presentation borghetti nucci paolone dallas 04
TRANSCRIPT
Estimation of the statistical distributionsof lightning current parameters
at ground level from the data recorded by instrumented towers
Paper TPWRD 00442-2002.R1
Alberto Borghetti Carlo Alberto Nucci Mario Paolone
University of BolognaItaly
Outline of presentation
1. Introduction The problem What has been done by other Authors
2. Numerical procedure for evaluating lightning current distributions at ground.Application to the Berger’s distributions and comparisonwith results obtained by other Authors
3. Application of the results to the evaluation of indirect lightning performance of overhead lines (not included in Transaction paper)
4. Conclusions
1.Introduction
The problemThe probabilistic approach to power insulation coordination requires the knowledge of the statistical distributions of lightning current parameters.
The lightning current distributions currently used are those derived from experimental data gathered by means of elevated instrumented towers.The ‘attractive radius’ r of the tower tends to increase for flashes with larger currents
lightning current amplitudes are ‘biased’ towards higher values.
General relations between pdf of lightningpeak current to a tower and at ground
( ) ( ) ( )( ) ( )
2
2
0
,,
,
p g pt p
p g p p
r I h f If I h
r I h f I dI∞=
∫r
nearby stroke
direct stroke
h
(Whitehead and Brown, 1969)
The problem is to determine fg being ft and h known
General relations between pdf of lightningpeak current to a tower and at ground
( ) ( ) ( )( ) ( )
2
2
0
,,
,
p g pt p
p g p p
r I h f If I h
r I h f I dI∞=
∫
(Whitehead and Brown, 1969)
We shall disregard current reflections at tower top and base, althoughthey can certainly alter the measured current (e.g. Guerrieri et al, IEEE Trans. PWDR, 1998; Rachidi et al., JGR, 2003) and we shall focus on downward discharges, assuming them perpendicular to flat ground.
We shall disregard current reflections at tower top and base, althoughthey can certainly alter the measured current (e.g. Guerrieri et al, IEEE Trans. PWDR, 1998; Rachidi et al., JGR, 2003) and we shall focus on downward discharges, assuming them perpendicular to flat ground.
Studies performed by other AuthorsThe problem has been studied by several Authors, e.g:Sargent [IEEE Trans PAS, Sept/Oct 1972], by using an attractive-radius three-dimensional electrogeometric model and on the basis of the lightning current amplitude experimental data available at that time, derived a so-called synthetic current amplitude distribution to ground level, which, as shown by Brown[IEEE Trans PAS, Sept/Oct 1972], can be approximated by a lognormal distribution with µg =13 kA and σg =0.32.
Mousa and Srivastava [IEEE Trans. PWDR,1989],have proposed a lognormal distribution of current amplitudes at ground level with µg =24 kA and σg =0.31.
Other forms of distribution have been investigated for the problem of interest by Chisholm et al. [Proc. 1st PMAPS, Toronto, Canada, 11-13 July 1986.
Here we shall focus on the analytical formula derived by Pettersson(see later).
Exposure of a tower to direct lightningLightning leader approaching ground: downward motion unperturbedunless critical field conditions develop juncture with the nearby tower, called final jump. Assuming leader channel perpendicular to the ground plane the flash will stroke the tower if its prospective ground termination point, lies within the attractive radius r. r depends on several factors, such as
charge of the leader, its distance from the structure, type of structure (vertical mast or horizontal conductor), structure height, nature of the terrain (flat or hilly)ambient ground field due to cloud charges.
Several expressions have been proposed to evaluate such a radius. Some of them are based on the electrogeometric model.
( )22 for s g gr r r h h r= − − < for s gr r h r= ≥
Electrogeometrical expressions describing the exposure of a tower to direct lightning
rs
rg
nearby strokedirect stroke
h r
rs = r
rg
nearby strokedirect stroke
h
Where rs and rg are the so called ‘striking distances’ to the structure and to ground respectively.
psr I βα= ⋅ g sr k r= ⋅
Electrogeometrical expressions describing the exposure of a tower to direct lightning
ElectrogeometricalAttractive radius
expressionα β k
Armstrong and Whitehead 6.7 0.80 0.9
IEEE 10 0.65 0.55
psr I βα= ⋅ g sr k r= ⋅
Other expressions describing the exposure of a tower to direct lightning
rnearby stroke
direct stroke
h
They have been inferred, by regression analysis, from the results of more complex and physically-oriented models than the Electrogeometric one.
