Chaos and Multistability in Fractional Order Power System: Dynamic Analysis and Implications

This paper presents a comprehensive study about the dynamic behavior of a fractional ordered three-machine infinite bus (TMIB) power system model using Grunwald–Letnikov’s method. The study investigates nonlinear behaviors including chaos, coexisting behavior and multistability behaviors, using nonlinear tools such as phase portraits, bifurcation analysis, Lyapunov exponents and Lyapunov dimensions. The results demonstrate that the TMIB system exhibits chaos behavior, which is resulting instability in rotor angle through multiscroll chaotic attractors. Furthermore, it is found that the presence of coexisting attractors and multistability leads to undesired state switching and pose a potential threat to the stability of the TMIB power system. These findings provide valuable insights into the nonlinear behavior of TMIB power system via varying fractional order range and can be used to develop effective countermeasures to address potential stability issues arise in TMIB and similar modern power systems. The simulation is conducted in MATLAB, and the obtained results illustrate the efficacy of the work.