This paper aims to present a simplified method to analyze the transient characteristics of a fractional-order very high frequency (VHF) resonant boost converter. The transient analytical solutions of state variables obtained by this method could be used as a guide for parameter design and circuit optimization.
The VHF converter is decoupled into a simplified equivalent circuit model and described by the differential equation. The solution of the simplified equivalent circuit model is taken as the main oscillation component of the transient state variable. And the equivalent small parameter method (ESPM) and Kalman filter technology are used to solve the differential equation of the converter to obtain the steady-state ripple component. Then, by superimposing the abovementioned two parts, the approximate transient analytical solution can be acquired. Finally, the influence of the fractional order of the energy storage elements on the transient process of the converter is discussed.
The results from the proposed method agree well with those from simulations, which indicates that the proposed method can effectively analyze the transient characteristic of the fractional-order VHF converter, and the analytical solution derived from the proposed mathematical model shows sufficient accuracy.
This paper proposes for the first time a method to analyze the transient characteristics of a fractional-order VHF resonant boost converter. By combining the main oscillated solution derived from the simplified equivalent circuit model with the steady-state solution based on ESPM, this method can greatly reduce the computation amount to estimate the transient solution. In addition, the discussion on the order of fractional calculus of energy storage components can provide an auxiliary guidance for the selection of circuit parameters and the study of stability.
