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

Abstract

Summary In this paper, the equivalent small parameter method (ESPM) is used to establish the nonlinear mathematical model of the fractional‐order buck–boost converter in continuous current mode (CCM), and the analytical expression of approximate steady‐state period of converter state variable is obtained by using equivalent small parameter method and combining with harmonic balance principle. The Matlab/Simulink is used to construct the fractional‐order capacitance and inductance and to build the circuit model as well as the simulation model of fractional‐order buck–boost converter. Moreover, the simulation results of Oustaloup circuit model and numerical simulation model are compared with those of ESPM model to verify the validity and accuracy of the ESPM. The model is simulated by changing the orders of the capacitor and inductor to obtain the influence rule of the order of fractional element on harmonic characteristics of the state variables.

Analog Modeling of Fractional-Order Elements: A Classical Circuit Theory Approach

“…In recent publications [5], [12], [24] and [25], researchers designed FOC and FOI elements using physical RC or RL networks to perform measurements in laboratory setups. We have designed the same networks with the same specifications using the minimax approach and found that this results in more accurate networks with a lower number of components.…”

“…In [24] Fang and Wang designed a FO capacitor of order 0.95 (85.5), using Oustaloup's eighth-order network and obtained a maximum error =0.35 in the frequency range from 3Hz to 10kHz. With our minimax approximation, we obtained an eighth-order network with the same topology and the same bandwidth, but with a reduced error of =0.0044.…”

“…This property of capacitors directly affects modelling and measurement of supercapacitors, which can be fitted more precisely with an FO RC model than with a conventional RC model [22] [23]. Some authors have recently used FO mathematical models of capacitors and inductors in buck-boost and buck-converters, that allow a more accurate analysis of many properties, including the voltage gain of these converters [24] [25]. There are many other applications of FO models in the literature, including those in the digital domain [26].…”

Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method

“…The importance and the very wide range of applications of the fractional models (described by the fractional derivatives) directed mathematicians and physicians to study the numerical and approximate solutions for fractional differential equations (FDEs) using many approximate techniques. We have a lot of examples for the applications of such kind of equations in our life as in fluid mechanics, [1][2][3] image processing, 4 biology, [5][6][7][8][9][10][11][12] engineering, [13][14][15] physics, [16][17][18][19][20] electrical circuits and filters, [21][22][23][24][25][26][27][28][29][30][31][32] and others. [33][34][35][36] Definition 1.…”

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

“…In [23,24], based on the circuit averaging technique, the mathematical models of the fractional-order buck-boost converter in CCM and DCM were established. The fractional-order buck-boost converter was further modeled and studied by the equivalent small parameter method and the Riemann-Liouville definition [25,26]. The modeling and analysis of fractional-order DC-DC converters such as buck, boost, and buck-boost under DCM and CCM were summarized in [27].…”