A converter system for converting a three-phase or a single-phase AC voltage into a DC voltage, wherein the converter system comprises three converter branches, each converter branch comprising a first input and a second input configured to be supplied with a single-phase AC voltage and a first output and a second output providing a DC voltage; wherein each converter branch comprises an AC-to-DC stage and a DC-to-DC stage, which are connected between the first and second input (16a, 16b) and the first and second output (18a, 18b); wherein each AC-to-DC stage comprises a passive rectifier and a power factor corrector, wherein the passive rectifier, power factor corrector and DC-to-DC converter stage are cascade-connected in this order; wherein the power factor corrector comprises a boost converter, which comprises at least two interleaved corrector branches each of which comprises an inductivity and a diode connected in series between an input and an output of the power factor corrector and a semiconductor switch connected between the inductivity and the diode on one side and to another input and output of the power factor corrector on another side; wherein the converter system is configured for either interconnecting the first input of each converter branch with a phase of a three-phase grid or for interconnecting the first inputs of the converter branches with a phase of a single-phase grid; and wherein the converter system is configured for interconnecting the second inputs, which are interconnected with each other, of the converter branches with a neutral point of the three-phase grid or the single-phase grid; wherein the converter system comprises one or more controllers (50, 60, 62) adapted for controlling the converter branches independently from each other, wherein only measurement values collected in a converter branch are used for controlling this converter branch; and wherein further, when the converter branches are controlled based on power sharing among the converter branches, the converter system is configured to operate independent from being supplied by the single-phase grid or the three-phase grid. wherein the converter system comprises three converter branches, each converter branch comprising a first input and a second input configured to be supplied with a single-phase AC voltage and a first output and a second output providing a DC voltage; wherein each converter branch comprises an AC-to-DC stage and a DC-to-DC stage, which are connected between the first and second input (16a, 16b) and the first and second output (18a, 18b); wherein each AC-to-DC stage comprises a passive rectifier and a power factor corrector, wherein the passive rectifier, power factor corrector and DC-to-DC converter stage are cascade-connected in this order; wherein the power factor corrector comprises a boost converter, which comprises at least two interleaved corrector branches each of which comprises an inductivity and a diode connected in series between an input and an output of the power factor corrector and a semiconductor switch connected between the inductivity and the diode on one side and to another input and output of the power factor corrector on another side; wherein the converter system is configured for either interconnecting the first input of each converter branch with a phase of a three-phase grid or for interconnecting the first inputs of the converter branches with a phase of a single-phase grid; and wherein the converter system is configured for interconnecting the second inputs, which are interconnected with each other, of the converter branches with a neutral point of the three-phase grid or the single-phase grid; wherein the converter system comprises one or more controllers (50, 60, 62) adapted for controlling the converter branches independently from each other, wherein only measurement values collected in a converter branch are used for controlling this converter branch; and wherein further, when the converter branches are controlled based on power sharing among the converter branches, the converter system is configured to operate independent from being supplied by the single-phase grid or the three-phase grid.