Page 316 - Power Electronic Control in Electrical Systems

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304 Transient studies of FACTS and Custom Power equipment

From Equations 8.3 and 8.4 and considering a fundamental frequency of f ˆ 50 Hz,
the capacitance and inductance values are
C ˆ 14:04 mF
L ˆ 0:361 mH

Once the capacitance and inductance have been sized, it is necessary to determine the
initial operating condition of the SVC. Initially, Brk is open and there is no need for
the SVC to be in operation. However, it is already connected and interacting with the
AC system. Then the selection of the initial firing angle a must be such that under this
operating condition the SVC does not exchange any power with the AC system.
This firing angle corresponds to the case when the effective reactances X C and X L
cancel each other out. In this case, the SVC effective reactance X SVC is infinite and
there is no current leaving or entering the SVC, i.e. the power exchange between the
SVC and the AC system is zero.
According to the inductive and capacitive reactances, each SVC has its own firing
angle-reactive power characteristic, Q SVC (a) which is a function of the inductive and
capacitive reactances. The firing angle initial condition may be determined using a
graph similar to that shown in Figure 8.15(b). The following steps may be used to
determine this plot. Firstly, it is necessary to obtain the effective reactance X SVC as a
function of the firing angle a, using the fundamental frequency TCR equivalent
reactance X TCR
pX L
X TCR ˆ (8:5)
s sin s
and
s ˆ 2(p a) (8:6)
where X L is the reactance of the linear inductor, and s and a are the thyristors'
conduction and firing angles, respectively.
At a ˆ 90 the TCR conducts fully and the equivalent reactance X TCR becomes

X L .At a ˆ 180 , the TCR is blocked and its equivalent reactance becomes extremely

large, i.e. infinite.
The total effective reactance of the SVC, including the TCR and capacitive
reactances, is determined by the parallel combination of both components

X C X TCR
X SVC ˆ (8:7)
X C ‡ X TCR
which as a function of the conduction angle s becomes

pX C X L
X SVC ˆ (8:8)
X C (s sin s) pX L
And finally as a function of the firing angle a becomes

pX C X L
X SVC ˆ (8:9)
X C [2(p a) ‡ sin 2a] pX L