Methods of operating a wind turbine, wind turbines and wind parks

A method of operating a variable speed wind turbine as a function of a wind speed, the wind turbine having

• a rotor with a plurality of blades, a generator having a rated output power, and one or more pitch mechanisms for rotating the blades around their longitudinal axis, and a system for varying a torque of the generator,
• a sub-nominal zone of operation for wind speeds below a nominal wind speed and a supra-nominal zone of operation for wind speeds at or above the nominal wind speed,
• the method comprising:
• at wind speeds at or near the nominal wind speed, allowing the generator to generate an adapted output power that is more than the rated output power for a pre-defined period of time, the adapted output power having a maximum limit;
• and
• wherein the adapted output power limit is variable and determined as a function of temperature of a component of the wind turbine and the pre-defined period of time is set by a time constant before generation of the adapted output power such that the adapted output power decays exponentially substantially zero over an entirety of the pre-defined period of time regardless of temperature change of the component of the wind turbine during the pre-defined period of time.