A formula of the following type can be used
bpr c a I= + ⋅
Model c a b
Eriksson 0 0.84 h0.6 0.76
from Rizk 0 2.83 h0.4 0.63
from Dellera-Garbagnati * 3h0.6 0.80 0.9
* The values reported have been derived by M. Bernardi, by interpolation of plots of the lateral distance of a slim structure vs. its height (in the range 5 to 100 m), calculated using the leader progression model of Dellera-Garbagnati
Studies performed by other Authors Cont.Analytical relation between pdf of lightning peak current to a tower and at ground
We now focus on the analytical formula derived by Petterson [IEEE Trans. PWDR,1991]
1st hypothesis:
( ), bp pr I h a I= ⋅
2nd hypothesis:
( ) ( ) ( )2
1 1 1 1 1 1exp ln ln22g p p g p g
p g g p g g
f I I II I
µ φ µσ σ σ σπ
⎡ ⎤⎛ ⎞ ⎡ ⎤⎢ ⎥= − =⎜ ⎟ ⎢ ⎥⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎣ ⎦⎣ ⎦
( ) ( ) ( )( ) ( ) ( ) ( )
( )2 2
2
2 2
0 0
, 1 1, ln, ,
p g p bt p p p g
p g gp g p p p g p p
r I h f I af I h I II
r I h f I dI r I h f I dIφ µ
σ σ∞ ∞
⎡ ⎤= = ⎢ ⎥
⎢ ⎥⎣ ⎦∫ ∫
exp(2 ln )pb I
Studies performed by other Authors Cont.Analytical relation between pdf of lightning peak current to a tower and at ground
We now focus on the analytical formula derived by Petterson [IEEE Trans. PWDR,1991]
1st hypothesis:
( ), bp pr I h a I= ⋅
2nd hypothesis:
( ) ( ) ( )2
1 1 1 1 1 1exp ln ln22g p p g p g
p g g p g g
f I I II I
µ φ µσ σ σ σπ
⎡ ⎤⎛ ⎞ ⎡ ⎤⎢ ⎥= − =⎜ ⎟ ⎢ ⎥⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎣ ⎦⎣ ⎦
( ),t pf I h
( )22expt g g g tbµ µ σ σ σ⎡ ⎤= ⋅ =⎢ ⎥⎣ ⎦
is lognormal
Pettersson’s formula
2. Numerical procedure for evaluating lightning
current distributions at ground.
Proposed numerical procedure for evaluating lightning current distributions at
groundIp* minimum peak current observedr* its attractive radius
All the strokes with perspective stroke location within 2πr*2
are collected by the tower
I. Generation of a population of events Ip, tf, … and xg∈[0,r(Ip)]- IP, tf … are generated from the p.d.f. of strokes to the tower- xg are generated assuming the stroke locations be uniformlydistributed (correlations are taken into account)
II. Selection of the events with xg<r*
III. Determination of the statistical distributions of the currentparameters related to such events
Application to the Berger’s distribution
Application to the Berger’s distribution
27,7
Application to the Berger’s distribution
Application to the Berger’s distribution
2,3
Application to the Berger’s distribution Cont
From Andersson and Eriksson, Electra , 1980
Application to the Berger’s distribution Cont
Application to the Berger’s distribution Cont
Application to the Berger’s distribution Cont
= T30/90 / 0.6 = 3,8
I p
t f
Attractive radiusexpression a b
Eriksson 0.84 h0.6 0.76
Rizk 2.83 h0.4 0.63
( ), bp pr I h a I= ⋅
Parameter Expression
Eriksson Rizk
µg 20.1 21.3
σg 0.20 0.20
µg 3.2 3.3
σg 0.24 0.24
ρg 0.48 0.47
tf (µs)
Ip (kA)
0.47tρ =σt
Application to the Berger’s distribution Cont
