Lightning Attachment Models and Perfect Shielding Angle of Transmission Lines

Transcription

1 Lightning Attachment Models and Perfect Shielding Angle of Transmission Lines Pantelis N. Mikrooulos 1 and Thomas E. Tsovilis High Voltage Laboratory, School of Electrical & Comuter Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece, 1 nm@eng.auth.gr Abstract- General relationshis for the estimation of the erfect shielding angle of overhead transmission lines have been derived by erforming shielding analysis on the basis of several lightning attachment models, including a recently introduced statistical model. The interdeendence of erfect shielding angle, transmission line and minimum current causing flashover of insulation is demonstrated as influenced by the lightning attachment model emloyed in shielding analysis. There is a great variability in erfect shielding angle among lightning attachment models; this is demonstrated for 15 kv and 4 kv lines of the Hellenic transmission system. The alicability of lightning attachment models in erfect shielding angle calculations is evaluated based on the shielding erformance of transmission lines; the :1997 yields consistent results with resect to the shielding erformance of the lines. Index Terms-- Direct stroke shielding, lightning, erfect shielding angle, overhead transmission lines. I. INTRODUCTION The shielding design of transmission lines against direct lightning strokes to hase conductors, that is the aroriate ositioning of shield wires with resect to hase conductors, can be achieved by imlementing electrogeometric models [1], reresentative of their alication is the method suggested by IEEE Standard 1243:1997, which emloy a relation between striking distance and lightning eak current in their calculations [3]-[12]. Alternatively, shielding design may be realized by emloying models based on more solid hysical ground of lightning attractiveness [13]-[21], called hereafter, in accordance with Waters [22], generic models. Recently, a statistical aroach in shielding design has been introduced [23]-[25] by imlementing a lightning attachment model derived from scale model exeriments [26]-[28]. A erfect shielding is achieved when lightning strokes ossessing eak current greater than the minimum current causing flashover of insulation are interceted. Aarently, some of the less intense strokes may not be interceted by the shield wires and strike to hase conductors, however these are not exected to cause flashover. In ractice, an effective shielding of transmission lines against direct lightning strokes to hase conductors is realized based on an accetable shielding failure flashover rate. The resent study rovides general relationshis for the estimation of the erfect shielding angle of transmission lines, which have been derived by erforming shielding analysis on the basis of electrogeometric, generic and the recently roosed statistical model. The interdeendence of erfect shielding angle, transmission line and minimum current causing flashover of insulation is demonstrated as influenced by the lightning attachment model emloyed in shielding analysis. Findings are discussed and further elucidated through an alication to tyical 15 kv and 4 kv lines of the Hellenic transmission system. The alicability of lightning attachment models in erfect shielding angle calculations has been evaluated based on the shielding erformance of transmission lines. II. PERFECT SHIELDING ANGLE FORMULATION ASED ON DIFFERENT LIGHTNING ATTACHMENT MODELS A. Electrogeometric models Electrogeometric models have historically been emloyed in transmission line shielding roviding accetable rotection against direct lightning strokes to hase conductors and they are still widely used. Shielding analysis according to electrogeometric models follows based on Fig.1. The striking distance to conductors, S, is assumed to be related solely to the rosective lightning eak current, I and can be associated to striking distance to earth surface, D, by using a factor γ as S = AI = γ D (1) where I is in ka, S, D are in meters and factors A, and γ are given in Table I as roosed by different authors. For a design lightning eak current equal to the minimum current causing flashover of insulation, I c, the latter can be calculated based on the geometrical and electrical characteristics of the transmission line, a descending lightning leader will strike to the hase conductor when reaching the arc between M and N; hence, a shielding failure width, W, is defined (Fig. 1). With decreasing shielding angle α, W decreases, thus there is a critical shielding angle which corresonds to W =, hereafter called erfect shielding angle, α. Geometrical analysis similar to that given in [29] yields the following exression, aroximating well the erfect shielding angle a 1 1 sin hm+ h = (2) γ 2AI c where, factors A,, γ are given in Table I, I c is in ka, and h m (m), h (m) are defined in Fig. 1.

