Analysis of the Stability and Ripple of PSM Converter in DCM by EB Model

Abstract

Based on the theory of energy conservation, the Energy Balance (EB) model of a PSM (Pulse Skip Modulation) converter in DCM (Discontinuous Current Mode) is proposed in this paper. The relationships of the output voltage versus modulation factor M and load resistances R are given. The stability of a PSM converter in DCM is analyzed based on this proposed EB model. Simulation results show that chaos never occurs but bifurcations happen for a PSM converter in DCM. The PSM converter will be stable at either period-(n+m) bifurcation mono-cycle stabilization or (n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sub> m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ) multi-cycle stabilization. n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> =1 or m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> =1 always occurring whenever a PSM converter operating in DCM is proved by simulation. The boundary resistances of period-(n+m) bifurcation and the output voltage ripples are also given in this paper.