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

Area of Science:

• Electrical Engineering
• Power Electronics
• Non-linear Dynamics

Background:

• Fractional-order modeling offers higher accuracy for DC-DC converters compared to integer-order models.
• Computational complexity limits the application of fractional-order modeling in pulse width modulation (PWM) converters.

Purpose of the Study:

• To propose a modified fractional-order modeling methodology for DC-DC converters that overcomes computational limitations.
• To verify the effectiveness of the proposed methodology on fractional-order positive Luo converters.

Main Methods:

• Analyzes harmonic components of PWM converters using non-linear vector differential equations of periodically time-variant systems, avoiding direct fractional-order calculus.
• Obtains steady-state solutions using the equivalent small parameter (ESP) method and harmonic balance theory.
• Determines the transient solution using the explicit Grünwald-Letnikov (GL) approximation.

Main Results:

• The proposed model accurately presents time-domain information, revealing non-linear behaviors of DC-DC converters.
• Discusses the influence of fractional orders on converter performance and dynamic behaviors.
• Simulation and experimental results validate the effectiveness of the model using fractional-order components.

Conclusions:

• The modified fractional-order modeling methodology provides a computationally efficient and accurate approach for analyzing DC-DC converters.
• The method enhances the understanding and design of fractional-order DC-DC converters, particularly those employing PWM.