Electrical Power Systems

140 Electrical Power Systems
\ gl = 033 . 812 . °
ZC = Z 10911 . 72. 4°
=
Y -3
j ´ 10
= 330. 31 - 8. 8°
YZI
A = D = cosh (g l) = 1 + = 0. 9481 1°
HG 2 KJ
YZI
sinh (g l) » YZ 1 + = 033 . 812 . ° HG 6 KJ
B = ZC sinh (g l) = 330. 31 - 8. 8° ´ 0. 33 812 . °
= 109 72. 4°
sinh ( g l)
033 . 812 . °
C = =
» j ´
Z 330. 31 - 8. 8°
C
V S = AV R + BI R
-
10 3
= 0. 9481 1°´ 120. 08 0°+ 109 72. 4°´ 0. 173 - 36. 87°
= 113. 84 1°+ 18. 85 35. 53°
= 129. 806 5. 72°
kV
\ VS (L-L) = 3 ´ 129. 806 5. 72°
kV
= 224. 83 5. 72°
kV
I S = CV R + DI R
\ IS = -3
j ´ 10 ´ 120. 08 0° + 0. 948 1° ´ 0. 173 - 36. 87°
= 0.135 10. 23°
kA.
Sending end power factor = cos (10.23° – 5.72°)
= 0.997 (leading)
Results are tabulated below:
PS = 3 ´ 224. 83 ´ 0135 . ´ 0. 997 = 52. 4 MW
Short line approx. Nominal-p Exact
V S (L-L) 235.33 kV 224.85 kV 224.83 kV
|I S | 0.173 kA 0.135 kA 0.135 kA
pf 0.75 0.997 0.997
p s 52.88 MW 52.40 MW 52.40 MW
rom the above table, we can see that the results obtained by the nominal-p and exact
methods are practically the same. On the other hand, the results obtained by the short line
approximation are in considerable error.
Therefore, for a long line, it is sufficiently accurate to use the nominal-p method.