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3. Modification of the conventional theory for induced voltage estimation in
practical applications
3.1 Generalization of rusck's methodology for generic discharge current waveform
Rusck's formulation presupposes that the atmospheric discharge can be represented by a
waveform represented by a step function. However, measurements achieved in field have
evidenced that the current waveform characteristics influence in the induced voltage in
distribution lines located nearby the discharge occurrence point.
More specifically, parameters such as rising time and current waveform peak time have
high correlation with the voltage induction process in distribution lines. Therefore, it is
suggested that the induced voltage estimation in distribution lines to be achieved
considering a waveform for discharge current near to that found in nature.
An approach often adopted for the atmospheric discharge current modeling can be
provided as in (5), that is:
i(t)
i
(t)
i
(t)
i
(t)
(5)
h1
h2
de
where:
nm
t
I
t

m1
0m
i
t
p
(6)
hm
nm
t
m
m2
1
m1
 
d i t (1exp( )(1exp( ]

(7)
and:
1
nm
 
m1
m2

exp
nm
 
(8)
m
 
m2
m1
Equation (6) is an example of Heidler's functions. An alternative frequently employed in
atmospheric discharge modeling is double exponential.
Nevertheless, the modeling through two Heidler's function, as presented in (5), provides a
more appropriate approximation for representation of the real phenomenon since the
derivative of current at the instant t=0s is null. This fact is proved by innumerous practical
cases.
In Fig. 7 is illustrated the current waveform results from modeling presented in this section,
where the current has a peak value near to 12kA with a time of 0,81x10 -6 s.
Supposing that the system to be linear, it is possible the use of Duhamel's integral
(Greenwood, 1992) in order to represent the current waveform through a successive series of
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