A stator winding of a directly cooled turbogenerator comprises directly gas cooled double Roebel bars is arranged as active parts in slots of a stator body. Each double Roebel bar has two single Roebel bars, which includes each a stack of a plurality of transposed individual strands, and are separated by an intermediate stack of cooling tubes. Mounting space is saved by constructing, for the compensation of stray field voltages, at least one double Roebel bar as a cross-over bar with the strands being transposed over the stack of cooling tubes in the middle in order to change the sides of the single Roebel bars along the active part.