Analysis and Modeling of Fractional-Order Buck Converter Based on Riemann-Liouville Derivative

In previous studies, researchers used the fractional definition of Caputo to study fractional-order power converter. However, it is found that the model based on Caputo fractional definition is inconsistent with the actual situation. The fractional definition is crucial for the application of fractional-order theory into electric engineering, which directly influences the accuracy of model and operational characteristics of power converter. This paper analyzes fractional-order Buck converter according to the fractional definition of Riemann-Liouville. Firstly, the converter model operating in continuous conduction mode (CCM) is established under Riemann-Liouville fractional definition, and it shows that voltage gain and inductor current are relative with the order, but they are independent of order in the model of Caputo fractional definition. Secondly, the different steady-state characteristics of CCM Buck converter are researched under the models of Caputo and Riemann-Liouville derivative. Finally, the feasible simulations and experiments verify that the model derived by Riemann-Liouville fractional definition is more accurate and suitable for analyzing Buck converter.