A method for controlling a back-to-back three-phase three-level converter having a grid-side AC/DC converter and a machine-side DC/AC converter connected by a split DC link which defines a DC link midpoint. The method includes controlling the grid-side converter to convert AC power from a grid into DC power of the DC link, controlling the machine-side converter to convert DC power from the DC link to AC power to feed a low frequency machine, and concurrently performing common mode voltage injection for the machine-side converter so as to at least partially compensate midpoint voltage ripple caused by the machine-side converter. The method further includes performing common mode voltage injection for the grid-side converter so as to at least partly further compensate the portion of the midpoint voltage ripple which remains uncompensated by controlling the machine-side converter. A control system implementing the control method and a power conversion system utilizing same.