Stevenson J. Power system analysis
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218
CHAPTER
6
CURRENT AND VOLTAGE RELATIONS ON A TRANSMISSION LINE
6.9 REACTIVE COMPENSATION
OF TRANSMISSION LINES
The performance of transmission lines, especially those of medium length and
longer, can be improved by reactive compensation of a series or parallel type.
Series com
p
ensation consists of a capacitor bank placed in series with each phase
conductor of the line. Shunt compen
s
ation refers to the placement of inductors
from each line to neutral to reduce partially or completely t
h
e shunt suscep
tance of a high-voltage line, which is particularly important at light loads when
the
voltage at the receiving end may othe rwise become very high.
Series compensation reduces the series impedance of the line, which is the
principal cause of voltage drop and the most important factor in determining
the maximum power which thc line can transmit. In order to understand the
eect of series impedance Z on maximum power transmission, we examine Eq.
(6.61) and see that maximum power transmitte d is dependent on the reciprocal
of the generalized circuit constant B, which for the nominal- equals Z and for
the equivalent- equals Z (sinh 1)/1. Because the A,
C
, and D constants are
functions of Z, they will also change in value, but these changes will be small in
comparison to the change in B.
The desired reactance of the capacitor bank can be determined by
compensating for a specic amount of the total inductive reactance of the line.
This leads to the term "compensation factor," which is dened by
X
c
i
X
L
>
where
X
c
is the capacitive reactance of the series capacitor bank per phase and
XL is the total inductive reactance of the line per phase.
When the nominal- circuit is used to represent the line and capacitor
bank, the physical location of the capacitor bank along the line is not taken into
account. If only the sending- and receiving-end conditions of the line are of
interest, this will not create any signicant error. However, when the operating
conditions along the line are of interest, the physical location of the capacitor
bank must be taken into account. This can be accomplished most easily by
determining ABeD constants of the portions of line on each side · of the
capacitor bank and by representing the capacitor bank by its ABeD constants.
The equivalent constants of the combination (actually referred to as a ca
s
caded
connection) of line-capacitor�line can then be determined by applying the
equations found in Table A.6 in the Appendix.
In the southwestern part of the United States series compensation is
especially
i
mportant because large generating plants are located hundreds of
miles from load centers and large amounts of power must be transmitted over
long distances. The lower vol tage drop in the line with series compensation is an
additional advantage. Series capacitors are also useful in balancing the voltage
drop of two parallel lines.
Example 6.6. In order to show the relative changes in the B constant with respect
to the change of the A, C, and D constants of a line as series compensation is
applied, nd the constants for the line of Example 6.3 when uncompensated ,and
for a series compensation of 70%.
6.9
REAIVE COM PENSATION OF TRANSM ISSION LI NES
219
Solution. The equivalent- circuit
and
quantities found in Examples 6.3 and 6.5
can be used with Eqs. (6.37) to nd, for the uncompensated line
A
= D = cosh yl
=
0.8
90
4/1.
3
40
B
=
2'
=
186.78/79.460
n
'
=
_
si
_
n
_
h
_
y
_
'
=
0.4590
/
84.940
406.4/
-
5
.48°
=
0.001131
/
90.420
S
The series compensation alters only the series arm of the equiv,l
I
ent- circuit. The
new series ;Irm imped;ll1ce is also the generalized constant D. So,
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