kimbark recierre monopolar

6. The wvet switching surge strength of station post insula- Referencestors in the 1,300 to 2,100 BIL range, both positive and 1. THE FLASHOVER STRENGTH OF EXTRA-HIGH-VOLTAGE LINE AND

has been found to slightly exceed that of the wet STATION INSULATION, J. G. Anderson, H. E. Fiegel, J. H. Hagenguth,negaive,ak A. F. Rohlfs. Paper No. 401, CIGRE, Paris, France, 1962.2. HOW THE SWITCHING SURGE FAMILY AFFECTS LINE INSULATION,

7. The negative dry switching surge strength of station post J. W. Kalb. IEEE Transactions on Power Apparatus and Systems,insulators can be greatly reduced with gaps, while the positive vol. 82, Dec. 1963, pp. 1024-33.

3. AMERICAN STANDARD FOR MEASUREMENT OF VOLTAGE IN DI-dry switching surge strength is basically unchanged. ELECTRIC TESTS. Standard C68.1, American Standards Association,8. Much work still remains to be done before switching surge New York, N. Y., 1953.

values on st n i4. AMERICAN STANDARD TEST METHODS FOR ELECTRICAL POWERvalues on station insulation can be properly defined and stand- INSULATORS. StandardC29.1, American Standards Association, 1961.ardized. 5. REPORT OF SPECIAL COMMITTEE ON RAINFALL RESISTIVITIES,

9. The insertion of larger diameter units or metallic rain IEEE Committee Report. IEEE Transactions on Power Apparatusand Systems, vol. 83, 1964, paper 64-42.

shields into a standard EHV vertical suspension string will 6. SwItCHING SUG ISLTO LeV O REIN A6. SWITCHING SIJRGE INS1JLATION LEVEL OF PORCELAIN INSULATORmaterially raise the wet negative switching surge flashover STRINGS, D. E. Alexander, E. W. Boehne. Ibid., paper 64-38.value and the over-all withstand. 7. United States Patent NTo. 2,884.479, Washington, D. C.

Suppression of Ground-Fault Arcs on Single-Pole-Switched EHV Lines by Shunt ReactorsE. W. Kimbark, Fellow IEEE

Summary: Arcing line-to-ground faults isolated by single-pole 1. Before extinction of the fault arc, it feeds current to the faultswitching are maintained by capacitive coupling between the and maintains the arc.faulted and unfaulted phases. Such faults are difficult to ex- 2. After the arc current becomes zero (as it does twice per cycle),tinguish on long EHV (extra-high-voltage) lines because the fault the coupling causes a recovery voltage across the arc path. Ifcurrent is proportional to both length and voltage of the line, the rate of rise of recovery voltage is too great, it will reignite theA promising remedy consists of neutralizing the capacitive cou- arc.pling by shunt reactors, which are required anyhow on many linesfor compensating the normal charging current. Of the two types of coupling, the capacitive coupling is the

more important. Its importance increases with increase ofSingle ta-c tie lines between power systems ordinarily circuit voltage, and it is the only type of coupling consideredSingle-circuit inc dtal imsbtenpoeythispdaprl..'

cannot be regarded as having firm-power capability because m detarl nthespaper.3-pole opening and reclosing cannot be accomplished quickly The arc on the faulted conductor after it has been switchedenough to retain synchronism. Because about 90% of the off S called the secondar are. Extinction of the secondaryfaults on high-voltage steel-tower transmission lines without arc depends on its current, recovery voltage, length of arcoverhead ground wires are of the one-line-to-ground type, path, wind velocity, and perhaps on other factors. Recoverynearly all of these being transitory, it would seem reasonable voltage and length of arc path both increase with circuit volt-nearlyate ofthesebeingtrans cpbity wofuc a tealinebyi age and thus the effect of one factor may partially offset theto rateother. This leaves the magnitude of the secondary arc cur-stability limit for one-line-to-ground faults, provided that such ot a s the m antide of these are cur-

