A wind-turbine converter system arranged to convert variable-frequency electrical power produced by a variable-speed wind turbine into fixed-frequency electrical power to be fed into an electricity grid, wherein operation of the wind turbine is controlled by a wind-turbine controller; the wind-turbine converter system comprising: a converter and a converter controller; the converter comprising a plurality of converter strings (24, 25) arranged to perform conversion operation, wherein at least a first converter string and a second converter string are provided; the converter strings (24, 25) comprise grid-side string inverters and generator-side string inverters, and the converter controller comprising a plurality of converter-string controllers associated with the converter strings (24, 25), wherein at least a first converter-string controller and a second converter-string controller are provided to control the conversion operation of the first and second converter strings (24, 25), respectively; characterized in that the generator-side string inverters of the plurality of converter strings are electrically connected in series, the grid-side string inverters of the plurality of converter strings are electrically connected in series; the first and second converter-string controllers being arranged to operate in a master-slave relation relative to each other, the first converter-string controller being arranged to operate as a master-converter controller, and the second converter-string controller being arranged to operate as a slave-converter controller; wherein the master-converter controller is arranged to receive superordinate control commands from the wind-turbine controller, to provide the slave-converter controller with string-control commands on the basis of the superordinate control commands, and to control the conversion operation of the first converter string on the basis of the superordinate control commands; and wherein the slave-converter controller is arranged to receive the string-control commands from the master-converter controller and to control the conversion operation of the second converter string on the basis of the string-control commands received. a converter and a converter controller; the converter comprising a plurality of converter strings (24, 25) arranged to perform conversion operation, wherein at least a first converter string and a second converter string are provided; the converter strings (24, 25) comprise grid-side string inverters and generator-side string inverters, and the converter controller comprising a plurality of converter-string controllers associated with the converter strings (24, 25), wherein at least a first converter-string controller and a second converter-string controller are provided to control the conversion operation of the first and second converter strings (24, 25), respectively; characterized in that the generator-side string inverters of the plurality of converter strings are electrically connected in series, the grid-side string inverters of the plurality of converter strings are electrically connected in series; the first and second converter-string controllers being arranged to operate in a master-slave relation relative to each other, the first converter-string controller being arranged to operate as a master-converter controller, and the second converter-string controller being arranged to operate as a slave-converter controller; wherein the master-converter controller is arranged to receive superordinate control commands from the wind-turbine controller, to provide the slave-converter controller with string-control commands on the basis of the superordinate control commands, and to control the conversion operation of the first converter string on the basis of the superordinate control commands; and wherein the slave-converter controller is arranged to receive the string-control commands from the master-converter controller and to control the conversion operation of the second converter string on the basis of the string-control commands received.