Estimating the Switching-Surge Performance of Transmission Lines

IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, VOL. PAS-89, NO. 7, SEPTEMBER/OCTOBER 1970

Estimating the Switching-Surge Performance of

Transmission Lines

ANDREW R. HILEMAN, FELLOW, IEEE, PIERRE R. LEBLANC, MEMBER, IEEE, AND

GORDON W. BROWN, MEMBER, IEEE

Abstract-From the results of an ANACOM study to investigatethe frequency function of the occurrence of a switching surge, asimplified method to estimate the switching-surge flashover prob-ability of a transmission line is developed and presented in a seriesof curves.

INTRODUCTIONAT 550 kV, the switching-surge design of transmission lines

consisted of the selection of a tower strike distance andinsulator string length whose withstand voltage is equal tothe maximum switching-surge voltage that can appear on theline. The withstand voltage was defined as the critical flashover(CFO) voltage minus three standard deviations Of. It wasrecognized by many investigators that this design method,although offering the advantage of simplicity, was not the bestmethod to employ. Rather, it was noted that switching-surgeline design should be based on a probability of switching-surgeflashover or, preferably, the line insulation design should bebased on the probability of line outage-a combination of light-ning and switching-surge flashover probabilities [1].

Previous estimates of UHV transmission line design haveemployed the selection criterion as discussed previously [2], [3].However, the importance of the use of probability methods inswitching-surge design is accentuated at UHV. It is believedthat the present switching-surge flashover probability for 550-kVlines is extremely low. If this assumption is shown to be correctby operating records, then increases in the design probability offlashover could be made.

Investigations into the estimates of switching-surge flashoverprobabilities have been performed by many noted investigators[4]-[7]. However, a need exists for a simple, accurate method[8].This paper presents a method to estimate the probability of

switching-surge flashovers on transmission lines. However,any simplified method requires two obvious assumptions: 1)the frequency of occurrence of switching-surge voltages, and 2)the probability of flashover of tower insulation as a function ofvoltage. Although the switching-impulse flashover probabilityhas been shown to approximate a cumulative Gaussian distri-bution to at least 4or below the CFO voltage [9], the frequencyfunction of the occurrence of a switching surge is not known witha similar degree of accuracy.

In addition, it has been common practice to assume that the

Paper 70 TP 38-PWR, recommended and approved by the Trans-mission and Distribution Committee of the IEEE Power Group forpresentation at the IEEE Winter Power Meeting, New York, N. Y.,January 2.5-30, 1970. Manuscript submitted September 16, 1969;made available for printing December 3, 1969.

A. R. Hilemen and P. R. Leblanc are with the WestinghouseElectric Corporation, East Pittsburgh, Pa. 15112.G. W. Brown is with the University of Pittsburgh, Pittsburgh,

Pa. 15213.

BKR.

-Q30

30;

00 lri LINE

f.62.0LC

125 mi LINE

SLG FAULT

BASE: 1000kV, 4000 MVA

LINE CONSTANTS

Ric 0.12 n/mi Ro 0.25fAniL - 1.27 mHAli Lo 3.34 mAnWiCl =0.0233PF/mi COs0.0151EpF/rNi

Fig. 1. Simplified diagram of 1100-kV transmission circuit used inANACOM study.

II

1t2

t2-4

lt =o.7ms

at, PHASE

t3 7AP

-/ts >-1& PHASE 3

t'o

Fig. 2. Random selection of closing times for aiming point to;At are Gaussian deviates about to.

distribution of occurrence is only composed of the absolute casepeak voltages; i.e., the maximum surge voltage on any of threephases irrespective of its polarity. That is, the surge voltagesappearing on the other two phases were assumed to be sufficientlylow in magnitude that they would not significantly contribute tothe total line flashover probability. It has also been tacitlyassumed that surge voltages appearing later or earlier in time,but on the same phase as the absolute peak voltage, did notsignificantly alter the total line flashover probability, either.Therefore, a miniature system study was performed to in-vestigate the probability distribution and the validity of theabove assumptions. The results of this study were then usedto produce sets of curves from which estimates of the switching-surge flashover probability can be obtained.

MINIATURE SYSTEM STUDY

To investigate the frequency of occurrence of switching-surgevoltages, a 125-mile 1100-kV line was set up on the ANACOMas shown in Fig. 1. A single line-to-ground fault was placed at theend of the opened line, resulting in a trapped charge voltage ofi 1.0 pu on the unfaulted phases when the breakers were opened.The breaker was then reclosed onto the line with the fault re-moved. The 1-pu voltage reference was chosen as the peak line-to-ground steady-state voltage on the line side of the transformerwith the line connected but unloaded. Under this condition

1455

XI=35% X1.15%

rr-A

IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, SEPTEMBER/OCTOBER 1970

the voltage at the end of the line was 1.035 pu. With the linedisconnected the voltage on the line side of the transformerwas 0.90 pu.Two cases were studied: 1) a circuit breaker with no resistor

inserted in the closing stroke, and 2) a circuit breaker with asingle 450-ohm resistor inserted in the closing stroke. Openingresistors in the breaker were not used. The closing times of thefirst breaker contact were assumed to be normally distributedabout uniformly random aiming points to over a 16.67-ms in-terval, as shown in Fig. 2, where At,, /t2, and At3 are Gaussiandeviations from the aiming point for each phase. For the casewhere a 450-ohm resistor was used, the second breaker contactwas assumed to close 10 ms after the first contact. No prestrikeof the breaker contacts was assumed.

Breakers with No-Insertion ResistorsSince resulting overvoltages may exceed 3.0 pu with this

configuration, a large numbei of random cases would be requiredto obtain an accurate distribution over the entire range ofovervoltages. However, since only the absolute peak voltage foreach case was initially required, a digital readout voltmeterwas used to simplify the task of recording values. Breaker pre-strike was ignored both because of the difficulty in determiningthe breaker voltages during closing and because of the largenumber of cases that would be used.Rather than select breaker closing times at random, a system-

atic method of selection was used to cover the range of breakerclosings. Aiming points were taken from -0.5 to 16.0 ms, at0.5-ms intervals. Actual closings were allowed to vary 42atfrom the aiming point. With at = 0.7 ms, and a step size of 0.5ms, this resulted in deviations of 1.5, 4±1.0, 40.5, and 40.0ms the aiming point for each phase. Thus, for each aiming pointthere are 343 combinations of closing times for the three phases.Since there are 33 different aiming points, the total number ofcases required is 11 319. However, because of duplicate closingtimes for more than one aiming point, the number of differentcases is reduced to 4407. The absolute peak voltage was recordedto the nearest 0.05 pu at three points on the line: 41.7, 83.3, and125 miles from the sending end.To obtain the frequency of occurrence distribution of absolute

peaks, the probability of each combination of closing timesmust be considered. The probability P of occurrence of a voltageresulting from selection of an aiming point to and closing timesAtl, At2, At3 relative to the aiming point is

~-3.0

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>t' 2.2 't 00Ms 't

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AIMING POINT-ms

Fig. 3. Maximum absolute peak voltage as a function of aimingpoint (o-7 = 0.7 ins) and simultaneous closing (ot = 0).

E'Li0z4c

-J

1.5

OA CLOSING a 2.0 ms

Fig. 4. Topographical view of absolute peak voltage, 2 ms.

