Efficient reduction of fault current through the grounding ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 15, NO. 2, APRIL 2000

Efficient Reduction of Fault Current Through the Grounding Grid of Substation Supplied by Cable Line Ljubivoje M. Popovic´, Senior Member, IEEE

Abstract—The paper presents an analytical procedure suitable for the determination of the part of the ground fault current emanating from the substation grounding grid in the conditions when a particular measure has been taken to reduce it. The practical realization of this measure can be simply described as burying one bare copper wire of a certain length in the same trench as the cable feeding line. In the case of an overhead feeding line the similar measure is denoted in the expert literature as the “counterpoise”. The presented method enables a quick, and, for practical purposes, sufficiently accurate evaluation of the copper wire length providing the maximum possible reduction of the substation grid current. The conveniences of the method result from the simplicity of the formulae for the determination of the realized grid current reduction at the effective copper wire length. Index Terms—Ground fault current distribution, safety conditions.

I. INTRODUCTION HE GROUNDING system of a high voltage installation, in general, fulfills its function only in the moment of an unbalanced fault, when increased potentials appear at places where they normally do not exist. In order to ensure protection against undesired consequences, such as the loss of human lives, burndown of grounding wires and damages to sensitive telecommunication equipment entering the station, it is necessary to evaluate the value of these potentials as accurately as possible [1]–[3]. The magnitudes of these potentials as well as of all the potential differences significant for the safety conditions (touch and step voltages) are proportional to the fault current emanating from the substation grounding grid and flowing into the surrounding ground. This current represents only a part of the total ground fault current. The remaining parts of the ground fault current circulate only through the metal conductors (transmission line ground wire, and cable sheath) and ground connections, so that they do not contribute to the creation of the touch and step voltages [1], [2], [6], [7]. Therefore, when designing a substation grounding system it is of prime importance to evaluate correctly the ground-fault current distribution. This is the only way in which we can arrive at the solutions in accordance with the actual requirements and it means without excessive expenditures. However, it can happen that this is not sufficient under unfavorable circumstances and conditions (high value of soil resistivity, high value of the ground-fault current, confined space

T

Manuscript received December 22, 1998; revised October 15, 1999. The author is with J.P. “Elektrodistribucija-Beograd,” Beograd, Yugoslavia. Publisher Item Identifier S 0885-8977(00)03471-3.

for laying down an adequate ground grid, etc.). It is thus necessary to take measures which, by changing the ground fault current distribution, lead to an overall reduction of dangerous voltages appearing in the station and in its vicinity (e.g. [1], [4], [5], [7].) This is especially the case with large distribution stations with power ratings of several tens of megavoltamperes, which as it is known can be either conventional or gas-insulated. First of all, the neutrals of the networks that supply these stations are, as a rule, solidly grounded and the ground-fault currents reach very high values that often exceed 20 kiloamperes. Furthermore, it is desirable to place these stations at load centers, i.e. deep within the city, where normally there is no space for laying large grounding grids and where there are many public buildings. Finally, today in medium voltage (10 and 20 kV) networks cables with insulated outer sheath are mostly used instead of the oil-filled cableswhose contribution to the solution of the grounding problems is of a prime importance [3]. Under such conditions the rise of the station ground potential has a value of up to several kilovolts and its reduction is in many cases posed to the designer as an imperative (e.g. [5]). The solution can be achieved by choosing a special custom constructed supply cable furnishing sufficiently low value of the reduction factor. However, especially if the feeding line is relatively long, the solution may prove itself very expensive. Here it will be shown that the problem can be overcome by installing an external electrode-copper wire, buried along a cable line. This wire would provide an alternative path for the fault current [5]. Such a way of solving the problem is more economical even under the conditions when there is enough free space for laying a large grounding grid. There are two essential reasons to that. The strong inductive coupling of the wire with the cable line significantly intensifies the fault current dissipation into the ground through the wire. There is no need to dig a separate trench to lay the wire down. Finally, this solution opens the possibility to apply cables with the standard design only. This saving causes additional savings. The number of necessary cable joints is reduced when compared to the cables with a lower reduction factor (the extemal diameter of the cable is increased). II. PROBLEM DESCRIPT1ON Nowadays, the evaluation of a ground fault current distribution for faults in substations supplied by a homogeneous line is a routine designer’s work. Difficulties appear when the feeding line cannot be treated as homogeneous. Such a case is encountered in practice when measures affecting the relative distribution of the ground-fault current are taken [7]. Our example is schematically shown in Fig. 1.

