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An electrically excited synchronous machine (EESM) is a promising alternative to the permanent magnets synchronous machines being used in the automotive industry. However, the main disadvantage of the EESM with the conventional excitation system with brushes is the presence of slip rings on the shaft, which need regular maintenance. A promising alternative to the conventional excitation system of the EESM is a wireless power transfer (WPT) system. In this paper, we focused on WPT excitation system based on the rotary transformers. First, the model of the EESM in the d-q reference frame with vector control system has been built (based on the parameters of the real machine) and analyzed using MATLAB/Simulink software. Second, the influence of the rotary transformer design parameters on the dynamic performance of the EESM has been investigated. Finally, different topologies of the rotary transformers found in the literature have been analyzed, modeled and compared using an analytical and numerical approach. Based on the obtained results, the most suitable electrical parameters (i.e., geometry parameters, supply frequency, magnetizing and leakage inductance, winding resistance and efficiency) of the rotary transformer have been identified and implemented into the d-q model of EESM.