Slow-Scale Instability Analysis of Voltage Controlled Z-Source Converter

The slow-scale instability of a voltage controlled Z-source DC-DC converter is analyzed. First, its state space average model is built. The computation of Jacobian matrix eigenvalues reveals that Hopf bifurcation will emerge as certain circuit or control parameter varies. The simulation results in PLECS show that the bifurcation points derived by the state space model roughly correspond to those derived by the simulation. The simulation also reveals that this circuit operates in a pattern where continuous conduction mode (CCM) and discontinuous conduction mode (DCM) occur alternately when the Hopf bifurcation takes place. To fill in the gap between theoretical analysis and simulation results, the discrete iterative mapping of voltage controlled Z-source DC-DC converter is presented. Compared with the state space average model, the discrete iterative mapping can portray the slow-scale stability boundary with better precision. In addition, with consideration of the switching between CCM and DCM, a non-smooth discrete iterative mapping of the system is derived.