Supercritical carbon dioxide (SCO2) recompression Brayton cycle (RBC) is an encouraging technology for thermal power conversion and heat harvest for a wide range of heat sources due to its high-efficiency, low auxiliary power consumption, and compact size. However, most studies on its design and off-design performance analysis have been limited to the simple zero-dimensional component models without considering aerothermodynamics and ambient conditions. In this study, we developed a set of fully one-dimensional components models for SCO2 compressors, turbines, and heat exchangers, and, then, applied them to the multi-objective design optimization of a SCO2 cycle targeting a 50 MW net power output. The cycle off-design performance analysis methods and the control strategies were developed to countermeasure the performance degradation against the varying cooling water temperatures and part loads. The multi-objective cycle design optimization demonstrates that the cycle thermal efficiency and total product unit cost can be 0.476 and 11.652$/GJ, respectively, for the 50 MW SCO2 RBC cycle. The choke margin of the main compressor is 0.136 less than that of the re-compressor, and condensation can lead to a sharp decline in efficiency under high-flow conditions, causing the earlier onset of choking. The off-design performance analysis shows that the turbine inlet pressure control improves cycle efficiency below the design point of 317 K but does otherwise above the point. In contrast, inventory control strategies can maintain stable cycle efficiency and achieve adjustable net power output between 10 % and 110 %. The findings have the potential to advance further the commercial application of SCO2 cycles in high-temperature thermal energy systems.