2 C. Generic models Following Eriksson s work, generic lightning attachment models have been develoed which also consider the incetion of the uward connecting discharge emerging from the rosective struck object [14]-[21]. Thus, based on different leader incetion criteria, exressions of the attractive radius of an object, R, defined as the longest lateral distance from the object where lightning attachment occurs, have been roosed in the general form E F R = ξ h I (5) Fig. 1. Shielding analysis according to electrogeometric models. h m shield wire ; h hase conductor ; α shielding angle; S striking distance to shield wire and hase conductor; D striking distance to earth surface; W shielding failure width. TALE I FACTORS A, AND γ TO E USED IN (1) Electrogeometric model A γ Wagner & Hileman [3] Young et al. [4] 27γ.32 1 for h < 18 m 444 for h >18 m 462 h h: shield wire Armstrong & Whitehead [5] rown & Whitehead [6] Love [7].65 1 Whitehead [8] Anderson [11] and IEEE WG [12] /β *.65 1/β ** * β =.64 for UHV lines,.8 for EHV lines, and 1 for other lines * * β = ln(43-h) for h < 4 m, β =.55 for h > 4 m where h is the hase conductor. Eriksson s model Eriksson [13], roosed a modified electrogeometric model by introducing the attractive radius in shielding design, defined as the cature radius at which the uward leader initiated at the struck object intercets the downward lightning leader. Attractive radius, R, is given as.6.74 R =.67h I (3) where R is in meters, h (m) is the struck object and I (ka) is the rosective lightning eak current. Eriksson, erforming a shielding analysis similar to that of the electrogeometric models, used, instead of S in Fig. 1, the attractive radius to draw arcs from the shield wire and hase conductor u to the hase conductor. ased on geometrical analysis similar to that given in [29], the erfect shielding angle can be exressed as Rm hm h R α = tan (4) hm h where h m (m) and h (m) are defined in Fig.1, and R m (m), R (m) are calculated from (3) for I = I c. where R is in meters, I (ka) is the rosective lightning eak current, h (m) is the struck object and factors ξ, E and F are listed in Table II according to different authors. TALE II FACTORS ξ, E AND F TO E USED IN (5) Generic model ξ E F Rizk [15] Petrov et al. [19] * Ait-Amar & erger [21] * using as h in (5) the object lus 15 m. Following a shielding analysis similar to that of Rizk [15], according to Fig. 2 a shielding failure will occur when the descending lightning leader enters the shielding failure width W, which is given as W = R +Δ R R. (6) Thus, for a design lightning eak current equal to the minimum current causing flashover of insulation, I c, the erfect shielding angle, corresonding to W =, is given with the aid of (5) and (6) as α = tan 1 m ( ) ξ h h I hm h E E F m c where factors ξ, E, and F are given in Table II, I c is in ka, and h m (m) and h (m) are defined in Fig. 2. It must be mentioned that models [19] and [21] do not refer to the transmission line geometry; however, emloying these models in erfect shielding angle calculations may rovide useful information concerning their alicability. D. Recently, investigations on the intercetion robability of an air terminal through scale model exeriments made ossible the formulation of distributions for striking distance and intercetion radius [27], and, thus, a statistical aroach in shielding design has been roosed in [24]. Intercetion radius is considered as statistical quantity with a mean value, referring to 5% intercetion robability, called critical intercetion radius, R ci, and a standard deviation σ. It is given with reference the striking distance to earth surface as (7)

3 Adoting from [7] the values of and.65 for factors A and, resectively and by using the value of c 1 for negative lightning according to Table III, equation () becomes α I ln h h.12h = tan ( hm h ) c m m. (12) Fig. 2. Shielding analysis according to generic models. α shielding angle; h m, h of shield wire and hase conductor, resectively; R m, R attractive radius of shield wire and hase conductor, resectively; W shielding failure width; ΔR horizontal searation distance between shield wire and hase conductor. Rci h, c ln c D σ = D where R ci is in meters, h (m) is the struck object and D (m) is the striking distance to earth surface. The coefficients c 1 and c 2, and σ in formula form are given in Table III [27]. TALE III COEFFICIENTS c 1, c 2 AND EXPRESSION OF σ TO E USED IN (8) Equation (8) can be used