A modified modeling and dynamical behavior analysis method for fractional-order positive Luo converter

Compared to the integer-order modeling, the fractional-order modeling can achieve higher accuracy for designing and analyzing the DC-DC power converters. However, its applications in pulse width modulation (PWM) converters are limited due to the computational complexities. In this paper, a modified fractional-order modeling methodology for DC-DC converters is proposed, and its effectiveness is verified on the fractional-order positive Luo converters. Instead of using fractional-order calculus, the proposed methodology analyzes the harmonic components of the PWM converters by utilizing the non-linear vector differential equations of the periodically time-variant system. The final solution of the state variables is composed of two parts: the steady-state solution and the transient solution. The approximate steady state solution can be obtained by using the equivalent small parameter (ESP) method and the harmonic balance theory, while the main part of the transient solution can be obtained according to the explicit Grünwald-Letnikov (GL) approximation. In addition, the influence of the fractional orders on the performance of the DC-DC converters, and on the dynamic behaviors of the fractional-orders systems are also discussed in this paper. Compared to the conventional fractional-order numerical models, the proposed model is able to present the time-domain information more precisely, which helps to better reveal and analyze the non-linear behaviors of the DC-DC converters. The effectiveness of the work is demonstrated by the simulation and experimental results of the equivalent circuits built with fractional-order components.