P(to,Atl,At2,At3) = P(to)P(Atl)P(At2)P(At3) (1)

where to, Atl, At2, and At3 are assumed to be statistically inde-pendent. For this case, P(to) is equal to 0.0333 since there are 33equally likely aiming points.The distribution for each aiming point resulted in maximum

absolute peak voltages as a function of aiming point as shown inFig. 3. Also shown are the absolute peaks for simultaneousbreaker closing, which is equivalent to a o° of zero. This in-dicates the regions of breaker closing where significantly highovervoltages occur. A portion of the peak region is illustratedtopographically in Fig. 4, holding the closing time of phase A,the faulted phase, constant at 2.0 ms and allowing the closings ofthe other two phases to vary between i 1.5 ms. If the closing onphase A were then allowed to vary, the peak areas shown wouldbe closed surfaces with roughly ellipsoidal shapes.The resulting histogram for the entire range of aiming points

is shown for the receiving end of the line in Fig. 5, with itsestimated distribution superimposed. The cumulative prob-

16 lS 2.0 Z2 2.4 26 2.8ABSOWTE PEAK VOLTAGE,PU

Fig. 5. Histogram of absolute peak voltages for receiving end ofline with no-resistor breaker, and estimate of actual frequencyfunction.

1456

HILEMAN et al.: ESTIMATING SWITCHING-SURGE PERFORMANCE

TABLE ISUMMARY OF RESULTS-NO-INSERTION RESISTOR

Per-unit line length, l/L 1/3 2/3 1Mean, A 1.920 2.100 2.325Standard deviation, 0o0 0.200 0.215 0.250ao,p, percent 10.4 10.2 10.8Maximum voltage 2.75 2.95 3.30Upper truncation point, 4.15 3.95 3.90number of oTO's above,

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CUMULATIVE PROBABILITY. PER CENT

Fig. 6. Cumulative probability of occurrence for three points on linewith no-resistor breaker and Gaussian fit at high end.

ability of occurrence is shown for the three points on the line inFig. 6, and it will be noted that the high-probability end of thedistribution can be closely approximated by a Gaussian curvewith means and standard deviation as shown, where l/L is theper-unit line length as measured from the sending end. Theresults are summarized in Table I.

It can be seen that the mean and the standard deviation arefairly linear with per-unit distance l/L; that oo/IL ranges between10 and 11 percent; and that the upper truncation, the pointat which the maximum voltage occurs, is at approximately 4.Ouoabove the mean throughout the length of line considered.The validity of using only the absolute case peak voltage is

based on the assumption that only this peak will be significantin the calculation of flashover probability. Therefore, oscillo-grams of cases with peak voltages of 2.7 pu or greater wereobtained and examined to determine the significance of

1) the second highest peak voltage of the same polarity as theabsolute peak voltage, which occurs on the same phase as doesthe absolute peak voltage;

2) the second highest peak voltage of the same polarity as theabsolute peak voltage, which occurs on one of the other twophases.The results, given in Fig. 7 as scatter diagrams, show that1) the second highest peak voltage of the same polarity and

on the same phase as the absolute peak voltage never exceeded2.2 pu, or 0.5ao below the mean;

2) the second highest peak voltage of the same polarity neverexceeded 2.7 pu, or 1.5ao above the mean.As shown in Appendix I, ignoring these values does not

seriously affect line flashover probabilities.

1.2 1.4 1.6 Is 2.0 2.2 2.4NEXT HIGHEST PEAK OF SAME POLARITY ON PEAK PHASE,PU VOLTS

(a)

<3.4 _-1'

3 2 --- 4 -__ - -

,'1B

EXT 2.02P Z4 L T VO L

NEXT HIIGHEST PH1ASE PEAK OF SAME POLARITY,PU VOLTS

(b)Fig. 7. Scatter diagrams for high end of no-resistor voltage distribu-

tion. (a) Absolute case peak voltage versus second highest peakvoltage of same polarity on same phase. (b) Absolute case peakvoltage versus second highest phase peak of same polarity.

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ABSOLUTE PEAK OVERVOLTAGE3.2 34

Fig. 8. Comparison of cumulative frequency of occurrence for 50,100, and 200 random cases with actual cumulative probabilitycurve.

A point of interest, which can be estimated from this study,is how many randomly selected combinations of closing times

are required to obtain a good fit at the tail end of the distribution.Two sets of 50 cases and one set each of 100 and 200 cases were

randomly generated on the digital computer and the absolute

peak voltages at the receiving end were determined from the

4407 cases run on the ANACOM. The upper half of the cumulative

probability curves obtained from these four sets of cases are

shown in Fig. 8, with the actual probability curve shown for

comparison. Fifty cases seemed totally inadequate for obtaining a

tail-end fit, but 100 cases fit quite well up to the 95-percentprobability level. On the other hand, the 200 random cases

had a good fit between 92 and 99 percent, corresponding to peakvoltage levels of 2.70 and 2.95 pu, respectively, and a maximum

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1457

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Fig. 9. Histogram of absolute peak voltages at receiving end for200 random cases with single-step resistor breaker.

CUMULATIVE PROBABILITY, PER CENT

Fig. 10. Extreme value regression lines representing cumulativeprobability of occurrence for four points on line (1/L = 0, 1/3,2/3, 1) for single-step resistor breaker.

TABLE IISUMMARY OF RESULTS-SINGLE-STEP RESISTOR

Per-unit line length, 1/L 0 1/3 2/3 1Mode, u 1.17 1.23 1.29 1.33Slope 0.072 0.083 0.086 0.091pl/u,yercent 6.1 6.8 6.7 6.8Maximum voltage 1.6 1.65 1.70 1.70Upper truncation 5.8 5.1 4.8 4.1

points, number of B'sabove mode

j)b

4

. 0

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IL) L~ L4 l U

AC -I - - -I -

1.0 L2 L4 1.6 1.8 2.0NEXT HIGHEST PEAK OF SAME POLARITY ON PEAK PASE PU VOLS

(a)

1.0 1.2 1.4 1.6 i.B 2.0NEXT HIGHEST PHASE PEAK OF SAME POLARITY, P U VOLTS

(b)Fig. 11. Scatter diagrams for single-step resistor cases. (a) Absolute

case peak voltage versus second highest peak voltage of samepolarity on same phase. (b) Absolute case peak voltage versus sec-ond highest phase peak of same polarity.

of 0.7 ms; actual closing times were permitted to vary 42atfrom the aiming point;

3) a constant resistor insertion time of 10 ms was chosen.A resistor value of 450 ohms was used, and prestrike was

ignored for the reasons mentioned earlier. Absolute peaks wereobtained in the same manner as the above no-resistor case, withthe exception that the sending-end absolute peaks were alsorecorded. The resulting histograms for the four points on theline illustrate a marked skewness to the high end. The receiving-end histogram is shown in Fig. 9. Since the normal curve willnot fit this type of distribution, the application of the extremevalue function was examined. This is a cumulative probabilityfunction of the form

value of 3.05 pu. Therefore, it appears that at least 200 randomcases should be used to obtain a reasonable tail-end fit for adistribution with the range of values of 1.2 to 3.3 pu. The numberof cases required will decrease with a decreased range of possiblevalues.

Breakers with Single-Step Insertion ResistorOne method for limiting switching-surge overvoltage is by the

insertion of a resistor for a short period of time (8-10 ms), beforethe main breaker contacts are closed. Two hundred cases weregenerated for this study as follows:

1) aiming points for resistor contact were uniform randomnumbers between 0 and 16.66 ms;

2) closing times of the resistor contacts are random normaldeviates about this aiming point with a standard deviation

P(y) = e-e-Y

where y is a reduced variate defined by

(x - u)Y =

(2)

(3)

where x is the true variable, per-unit voltage, u the mode, and ,3the slope on extreme probability paper.These two quantities can be related to the mean and standard

deviation of the distribution as follows:

/ = u + 7(3

0,0= - -' (4)

where -y is Euler's constant, equal to 0.57722. Fig. 10 showsthe application of extreme value theory to the distribution of

1458


absolute peaks at the four points on the transmission line, andthe summarized results appear in Table II.

