Stevenson J. Power system analysis
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208
CHAPTER 6 CURRENT AN
D
VOLTAGE RELATIONS ON A TRANSMISSION LINE
By rearranging Eqs. (6.23) and (6.24) and substituting hyperbolic functions for
the exponential terms, we nd a new set of equations. The new equations, giving
voltage and current anywhere along the line, are
V
R
I
= Iu cosh X
+
-sinh "IX
Z(
(6.33
)
(6.3
4 )
Letting x = / to obtain the voltage and the current (It the senuing enu, we have
(
6.
35
)
VI?
Is = If( cosh
/
+
Z
sinh yl
c
(
6.36)
From examination of these equations we see that the generalized circuit
constants for a long line are
A = cosh yl
B
= Zc sinh yl
sinh 1
c
=
-
D
=
cosh 1
( 6.3
7)
Solving Eqs. (6.35) and (6.36) for V
R
and
I
R
in terms of Vs and
I
s
, we obtain
(6.38
)
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