Lightning Attachment Models andPerfect Shielding Angle ofTransmission Lines

Pantelis N. Mikropoulos' and Thomas E. TsovilisHigh Voltage Laboratory, School ofElectrical & Computer Engineering, Faculty ofEngineering,

Aristotle University ofThessaloniki, Thessaloniki, Greece,lpnm@eng.auth.gr

(2)

(1)BS=AI =yD

a =sin- l (1_hm+hpJp r 2AI:

II. PERFECT SHIELDING ANGLE FORMULATION BASED ONDIFFERENT LIGHTNING ATTACHMENT MODELS

proposed statistical model. The interdependence of perfectshielding angle, transmission line height and minimumcurrent causing flashover of insulation is demonstrated asinfluenced by the lightning attachment model employed inshielding analysis. Findings are discussed and furtherelucidated through an application to typical 150 kV and400 kV lines of the Hellenic transmission system. Theapplicability of lightning attachment models in perfectshielding angle calculations has been evaluated based on theshielding performance of transmission lines.

where I is in kA, S, D are in meters and factors A, Band yaregiven in Table I as proposed by different authors. For adesign lightning peak current equal to the minimum currentcausing flashover of insulation, L, the latter can be calculatedbased on the geometrical and electrical characteristics of thetransmission line [2], a descending lightning leader will striketo the phase conductor when reaching the arc between M andN; hence, a shielding failure width, W, is defmed (Fig. 1).With decreasing shielding angle a, W decreases, thus there isa critical shielding angle which corresponds to W = 0,hereafter called perfect shielding angle, ape Geometricalanalysis similar to that given in [29] yields the followingexpression, approximating well the perfect shielding angle

A. Electrogeometric modelsElectrogeometric models have historically been employed

in transmission line shielding providing acceptable protectionagainst direct lightning strokes to phase conductors and theyare still widely used [2]. Shielding analysis according toelectrogeometric models follows based on Fig.l. The strikingdistance to conductors, S, is assumed to be related solely tothe prospective lightning peak current, I and can be associatedto striking distance to earth surface, D, by using a factor y as

INTRODUCTIONI.

The shielding design of transmission lines against directlightning strokes to phase conductors, that is the appropriatepositioning of shield wires with respect to phase conductors,can be achieved by implementing electrogeometric models[1], representative of their application is the methodsuggested by IEEE Standard 1243:1997 [2], which employ arelation between striking distance and lightning peak currentin their calculations [3]-[12]. Alternatively, shielding designmay be realized by employing models based on more solidphysical ground of lightning attractiveness [13]-[21], calledhereafter, in accordance with Waters [22], generic models.Recently, a statistical approach in shielding design has beenintroduced [23]-[25] by implementing a lightning attachmentmodel derived from scale model experiments [26]-[28].

A perfect shielding is achieved when lightning strokespossessing peak current greater than the minimum currentcausing flashover of insulation are intercepted. Apparently,some of the less intense strokes may not be intercepted by theshield wires and strike to phase conductors, however these arenot expected to cause flashover. In practice, an effectiveshielding of transmission lines against direct lightning strokesto phase conductors is realized based on an acceptableshielding failure flashover rate.

The present study provides general relationships for theestimation of the perfect shielding angle of transmission lines,which have been derived by performing shielding analysis on where, factors A, B, yare given in Table I, Ie is in kA, andthe basis of electrogeometric, generic and the recently h (m), hp (m) are defmed in Fig. 1.

978-0-947649-44-9/09/$26.00 2009 IEEE

Abstract- General relationships for the estimation of theperfect shielding angle of overhead transmission lines have beenderived by performing shielding analysis on the basis of severallightning attachment models, including a recently introducedstatistical one. The interdependence of perfect shielding angle,transmission line height and minimum current causing flashoverof insulation is demonstrated as influenced by the lightningattachment model employed in shielding analysis. There is agreat variability in perfect shielding angle among lightningattachment models; this is demonstrated for 150 kV and 400 kVlines of the Hellenic transmission system. The applicability oflightning attachment models in perfect shielding anglecalculations is evaluated based on the shielding performance oftransmission lines; the IEEE Std 1243:1997 yields consistentresults with respect to the shielding performance of the lines.

Index Terms-- Direct stroke shielding, lightning, perfectshielding angle, overhead transmission lines.

