Fast-scale bifurcation in power-factor-correction buck-boost converters and effects of incompatible periodicities

In this paper, we derive the discrete-time model for the power-factor-correction (PFC) buck-boost converter in terms of a stroboscopic switching map. Fast-scale instability is analysed through a fold diagram, which exposes the periodicity of the operation as well as the locations of the critical phase angles of the line voltage at which instability begins to occur along a half-line cycle. The asymmetrical locations of the critical phase angles along a half-line cycle is explained in terms of 'under-developed' bifurcation. Border collision bifurcations are observed and analysed in detail.