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U
(-
x
0,
t
)
U
(
x
0,
t
)
x
0
Fig. 10. Induced voltage composition at the point x
0
of the line.
U
(-
x
1,
t
)
x
1
R
f
Fig. 11. Induced voltage in a finite line.
If the line was infinite, the voltage at the point
x
1
would be given by:
V(x,t) U(x,t) U( x,t)
(10)
1
1
1
As there is no line located at the right part of the point
x
1
, there is no contribution of loads
coming from the right of
x
1
, that is, the voltage contribution
U
(
x
1
,
t
) is null. As the line has
termination impedance, the voltage at the point
x
1
can be computed as follows:
V(x,t) U( x,t)
U( x,t)
(11)
1
1
1
where is the reflection coefficient. The expression to obtain is given by:
RZ
RZ
f
L
(12)
f
L
where
Z
L
is the characteristic impedance of the distribution line. The numeric value for
Z
L
is
provided by:
h
Z
138 log
2
(13)
L
r
where
h
is the height of the distribution line and
r
is the conductor diameter.
Supposing that the discontinuity at the point
x
1
to be substituted by a compensation source,
the value of this source can be computed according to the following development:
V(x,t)
V U(x,t)
U(x,t)
(14)
1
1
1