This article focuses on the control of Modular Multilevel Converters (MMC) for High Voltage DC (HVDC) applications during unbalanced AC grid voltage sags where positive and negative sequence voltages are equal. The control scheme is based on six arm energy regulators, six independent current controllers and two reference calculation stages that convert the power references into grid and inner current references. Conventional inner AC currents reference calculation fails if the amplitude of the positive and the negative sequence AC grid voltages are equal, a state which is referred to in this paper as singular voltage condition. This article discusses the types of network faults that cause this condition and proposes three different solutions to operate the converter in such scenarios. The adequacy of the proposed solutions is validated through simulations considering each of the problematic fault scenarios.