05458024

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 3, JULY 2010 1855

Estimation of Lightning Incidenceto Overhead Transmission Lines

Pantelis N. Mikropoulos, Member, IEEE, and Thomas E. Tsovilis, Student Member, IEEE

AbstractGeneral expressions for the estimation of lightning in-cidence to overhead transmission lines on the basis of electroge-ometric and generic models are introduced, which consider, be-sides transmission-line geometry, lightning crest current distribu-tion and, based on the recently proposed statistical model, intercep-tion probability distribution. An application to typical 115 kV upto 765 kV and large scale 500 kV and UHV overhead transmissionlines is performed and the computed results, varying significantlyamong lightning attachment models, are validated through com-parisons with field data from literature; the IEEE Std 1243 over-estimates significantly lightning incidence to shield wires of largescale transmission lines. The expected annual number of lightningstrikes to shield wires of transmission lines depends on lightningcrest current distribution; this dependence, easily quantified withthe aid of the introduced general expressions, is not considered bythe relevant IEEE standard. Lightning incidence results are dis-cussed in the context of the backflashover rate of overhead trans-mission lines.

Index TermsInterception probability, lightning, lightning at-tachment models, lightning incidence, overhead transmission lines.

I. INTRODUCTION

L IGHTNING is the main cause of transmission-lineoutages affecting reliability of power supply thus, con-sequently, resulting in economic losses. Therefore, shieldingagainst direct lightning strokes to phase conductors of trans-mission lines is provided by shield wires, which are metallicelements that are able to, by physical means, launch a con-necting upward discharge that intercepts the descendinglightning leader from a distance called striking distance withina capture radius commonly called attractive radius or lateral dis-tance. Lightning strokes intercepted by shield wires, increasingthe potential of the transmission-line tower, may result in trans-mission-line outages due to backflashover, that is, insulationflashover between the tower and a phase conductor. Apparently,some of the less intense lightning strokes, not being interceptedby shield wires terminating thus to the phase conductors, maycause transmission-line outages due to shielding failure.

Transmission-line outages due to shielding failure can beestimated by implementing electrogeometric models [1][15],which, employing the striking distance as the basic shielding

Manuscript received July 08, 2009; revised October 06, 2009 and February16, 2010. First published May 03, 2010; current version published June 23,2010. Paper no. TPWRD-00499-2009.

The authors are with the Department of Electrical Energy, School of Electricaland Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki,54124 Greece (e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TPWRD.2010.2046918

design parameter, are widely used for shielding analysis inaccordance to the relevant IEEE Std [16]. The same standardfor the estimation of the transmission-line outages due tobackflashover suggests the use of Erikssons method [17]in lightning incidence calculations, that is, the estimation ofthe number of lightning strikes to shield wires. Erikssonsmethod [17] employs the attractive radius as the basic lightninginterception parameter; the latter is commonly employed inmany other models based on physical ground of lightningattractiveness [17][30], called hereafter as generic modelsin accordance with Waters [31]. An alternative approach forevaluating the lightning performance of overhead transmissionlines is through computer simulations employing leader propa-gation models [22], [32][35].

However, shielding analysis and lightning incidence calcula-tions for overhead transmission lines, both being associated tothe lightning attachment phenomenon, should be possible to becarried out by applying the same lightning attachment model.There is a lack of simple expressions in literature to performboth tasks on the basis of either electrogeometric or genericmodels. Also, shielding analysis and lightning incidence calcu-lations should take into account, besides transmission-line ge-ometry and lightning crest current distribution, the interceptionprobability distribution, i.e. the probability distribution of anupward connecting discharge, by considering the striking dis-tance and attractive radius of a conductor as statistical quanti-ties; this is not considered by either electrogeometric or genericmodels. A probability distribution of the striking distance, witha mean value and a fixed standard deviation, was estimatedthrough shielding analysis in [7][9]. Recently, investigationsthrough scale-model experiments made possible to obtain prob-ability distributions of striking distance and interception radius,thus a statistical lightning attachment model has been proposed[36][39].

