This study focuses on proposing a heat source storage mode for the indirect recompression supercritical CO2 cycle (RSCC) coupled with a sodium-cooled fast reactor, aiming to achieve low-frequency regulation of the reactor and enhance the load capacity of system. A deep neural network-based turbomachinery performance prediction approach is employed to assess the system's part-load and overload performance under several typical control strategies. The turbine inlet temperature of the system under all control strategies except the intermediate heat exchanger (IHX) bypass rises with decreasing load. The system's part-load performance is positively correlated with its corresponding overload power. The findings reveal that the adjustable load ranges of the heat source storage tanks under inventory, turbine bypass, turbine throttle, and IHX bypass controls are 10%–156.10%, 10%–156.10%, 30%–147.30%, and 10%–146.88%, respectively, along with the safe compressor operation. As the near-choke operation of the compressor limits the rise in overload power, a turbine fitted with variable inlet guide vanes is tried. The optimization results demonstrate that the largest overload power of the system can reach 161.18 % without reducing the thermal efficiency. This study provides a heuristic insight into the variable load operation for indirect nuclear-powered Brayton cycles under low-frequency reactor regulation.