Numerical study and chaotic oscillations for aerodynamic model of wind turbine via fractal and fractional differential operators

Abstract

AbstractThe aeroelastic analysis has become important for aerodynamical model of wind turbine in predicting the wind turbine; such phenomenon is based on aerodynamic performance to have accuracy and feasibility through modeling of fractal and fractional differential techniques. In this context, the mathematical modeling is developed based on fractal and fractional differential techniques for three‐dimensional nonautonomous model of a permanent magnet synchronous generator. The fractal and fractional differential techniques so called Caputo, Caputo–Fabrizio and Atangana–Baleanu differential operators have been invoked for the controllability of the stability of system. Numerical schemes for the mathematical model of wind turbine have been established via Adams–Bashforth–Moulton method. The comparative analysis of mathematical model of wind turbine is tackled by means of classical, fractal, fractional and fractal–fractional techniques through chaotic behavior. The role of chaotic oscillations has been depicted on the basis of parametric study of tip speed ratio, pitch angle, drag coefficients, power coefficient, air density and rotor angular speed.