Method for operating a multilevel converter having multiple phase modules , which are arranged connected in parallel with one another between a first DC voltage connection and a second DC voltage connection of the multilevel converter and each have a plurality of modules (1_1 ... 1_n; 2_1 ... 2_n; 408_1 ... 408_n) each having at least two electronic switching elements and an electrical energy store , wherein each phase module has a first phase module branch (11, 11', 11"), which is connected to the first DC voltage connection , a second phase module branch , which is connected to the second DC voltage connection , a third phase module branch , which connects the first phase module branch to the second phase module branch , and has a switching device , which in a first switching position connects an AC voltage connection of the phase module (400, 400', 400") to a first connecting point between the first phase module branch and the third phase module branch and in a second switching position connects the AC voltage connection (5, 5', 5") to a second connecting point between the third phase module branch and the second phase module branch , wherein the third phase module branch has at least one module (408_1) with a full-bridge circuit, characterized in that , in the method - an energy summation variable (W Σ1 , W Σ2 , W Σ3 ), which is a measure of the sum of the energies of the first phase module branch and the second phase module branch , is determined for each phase module , - an energy difference variable (W Δ1 , W Δ2 , W Δ3 ), which in the first switching position is a measure of the difference between the energies of the second phase module branch and the third phase module branch and in the second switching position is a measure of the difference between the energies of the first phase module branch and the third phase module branch , is determined for each phase module depending on the switching position of the switching device of the phase module (400, 400', 400"), and - circulating currents of the multilevel converter are controlled depending on the energy summation variables (W Σ1 , W Σ2 , W Σ3 ) and energy difference variables (W Δ1 , W Δ2 , W Δ3 ) of the phase modules in order to compensate for energy imbalances between the phase module branches (11, 11', 11'', 13, 13', 13", 404, 404', 404"). - an energy summation variable (W Σ1 , W Σ2 , W Σ3 ), which is a measure of the sum of the energies of the first phase module branch and the second phase module branch , is determined for each phase module , - an energy difference variable (W Δ1 , W Δ2 , W Δ3 ), which in the first switching position is a measure of the difference between the energies of the second phase module branch and the third phase module branch and in the second switching position is a measure of the difference between the energies of the first phase module branch and the third phase module branch , is determined for each phase module depending on the switching position of the switching device of the phase module (400, 400', 400"), and - circulating currents of the multilevel converter are controlled depending on the energy summation variables (W Σ1 , W Σ2 , W Σ3 ) and energy difference variables (W Δ1 , W Δ2 , W Δ3 ) of the phase modules in order to compensate for energy imbalances between the phase module branches (11, 11', 11'', 13, 13', 13", 404, 404', 404"). <EOS>