Modeling and performance analysis of the fractional order quadratic Boost converter in discontinuous conduction mode-continuous conduction mode

Based on the fact that the inductors and the capacitors are fractional order in nature, the four-order mathematical model of the fractional order quadratic Boost converter in discontinuous conduction mode (DCM)-continuous conduction mode (CCM) is established by using fractional calculus theory. Direct current (DC) analysis is conducted by using the DC equivalent model and the transfer functions are derived from the corresponding alternating current (AC) equivalent model. The DCM-CCM region is obtained and the relations between the region and the orders are found. The influence of the orders on the performance of the quadratic Boost converter in DCM-CCM is verified by numerical and circuit simulation. Simulation results demonstrate the correctness of the fractional order model and the efficiency of the proposed theoretical analysis and indicate the fractional model has an important theoretical significance and practical applied value for design and performance analysis of the quadratic Boost converter.