for shielding analysis by using a known relation between striking distance to earth surface, D, and lightning eak current, I, commonly exressed as D = A I. Thus, based on Fig. 2 and by using the critical intercetion radii of shield wire and hase conductor as calculated from (8), the shielding failure width W at critical intercetion is (8) W = c1dln h hm +Δ R. (9) Hence, the erfect shielding angle at critical intercetion is given as α = tan 1 AIc c1 ln hm h ( hm h) () where h m (m) and h (m) are defined in Fig. 2 and c 1 is given in Table III. y considering also the neighboring effects on the shield wire intercetion radius of the hase conductor [25], [28], equation (9) becomes.14 1 h D W = m c Dln h hm +Δ R. (11) ln ( hm h) Equation (12) refers to critical intercetion and is used hereafter for erfect shielding angle calculations according to the statistical model. It is imortant to note that for a given transmission line geometry the intercetion radii R m and R are statistical quantities; they vary, besides lightning eak current, with intercetion robability according to (8). Therefore also the shielding failure width, as given by (6), is accordingly statistically distributed indicating, thus, a non deterministic value for the erfect shielding angle. III. RESULTS AND DISCUSSION Fig. 3 shows the variation of the erfect shielding angle, α, with shield wire, as calculated by emloying the lightning attachment models described in Section II. It is obvious that there is a great variability in α among models; however, all models are consistent in redicting smaller α with increasing shield wire and decreasing minimum current causing flashover of insulation, I c. Considering that the curves in Fig. 3 were obtained for a fixed ratio of h /h m and that I c is directly related to the basic insulation level of the transmission line, it can be deduced that all models are consistent in redicting smaller erfect shielding angle with increasing transmission line and decreasing insulation level of the line. However, the effect of transmission line is much more ronounced for the electrogeometric models; the latter, thus also IEEE Std, generally yield smaller α, even negative values for relatively high lines contrary to the generic, Eriksson s and statistical model yielding ositive α values. The variability of erfect shielding angle among lightning attachment models is also obvious in Table IV referring to tyical 15 kv and 4 kv [3] h /h m =.75, I c = 4 ka Electrogeometric models [7] [8] [12] [5], [6] Shield wire (m) [12] h /h m =.75, I c = 8 ka Electrogeometric models Shield wire (m) [4] [4] [7] [8] [3] [5] [6] h /h m =.75, I c = 4 ka Generic models [15] [19] [21] [13] Shield wire (m) [15] h /h m =.75, I c = 8 ka Generic models Shield wire (m) Fig. 3. Perfect shielding angle as a function of shield wire. [19] [13] [21]

4 lines of the Hellenic transmission system. In Table IV, the calculated values of α corresond to line geometries at the tower and average along the line; the basic line arameters are given in Table V. All models yield greater α at average transmission line than at the tower as a result of the sag of the shield wire and hase conductor; this also indicates that α varies along the length of the line. The electrogeometric models yield generally negative α values, which deviate considerably from the actual shielding angles of the studied transmission lines. However, in ractice an effective shielding of transmission lines is realized based on an accetable shielding failure flashover rate, SFFOR (flashovers/km/year). The latter, normally used together with backflashover rate to estimate the exected outage rate of a transmission line, is given as I MSF SFFOR =.2N W ( I ) f ( I ) di (13) g where N g (flashes/km 2 /year) is the ground flash density, f(i) is the robability density function of the stroke current amlitude distribution, W (m) is the shielding failure width and I MSF (ka) is the maximum shielding failure current. For a design value of SFFOR =.5 flashovers/km/year, commonly used in shielding design and by assuming N g = 5 flashes/km 2 /year, the effective shielding angles for the studied overhead lines are listed in Table VI. These calculations refer to average line, emloy the f(i) distribution suggested in [3] and values for I c and I MSF found according to and [31], resectively, and consider the variation of W with the lightning attachment model used for shielding analysis. TALE IV PERFECT SHIELDING ANGLE