I'~,I,I

hm I DII hpIIII

C. Generic modelsFollowing Eriksson's work, generic lightning attachment

models have been developed which also consider theinception of the upward connecting discharge emerging fromthe prospective struck object [14]-[21]. Thus, based ondifferent leader inception criteria, expressions of the attractiveradius of an object, R, defined as the longest lateral distancefrom the object where lightning attachment occurs, have beenproposed in the general form

(5)Fig. 1. Shielding analysis according to electrogeometric models. hm shieldwire height; hp phase conductor height; a shielding angle; S striking distanceto shield wire and phase conductor; D striking distance to earth surface;W shielding failure width.

TABLE IFACTORSA, B AND)ITO BE USEDIN(I)

where R is in meters, I (kA) is the prospective lightning peakcurrent, h (m) is the struck object height and factors ~ E andF are listed in Table II according to different authors.

TABLE IIFACTORS?,E ANDF TO BE USEDIN(5)

where hm (m) and hp (m) are defined in Fig.l, and Rm (m),Rp (m) are calculated from (3) for I = L;

(7)

(6)

Generic model ? E FRizk [I5] 1.57 0.45 0.69

Petrov et al. [19]' 0.47 0.67 0.67S. Ait-Amar & Berger [21] 3 0.20 0.67

where factors ~, E, and F are given in Table II, Ie is in kA,and h (m) and hp (m) are defmed in Fig. 2. It must bementioned that models [19] and [21] do not refer to thetransmission line geometry; however, employing thesemodels in perfect shielding angle calculations may provideuseful information concerning their applicability.

D. Statistical modelRecently, investigations on the interception probability of

an air terminal through scale model experiments madepossible the formulation of distributions for striking distanceand interception radius [27], and, thus, a statistical approachin shielding design has been proposed in [24]. Interceptionradius is considered as statistical quantity with a mean value,referring to 50% interception probability , called criticalinterception radius, Rei> and a standard deviation a. It is givenwith reference the striking distance to earth surface as

Thus, for a design lightning peak current equal to theminimum current causing flashover of insulation L; theperfect shielding angle, corresponding to W= 0, is given withthe aid of(5) and (6) as

Following a shielding analysis similar to that of Rizk [15],according to Fig. 2 a shielding failure will occur when thedescending lightning leader enters the shielding failure widthW, which is given as

using as h in (5) the object height plus 15 m.

(3)

(4)

R = 0.67ho.6 I.74

Electrogeometric model A B )IWagner & Hileman [3] 14.2 0.42 I

Iforh 18m462-hh:shield wire height

Armstrong & Whitehead [5] 6.72 0.80 l.llBrown & Whitehead [6] 7.1 0.75 l.ll

Love [7] 10 0.65 IWhitehead [8] 9.4 0.67 I

Anderson [Ill and IEEE WG [121 8 0.65 liP'IEEE Std 1243 [2] 10 0.65 liP"

.

B. Eriksson's modelEriksson [13], proposed a modified electrogeometric model

by introducing the attractive radius in shielding design,defmed as the "capture" radius at which the upward leaderinitiated at the struck object intercepts the downwardlightning leader. Attractive radius, R, is given as

p= 0.64 for UHV lines, 0.8 for EHV lines, and I for other hnes'p = 0.36+0.17In(43-h) for h < 40 rn, p = 0.55 for h > 40 m where h isthe phase conductor height

where R is in meters, h (m) is the struck object height and I(kA) is the prospective lightning peak current. Eriksson,performing a shielding analysis similar to that of theelectrogeometric models, used, instead of S in Fig. I, theattractive radius to draw arcs from the shield wire and phaseconductor up to the phase conductor height. Based ongeometrical analysis similar to that given in [29], the perfectshielding angle can be expressed as

Fig. 2. Shielding analysis according to generic models . a shielding angle; hm,hp height of shield wire and phase conductor, respectively ; Rm, Rp attractiveradius of shield wire and phase conductor, respectively; W shielding failurewidth; LlR horizontal separation distance between shield wire and phaseconductor .