Again, with the exception of the sending end, the mode andslope are fairly linear with distance l/L, and the per-unitizedslope 13/u is nearly constant at 6.8 percent. However, thereis a drop in the upper truncation points at the receiving end,mainly because of the high frequency of the maximum value.It is suspected, however, that the actual maximum may be at1.8 pu, which would result in a truncation at 5.01.As in the no-resistor cases, the validity for using only the

absolute case peaks is demonstrated in the scatter diagrams inFig. 11, indicating that

1) the second highest peak voltage of the same polarity andon the same phase as the absolute peak voltage never exceeded1.4 pu, or 0.771 above the mode;

2) the next highest phase peak of the same polarity neverexceeded 1.5 pu, or 1.8713 above the mode.

Again, as shown in Appendix I, these values may be ignored.

SUMMARY OF MINIATURE SYSTEM STUDY RESULTS

From the miniature system study, the following conclusionsfor the specific system studied were derived.

1) The probability distribution of the occurrence of a switching-surge voltage was either a Gaussian distribution or an extremevalue distribution.

2) The point at which the maximum voltage occurred, definedas the truncation point, was 4fof above the mean for the normaldistribution and 51 above the mode for the extreme valuedistribution.

3) The per-unitized standard deviation co/y for the normaldistribution and 13/u for the extreme value distribution wereapproximately constant along the line.

4) The mean g of the normal distribution and the mode uof the extreme value distribution at measuring points along theline vary approximately linearly with l/L. It can be shown thatthe assumption of a linear variation of , with l/L necessitatesthe assumption of a linear variation of voltage along the line.In the cases studied M5/,iA is approximately 0.70 for the normaldistribution and u,/u, is approximately 0.90 for the extremevalue distribution. The assumption of linearity of the maximumvoltage in the latter case is questionable since at l/L = 2/3the voltage is equal to that at l/L = 1.0. However, as stated pre-viously, it is suspected that the actual maximum voltage atl/L = 1.0 is greater than 1.7 pu and that the rounding of allmeasurements to the closest 0.05 pu contributed to this problem.

5) Surge voltages other than the absolute case peak voltagemay be neglected.

Therefore, for purposes of estimating the probability of lineflashover caused by switching surges, the following assumptionsare made:

1) probability of occurrence of switching surges may have twodistributions: Gaussian or extreme value;

2) the truncation point is,u + 4o-o and u + 51;3) uo/y or 13/u is constant along the line;4) the mean IA and mode u vary linearly along the line;5) surge voltage other than the absolute case peaks can be

ignored;6) the absolute case peaks may be equally of positive or

negative polarity;7) the single tower probability of flashover is a cumulative

Gaussian function, with mean, CFO, and standard deviationI.f

VOLTAGE

Fig. 12. Line flashover probability (shaded area).

PROBABILITY OF SWITCHING-SURGE FLASHOVER

Theory and CalculationsAssuming that the largest positive voltage peak per switching

operation is, as indicated above, the significant surge, theprobability of flashover of a line may be written

Pr,= [ (-kPk) f(V) dv,

flashovers per switching operation (5)

where Pk is the probability of flashover at the kth tower for asurge of voltage magnitude v at the kth tower and f(V) is thefrequency distribution of the occurrence of voltage magnitudes.The factor 1/2 reflects the fact that the switching-surge strengthof tower insulation for negative polarity greatly exceeds that forpositive polarity and therefore only positive polarity switchingsurges need be considered.The above probability may be visualized by referring to Fig

12. The shaded area is the probability of line flashover. It shouldbe noted that Fig. 12 is not to scale.

Estimating CurvesThe results of this study are presented in Figs. 13-18, in

which the probability of line flashover per switching operationis shown as a function of ,/CFO (or u/CFO) with oa-/CFO,ao/,u (or 13/u), n (the number of towers), and Ms/MUT (or uS/uT) asparameters. For estimating purposes, linear interpolation be-tween values presented gives sufficiently accurate results forother assumed values of the parameters. However, the curvefor n = 1000 lies approximately midway between the curve forn = 500 and n = 2000.Where it is within the range of probability values shown on

the curves, a dot on the curve indicates the design criterionpreviously used at 550 kV; i.e., the maximum switching-surgevoltage is equal to CFO - 3Tf. In terms of these curves, thisoccurs at the point where,u + 4f0o = CFO -3of for the Gaussiandistribution and at u + 51 = CFO - 3o-f for the extreme valuedistribution. As noted, this method of design produces a change-able probability of surge flashover dependent on the assumedparameters. Also the values of probability are below 10-3 forpractical design parameters-less than 1 flashover per 1000breaker operations.These curves can be used in two ways. First, if a new design is

contemplated and a miniature system study is performed, valuesof A (or u), ao (or 1), and M,s/,M (or us/uT) are known. Enteringthe curve at a desired flashover probability gives a M/CFO (oru/CFO) from which the CFO can be obtained. The tower

1459


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lrL

Aa:

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a:

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-i

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am

co

(a)

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(b)

Fig. 13. Probability of switching-surge flashover for Gaussian Fig. 14. Probability of switching-surge flashover for Gaussiandistribution of switching-surge voltages. distribution of switching-surge voltages.

1460

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HILEMAN et al.: ESTIMATING SWITCHING-SURGE PERFORMANCE 1461

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Fig. 15. Probability of switching-surge flashover for Gaussian Fig. 16. Probability of switching-surge flashover for extreme valuedistribution of switching-surge voltages, distribution of switchin-surge voltages.

1462 IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, SEPTEMBER/OCTOBER 1970

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insulation dimensions can be obtained from laboratory testdata such as shown in [3]. Alternatively, for an existing towerdesign the probability of flashover can be found.

DISCUSSION OF RESULTS

Several items in this paper require further discussion, butchief among these is the observation that the results of a minia-ture system study on a specific system were used to establish theassumptions and parameters of the estimating method. Criticismof the miniature system study is justified in that it did not en-compass various line lengths, sources, fault locations, etc., anddid not include the prestrike characteristics of breakers. Forexample, additional studies may reveal distributions otherthan the Gaussian or the extreme value are more representative.It should also be noted that the value of o, was fixed at 0.7 msand the procedure used only permits deviation around the aimingpoint of 42o-t. Increasing this range may have produced adistribution different from that shown in Fig. 5. It is hoped thatthe parameters presented have sufficient variation that the es-timating method will be useful in future studies.The authors employed a "brute force" method of attack in an

attempt to determine an exact distribution of occurrence for theno-insertion-resistor case. Then a 200-case random samplingmethod was used for the single-resistor case. However, the"brute force" method suffers from the exhaustive time required,whereas the limited random sample method does not produce theexact distribution and may vary depending upon the randomnumbers used. Since only the tail of the distribution is of im-portance, alternate methods should be considered. For example, ashort search at various aiming points could produce a curvesuch as that of Fig. 3. This could be followed by a topologicalsearch at these aiming points such as illustrated in Fig. 4.From these figures, the distribution could be accurately esti-mated. It was recently noted that H. Glavitsch of CIGRE Work-ing Group 33.02 independently proposed a similar method.

It presently appears that a large magnitude of effort has beenand is being devoted to the determination of tower insulationflashover characteristics, whereas the effort devoted to thedetermination of the probability distribution of occurrence andits variables has been at a low level. It is hoped that otherinvestigators will perform studies to adequately determine thisdistribution and its parameters. Field studies would also help todetermine the probability distribution.

