REDUCTION FACTOR OF FEEDING LINES THAT HAVE A CABLE AND AN OVERHEAD SECTION

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1 C I E 17 th International Conferene on Eletriity istriution Barelona, 1-15 May 003 EUCTION FACTO OF FEEING LINES THAT HAVE A CABLE AN AN OVEHEA SECTION Ljuivoje opovi J.. Elektrodistriuija - Belgrade - Yugoslavia ljuivoje@eotel.yu SUMMAY The paper presents an analytial proedure whih enales a quik and, at the design stage, orret evaluation of the ground fault urrent distriution, for a fault in a sustation supplied y a line omposed of two or more mutually different (overhead and underground) setions. The advantages of the method are ased on the simpliity and auray of the formulae for solving uniform lumped parameter ladder iruits of any size and under any terminal onditions. INTOUCTION uring ground faults in an HV installation, raised potentials appear in plaes where they do not exist under normal operating onditions. The magnitudes of these potentials, as well as all of the potential differenes signifiant for the safety onditions (touh and step voltages) are proportional to the urrent emanating from the sustation grounding system into the surrounding earth. It is known that only a part of the total fault urrent flows into the earth, and the rest returns to its soures (power system) through various metal ondutors (ground wire(s) of the overhead line, the ale sheath(s) and grounding onnetions), so that it does not ontriute to the reation of the elevated potentials in the grounding system of the sustation []. Therefore, when designing grounding systems of high voltage plants the primary task is to evaluate as preisely as possile the part of the fault urrent flowing through the grounding system into the earth. This is the only way to e sure that the prolem is solved aording to atual requirements, whih pratially means that the safety onditions are reahed without exessive expenditures. The evaluation of the distriution of the ground fault urrent for faults in sustations supplied y transmission lines homogenous through their entire length is performed y a relatively simple proedure. This ase has een studied, systematized and presented in [7] for various types of stations and for different types of transmission towers. However, the prolem gains in omplexity if the feeding line has two or more setions with one or more mutually different relevant parameters. Examples for suh feeding lines are enountered in distriution networks of various voltage levels and are a onsequene of different degree of uranization of the areas where the feeding line passes. egarded as a whole, these lines are usually a omination of ale and overhead setions with different lengths. As a rule, the overhead setion is loser to the soure station, and the ale setion is loser to the supplied station. When ground faults appear, suh lines form a very omplex eletrial iruit with a large numer of ondutively and indutively oupled elements. eferenes [5] and [8] point to the prolem and give some analytial expressions enaling its solution in some pratial situations. However, these papers do not enompass all the ases of importane for urrent engineering pratie. Thus it may e said that this work represents a logial ontinuation of the efforts to solve this kind of prolems. The possiility to simplify the prolem is found in the redution of the numer of the elements of the equivalent iruit. To this purpose, we have derived formulae for an exat representation of lumped parameter ladder iruits of any size (from one pi to an infinite numer of pis) y only one pi. This is ahieved using the General equations of uniform ladder iruits [3], [4], [5]. Starting from the usual and unavoidale approximations at the design stage and using the mentioned solution for ladder iruits, the paper derives analytial expressions for evaluating the ground fault urrent distriution when the feeding line ontains a ale setion of an aritrarz length. With a permanent elevation of the ground fault urrent level and with an inreasing defiieny of free uran areas for the uilding of large sustations, a orret solution of the prolem of ground fault urrent distriution in various pratial situations gains in importane. OBLEM ESCITION If the feeding line is solely a ale or an overhead line along the whole of its length from the soure station to the supplied station, the alulation of the ground fault urrent distriution in supplied sustation is a routine engineer s jo [7]. rolems appear when a sustation is supplied diretly y an underground ale representing the ontinuation of an overhead line, as shown in Fig. 1. Fig. 1. Typial situation The situation represented in Fig. 1 is typial for the feeding lines in distriution networks and appears as a onsequene of the following fats. The large soure stations supplying distriution networks of ig ities require large areas and are thus uilt outside of uran zones. Lines emerge from them and form a radial network supplying high-voltage distriution stations (e.g. 110/10 kv), situated deep within uran surroundings (the enter of eletri energy onsumption). Eah of the outgoing lines usually supplies two or three suh stations in a suession (or in the so-alled radial distriution system). ELE_opovi_A1 Session 3 aper No

