**Abstract**

Wind energy researchers have recently invited the scientific community to tackle three significant wind energy challenges to transform wind power into one of the more substantial, low-cost energy sources. The first challenge is to understand the physics behind wind energy resources better. The second challenge is to study and investigate the aerodynamics, structural, and dynamics of large-scale wind turbine machines. The third challenge is to enhance grid integration, network stability, and optimization. This chapter book attempts to tackle the second challenge by detailing the physics and mathematical modeling of wind turbine aerodynamic loads and the performance of horizontal and vertical axis wind turbines (HAWT & VAWT). This work underlines success in the development of the aerodynamic codes CARDAAV and Qbalde, with a focus on Blade Element Method (BEM) for studying the aerodynamic of wind turbines rotor blades, calculating the induced velocity fields, the aerodynamic normal and tangential forces, and the generated power as a function of a tip speed ration including dynamic stall and atmospheric turbulence. The codes have been successfully applied in HAWT and VAWT machines, and results show good agreement compared to experimental data. The strength of the BEM modeling lies in its simplicity and ability to include secondary effects and dynamic stall phenomena and require less computer time than vortex or CFD models. More work is now needed for the simulation of wind farms, the influence of the wake, the atmospheric wind flow, the structure and dynamics of large-scale machines, and the enhancement of energy capture, control, stability, optimization, and reliability.

**Keywords:** wind turbine, DMS, performance, loads, dynamic stall, induced velocity, power, normal and tangential forces
