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Software Development for the Evaluation of the Lightning Performance of Overhead Distribution Lines on the basis of the Statistical Method P. N. Mikropoulos1, T. E. Tsovilis2 and P. P. Papaioannou3 High Voltage Laboratory, School of Electrical & Computer Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece 1 [email protected], [email protected], [email protected] Abstract- A useful application software for the evaluation of the lightning performance of overhead distribution lines is introduced. The SM-LPDL software has been developed in Matlab, runs as a Microsoft Windows application and features a user-friendly graphics interface. It incorporates a statistical method for the estimation of the flashover rate of overhead distribution lines, implementing a recently introduced statistical lightning attachment model and the simplified coupling model suggested by the IEEE Std. 1410:2011. The SM-LPDL yields a range for the expected flashover rate of a distribution line associated with the lightning interception probability distribution of the line conductors. It allows for the easy quantification of the effects of line parameters, soil resistivity, surge arresters, shielding of nearby objects and lightning crest current distribution on lightning performance of distribution lines. SM-LPDL results are discussed and compared with those obtained by the recently released IEEE Std. 1410:2011. Index Terms-- Direct-stroke flashover rate, induced-voltage flashover rate, interception probability, distribution lines.

I. INTRODUCTION Lightning is a major cause of distribution line outages affecting reliability of power supply thus resulting in economic losses. Lightning-caused flashover in overhead distribution lines is associated with overvoltages at the line conductors either arising due to direct strokes or induced owing to nearby strokes. Thus, the lightning performance of overhead distributions lines can be evaluated by estimating the direct-stroke and induced-voltage flashover rates. This task can be easily accomplished with the aid of the application software (SM-LPDL) introduced in this paper. The SM-LPDL software has been developed in Matlab, it runs as a Microsoft Windows application and features a userfriendly graphics interface. It incorporates a statistical method for the evaluation of the lightning performance of overhead distribution lines. Actually, the SM-LPDL software implements the statistical lightning attachment model [1], [2] and the simplified coupling model suggested by the IEEE Std. 1410:2011 [3] to estimate an expected range of flashover rate associated with lightning interception probability. With the aid of the SM-LPDL software, the lightning performance of a typical 10 m overhead distribution line has been evaluated. The effects of line parameters, soil resistivity, shielding of nearby objects, surge arrester characteristics and lightning crest current distribution on lightning performance

of distribution lines have been easily quantified. Results are discussed and compared with those obtained by the recently released IEEE Std. [3]. II. METHODOLOGY A. Induced-voltage flashover rate The annual rate of line insulation flashovers of an overhead distribution line due to induced voltages caused by nearby lightning strokes, Fp (flashovers/100km/yr), can be estimated from the following set of equations ∞

Fp = 0.2 N g ∫ WI ( I ) f ( I )dI Imin

(1)

WI ( I ) = RI ( I ) − R( I ) where − Ng (flashes/km2/yr) is the ground flash density. − f(I) is the probability density function of the lightning crest current distribution given as [4]

⎡ ( ln I − ln I )2 ⎤ ⎥ exp ⎢− f (I ) = 2σ ln2 2πσ ln I ⎢ ⎥ ⎣ ⎦ 1

(2)

where Ī (kA) and σln are the median value and the standard deviation of the natural logarithm of the lightning crest current distribution, respectively. − RI is the induced-voltage flashover radius, defined as the maximum lateral distance of a nearby lightning stroke from the line within which the induced voltage in the line causes flashover of line insulation. According to IEEE Std. 1410:2011 [3], RI (m) can be expressed as RI =

(

28I h + 0.25 ρ 1.5CFO

)

(3)

where I (kA) is the lightning crest current, h (m) is the line height, ρ (Ωm) is the soil resistivity and CFO (kV) is the critical flashover voltage under standard lightning impulses. − R is the interception radius, that is, the lateral distance from the line within which the phase conductor intercepts the descending lightning leader. According to the statistical model [1], [2] interception radius follows a normal distribution with a mean value, Rci, corresponding to 50% interception probability, and a standard deviation,

