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The mainstream researches focus on the linearised impedance/admittance model and its related coupling effects or stability problems. However, since various non‐linear components exist in control loops, their non‐linear dynamics shall be described to improve the modelling accuracy. To fill in this gap, this study develops a large‐signal impedance/admittance model (LSIM/LSAM) to describe the dominant non‐linearity of modulation saturation in a grid‐connected voltage‐source converter (VSC). The LSAM represents the non‐linearity with the equivalent saturation gains based on the describing function theory and then incorporates the derived gains into conventional small‐signal AM (SSAM) to obtain a partially non‐linear admittance. The proposed LSAM distinguishes itself from SSAM by reflecting the improvement in the magnitude‐ and phase‐response of admittance during non‐linear oscillations. Case studies on a grid‐connected VSC containing saturation non‐linearity are conducted to validate the model's effectiveness in stability analysis. It is found that the frequency deviation and sustained oscillation caused by non‐linearity, which can hardly be assessed using SSAM, can be well captured by LSAM. The results of parameter analysis verify that the modulation saturation dominates the system non‐linearity. [ABSTRACT FROM AUTHOR]