Using the curves of Figs. 13-18 gives an estimate of the prob-ability of switching-surge flashover per breaker operation.However, the primary design criterion is outage rate, whichis a function of both the lightning and switching-surge flashoverprobabilities. If, for example, the lightning flashover rate is 1per year for a 100-mile line and the switching-surge flashoverprobability when reclosing after a lightning flashover is 1 X 10-2per switching operation, then the outage probability for thiscase is 1 X 10-2 or 1 in 100 years for a 100-mile line. ConsideringUHV transmission design, it appears that the lightning flash-over rate may decrease, and therefore a higher switching-surgeflashover rate could be permitted to achieve the same outagerate.The curves of Figs. 13-18 indicate that the switching-surge

flashover rates using the design criterion of maximum switching-surge equals CFO -3f are extremely low. Therefore, if thisobservation is verified by operating experience at 550 kV,consideration should be given to using a design probability ofswitching-surge flashover in the range of 1 X 10-2 or per 100breaker operations. This could decrease the required tower

insulation dimensions significantly. For example, assuming aGaussian distribution of switching-surge voltages, a o0o4 of10 percent and a u of 1.5 pu would give a maximum voltage of2.1 pu at u + 4o-o. Using the previous design rules would resultin a CFO of 2.39 pu for a af/CFO of 4 percent. Using Fig. 14(a)for a probability of 1 X 10-2, the resulting ,/CFO is 0.755 forn = 500. The CFO should therefore be set at 1.99 pu. Assuming alinear relation between the CFO and tower strike distance, a16.7-percent decrease in insulation distance would be indicated.At UHV transmission, control of the maximum switching-

surge voltage to 1.5 pu or less has been proposed. As the maxi-mum per-unit over-voltage is decreased, ai (or u) will decreaseand from Figs. 13-18, assuming constant probability, aO/lq(or p3/u) will increase. Therefore, the required CFO voltage willdecrease, as would be expected. However, this decrease in CFOvoltage as determined from these curves should be comparedwith the decrease in required CFO voltage if it is assumed thatthe CFO voltage decreases in a direct proportion to the per-unitovervoltage. Sample calculations, assuming that both CFO volt-ages are equal at 2.0 pu for 1100-kV transmission showed thatthe required CFO voltage using the probability method wasabout 4 percent higher than the CFO voltage for the simple ratiomethod when the maximum voltage decreased from 2.0 to 1.4 pu.This is amplified to 7 percent when the strike distances arecompared as a result of the shape of the curve of CFO voltageversus strike distance.

Also, it appears that as the maximum voltage is decreased theratio of uJdr (or u,/u,) increases. This factor would increasethe required CFO voltage. Sample calculations showed that therequired CFO voltage is increased by an additional 2 percentover that calculated above. That is, considering the increase of141,4 the decrease of ao4, and the decrease of u, the probabilitymethod calculations indicated a CFO voltage about 6 percenthigher than that calculated using the simple ratio method. Thisagain is amplified to about 9 percent when the strike distancesare compared.

SUMMARY AND CONCLIJSIONS1) The results of a miniature system study showed that the

frequency distribution of absolute case peak voltage approximateseither a Gaussian or an extreme value distribution.

2) Analysis of the above results indicated that for the systemstudied, the voltages on the other two phases and the voltagepeaks (other than the absolute peak voltage) on the same phasedo not significantly contribute to the total line flashover prob-ability.

3) From the results of the above study, parameters wereassumed for the frequency of occurrence of switching-surgevoltages and combined with the probability of flashover oftower insulation to obtain curves that can be used to estimatethe probability of switching-surge flashover of a transmissionline.

4) "Brute force" and random sampling methods were used toobtain the probability of occurrence frequency distribution.Since only the tail of the distribution is important, other methodsare suggested to accurately obtain the distribution in thisprobability area.

5) Maintaining a constant probability of switching-surgeflashover, decreasing the maximum switching-surge voltagedoes not produce a proportional decrease in the required CFOvoltage or the tower strike distance.

6) Switching-surge design criterion used at 550 kV results inprobabilities of switching-surge flashover of less than 1 in 1000

1463


breaker operations. It is suggested that values of 1 in 100 years orless should be considered, providing that operating experienceat 550 kV verifies the calculated performance.

7) Additional miniature system studies are required to sub-stantiate and expand the results of this study.

APPENDIX ISIGNIFICANCE OF SECONDARY VOLTAGE PEAKS

Only the absolute peak voltage, the highest voltage thatoccurred on any of the three phases after the switching operation,was considered in the calculation of line flashover probability.Fig. 19 shows how the total probability is accumulated as thedeviation above the mean A or mode B increases toward themaximum overvoltage at 4o0O or 5t. Various probability levelswere obtained by varying both the location of the CFO and thevalue of its standard deviation (4-8 percent). In the case of theno-resistor breaker, the highest secondary peak on the samephase and of the same polarity as the absolute peak was at the-0.5-ro level, and it is obvious from Fig. 19(a) that these may beneglected. Regarding the next highest phase peak, only one of theremaining two phases will have a peak of the same polarityof significant value. Since this peak is at most equal to theabsolute peak, the total flashover probability will no more thandouble when the effect of its probability is included. However,for cases where the overall probability of flashover is very low(i.e., 1 per 1000) and the standard deviation of the CFO is small(4 percent), the assumption of using only absolute peaks resultsin very little error.For example, as stated earlier, the second highest phase peak

had a maximum of 2.7 pu, or 1.50o above the mean. Sincenothing is known about the distribution of these peaks, it isassumed that for all absolute peaks less than 2.7 pu, the nexthighest phase peak is of equal magnitude; for all absolute peaksgreater than 2.7 pu, let it be equal to 2.7 pu. Consider the case inFig. 19(a) with a probability of 1.8 X 10-3. The probability ofline flashover accumulated up to the 1.5ao point is only 0.1percent of the total or 1.8 X 10-6. This is so small in comparisonwith the total that it may be ignored. The probability of occur-rence for values greater than 1.5ao is 0.06681, and the probabilityof flashover at 2.7 pu, determined from the CFO and o,a is 4.3 X10-6. Assuming also that the 2.7-pu secondary peak is presentacross the entire line, 500 towers, the contribution to the totalprobability is

P = (500) (0.06681) (4.3 X 10-6) = 1.4 X 10-4.

The probability based on only absolute peaks was 1.8 X 10-3,so there is a difference of more than an order of magnitude be-tween the two. Therefore, based upon these very conservativeassumptions, the error would be no more than 10 percent. Asimilar calculation was performed for a crf of 8 percent and aflashover probability of 4.5 X 10-3 with the additional assump-tion that the 2.7-pu secondary phase peak decreased linearlyacross the line with 1.9 pu at the sending end. This resulted in a75-percent increase in the original value of probability, not quitedouble the original values, and again the assumptions are veryconservative.Regarding the one-resistor cases shown in Fig 19(b), the

levels of 0.77 and 1.87,B for the two types of secondary peaksconsidered will contribute very little if at all to the overallflashover probability. This is primarily due to the skewness of thevoltage frequency distribution, which requires a large separationbetween the mode of this distribution and the CFO to obtainacceptable flashover probabilities.

(0

Co um

ak:> tu

Jo

zwU

w

a.

c3o:

LLI>h

0\

-J

LOXcr:LJ(L

DEVIATION ABOVE THE MEAN,MULTIPLES OF°o

(a)100

f/CFO -O04 A

'f/CFO.0S/'CU *-07 _ t

O--'wi-"Yv0

N.500 P.L3xt5e

60

I.0 .0 3D 4ID 0DEVIATION ABOVE THE MaX.MULTIPLES OFB

(b)Fig. 19. Accumulation of line flashover probability P. (a) For no-

,resistor breaker case using Gaussian distribution. (b) For single-step resistor breaker case using extreme value distribution.

