Harmonic domain modelling of three phase thyristor-controlled reactors by means of switching vectors and discrete convolutions

The main objective of this paper is to report on a newly developed three phase TCR model for SVC which is based on the use of harmonic switching vectors and discrete convolutions. This model is amenable to direct frequency domain operations and provided a fast and reliable means for assessing 6- and l2-pulse TCR plant performance at harmonic frequencies. The use of alternate time domain and frequency domain representations is avoided as well as the use of FFTs. In this approach, each single phase unit of the TCR is modelled as a voltage-dependent harmonic Norton equivalent where all the harmonics and cross-couplings between harmonics are explicitly shown. This model is suitable for direct incorporation into the harmonic domain frame of reference where all the busbars, phases, harmonics and cross-couplings between harmonics are combined together for a unified iterative solution through a Newton-Raphson technique exhibiting quadratic convergence.