A static converter with parallel architecture or series architecture comprises a plurality of switching cells, arranged in parallel or in series, and controlled in a decentralized manner by associated control modules, strung together according to a loop by a series of communication links.Each control module comprises a single and different local unit for generating the triangular carrier of the module which controls the positioning of its interleaving phase as a function only of the signals of the triangular carriers of the two adjacent modules.Each control module comprises a local unit for balancing the currents of branches and/or a unit for internal regulation of the output voltage of AVP type, or a local unit for balancing the cell voltages and/or a unit for internal regulation of the input current or output current of the ACP type.