Bifurcation and Chaotic Characterization of Incommensurate Fractional-Order Model for AC/DC Parallel Transmission System

Abstract

This paper presents a novel investigation into the nonlinear dynamics of an AC/DC parallel transmission system through the development of an incommensurate fractional-order model. This model, incorporating Caputo’s fractional-order calculus, is specifically designed to analyze the fractional-order characteristics of the system. Numerical simulations are conducted under varying system parameters and model orders, producing bifurcation diagrams, spectra, phase diagrams, and dynamic parameter spaces using the 0-1 test. The findings reveal that changes in the fractional order significantly influence the size of chaotic attractors and the stability intervals of the system. Notably, a higher control gain in the excitation link triggers interior crises and expands chaotic attractors, while variations in the rectifier trigger lag angle result in merging, boundary, and interior crises. This research offers a new theoretical foundation for understanding and controlling bifurcation and chaos in AC/DC parallel transmission systems, thereby contributing to enhanced system stability and the design of control strategies.

Keywords

• AC/DC transmission system
• bifurcation
• chaos
• fractional-order
• mathematical modeling