OF TYPICAL 15 kv AND 4 kv OVERHEAD LINES OF THE HELLENIC TRANSMISSION SYSTEM 15 kv 4 kv Average Average Tower Tower Lightning attachment model Wagner & Hileman [3] Young et al. [4] Armstrong & Whitehead [5] rown & Whitehead [6] Love [7] Whitehead [8] Anderson [11] and IEEE WG [12] Eriksson [13] Rizk [15] Petrov et al. [19] Ait-Amar & erger [21] TALE V PARAMETERS OF TYPICAL 15 kv AND 4 kv OVERHEAD LINES OF THE HELLENIC TRANSMISSION SYSTEM Oerating voltage (kv) I c (ka) Shield wire (m) I Uer hase conductor (m) c Shielding angle at tower (Deg) Shielding angle at average (Deg) Sag of shield wire and hase conductor: 5.5 m and 8.6 m, resectively TALE VI EFFECTIVE SHIELDING ANGLE OF TYPICAL 15 kv AND 4 kv OVERHEAD LINES OF THE HELLENIC TRANSMISSION SYSTEM Lightning attachment model 15 kv 4 kv Wagner & Hileman [3] Young et al. [4] Armstrong & Whitehead [5] rown & Whitehead [6] Love [7] Whitehead [8] Anderson [11] and IEEE WG [12] Eriksson [13] 7 15 Rizk [15] 3 29 Petrov et al. [19] Ait-Amar & erger [21] From Tables IV and VI it can be deduced that the effective shielding angle shows less variability than erfect shielding angle among models. It is imortant to note that for SFFOR =.5 flashovers/km/year the electrogeometric models, in agreement with the other models, yield ositive shielding angles agreeing with the actual shielding angles (Table V). The alicability of a lightning attachment model in erfect shielding angle calculations can be evaluated based on the shielding erformance of transmission lines; this is illustrated in Fig. 4. Lines with actual shielding angles greater than the corresonding calculated erfect shielding angle should exerience shielding failures, whereas lines with actual shielding angles smaller than the corresonding calculated erfect shielding angle should show suerior shielding erformance. The shielding erformance of the lines is generally underestimated for Eriksson s model [13] (Fig. 4a) and for the electrogeometric models [5] and [6], whereas overestimated for Rizk s [15] (Fig. 4b) and Young et al. [4] models. The IEEE Std (Fig. 4c), electrogeometric models [3], [7] and [8] as well as the statistical model [25] (Fig. 4d) yield generally consistent results with resect to shielding erformance of transmission lines, whereas inconsistency have been found for the generic models [19] and [21] (a) Eriksson [13] (c) (b) Rizk [15] (d) Fig. 4. Perfect shielding angle versus actual shielding angle. Emty and solid oints deict lines showing suerior shielding erformance [5] and exeriencing shielding failures [32], resectively.

5 Finally, it must be mentioned that in the resent analysis subsequent strokes ossessing current magnitudes bigger than minimum current causing flashover of insulation have not been considered in determining SFFOR of transmission lines. IV. CONCLUSIONS General relationshis for the estimation of the erfect shielding angle of transmission lines have been derived by erforming shielding analysis on the basis of several lightning attachment models. There is a great variability in erfect shielding angle among lightning attachment models. The effect of the transmission line is much more ronounced for the electrogeometric models; the latter, thus also IEEE Standard 1243:1997, generally yield smaller erfect shielding angles, even negative ones for relatively high transmission lines contrary to the generic, Eriksson s and statistical model yielding ositive erfect shielding angles. The effective shielding angle calculated by assuming an accetable shielding failure flashover rate is less variable among lightning attachment models. These findings are demonstrated through an alication to tyical 15 kv and 4 kv overhead lines of the Hellenic transmission system. The alicability of lightning attachment models in erfect shielding angle calculations has been evaluated based on the shielding erformance of transmission lines reorted in literature. Consistent results have been derived for the statistical model and some electrogeometric models, as well as for the IEEE Standard 1243:1997. ACKNOWLEDGEMENTS Th. E. Tsovilis wishes to thank the Research Committee of Aristotle University of Thessaloniki for the suort rovided by a merit scholarshi. REFERENCES [1] R. H. Golde, Lightning Protection. London U.K.: Academic Press, 1977, vol. 2, IEEE Guide for imroving the Lightning erformance of Transmission Lines, IEEE Std , Dec [3] C. F. Wagner and A. R. 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