Switching Time Bifurcations in a Thyristor Controlled Reactor

Thyristor controlled reactors are high power switching circuits used for static VAR control and the emerging technology of flexible ac transmission. The static VAR control circuit considered in the paper is a nonlinear periodically operated RLC circuit with a sinusoidal source and ideal thyristors with equidistant firing pulses. This paper describes new instabilities in the circuit in which thyristor turn off times jump or bifurcate as a system parameter varies slowly. The new instabilities are called switching time bifurcations and are fold bifurcations of zeros of thyristor current. The bifurcation instabilities are explained and verified by simulation and an experiment. Switching time bifurcations are special to switching systems and, surprisingly, are not conventional bifurcations. In particular, switching time bifurcations cannot be predicted by observing the eigenvalues of the system Jacobian. We justify these claims by deriving a simple formula for the Jacobian of the Poincare map of the circuit and presenting theoretical and numerical evidence that conventional bifurcations do not occur.