> . ~~~~rent as the most significant index of whether the arc will befaults could be successfully cleared and reclosed by single-pole self-extinguishing. For given interphase capacitance, theswitching. secondary arc current is proportional to the circuit voltageEffective single-pole switching would increase the reliability

a

of a line approximately as much as would the addition of over- and to the length of the line section that is switched out.* ~~~~~~~~~~~~~Hence,the length of section on which single-pole switching canhead ground wires and at a much lower cost. 2

be employed successfully is inversely proportional to the cir-Arc Extinction with Single-Pole Switching cuit voltage. The situation is unfavorable on EHV lines be-When one conductor of a 3-phase line is opened at both cause the circuit breakers are expensive, and it would be

* * l l ~~~~~~~~~~~desirableto make the sections even longer than is customervends in order to clear a, ground fault, this faulted conductor is d.. . . 1 ~~~~~~~~atlower voltages. At 500 kv, the estimated permissiblecapacitively and inductively coupled to the two unfaulted a l.A

conductors, which are still energized at approximately nornmal length iS about 50 miles.circuit voltage and carrying load current. This coupling has Proposed Method of Arc Suppressiontwo effects:

Since coupling of the faulted conductor to the sound con-ductors through the shunt capacitive reactance between phases

Paper 64-56, recommended by the IEEE Transmilssion and Distri- istecifcueo h eonayaccretadrcvrbution Committee and approved by the IEEE Technical Operations voltage, it is proposed to neutralize this capacitive reactanceCommittee for presentation at the IEEE Winter Power Meeting, by means of lumped shunt inductive reactanlce, equal andNew York, N. Y., FVebruary 2-7, 1964. 1Manuscript submitted...November 4, 1963; made available for printing December 10, 1963. opposite to the capacitive reactance. The proposed schemeE.~~~~~~~~~~~~~~~~W.K.BRswth onvle oe diitainot is analogous to the use of a Peterson coil, and both might wellland, Greg. be called ground-fault neutralizers. However, the scheme

MARSCH 1964 Kimbarl'~- Suppression of Arcs on Single-Pole-Switched EHV Lines 285

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now proposed would neutralize the capacitance between Fig. 1. Equivalent EACH (B;-B )/3 EACH B- B'phases, amounting to Ci-Co per phase; that is, the difference circuits of the ac a b c

between the positive-sequence and zero-sequence capacitances, shunt capaci- JI\L B'IB;lIwhereas the Peterson coil neutralizes the capacitances to tancesofa3-phase TTT ',ground, 3Co. A further difference is that, whereas one Peter- transmission line b a bj c

son coil can suppress ground faults anywhere on an entire Bo Bn8 _,transmission network, the reactors used with single-pole Txfswitching must be used on every transmission line too longfor secondary arc extinction without them and must be -rswitched with the line. Thus, a large number of reactors (A) (B) (C)might be required.

However, many EHV lines require shunt reactors for whollyor partly compensating the normal, positive-sequence chargingcurrent. By proper connection, these reactors can be made nection of Fig. 2(C), hence the analysis to be made of theto serve the additional purpose of ground-fault suppression at latter is applicable to the former also.a moderate additional expense.

COMPARISON OF SCHEMES

Connection Schemes and Susceptances of Shunt Reactors The aggregate reactive-power rating of the group of shuntreactors is the same in the schemes of Figs. 2(A), 2(B), and

EQUIVALENT CIRCUITS OF SHUNT CAPACITANCES 1(D), being that required for shunt compensation under nor-To understand the ways in which shunt reactors may mal conditions. In the 4-reactor scheme of Fig. 2(C), the

be connected, one must first know the equivalent circuits aggregate rating of the three main reactors has that samefor the shunt capacitances of a 3-phase line. The most gen- value. In addition, there is the fourth or grounded reactoreral equivalent circuit for the capacitances between four con- which is energized only during a line-to-ground fault andductors (line conductors a, b, c, and ground) has a branch join- which, for high degrees of shunt compensation, has a momen-ing each pair of conductors, Fig. 1(A). The three capaci- tary rating equal to only a small per cent of the aggregatetances of the delta terminating on a, b, and c can always be rating of the three main reactors.replaced by an equivalent Y as in Fig. 1(B). These two cir- If the cost of reactors were directly proportional to theircuits are valid for both balanced and unbalanced lines, ratings, all schemes would cost approximately the same.though the labels on the capacitances are valid only for bal- But, because the cost per kilovar decreases with increasinganced lines. For balanced lines, the 4-branched star circuit rating, the scheme having the fewest and biggest reactorsof Fig. 1(C)is also correct. costs the least, provided that the reactors are not too bigThe capacitances of all these circuits are labeled in terms for shipping and handling. The number of high-voltage

