A driving arrangement for rolling stands of a rolling mill, is described. The driving arrangement includes a control system which prescribes desired values for the rolling stands via control units, the rolling stands having at least one electric motor which is supplied with electric energy by a power supply system via at least one converter having turn-off power semiconductors. The converter has an air-cooled design. The cooling power is dimensioned such that the temperature of the turn-off power semiconductors does not exceed a critical temperature limit for continuous operation. The converter includes heat sinks which have an optimum design. At least some of the heat sinks are connected thermally in parallel.