In this paper, based on the fact that the inductors and capacitors are of fractional order in nature, the four-order mathematical model of the fractional order quadratic Boost converter in type I and type II discontinuous conduction mode (DCM) — DCM 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–DCM regions of type I and type II are obtained and the relations between the regions and the orders are found. The influence of the orders on the performance of the quadratic Boost converter in DCM–DCM is verified by numerical and circuit simulations. Simulation results demonstrate the correctness of the fractional order model and the efficiency of the proposed theoretical analysis.
Design and Performance Analysis of a Photovoltaic Water Pumping System based on DC-DC Boost Converter and BLDC Motor