Stability and harmonics in thyristor controlled reactors

Harmonics that arise from the interaction of thyristor controlled reactors (TCRs) and power systems can sometimes cause stability problems. The classical method for calculating harmonics is to calculate the harmonic current assuming an infinite bus at the high side of the TCR transformer. This current is then used as a harmonic current source on the AC system. The basic problem with this method is that many of the interactions between the AC system and the TCR are neglected. Two methods for studying the neglected interactions are described. The first uses state variables to analyze the circuit containing the TCR. The resulting equations are linear differential equations with periodic coefficients. This formulation allows the study of stability, periodic operation, and resonance, which cannot be achieved by other methods. The second method uses a Fourier matrix description of the TCR. In this model the coupling between the different harmonics due to the switching is clearly shown.>