Theoretical Equation for Frequency Responses of Thyristor-Controlled Reactor

Abstract

In power systems, power electronics apparatuses such as static var compensators (SVC) and thyristor-controlled series capacitors (TCSC) have been introduced. SVC and TCSC both consist of a thyristor-controlled reactor (TCR) in parallel with capacitor banks. By adjusting the current through the reactor with the thyristors, we can change their reactances at a fundamental frequency. However, their admittances at other frequencies are important in studies of harmonic resonance and subsynchronous resonance. The admittance of a capacitor is clear, so we study that of TCR. First, we calculate its admittance by superimposing a small voltage of a frequency on the fundamental voltage, and then extracting the current change of the frequency. The conventional theoretical equations prove to be applicable only to the fundamental and the harmonic frequencies. TCR has conductance, and it can take negative values at other frequencies. We derive a theoretical equation applicable to general frequencies. The admittance is a function of the frequency and the firing angle. For the harmonic frequencies, it also depends on the phase difference between the fundamental and superimposed voltages. Lastly, we compare it with the simulation result to show the validity of the theoretical equation.