2 C I E 17 th International Conferene on Eletriity istriution Barelona, 1-15 May 003 The urrent whih appears due to the indutive oupling faulted phase ondutor/ground wire (or ale/sheath) in suh situations (Fig. 1) annot e determined y standard alulation proedures [5]. One part of the omponent of the ground fault urrent at the point of disontinuity flows towards the supply soure through the ground. Beause of this the redution of the fault urrent through the grounding system of the supplied station is smaller than in the ase when the feeding line is a ale along the whole of its length, ut is larger than in the ase when it is an overhead line along the whole length. In pratie, however, when determining the fault urrent suh a line is treated either as a ale only, or as a overhead line only. This may result in serious errors when estimating and ensuring the safety onditions in the supplied station. Beause of the strong indutive oupling of the ale/sheath, most of the fault urrent an e injeted into the ground at the plae of disontinuity rather than at the fault loation. When the plae of disontinuity is in a transition station, this phenomenon is desried as the fault appliation transfer effet [8]. EQUIVALENT CICUIT AN NECESSAY ANALYTICAL EXESSIONS General ase Let us assume that a distriution sustation, B, is supplied from the station, A, y a ale whih is an elongation of an overhead line. We will adopt the most omplex ase when the ale has a non-insulated sheath, and the overhead line has a ground wire. The following theoretial foundation Method of symmetrial omponents, riving point tehnique, eoupling tehnique [9] and edution of ladder iruits [5] is used to represent suh a line under the onditions of a ground fault at the sustation B y the equivalent iruit in Fig.. A I ia I a ~ Q a ~ Q Z B Z a a a N Z I e Fig.. Equivalent iruit The symols in the iruit have the following meaning F - fault position (sustation B) V f - auxiliary driving soure at fault loation with the voltage equal to the voltage at the soure station I f - total ground fault urrent I e - urrent injeted into the earth through the sustation grounding grid and through the onneted long I f ~ F B G external grounding ondutor (metal ale sheath(s), neutral ondutors of the low voltage network, metal pipelines, et). I i - urrent soure whih replaes the influene of the indutive oupling etween the faulted phase ondutor and the metal ale sheath(s) I ia - urrent soure whih replaes the influene of the indutive oupling etween the faulted phase ondutor and ground wire of the overhead line Z B - impedane of the power system at fault loation Q, - impedanes of the equivalent pi replaing the influene of galvani oupling of metal ale sheath(s) on the ale setion Q a, a - impedanes of the equivalent pi replaing the influene of galvani oupling of ground wire(s) of the overhead line Z a (Z ) - impedane of the grounding system of station A (B), not inorporating the grounding effets of the feeding line N - footing resistane of the tower at the point of disontinuity of the line G - remote ground. In the ase when the station B has a grounded neutral point(s), the equivalent iruit in Fig. should have an additional ranh ontaining the zero sequene impedane of the loal transformer and onnets the points F and B (Fig ). Aording to [5], the elements representing the ale setion of the line in the given equivalent iruit are determined y the following expressions Q ( ) I f I 1 r (1) i L L k k Z' L k + 1 Z' L k 1 (). (3) In the given expressions r is the redution fator of the ale (usually given as fatory data,) and L the relative length of the ale setion (expressed relative to a one meter length), while the other parameters are defined y the following relations k Z 1 + (4) Z Z Z + Z + (5) 4 ( Z ) 1 Z '. (6) + The parameters Z and represent the elements of the uniform ladder iruit otained y the disretization of the ale sheath as a grounding ondutor. By this, the impedane Z represents the self-impedane of the sheath on a length of one meter, while represents the grounding resistane of the sheath on a length of one meter. Aording to [5] the resistane is given y ELE_opovi_A1 Session 3 aper No

