Method for operating a multilevel converter having multiple phase modules (400, 400', 400''), 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 (902, 906) and an electrical energy store, wherein each phase module (400, 400', 400'') has a first phase module branch (11, 11', 11"), which is connected to the first DC voltage connection, a second phase module branch (13, 13', 13''), which is connected to the second DC voltage connection, a third phase module branch (404, 404', 404''), which connects the first phase module branch (11, 11', 11'') to the second phase module branch (13, 13', 13''), and has a switching device (420, 420', 420''), which in a first switching position connects an AC voltage connection (5, 5', 5'') of the phase module (400, 400', 400") to a first connecting point (412, 412', 412'') between the first phase module branch (11, 11', 11'') and the third phase module branch (404, 404', 404'') and in a second switching position connects the AC voltage connection (5, 5', 5") to a second connecting point (416, 416', 416'') between the third phase module branch (404, 404', 404'') and the second phase module branch (13, 13', 13''), 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 (11, 11', 11'') and the second phase module branch (13, 13', 13''), is determined for each phase module (400, 400', 400''), - 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 (13, 13', 13'') and the third phase module branch (404, 404', 404'') and in the second switching position is a measure of the difference between the energies of the first phase module branch (11, 11', 11'') and the third phase module branch (404, 404', 404''), is determined for each phase module (400, 400', 400'') depending on the switching position (421, 422) of the switching device (420, 420', 420'') 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 (400, 400', 400'') 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 (11, 11', 11'') and the second phase module branch (13, 13', 13''), is determined for each phase module (400, 400', 400''), - 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 (13, 13', 13'') and the third phase module branch (404, 404', 404'') and in the second switching position is a measure of the difference between the energies of the first phase module branch (11, 11', 11'') and the third phase module branch (404, 404', 404''), is determined for each phase module (400, 400', 400'') depending on the switching position (421, 422) of the switching device (420, 420', 420'') 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 (400, 400', 400'') in order to compensate for energy imbalances between the phase module branches (11, 11', 11'', 13, 13', 13", 404, 404', 404").