## 4 Load Frequencies of a Wind Turbine  
Wind turbines are subject to various load frequencies during operation. These frequencies arise from different mechanical and aerodynamic processes within the turbine system. Some of the key frequencies include the following:  
* **Rotational frequency:** This is one of the most significant load frequencies and is directly related to the rotational speed of the turbine blades. These cyclic loads can cause fatigue in the turbine components over time. It occurs when each blade passes a fixed point, generating a load corresponding to the number of blades and the rotor speed. Rotational frequency is calculated based on \(f_{rot}=\frac{RPM}{60}\), where RPM is the revolutions per minute of the rotor. For a turbine with three blades, the passing frequency is three times the rotor speed. For example, if a turbine operates at a rotor speed of 15 RPM with 3 blades, the frequency can be calculated using \(f_{rot}=\frac{15\times 3}{60}=\) 0.75 Hz. This indicates that the frequency at which each blade passes a fixed point is 0.75 Hz [18];
* **Gear frequency:** The gear frequencies in a wind turbine are related to the rotational speeds of the gear system, which are influenced by the rotation speed of the turbine's components. In a wind turbine, the gear system transfers power from the low-speed shaft, connected to the rotor blades, to the high-speed shaft that drives the generator, typically through a gearbox. The key gearbox frequencies in a wind turbine include the low-speed shaft (rotor frequency) at 0.25 Hz, the high-speed shaft frequency at 25 Hz, the meshing frequency of the input gear at 7.5 Hz, and the meshing frequency of the output gear at 1000 Hz [19]. Notice that these numbers are approximate and not exact, as they depend on specific design parameters such as rotor speed, gear ratio, and the number of teeth on the gears, which can vary across different wind turbine models;
* **Yawing frequency:** The yawing frequency of a wind turbine refers to the rate at which the nacelle rotates to keep the rotor aligned with the wind direction. This frequency depends on several factors, including the turbine's design, the control system, and the wind conditions. Typically, the yawing frequency for wind turbines is low, generally in the range of 0.05 to 0.1 Hz [20]. However, the exact yaw frequency can vary based on the wind turbine's specifications, the wind conditions, and the operational strategy of the turbine;
* **Generator frequency:** The generator in a wind turbine operates at a frequency that matches the electrical grid, either 50 Hz or 60 Hz. When the turbine operates at low speeds or under varying load conditions, the mechanical loads generated by the generator can cause vibrations. This can put stress on parts like the generator, bearings, and shafts, potentially leading to damage or failure. Designers account for these risks by optimizing the turbine's mechanical system and using vibration-damping techniques to ensure stable operation [21];
* **Wind turbine blade natural frequency:** The natural frequencies of wind turbine blades typically range between 1 to 3 Hz, depending on factors such as the blade's design, material properties, and length. The blades are subject to aerodynamic forces, including wind gusts and changes in wind speed, which can cause vibrations at certain frequencies. A typical 1-3 MW wind turbine might experience blade frequencies around 1.5 to 2.5 Hz, but this can vary based on blade material, geometry, and overall design. Larger or offshore turbines, which often use longer blades, may have lower natural frequencies [22].  
The key load frequencies of wind turbine components during operation are listed in Table 1.