of the zero-sequence capacitive susceptance Bo' or reactance bushings also significantly affects the cost.X0' and the positive-sequence capacitive susceptance B1' or The numbers of reactors and bushings required are asreactance Xi' of the line. The correctness of the labeled listed, assuming single-phase construction except for Fig.values is most readily checked in Fig. 1(B), as follows: If zero- 2(D).sequence voltages are applied from a, b, c to ground, chargingcurrent flows only in the grounded capacitances, each of which Scheme of Figures 2(A) 2(B) 2(C) 2(D)should therefore have susceptance Bo'. If positive-sequencevoltages are applied, the grounded Y and the ungrounded Y Number of:are effectively in parallel. Hence, the total susceptance per Reactors 6 6 4 1phase must be B1', and the ungrounded capacitances must High-voltage bushings 9 6 3 3make up the difference Bi'-Bo'. In Fig. 1(C), with positive- MIedium-voltage bushings 0 3 0 0sequence voltage applied, currents are confined to the Y- Low-voltage bushings 0 0 4 0connected capacitances, which should therefore have re-actances X1'. With zero-sequence current 1o' applied, the On these grounds, the 3-phase reactor of Fig. 2(D) is pre-zero-sequence voltage is ferable if it is not too big. If it is, the 4-reactor scheme

of Fig. 2(C) is the next choice. In both these schemes,V0 =jXo'Io' =jX,'I,' =jX '3Io' (1) however, the degree of shunt compensation cannot bewhence switched without losing the correct neutralization of inter-

phase capacitance for fault suppression. The 6-reactor2 (2) scheme of Fig. 2(B) has the advantage that the grounded

3 reactors can be switched on or off or their reactance variedand without affecting the neutralization.

The 6-reactor scheme of Fig. 2(A), as compared with thatBr3B01B1' (3) of Fig. 2(B), requires three additional high-voltage bushingsnB1'-B0' and better insulation for the delta-connected reactors, and it

has no compensatory advantages. The scheme of Fig. 2(A)CONNECTIONS OF REACTORS will be dismissed, therefore, from further consideration.The shunt-reactor schemes of Figs. 2(A) through 2(C) are

analogous to the equivalent-capacitance circuits of Figs. 1(A) REQUIRED SUSCEPTANCES OR REACTANCESthrough 1(C), respectively. Fig. 2(D) indicates a 3-phase re- Because the reactors are in parallel with the line capaci-actor having mutual reactance Xm between phases. Its equiv- tances, it is more convenient to express their values in termsalent circuit in Fig. 2(E) has the same form as the star con- of susceptance B than reactance X. Unprimed letters B and

286 Kimbark-Suppression of Arcs on Single-Pole-Switched EHV Lines MARCH 1964


X will be used to denote inductive susceptance and reactance, which, for a typical EHV line without ground wires, is aboutand the corresponding primed letters B' and X' stand for 3070. If a higher degree F of shunt compensation is desired,the respective capacitive quantities. it may be obtained by the addition of grounded reactors hav-The requirements are: ing the susceptance given by equation 14. For 100% shunt

compensation F=lj) this susceptance is simply B'1 o =Bo'.1. For fault suppression by neutralization of the interphase The grounded reactors play no part in fault suppression.capacitances, For the 4-reactor scheme, Fig. 2(C), equations 9 and 5, yield

B,-Bo =cw(Cl-Co) = Bo'-Bo' (4) Bp = FBI' (16)

2. For shunt compensation of degree F, while 10, 6, 5, 4 yield:Bi =FwC,=FB1' (5) 3B1B11FB1

Bn= 3FB'[B(1F)B] = Bn'[I -(1 -F)BI,B0'] (17)From equations 4 and 5, it follows that Bl' -Bo'Bo=Bo' -(1 -F)B1' (6) Equation 16 shows that the phase reactors furnish the desired

The required susceptances or reactances of the reactors are degree F of shunt compensation. The minimum degree,> . . - l.. . . l ~~~~~~however,iS given by equation 15. At this degree Bn, givenfound by using equations 4, 5, and 6 in conjunction withthe appropriate pairof equations which follow, by equation 17, vanishes, showing that the phase reactorsthe susceptan of t eators in fi.( itrmso must have ungrounded neutral. At any greater degree, B,r a te suseptances are is positive and the neutral reactor is required for faultzero- andl positive-sequlence susceptances are

suppression. Its susceptance depends on F, as shown byBg= Bo (7) equation 17. For F= 1, it becomes

