BIFURCATION OF POWER ELECTRONIC-CIRCUITS

This paper studies various bifurcations of per iodic orbits in power e lectronic circuits : cyclic fold bifurcations, period-doubling bifurca tions, and bifurcations due to Poincare map discontinuities. We focus on circuits operating under closed-loop control and/or containing nonl inear reactive components. Section III contains an exploration of cycl ic fold bifurcations and the associated resonant jump phenomenon in ci rcuits containing saturable reactors. Section IV gives a comprehensive overview of period-doubling phenomena in closed-loop DC-DC conversion circuits. We study circuits with homeomorphic and unimodal Poincare m aps, those that period-double a single time and those that period-doub le repeatedly in a cascade to chaos. This section ends with a result r elating non-genericity of a period-doubling bifurcation to halfwave or bital symmetry. An interesting feature of power electronic circuits is that they may have Poincare maps that are continuous but not everywhe re differentiable, or discontinuous. In Section V we study, in detail, bifurcation behavior in a thyristor controlled VAR compensator, under stood in terms of Poincare map discontinuities. We show that Poincare map discontinuities are due to jumps in circuit switching times. We sh ow how map discontinuities lead to steady state jump phenomena, and di stinguish between transient behavior related to switch time jumps and steady slate bifurcations. The paper ends with an Appendix, in which c oncepts underlying cyclic fold bifurcations for the case of a continuo us but not everywhere differentiable map ale developed.