Application to the Berger’s distribution Cont
Attractive radiusexpression a b
Eriksson 0.84 h0.6 0.76
Rizk 2.83 h0.4 0.63
( ), bp pr I h a I= ⋅
Parameter Expression
Eriksson Rizk
µg 20.1 20.0 21.3 21.2
σg 0.20 0.20 0.20 0.20
µg 3.2 3.3
σg 0.24 0.24
ρg 0.48 0.47
tf (µs)
Ip (kA)
0.47tρ =σt
Pettersson’s formula
( )22expt g g
g t
bµ µ σ
σ σ
⎡ ⎤= ⋅⎢ ⎥⎣ ⎦=
Comparison with the Pettersson’s formula for the case of electrogeometric expressions
rs = rl
rg
nearby strokedirect stroke
h
rs
rg
nearby strokedirect stroke
h rl
psr I βα= ⋅
g sr k r= ⋅
( )22 for s g gr r r h h r= − − < for s gr r h r= ≥
( ), bp pr I h a I= ⋅
b β=gh r≥If
/ 22 pr h I βα= ⋅2
b β= and g g sh r r r<< =or
ElectrogeometricalAttractive radius
expressionα β k
Armstrong and Whitehead 6.7 0.80 0.9
0.55IEEE (1243) 10 0.65
0.47tρ =σt
Application to the Berger’s distribution Cont
Parameter Expression
A&W IEEE
µg 20.2 21.1
σg 0.21 0.20
µg 3.2 3.3
σg 0.24 0.24
ρg 0.49 0.47
tf (µs)
Ip (kA)
ElectrogeometricalAttractive radius
expressionα β k
Armstrong and Whitehead 6.7 0.80 0.9
0.55IEEE 10 0.65
0.47tρ =σt
Application to the Berger’s distribution Cont
Parameter Expression
A&W IEEE
b= β /223.4
b=β19.7
b= β /224.1
b=β21.0
0.20 0.20
Probabilitythat conditions are verified 4.2% 28.8% 0.02%
0.20
80%
0.20
µg 20.2 21.1
σg 0.21 0.20Ip (kA)
Attractive radiusexpression c a b
From Dellera & Garbagnati 3h0.6 0.80 0.9
0.47tρ =
( ), bp pr I h c a I= + ⋅
σt
Application to the Berger’s distribution Cont
Parameter Dellera & Garbagnati Expression
µg 22.1
σg 0.19
µg 3.4
σg 0.24
ρg 0.45
tf (µs)
Ip (kA)
Attractive radiusexpression c a b
From Dellera & Garbagnati 3h0.6 0.80 0.9
0.47tρ =
( ), bp pr I h c a I= + ⋅
σt
Application to the Berger’s distribution Cont
Parameter Dellera & Garbagnati Expression
µg 22.1 18.1
σg 0.19 0.20
µg 3.4
σg 0.24
ρg 0.45
tf (µs)
Ip (kA)
Pettersson’s formula
( )22expt g g
g t
bµ µ σ
σ σ
⎡ ⎤= ⋅⎢ ⎥⎣ ⎦=
Application to the CIGRE distribution
1: AW; 2: IEEE 4: Eriksson; 5: from Rizk; 6: from Dellera-Garbagnati
Influence of the Tower Height
1: AW; 2: IEEE 4: Eriksson; 5: from Rizk; 6: from Dellera-Garbagnati
First Conculsions
The proposed method is more general than the other proposed so far in the literature.
What are the applications?
3. Application of the results to the evaluation
of indirect lightning performance of overhead lines
Application of the results to the evaluation of indirect lightning performance of overhead lines
The ___ is represented by the following curve:
VOLTAGE [kV] (or CFO)
Lightning Performance of a Distribution Linerelevant to induced voltages
Lightning Performance of a Distribution Linerelevant to induced voltages
Annual number of induced voltagesexceeding the value in abscissa(or Annual number of flashovers)
Application of the results to the evaluation of indirect lightning performance of overhead lines Cont.
How to calculate the ____?
Application of the results to the evaluation of indirect lightning performance of overhead lines Cont.