APPENDIX IIPROBABILITY OF LINE FLASHOVERINCLUDING ALL PEAK VOLTAGES

The significant parameters of a given surge that will affectthe probability that the surge will cause flashover are thevoltage magnitude, voltage polarity, and waveshape. For a giventower structure, surge voltage, polarity, and waveshape, it canbe assumed with reasonable confidence [9] that the relationbetween voltage magnitude and flashover probability is thecumulative normal distribution, with parameters CFO and 07f.Both of these parameters will be dependent on polarity andwaveshape. If it is assumed that one parameter w is sufficient todescribe waveshape, the probability of flashover of a given towerstructure can be expressed

P(V,w).

A surge voltage VI at tower 1 on a given line will yield prob-abilities

P(V1,W1),P(V2,W2), ' * * 2 P(VkiWk)i ...* *P(Vn,wn)at towers 1,2,* ,k,** ,n, respectively. This expresses thefact that voltage and waveform can change. Given the variationof voltage and waveshape with tower number (i.e., distance),the probability of line flashover PLj for the jth surge becomes

-n

PLi = 1 - i [1 - P(Vl,Wk)].k= 1

(6)

Unfortunately, the variation of waveshape is not known insufficient detail to make computation practical according to (6).

1464

HILEMAN et al.: ESTIMATING SWITCHING-STJRGE PERFORMANCE

2i--] 1r

0L

w

l-j

-2.

14_yr

0 20TIME-ms

40

Fig. 20. Typical oscillogram from ANACOM study; important voltagepeaks are shown.

Hence the approximation is made that the waveshape is constantand flashover probability is dependent only on voltage. Then

n

PL= 1-JjJ[1-P(Vk)]. (7)k=1

Now any given switching operation will result in many surgeson each of three phases. A typical ANACOM result is shown inFig. 20. The important peaks have been numbered in the oscillo-gram. There are quite obvious questions regarding the definitionof an "important" peak, and of the effect of previous peaks onthe probability of flashover, all of which are relevant, butwill require much more study. However, if the peaks indicatedare assumed to be the important ones, and if they result inindependent flashover probabilities, then the overall probabilityof line flashover becomes

M

PL =1 H (1-PL)) (8)

where the numbering system encompasses all "important"surges on all phases and M is the number of the last significantsurge. The analysis of Appendix I, however, indicates that it isadequate to consider only the highest peak.

REFERENCES[1] G. E. Grosser and A. R. Hileman, "Ecomonic optimization of

transmission tower grounding and insulation," IEEE Trans.Power Apparatus and Systems, vol. PAS-86, pp. 979-986,August 1967.

[2] J. K. Dillard, A. R. Hileman, and J. P. McKinnon, "1100-kVstation and line insulation design," CIGRE, Paper 25-06,June 1968.

[3] J. K. Dillard and A. R. Hileman, "UHV transmission towerinsulation tests," Paper 70 TP 78, presented at the IEEEWinter Power Meeting, New York, N. Y., January 25-30,1970.

[4] R. Gert, J. Jirku, S. Kriz, J. Kucera, and J. Vokalek, "Switch-ing surges in EHV systems and their influence on the electricalstrength of external insulation," CIGRE, Rept. 406, June 1966.

[5] G. N. Aleksandrov, "Methods of choosing insulation fordistribution networks with the view to reliable operation in thepresence of internal voltage surges," Energetika, no. 7, pp.16-24, 1932.

[6] A. J. McElroy and J. H. Charkow, "Probabilistic aspects cftransmission system switching-surge reliability," IEEE Trans.Power Apparatus and Systems, vol. PAS-86, pp. 1012-1024,August 1967.

[7] J. G. Anderson and R. L. Thompson, "The statistical computa-tion of line performance using METIFOR," IEEE Trans. PowerApparatus and Systems, vol. PAS-85, pp. 677-686, June 1966.

[8] J. D. M. Phelps, P. S. Pugh, and J. E. Beehler, "765-kV stationinsulation coordination," IEEE Trans. Power Apparatus andSystems, vol. PAS-88, pp. 1372-1382, September 1969.

[9] T. Suzuki, I. Kishijima, Y. Ohuch, and K. Anjo, "Parallelmuligap flashover probability," IEEE Trans. Power Ap-paratus and Systems, vol. PAS-88, pp. 1814-1823, December1969.

Discussion

H. Glavitsch (Brown Boveri AG, Baden, Switzerland): In thispaper the authors bring to light the relevant aspects of employingprobabilistic methods in the field of insulation coordination and theyare to be congratulated for their excellent work.In their discussion of the results it is mentioned that there is a

need for more effective methods for the determination of distributionfunctions, especially in the area of the highest switching overvoltages,and reference is made to the work of CIGRE Working Group33-02.The method proposed there relies on the determination of the

magnitude of the switching overvoltage by the triple of electricalclosing instants (in degrees or milliseconds for the three phases).In a three-dimensional space, the area around the maximum over-voltage magnitudes can be represented as a cigar-shaped body withseveral layers denoting surfaces of constant overvoltage magnitude.

In the determination of the electrical closing instants, randomnumber generators on a digital computer are used to take intoaccount the probabilistic behavior of the aiming point, the me-chanical closing of the breaker contacts around the aiming point, andthe prestrike of the closing poles. This simulation of the breakeroperation yields the effects of various breaker parameters on thedistribution of the maximum overvoltage magnitudes, i.e., on alimited portion of the distribution function that is of interest.For a given line and power system, the determination of over-voltages as a finction of the aforementioned three closing angleshas to be done only once, which is highly advantageous. The simula-tion runs with this given system showed that the distribution at thetail end, being of interest, is quite sensitive to the permanent dis-placement of the mechanical closing instants, their dispersion, andprestrike.

This kind of investigation is very valuable in the development ofbreakers and of measures for the reduction of overvoltage mag-nitudes. For system planning the presence of a great number ofbreakers and various system configurations must be accounted for,and therefore a composite distribution, as mentioned by otherdiscussers, will be appropriate. The consideration above will givesome guidance on the establishment of such a composite distributionwhere the selected area of the highest overvoltage magnitudes willbe of main interest.

Manuscript received February 9, 1970.

A. Clerici and A. Colombo (Centro Elettrotecnico SperimentaleItaliano [CESI], Milan, Italy): We would like to offer the follow-ing comments on the paper.

1) Although further investigation may be needed to substantiatethe source of the authors' suggestions, we completely agree on theimportance of a better knowledge of the frequency function ofswitching surges. The influence of the assumptions adopted insimulating a breaker operation should be investigated in par-ticular. For instance, the authors have assumed equal "aimingpoints" for all three phases, which may be invalid when consideringan individual breaker installed on a particular line. It should also


1465

I 4


be taken into account that for UHV systems other overvoltage(fault initiation and clearing) are to be considered as part ofthe actual switching-surge frequency distribution. The great amountof work necessary to determine such distribution functions withreasonable reliability makes cooperation among specialists highlydesirable.

2) In connection with the above reliability considerations, Fig. 8seems to indicate that an estimate of the switching-surge distribu-tion based on 200 cases is more accurate than one based on 50 cases.However, the problem in both situations remains that of how tomnake an extrapolation from a point, which is placed between 2 and3 or above the 50-percent value, up to a point around 4, where thedistribution is likely to be truncated. Obviously under such condi-tions large errors can always be introduced on the last part of thecurve, even when extrapolating a curve based on 200 cases. Nothingcan assure that the estimate of the distribution will be conservative.We think therefore that instead of increasing the number of

cases it is better to assess the accuracy of the evaluation by con-sidering several random shorter series of cases. Furthermore, thedetermination of the maximized overvoltage is of the greatestimportance in this respect.

