Modeling and Analysis of the Fractional Order Buck Converter in DCM Operation by using Fractional Calculus and the Circuit-Averaging Technique

Abstract

By using fractional calculus and the circuit-averaging technique, the modeling and analysis of a Buck converter with fractional order inductor and fractional order capacitor in discontinuous conduction mode (DCM) operations is investigated in this study. The equivalent averaged circuit model of the fractional order Buck converter in DCM operations is established. DC analysis is conducted by using the derived DC equivalent circuit model. The transfer functions from the input voltage to the output voltage, the duty cycle to the output voltage, the input impedance, and the output impedance of the fractional order Buck converter in DCM operations are derived from the corresponding AC-equivalent circuit model. Results show that the DC equilibrium point, voltage ratio, and all derived transfer functions of the fractional order Buck converter in DCM operations are affected by the inductor order and/or capacitor order. The fractional order inductor and fractional order capacitor are designed, and PSIM simulations are performed to confirm the correctness of the derivations and theoretical analysis.

Modeling and Characteristics Analysis for a Buck-Boost Converter in Pseudo-Continuous Conduction Mode Based on Fractional Calculus

“…As shown in (8), (9), and (10), the inductor order and the capacitor order can be considered as extra parameters of the fractional-order mathematical models in PCCM. The influence of these extra parameters on the performance of the converter will be discussed in the next section.…”

“…In recent years, fractional calculus has been accepted as a new instrument that can extend the descriptive power of the traditional calculus. It has turned out that many phenomena in widespread fields of science and engineering can be described very successfully by fractional-order models [3][4][5][6][7][8][9]. Comparing with integer-order models, the significant advantage of fractional-order models is that they are characterized by hereditary and memory properties.…”

The fractional-order state-space averaging modeling of the Buck–Boost DC/DC converter in discontinuous conduction mode and the performance analysis

“…It can be proved that the order of the model has influence on the performance of the DC/DC converter and can be considered as an extra parameter. So fractional-order models can increase the flexibility and degrees of freedom by means of fractional parameters [23][24][25][26][27][28][29].…”

Modeling and analysis method of fractional‐order buck–boost converter

“…11 The analytical modeling rule is derived by reasonably modeling the system and expanding the variables into analysis expressions. The existing analytical modeling methods include state-space averaging method 12 and equivalent small parameter method (ESPM). 13,14 Compared with the numerical method, the analytical method has a slightly lower precision, but its physical meaning is intuitive and clear, which helps to understand the working mechanism of the circuit and provides a reference for optimizing the circuit parameters.…”