0885–8977/00$10.00 © 2000 IEEE

POPOVIC´: EFFICIENT REDUCTION OF FAULT CURRENT

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Fig. 2. Uniform ladder circuit.

well known, mandatory before putting a newly built substation in operation. III. GENERAL SOLUTIONS OF UNIFORM LADDER CIRCUITS A. Circuit Representing a Transmission Ground Wire Fig. 1. Basic problem description. a) Cable feeding line; b) cable and copper wire in the same track.

In a grounded power network the fault current distributions in phase conductors and in the ground return circuits can be distinguished. Thus, these two distributions can be analyzed separately. An analysis of the both distributions together would be more complicated and unnecessary (e.g. [1], [2], [7]). Thus, we can assume that the fault currents supplying the location of the ground fault are known from the prior ground-fault analysis. The problem is how to determine the part of the fault current appeared at the fault place, the station B (Fig. 1), due to the inductive coupling between the line conductors and the copper wire buried in parallel. This component of the ground fault current at the point of the copper wire end E continues its path toward the supply sources through the ground. The soil through which the external electrode (copper wire) passes is rarely homogeneous. In most cases the soil is heterogeneous (multilayer) with each layer having a different resistivity. These resistivities are affected by seasonal changes. Therefore, an accurate determination of the ground structure is difficult. For practical purposes it is enough to adopt that the soil is homogeneous with a resistivity equal to the equivalent resistivity. However, it means that it is necessary to carry out series of measurements in the ground along the route of the ftiture underground conductor and to analyze them. Unfortunately, in urban conditions, because of the presence of metallic structures in the vicinity (water and gas pipes, metallic foundations of buildings, etc.) the results of such measurements are very uncertain. It is therefore more appropriate to use the global geological characteristics of the soil to adopt an approximate value of the soil resistivity and use it in the calculations. The earlier investigations of the soil effects on the long grounding conductors [7], [10] showed that the adoption of the value pretty higher (up to 20%) than the one roughly estimated insured results which were slightly on the safe side. As a conclusion, the following can be said. For the design of a grounding system, a high degree of accuracy is not necessary because of the uncertainty of the basic data on the soil resistivity. Accurate results and a final judgement about the safety conditions can be obtained only after measurements that are, as it is

To solve the presented problem we will use the general solutions of uniform ladder circuits [7]. The form of these circuits that we use to represent the ground wire(s) of the transmission line or one of its sections during ground faults is shown in Fig. 2. The symbols used in Fig. 2 have the following meaning: Zs —self impedance of the ground wire(s) per span, R—towers footing resistance, N —total number of spans. The voltages and currents at the ends of this circuit, according to [7], are related by the following general equations:

2N 2N = kNk + k+Nk+1 VN + (kkN +0k1)N Z+11 IN k2N 0 k2 k2N + k I0 = N VN + N I : N +1 (k + k )Z1 k + kN +1 N

1) V0 2)

(1)

The parameter k is the “current distribution factor” at any node, assuming that the number of spans (N ) is infinite. It is determined by the expression

Z1 ; R

k = 1+

(2)

in which Z1 represents the grounding impedance of the ground wire(s) of a line with an infinite number of spans and is given by

Z1 =

Zs 2

r

+

Z2 RZs + s : 4

(3)

B. Circuit Representing the Buried Copper Wire The ladder circuit used for the representation of an underground conductor which is in effective and continuous contact with the ground has a somewhat different form, as shown in Fig. 3. The parameters Zs , and R are the lumped parameters of the buried conductor on a segment of arbitrary length, which we will assume for practical reasons to be one meter. In that case, the resistance R, according to [3], [4] can be determined by

R=

2

ln

pLc

dh

;

(4)

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Fig. 3. Chain of identical pis.

where Lc —length of the conductor in meters; d—diameter of the conductor in meters; h—conductor burial depth in meters (Fig. 1b), whereas the impedance Zs is given by

s = z ( =m) 2 1 m;

Fig. 4. Ground fault current distribution in the substation grounding system.

Z

where z —self-impedance of the buried conductor per meter. The impedance z is calculated by using the formulae based on Carson’s theory of the ground-fault current return path (e.g. [9]). The voltages and currents at the ends of the circuit in the Fig. 3, according to [7], are related by the following equations 1) 2) where

V0

=

I0

=

k

N + k0N

N+

2

V

2 c

V

N 0 k0N k Z

N+

2RZ1 c = 2R + Z 1

Z

0

k

N 0 k0N 1 Zc

2

N + k0N k

2

p

s

RZ ;

N;

I

N

I

(5)

(6)

or, in accordance with the assumption that the discretized segments are only one meter long (N = Lc =1 m)

c Z1 :

(7)

Z

The parameters k and Z1 are determined by (2) and (3), respectively, only parameters Zs and R are not the same. C. Impedances of Equivalent Pi Both of the types of ladder circuits (Figs. 2 and 3) can be substituted by only one pi consisting of one longitudinal impedance Q and two transversal impedances P [8]. For the circuit in Fig. 3 these impedances are determined by the following expressions Q

=

k

P

N 0 k0N

2

1

N 1 = N+ 01 1 k

k

and

Z

Z

:

(8)

(9)

By applying the impedances Q and P the equivalent circuits for ground fault current analysis become essentially simpler and calculations can be performed without the aid of a computer [7], [8].

