Analytical Derivation and Performance Evaluation of Wind Turbine Power at Rated Wind Speed

Abstract

Accurate modeling of wind turbine power output is essential for design, performance assessment, and economic evaluation in renewable energy systems. The extractable power depends primarily on-air density, rotor swept area, wind velocity, and aerodynamic efficiency. Among these, wind speed exerts the most significant influence due to its cubic relationship with power. Although the wind power equation is commonly applied, its derivation from basic mechanical principles is often condensed, limiting practical understanding (Manwell et al., 2009; Burton et al., 2011). This study presents a systematic derivation of the wind turbine power equation using classical mechanics and steady-flow analysis. Starting from the kinetic energy expression of moving air masses, the governing power equation is derived and modified to include the aerodynamic power coefficient. The theoretical upper limit established by Albert Betz is considered in relation to practical turbine operation (Betz, 1919). The model is applied to calculate rotational kinetic power at rated wind speed, and a parametric analysis confirms the cubic dependence of power on wind velocity. The results strengthen theoretical understanding in wind energy modeling and provide a clear framework for turbine performance assessment, energy forecasting, and system evaluation. Implications for wind farm planning, marine turbine adaptation, and energy yield optimization are discussed.

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