Optimization of power coefficient equation for standalone wind energy systems

Abstract Accurate modeling of wind turbine performance is essential for improving energy yield, with the power coefficient ( $$\:{C}_{p}$$ ) playing a key role in aerodynamic energy conversion. However, many existing $$\:{C}_{p}$$ models exhibit limited predictive accuracy and insufficient experimental validation across different rotor configurations. This study develops and evaluates three hybrid— $$\:{C}_{p}$$ models; exponential, sinusoidal, and polynomial which are implemented in MATLAB and validated using wind tunnel data from the National Renewable Energy Laboratory (NREL) Phase VI Unsteady Aerodynamics Experiment (UAE) and the Offshore Code Comparison Collaboration, Continuation (OC6) Unsteady Aerodynamics of Floating Offshore Wind (UNAFLOW) databases for two- and three-bladed rotors, respectively. Model performance is assessed using $$\:{C}_{p}$$ –tip-speed-ratio characteristics and least-squares fitting. The exponential hybrid model achieves the lowest normalized root mean square error (nRMSE = 0.0869) and the closest agreement with experimental data, demonstrating its suitability for maximum power point tracking (MPPT) and performance optimization in standalone and small-scale wind energy systems.