Clearly, the ___ depends on:
• models used to calculate the induced voltages
• lateral distance expression
• statistical distribution of lightning parameters
Models used to calculate the induced voltages
i (0,t)Return-Stroke Current
RSC i (z,t)
Lightning ElectroMagnetic Pulse
i (z,t) LEMP E, B
ElectroMagnetic Coupling
E, B EMC U(t)
Models used to calculate the induced voltages
i (0,t)Return-Stroke Current
RSC i (z,t)
Lightning ElectroMagnetic Pulse
i (z,t) LEMP E, B
ElectroMagnetic Coupling
E, B EMC U(t)
LIOVLIOVLIOV
The LIOV codeThe LIOV code
www.ing.unibo.it/die/liov
LIOV codeModels
The LIOV codeThe LIOV code
• Return-stroke model: MTLE (and TL)• LEMP: Uman and McLain and Cooray-Rubinstein• Coupling model: Agrawal extended to the case of
lossy ground
This allows to take into account more realistic line configurations than the simplified Rusck expression
The Agrawal coupling modelThe LIOV codeThe LIOV code
),,(),()(),('),(0
' htxExittxit
Ltxvx
ix
t
giijsi =
∂∂
−+∂∂
+∂∂
∫ τττξ
0),('),( =∂∂
+∂∂ txv
tCtxi
xsiiji
Transmission line coupling equations(Agrawal et al.)
Overhead line above lossy ground
The Agrawal coupling modelThe LIOV codeThe LIOV code
=∂
∂−+
∂∂
+∂∂
∫ τττξ ),()(),('),(
0
' xittxit
Ltxvx
t
giijsi
0),('),( =∂∂
+∂∂ txv
tCtxi
xsiiji
),,( htxEix
The ground resistivity plays a role in
1) the calculation of the line parameters
2) the calculation of the electromagnetic field
The LIOV codeThe LIOV codeThe LIOV code allows for the calculation of lightning-induced voltages along a multiconductor overhead line as a function of- lightning current waveshape (amplitude, front steepness, and duration), - return stroke velocity, - line geometry (height, length, number and position of conductors), values of resistive terminations, - ground resistivity and relative permittivity.
It allows also taking into account induction phenomena due to - the leader field, - non-linear phenomena such as corona - and the presence of surge arresters.
In order to take into account the presence of more complex types of terminations, as well as of line discontinuities and complex system topologies, the LIOV code has been interfaced with EMTP96.
The LIOVLIOV code calculates:• LEMP• Coupling
The EMTPEMTP :• calculates the boundary conditions• makes available a large library of power components
Γ0
LIOV-line
n-port
Concept at the basis of the interfaceConcept at the basis of the interface
0
u (x,t)
i(x,t) L'dx
C'dx
x x+dx
+- i(x+dx,t)
L
u (x+dx,t)
ui(x,t)
Eix(x,h,t)dx
ss+-
Γ0
i0
+-
ΓL
u0 iL uL
-u(L,t)i-ui(0,t)
Node ‘0’
+ -
u0(t), i0(t)
G2 +
-+
-
Γ0(t)
u1(t), i1(t)
Zc
u0’(t)
i0’(t) ve(t)
Node ‘1’
LIOV line Bergeron Line EMTP termination
+ -
-ve(t)
G1
Zc
u2(t), i2(t)
Node ‘2’∆x
Link between LIOV and EMTPLink between LIOV and EMTP
Treatment of the boundary conditions, data exchange between the LIOV code and the EMTP96:
Treatment of the boundary conditions, data exchange between the LIOV code and the EMTP96:
Link of the LIOV code with EMTP96Link of the LIOV code with EMTP96
EMTP(1) Line terminals node voltages at time step N TACS LIOV
LINE
(2) Line terminals node voltages at time step N
(3) Line terminals branch current at time step N+1
(4) Line terminals branch current at time step N+1
N=N+1
(6) Line terminals branch current at time step N+1 injected in the EMTP by current controlled generators (5) EMTP time step
increment for node voltages and branch currents
TACS – LIOV LINE V (1) V (1)
(2) (3)
(6) (6)
EMTP (4) (5)
V - voltage signal generator I – current controlled generator
I I
Link of the LIOV code with EMTP96Link of the LIOV code with EMTP96
Comparison with data measured on real scale complex line model at the ICLRT of the University of Florida (July-August 2002/2003)
0
10
20
30
40
50
60
70
80
90
0 5 10 15 20 25 30 35 40Current [kA]
Vol
tage
[kV
]
Surge arrester characteristic
LIOVLIOV--EMTP96: simulations and comparison with EMTP96: simulations and comparison with experimental data experimental data Cont.Cont.
LIOVLIOV--EMTP96: simulations and comparison with EMTP96: simulations and comparison with experimental data experimental data Cont.Cont.
Experimental overhead distribution line installed at the ICLRT. The indicated quantities are the measured lightning-induced currents.
