A power generation system and related method for repowering a fossil-fueled power plant using a carbon-free nuclear steam supply system (NSSS) which replaces the existing fossil plant steam generator which burns fossil fuel such as coal, oil, or natural gas. The existing fossil plant energy conversion system including the turbine-generator (turbogenerator) and auxiliary components of the Rankine cycle is retained. The NSSS may include a small modular reactor (SMR) unit comprising a reactor vessel with nuclear fuel core and steam generator which receives heated primary coolant from the reactor to produce main steam to operate the Rankine cycle. The main steam output by the SMR unit is compressed in a steam compressor to increase its pressure to a level necessary to operate the turbogenerator. The compressor may be operated via a portion of the main steam. An intercooler of the compressor may be used for main steam reheating.