This study introduces general expressions for the estimationof lightning incidence to overhead transmission lines on thebasis of several lightning attachment models. Thus, the numberof lightning strikes to shield wires of overhead transmissionlines can be easily estimated by considering, besides transmis-sion-line geometry, the lightning crest current distribution; therewas a lack of such expressions in literature. Also, simple ex-pressions for lightning incidence calculations on the basis of thestatistical model are presented, which yield an expected rangeof lightning strikes to shield wires depending on interceptionprobability distribution; a preliminary account has been givenin [40]. The effects of lightning attachment model and light-ning crest current distribution on lightning incidence to shieldwires are demonstrated quantitatively through an application totypical 115 kV up to 765 kV and large scale 500 kV and UHV

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1856 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 3, JULY 2010

TABLE IFACTORS AND TO BE USED IN (4)

overhead transmission lines. Lightning incidence results are val-idated through comparison with field data [17], [41], [42] anddiscussed with respect to the backflashover rate of transmissionlines.

II. LIGHTNING INCIDENCE CALCULATIONS METHODOLOGY

The annual number of lightning strikes to shield wires per 100km of a transmission line is given as

(1)

where is the ground flash density, (inmeters) is the separation distance between shield wires, and(in meters) is the equivalent interception radius of the shieldwire. can be calculated by integrating the conductor inter-ception radius , commonly called attractive radius or lateraldistance, weighted by the probability density function of thelightning crest current distribution as

(2)

where is the prospective lightning crest current and is theheight of the conductor.

According to [43], the probability density function of thelightning crest current is lognormally distributed as

(3)

where and are the median value and the standard de-viation of the natural logarithm of the lightning crest current,respectively.

Simplified expressions for are summarized in [44]. Fromthese expressions and (1), the equivalent interception radius ofa conductor can be given as

(4)

where (in meters) is the height of the conductor and factorsand listed in Table I.

It is noteworthy that Andersons method [13], commonlycalled the electrical shadow method, and Erikssons method[17], adopted by IEEE Std. [16], are widely used for lightningincidence calculations.

According to (1), the task of estimating lightning incidenceto transmission lines can be reduced to the estimation of theequivalent interception radius.

Fig. 1. Lightning interception according to electrogeometric models; striking distance to conductor; striking distance to earth surface; intercep-tion radius; and height of the conductor.

TABLE IIFACTORS , AND TO BE USED IN (5)

III. EQUIVALENT INTERCEPTION RADIUS FORMULATIONBASED ON DIFFERENT LIGHTNING ATTACHMENT MODELS

A. Electrogeometric ModelsAccording to electrogeometric models, the striking distance

, which is defined as the distance between the descendinglightning leader and the struck object at which the upward con-necting discharge is initiated, is related solely to the prospectivelightning crest current and can be associated to striking distanceto earth surface by using a factor as

(5)

where (in kiloamperes) is the prospective lightning crest cur-rent and , are in meters; factors , , and are listed inTable II as proposed by different authors.

The implementation of electrogeometric models in lightninginterception is described, based on Fig. 1, as follows. For a de-sign lightning crest current, the striking distances to conductor

and to the earths surface are calculated according to (5)and Table II. Next, an arc of radius from the conductor and aline parallel to earths surface at a height are drawn. A ver-tically descending lightning leader reaching the arc betweenand will strike the conductor. Hence, the interception radius

of a conductor with height (in meters) is given as

for (6a)for (6b)

MIKROPOULOS AND TSOVILIS: ESTIMATION OF LIGHTNING INCIDENCE 1857

Despite their simplicity and widespread applicability, theelectrogeometric models, with the only exception of [3], donot consider the effects of the struck object height on strikingdistance . Also, most electrogeometric models employ in (5)a constant value for factor (Table II). However, shoulddepend on the struck object height, lightning crest current, andinterception probability [37].

