The cryogenic system of the upgrade project of Beijing Electron Position Collider (BEPCII) is being built at Institute of High Energy Physics (IHEP). The system has a total capacity of 1.0 kW at 4.5 K for cooling three kinds of superconducting devices, superconducting RF (SRF) cavities, superconducting quadrupole (SCQ) magnets and the superconducting solenoid magnet (SSM). Two sets of refrigerators, each with a capacity of 500 W at 4.5 K are adopted. In order to prepare for the commissioning of the cryogenic system, the refrigeration process was simulated and analyzed numerically. The simulation was conducted based on the latest engineering progresses and focusing on the steady state operation mode. The simulation results, such as the helium mass flow rates and pressure drops over the control valves of different cooling channels, thermodynamic parameters of each superconducting device, etc., are presented in this paper. When considering the heat loads, the powers of heaters of each device were figured out to realize the nominal operation modes.