Hierarchical Physics-Embedding Neural Network Framework for 3D Magnetic Modeling of Medium-Frequency Transformers

Neural network (NN) technology is revolutionizing the modeling paradigm in the engineering arena, simultaneously enhancing model precision and process speed. Nevertheless, a large amount of training data is an unattainable requirement in the magnetic component modeling issue, especially when dealing with the 3D magnetic behaviors in complex geometry. In this work, to establish an accurate 3D magnetic model of medium-frequency transformers with limited data sources, the 2D FEM data, 3D FEM data, and analytical model are structurally integrated into a unified NN training framework. First, the low-cost 2D FEM data is abundantly fed into the inferior 2D section model to capture the winding fringe effect, which is missing in the conventional 1D Dowell's equation. The considerable data information and prior physics knowledge jointly ensure the high accuracy of section modeling. The layer-precision region model transition pipelines are then established between the 2D section model and the 3D region model. These pipelines alleviate the error propagation from the 2D section model, thus the error of partial length in the corner region can be well amended with minor 3D FEM data. Accordingly, this proposed hierarchical physics-embedding neural network (HPENN) framework improves the physical interpretability of NN-based models and relieves the strict computing requirement at the data generation stage. According to the training and experiment results, the computation burden for data generation is reduced to 1/10 with the proposed framework compared with classic NN methods. Besides, the average error of the proposed HPENN framework is only 1%, and the maximum error does not exceed 7%.