Fault ride-through specifications listed in modern transmission and distribution grid codes specify that wind-turbine generators (WTGs) must remain connected to electricity networks at voltage levels well below nominal. Achieving reliable operation at greatly reduced voltage levels is proving problematic. A particular problem regarding power converter-based WTGs is that standard controllers designed for reliable operation around nominal voltage levels will not work as designed during low network voltages that can occur during a fault. A consequence of this is greatly increased converter currents, which may lead to converter failure. This paper presents a nonlinear controller design for a power converter-based WTG that ensures that current levels remain within design limits, even at greatly reduced voltage levels, thus enhancing the WTG's fault ride-through capability.