B.= B1-Bo (8) 3Bo'B,_Bnl0B -B=nB,' (18)In Fig. 2(C), the susceptances are B,'-Bo'B B,B(9) The corresponding reactance is

3BOB,~~ ~ ~ ~ ~ ~ ~ Y y,1xlB,,, oB (lO) Xnl '° -=t Xn' (19)

B, -Bo 3

and the corresponding reactances areHow Shunt Reactors Suppress Fault Arcs

Xp=X(11) The manner in which a Peterson coil suppresses arcing line-

and to-ground faults on an otherwise-ungrounded network is wellknown from both the theoretical and practical standpoints.

Xn XO-l 3BoB (12) Shunt reactors operate on the same principle when suppressing3 3BoBI line-to-ground faults on conductors isolated by single-pole

For the 6-reactor scheme, Fig. 2(B), equations 8 and 4 yield: switching from the rest of a well-grounded network. In bothcases, parallel resonance between distributed shunt capaci-B,=B,'-B0' (13) tance of one or more lines and lumped shunt inductance is

while 7 and 6 yield employed.As previously stated, the addition of the resonant shunt in-

sB=B,'-(1 -F)B1'=FB1t-B,, (14) ductance decreases (1) the current in the fault and (2) the

Equation 13 shows that the ungrounded reactors must res - voltage across the fault path after the current ceases.onate with the interphase capacitive susceptance. These Theoretically, in a lossless parallel LC (inductance-capaci-reactors provide a degree of shunt compensation tance) circuit, the net current can be made zero by proper

B,' -B,' Bo',

11 tuning. Actually, in either form of resonant ground-faultFmin =1-_ = 1_l-- (15) suppression, the fault current does not become zero because

B, B1' XO' of (1) imperfect tuning, (2) losses, or (3) harmonics. How-ever, the neutralized current is only 10% to 20% of the un-neutralized, capacitively fed fault current. The lower valueseems probable with single-pole switching.The parallel LC circuit continues to oscillate after the fault

Bu/3 p Bp BU arc is extinguished. In a perfectly tuned, lossless LC eircuit,u Bu Bu Xp Xp the frequency and amplitude of the free voltage oscillation

v ;89Bg ABg Bn Xn would exactly match those of the forced oscillation existing| BgiBg~B0 i-8 i before extinction of the arc. Consequently the faulted con-

Fig. 2. A, B, C, _ ductor would remain at ground potential after extinction ofD - Possiblei the arc, and there would be no recovery voltage across theconnections of (A) (B) (C) arc path. Actually, there would be some difference in fre-shunt reactors

for fault sup- ~~~~~~~~quency due to imperfect tuning and some decrease of ampli-pression and A4 EACH tude caused by losses. Consequently, the amplitude of thecomenaton XmD gXsXm power-frequency recovery voltage would slowly increase.

Of charging AX,xgg; Mroe,because a parallel resonant circuit has unitycurrent. E_ tX Xx5 TXS power factor, the instantaneous recovery voltage increasesEquivalent cir- - -very slowly in the first quarter cycle after arc extinction at a

cuit of D (D) (E) normal current zero, thereby making arc reignition unlikely.

MARCH 1964 Kimbark-Suppression of Arcs on Single-Pole-Switched EHV~Lines 287


Fig. 3. Equiva- EACH Bl-B EACH B-sB Information on the unneutralized secondary arc currentlent of source LI that permits successful reclosure has been compiled byand faulted line SOURCE Maikopar2 from installations of single-pole switching in manysection, isolated _2E - - parts of the world. It indicates that with 0.4-second deadby single - poles- - - time, there is a high probability of successful reclosure if the

5wimpedanc berinsg 1- - - secondary arc current does not exceed 18 amperes. How-

neglected C.B. Bo BO B0 If ever, the actual secondary arc current without fault neutraliza-1 Vf tion may be as high as twice the value computed from the