By using (6), (2) becomes

(7)where is the lightning crest current for which

and , , and are given in Table II. Equation (7) hasbeen solved by performing numerical integration with the aid ofa mathematical software package, on the basis of the electroge-ometric models shown in Table II. The equivalent interceptionradius was found to be well approximated, errors generally lessthan 10%, by the following expression:

(8)

where

(8a)(8b)(8c)

where (in kiloamperes) and are the median value andthe standard deviation of the natural logarithm of the lightningcrest current, respectively, and factors , and are given inTable II. Equations (8a)(8c) are valid for the conductor heightin the range of 10 m up to 70 m and for ; the latter valuecorresponds to the ultra-high voltage (UHV) lines according to[13]. For 1.56 and/or for conductors higher than 70 m, validexpressions for factors , , and in (8) are , ,and .

An attempt to calculate the equivalent interception radius ofa conductor on the basis of electrogeometric models was madebefore by Pettersson [45]. However, as this was also discussed in[46], Petterssons method can be applied only for those modelsemploying 1 and gives satisfactory results for relatively lowconductor heights; this is evident in Fig. 2 where the equiva-lent interception radius calculated by (7) is compared to that de-rived from Petterssons method [45] and to that calculated fromthe simplified expression (8) on the basis of models [5] and [8]which employ for values of 1.11 and 1, respectively. It must benoted that (8), which approximates the equivalent interceptionradius well (Fig. 2), considers conductor height, lightning crestcurrent distribution, and the electrogeometric model employedin calculations.

B. Generic ModelsEriksson [17], [18] introduced in shielding analysis and light-

ning incidence calculations the attractive radius, which is thecapture radius within which the upward discharge emanatingfrom an air terminal intercepts the downward leader. FollowingErikssons work, lightning attachment models that consider the

Fig. 2. Equivalent interception radius as a function of conductor height; 30.1 kA, 0.76.

inception of the upward connecting discharge emerging fromthe prospective struck object were developed [19][30]. Thus,based on different leader inception criteria, striking distance andattractive radius expressions taking into account, besides light-ning parameters, air terminal height were derived. The intercep-tion radius of a conductor, , defined as the longest lateral dis-tance from the conductor where lightning attachment occurs,can be generally expressed as

(9)where is in meters, (in kiloamperes) is the prospective light-ning crest current, (in meters) is the conductor height, and fac-tors , , , and are listed in Table III according to differentauthors. It must be noted that the values for factors , , andcorresponding to models [25] and [30] in Table III do not referto the transmission-line geometry; however, employing thesemodels in lightning incidence calculations for overhead trans-mission lines may provide useful information concerning theirapplicability.

By combining (2) and (9), the equivalent interception radiuson the basis of generic models can be given as

(10)

where (in kiloamperes) and are the median value and thestandard deviation of the natural logarithm of the lightning crest


TABLE IIIFACTORS , , , AND TO BE USED IN (9)

TABLE IVCOEFFICIENTS AND EXPRESSIONS OF TO BE USED IN (11)

current, respectively, and factors , , , and are given inTable III. It must be mentioned that (10), as (8), takes the con-ductor height, lightning crest current distribution, and the light-ning attachment model employed in calculations into account.

Generic models [17][30], although adding significant valueto the knowledge of lightning attachment, do not consider in-terception probability. For a given conductor height and light-ning crest current, they yield a specific value of interception ra-dius instead of a range of interception radii corresponding todifferent interception probabilities; the latter is more realisticwhen considering the stochastic nature of lightning interceptionphenomenon. Thus, generic models, such as electrogeometricmodels, may attribute statistical behavior of interception radiusonly through the lightning crest current distribution.

