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.
Highlights
In nature, many materials, phenomena, and complex processes exhibit fractional characteristics.It has been proved that fractional calculus is more accurate than integer calculus in the modeling of dynamic processes [1]
The Caputo fractional definition is more widely used in the engineering field because the derivative of the initial value involved in the Laplace transform expression under the definition is integer order, which has a clear physical meaning
Assuming that a disturbance occurs near the operating point, the average values of the inductor current im, the capacitor voltage uc, the duty ratio d, and the input voltage uin are expressed as the sum of the direct current (DC) component and the alternating current (AC) component
Summary
Many materials, phenomena, and complex processes exhibit fractional characteristics. In [17,18,19], mathematical models and state-space average models of the fractional-order boost converter with a fractional-order inductor and capacitor in continuous conduction mode (CCM), discontinuous conduction mode (DCM) and pseudo continuous conduction mode (PCCM) were established to study the characteristics of the converter. Few researches focus on the fractional-order modeling and analysis of power electronic converters with mutual inductance This would be more difficult because it would involve complex electromagnetic processes and the fractional-order model of mutual inductance. The main innovations of this research are as follows: (1) The equivalent circuit model of the fractional-order mutual inductance for power electronic converters is derived.
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