.- - 1 IFAULT voltage and shunt capacitive susceptance. Therefore, wemay take the value of 9 amperes of so-computed unneutralizedsecondary arc current as the maximum permissible value.This value agrees well with the 5 to 10 amperes fault current

By contrast, conditions in the capacitively fed, unneutral- permissible on an ungrounded system.ized secondary fault arc make extinction more difficult. The As no information has been found on maximum permissiblefault current and the a-c recovery voltage are in quadrature, neutralized secondary arc current for single-pole switching, theso that when the current is broken at a natural zero, the alter- value obtained from Peterson coil experience (150 amperes)nating voltage is at its crest value. Consequently, there is a may be used as a rough guide. Even if this be reduced to 75d-c component of voltage due to charge trapped on the isolated amperes to give a factor of safety, and if it be assumed thatconductor. The resultant voltage of the a-c and d-c com- neutralization reduces the secondary arc current to only 20%ponents is zero at the moment of interruptions, giving a com- (instead of 10%) of its unneutralized value, the maximum per-pletely offset voltage wave. Half a cycle later, however, the missible lengths of section of a typical 500-kv line withoutinstantaneous recovery voltage reaches twice the crest value ground wires: computed in the Appendixes, are:of its a-c component. Delayed restriking of the arc is prob- 1. Unneutralized, 45 miles.able. 2. Neutralized, 1,800 miles.

Because of the low recovery voltage and high power factorof the neutralized fault arc, the current that can extinguish The former length is uneconomically short, whereas theitself is 15 to 30 times higher than in an unneutralized arc. latter is much longer than would be used in practice.

Arc Current That Can Be Extinguished Conclusions

In order to estimate the length of line section on which It appears from theory and from experience with Petersonsingle-pole switching can successfully clear line-to-ground coil grounding that the use of shunt reactors for neutralizingfaults, both with and without inductive neutralization, we can the interphase shunt capacitance Cl-Co of an EHV transmis-utilize (1) the values of arc current that are self-extinguishing sion line could increase, by a factor of 40 or more, the lengthon ungrounded systems and systems grounded through Peter- of line on which line-to-ground transitory faults could be suc-son coils and (2) the values of unneutralized are current on cessfully cleared by single-pole opening and 30-cycle reclosure.lines having successful single-pole switching. Moreover, the same shunt reactors would supply part of the

shunt compensation that is usually needed on EHV lines.PETERSON COILS Thus, fault suppression would be provided at a small addi-

Extensive experience with Peterson coils' has shown that tional cost. The scheme merits field tests of its effectiveness.the maximum-fault arc currents that are self-extinguishing are: Successful clearing of transitory line-to-ground faults would

greatly improve the reliability of EHV lines without grouind1. Unneutralized, 5 to 10 amperes.2. Neutralized, about 150 amperes.

Experience has shown also that faults are successfullycleared with the Peterson coil detuned by 10% or 20%.There is still a resonant circuit which decreases the rate of i.Fig.3applica- b AND C

rise of recovery voltage, even though the frequency of that able to first set of '/3Bs-BO '/3(B-Bcircuit differs somewhat from the power-system frequency. emf's BoIn a system grounded through a Peterson coil, the detuning O.5E,( T2B B.arises from switching lines on or off. This cause of detuning I B B -0Vf Awill not occur with the scheme herein proposed in which the IULTneutralizing reactors would be switched with the associatedline sections. The cited fact shows, however, that, sincetuning is not critical, the reactors need not be tunable, andno allowance need be made for differences between capaci-tances of the three conductors of the untransposed line.c

SINGLE-POLE SWITCHING 1 IB'' 1IBThere are two factors in single-pole switching that differ jO.B66E|' °0 3B0 B' B-BAfrom Peterson~coil operation: l i FAUL |aBB

1. The primary arc current is greater than the secondary arc - I_ ncurrent and may, therefore, establish greater initial ionization. Fig. 5. Simpli- jo.866E~ "k. , ABB lBFBoh2. The time in which the secondary arc is extinguished is im- fication of Fig. T B0 Mj Bo B',_-B' 7portant so that reclosure rapid enough to give a reasonably high 3 applicable toI ll lstability limit will be successful. 2nd set of emf's b

