DOI: 10.3390/en17061378 ISSN: 1996-1073

# Multi-Step Approach for Fast Calculation of Magnetic Field in Transformer Tank Shields

Zvonimir Jurković, Bruno Jurišić, Tomislav Župan
• Energy (miscellaneous)
• Energy Engineering and Power Technology
• Renewable Energy, Sustainability and the Environment
• Electrical and Electronic Engineering
• Control and Optimization
• Engineering (miscellaneous)
• Building and Construction

A multi-step approach for the fast calculation of the magnetic field inside transformer tank shields, based on the 2D FEM, is presented in the paper. Due to the limitations of the 2D FEM, the proposed approach utilizes several 2D FEM models and calculates the magnetic field in multiple steps to account for the 3D geometry of the problem. In the first step, a distribution of the magnetic flux density that enters the tank shields is calculated using the quasi-3D model of the transformer. This quasi-3D model is obtained by superimposing the solution of multiple axisymmetric 2D FEM models, and assumes a considerably simplified transformer geometry. To account for the tank shield geometry that is neglected in the quasi-3D FEM model, an additional 2D FEM model with tank shields is introduced. After the distribution of the magnetic flux density that enters the tank shields is calculated, it is imposed in the final 2D FEM model with a non-linear tank shield which is used to calculate the magnetic flux density distribution inside the tank shields. The proposed approach enables a fast calculation of magnetic field distributions, both in the vertical and horizontal directions. The results of the proposed approach are compared against the 3D FEM. The relative error of the maximum magnetic flux density is under 2%, while the NRMSE of the magnetic flux density distribution within the tank shields is under 10%. The key contribution of the proposed approach is a low computation time. In the presented case study, the total computation time of the proposed approach is ~30 s, while the computation time of the 3D FEM is ~1 h. As the computation time is significantly reduced, while the accuracy is acceptable, the proposed approach can be a good alternative to the 3D FEM for design purposes. Therefore, it has industrial value.