3 C I E 17 th International Conferene on Eletriity istriution Barelona, 1-15 May 003 ρ L' ln, (7) π dh where ρ is the speifi soil resistivity along the ale in Ωm, L' is the ale length in m, d is the outer ale diameter in m and h is the urial depth of the ale, also expressed in meters. For the part of the equivalent iruit of the line overhead setion, aording to [4], [5] the following relations are valid ia ( ) I f I 1 r (8) N k Qa Z N N + 1 k + k (9) N k + 1 a Z N k k (10) Z m r 1. Z s (11) In the given expressions Z s is the self-impedane of the ground wire(s) per span and Z m is the mutual impedane etween the ground wire(s) and the faulted phase ondutor per span, while N is the total numer of spans of the overhead setion. The parameters k and Z are defined y the following relations Z k 1 + (1) Z s Z s Z + Z s +, (13) 4 where is the towers' footing resistane (the average value). The impedanes Z, Z s and Z m are alulated using the formulae ased on the Carson s theory of ground fault urrent return path (e. g. [1]). Sine to estimate the safety onditions it is neessary to determine the maximum of the urrent I e, the impedane Z m should e determined under an assumption that the fault ourred on the phase ondutor whih is the farthest one from the ground wire(s). The equivalent iruit does not omprise the proximity effet of the ale and the grounding grid [6] of the supplied station B. However, it is neessary to ear in mind that under the onsidered irumstanes thus effet is very weak. The reason for this is the fat that due to the strong indutive oupling ale-metal sheath the most part of the ground fault urrent goes into the earth at the point of disontinuity whih is in the ase of any larger ale setion far enough from the station B. In pratial situations the influene of the impedane Z a an e negleted (Z a 0). Thus to determine the urrent I f distriution we an use the equivalent iruit shown in Fig. 3. r (1 r )I f Z Q Fig. 3. Simplified equivalent iruit Aording to the iruit shown in Fig. 3 and using the Kirhhoff s rules we an write a losed system of equations. Its solution gives us I rt I e f Z (1 r ) Z + r ( Q + Z + r 1 Z B ( Q + Z ) + Z r If I e ), (14) where the impedane Z d and the grounding impedane of the ground wire at the pint of disontinuity, Z N, are given y Z N Z N (15) Z N k ( Za 0) Z N. (16) k + k N The oeffiient r t defines the ground fault urrent distriution inluding the grounding effets of the feeding line. At the design stage the impedane Z is often alulated to inlude the grounding effets of the feeding line. In suh ases the redution fator should exlude these effets. We will eliminate them if we adopt Z 0. Then aording to (14) we otain r(1 r ) Z ri r +. (17) Q + Z The oeffiient r i expresses only the influene of the indutive oupling ale/metal sheath(s) and phase ondutor/grounding wire(s) to the distriution of the ground fault urrent I f. The seond addend in the equation (17) oviously represents the inrement of the redution fator of the feeding line in omparison to its value when the feeding line is a ale along the whole of its length. If we assume that the length of the ale setion tends to infinity (Q ), the value of the redution fator r i tends to r. Sine under real onditions the redution fator of a ale is lower than the redution fator of an overhead line (r <r), it an e said that the value of r i is situated etween two limiting values (r <r i <r). In pratie, however, when designing a grounding system of a supplied station, the line under onsideration is often treated as if it were solely a ale or an overhead line along the whole of its length. In the first ase it produes results on the unsafe side (more favorale than in reality), while in the seond ase the estimation of the safety onditions is too severe. What is the value of the deviation from the redution fator of the real ELE_opovi_A1 Session 3 aper No