C. Statistical Model

Lightning attachment is a stochastic phenomenon; thus, themost commonly employed parameters in shielding analysis,namely, striking distance and attractive radius, should be con-sidered as statistical quantities varying, besides struck objectheight and lightning crest current, with interception probability[36][39]. The interception radius, being statistically normallydistributed [37], is expressed by its mean value and standarddeviation as

(11)

where (in meters) is the conductor height, (in meters) is thestriking distance to earth surface, and values for the coefficients

, , and , in formula form, are given in Table IV [39].Equation (11) is valid for ; for the

asymptotic value of (11) at unity (i.e., the coefficient )may be adopted. Taking into account that the striking distanceto earth surface is a function of the lightning crest current

(12)

by combining (11) and (12), the interception radius can be de-fined as a function of conductor height, lightning parameters,and interception probability. For negative lightning, a widelyused expression in literature for (12) is

(12a)

where is in meters and is in kiloamperes. Thus, by usingthe set of (2), (3), (11), and (12a), the equivalent interceptionradius probability distribution can be readily described by itsmean value and standard deviation, the latter formulatedwith the aid of mathematical software, as [40]

(13a)

(13b)

where (in meters) is the conductor height, and (is in kilo-amperes), are the median value and the standard deviationof the natural logarithm of the lightning crest current, respec-tively. Equations (13a) and (13b) take into account in equiva-lent interception radius calculations, besides conductor heightand lightning crest current distribution, the interception proba-bility distribution. Thus, the equivalent interception radius ,being statistically normally distributed, can be calculated at dif-ferent interception probabilities; hereafter is estimated at2.5% (failure), 50% (critical), and 97.5% (attractive) intercep-tion probabilities.

IV. LIGHTNING INCIDENCE CALCULATION RESULTS

A. Effect of Lightning Attachment ModelFig. 3 shows the variation of the equivalent interception ra-

dius with conductor height, together with field observation datareported in [17] and [41]. The curves in this figure were drawnby using the simplified expressions of given in Table I andthe expressions of shown in Table V, which were derivedwith the aid of (8) for , (10) and (13) for the lightningcrest current distribution with 30.1 kA and 0.76 sug-gested in [43]. From Fig. 3, it is obvious that there is a great vari-ability in equivalent interception radius among lightning attach-ment models in respect of both value and rate of increase withincreasing conductor height. As a general result, the electroge-ometric models yield shorter , especially for higher conduc-tors. The statistical model [39]; electrogeometric models [5] and[16]; generic models [20], [21], [25], and [30]; as well as themethods suggested in [44], with the exception of the electricalshadow method [13], agree satisfactorily with the data points TLand PA. It is important to note that TL, referring to an 11-kV testline studied over some six years, is regarded as the most reliabledata point according to Eriksson [17], and that PA, referring toa 20-kV distribution line under study for eight years, has beenderived from [41]; in both studies, direct flashes to line wererecorded together with the local ground flash density. Genericmodels [18] and [27] as well as most of the electrogeometricmodels underestimate for lower conductor heights as theydeviate significantly from TL and PA data points (Fig. 3); this isalso true for the electrical shadow method [13], as stated in [44].


Fig. 3. Equivalent interception radius as a function of conductor height. Pointsdepict field data; the empty point PA has been derived from [41] and solid points,including TL, are from [17]. Vertical bars denote the dispersion in observedover the period of study and the recorded uncertainties in the observed strikeincidence; horizontal bars represent the range of conductor height along the spanof the lines [17].

Yuans model [26] is not included in Fig. 3 since it significantlyoverestimates the equivalent interception radius.

Table V also shows the expected annual number of lightningstrikes to shield wires per 100 km, , of typical 115 kV up to765 kV overhead transmission lines; line parameters are shownin Table VI. The results of Table V were obtained for the light-ning crest current distribution with 30.1 kA and 0.76and by assuming a ground flash density strikes/km yr.

