Due to the devastating impact of climate change, many developing countries are turning to cleaner energy sources like wind power. Wind turbines produce minimal greenhouse gas emissions during operation, highlighting the importance of developing robust wind turbine designs. To this end, this study aims to investigate the dynamic performance of wind turbines in the presence of various interval parameters. To accurately capture the system’s excitation, the mesh stiffness is modeled using the potential energy method and the theoretical Heaviside function, while the external excitation is modeled by considering all components of wind velocity. Three interval methods were employed to solve the differential equations with interval variables: Legendre interval method, Chebyshev collocation method, and Scanning method. The findings suggest that the Chebyshev collocation technique is more effective at reducing the wrapping effect; however, it struggles with high-dimensional systems when compared to the Legendre interval method. By selecting suitable collocation points for the Legendre approach, one can overcome its limitations. Nonetheless, in the case of highly complex systems, interval arithmetic may pose difficulties, which restricts the usability of this method. Therefore, employing a scanning technique can help establish the bounds.