Analysis of Bifurcation Characteristics of Fractional‐Order Direct Drive Permanent Magnet Synchronous Generator

Abstract

In this study, we establish a fractional‐order direct drive permanent magnet synchronous wind turbines (DPMSG) model defined by Caputo based on the fractional calculus theory to overcome the singularity and limitations of integer‐order DPMSG models. The path and characteristics of the DPMSG system entering the bifurcation and chaos caused by the internal parameter changes and external disturbances were analyzed. First, we established a nonlinear fractional‐order mathematical model of a DPMSG system. Second, a bifurcation diagram was drawn using the maximum algorithm, and the path to chaos of the system at different orders was analyzed by combining its chaotic phase portrait and temporal sequence diagram. Subsequently, the impact of variations in the system order on the chaotic features of the original system was analyzed. The internal parameter adjustments of the system and changes in the system stability under external disturbances and other external excitations were analyzed. The influence of the system on its bifurcation phenomenon and chaotic behavior under multidimensional orders was determined, and it was observed that its path into chaos was opened by period‐doubling bifurcation. Lastly, the dual‐parameter stability domain of the system order corresponding to the internal parameters of the system was obtained by determining the parameter conditions for the critical stability of the system.