3) We should like to learn why the authors have considered peaksof the same polarity to assess the importance of the peaks subsequentto the highest one. We would have included all polarity peaks. Wehave checked' anyway that when preinsertion resistors are used theincrease of the insulation strength to keep the risk of failure at therequired level is of the order of 5 percent.

4) The influence of the overvoltage waveshape is often moreimportant (order of 10-percent) and should not be forgotten inseeking a real improvement of the design criteria. A simplifiedmethod is being developed by the discussers for the purpose, andsome examples of its application will appear in a paper at the nextCIGRE meeting. The consideration of the surge shape may implythat a review of certain other conclusions is necessary. For instance,if the absolute peak on one phase is 2 pu but its equivalent fronttime is far from the critical, a critical surge of 1.7 pu on anotherphase may have greater probability of determining the flashover.

N. Dag Reppen (Power Technologies, Inc., Schenectady, N. Y.):This paper contains some very interesting information about thestatistics of switching surges. The authors have investigated twoswitching situations and found that the surge distribution for one

case could be represented by a Gaussian distribution and the secondcase could be represented by an extreme value distribution. They thenproceeded, in the second half of the paper, to display curves showingthe probability of flashover of switching operations for variousparameters of the two distribution types. This discusser feels thatpractical estimating curves for switching-surge flashover probabili-ties can be presented in a much simpler format. One approach ispresented at the end of this discussion. The thoroughness of theswitching-surge investigation is impressive and the execution of 4407cases on the ANACOM to obtain one single surge distribution indicatesthat the authors are in possession of the stubborn endurance thatsometimes is needed to produce reliable information.The scatter diagrams of Fig. 7 show the correlation of maximum

surges on the three phases and the correlation of the magnitude of thefirst peak and subsequent peaks on the same phase. From thisinformation, the authors draw the following conclusions: 1) that theswitching-surge flashover probability of the transmission line isnot significantly influenced by the surges on the phases that are notexposed to the maximum surge, and 2) that the existence of multiplepeaks on the phase exposed to the highest surge is of no consequencefor the flashover probabilities. The first conclusion seems validenough. As a matter of fact, a statistical analysis would show thateven if all phases were exposed to the same maximum surge, theincrease in the probability of flashover would be of little practicalsignificance. As to the second conclusion, the authors' findings are

undoubtedly correct from the standpoint of probability calculationsas carried out in this paper. However, the effects of multiple peaksmay be important from the standpoint of the resulting insulationstrength. Very little information exists on the flashover voltage ofcomplex switching surges, but it does not seem proper to assume that


Xou-

z0C9x.>

Z

n

0.95

DISTR'IBUTION0.5SEVERITY __

A MOST SEVERE

080 8 MODERATELY SEVERE ___C LEAST SEVERE

0.01 0.1 1.0 10 20 40 60 80 90PERCENT OF SURGES EXCEEDING ORDINATE VALUES

99

Fig. 21. Cumulative distributions of switching-surge voltage in per-unit maximum surge-Gaussian probability paper.

0.9V MAX.

C FO

Fig. 22. Probability of transmission line flashover as function ofratio of maximum switching surge Vmax and critical flashovervoltage CFO-semilog paper.

flashover during the second peak is independent of the magnitudeof the first peak. The authors' comments on this would be appreci-ated.

In evaluating the flashover probability curves, the authors did notseem to have included weather statistics to obtain the variation ininsulation strength with varying humidity and air density. Inclusionof such weather-based insulation strength corrections will signifi-cantly modify the shape of the probability functions presented here.Will the authors comment on their philosophy in this area?

In the context of line performance, the paper appears to over-emphasize the importance of accurately determining the surgevoltage distribution. For one thing, the actual distribution of surgeson the line is determined by more than one system condition. Acomposite distribution may be obtained by weighting and combiningthe surge distributions representing each system condition. Further-more, the composite distribution will change with time as the systemitself as well as operating modes change. This discusser feels that themost one can expect to know of the switching surges and theirstatistical properties are 1) the maximum surge voltage, and 2)the approximate severity of the distribution, roughly classified.Based on this belief, the discusser offers the following approach as apractical method for estimating flashover probabilities.For a specific surge voltage V and a specific critical flashover

voltage CFO the flashover probability PFO is a function of the stan-dardized variable z:

PFO = F(z)V - CFO (V/CFO - 1)

f al/CFOThen for a specific value of c/CFO, for example, 5 percent

PFO = F'(V/CFO).

1466


TABLE IIIINDICATION OF MAXIMUM LIKELY ERROR IN TOWER WINDOW CLEARANCE OBTAINED BY USING FIG. 22

Maximum Surge SurgeVoltage Surge Profile Weather Statistics Distribution(kV) (feet) (meters) (feet) (meters) (feet) (meters)

600 0.3 0.1 0.3 0.1 0.2 0.1900 0.6 0.2 0.6 0.2 0.4 0.11200 1.2 0.4 1.5 0.5 0.7 0.21500 2.0 0.6 2.2 0.7 1.5 0.5

With the surge distribution defined the flashover probability canbe written as a function of the assumed maximum surge voltageVmax and CFO:

PFO = F" V(ax

Fig. 21 shows three switching-surge distributions representingthree classes of different surge distribution severity. This mayseem like a rather rough classification but up till now very fewinvestigations, if any, have succeeded in establishing the compositesurge distribution with an accuracy requiring a finer classification.Fig. 22 shows the probability curves for the three classes of surgedistribution severity. These curves were evaluated from the basecase of [10] and include the following assumptions.

1) On the average the surge voltages decrease with 0.4 percentper mile from the receiving end. The relative surge magnitude alongthe line is later referred to as the surge profile.

2) The effects of air density and humidity are included using theresults of a weather based analysis for Portland, Oreg. [11]. Theweather correction statistics for Portland are typical for sea-levellocations with moderate humidity.To the extent that these assumptions are not representative for

the particular transmission line considered, the flashover prob-abilities will be in error. Since the significance of a certain deviationin the flashover probabilities is not always apparent, the investiga-tion described in [10] gives the effect of erroneous assumptions interms of tower window clearance.

Table III contains an indication of the error in tower windowdimensions resulting when the estimating curves in Fig. 22 are usedand the differences between actual and assumed surge profiles andweather correction statistics are quite extreme [101. The surge distri-bution column indicates the maximum possible clearance error,assuming that the proper distribution severity class is used. It canbe concluded from this table that:

1) the significance of misjudgments increases with the maximumsurge voltage and the voltage level;

2) assuming that the surge distribution is correctly classified inone of the three classes, the surge profile and the weather correctionare at least as critical as the surge distribution itself;

3) the curves should be quite adequate for 345 kV and below, andmay be used for preliminary investigations at 500-kV, 765-kV, andUHV voltages.The use of the curves may be best illustrated by an example.

Consider a 500-kV line 3000 feet (915 meters) above sea level.What is the required tower window CFO voltage that will produce1-percent probability of flashover if the maximum surge (Vmax) is2.0 pu and the composite surge distribution is classified as moderatelysevere? It is seen that V1max/CFO = 0.87 and with Vmax = 2.0 X500 X V/2/3 = 816 kV, a CFO of 816/0.87 = 940 kV is required.This value may now be corrected to sea-level conditions and theproper clearances evaluated based on flashover test data. Table IIIindicates that in the worst case the clearance estimated is not likelyto be off by more than 1 foot (0.3 meter), and less than one-half ofthis would be on account of the switching-surge distribution; 1foot is thus a proper safety adder for the tower window clearance.The authors have presented a very interesting paper and it is

hoped that they, as well as other investigators having access to atransient network analyzer, will continue to use these tools for thistype of general studies and that results will be reported in thisTRANSACTIONS. What is particularly needed in the future is someinvestigation of distributions composed from several system condi-tions and some thinking on how distributions will change with time.

