Stability of ideal thyristor and diode switching circuits

This paper analyzes the stability of a general RLC circuit with ideal thyristors or diodes and periodic sources. Applications include high power thyristor controlled reactor and bridge rectifier circuits. The periodic steady states of the circuit are analyzed using a Poincare map and transversality conditions are given to guarantee the smoothness of the Poincare map. A simple and exact formula for the Jacobian of the Poincare map is proved. Account is taken of the varying state space dimension as diodes switch on and off. When the transversality conditions fail, switching times can jump or bifurcate. Examples show that these switching time bifurcations can cause instability of thyristor circuits and mode changes of diode circuits. The simplification of the Jacobian formula is used to explain why the switching time bifurcations occur and are not predicted by the eigenvalues of the Jacobian. Periodic orbits of ideal diode circuits are proved to be stable using Jacobian and incremental energy methods. A source of damping in switching circuits is identified