TABLE VLIGHTNING INCIDENCE RESULTS FOR TYPICAL 115 765-kV

OVERHEAD TRANSMISSION LINES, (strikes/100 km/yr)

As expected, due to the equivalent interception radius variationsamong lightning attachment models (Fig. 3), there is a greatvariability in ; differences in value of among modelsare up to 170%, with electrogeometric models yielding gen-erally smaller . This is considered significant since the ex-pressions of equivalent interception radius shown in Table Vinvolve approximation error only for electrogeometric models,generally less than 10%. It must be mentioned that Erikssonsmethod [17], which has been adopted by the IEEE Std [16],yields the greatest values, up to 70% greater, among themethods suggested in [44] for lightning incidence calculations(Table V). The statistical model, by taking into account the in-terception probability distribution, yields instead of a specificvalue an expected range of ; within this range are the resultsof the methods suggested by IEEE Working Group [44], thusalso IEEE Standard [16], for estimating lightning incidence tooverhead transmission lines (Table V).

B. Effect of Lightning Crest Current DistributionThe equivalent interception radius of a conductor depends,

besides lightning attachment model, on lightning crest current


TABLE VIPARAMETERS OF TYPICAL 115 765 kV OVERHEAD LINES [47]

TABLE VIILIGHTNING CREST CURRENT DISTRIBUTION PARAMETERS

Fig. 4. Equivalent interception radius as a function of conductor height withlightning crest current distribution as the parameter.

distribution. It is well established that the latter varies, as also, seasonally and geographically [43]. For engineering appli-

cations the use of the lightning crest current distribution witha median value and is suggestedin [43]. Table VII shows the statistical parameters of three dif-ferent lightning crest current distributions, which hereafter areemployed to show the effect of the lightning crest current dis-tribution on , thus also on , calculations; the distributionwith a median value and refers to strokesto flat ground [48] and is adopted by the IEEE Std 998 [50].Fig. 4 shows the equivalent interception radius as a function ofconductor height with the lightning crest current distribution asparameter. increases with increasing ; this is more evidentfor higher conductors, generic models and at the lower intercep-tion probabilities according to the statistical model.

Fig. 5 shows the variation of with lightning crest currentdistribution by employing in calculations the lightning attach-ment models [5], [21] and [39]. Obviously, due to varia-tions with lightning crest current distribution (Fig. 4), in-creases with increasing . Actually, it was found that, dependingon lightning attachment model used in calculations, variesup to 45% in the range of shown in Table VII. It is must benoted that these effects of the lightning crest current distribution

Fig. 5. Annual number of lightning strikes to shield wires per 100 km of typical115 765-kV transmission lines with lightning crest current distribution as theparameter; , values obtained from the statisticalmodel refer to 2.5% interception probability.

on are not considered by the lightning incidence calculationmethod suggested by IEEE Std [16] as evinced by the straightlines parallel to -axis in Fig. 5.

C. Application to Large-Scale Transmission LinesField observations of lightning strokes to large scale 500-kV

and UHV transmission lines have been reported recently [42].Table VIII shows the actual values quoted in [42] togetherwith the expected values calculated on the basis of differentlightning attachment models, with the aid of (8), (10), and (13)and by assuming a lognormal lightning crest current distributionwith 30.1 kA and 0.76. Deviations approximatelyup to 2.5 times the actual are observed among lightning at-tachment models; electrogeometric models yield expectedvalues smaller compared to the actual values, whereas theopposite is true for generic models. The IEEE method [16] forboth lines overestimates by about 70% whereas among themethods suggested in [44], Rizks method yields the smallestdeviations from the actual values. The application of thestatistical model yields satisfactory results; deviations betweenthe mean value (critical) of the expected range of and theactual values are 3% and 11% for the 500-kV and UHVlines, respectively. These results can also be deduced from Fig. 6which shows as calculated by employing the lightning crestcurrent distributions shown in Table VII. Obviously, deviationsfrom the actual values depend, besides lightning attachmentmodel, on lightning crest current distribution; the latter depen-dence is not considered by the electrical shadow method [13]and Erikssons method [17], thus also by the method adoptedby IEEE Standard [16] (Fig. 6).

