In this paper, we propose a method of analytically calculating an impedance of a thyristor-controlled series capacitor (TCSC). The TCSC consists of a thyristor-controlled reactor (TCR) and a capacitor. If a small voltage component of frequency
f superimposes TCSC voltage of frequency
fo, then current components of frequency (
nfo±
f) flow through the TCR, where
n takes even numbers. We derive theoretical equations for them. In the derivation, we consider an influence of odd harmonics in the TCSC voltage. We also consider deviations in its zero-crossing times due to the superimposed voltage. The current components flow through the capacitor and the transmission line, and produce new voltage components of frequency (
nfo±
f). In order to count their influence, we introduce admittance matrices for the TCR, the capacitor, and the transmission line. By solving a network equation consisting of the matrices, we can obtain distribution of the voltage and current components. We define the impedance of TCSC as a ratio of the voltage component of frequency
f to the current one of the same frequency. The impedance analytically obtained corresponds well with that obtained by simulations. Its frequency responses vary with the firing method of thyristors.
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