A variable speed wind turbine for connection to an electrical grid, arranged to provide additional electrical power to counteract non-periodic disturbances in the electrical grid, comprising: - a rotor with blades coupled to an electrical generator, - a controller arranged as a microprocessor with associated memory which is arranged to execute control software, - the controller being arranged to monitor events indicating a need to increase the electrical output power (P e) from the wind turbine to the electrical grid to support the stability of the electrical grid, - the controller being arranged to control the wind turbine to perform grid-stability supporting activity, in a non-periodic manner, as follows: - the controller is arranged to, when the wind turbine operates in a partial-load mode, i.e. at a power below the wind turbine's rated power, at a working point with maximum aerodynamic efficiency and after an indicating event has been detected, control the wind turbine to enter an overproduction period in which the electrical output power (P e) is increased beyond the electrical operating power (P e0) at maximum aerodynamic efficiency, wherein the additional electrical output power is taken from kinetic energy stored in the rotor and without changing the operation of the wind turbine to a more efficient working point, - the controller is arranged to, at the latest, when the rotational speed of the rotor reaches a predetermined minimum value (ω min), control the wind turbine to enter a recovery period to re-accelerate the rotor to the rotational speed (ω 0) at the working point with maximum aerodynamic efficiency while further contributing to the stability of the electrical grid by outputting at least a predetermined minimum electrical power (P emin) to the electrical grid. - a rotor with blades coupled to an electrical generator, - a controller arranged as a microprocessor with associated memory which is arranged to execute control software, - the controller being arranged to monitor events indicating a need to increase the electrical output power (P e) from the wind turbine to the electrical grid to support the stability of the electrical grid, - the controller being arranged to control the wind turbine to perform grid-stability supporting activity, in a non-periodic manner, as follows: - the controller is arranged to, when the wind turbine operates in a partial-load mode, i.e. at a power below the wind turbine's rated power, at a working point with maximum aerodynamic efficiency and after an indicating event has been detected, control the wind turbine to enter an overproduction period in which the electrical output power (P e) is increased beyond the electrical operating power (P e0) at maximum aerodynamic efficiency, wherein the additional electrical output power is taken from kinetic energy stored in the rotor and without changing the operation of the wind turbine to a more efficient working point, - the controller is arranged to, at the latest, when the rotational speed of the rotor reaches a predetermined minimum value (ω min), control the wind turbine to enter a recovery period to re-accelerate the rotor to the rotational speed (ω 0) at the working point with maximum aerodynamic efficiency while further contributing to the stability of the electrical grid by outputting at least a predetermined minimum electrical power (P emin) to the electrical grid.