σ, given as Rci = 6.2h0.3 I 0.455

σ (%) = 13.5h

(4a)

−0.43 0.28

I

(4b)

where I (kA) is the lightning crest current, h (m) is the line height. − WI (m) is the induced-voltage flashover width, defined as the difference between RI and R. As interception radius, R, varies with lightning interception probability according to (4), WI can be treated as a statistical quantity. − Imin (kA) is the minimum induced-voltage flashover current, defined as the lightning crest current of all possible nearby lightning strokes corresponding to RI = R, or equivalently WI (Imin) = 0 according to (1). Imin varies with lightning interception probability as WI is related to the distribution of R. The effects of surge arresters and grounded wire on induced-voltage flashover rate, Fp, can be considered based on the simplified methods [5] and [6], respectively, by modifying RI as 2L 28I hp + 0.25 ρ ctf RI = (5a) η 1.5CFO − VIR

(

)

where hp (m) is the phase conductor height, VIR (kV) is the residual voltage of surge arresters, L (m) is half of the separation distance between line surge arresters, c (m/μs) is the velocity of light, tf (μs) is the induced-voltage wavefront duration and η is the ratio of improvement due to the presence of the grounded wire. This ratio can be expressed as

η = 1−

hg + 0.25 ρ

Zg− p

(5b)

hp + 0.25 ρ Z g + 2 Rg

where hg (m) is the grounded wire height, Rg (Ω) is the grounding resistance, Zg-p (Ω) is the mutual surge impedance between grounded wire and phase conductor and Zg (Ω) is the surge impedance of the grounded wire, calculated by (5c) and (5d), respectively [3] Z g − p = 60 ln ⎡⎣( hp + hg ) hp − hg ⎤⎦ Z g = 60 ln ⎡ 2000 hg + 4.7 1000 ρ r ⎤ ⎣ ⎦

(

)

(5c)

(5d)

where r (mm) is the grounded wire radius. B. Direct-stroke flashover rate The annual rate of line insulation flashovers of an overhead distribution line due to direct lightning flashes, Fd (flashovers/100km/yr), can be expressed as ∞

Fd = N ∫ f ( I )dI

(6)

IF

where − N (flashes/100km/yr) is the rate of direct lightning flashes to the distribution line, given as

N = 0.1N g ( 2R eq +b )

(7)

where Ng (flashes/km2/yr) is the ground flash density, b (m) is the separation distance between the outer line conductors and Req (m) is the equivalent interception radius of the line. Req is defined as ∞

Req = ∫ R( I ) f ( I )dI

(8)

0

where R is the interception radius and f(I) is the probability density function of the lightning crest current distribution given by (2). According to the statistical method, Req follows a normal distribution with a mean value, Reqci (m), and a standard deviation, σ, given as [7] Reqci = 6.2 exp ( 0.455 ln I + 0.1σ ln2 ) h 0.3

(9a)

σ (%) = 13.3e0.18σ ln I 0.27 h −0.43

(9b)

where h (m) is the line height and (kA) and σln are the median value and the standard deviation of the natural logarithm of the lightning crest current distribution, respectively. − f(I) is the probability density function of the lightning crest current distribution, given by (2). − IF (kA) is the minimum direct lightning stroke current causing flashover of line insulation; it can be calculated analytically [3] or through computer simulations [8]. C. Flashover rate The lightning performance of overhead distribution lines is associated with line insulation flashover due to direct and nearby lightning strokes. The flashover rate, F, of an overhead distribution line can be estimated as F = K ⎡⎣ Fp (1 + S f ) + Fd (1 − S f ) ⎤⎦

