A wind turbine having a rotor, a generator driven by the rotor, a converter, a control device having an input for a control signal for reactive power output and a controller for the converter, the controller determining a reactive power target value for the wind turbine and correcting the output reactive power in dependence on the voltage present at the wind turbine, and an additional module for the controller having separate small and large signal paths and interacting with the controller such that the small signal path has an additional storage element in comparison with the large signal path, which additional storage element stores state values of the small signal path for the past. Thus, small voltage changes can be reacted to more slowly and while taking into account past values, whereas large changes can be reacted to quickly, in particular in the event of a network short circuit.