Operating method for a multilevel converter which has a number of converter phases (8 to 10) which are connected to the phases (2 to 4) of a three-phase network in a star or delta connection, - wherein an active component (w) and at least two asymmetrical components (w', b') are determined on the basis of phase voltage values (U2 to U4) and phase current values (IL2 to IL4), - wherein the active component (w) is characteristic of the total active current flowing in the three-phase network, and the at least two asymmetrical components (w', b') are characteristic of a distribution, among the phases (2 to 4), of the total active and reactive currents flowing, - wherein the active component (w) and the at least two asymmetrical components (w', b') are filtered with one filter characteristic each, - wherein the phase voltage values (U2 to U4) are each multiplied by the filtered active component (w) and the at least two filtered asymmetrical components (w', b'), - wherein the multiplied phase voltage values (U2 to U4) are each multiplied by a respective weighting factor (ga to gc), - wherein a zero current is determined on the basis of the asymmetrical components (w', b') and the phase voltage values (U2 to U4), - wherein the zero current is determined in such a way that in a two-component system corresponding to the phases (2 to 4) of the three-phase network said zero current satisfies the relationship: I 0 = 2 3 ⋅ u 1 ⋅ b ′ + u 2 ⋅ w ′ u 1 2 + u 2 2, where u1 and u2 are the phase voltage values of the two-component system and b' and w' are the asymmetrical components, - wherein the phase voltage values (U2 to U4) weighted with the weighting factors (gatogc) and the zero current are subtracted from the phase current values (I2 to I4),and - wherein an actuation state for the converter phases (8 to 10) is determined on the basis of the phase current values (IL2 to IL4) which are modified in such a way, and the converter phases (8 to 10) are actuated in accordance with the actuation state which is determined. - wherein an active component (w) and at least two asymmetrical components (w', b') are determined on the basis of phase voltage values (U2 to U4) and phase current values (IL2 to IL4), - wherein the active component (w) is characteristic of the total active current flowing in the three-phase network, and the at least two asymmetrical components (w', b') are characteristic of a distribution, among the phases (2 to 4), of the total active and reactive currents flowing, - wherein the active component (w) and the at least two asymmetrical components (w', b') are filtered with one filter characteristic each, - wherein the phase voltage values (U2 to U4) are each multiplied by the filtered active component (w) and the at least two filtered asymmetrical components (w', b'), - wherein the multiplied phase voltage values (U2 to U4) are each multiplied by a respective weighting factor (ga to gc), - wherein a zero current is determined on the basis of the asymmetrical components (w', b') and the phase voltage values (U2 to U4), - wherein the zero current is determined in such a way that in a two-component system corresponding to the phases (2 to 4) of the three-phase network said zero current satisfies the relationship: I 0 = 2 3 ⋅ u 1 ⋅ b ′ + u 2 ⋅ w ′ u 1 2 + u 2 2, where u1 and u2 are the phase voltage values of the two-component system and b' and w' are the asymmetrical components, - wherein the phase voltage values (U2 to U4) weighted with the weighting factors (gatogc) and the zero current are subtracted from the phase current values (I2 to I4),and - wherein an actuation state for the converter phases (8 to 10) is determined on the basis of the phase current values (IL2 to IL4) which are modified in such a way, and the converter phases (8 to 10) are actuated in accordance with the actuation state which is determined. - wherein the phase voltage values (U2 to U4) weighted with the weighting factors (gatogc) and the zero current are subtracted from the phase current values (I2 to I4),and - wherein an actuation state for the converter phases (8 to 10) is determined on the basis of the phase current values (IL2 to IL4) which are modified in such a way, and the converter phases (8 to 10) are actuated in accordance with the actuation state which is determined.