(10)

where Fp and Fd are the induced-voltage and direct-stroke flashover rates, respectively. Sf is the shielding factor as defined in IEEE Std. [3], taking values from 0 up to 1 depending on the shielding effect against direct lightning strokes owing to nearby objects. K is the orographic factor as defined in CIRED [9], taking values up to approximately 3 for distribution lines crossing a region along a mountain top. III. SOFTWARE DEVELOPMENT The presented statistical method for evaluating the lightning performance of overhead distribution lines has been incorporated in Microsoft Windows application software developed in Matlab, called SM-LPDL. Fig. 1 shows the input data and results window of the developed software. The user enters the basic input data referring to overhead distribution line parameters, namely geometry of line conductors, CFO of line insulation, minimum current causing flashover of line insulation, IF, soil resistivity in the region along the line, ρ, and grounding resistance of ground wires, Rg. Also, lightning activity parameters, that is, the ground flash density, Ng, and the median value and standard deviation of the natural logarithm of the lightning crest current distribution are requested. Shielding and orographic

Fig. 1. Input data and results window of SM-LPDL software.

Fig. 2. Induced-voltage flashover rate, Fp, of a 10 m overhead distribution line; Ng = 1 flash/km2/yr, lightning crest current distribution suggested in [4].

effects are considered by entering appropriate values for the corresponding factors Sf and K. Moreover, there is an option for considering the effect of surge arresters on the lightning performance of the line. Finally, in the same window results on the expected range of the flashover rate of the overhead distribution line associated with the lightning interception probability distribution are presented and can be saved in excel format. IV. SOFTWARE APPLICATION AND DISCUSSION A. Induced-voltage flashover rate The induced-voltage flashover rate, Fp, of a 10 m overhead distribution line has been estimated with the aid of SM-LPDL software by using the lightning crest current distribution with Ī = 30.1 kA and σln = 0.76 [4]. Fig. 2 shows the variation of Fp with CFO of the line together with IEEE Std. 1410:2011 [3] results. The latter are within the expected range of Fp, associated with lightning interception probability distribution of line conductors, obtained by the statistical method. Actually, there is a close consistency between the Fp values yielded by the IEEE Std. [3] and those obtained by SM-LPDL at 50% interception probability (Fig. 2); it must be mentioned that the latter should be considered when evaluating the long term lightning performance of overhead distribution lines. From Fig. 3 it is obvious that the satisfactory agreement between SM-LPDL Fp results and those of IEEE Std. [3] applies also when line surge arresters are considered. In addition, Fp is higher for higher soil resistivity and significantly lower when line surge arresters are utilized, especially for higher CFO. However, it must be noted that this may reverse itself for lines of relatively low insulation level (Fig. 3), and relatively large separation distance between surge arresters as discussed in detail in [10], [11]. Mitigation of induced voltages on overhead distribution lines can also be achieved by employing a grounded wire. This can be deduced by a comparison of results of Figs. 2 and 4; as an example for a CFO of 170 kV Fp decreases from 1 (Fig. 2) to 0.2 (Fig. 4) flashovers/100km/yr. From the above analysis it follows that SM-LPDL allows

Fig. 3. Induced-voltage flashover rate, Fp, of a 10 m overhead distribution line; Ng = 1 flash/km2/yr, lightning crest current distribution suggested in [4], surge arresters located every 500 m, VIR = 40 kV, tf = 3 μs.

for a straightforward estimation of the induced-voltage flashover rate of overhead distribution lines, yielding results consistent with those obtained by IEEE Std. method [3]. Results are obtained without requiring extensive computing effort; this is not the case of the IEEE Std. method [3], suggested by Borghetti et al. [12], which combines Monte Carlo simulation and lightning induced overvoltage computer code (LIOV [13]). Moreover, the SM-LPDL software, by

C. Flashover rate Fig. 6 shows the flashover rate, F, of a 10 m overhead distribution line with a CFO of 150 kV estimated with the aid of the SM-LPDL software for different lightning crest current distributions (Table I). It is obvious that F is significantly greater (up to 2.5 times) for lightning

Fig. 4. Induced-voltage flashover rate, Fp, of a 10 m distribution line with a grounded wire 1 m below the phase conductor; Ng = 1 flash/km2/yr, lightning crest current distribution suggested in [4], r = 4 mm, Rg = 70 Ω.

