Relations Between Wind Turbine Rotational Speed and Power Under Different Wind Speeds

Wind turbines exhibit a typical nonlinear relationship between rotational speed/power output and wind speed, commonly characterized through power curves and rotational speed curves.

Startup Phase (Below Cut-in Wind Speed) When wind speed falls below the turbine's cut-in speed (typically 3-4 m/s), aerodynamic torque is insufficient to overcome mechanical resistance. The turbine remains stationary with zero power output. In code implementations, this can be modeled using conditional statements that check wind speed thresholds before activating turbine operation.

Variable Speed Operation Phase (Below Rated Wind Speed) As wind speed increases, the turbine begins rotating. Rotational speed is dynamically adjusted through variable speed control strategies (such as Maximum Power Point Tracking - MPPT) to maintain optimal tip-speed ratio. Power output approximately follows a cubic relationship with wind speed (P∝v³), while rotational speed increases linearly to sustain optimal aerodynamic efficiency. Algorithm implementations typically use PID controllers or lookup tables to dynamically adjust generator torque based on real-time wind measurements.

Rated Power Phase (Above Rated Wind Speed) When wind speed exceeds the rated value (typically 12-15 m/s), the pitch control system limits captured wind energy to maintain power output at the rated level. Rotational speed remains constant or experiences minor fluctuations through regulation systems to prevent mechanical overload. Control algorithms implement blade pitch adjustment routines that continuously monitor power output and adjust blade angles accordingly.

Cut-out Phase (Above Cut-out Wind Speed) Under extreme wind conditions (approximately 25 m/s), the turbine initiates shutdown procedures for protection, reducing both rotational speed and power output to zero. Safety systems can be programmed with emergency shutdown protocols that trigger when wind sensors detect dangerous conditions.

Key Influencing Factors: Rotor diameter and pitch angle adjustment capabilities determine the steepness of the characteristic curves; Control system algorithms (such as PID regulation) impact the dynamic response of rotational speed; Turbulence intensity may cause instantaneous fluctuations, though the curves primarily reflect steady-state characteristics. Simulation models often incorporate these factors using mathematical equations that account for turbine geometry and control system parameters.