Electrical Power Systems

Eqns (6.15) and (6.17) can be written in matrix form.
L
V
I SO
NM SQP
=
L
Characteristics and Performance of Transmission Lines 127
O L
I
HG KJ QP
NM
ZYI
1 +
Z HG 2 KJ
ZYI ZY
Y 1 + 1 + HG 4 KJ 2
NM
Therefore, the ABCD constants for the nominal p model are given by
HG I
KJ
+ HG I
4 KJ
ZY
A = 1 + , B = Z,
2
C = Y 1
6.5 LONG TRANSMISSION LINE
V
ZY ZY
, D = 1 +
2
I
R
R
O
QP
I
HG KJ
...(6.18)
or short and medium length lines, accurate models were obtained by assuming the line
parameters to be lumped. In case the lines are more than 250 km long, for accurate solutions
the parameters must be taken as distributed uniformly along the length as a result of which the
voltages and currents will vary from point to point on the line. In this section, expressions for
voltage and current at any point on the line are derived. Then, based on these equations, an
equivalent p model is obtained for long transmission line. igure 6.4 shows one phase of a
distributed line of length l km.
ig. 6.4: Schematic diagram of a long transmission line with
distributed parameters.
rom KVL, we can write,
V(x + Dx) = z.Dx.I(x) + V(x)
\ Vx x Vx
( + D ) - ( )
= z.I(x)
Dx
...(6.19)
As Dx ® 0
dV ( x)
= z.I(x) ...(6.20)
dx