_ -I [2.72I~.65ln(11m/hp )-0.0Izh1,;3 ]ap-tan () . (12)l1m-hp

Adopting from [7] the values of 10 and 0.65 for factors A' andB', respectively and by using the value of CI for negativelightning according to Table III, equation (11) becomes

Equation (12) refers to critical interception and is usedhereafter for perfect shielding angle calculations according tothe statistical model. It is important to note that for a giventransmission line geometry the interception radii Rm and Rpare statistical quantities; they vary, besides lightning peakcurrent, with interception probability according to (8).Therefore also the shielding failure width, as given by (6), isaccordingly statistically distributed indicating, thus, a nondeterministic value for the perfect shielding angle.(8)

- -0- - :..=- - '"L>: a ""o---.-----"-i---l~IIIIIIIII

TABLE IIICOEFFICIENTS C], Cz AND EXPRESSION OF a TO BE USED IN (8)

III. RESULTS AND DISCUSSION

Fig. 3 shows the variation of the perfect shielding angle, ap,with shield wire height, as calculated by employing thelightning attachment models described in Section II. It isobvious that there is a great variability in ap among models;however, all models are consistent in predicting a smaller apwith increasing shield wire height and decreasing minimumcurrent causing flashover of insulation, L: Considering thatthe curves in Fig. 3 were obtained for a fixed ratio of hlhmand that Ie is directly related to the basic insulation level ofthe transmission line, it can be deduced that all models areconsistent in predicting a smaller perfect shielding angle withincreasing transmission line height and decreasing insulationlevel of the line. However, the effect of transmission lineheight is much more pronounced for the electrogeometricmodels; the latter, thus also IEEE Std [2], generally yieldsmaller ap, even negative values for relatively high linescontrary to the generic, Eriksson's and statistical modelyielding positive ap values. The variability of perfectshielding angle among lightning attachment models is alsoobvious in Table IV referring to typical 150 kV and 400 kV

(9)

NegativeLightning

0.272 1.24 5.0{h/ Dt A 3Positive Lightning

0.235 0.90 1.9(h/DYO.7S

where Rei is in meters, h (m) is the struck object height andD (m) is the striking distance to earth surface. Thecoefficients CI and Cz, and (J in formula form are given inTable III [27].

Equation (8) can be used for shielding analysis by using aknown relation between striking distance to earth surface, D,and lightning peak current, I, commonly expressed asD = A'IB' . Thus, based on Fig. 2 and by using the criticalinterception radii of shield wire and phase conductor ascalculated from (8), the shielding failure width W at criticalinterception is

Fig. 3. Perfect shielding angle as a function of shield wire height.

30~ [,s'=:::----~20 ~~20-; ~~_ v ~,~~::::I': [.':[ '>.'.~:~ - '- ~.~~ '-~" .~ ::: : !i~' I': >.,,_.:~~~ ~:.~3.t.

~ '10 hpIh",-O .7S,I . -SkA I~ "' 10 -,~-20 - Eled rogeoll19lnc rrode ls ... Fsl ~-20 ~~O~~~I;':~~

lines of the Hellenic transmission system. In Table IV, thecalculated values of ap correspond to line geometries at thetower and average height along the line; the basic lineparameters are given in Table V. All models yield greater apat average transmission line height than at the tower as aresult of the sag of the shield wire and phase conductor; thisalso indicates that ap varies along the length of the line. Theelectrogeometric models yield generally negative ap values,which deviate considerably from the actual shielding anglesof the studied transmission lines. However, in practice aneffective shielding of transmission lines is realized based onan acceptable shielding failure flashover rate, SFFOR. For agiven line geometry SFFOR (flashovers/1 OOlan/year),normally used together with backflashover rate to estimatethe expected outage rate of a transmission line, is given as

LVSF

SFFOR = O.2Ng f W(I)j(I)dI (13)r.

where Ng (flashes/kmvyear) is the ground flash density,JtI) isthe probability density function of the stroke currentamplitude distribution, W (m) is the shielding failure widthand IMSF (kA) is the maximum shielding failure current. For adesign value of SFFOR = 0.05 flashovers/lOOkm/year,commonly used in shielding design and by assuming Ng = 5flashes/kmvyear, the effective shielding angles for the studiedoverhead lines are listed in Table VI. These calculations referto average line height, employ the JtI) distribution suggestedin [30] and values for Ie and IMSF found according to [2] and[31], respectively, and consider the variation of W with thelightning attachment model used for shielding analysis .

