Modeling, analysis and experimental verification of fractional high-order DC-DC converters

Abstract The concepts and techniques of fractional calculus (FC) have been increasingly used in the modeling and design of electrical components and circuits. Current research on fractional-order (FO) modeling focuses mainly on low-order converters. Since the FO characteristics of real inductors and capacitors can significantly affect the dynamic performance of high-order converters, this paper proposes an accurate modeling and analysis method for continuous conduction mode (CCM) FO-Zeta converters based on FC. The modeling uses the Caputo definition of FO operators and the state space method. The Oustaloup’s approximation and a new equivalent circuit are employed for implementing the FO components. A theoretical mathematical model and an average model are derived, and the steady-state and dynamic characteristics of the FO-Zeta converter are analyzed. CCM operating guidelines for the converter are discussed, and appropriate parameters are provided to ensure that the fractional high-order converter operates under CCM. Simulations on Matlab/Simulink and PLECS compare and verify the mathematical, average, and circuit models. It is also shown that the order effects the boundary between CCM and discontinuous conduction mode (DCM) operation. An experimental platform is set-up to validate the high efficiency of the proposed FO-Zeta converter.