A Modeling and Analysis Method for CCM Fractional Order Buck-Boost Converter by Using R-L Fractional Definition

Fractional definition is important for the application of fractional-order theory in electrical engineering, and fractional-order theory directly affects the accuracy of the model and the operating characteristics of the power converter. Most 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. A novel modeling and analysis method for the fractional buck-boost converter is proposed in this paper. Firstly, the fractional converter model operating in continuous conduction mode (CCM) is established and the DC analysis is completed by using Riemann-Liouville (R-L) fractional definition. The R-L fractional definition is nearly 1.1% more accurate than the Caputo definition in the DC analysis. Secondly, the influence of the capacitor and inductor orders on the converter is performed. The results show that the capacitor and inductor orders have great effect on the DC components of the state variable and the steady-state characteristics of the fractional order buck-boost converter. Finally, simulation and experiment results are provided that the validity of theoretical analysis.