A nuclear power system includes a reactor vessel that includes a reactor core that includes nuclear fuel assemblies configured to generate a nuclear fission reaction. A representative nuclear power system further includes a riser positioned above there actor core and a primary coolant flow path that extends from a bottom portion of the reactor vessel, through the reactor core, and through an annulus between the riser and the reactor vessel. A primary coolant circulates through the primary coolant flow path to receive heat from the nuclear fission reaction and release the heat to a power generation system configured to generate electric power. The nuclear power system further includes a control rod assembly system positioned in the reactor vessel and configured to position control rods in only two discrete positions.