Page 106 - Power Electronic Control in Electrical Systems

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94 Transmission system compensation

For an electrically short line, cos y ! 1 and Z 0 sin y ! X L , so that with E s ˆ E r
equation (3.28) reduces to
2
E (1 cos d)
Q s ˆ s ˆ Q r (3:29)
X L

3.4 Compensated transmission lines

Reactive compensation means the application of reactive devices

(a) to produce a substantially flat voltage profile at all levels of power transmission;
(b) to improve stability by increasing the maximum transmissible power; and/or
(c) to supply the reactive power requirements in the most economical way.
Ideally the compensation would modify the surge impedance by modifying the
capacitive and/or inductive reactances of the line, so as to produce a virtual surge-
impedance loading P that was always equal to the actual power being transmitted.
0
0
According to equation (3.4), this would ensure a flat voltage profile at all power
levels. However, this is not sufficient by itself to ensure the stability of transmission,
which depends also on the electrical line length y; see equation (3.26). The electrical
0
length can itself be modified by compensation to have a virtual value y shorter than
the uncompensated value, resulting in an increase in the steady-state stability limit P max .
These considerations suggest two broad classifications of compensation scheme,
surge-impedance compensation and line-length compensation. Line-length compensa-
tion in particular is associated with series capacitors used in long-distance transmis-
sion. A third classification is compensation by sectioning, which is achieved by
connecting constant-voltage compensators at intervals along the line. The maximum
transmissible power is that of the weakest section, but since this is necessarily shorter
than the whole line, an increase in maximum power and, therefore, in stability can be
expected.

3.4.1 Passive and active compensators

Passive compensators include shunt reactors and capacitors and series capacitors.
They modify the inductance and capacitance of the line. Apart from switching, they
are uncontrolled and incapable of continuous variation. For example, shunt reactors
are used to compensate the line capacitance to limit voltage rise at light load. They
increase the virtual surge impedance and reduce the virtual natural load P . Shunt
0
0
capacitors may be used to augment the capacitance of the line under heavy loading.
They generate reactive power which tends to boost the voltage. They reduce the
virtual surge impedance and increase P . Series capacitors are used for line-length
0
0
compensation. A measure of surge-impedance compensation may be necessary in
conjunction with series capacitors, and this may be provided by shunt reactors or by
a dynamic compensator.
Active compensators are usually shunt-connected devices which have the property
of tending to maintain a substantially constant voltage at their terminals. They do
this by generating or absorbing precisely the required amount of corrective reactive