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Abstract <p>To address the risk of chaotic oscillations in wind turbine systems subjected to external excitation arising from aerodynamic power fluctuations and electromechanical interactions under practical operating conditions, this paper incorporates fractional-order damping—commonly observed in large-scale torsional machinery—into the traditional two-mass model based on fractional calculus theory, enabling nonlinear modeling and systematic analysis of chaotic drivetrain dynamics. By applying a time-scale transformation, a structured model under small perturbations is derived to facilitate theoretical investigation. Equilibrium analysis confirms that the system satisfies the stiffness conditions required for the occurrence of Smale horseshoe chaos. Based on the homoclinic orbit of the unperturbed system, the Melnikov method is employed to derive chaos boundary conditions under different fractional damping parameters. The characteristics and evolutionary patterns of chaotic oscillations are further investigated using standard nonlinear dynamical analysis tools. Analytical and numerical results reveal that external excitation is the primary mechanism triggering chaotic oscillations: when the excitation frequency approaches the saddle-point characteristic frequency of approximately 0.7071&#xa0;rad/s, chaotic oscillations are readily induced in the system. Moreover, fractional-order damping plays a critical role in regulating the chaos threshold and oscillatory behavior; as the fractional order decreases from 1.0 to 0.2, the minimum excitation amplitude required to induce chaos is reduced by approximately 2.86 times, accompanied by a pronounced increase in oscillation intensity. The obtained results provide insight into the role of fractional-order damping in wind turbine power generators and offer a theoretical foundation for the development of fractional-order control strategies aimed at mitigating chaotic oscillations induced by the imbalance between aerodynamic power input and electrical load demand, thereby enhancing system stability, operational safety, and long-term reliability.</p> Graphical abstract <p></p>

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Nonlinear modeling and chaos analysis of wind turbine systems with fractional-order damping

  • 期刊论文

  • 发表日期：

    2026年4月8日

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  • Yuchen Zhang,
  • Yanling Lyu,
  • Samson S. Yu,
  • Mingze Zhang

摘要

Abstract

To address the risk of chaotic oscillations in wind turbine systems subjected to external excitation arising from aerodynamic power fluctuations and electromechanical interactions under practical operating conditions, this paper incorporates fractional-order damping—commonly observed in large-scale torsional machinery—into the traditional two-mass model based on fractional calculus theory, enabling nonlinear modeling and systematic analysis of chaotic drivetrain dynamics. By applying a time-scale transformation, a structured model under small perturbations is derived to facilitate theoretical investigation. Equilibrium analysis confirms that the system satisfies the stiffness conditions required for the occurrence of Smale horseshoe chaos. Based on the homoclinic orbit of the unperturbed system, the Melnikov method is employed to derive chaos boundary conditions under different fractional damping parameters. The characteristics and evolutionary patterns of chaotic oscillations are further investigated using standard nonlinear dynamical analysis tools. Analytical and numerical results reveal that external excitation is the primary mechanism triggering chaotic oscillations: when the excitation frequency approaches the saddle-point characteristic frequency of approximately 0.7071 rad/s, chaotic oscillations are readily induced in the system. Moreover, fractional-order damping plays a critical role in regulating the chaos threshold and oscillatory behavior; as the fractional order decreases from 1.0 to 0.2, the minimum excitation amplitude required to induce chaos is reduced by approximately 2.86 times, accompanied by a pronounced increase in oscillation intensity. The obtained results provide insight into the role of fractional-order damping in wind turbine power generators and offer a theoretical foundation for the development of fractional-order control strategies aimed at mitigating chaotic oscillations induced by the imbalance between aerodynamic power input and electrical load demand, thereby enhancing system stability, operational safety, and long-term reliability.

Graphical abstract