• The decoupling technique [4] and • The analytical expressions for the reduction of uniform ladder circuits [7], [8], the example system shown in Fig. 1 can be represented by the equivalent circuit given in Fig. 4. The notation has the following meaning: ground fault current component passing If — through the grounded neutral(s) in the feeding network; fault current appearing through the cable Ish — sheaths only as the consequence of its galvanic connections with grounding grids of the stations A and B; fault current flowing through the substation Ig — grid; Id — fault current diverting from the substation grid and flowing through the buried copper wire; current source which replaces the influence of Ii — the inductive coupling of the feeding cable line and buried copper wire; r — reduction factor of the feeding cable line; Zsh — self-impedance of the feeding cable sheaths; impedances which make up the equivalent pi for Q and P — the ladder circuit formed by the buried copper wire; G — remote ground. The reduction factor r is defined as the relative value of the fraction of the current If returning through the ground under the assumption that the resistances RA and RB are equal to zero. In practical conditions (a real distributive network) the lengths of the feeding lines are so great (over 3 km) that the influence of the galvanic connection through the cable sheaths in many cases can be disregarded (Ish 0.) In this manner the obtained results are slightly on the safe side. The total reduction of the grid current Ig on the basis of the Kirchhoff’s rules and of the equivalent circuit in Fig. 4 is defined by the following coefficient

t=

IV. EQUIVALENT CIRCUIT AND NECESSARY ANALYTICAL EXPRESSIONS We will assume that the substation A (Fig. 1a) is either a source or a transit one, supplied by a cable line. Starting from the above assumptions and by using • The method of symmetrical components,

r

c + = f 0 sh 2+ B+ + g

I

rI

r Q

Q

I

P

R

P

Q

;

(10)

P

where

c = 1 0 Zm =Zs :

r

(11)


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The coefficient rc is the reduction factor defined under the assumption that the copper wire is prolonged to the source station and grounded at its end (e. g. [5]). The impedance Zm represents the mutual impedance between the buried wire and the parallel cable line conductors, including their sheaths (Fig. 1b). It is determined by the procedure described in [9], with the approximation that each phase conductor and its sheath represent a single conductor with an unchanged disposition with respect to the buried wire. Based on such assumptions the current source shown in the circuit in Fig. 4 generates the current determined by the following expression:

Z Ii = m (rIf Zs

0 Ish ):

(12)

The expression for the reduction coefficient due to the inductive coupling between the buried wire and the feeding line ri is obtained from (10) under the assumption that RB = 0 (Fig. 4). Thus we obtain

ri = rt (RB

= 0) =

rcQ + P : Q+P

(13)

According to (10) and (13) the reduction coefficient expressing solely the galvanic coupling between the copper wire and the grounding grid, rg , is determined. by

r rg = t ri

=

2+

Q + P : Q RB + Q + P P

(14)

According to the given expressions the total reduction of the current Ig increases with an increase of the wire length, Lc . However, an infinite reduction is not possible. At the length for which the wire from the point of view of grounding effects can be treated as infinite, the coefficient rt reaches its limit value. We will determine it by assuming that the length Lc increases infinitely. In that case, according to (8) the impedance Q becomes infinitely large (Q ! 1), while the impedance P , according to (9) becomes equal to the impedance Z1 (P ! Z1 ), hence

rc Q + P lim r = lim LC !1 t Q!1 Q P !Z1 2 + P RB + Q + P Z1 = rc : Z1 + RB

A. Proximity Effect Expression (15) can be corrected to include the proximity effect between the buried copper wire as an external electrode and grounding grid. According to [3] this effect can be wholly taken into account via the impedance Z1 using the following expression:

0 Z1

1:

= (1 + p)Z

The relative increase of the impedance Z1 in (16), the coefficient p can be estimated by

p

re Z1 0 Z1 :

(17)

2R

In (17) re designates the relative length (per meter) of the grid equivalent radius and is determined by

re =

p

a=;

