In recent years, fractional calculus has been used as a novel modeling tool by many converters. This paper studies the modeling of a pseudo-continuous conduction Buck-Boost converter based on the R-L fractional definition and the state-space averaging method. The expressions of DC static operating point, small signal transfer function and inductor current ripple are derived. It is found that compared with the Caputo fractional-order, the DC static operating point of the R-L fractional-order is not only related to the duty cycle, but also affected by the inductance and capacitance order and load. Finally, a fractional order model of PCCM Buck-Boost converter is built to verify the accuracy of the model. The results show that the fractional-order model can describe the operating characteristics of the Buck-Boost converter more accurately.
Zhang et al. (2026) studied this question.