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Abstract A high‐temperature superconducting (HTS) dynamo flux pump can inject DC currents into closed‐loop HTS magnets without contact. It enables the realisation of current‐lead‐free or even through‐wall charging systems for high‐field applications such as nuclear magnetic resonance/magnetic resonance imaging (MRI) magnets, fusion reactors and accelerators. Researchers have proposed many simulation models to understand the working principle of HTS dynamos, few of which are in 3D because of converging problems. Therefore, the influences of many key 3D parameters in the HTS dynamo are scarcely reported. The authors propose an efficient 3D modelling method of the HTS dynamo based on the T‐A formulation. The rotating magnets are modelled by a ring‐shaped permanent magnet with space‐time‐variant remanent flux density to avoid moving meshes. This, together with the T‐A formulation, makes the 3D model efficient and universal. The accuracy of the model is verified by the experimental instantaneous and time‐integrated dynamic voltages. Using this model, the authors present systematic case studies to thoroughly explore the influences of the key parameters of a dynamo flux pump on the dynamic voltage and losses. The proposed modelling method and results could significantly benefit the design and optimisation of HTS dynamos for high‐field magnets.