REFERENCES[10] N. D. Reppen, "Significance of assumptions in switching-surge

flashover calculations," Paper 70 CP 39, presented at theIEEE Winter Power Meeting, New York, N. Y., January25-30, 1970.

[11] S. Annestrand, E. F. Bossuyt, and N. D. Reppen, "Insulationanalysis of a 500-kV transmission line design," IEEE Trans.Power Apparatus and Systems, vol. PAS-89, pp. 429-437,March 1970.

A. J. McElroy (American Electric Power Service Corporation,New York, N. Y.): The authors have prepared a thought-provokingpaper on a timely subject. From their list of references it wouldappear that the overvoltage probability aspect of transmission lineswitching-surge reliability has remained dormant for some 3years. Perhaps in the interim period it has proven a more simpleand direct task to publish laboratory data on transmission towerflashover behavior than to come to grips with what the authors haveagain demonstrated to be a highly complex problem in overallline design.The authors present a plethora of original ideas based on the

exhaustive study of a particular transmission system. By presentinga self-criticism they acknowledge that the validity of their resultsmay be restricted in application to an extent yet unknown. There-fore, many questions this discusser might raise are best withhelduntil the other investigations the authors call for are carried out.

Perhaps the authors would consider the following specific ques-tions. With what statistical confidence do the Gaussian and theirextreme value distributions fit the data of Figs. 5 and 9, respec-tively? Since the overvoltage distribution functions must be sub-ject to a cutoff (truncation), then by what approximate factor willthe probability of flashover per switching operation be modified byassuming a smooth (continuous second derivative) functionaltransition between either the Gaussian or their extreme value dis-tribution and the voltage level of truncation?

In the text the authors suggest that consideration be given todesigning a transmission line for 1 switching-surge flashover per 100breaker operations. This significant suggestion is however apparentlyobscured in their summary and conclusions where they call upon arather different arguement, i.e., that of 1 flashover per 100 years orless. Based on [6] the discusser suggests that the following reliabilitycriterion be considered: with 99.9-percent confidence require thatthe number of flashovers be no more than 1 per 100 breaker oper-ations; on this basis specify the mean flashover rate, the preciselevel being established by suitable statistical procedures once anappropriate density function is established-in [6] a Poisson func-tion is assumed whereby the mean flashover rate for the presentexample would be significantly reduced to 1 per 500 breaker opera-tions. Once the adjusted mean is established, the procedure sug-gested in the paper might be pursued. (In this regard would theauthors define the meaning of s and 1ii.)In conclusion, the discusser notes with great interest the authors'

suggestion of a topological search. Relations should be establishedto- obtain the overvoltage probability density function directlyfrom the constant voltage contours of Fig. 4, once a breaker closingprobability function, even in its most general form, has been as-signed.

Manuscript received April 9, 1970.

1467


TABLE IV500-KV DESIGN DEMONSTRATION

Air Gap Tower Flashover Location Cost per MileInsulators Leg Truss CFO Insulators Leg Truss Surges Years Installed(number) (feet) (feet) (kV) (percent) (percent) (percent) per Flashover per Flashover (dollars)

27 15 16.5 1358 37 30 33 1 069 000 000 106 900 00027 14 15.4 1307 23 38 39 57 260 000 5 726 000 99 00027 13 14.3 1251 11 45 44 2 510 000 251 00027 12 13.2 1191 4 50 46 118 500 11 850 85 00027 11 12.1 1128 1 53 46 6 420 64227 10 11.0 1062 0 56 44 459 46 77 00027 9 9.9 994 0 57 43 50 527 8 8.8 924 0 60 40 9 1

Single-circuit rigid towers.All V Strings, specific creep = 1 in/kV.2-pu switching surge-700 kV mean, 7.5-percent c.100-mile line, 500 towers.Assume 10 high-speed reclose operations per year.

W. S. Price (Bechtel Corporation, San Francisco, Calif.): EffectiveEHV line design requires calculatioin of the line performance bystatistical consideration of the tower flashover and switching-surge distributions. Although this problem has been studied before,this is the first paper that permits easy determination of line switch-ing-surge performance for any tower and switching-surge distri-bution.At long intervals a TRANSACTIONS paper appears that is so valuable

that it serves as a source paper for much future work. We believethat this excellent paper is in this category and predict that it will beused for many future EHV line designs.Our only disappointment with the paper is that it came 2 years

too late to assist in the design of the Churchill Falls, Labrador,735-kV system. During this work, we were interested in reducingphase spacing from 50 to 45 feet, which eventually saved $5 out of$65 million in installed cost, primarily in tower and foundation steel.However, because of the importance of this 5000-MW transmissionsystem, this gap reduction required a reasonable calculation of theeffect on line switching-surge performance. Therefore, a time-sharecomputer program called TPROB was developed which made a pre-cision integration of [6, eq. (5)].

It seemed worthwhile to compare TPROB results with the paper,as shown in Fig. 23. The curves of 5-, 10-, and 20-percent switching-surge slope, 500 and 2000 towers, were traced from Fig. 13(a).The circles are TPROB calculations, indicating a 1/1 correspondence.Similar results were obtained with a TPROB calculation of Fig. 16(a),using an extreme value switching-surge distribution. Obviously,the curves in the paper are quite correct and can be used withconfidence.Perhaps the importance of using these curves during EHV line

design work can be emphasized by presenting a recent study of 8hypothetical 500-kV lines, as shown in Table IV.For all designs, 27 standard insulators were used to prevent 60-Hz

contamination flashovers, such as might occur in the Ohio Rivervalley or in agricultural regions. Leg gaps were reduced in 1-footincrements from 15 to 8 feet.The composite tower CFOs were calculated by a TOWER program,

based on the air gap and insulator curves in [121. This program haschecked to within a few percentage points the tower CFOs of allpublished full-scale tests.TPROB then calculated the surges per flashover for each of the

designs, assuming 2-pu switching surges with normal distributionand a 100-mile line. Note that the 15-foot tower would require morethan 1 billion surges to produce 1 flashover, or 100 million years,assuming 10 high-speed reclose operations per year. At the otherend of the scale, the 8-foot tower would require only 9 surges perflashover, or 1 per year.

All this would be little more than an interesting academic exercise,were it not for the cost saving associated with gap reductions. Note


z PS/Yr 1. X d-f/C-FO-.4% /4/~~~~~~~~~~

----4-0.-

0~~~~~f/FFig. 23.

Z~~~~~~~~

a.

10

reduced~~~~>brkn ietoe orus

0

0.5 Ai 0.7

,0/CFO

Fig. 23.

in the last column of Table IV that the 10-foot tower will reducetotal installed costs by $22 000 per mile over the 14-foot tower.This assumes average material and labor costs, for single-circuitrigid steel towers. Most of this saving is in tower leg steel, throughreduced broken wire tower torques.

It is interesting to note in Table IV that the insulators are com-pletely out of control of the flashover path for gaps of 12 feet or less.Therefore, the performance figures calculated for the smaller towersare good for rain along the entire line, since the air-gap strength isnot appreciably affected by rain.Good line design requires a happy balance of all design parameters.

Therefore, the smaller designs noted would require full considerationof hot line maintenance, radio and audible noise, and bad weathercorona losses.In the overall line coordination problem, the surge distribution

is just as important as the tower distribution. Unfortunately, in-dustry effort during the past seven years has been heavily biasedtoward the tower side, with several million dollars worth of full-scale tower tests. Therefore, the authors certainly deserve thegratitude of the industry for their heroic efforts to better definesurge distributions with miniature system studies.

