A generalized geometrical piecewise-affine model of DC-DC power electronic converters

摘要

A generalized model of the dynamics (GMD) of DC-DC power electronic converters (PECs) is discussed in this paper. It is a geometrical piecewise-affine continuous-time model. The general idea of the GMD is to determine the local dynamic behavior of trajectories on the faces of the PEC commutation structure, which is a geometrical model of its commutation. This allows us to establish the direction of PEC dynamics on these faces. It can be either 'entering' into specific regions in state space or 'exiting' from them. Therefore, the local PEC dynamics can be treated as logical (two-state). In practice, the GMD can be used for the analysis of PEC practical stability, which is a completely different concept from the concept of PEC stability in the classical Lyapunov sense. An outline of the design-oriented approach to PEC practical stability analysis, which is based on the GMD, has also been presented. As illustrative examples, the GMD of a boost converter under peak current-mode control and its application are presented. These examples show that the Lyapunov stability of a given PEC does not imply its practical stability, and that the results of PEC Lyapunov stability analysis and practical stability analysis are complementary to each other.