Study of bifurcation rules of PSM converter in DCM based on Energy Balance model

Based on the theory of energy conservation, the Energy Balance (EB) model of DC-DC converter in Discontinuous Conduction Mode (DCM) is proposed in this paper and its validity is proved by analyzing a PWM converter. Based on this proposed EB model for Pulse Skip Modulation (PSM) converter, the relationships between output voltage and modulation factor M and load resistance R are given, and the stability of PSM converter in DCM is also analyzed. According to the simulation results, it is shown that bifurcations occur for PSM converter, but no chaos happens when PSM converter operates in DCM. The PSM converter will be stable at either period-(n+m) bifurcations mono-cycle stabilization or (n_i +m_i) multi-cycle stabilization. It is also proved that n_i=1 or m_i=1 always occurs whenever the PSM converter operates in DCM. The bifurcation rules and the boundary resistances of period-(n+m) bifurcations are also given.