288 Kimbark-Suppression of Arcs on 6jngle-Pole-$witched EHV Lines MARCH 1964


Fig. 6. Equiva- Tl l -E B-' - lEL-Bo1/B1 (22)lent circuit for 2B11+Bol 2±Bo1/Bl'finding the volt- 2B8age across the E 1,'12/(B-B )+2B Comparison of equations 21 and 22 shows that shunt compensa-grounded reac- - 2 1@ 1 3 1 o tion by grounded reactors only causes the recovery voltage to betor ofuhed 4-reac- higher than it would be with no shunt compensation.tor of the 4-reac- Jktor scheme dur- In Vn Secondary Arc Currenting an isolated This is the current through the closed fault switch of Fig. 4,line - to -ground - which short-circuits the lower part of the voltage divider. It is

fault -E 2

= (-jE/3)[(B1 -Bo') -(B1-Bo)] (23)

wires and would make it reasonable to rate the transmission The fault current becomes zero under the same condition undercapability of single-circuit a-c ties by their transient stability which the fault voltage became zero; namely, by correct neu-limits for such faults. tralization of Bl' -Bo' by B1 -Bo.A more detailed analysis of the subject appears in the Without neutralization, the fault current is

Appendixes. Appendix I derives equations for the secoindary If= ( -jE/3)(B1'-Bo') (24)arc current and the recovery voltage of lines with and without It is not affected by grounded shunt reactors.neutralization and for the voltage and reactive power ratingsof the shunt reactors. Appendix II computes numerical 6-Reactor Schemevalues of these quantities for four typical 500-kv lines. Voltage of the neutral of the ungrounded Y-connected reac-

tors-6-reactor scheme with respect to ground during isolatedline-to-ground fault-is dealt with in this section.

Appendix 1. Circuit Analysis for Single-Pole During the fault, voltage -E/2 of the real set is impressed onSwitching the ungrounded reactors, marked (2/3) (B1 -Bo) in Fig. 4. The

marked value resulted from a simplification of the connection ofExcept as noted, longitudinal voltages and impedances are neg- two reactors from combined phases b and c to neutral point n';

lected. Consequently, the several shunt elements-the dis- one reactor thence to phase a, which is grounded by the fault.tributed capacitance, the reactors when used, and the line-to- Thus the voltage from n' to ground isground fault when present-may be regarded as in parallel;see Fig. 3. The 6-reactor scheme (grounded Y and ungrounded Y) Vn E 2E=_ (25)is assumed except when noted to the contrary, and the line capaci- 2 3 3tance is represented by a like connection. The source is assumedto have balanced, positive-sequence electromotive forces (emf's): where E is the line-to-neutral voltage of the source. Vn is notEa = E, Eb =aE =-0.500E -jO.866E, and E, =aE- = 0.500E+ affected by the imaginary components of source emf. EquationjO.866E. 25 shows that the neutral bushings of the three ungrounded reac-The emf's may be resolved into two sets: the real components tors would be momentarily subjected to a third of normal line-

and the imaginary ones. The first set is Ea'= E, Eb'= E,'= -E/2. to-neutral voltage.The second set is Ea"=O, Ec'= -Eb'=jO.866E. Simplificationof the circuit on which the first set acts yields Fig. 4, and simplifi- 4-Reactor Scheme Isolated Faultcation of the circuit on which the second set acts yields Fig. 5. Voltage across the grounded reactor of the 4-reactor schemeFrom the symmetry of the circuit of Fig. 5 with respect to phase during an isolated line-to-ground fault is described by equa-a, it is apparent that phase a is at ground potential. Therefore, tion 26. The circuit for real components of voltage as inthere is no voltage across the fault when the fault path is open Fig. 4 but with the reactors connected as in Fig. 2(C) simplifiesand no current in it when closed. Thus, the second set of emf's to the circuit of Fig. 6. The voltage across the grounded reactor iscontributes nothing to the fault current or recovery voltage andmay be ignored. In computing fault current and voltage, we VE= E 2B1 EBineed consider only the circuit of Fig. 4, disregarding the branches 2 (3B1+Bn) 3B1+Bndrawn in broken lines, which are directly across the source.

