Bifurcation phenomena studies of a voltage controlled Buck-inverter cascade system

Abstract

This paper studies the complex bifurcation phenomena of a voltage-controlled Buck-inverter cascade system. A state-flowchart is drawn to illustrate the complex relations among the linear operating modes. Combined with the state transition function of each mode, the time response of the system can be obtained.For period-one steady state, the periodic mapping function and its fixed point are further derived, on the basis of which the Jacobi matrix is developed and its maximum eigenvalue is analyzed to understand the bifurcation diagram. By globally analyzing the state space using this cell mapping method, the coexistence of attractors is revealed in the Buck-inverter system. All theoretical results have been verified experimentally on a prototype system. The results obtained can be used for guiding the design and analysis of the Buck-inverter system. The analyzing method can be helpful for studying other power electronics systems with compound topologies.