(18)

where a represents the area covered by the substation grid. 0 (16), When we replace the impedance Z1 in (15) by Z1 the distribution of the fault current is obtained by taking into account the proximity effect. The calculation results are at the safe side, since the effect is fully taken into account only by the 0 [3]. Thus the final expression for value of the impedance Z1 the ground fault current distribution is

0 Z1 : 1 + RB

rt = rc 0 Z

(19)

A question is posed, however, how to determine the length for which the copper wire can be regarded as infinite from the point of view of the grounding effects. B. Active Copper Wire Length The length to which there is a practical meaning to lay the copper wire into the ground, the so-called active length La , in accordance with [6], can be estimated by ln(1 + 1=")

La

r

ln

1+

jZs j

(15)

As it can be seen, the lowest possible value of the coefficient rt is equal to the product of the lowest possible values of the coefficients ri and rg . Here it should be mentioned that the strong inductive coupling between the wire and the cable conductors displaces the main fault current injection into the ground at the point most distant from the grid, i. e. at the opposite end of the wire. Thus the influence of the grounding grid in dissipating the inductive component of the current Id practically does not exist if the wire is long enough. Opposite to it, the mutual interference in dissipating the grid current and the galvanic component of the current Id is unavoidable. The so-called “proximity effect” is very complex, however according to [3] it is possible to express it in an analytical form.

(16)

!;

(20)

R

where "—the desired relative accuracy: j(Z1 0 Za )=Z1 j (an a priori adopted small number), Za —the grounding impedance of the wire with the length equal to the active length La . Since the length La depends on R, and according to (4) R is the function of Lc , the given formula cannot be directly applied. Its purpose is to define (by testing a large number of numerical examples) the next semiempirical formula:

La (" = const)

r x jz j ;

(21)

where x is an unknown, dimensionless number, different for different cross-sections of the wire and burial depth, determined from the condition that (20) should be approximately satisfied for different values of .

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Fig. 5. Current If distribution for a fault in an arbitrary section of the cable

When the length of the copper wire is equal to its active length, the potential appearing in the station B is, according to the previous analysis, determined by the following relation:

VB

= Z rc+Z R 0 1

0 1

B

RB (rIf

0 Ish );

Fig. 6. Absolute value of rt as a function of the copper wire length.

(22)

where the resistance RB is determined by some of the known formulas (e.g. [6]). C. Critical Fault Position Before giving the final judgement about the technical solution proposed here let us consider if its application leads to a change of the critical fault position. To this purpose we will use the circuit shown in Fig. 5. In order to provide a clearer view, the given circuit does not show the component of the ground fault current circulating through the grounded neutral(s) in the substation B. However, its influence is negligible, because for the faults near the station B this current almost completely returns into the network via the cable sheath. The inductive influences to the left and the right side of the fault location F are identical (Iil = Iir ), and the expression for the induced current is the same as in the case when the fault is in the station B (12). However, with an increase of the distance of the fault location the currents If and Ish increase, and since the increase of the current Ish is significantly larger, the current rIf which is injected into the ground decreases. It is thus clear that the critical fault position (within the station B) would remain unchanged after the application of the solution presented herein. V. AN ILLUSTRATIVE QUANTITATIVE ANALYSIS The analysis is performed with the aim to create a general impression about the efficiency of the measure for reduction of the fault current circulating through the substation grid. We will assume that the station B in Fig. 1a is supplied by a 110 kV cable line with the length so large that the current Ish can be neglected. The cable is of the type XHE49-A 110 kV and in the standard design its sheath has an outer diameter of d = 93 mm and is made of copper strings with the total cross-section 3 2 95 mm2 . According to the manufacturer’s catalogue the reduction factor for this cross-section of the cable sheaths is 0.297. By increasing the cross-section of the cable sheaths to 3 2 120 mm2 in total the reduction factor decreases to 0.235, while an increase of the sheaths cross-section to 3 2 185 mm2 decreases it to 0.157.

Fig. 7. Absolute value of rt as a function of the copper wire length.

As an alternative solution to such a way of decreasing the grid current Ig we will consider the effects achieved by the technical solution presented herein, when the copper wire has a cross-section of 120 mm2 and is buried in the depth h = 1:4 m, according to Fig. 1b. We will adopt a grounding grid of the station B with such dimensions and other relevant parameters that the grounding resistance RB is equal to 0.1 when the soil resistivity is = 20 m. Without any changes of the grounding grid we will consider the effects of the reduction of the current Ig for the following equivalent soil resistivities: = 20, 50, 100 and 200 m. The proximity effect is completely neglected. The results of the application of (14) and (10) are presented in Figs. 6 and 7, respectively. If the spatial position of the copper wire were such to reduce the inductive influence of the feeding cable to zero, the wire would represent a simpe external electrode with the effects of reduction as shown in Fig. 6. The additional reduction, ensuing as a consequence that the wire and the feeding cable are in the same trench (the influence of inductive coupling is maximal) can be seen by comparing the results shown in Fig. 7 to those in Fig. 6. By using (20) and (21) with " = 0:05 and the other previously adopted relevant data we obtain that x is 13, so that the wire active lengths are 596, 924, 1289 and 1798 mfor = 20, 50, 100 and 200 m, respectively. As it can be seen, these values


