Hydrogen production via water electrolysis is a promising pathway for decarbonizing renewable based energy systems by enabling large-scale energy storage and a flexible power supply through fuel cells. Among the available electrolysis technologies, solid oxide electrolysis stands out due to its higher efficiency potential compared to conventional alkaline and proton exchange membrane (PEM) methods. A critical component of such systems is the AC/DC power converter which significantly affects the overall performance of the electrolysis process. This paper presents a detailed modeling and experimental analysis of the power conversion system used in a solid oxide electrolysis-based Power-to-Hydrogen (PtH) platform. The study is conducted on a full-scale experimental setup at Aarhus University's research laboratory in Foulum and was carried out as part of the REACT-EU project in collaboration with Topsoe as the industrial partner. The modeling approach is grounded in real-time measurements, incorporating harmonic analysis of interfacing components that may influence the PtH system. A key contribution of this work is the development of a high-fidelity digital model or digital shadow of the power conversion system which is validated through experimental data. The model's accuracy is confirmed by direct comparison with dynamic and steady-state performance measurements from the operational platform. Moreover, through comprehensive power quality analysis the strengths and limitations of the system under real operating conditions are investigated. The experimental findings not only validate the proposed model but also present valuable insights to improve the efficiency and grid integration of PtH applications.