A method for controlling the operation of a wind turbine, wherein the wind turbine comprises (i) a mechanical drive train (222, 228), (ii) an electric generator being mechanically connected to the drive train (111, 228), and (iii) a power converter being electrically connected to the generator, wherein the wind turbine forms a part of a wind park which is connected to an AC power transmission system which is connectable to a utility grid (i) via a HVDC power transmission system and (ii) via an AC auxiliary power transmission system, the method comprising operating the wind turbine when the wind park is in a first operational mode in which the wind park and the AC power transmission system are connected to the utility grid solely via the AC auxiliary power transmission system and power is fed from the utility grid to the wind turbine via the AC auxiliary power transmission system, operating the wind turbine when the wind park is in a second operational mode in which the wind park and the AC power transmission system are connected to the utility grid solely via the HVDC power transmission system without requiring or reverting to a coordination by means of a superordinate wind power park controller, receiving, by means of a power controller, an active power reference signal (P*conv, PrefWT) being indicative for the active power which is supposed to be generated by the wind turbine and an active power feedback signal (Pfb) being indicative for the active power which is actually generated by the wind turbine; determining, by means of the power controller and based on the active power reference signal (P*conv, PrefWT) and the active power feedback signal (Pfb), a first voltage control signal (Vd) and a power controller frequency signal; receiving, by means of a HVDC power controller, the power controller frequency signal; determining, by means of the HVDC power controller and based on the power controller frequency signal, a second voltage control signal (Vq); receiving, by means of a frequency controller, a frequency reference signal ( ref); determining, by means of the frequency controller and based on the frequency reference signal ( ref), a frequency controller frequency signal; determining, by means of an integrator unit and based on the power controller frequency signal and the frequency controller frequency signal, an actual angle signal (θ0) being indicative for an actual angle between a rotating dq reference frame and a stationary abc reference frame; and controlling the operation of a network bridge of the power converter based on the first voltage control signal (Vd), the second voltage control signal (Vq), and the actual angle signal (θ0). operating the wind turbine when the wind park is in a first operational mode in which the wind park and the AC power transmission system are connected to the utility grid solely via the AC auxiliary power transmission system and power is fed from the utility grid to the wind turbine via the AC auxiliary power transmission system, operating the wind turbine when the wind park is in a second operational mode in which the wind park and the AC power transmission system are connected to the utility grid solely via the HVDC power transmission system without requiring or reverting to a coordination by means of a superordinate wind power park controller, receiving, by means of a power controller, an active power reference signal (P*conv, PrefWT) being indicative for the active power which is supposed to be generated by the wind turbine and an active power feedback signal (Pfb) being indicative for the active power which is actually generated by the wind turbine; determining, by means of the power controller and based on the active power reference signal (P*conv, PrefWT) and the active power feedback signal (Pfb), a first voltage control signal (Vd) and a power controller frequency signal; receiving, by means of a HVDC power controller, the power controller frequency signal; determining, by means of the HVDC power controller and based on the power controller frequency signal, a second voltage control signal (Vq); receiving, by means of a frequency controller, a frequency reference signal ( ref); determining, by means of the frequency controller and based on the frequency reference signal ( ref), a frequency controller frequency signal; determining, by means of an integrator unit and based on the power controller frequency signal and