminal conditions The advantage of using these formulae is demonstrated here on the example of solving the problem of predicting the maximum station grounding system fault current. It demonstrates that this problem can be solved without a computer even for cases when faults outside the station need to be considered. The approximations that are made are those that we are otherwise forced to assume in the design stage because of the uncertainty of the basic data of soil resistivity. Finally, the paper presents a formula for evaluating the line length above which the line can be considered as infinite from the point of view of groundmg effects of the ground wire(s) FAULTS ON OVERHEAD LINES NEAR THE STATION In designing grounding systems of HV mstallations, one of the objectives is to make the proposed solution as economical as possible, which means that it should satisfy real needs without excessive expenditure This can be done only if it is possible to accurately predict the part of the fault current which will be injected into the earth through the station ground grid and the extemal grounding circuits The problem appears when ?he fault location producing the mammum value of this part of the fault current, which we shall simply call the earth current as in 171, is not obvlous In that case, the number of fault studies which must previously be performed significantly increases [7] In principle, a ground fault anywhere in the power system causes fault currents through the grounding systems of all substations with grounded neutral@) However, for finding the worst fault location it is sufficient to analyze the faults occurring in the considered station itself and on the outgoing lines (e g [2]) A complete analysis can show that, in some cases, the worst fault is placed on one of the outgoing lines, at a certain, critical distance from the station Example system The simplicity and strength of the method will be demonstrated on a simple system composed of one overhead line through which generatmg station A supplies a hstnbution station B Fig 1 shows parts of the fault current when a single-line-to-ground fault occurs at an arbitrary (n-th) tower of the line In practice, the values of the grounding resistance of towers are not equal In the design stage, however, we are obliged to adopt an approximate value which we then attribute to a larger number of towers This is based on earth geological charactenstics common to the sites whcre the towers will be located [121 The impedances Z s apd Z , are calculated by using formulae based on
Carson's theory of the ground current retum path (e g [2]) Impedance Z, is determined only in relation to the faulted phase conductor [IO], because we cannot assume that a line section of a few spans is transposed Furthermore, keeping in mind that we need the cuirent I, in worst fault conditions, we assume that the faulted conductor is the most distant one from the ground wre(s) 0885-8977/98/$10.00 0 1997 IEEE
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I
Fig. 1. Parts of the ground fault current G
The notations used in this circuit have the following meanings: Fig.2. Equivalent circuit
If I,&)
total ground fault current ground currcnt componcnts Icft and right of the fault location,F I, earth current in station A I, fault current through the ground wire(s) on the first span, counted from station A Za(Zb) impedance of the grounding system of substation A (B) which does not include the grounding effects of the ground wire@) of the considcred line sclf impedance of the ground wire(s), per span Z, mutual impedance between the ground wire(s) and the faulted Zm phase conductor, per span tower footing resistance R number of spans to the fault location, counted from station A n N overall number of spans.
Currcnt I, circulates only through the neutral(s) in the station A, while currcnt Ib circulates through the neutral(s) in station B. When the fault occurs inside the station A, current I, circulates only in the axial direction through the ground grid elements and so it cannot cause any potential toward remote earth irrespectively of its value. However, when thefault occurs on the line, the value of current I, decreases in magnitude, but a part of it, current Ie (Fig 1) flows into earth and creates a potential in the grounding system of Station A. The remaining part of current Ia, current I,, returns to the system through the ground wire and grounding connections in station A. The nearer fault produces the larger current I,, but most of it, due to the proxlmity of station A, returns through the ground wire. It is necessary to dctcrminc thc currcnt IC at critical distance when it reaches its maximum. Equivalent circuit and necessary analytical expressions
Thc gotations used in thc circuit have thc following mcanings: auxiliary driving source at fault location whose voltage is the same as the voltage at the source station potential of the faulted tower currcnt source uscd to replace the inductive coupling between the ground wire(s) and phase conductor positive and negative sequence impedance at fault location zero sequcnce impedance of the system at station A (B) zero sequence impedance of the line from the fault location to the station A (B) and remote ground.
Pa =
k"+l
ZLV k"-k
k z 1 . t . I;G
The currents generated by current sources are determined by the foIIo;iing we11known relations:
The cquivalcnt impcdanccs Q, and Pa, according to Appendix I, are dctcrmincd by:
(3)
(5)
In expression (5), parameter Z, designates the grounding impedance of the ground wire of an infinite line. In accordance with 131, it is determined by:
Impedances Qb and Pb can also be determined from expressions (3) and (4), only then it is necessary to introduce the corresponding number of spans, i.e. to replace n with m = N n. On the basis of the equivalcnt circuit in Fig. 2 and thc givcn expressions, by varying n and by performing sequential calculations, it is possible to determine, for any line, the extreme values of the current I,, currcnt I, and the potcntial of any towcr, Vh. The analysis can be performed on a line of an arbitrarily complex power system, which means multiple lines, multiple sources, multiple substations, different voltage levels, substations with connected neutrals, etc. Before that, it is necessary to calculate the positive, negative and zero-sequcnce impedances of the system at terminal points of the considered line. Also, in order to calculate Ie, the equivalent circuit should be formed in such a way to retain one branch which directly wnncccts points A and G (Fig. 2). The equivalent impedance in this branoh should be determined so that the current I, is divided into two components. One of them circulates through the neutral(s) in station A, while the other flows through the remaining grounded ncutral(s) in the systcm, with thc cxccption of the part of the systcm supplicd by the considcred line. Also, the presented solution of ladder networks can be applied to reduce the amount of calculations necessary in methods which, by treating each phase conductor scparately, desire greatcr accuracy or analysis of other types of faults [7,11]. Finally, the presented analytical expressions can be used in evaluation of the ground fault currcnt distribution, for a fault in a substation supplicd by a line composcd of two or more diffcrent sections. Such cases are not rare in current appliaqces and usually appear whcn a newly built substation
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Thc powcr system that we have adopted in Fig.1 can be reprcscntcd by the equivalent circuit in Fig.2, by using: - method of symmetric components - driving point technique (e.g. [I 11) - dccoupling technique (e.g. [3,8]) and - general equations of the line represented by discrete parameters ~ 1 .
(4)
125 has to be connected to a nearby existing line.
The same equivalent circuit can be used for the prediction of the maximum value of current Iw.In that case the worst fault position is a priori known, the tower closest to the source station [6],so that we can use the following expression:
Simplified equivalent circuit and approximate expressions
In practice, the neutral(s) in distribution substations is frequently isolated and, even in cases when it is grounded, its contribution to the fault current in many cases can be neglected (ZoA