V. IMPLICATIONS IN BACKFLASHOVER RATE OFOVERHEAD TRANSMISSION LINES

A lightning stroke terminating to shield wires increasesthe potential of the transmission-line tower. If the potentialdifference across the line insulation exceeds the insulationstrength flashover occurs, a phenomenon commonly calledbackflashover. Thus, the annual number of backflashovers per


TABLE VIIILIGHTNING INCIDENCE RESULTS FOR LARGE-SCALE OVERHEAD

TRANSMISSION LINES, (strikes/100 km/yr)

100 km of a transmission line, , being a percentage of ,can be estimated by the following expression:

(14)

where is the probability of lightning crest currentbeing greater than the minimum lightning crest current causingbackflashover, , and , are given in (1) and (3), re-spectively. The factor 0.6 is used in (14) to consider the effectof strokes within the span [47]. By using an approximate expres-sion for , such as Andersons [13], (14) becomes

(15)

From (14) it is obvious that varies analogously toand depends, besides which is a function of several geomet-rical and electrical parameters [47], on lightning crest currentdistribution. Fig. 7 shows the variation of with for the765-kV line; line parameters are shown in Table VI. Evidently,the effect of lightning attachment model on the expected isanalogous to that found for ; thus, in general, is higherfor generic [Fig. 7(b)] than electrogeometric [Fig. 7(a)] models.The variation of with the lightning attachment model be-comes less important for relatively higher , which, accordingto [47], corresponds to higher insulation levels and lower towerfooting resistances. Also, from Fig. 7(c), it is evident that the ex-pected range of , estimated by using the statistical model,

Fig. 6. Annual number of lightning strikes to shield wires per 100 km of large-scale transmission lines with lightning crest current distribution as parameter;dotted lines depict the actual values.

agrees favorably with the values yielded by employing themethods suggested by the IEEE Working Group [44] and IEEEStandard [16] for calculations.

The effect of lightning crest current distribution on isdemonstrated in Fig. 8 by employing in calculations the light-ning crest current distributions shown in Table VII. It can bededuced that , augmenting notably with increasing , de-pends less upon the lightning attachment model [Fig. 8(a)] andinterception probability [Fig. 8(b)] as becomes lower. Closeexamination of the results shows that the increase of with

is more pronounced for higher , where for 39.2kA is 10 times higher than that found for 24 kA (Fig. 8).

VI. DISCUSSIONThe expected annual number of lightning strikes to shield

wires of a transmission line depends upon the ground flashdensity and equivalent interception radius of the shield wires.The equivalent interception radius of a conductor varieswith the lightning attachment model employed in calculationsand depends on the conductor height (Fig. 3) and lightning crestcurrent distribution (Fig. 4). In an analogous way to , theexpected annual number of lightning strikes to shield wires of atransmission line varies with the lightning attachment model(Table V) and depends on line geometry (Table V) and lightning


Fig. 7. as a function of with lightning attachment model as param-eter; 765 kV overhead transmission line, 30.1 kA, 0.76, strikes/km yr.

crest current distribution (Fig. 5). Lightning incidence calcula-tions for typical 115-kV up to 765-kV transmission lines showeddifferences in values of up to 170% among lightning attach-ment models and up to 45% among the lightning crest currentdistributions of Table VII.

Both IEEE Standard [16] and the IEEE Working Group [44]suggest for lightning incidence calculations for transmissionlines the use of height-dependent expressions for (Table I),which do not take into account the variation of the latter withlightning crest current distribution. This is important when

Fig. 8. as a function of with lightning crest current distribution asparameter; 765-kV transmission line, strikes/km yr .