TABLEIVPERFECT SHIELDING ANGLE OF TYPICAL 150kV AND 400 kV OVERHEAD

LINES OF THE HELLENIC TRANSMISSION SYSTEM150kV 400kV

Liahtninz attachmentmodel TowerAverage Tower Averageheizht height

Wagner& Hileman 3 -12 -I -12 -4Young et al. 4 16 23 12 18

Armstrong& Whitehead 5 -35 -21 -15 -7Brown& Whitehead 6 -36 -23 -18 -10

Love 7 -14 -3 -3 4Whitehead 8 -16 -5 -5 3

Anderson[J 1l and IEEEWG 12 -32 -18 -31 -22IEEE Std 1243 2 -24 -10 -22 -9

Eriksson 13 6 2 15 14Rizk 15 15 17 21 22

Petrovet al. 19 12 12 18 18Ait-Amar& Berger 21 5 6 7 7

Mikronoulos & Tsovilis 25 0 7 3 8TABLEV

PARAMETERS OF TYPICAL 150kV AND 400 kV OVERHEAD LINES OF THEHELLENIC TRANSMISSION SYSTEM

Operating Shield Upperphase Shielding Shieldinganglevoltage t, wire conductor angle at at average

(kV) (kA) height height tower height(m) (m) (Deg) (Deg)150 4 33.0 27.8 31 23400 8 45.1 36.5 19 16

Sag of shIeldWIre and phase conductor. 5.5 m and 8.6 m, respectIvely

TABLE VIEFFECTIVE SHIELDING ANGLE OF TYPICAL 150kV AND 400 kV OVERHEAD

LINES OF THE HELLENICTRANSMISSION SYSTEMLightningattachmentmodel 150kV 400kV

Wagner& Hileman 3 21 13Young et al. 4 34 26

Armstrong& Whitehead 5 17 12Brown& Whitehead 6 16 11

Love 7 24 18Whitehead 8 23 18

Andersonfill and IEEE WG 12 18 6IEEE Std 1243 2 18 9

Eriksson 13 7 15Rizk 15 30 29

Petrovet al. 19 24 25Ait-Amar& Berger 21 24 12

Mikropoulos& Tsovilis 25 19 15

From Tables IV and VI it can be deduced that the effectiveshielding angle shows less variability than perfect shieldingangle among models . It is important to note that for SFFOR =0.05 flashovers/lOOkm/year the electrogeometric models, inagreement with the other models, yield positive shieldingangles agreeing with the actual shielding angles (Table V).

The applicability of a lightning attachment model in perfectshielding angle calculations can be evaluated based on theshielding performance of transmission lines; this is illustratedin Fig. 4. Lines with actual shielding angles greater than thecorresponding calculated perfect shielding angle shouldexperience shielding failures, whereas lines with actualshielding angles smaller than the corresponding calculatedperfect shielding angle should show superior shieldingperformance. The shielding performance of the lines isgenerally underestimated for Eriksson's model [13] (Fig. 4a)and for the electrogeometric models [5] and [6], whereasoverestimated for Rizk 's [15] (Fig. 4b) and Young et al. [4]models . The IEEE Std [2] (Fig . 4c), electrogeometric models[3], [7] and [8] as well as the statistical model [25] (Fig. 4d)yield generally consistent results with respect to shieldingperformance of transmission lines, whereas inconsistencyhave been found for the generic models [19] and [21].

50(a) Eriksson [13)

."-rc

5040 (c) IEEE SId 1243(2 )

. "

.. '

Fig. 4. Perfectshieldingangle versus actual shieldingangle. Empty and solidpoints depict lines showing superior shielding performance [5] andexperiencingshieldingfailures [32], respectively.

Finally, it must be mentioned that in the present analysissubsequent strokes possessing current magnitudes bigger thanminimum current causing flashover of insulation have notbeen considered in determining SFFOR oftransmission lines.

IV. CONCLUSIONS

General relationships for the estimation of the perfectshielding angle of transmission lines have been derived byperforming shielding analysis on the basis of several lightningattachment models. There is a great variability in perfectshielding angle among lightning attachment models. Theeffect of the transmission line height is much morepronounced for the electrogeometric models; the latter, thusalso IEEE Standard 1243:1997, generally yield smallerperfect shielding angles, even negative ones for relativelyhigh transmission lines contrary to the generic, Eriksson'sand statistical model yielding positive perfect shieldingangles. The effective shielding angle calculated by assumingan acceptable shielding failure flashover rate is less variableamong lightning attachment models. These fmdings aredemonstrated through an application to typical 150 kV and400 kV overhead lines of the Hellenic transmission system.

The applicability of lightning attachment models in perfectshielding angle calculations has been evaluated based on theshielding performance of transmission lines reported inliterature. Consistent results have been derived for thestatistical model and some electrogeometric models, as wellas for the IEEE Standard 1243:1997.

ACKNOWLEDGEMENTS

Th. E. Tsovilis wishes to thank the Research Committee ofAristotle University of Thessaloniki for the support providedby a merit scholarship.

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