The variable speed pumped storage unit with a full-size converter (FSC-VSPSU) can provide fast and flexible regulation capacity for the power grid, assisting the rapid development of the new energy-dominated power systems, and its application is gradually becoming widespread. The excitation system of FSC-VSPSU is crucial for maintaining the motor-port voltage and further supports the stable operation of the entire unit. However, there is currently no research on excitation system modeling, and their essential operating characteristics have not been discussed in detail, which needs further study. With this aim, this paper firstly establishes a detailed transfer function model for FSC-VSPSU, which is then used to study the influence rules of FSC-VSPSU parameters on the operating characteristics. In addition, based on the summarized operating characteristics, the excitation system can be optimized, and its complexity is greatly reduced while ensuring the original performance of the unit. Finally, the results of the simulation can verify the correctness of the established model and the explored operating characteristics.