A method of operating a multilevel converter having multiple phase modules, each with three phase module branches. In a first switching position, a switching device of each phase module connects an alternating voltage connection of the phase module to a first connection point between a first phase module branch and a third phase module branch. In a second switching position, the switching device connects the alternating voltage connection to a second connection point between the third phase module branch and a second phase module branch. In the method, circulating currents of the multilevel converter are controlled in accordance with total energy variables and differential energy variables of the phase modules to balance the energy between the phase module branches.