considering that the lightning crest current distribution variesseasonally and geographically [43] and, even more so, that thereis a general concern that the lightning crest current distributionsuggested in [43] is probably biased to higher values and shouldnot be used directly to lightning incidence calculations [23],[48], [51], [52]. Hence, it is essential to employ in lightning in-cidence calculations for transmission lines an expression ofwhich considers, besides conductor height, the lightning crestcurrent distribution. These expressions of are given in (8)and (10) for electrogeometric and generic models, respectively.In addition, the expression given in (13), on the basis ofthe statistical model, considers, besides conductor height andlightning crest current distribution, interception probabilityand yields results in satisfactory agreement with field data[Fig. 3(c)]. An application of (13) in lightning incidence cal-culations yields instead of a specific value an expected rangeof (Table V), which is more realistic when considering thestochastic nature of lightning interception phenomenon. Thesimple working expressions (8), (10), or (13), depending on theemployed lightning attachment model, enable the estimationof lightning incidence to transmission lines without requiringextensive computing effort, such as numerical integration orcomputer simulation.

An application of (8), (10), and (13) in lightning incidencecalculations has been made for typical 115 kV up to 765kV (Table V and Fig. 5) and large-scale 500 kV and UHV(Table VIII and Fig. 6) transmission lines. Depending on the


lightning attachment model, increases with an increasingmedian value of lightning crest current distribution, a factthat is not considered by the lightning incidence calculationmethods suggested by IEEE Std [16] and IEEE Working Group[44] (Figs. 5 and 6). Electrogeometric models yield generallysmaller values, especially for relatively higher transmissionlines. The statistical model yields results in conformity with themethods suggested in [16] and [44] for typical lines (Table V),as was also shown for typical 150-kV and 400-kV lines ofthe Hellenic transmission system in [40]. Also, the statisticalmodel yields satisfactory results with respect to the actual

values reported from field observations [42] in large-scaletransmission lines (Table VIII and Fig. 6). However, this isnot true for the method adopted by IEEE Standard [16] sinceit overestimates by about 70%. Among the methods sug-gested in [44], deviations from the actual are greatest forthe electrical shadow method [13] whereas they are smallestfor the Rizks method [21] (Table VIII). Since the only wayto validate a lightning attachment model when employed inlightning incidence calculations is through a comparison ofcalculated results with field data, based on the findings of Fig. 3and Table VIII, it can be deduced that electrogeometric models[4] and [5], generic models [21] and [25], Rizks method [21],and the statistical model yield results consistent with field ob-servations in transmission lines. However, the authors believethat more and reliable field data are needed to better evaluatelightning attachment models with respect to lightning incidenceto transmission lines.

The IEEE Standard [16] suggests the use of an electrogeo-metric model (Table II) for shielding analysis and the Erikssonsmethod [17] (Table I) for lightning incidence calculations. Im-plementation of this electrogeometric model in lightningincidence calculations yields smaller values compared toErikssons method [17], especially for higher transmissionlines, as can be deduced from Table V and Fig. 9(a). Also,the electrogeometric model [13] (Table II) suggested by IEEEWorking Group [14] for shielding analysis yields differentvalues compared to the electrical shadow method [13] (Table I)suggested for lightning incidence calculations, as can be de-duced from Table V and Fig. 9(b). This approach, employingan electrogeometric model for shielding analysis and a method,commonly based on a generic model for lightning incidencecalculation, results in a safer transmission-line design in termsof shielding angle [53] and backflashover rate (Fig. 6). Nev-ertheless, this was considered as an inconsistency in [54] and[55].

The expected backflashover rate of a transmission linevaries analogously to , with the lightning attachment modelemployed in calculations and transmission-line geometry; theelectrogeometric models yield smaller values (Fig. 7)especially for relatively higher transmission lines and mediancurrent of lightning crest current distribution [Fig. 8(a)]. Also,

, augmenting significantly with increasing median valueof lightning crest current distribution , depends less upon thelightning attachment model [Fig. 8(a)] and interception proba-bility [Fig. 8(b)] as becomes lower. It is must be noted that

depends to a significantly greater extent upon lightningcrest current distribution than ; this is because the lightning

Fig. 9. Equivalent interception radius as a function of conductor height ac-cording to (a) IEEE Standard [16] and (b) IEEE Working Group [14].

crest current distribution affects (Section IV-B) and theprobability of lightning crest current being greater than(14). , together with the shielding failure flashover rate,determine the lightning performance of a transmission line;thus, also its expected outage rate due to lightning strokes.Hence, conscious selection of the lightning attachment modeland of the lightning crest current distribution is needed whenevaluating the lightning performance of transmission lines.

