Method for controlling a three-phase Vienna rectifier and a DC-to-DC converter, the rectifier comprising three parallel branches (1', 2', 3') each comprising two diodes (D 1H, D 1L, D 2H, D 2L, D 3H, D 3L) and forming a three-phase bridge, the rectifier also comprising three switching arms (1, 2, 3) each associated with an electrical phase (a, b, c), each switching arm (1, 2, 3) comprising a high controlled power switch (M 1H, M 2H, M 3H), connected in series and in opposition with a low controlled power switch (M 1L, M 2L, M 3L); the method comprising, when a switching arm comprises a faulty switch (M 2H, M 2L) that is blocked in the open state: - a step of identifying the faulty switching arm comprising said faulty switch (M 2H, M 2L), and the other two functional arms (1, 3); - a step of receiving a control voltage value (V 13), corresponding to a voltage value to be applied between the two functional arms (1, 3); - a step of keeping a value of output DC voltage (V DC) of the rectifier at a value higher than the voltage difference between two electrical phases at the input of said three-phase Vienna rectifier; - a step of receiving the DC voltage value (V DC) as measured at the output of the rectifier; - a step of calculating the duty cycles to be applied to the high and low controlled switches of the two functional arms, on the basis of said control voltage value (V 13) and said measured DC voltage value (V DC); and - a control step comprising the application of the calculated duty cycles to the three-phase Vienna rectifier, in which, when the electrical phase associated with the switching arm comprising said faulty switch provides a path favourable to the flow of current during a time interval, the conducting switch of the switching arm of which the associated electrical phase voltage is situated between the voltages of the two other electrical phases is kept closed during this time interval. - a step of identifying the faulty switching arm comprising said faulty switch (M 2H, M 2L), and the other two functional arms (1, 3); - a step of receiving a control voltage value (V 13), corresponding to a voltage value to be applied between the two functional arms (1, 3); - a step of keeping a value of output DC voltage (V DC) of the rectifier at a value higher than the voltage difference between two electrical phases at the input of said three-phase Vienna rectifier; - a step of receiving the DC voltage value (V DC) as measured at the output of the rectifier; - a step of calculating the duty cycles to be applied to the high and low controlled switches of the two functional arms, on the basis of said control voltage value (V 13) and said measured DC voltage value (V DC); and - a control step comprising the application of the calculated duty cycles to the three-phase Vienna rectifier, in which, when the electrical phase associated with the switching arm comprising said faulty switch provides a path favourable to the flow of current during a time interval, the conducting switch of the switching arm of which the associated electrical phase voltage is situated between the voltages of the two other electrical phases is kept closed during this time interval.