IEEE Modular multilevel converters (MMCs) are currently used in a number of high–voltage dc (HVdc) projects connecting very remote offshore wind power plants (WPPs) to shore. For this application the offshore high–voltage dc voltage– source converter (VSC–HVdc) provides the reference for voltage and frequency, i.e. grid–forming operating mode. In fault ride through (FRT) situations, however, the converter reactive current increases and has to be limited to protect the equipment. At the same time, the injection of maximum currents into the offshore grid is advantageous for fault detection and isolation by circuit breakers and to maintain the voltage level. State–of–the– art current limitation might underuse the converter capability in the grid–forming operating mode in specific unbalanced conditions. This paper proposes an extended limitation method for the converter current references for these conditions. It is demonstrated that the proposed method improves the voltage and current profile. Additionally, the impact on the internals of the MMC is outlined. Dynamic simulations are conducted to validate the proposed extended limitation for two operation scenarios. The results demonstrate an enhanced utilization of the MMC capability, a better voltage profile, and an improved transient behavior of the MMC for the proposed extended limitation compared to the normal limitation during specific unbalanced conditions.