Their work indicates that the distribution with breaker resistors isprobably extremal. Comparison of Figs. 13(a) and 16(a) shows thatline probability for the extremal surge is approximately 100 timesthat for the normal surge, which might be cause for some panicduring a close coordination study. However, comparison of Figs.13(a) and 17(a) indicates that probability with an extreme value

1468


distribution and a reasonable ratio of 0.8 between sending andreceiving ends is only about 10 times that of the normal distributionwith level voltage. Therefore, either one of these combinationsappears reasonable for future coordination work.

This is truly a fine and most imnportant paper.

REFERENCES[12] EHV Transmission Line Reference Book. New York: Edison

Electric Institute, 1969, ch. 6.

Andrew R. Hileman, P. R. Leblanc, and Gordon W. Brown: Theauthors are indebted to the discussers for their excellent critiques ofthe paper, which add greatly to its usefulness.As mentioned in the paper, Mr. Glavitsch has proposed a method

for determining the tail of the frequency distribution of switching-surge magnitudes. This method is similar to that referred to as atopological search technique in the paper. We are indebted to Mr.Glavitsch for his further discussion of his proposal.

In answer to Dr. Clerici and Dr. Colombo, equal aiming pointswere assumed for the three circuit breakers. That is, a class ofbreaker was assumed instead of specific breakers on a particularline, in which case, each of the three breakers could possess differentaiming points.From Fig. 19 it is noted that only 2 to 4 percent of the tail of the

frequency distribution is of importance in determining the prob-ability of line flashover. The problem then is to determine a methodthat can be used to determine this part of the distribution curvewith sufficient accuracy. The most important single value is themaximum overvoltage. This value can be found easily but itsprobability of occurrence is difficult. As shown in Fig. 8, even 200cases appears questionable with regard to an adequate description ofthe frequency distribution when the maximum overvoltage is 3.3pu. However, the number of random cases required tends to decreaseas the maximum overvoltage decreases. In this paper, the "bruteforce" or systematic method was used to develop the frequencydistribution when no preinsertion resistors were used in the breaker.This laborious method is certainly not suggested for normal use.We hope that other methods, such as the topological search, can bedeveloped. If sufficient cases are taken, the random method can beemployed.

In answer to Dr. Clerici and Dr. Colombos' third question, in thispaper it is assumed that the negative polarity insulation strength issufficiently greater than that for positive polarity that its effect maybe neglected in the line flashover calculations. Or in other words,V-string insulators are assumed. For vertical string, the negative wetstrength is equal to or less than the positive wet strength. There-fore, the maximum overvoltage of the three phase voltages was read.Assuming this to be positive polarity, the maximum positive polarityvoltages on the other two phases were obtained, and the positivepolarity overvoltage subsequent to or preceding the maximum over-voltage is recorded.

It is agreed that the wavefront of the switching surge is of im-portance in determining the line insulation design. For 1200-1800-Is"smooth" wavefronts,-the CFO voltage increases by 11 to 21-percent[3]. However, shorter front voltage spikes on top of the "smooth"wave decreases the insulation strength significantly. In this study nolarge variation of wavefronts occurred for the higher magnitudeovervoltages.-Mr. Reppen has proposed a simplified method of probability

estimation based on average conditions. Although not stated, itappears that Mr. Reppen has assumed a 100-mile line with 5 towersper mile and a Gaussian frequency distribution of switching-surgemagnitudes. Average weather conditions are assumed based onhistorical data from Portland at an elevation 30 feet above sea level.Also, it appears that Mr. Reppen has assumed V-strong insulators,thus neglecting wind swing and discounting the effects of negativepolarity flashover.The method is simple and direct and therefore could be used for

preliminary investigations at 500 kV and above. It is agreed that amore thorough study of the parameters should be made at 500 kV

Manuscript received April 6, 1970; revised April 16, 1970.

and above. In this regard, the authors feel that a comment on dis-tribution severity is in order. It seems clear that above 500 kV,increasing efforts will be made to reduce the maximum switchingsurge by use of preinsertion resistors and/or controlled closing of thebreaker. Such measures will reduce absolute maximums, but willresult in more "moderately high" voltage surges. That is, the slope ofFig. 21 will be reduced and the meaning of distribution severitybecomes less clear.

In contrast to Mr. Reppen, the authors are of the opinion that thetail of the overvoltage distribution is of prime importance andmethods are needed to describe this portion of the curve moreaccurately. We agree with Mr. Reppen that the variation of weatherconditions is of importance and must be considered in the line in-sulation design. The discusser's approach appears to be to employ astatistical distribution of all hourly weather observations. However,since as assumed in the paper, the majority of high-speed-reclosebreaker operations occurred during and as a result of lightning, itwould be logical to segregate weather distributions into two classes;i.e., those conditions that may produce high-speed circuit-breakerreclose operations that produce the higher values of overvoltageand those weather conditions during which no high-speed reclosingwill be employed. Of these two conditions, the first is of majorimportance in assessing the system's reliability and therefore shouldbe separately analyzed for its outage probability.Mr. Reppen's comment on the effects of multiple peaks is well

made. The effect of previous voltage surges on the flashover prob-ability of the surges is not well known. The effect of an oppositepolarity bias voltage has been investigated with conflicting results,and therefore at 500 kV most designers neglected this effect. In thispaper, the second peak was assumed to be independent of the firstpeak. However, additional laboratory investigations of this param-eter are needed.The authors agree fully with Mr. Reppen's last comment about

the need for a composite distribution and an assessment of itspossible changes with time.

Regarding Dr. McElroy's first question, for the Gaussian caseFig. 6 shows the assumed normal curve (dashed line) superimposedover a curve fit through the actual data points, and the corre-spondence appears to be fairly good above the 80-percent probabilitylevel. Confidence intervals were used, however, for the extrerme valuedistribution based on 200 cases. Nearly all data fell within 1 standarderror of the extreme value regression line, except where the readingerror (± .025 pu) exceeded the standard error.

Dr. McElroy also wishes to know how the probability of flashoverwill change if a smooth transition from the assumed distribution tothe truncation voltage. This of course is dependent on the kind oftapering that is used and at what point it should begin. Also, thedifference will be most evident when the probability of line flashoveris small (Fig. 19).

Regarding Dr. McElroy's final point, the probability of flashoverper switching operation must be brought into the correct perspectiveby accounting for the number of breaker operations per year. Oneoperation per year was assumed in the conclusions of the paper,but it is actually quite dependent on environmental conditions,particularly the frequency of lightning storms. Also, the authorsfeel that the 99.9-percent confidence suggested by Dr. McElroyis much too high for practical purposes.One final point is that I,r and ys were not properly defined in the

paper. The subscripts s and r denote the sending and receiving endsof the line, respectively, so that ,S//IT is a measure of the voltagevariation along the line.The authors would like to particularly thank Mr. Price for his

gracious discussion and to also thank him for placing in dramaticperspective the financial advantage of the use of probability methodsin line insulation design. In 1968, when Mr. Price and G. G. Sauv6presented [13], the discusser developed his TPROB program todetermine the required line insulation strength using probabilityanalysis.Again the authors wish to thank the discussers, all of whom are

recognized experts in this and related fields. Their encouragement andprobing comments are appreciated.

REFERENCES[131 W. S. Price and G. G. Sauve, "Insulation coordination and

conductor selection for the Churchill Falls 735-kV transmissionlines," presented at the IEEE EHV Conference, Montreal,P. Q., Canada, September 30-October 2, 1968.

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Estimating the Switching-Surge Performance of Transmission Lines