LIOVLIOV--EMTP96: simulations and comparison with EMTP96: simulations and comparison with experimental data experimental data Cont.Cont.
-40
-20
0
20
40
60
80
100
120
140
0.E+00 1.E-06 2.E-06 3.E-06 4.E-06 5.E-06Time [s]
Indu
ced
Cur
rent
IG10
Measured current
Simulated current
-50
0
50
100
150
200
250
0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 1.E-05Time [s]
Indu
ced
Cur
rent
[A]
IBN6 SimulatedIBN6 Measured
Experimental data are courtesy of ICLRT of University of Florida (US)
Current flowing through the phase B conductor of pole 6
First event of 02-08-03 6th return stroke
First event of 02-08-03 6th return strokeCurrent flowing through the arrester located at pole 6 phase B
-2.50E+02
-2.00E+02
-1.50E+02
-1.00E+02
-5.00E+01
0.00E+00
5.00E+01
1.00E+02
1.50E+02
0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 1.E-05Time [s]
Indu
ced
Cur
rent
[A]
IB6 Simulated
IB6 Measured
LIOVLIOV--EMTP96: simulations and comparison with EMTP96: simulations and comparison with experimental data experimental data Cont.Cont.
-600
-400
-200
0
200
400
600
800
1000
1200
1400
0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 1.E-05
Time [s]
Indu
ced
Cur
rent
[A]
IG6 SimulatedIG6 Measured
-500
0
500
1000
1500
2000
0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 1.E-0Time [s]
Indu
ced
Cur
rent
[A]
IG2 SimulatedIG2 Measured
First event of 02-08-03 6th return stroke
First event of 02-08-03 6th return strokeCurrent flowing through the grounding of pole 6
Current flowing through the grounding of pole 2
Experimental data are courtesy of ICLRT of University of Florida (US)
LIOVLIOV--EMTP96: simulations and comparison with EMTP96: simulations and comparison with experimental data experimental data Cont.Cont.
Application of the results to the evaluation of indirect lightning performance of overhead lines Cont.
Clearly, the ___ depends on:
• models used to calculate the induced voltages
• lateral distance expression
• statistical distribution of lightning parameters
IEEE Std 1410(solid curve)
- proposed method (ideal ground)
- proposed method (lossy ground σg= 0.001 S/m)
IEEE Std 1410(solid curve)
- proposed method (ideal ground)
- proposed method (lossy ground σg= 0.001 S/m)
Single conductor line
0 100 200 300CFO [kV]
0.01
0.1
1
10
1E+2
Flas
hove
r / 1
00km
/ ye
ar
IEEE Guide
proposed method (ideal ground)
proposed method (lossy ground)
Comparison with IEEE Std 1410-1997
tf is lognormally distributed with median value 3.83 µs.
Correlation factor between tfand IP : 0.49 i
0 100 200 300CFO [kV]
0.01
0.1
1
10
1E+2
Flas
hove
rs /
100
km /
year
IEEE Guide
LIOV - tf = 0.5 us
LIOV - tf = 1 us
LIOV - tf = 3 us
Note that with small values of tfthe two methods predict basically the same results
Comparison with IEEE Std 1410-1997
Ideal groundIdeal ground
Application of the results to the evaluation of indirect lightning performance of overhead lines Cont.
For the calculation of the indirect lighting performance of the overhead use is made of the procedure proposed by Borghetti and Nucci [ICLP, 1998; Sipda, 1999] , based on the Monte Carlo method.Each event is characterized By 4 random variables
• peak value of the lightning current Ip
• front time tf (correlated with Ip)
• two co-ordinates of the stroke location (x and y)
• peak value of the lightning current Ip
• front time tf (correlated with Ip)
• two co-ordinates of the stroke location (x and y)
For the calculation of the indirect lighting performance of the overhead use is made of the procedure proposed by Borghetti and Nucci [ICLP, 1998; Sipda, 1999] , based on the Monte Carlo method.Each event is characterized By 4 random variables
• peak value of the lightning current Ip
• front time tf (correlated with Ip)
• two co-ordinates of the stroke location (x and y)
• peak value of the lightning current Ip
• front time tf (correlated with Ip)
• two co-ordinates of the stroke location (x and y)
3. Application of the results to the evaluation of indirect lightning performance of overhead lines Cont.
3. Application of the results to the evaluation of indirect lightning performance of overhead lines Cont.
Application of the results to the evaluation of indirect lightning performance of overhead lines Cont.
