An analytical approach for obtaining the transient solution of the fractional-order buck converter in CCM

Abstract

This paper proposes a transient modeling and analysis method for the fractional-order DC-DC converters in continuous conduction mode (CCM), in which a fractional-order Buck converter is taken as an example. By extending the usage of equivalent small parameter method (ESP), the converter is modeled by a general state vector differential equation. Then by adopting the principle of harmonic balance, fractional differential of state variables is converted into linear operations of exponential functions, and different harmonic are separated. Thus the main transient oscillation components of state variables can be obtained according to Grunwald-Letnikov's definition of fractional derivation, and the data are processed approximately by polynomial fitting of triangular functions. The results are introduced back to the model to obtain the values of the rest harmonic magnitudes. So the final solution of state variables is in the form of the summation of harmonic contents. To confirm the correctness of the results of the proposed method, waveforms of the analytical solution are put together with those from circuit simulation in PSIM. These results demonstrate the high effectiveness of the proposed method.