4 C I E 17 th International Conferene on Eletriity istriution Barelona, 1-15 May 003 feeding line will e seen later from the result of quantitative analysis. Aording to the expression (17) it an e also seen that the redution fator r i depends on the value of the grounding impedane at the plae of disontinuity. With the derease of this impedane, if other relevant parameters remain unhanged (17), the value of the redution fator r i also dereases. If the value of this impedane eomes negligile, the value of the redution fator of the feeding line eomes pratially equal to the redution fator of the ale (r i r ). Speial Cases The presented equivalent iruit and the neessary analytial expression an e simply modified for various speial ases enountered in pratie. When the length of the overhead setion is suh that we an onsider it as infinite, instead of (15) we an use Z N Z. (18) a A line or its setion with N spans an e onsidered as infinite from the point of view of grounding effets if, aording to [4], the following ondition is satisfied N > N a 1 Z + s ln 1+ ln 1 (19) ε where N a - ative line length expressed in the numer of spans ε - desired relative auray, Z Z N /Z (an a priori adopted aritrarily small numer) Z N - grounding impedane of ground wire seen from the point. When the plae of disontinuity is a transition station, the impedane Z is equal to the grounding impedane of this station, or Z Z gt (0) where Z gt denotes the grounding impedane of the transition station. In the ase of a ground wire of steel the expressions (14) and (17) an e simplified y introduing the approximation r 1. When the overhead setion is without a ground wire (r1 and Z ), instead of (14) and (17), we have r t rq + Z + 1 ( Q + ) + Z (1) rq + ri () Q + Ative ale length an e estimated y using (19) and the orresponding parameters. However, sine the ative length L a depends on and, aording to (7), is a funtion of L', this expression annot e diretly applied. Its purpose is to define x (y testing a large numer of numerial examples) in the following semi-empirial formula xρ La ( ε onst), (3) Z /1m where x is an unknown, dimensionless numer, different for different ale ross-setions and urial depths, determined from the ondition that (19) should e approximately satisfied for different values of ρ. At that, we apply in (19) the appropriate parameters (instead on N, N a, Z s and we have L', L a, Z and, respetively). When the length of the ale setion tends to its ative length, aording to () and (3), Q tends to infinite and to Z, so that aording to () it follows rq + lim ri lim r. (4) Q + Q ZC Q ZC On the asis of (4) we an write r i (L' L a ) r. (5) As it an e seen from (5), the redution fator of a suffiiently long ale setion eomes equal to the redution fator of the feeding line that is ale along its whole length. Cales with insulated outer sheath This type of ales, eause the outer sheath is insulated, does not have grounding properties (the fault urrent is not onduted via the sheath into the surrounding ground). This is the reason why it is neessary to modify the iruit shown in Fig. 3. The impedane is omitted ( ), and for the impedanes Q and Z the following relations are valid Q z L' (6) ( 1 + Z ) Z (7) N N where z is the self-impedane of the ale sheath per meter. Then, on the asis of (), (6) and (7) we have r L' z + Z ri L' z + Z. (8) In the ommon ase when the overhead setion regarding the grounding effets may e treated as infinitely long, we have ( 1 + ) Z N Z (9) and when a plae of a disontinuity is a transition station, ELE_opovi_A1 Session 3 aper No

5 C I E 17 th International Conferene on Eletriity istriution Barelona, 1-15 May 003 then it is Z Z gt. (30) The last ase is espeially important for the sustations in the high voltage (e.g. 110 kv) distriution networks. The real values of the relevant magnitudes (L and Z gt ) in these networks are suh that the ondition Z gt /L z <0.05 is satisfied in many ases and the approximation r i r an e used. If the disontinuity point is on the line itself, the redution effet of this type of ales is less pronouned, eause the grounding impedane Z is larger in that ase ( ). The parameters k and Z are defined y the following relations In the mid-voltage distriution networks it is ommon ase that two or more sustations are suessively supplied through the same ale setion. If the ale is with an insulated outer sheath, the redution fator for these sustations is also defined y (8). However, in that ase L' represents the length from to the onsidered sustation, while the grounding impedane Z inludes the influene of the galvani onnetions (through the ale sheath(s)) with the grounding systems of all of these sustations. QUANTITATIVE ANALYSIS At first we shall assume that the sustation is diretly fed y a ale with an uninsulated outer sheath whih is onneted at the other end to an overhead line without any ground wire (Z N and N are treated as infinitely large). This situation is quite ommon in mid-voltage distriution network with oil-filled ales. After the disretization of the ale sheath ased on the following ale data: outer