VII. CONCLUSION

General expressions for the estimation of lightning incidenceto overhead transmission lines, on the basis of electrogeometricand generic models, have been introduced, which consider,besides transmission-line geometry, lightning crest currentdistribution and based on the recently proposed statisticalmodel interception probability distribution. Hence, with the aidof simple working expressions, lightning incidence to shieldwires of transmission lines can be estimated without exten-sive computing effort. In addition, the effects of the lightningattachment model and lightning crest current distribution onlightning incidence calculations can be easily quantified.

The estimated lightning incidence to shield wires is smallerfor electrogeometric models, especially for relatively highertransmission lines, and increases with increasing median valueof lightning crest current distribution; the latter dependence is


not considered by the relevant IEEE Standard. Lightning inci-dence calculations for typical 115-kV up to 765-kV overheadtransmission lines showed differences in the expected numberof lightning strikes to shield wires up to 170% among light-ning attachment models and up to 45% among the lightningcrest current distributions employed in calculations. Lightningincidence calculation results have been validated through com-parisons with field data available in literature; for large-scale500-kV and UHV transmission lines, deviations approximatelyup to 2.5 times the actual number of lightning strikes to shieldwires have been observed among lightning attachment models.Certainly more and reliable field data are needed to betterevaluate lightning attachment models with respect to lightningincidence to overhead transmission lines.

Lightning incidence calculations employing the statisticalmodel yield, instead of a specific value, a range of an expectednumber of lightning strikes to shield wires associated withinterception probability distribution; within this range is theresult of the lightning incidence calculations method suggestedby the relevant IEEE Standard for typical transmission lines.Lightning incidence calculation results, according to the statis-tical model, are in good agreement with field observations inlarge-scale 500-kV and UHV transmission lines; this is not truefor the relevant IEEE standard which overestimates by about70% lightning incidence.

The expected backflashover rate of an overhead transmissionline varies with the lightning attachment model and lightningcrest current distribution employed in calculations; this has beendemonstrated for a typical 765-kV line. The expected back-flashover rate is smaller for electrogeometric models, augmentssignificantly up to ten times with an increasing median value oflightning crest current distribution, and as the latter decreases, itvaries less with the lightning attachment model and interceptionprobability.

ACKNOWLEDGMENTThe second author would like to thank the Research Com-

mittee of AUTh for the support provided by a merit scholarship.

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Pantelis N. Mikropoulos (M06) was born inKavala, Greece, in 1967. He received the M.Eng.and Ph.D. degrees in electrical and computer engi-neering from Aristotle University of Thessaloniki(AUTh), Thessaloniki, Greece, in 1991 and 1995,respectively.

He held postdoctoral positions at AUTh and theUniversity of Manchester, Manchester, U.K. Hewas Senior Engineer with Public Power Corp. SA,Athens, Greece. In 2003, he was elected AssistantProfessor in High Voltage Engineering at AUTh,

and since 2005, he has been the Director of the High Voltage Laboratory there.His research interests include the broad area of high-voltage engineering withan emphasis on air and surface discharges, electric breakdown in general, andlightning protection.

Thomas E. Tsovilis (S09) was born in Piraeus,Greece, in 1983. He received the M.Eng. degree inelectrical and computer engineering from AristotleUniversity of Thessaloniki, Thessaloniki, Greece,in 2005, where he is currently pursuing the Ph.D.degree in the High Voltage Laboratory.

His research is dedicated to lightning protection,including theoretical analysis and scale-modelexperiments.

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