EX,, E(Xo-Xi) (26Voltage Across Switch Symbol X3 3XX (26)XI +3X,, 3X0The source-frequency recovery voltage across the arc path

after the secondary arc is extinguished is the voltage across the where X = (X0-X1)/3.switch symbol marked "fault" in Fig. 4 when the switch is open.1 rta* 1- 1 1 1- '1 t P ~~~~4-Reactor Scheme UnisolatedThe voltage -E/2 is applied to a voltage divider, each part ofwhich has capacitance and inductance in parallel. The voltage Voltage across the grounded reactor of the 4-reactor schemeacross the lower part of it is during an unisolated line-to-ground fault before the circuit

breakers open is calculated herewith.Vf E (2/3)[(B='-B0) (B1-B0)] The calculation consists of two parts. First, the voltage V.

f 2 (2B1'/3+Bo'/3)-(2B1/3+BO/3) across the grounded reactor is expressed as a fraction of the zero-

E(B1'-B0')-(B1 -B0)(2B1'+B01)-(2B1-B0) (20)

This voltage vanishes with proper neutralization of B1'-B0' by Table I. 500-Ky 60-Cycle 3-Phase Lines Used for Illustrationan equal B1 -B0 supplied by each ungrounded reactor.Lienmr1 2 3The voltage with no neutralization of interphase capacitance neum r1 2 3

is found by putting B1-B0=0. It is Number of Conductors per Phase 2 1 2Name of Conductor Falcon Special Chukar

Vf= E(B,Bo) ~~~~~~~~(21)Outer Diameter of Conductor, Inches 1.545 2.50 1.602Bo-(2B11+Bo') Separation Between Conductors of

Same Phase, Inches 16 - 60wherein Bo is furnished by the grounded reactors. -With no shunt Spacing Between Centers of Adjacent--.compensation whatever, B0=0 also, and Phases. Feet 37 33.5 40.7

MARCH 1964 Kimbarkc-Suppression of Arcs on Single-Pole-Switched EHV Lin-es 289


Table II height of the conductors above ground is assumed to be 50 feet,corresponding to a minimum ground clearance of 35 feet. In

Line Number order to determine the effect of ground wires, similar computations1 2 3 4 were made for a variant of line 2:

Postive-Sequence Shunt Ca- Line 4 is like line 2 except that two ground wires are added.pacitive Susceptance, Bi', They are assumed to be 33.5 feet apart and 16.8 feet above theMicromhos/Mile 6.65 5.61 7.52 5.61 line conductors.

Zero-Sequence Shunt Capaci- Results of the computations are given in Table II. The ratiotive Susceptance, Bo' Micro-tivehusceptane Bo' 59M3.92c5. B0'/B1' is very nearly the same for each of the three basic de-mhos/ Mile 4.59 3.92 5.19 4.42

Ratio Bo'/B1 ' 0.69 0.70 0.69 0.79 signs, being about 0.7. The addition of ground wires increasesNormal Charging Current, Am- this ratio to approximately 0.8, but ground wires presumably

peres/Mile 1.92 1.62 2.17 1.62 would not be used with single-pole switching.Normal Charging ReactivePower, Mvar's/Mile 1.66 1.40 1.88 1.40

Current in Secondary Arc, Am- Nomenclatureperes/Mile Without Neutrali-zation 0.20 0.16 0.22 0.12 a=exp(j2w7r/3) =,(I +jV\/3)/2

Normal-Frequency Recovery B = 1/X= inductive susceptance of the shunt reactors of a sectionVoltage, Kv, Without Neu- of Iinetralization 33 32 33 22

Length of Line, Miles, for which Bo = zero-sequenceSecondary Arc Would Be Self- B, = positive sequence

Extinguishing: B = inductive susceptance of each grounded reactor of theWithout neutralization, 9amperes 45 55 40 78 6-reactor scheme

With Neutralization, 75 am- Bgloo = value of Bo required for F= 1peres 1,850 2,250 1,650 3,300 B =inductive susceptance of each ungrounded reactor of

Grounded Reactor of 4-Reactor the 6-reactor scheieSchemeVoltage Vn Ky for F=1: Bn= inductive suseeptance of the grounded reactor of theDuring Isolated Fault 30 29 30 20 4-reactor schemeDuring U nisolated Fault, 29 28 29 20 Bn100=value of Bn required for F= 1Z1/Zl= 22-9- - 30 B =inductive susceptance of each ungrounded reactor ofZoIZ1={2- 3

3 54 52 54 - the 4-reactor schemeMomentary Rating Qn, Kvar's/ B'=wC =distributed capacitive suseeptance of a section of line