diameter d44 mm and experimentally determined Z m /Z s 0.8 and Z s ( j 0.00) Ω, we performed the alulations and for differential soil resistivity otained the results displayed in Fig. 4. disontinuity [8]. Now we shall assume that one ale of a voltage 110 kv supplies a distriution station with a transformation 110/X kv, while, at the other end, the ale is onneted to the overhead setion of the feeding line. The ale has three lead sheaths and their external and internal diameters are equal: 54.6 mm and 51.4 mm, while the value of the redution fator of the ale, aording to the manufaturer s data, is equal to 0.. For the overhead part of the line we assume that in one ase it is equipped y a steel ground wire, so that it an e taken that r 1, while in the other ase we have a ground wire ACS 95/55 mm with a redution fator of r The alulation results of the feeding line redution fator versus ale length for the first and the seond ase are shown in Figs. 5 and 6, respetively r i Zgt 0. Ω Zgt Ω Zgt 1 Ω Zgt 0.5 Ω Zgt 0.1 Ω Fig. 5 Cale with insulated outer sheath in the ase r1 0.8 r i Zgt Ω L (km) r i 100 Ωm 0.6 Zgt 1 Ω Ωm 40 Ωm 0.4 Zgt 0.5 Ω Ωm 0. Zgt 0. Ω Zgt 0.1 Ω Fig. 6 Cale with insulated outer sheath in the ase r0.675 L (km) L' (km) Fig. 4. Cale with uninsulated outer sheath in the ase r1, Z N, N. As the ale length L' inreases, it is evident that the redution fator r i tends to the value it would have if the ale were laid along the whole length of the feeding line. Certainly, for the equal ale length, the effet would e still more pronouned if a transition station were at the point of If we assume that the length of the ale setion is 3 km (the average length of the ale lines in the 100 kv network of Belgrade is approximately 4 km), the inrease of the redution fator r i in omparison to r is for the first ase (Fig. 5) 6.4%, 13%, 49%, 110% and 195%; while for the seond ase (Fig. 6) it is 4%, 10%, 3%, 71% and 18%. The asolute value of the grounding impedane of stations in 110 kv distriution networks larger than 0.1 Ω ( Z gt >0.1 Ω) is rare and may e expeted only in the ases of unfavorale ELE_opovi_A1 Session 3 aper No

6 C I E 17 th International Conferene on Eletriity istriution Barelona, 1-15 May 003 natural onditions (high soil resistivity). However, aording to the presented alulation results one an gain a gloal insight into the redution fator r i in omparison to the ale redution fator when the impedane Z gt has different values. On the asis of the given results the following an e onluded. The safety onditions ased on the ale redution fator r would give more favorale results (lower values of touh and step voltages). This means that it ould happen that the required safety onditions in the supplied station would not e met. It should e stressed that the standard measurements of safety onditions, whih are mandatory efore a newly uilt station is put in operation, do not omprise hek of the redution fator value of the feeding line (e.g. []). CONCLUSIONS The paper presents a diretly appliale and pratial method for the determination of the ground fault urrent distriution in sustations supplied y a ale setion of the feeding line ontaining at least one overhead setion as well. The alulations are very simple and take into aount all relevant data availale at the design stage. EFEENCES [1] Current uring Two Separate Simultaneous Single hase Line-To-earth Short Ciruits and artial Short- Ciruit Currents Flowing Through Earth, International Standard, ref. No. CEI/IEC 909-3, [] IEEE Guide for Safety in Sustation Grounding St. d [3] Lj.M. opović, 000, Effiient edution of Fault Current Through the Grounding Grid of Sustation Supplied y Cale Line, IEEE Trans. ower elivery, 15, [4] Lj.M. opović, 1998, ratial Method for Evaluating Ground Fault Current istriution in Station, Towers and Ground Wire, IEEE Trans. ower elivery, 13, [5] Lj.M. opović, 1997, ratial Method for Evaluating Ground Fault Current istriution in Station Supplied y an Inhomogeneous Line, IEEE Trans. ower elivery, 1, [6] Lj.M. opović, 1993, ratial Method for the Analysis of Earthing Systems with Long External Eletrodes, IEE ro. C, 140, [7] B. Thapar, S. Madan, 1981, Current for esign of Grounding Systems, IEEE Trans. ower Apparatus and Systems, 100, [8] J. Villas,. Mukhedkar, V. Fernandes, A. Magalhaes, 1990, Grounding Grid esign of a Transition Station System - a Typial Example of Fault Transfer, IEEE Trans. ower elivery, 5, [9] S. Soral, V. Costa, M. Campas,. Mukhedkar, 1988, imensioning of Neary Sustations Interonneted Ground System, IEEE Trans. ower elivery, 3, ELE_opovi_A1 Session 3 aper No