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Power electronic control in electrical systems 135

power from the network depending on whether they are operated in an over-excited
or in an under-excited mode, in a not dissimilar manner as synchronous generators
do, except that they do not produce active power. Advances in power electronics
together with sophisticated electronic control methods made possible the develop-
ment of fast SVC equipment in the early 1970s, leading to a near displacement of the
synchronous condenser (Miller, 1982). The most recent development in the area of
electronically controlled shunt compensation is the STATCOM (Hingorani and
Gyugyi, 2000). It is based on the VSC and combines the operational advantages of
the rotating synchronous condenser and the SVC. For most practical purposes, it is
expected to replace the SVC once the technology becomes more widely understood
among practising engineers and prices drop.
4.5.2 SVC power flow modelling

There are several SVC models available in the open literature for power flow studies.
In particular, the models recommended by Confe  rence Internationale des Grands
Â
Reseaux Electriques (CIGRE) (Erinmez, 1986; IEEE Special Stability Controls
Working Group, 1995) are widely used. To a greater or lesser extent, these models
are based on the premise that the SVC may be represented as a synchronous
generator, i.e. synchronous condenser, behind an inductive reactance.
The simplest model represents the SVC as a generator with zero active power
output and reactive power limits. The node at which the generator is connected is
represented as a PV node. This assumption may be justified as long as the SVC
operates within limits. However, gross errors may result if the SVC operates outside
limits (Ambriz-Perez et al., 2000). An additional drawback of the SVC models based
on the generator principle is that it assumes that the SVC draws constant reactive
power in order to keep the voltage magnitude at the target value whereas, in practice,
the SVC is an adjustable reactance, which is a function of voltage magnitude.
A simple and efficient way to model the SVC in a Newton±Raphson power flow
algorithm is described in this section (Fuerte-Esquivel and Acha, 1997). It is based on
the use of the variable susceptance concept, which it is adjusted automatically in order
to achieve a specified voltage magnitude. The shunt susceptance represents the total
SVC susceptance necessary to maintain the voltage magnitude at the specified value.
Its implementation in a Newton±Raphson power flow algorithm requires the
introduction of an additional type of node, namely PVB (where P relates to active
power, Q to reactive power and B to shunt susceptance). It is a controlled node where
the nodal voltage magnitude and the nodal active and reactive powers are specified
while the SVC's variable susceptance B SVC is handled as state variable. If B SVC is
within limits, the specified voltage is attained and the controlled node remains PVB
type. However, if B SVC goes out of limits, B SVC is fixed at the violated limit and the
node becomes PQ type in the absence of any other regulating equipment connected to
the node and capable of achieving voltage control.
As discussed in Section 4.2.1, the active and reactive powers drawn by a variable
shunt compensator connected at node l are

P l ˆ 0
(4:65)
2
Q l ˆ jV l j B SVC