Mile for F=1; Bo'= zero-sequenceDuring Isolated Fault 40 33 45 26 B'= positive-sequenceDuring Unisolated Fault,

( 1 38 32 43 25 Bn' = capacitive suseeptance of grounded leg of 4-branched

ZO/Z= 2 130 116 144 58 star equivalent circuit3_______130_____________116_____________ 144________________ C = distributed shunt capacitance of a section of lineC0 = zero-sequenceCl = positive-sequence

E = rms positive-sequence line-to-neutral emf of the sourcesequence voltage of the line at the point where the group of reac- E,, Eb, E, = line-to-neutral phase emf'stors is connected. It is Ea,t Eb', E,'= real components of Ea, Eb, E,

EaVit3B Eb, E,' = imaginary componentsV. 3Bn (27) F=B1/B,'=degree of shunt compensation, per unitVo B1+3Bn Fm.n=at least degree of shunt compensation when reac-

tors are used for fault neutralization.Second, the zero-sequence voltage Vo is expressed as a fraction If= rms current of secondary are, isolated line-to-ground fault

of the normal line-to-neutral voltage E. Now we must take into Io' = zero-sequence charging current of lineaccount the series impedances which were neglected when the v 1fault was isolated. Use of the well-known equivalent circuit of a j =raline-to-ground fault-series connection of the three sequence net- Q 4rearetve power ceonsumed by neutral (grounded)reautor of

works-gives: ~~~~~~~~~~~~~the4-reactor scheme during a line-to-ground faultworks-gives: Vf=rms source-frequency recovery voltage across path of sec-Vo zo Zo/Z1 ondary areE Z1 -j--Z2 -J-Z( 2+Z0/Z1 (28) V,,= rms source-frequency voltage from neutral of reactor group

to groundat the point of fault. Elsewhere V0 is less. The highest V0 at the Vo = zero-sequence voltage of line at shunt reactors or at the faultfault is obtained if the fault is distant from a grounding point, in X = = inductive reactance of shunt reactors, with subscriptswhich case Z0/Z, is substantially that of the line itself. The high- as for B. In addition,est Vo on the shunt reactors occurs if the fault is near the reactors Xs = self-reactance per phase of 3-phase reactorand far from the grounding points excluding the reactors, and Xm= mutual reactance between phases of 3-phase reactorthis condition is assumed in some of the calculations of V, in X' = 1/B' = shunt capacitive reactance of line, with subscripts asAppendix II, Z0/Z1 being taken as 2 or 3. However, as some for B'reactors may be near grounding points, V, is calculated also for Z = impedance of system seen from point of fault

Z/ = 1. Z= zero-sequenceZ, = positive-sequence

Reactive Power in Grounded Reactor of 4-Reactor Scheme Z= negative-sequence1 2,-co= 2rf=angular frequency, in radians per second

Q,. V.l9B. (29)Qn Vmo(9 References. . . ~~~~~~1.NEUTRAL GROUNDING IN HIGH-VOLTAGE TRANSMISSION (book),

Appendix 11. Numerical Calculation for Typical R. Willheim, M. Waters. Elsevier, Amsterdam, The Netherlands,- ~~500-Kv Lines 1956, esp. pp. 612-13 and 631.

2. MINIMUM TIME OF AUTOMATIC REcLosING, A. S. Maikopar.Description of Lines Electric Technology, UJ.S.S.R., Pergamon Press, New York, N.Y.,

Computations of normal charging current and reactive power, 1960, pp. 302-15, esp. Fig. 3, p. 311.Of secondary fault current and recovery voltage for a line-to- 3. SINGLE-PHASE SWITCHING OF TRANSMISSION LINES USING REAC-ground fault without neutralization,- and of the shunt compensa- TOES FOR EXTINCTION OF THE SECONDARY ARC, N!. Enudsen. Papertion required for fault neutralization are made for three different No. 310, CIGRE, Paris, France, 1962.designs of 500-kyr lines described in Table I. Note: t:This last reference was called to the author's attention by aNone of the lines in Table I has ground wires, and the average reviewer after submission of the present paper to the IEEE.

290 KimbaLrk-SUPPreSSion of Arcs on Single-Pole-Switchedl EHV Liines MARCH 1964


kimbark recierre monopolar

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