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Power electronic control in electrical systems 139

4.6 Active power control

4.6.1 General aspects

A well-established method to increase the transmission line capability is to install
series compensation in order to reduce the transmission line's net series impedance.
From the control point of view there is great incentive to provide compensation by
electronic means. For instance, the TCSC enables effective active power flow
regulation in the compensated transmission line. The TCSC has the ability to
operate in both the inductive and the capacitive regions. TCSC operation in the
inductive region will increase the electrical length of the line thereby reducing the
line's ability to transfer power. Conversely, TCSC operation in the capacitive
region will shorten the electrical length of the line, hence increasing power transfer
margins.
The structure of a modern series compensator may consist of a large number of
small inductive-capacitive parallel branches connected in tandem and each branch
having independent control. Nevertheless, for the purpose of fundamental fre-
quency, power flow studies, a variable series reactance provides a simple and very
efficient way to model the TCSC. The changing reactance adjusts automatically to
constrain the power flow across the branch to a specified value. The amount of
reactance is determined efficiently by means of Newton's algorithm. The changing
reactance X TCSC represents the total equivalent reactance of all the TCSC modules
connected in series.
Active power flow can also be controlled by adjusting the phase angle difference
across a series connected impedance. As outlined in Section 4.2.3, this is the power
transmission characteristic exploited by mechanically controlled phase shifting trans-
formers and by electronic phase angle controllers. The latter has an almost instantan-
eous speed of response and it achieves its objective of controlling active power flow
by inserting a variable quadrature voltage in series with the transmission line. The
effectiveness of traditional phase shifters in performing this function has been well
demonstrated in practice over many years (IEEE/CIGRE, 1995).

4.6.2 TCSC power flow modelling

For inductive operation the TCSC power equations at node l are

jV l kV m j
P l ˆ sin(y l y m ) (4:76)
X TCSC
2
jV l j jV l kV m j
Q l ˆ cos(y l y m ) (4:77)
X TCSC X TCSC
For capacitive operation, the signs of the equations are reversed. Also, for the power
equations corresponding to node m the subscripts l and m are exchanged in equations
(4.76)±(4.77).