Modeling and Analysis of the Fractional-Order Flyback Converter in Continuous Conduction Mode by Caputo Fractional Calculus

Abstract

In order to obtain more realistic characteristics of the converter, a fractional-order inductor and capacitor are used in the modeling of power electronic converters. However, few researches focus on power electronic converters with a fractional-order mutual inductance. This paper introduces a fractional-order flyback converter with a fractional-order mutual inductance and a fractional-order capacitor. The equivalent circuit model of the fractional-order mutual inductance is derived. Then, the state-space average model of the fractional-order flyback converter in continuous conduction mode (CCM) are established. Moreover, direct current (DC) analysis and alternating current (AC) analysis are performed under the Caputo fractional definition. Theoretical analysis shows that the orders have an important influence on the ripple, the CCM operating condition and transfer functions. Finally, the results of circuit simulation and numerical calculation are compared to verify the correctness of the theoretical analysis and the validity of the model. The simulation results show that the fractional-order flyback converter exhibits smaller overshoot, shorter setting time and higher design freedom compared with the integer-order flyback converter.

High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point

“…In order to obtain dimensionless dynamics for Equation (13), let 𝑖 = 𝑥, 𝑣 = 𝑦, 1/L = d, and 1/C = g; therefore, the fractional-order memristive chaotic system can be described by the following Equation (14). The following Equation ( 12) is obtained by applying Kirchhoff's current law for the fractional-order memristive chaotic circuit in Figure 7 and using the internal state of the fractional-order memristor described by Equation (8).…”

“…In the numerical simulation, the proposed system (14) exhibits chaos when its parameters are chosen as d = 4, g = 0.5, α = 1, β = 1, a = 0.25, b = 5, and k = 4 with initial conditions (x 0 , y 0 , z 0 ) = (0.8, 0.8, 0) and different fractional orders (q = 0.95 and q = 0.98). The chaotic behavior of the fractional-order memristive chaotic system (14) corresponding to these parameters, initial conditions, and fractional orders is displayed in Figure 8 by a form of phase portrait chaotic attractors in two-dimensional (2D) and 3D arrangements. The Therefore, with the selected parameters d = 4, g = 0.5, α = 1, β = 1, a = 0.25, b = 5, and k = 4, the eigenvalues have been obtained as (λ1 = −5, λ2,3 = 0.25 ± 1.3919i).…”

“…Many systems in transdisciplinary disciplines can be described using fractional calculus. Additionally, the fractional-order model can provide an explicit description of the physical process as well as supplementary information [14]. Control, oscillators, bioengineering, circuit theory, analog filters, chemistry, and image processing encryption systems are all examples of where fractional calculus can be applied [15].…”

Complexity Analysis of Three-Dimensional Fractional-Order Chaotic System Based on Entropy Theory

“…In recent years, fractional-order differential operators are introduced into nonlinear dynamical system, and the study of chaos in fractional-order nonlinear dynamical systems becomes a hot topic. At present, there are many definitions of the fractional derivatives, including Grünwald-Letnikov (G-L) definition [38,39], Riemann-Liouville (R-L) definition [40,41] and Caputo definition [42,43].…”

Three-Output Flyback Converter with Synchronous Rectification for Improving Cross-Regulation and Efficiency

“…A flyback converter [1][2][3][4] is a common choice for low to medium power supply design. The advantage of a flyback converter includes galvanic isolation, wide output voltage range, its simple structure, less peripheral devices and its cost effectiveness, etc.…”