agree well with the results of the calculations shown in Figs. 6 and 7. As it can be seen, by the application of the technical solution presented herein the same effect is achieved as if the level of the ground fault current in the supply network were decreased five to ten times, depending on the soil resistivity. It may be especially important under the conditions when all technical possibilities for its limitation are already utilized. Under the conditions when the reduction of the grid current Ig is necessary to the designers, generally speaking, we have two possibilities: the application of the measure considered herein or an order to manufacturers to fabricate a special design cable with sufficiently low value of the reduction factor. However, the question is posed which of these two technical solutions is more economical. Certainly, to give the right answer we need a quantitative analysis for many specific cases. However, bearing in mind that an average length of a 110 kV feeding cable is approx. 4 km (the data from the distribution network in Belgrade, Yugoslavia) we may make a global estimation. To decrease the value of the reduction factor of an average long cable from 0.297 to 0.235 and 0.157 the required quantity of the copper wire is 2672 and 9618 kg, respectively. The same effects are achieved by the herein presented method with significantly lower consumption of copper strings, i.e., according to Fig. 7, with approx. 250 and 400 kg, respectively, and for the most unfavorable case ( = 200 m). Based solely on this data we can say that the advantage is doubtlessly on the side of the solution proposed herein. In some specific case, an advantage could also be a smaller number of necessary cable joints. The wire for the reduction of the grid current (WRGC) can be additionally utilized if the safety conditions in an already built substation are significantly worsened, for example by an increase of the ground fault current in a supply network. VI. CONCLUSION The paper offers an economical and efficient technical solution for the grounding problem of high voltage substations built in urban surroundings and supplied by cable.

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REFERENCES [1] r. Verma and D. Mukhedkar, “Ground Fault Current Distribution in SubStation, Towers and Ground Wire,” IEEE Trans. Power Apparatus and Systems, vol. 98, no. 3, pp. 724–730, May/June 1979. [2] H. Seljaseth, A. Campling, K. H. Feist, and M. Kuussaari, “Station Earthing and Interference Aspects,” Electra, vol. 71, pp. 47–69, 1980. [3] Lj. M. Popovic´, “Proximity Effect Between an Earthing Grid and External Electrodes in an Earthing System of High-Voltage Installations,” IEE Proc., pt. C, vol. 133, no. 6, pp. 346–352, Sept. 1986. [4] S. T. Sobral, V. S. Costa, M. S. Campas, and D. Mukhedkar, “Dimensioning of Nearby Substations Interconnected Grounding System,” IEEE Trans. Power Delivery, vol. 3, no. 4, pp. 1605–1614, Oct. 1988. [5] 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 Delivery, vol. 5, no. 1, pp. 124–129, Jan. 1989. [6] Lj. M. Popovic´, “Practical Method for the Analysis of Earthing Systems with Long External Electrodes,” IEE Proc., pt. C, vol. 140, no. 3, May 1993. , “Practical Method for Evaluating Ground Fault Current Distri[7] bution in Station Supplied by an Unhomogeneous Line,” IEEE Trans. Power Delivery, vol. 12, no. 2, pp. 722–727, Apr. 1997. , “Practical Method For Evaluating Ground Fault Current Distribu[8] tion in Station, Towers and Ground Wire,” IEEE Trans. Power Delivery, vol. 13, no. 1, pp. 123–128, Jan. 1998. [9] International Standard, ref. no. CEI/IEC 909-3, 1995. [10] Lj. M. Popovic´, “The Effect of Partial Compensation of the Unfavorable Influence of Increased Soil Resistivity in Long Earthing Conductors,” in Proceedings of the CIGRÉ Symposium, Brussels, June 1985.

Ljubivoje M. Popovic´ was born in Markovac, Serbia, Yugoslavia, on Feb. 24, 1944. He received his BS, MS and PhD degrees in electrical engineering from the University of Belgrade in 1969, 1983 and 1991 respectively. He has worked on the design of different power system installations in “Elektrodistribucija—Beograd”. For the last eighteen years he has been a leading research engineer in the field of grounding problems and short circuit currents. Since 1991 he is a Senior Member of the IEEE Power Society.