Slow‐Scale Instability in the Two‐Phase Interleaved Fractional‐Order Boost DC–DC Converter: Analysis and Confirmation

ABSTRACT A steady‐state analytic approach based on the equivalent small parameter method (ESPM) is proposed for fractional‐order systems in which the state variables have non‐consistent periods. This approach is systematically employed to formulate a mathematical model for a two‐phase interleaved parallel fractional‐order boost DC–DC converter, considering parasitic effects. Through rigorous theoretical analysis, the underlying mechanism governing slow‐scale instabilities in such systems is fundamentally elucidated. The effectiveness of the proposed method and theoretical analysis is verified by means of simulations and experiments, showing that the theoretical prediction is basically consistent with the observed results.