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Power electronic control in electrical systems 287

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DV ˆ H R ‡ Y C † I TCSC ˆ Z TCSC I TCSC (7:47)
where the voltage drop is DV ˆ V s V r . Also, Z TCSC and I TCSC are the equivalent
impedance and the current across the TCSC, respectively. It should be noted that
Z SVC is a function of the conduction angle s via H R .

7.6.2.3 Three-phase TCSC representation
Equation (7.46) represents a single-phase TCSC in harmonic domain. However,
expanding this model to encompass three-phase TCSCs is straightforward because
of the decoupled nature of the three phases
0 1
0 1 Y TCSC,A 0 0 Y TCSC,A 0 0 0 1
I A,s V A,S
0 0 0 0
B Y TCSC,B Y TCSC,B C
B I B,s C B CB V B,s C
B C B 0 0 Y TCSC,C 0 0 CB C
I C,s V C,s
B C B Y TCSC,C CB C
B C ˆ B CB C (7:48)
B C B 0 0 0 0 CB C
Y TCSC,A Y TCSC,A
B I A,r C B CB V A,r C
I B,r Y TCSC,B Y TCSC,B V B,r
@ A B 0 0 0 0 C@ A
@ A
I C,r 0 0 Y TCSC,C 0 0 Y TCSC,C V C,r
7.7 TCSC systems
Equation (7.46) represents one single-phase TCSC module in the harmonic domain.
If the TCSC comprises more than one module, or if the TCSC module is part of a
series compensation scheme comprising conventional capacitor banks, then two-port
representations may be used instead. The former case corresponds to the series
compensation scheme found in the Slatt substation, where six identical TCSC mod-
ules are used (Piwko et al., 1996). This compensating scheme has been dubbed,
Advanced Series Compensator (ASC). The latter compensation scheme is found in
the Kayenta substation, where one 15
TCSC module is connected in tandem with
two capacitor banks, with values of 40
and 55
, respectively (Christl et al., 1991).
The two-port, ABCD representation of a generic transmission element connected
between nodes s and r is

V s A B V r
ˆ (7:49)
I s C D I r
Due to the lumped nature of the TCSC module, as opposed to a transmission line
or a cable, where the distributed inductive and capacitive effects are very pro-
nounced, the ABCD representation of one TCSC module is very simple

1
V s Z TCSC V r
ˆ (7:50)
I s 0 1 I r
where 1 and 0 are the unity and null matrices, respectively.
A similar representation exists for the conventional series capacitor bank in this
frame of reference, i.e.

V s 1 Z SC V r
ˆ (7:51)
I s 0 1 I r
where Z SC is the impedance of the series capacitor.