1 Inputs:- lightning current parameters (Ip and tf)- return stroke velocity- line and ground data
2 Random generation of events ( Ip ; tf : x ; y) > 20 000
3 Induced overvoltage calculation using LIOV or LIOV-EMTP96
4 Counting of the events generating overvoltages greaterthan 1.5 x CFO
5 Plot the graph:No. of flashovers/100 km/year vs CFOwhere No. of flashovers/100 km/year =
(n/ntot) • ng • S • 100/L (with ng=ground flash density)
Application of the results to the evaluation of indirect lightning performance of overhead lines Cont.
Let us now calculate the indirect lightning performance of an overhead line by using either:
• the lightning current statistical distribution by Berger (CIGRE distribution) biased by the presence of the tower;
• the statistical distributions at ground inferred using the proposed method.
• the lightning current statistical distribution by Berger (CIGRE distribution) biased by the presence of the tower;
• the statistical distributions at ground inferred using the proposed method.
We consider a single-conductor overhead line with the following characteristics:
• 2 km long; • 10 m high line;• ‘matched’ at both end;• “striking area” around the line about 20 km2.
• 2 km long; • 10 m high line;• ‘matched’ at both end;• “striking area” around the line about 20 km2.
Application of the results to the evaluation of indirect lightning performance of overhead lines Cont.
0.01
0.10
1.00
10.00
100.00
50 100 150 200 250 300Voltage [kV]
No.
of i
nduc
ed o
verv
olta
ges
with
mag
nitu
de
exce
edin
g th
e va
lue
in a
bsci
ssa/
(100
km
yea
r) Armstrong-WhiteheadIEEEErikssonRizkDellera-Garbagnati
Ideal groundIdeal ground
CIGRE distributionCIGRE distributionCIGRE distribution
Application of the results to the evaluation of indirect lightning performance of overhead lines Cont.
0.01
0.10
1.00
10.00
100.00
50 100 150 200 250 300Voltage [kV]
No.
of i
nduc
ed o
verv
olta
ges
with
mag
nitu
de
exce
edin
g th
e va
lue
in a
bsci
ssa/
(100
km
yea
r) Armstrong-WhiteheadIEEEErikssonRizkDellera-Garbagnati
UNBIASED distributionUNBIASED distributionUNBIASED distribution
Ideal groundIdeal ground
Application of the results to the evaluation of indirect lightning performance of overhead lines Cont.
0.01
0.10
1.00
10.00
100.00
50 100 150 200 250 300
Voltage [kV]
No.
of i
nduc
ed o
verv
olta
ges
with
mag
nitu
de
exce
edin
g th
e va
lue
in a
bsci
ssa/
(100
km
yea
r)
Armstrong-Whitehead
IEEE
Eriksson
Rizk
Dellera-Garbagnati
Lossy ground(0.001 S/m)
Lossy ground(0.001 S/m)
CIGRE distributionCIGRE distributionCIGRE distribution
Application of the results to the evaluation of indirect lightning performance of overhead lines Cont.
0.01
0.10
1.00
10.00
100.00
50 100 150 200 250 300
Voltage [kV]
No.
of i
nduc
ed o
verv
olta
ges
with
mag
nitu
de
exce
edin
g th
e va
lue
in a
bsci
ssa/
(100
km
yea
r )
Armstrong-WhiteheadIEEEErikssonRizkDellera-Garbagnati
UNBIASED distributionUNBIASED distributionUNBIASED distribution
Lossy ground(0.001 S/m)
Lossy ground(0.001 S/m)
Conclusions
The use of unbiased current statistical distributions results, as expected, in a better performance of the distribution line to indirect lightning, these distributions being characterized by a lower median value.
We have shown how the results vary depending on the expression adopted to evaluate the lateral distance (attractive radius).
Also, the ground resistivity acts in minimizing the difference between the line performance calculated using the biased and unbiased lightning current distributions.
Conclusions
It appears, however, that additional study on attractive radius expressions is badly needed.
The results obtained show that statistical current distributions at ground are probably characterized by lower median values than the relevant distributions gathered by means of instrumented towers.
This is in line with lower median values obtained by means of lightning location systems, although …