Analysing the heat states of transformers under DC bias requires careful consideration of their own structural and material characteristics. Although the 3D finite element method (FEM) is a reliable way of simulating all the details of transformers

it may be time-consuming or have encountered convergence difficulties due to the complex internal structure of the transformer. To address the issues

this paper proposes a fast calculation model for estimating the top-oil temperature rise and the winding hotspot temperature rise of single-phase three-limb transformers under DC bias. This model is based on the coupling principle of electric circuits

magnetic circuits and thermal circuits

and it considers the winding loss and core loss of the transformer under DC bias as key factors linking electromagnetic and thermal effects. All the model parameters can be obtained from nameplate data and regular test data to ensure the method's engineering practicality. The results were compared with 3D FEM

demonstrating favourable performance in terms of computational speed and availability.