The electric propulsion system (EPS) xenon storage and supply system (SSS) is a complex pipeline network system, which involves the multi-physics coupled fields of transcritical flow, heat transfer, rigid body motion, electromagnetics, and control. Based on the fundamental equation of state, a one-dimensional finite volume model system is proposed for compressible transcritical transient pipe flow. Six typical components of the SSS are modularization modeled by using an object-oriented programming method in Fortran 2018. To evaluate the performance of the algorithm, a simulation model consisting of 77 components is developed for a proportional controlled EPS xenon SSS, and a system-level simulation is performed. Compared with the standard case constructed on the Amesim platform, the model has a pressure rise time error lower than 6%, and the restrictors mass-flow-rate errors of the anode, cathode, and neutralizer are less than 2.8% of the rated flow rate after stabilization. Moreover, the proposed model yields more accurate results at certain operating points. The model system provides an efficient reference for the design and optimization of EPS SSSs, and offers a new approach to simulate complex cryogenic pipe flow systems.