Analysis and Modeling of Fractional Order LC Series Resonant Boost Converter Based on Fractional Calculus and Laplace Transform

Abstract

Based on the fractional-order (FO) characteristics of inductors and capacitors, many basic PWM DC–DC converters are defined and modeled by FO calculus in previous studies, but the research of FO resonant dc converters is still in its early stage. Therefore, this paper adopts FO calculus and Laplace transform to model and analyze a ZCS boost converter with an LC resonant tank, which mainly focuses on the influence of the FO component on the soft switching characteristics, converter efficiency, and output voltage gain of this isolated dc converter. This paper extends the topology to the fractional order domain and conducts FO modeling. The order of the resonant inductor and capacitor will affect the amplitude/phase of the resonant current and then affect the converter ZCS characteristic. The analysis demonstrates that the reduction of FOI and FOC order is not conducive to the ZCS of switching devices and converter efficiency. Based on the voltage and current relationship of the FO LC resonant tank, a parameter design guideline is presented. Numerical tools are used to solve the FO output voltage gain and draw the gain curve. And the order of FOI and FOC provides new flexibility for the converter output gain and soft switching design. Finally, simulations and a 360 W hardware experimental prototype are conducted to verify the accuracy and effectiveness of theoretical analysis.