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localization in relation to incidence point of the atmospheric discharge, that is, the

induced voltage values produced in a line composed by several conductors of same height

and with a small horizontal spacing, such as in distribution lines, would be equal in each

conductor.

Measurements achieved with the reduced model technique (Paula et al., 2001; Salari &

Portela, 2007), as well as measurements in fields made in South Africa, demonstrate that the

results provided by Rusck's theory is coherent with those obtained by experimental results

(Eriksson et al., 1982). Originally, Rusck proposed a current wave to the atmospheric

discharge represented by a step function with amplitude
I
. The induced voltage produced

by this discharge in relation to an infinite line can be computed by:

V x,t

U x,t

U

x,t

(1)

where:

2

(ctx)

x

(ctx)

(

)

U(x, t)

30 I h

.

1

(2)

2

2

2

2

2

2

2

[y

c t

x

]

(c ) 1

(x y )

v

1

(3)

5

c

5.10

1

I

In this case,
V
(
x
,
t
) is the induced voltage (V) at a point
x
of the line;
t
is the time in seconds;
c

is the velocity of light in free space (m/s);
I
is the return-peak current value (A);
h
is the

average height of the distribution line;
y
is the closest distance between the discharge

incidence point and the distribution line (m) and
x
is a point along the line (m).

Equations (1), (2) and (3) express Rusck's theory basis. In (4) the expression for the

maximum induced voltage at the point
x
=0m is given by:

38.8 I h

V

(4)

max

y

From the previous expressions is possible to identify that they provide an analytic form for

the computation of induced voltage in a distribution line, whereas other existent theories

provide just iterative expressions that have high computational effort to perform the same

estimation.

In Fig. 1 is presented the induced voltage at the point
x
=0m for an atmospheric discharge

represented by a step function with amplitude
I
=10 kA in relation to an infinite line with 10

meters of height, where the distance between the atmospheric discharge from the

distribution line is 100 meters.

In order to illustrate how the proposed formulation in this section is efficient for induced

voltage estimation in overhead distribution lines, the induced voltage profile for different

positions along the distribution line is presented in Fig. 2.