Method and system for optimizing power output of a wind turbine with yaw misalignment

A system comprising a wind turbine and a first control device, wherein

• the wind turbine comprises:
• a tower;
• a nacelle being mounted rotatable relative to the tower around a yaw axis so that the nacelle is orientated in an actual yaw angle;
• a hub being mounted rotatable relative to the nacelle around a rotational axis;
• at least one blade mounted to the hub;
• and
• a generator arranged in the nacelle and comprising an electromagnetic rotor connected to the hub, wherein the generator is configured to convert a rotational energy from the electromagnetic rotor into an electrical energy;
• and
• the first control device is configured to:
• acquire a yaw misalignment of the wind turbine, which yaw misalignment is a difference between the actual yaw angle and a wind direction at the wind turbine;
• and
• determine a target pitch angle of the blade by calculating the target pitch angle of the blade as a function of an incoming wind speed, a rotor speed of the hub and the yaw misalignment to optimize a power output from the wind turbine, or a target torque of the generator based on operating in the yaw misalignment to optimize a power output from the wind turbine, wherein the first control device is configured to determine the at least one of the target pitch angle of the blade and the target torque of the generator such that at a tip-speed ratio is set, at which a power coefficient of the wind turbine is an optimum power coefficient at the given yaw misalignment.