With the high penetration of renewable energy, future power systems are becoming increasingly power electronics dominated, which raises significant stability concerns. Impedance-based analysis is widely recognized as an effective method to evaluate and verify small-signal stability in such systems. This paper focuses on the modeling of modular electrolyzer systems, which are expected to play an important role in large-scale green hydrogen production. A single-module averaged model is established to represent the dynamic behavior of a buck-type converter interfacing the electrolyzer. The dynamics of the DC-link capacitor are explicitly included, since they have a critical influence on wideband impedance characteristics but are often simplified in existing studies. Based on the derived model, the impedance formulation is obtained and validated through frequency sweep simulations. The results show good agreement between the theoretical calculations and sweep data, which confirms the accuracy of the proposed method.