incorporating the statistical method yields a range for the expected induced-voltage flashover rate of distribution lines associated with the lightning interception probability distribution of the line conductors; this is more realistic when considering the stochastic nature of lightning interception phenomenon, as also discussed in [14]. B. Direct-stroke flashover rate Fig. 5 shows the direct-stroke flashover rate of a 10 m overhead distribution line, Fd, as a function of the minimum direct lightning stroke current causing flashover of line insulation. It also shows the variation of Fd, according to the IEEE Std. [3], which has adopted, based on Eriksson’s work on lightning incidence [15], a solely height dependent expression for estimating the direct-stroke rate to the line, that is, N = 0.1Ng(28h0.6+b). It is obvious from Fig. 5 that the IEEE Std. method results are within the range of Fd calculated according to the statistical method. Moreover, the SM-LPDL software, by using for calculating N the set of equations (7)-(9), considers the effect of lightning crest current distribution on Fd; this is not the case for the IEEE Std. method [3], as also discussed in detail in [7].

Fig. 6. Flashover rate, F, of a 10 m overhead distribution line at different lightning interception probabilities; bars (1)-(5) are numbered according to the lightning crest current distributions of Table I; CFO = 150 kV, ρ = 100 Ωm, b = 2.5 m, Ng = 1 flash/km2/yr, ΙF = 3 kA. TABLE I LIGHTNING CREST CURRENT DISTRIBUTION PARAMETERS

Fig. 5. Direct-stroke flashover rate, Fd, of a 10 m overhead distribution line as function of the minimum direct lightning stroke current causing flashover of line insulation, IF; Ng = 1 flash/km2/yr, Ī = 30.1 kA and σln = 0.76.

crest current distributions with relatively high Ī since both Fd and Fp increase with Ī. It is noteworthy that for distributions with relatively low Ī, Fp is only a small fraction of F. The pronounced effect of lightning crest current distribution on F indicates that the use of a globally uniform distribution, such as the CIGRE distribution suggested by the IEEE Std. [3], may lead to incorrect evaluation of the lightning performance of an overhead distribution line. Fig. 7 shows the flashover rate of a 10 m overhead distribution line partially-shielded (Sf = 0.5) and not shielded (Sf = 0) by nearby objects against direct lightning strokes. As expected the lightning performance of partially-shielded distribution lines is better than that of non-shielded distribution lines, especially for higher CFO. It is important that for lower insulation levels (CFO < ~70 kV) partiallyshielded distribution lines may experience a higher flashover rate. This is in contrast with results of [20] where the lightning performance of distribution lines crossing a region without neighboring objects was found always worse than that of shielded lines by nearby objects; this could be attributed to the fact that Sf was not considered in the induced-voltage flashover rate estimations in [20].

distribution lines as well as for the selection of the necessary protection measures. The SM-LPDL software can also be used for educational purposes in high voltage engineering courses and it is available at http://www.eng.auth.gr/hvl/. VI. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

[11]

[12]

[13] [14] Fig. 7. Flashover rate, Fd, of a 10 m overhead distribution line as function of CFO with shielding factor as parameter; h = 10 m, b = 2.5 m, ρ = 100 Ωm, Ng = 1 flash/km2/yr, Ī = 30.1 kA and σln = 0.76, K = 1.

V. CONCLUSIONS A user-friendly Windows application software, called SMLPDL, has been developed for the evaluation of the lightning performance of overhead distribution lines. The SM-LPDL software estimates, without extensive computing effort, the induced-voltage and direct-stroke flashover rates of an overhead distribution line. With the aid of the SM-LPDL software the effects of line parameters, soil resistivity, shielding of nearby objects, surge arrester characteristics and lightning crest current distribution on the lightning performance of overhead distribution lines can be easily quantified. The developed software is a useful tool for utilities for assessing the lightning performance of

[15] [16] [17] [18]

[19]

[20]

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