Abstract: Apparatus for controlling a static AC/AC thyristor converter which supplies power to a synchronous rotating machine (7) at a variable frequency. The converter comprises a "machine" bridge (PM) and a "mains" bridge (PRA, PRB) connected to each other by a first conductor (9) and by a second conductor (10), together with an auxiliary connection (8) which connects the neutral point of the synchronous machine to a point (11) at the "mains" bridge end via which point current can be returned to a transformer which supplies power to said "mains" bridge. The control apparatus comprises means for controlling the "mains" bridge in such a way that the sum of the currents IA+IB of said first conductor (9) and of said second conductor (10) interconnecting the "machine" and "mains" bridges are equal to an average reference current.