On the Dynamics of Fractional Models for Power Systems with Incommensurate Orders: Chaos, Multistability, and Control

Abstract

This paper presents the nonlinear chaotic dynamics of a power system model within an incommensurate fractional-order framework. Equilibrium points are derived and analyzed using Jacobian-based local stability theory adapted to fractional-order systems. Furthermore, bifurcation analysis is employed to examine how variations in system parameters and incommensurate fractional orders influence the emergence of period-doubling cascades and chaotic motion. The study investigates multistability phenomena characterized by the coexistence of multiple attractors under identical system parameters. The simulation is run in MATLAB R2020a, and nonlinear tools such as time series, bifurcation diagrams, Lyapunov exponents, and phase portraits in 2D and 3D projections are used to visualize the findings.