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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
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