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 connectable to a utility grid (i) via a HVDC power transmission system and (ii) via an AC auxiliary power transmission system, and wherein the wind park is in a third operational mode in which the wind park is connected to the utility grid both via the HVDC power transmission system and via the AC auxiliary power transmission system in which power is transferred from the utility grid to the wind park, the method comprising 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 on the active power feedback signal (Pfb), a first voltage control signal (Vd) and a power controller frequency signal; receiving, by means of an umbilical power controller a power reference signal (Pumb*) being indicative for a desired power flow through the AC auxiliary power transmission system and a power feedback signal (Pumbfb) being indicative for the actual power flowing via the AC auxiliary power transmission system; determining, by means of the umbilical power controller and based on the power reference signal (Pumb*) and on the power feedback signal (Pumbfb), a power offset frequency signal ( uPC) being indicative for an actual power offset within the AC auxiliary power transmission system; 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 an integrator unit, the power offset frequency signal ( uPC); determining, by means of the integrator unit and based on the power offset frequency signal ( uPC), 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). 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 on the active power feedback signal (Pfb), a first voltage control signal (Vd) and a power controller frequency signal; receiving, by means of an umbilical power controller a power reference signal (Pumb*) being indicative for a desired power flow through the AC auxiliary power transmission system and a power feedback signal (Pumbfb) being indicative for the actual power flowing via the AC auxiliary power transmission system; determining, by means of the umbilical power controller and based on the power reference signal (Pumb*) and on the power feedback signal (Pumbfb), a power offset frequency signal ( uPC) being indicative for an actual power offset within the AC auxiliary power transmission system; 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 an integrator unit, the power offset frequency signal ( uPC); determining, by means of the integrator unit and based on the power offset frequency signal ( uPC), 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).