To achieve accurate and rapid calculation of high-frequency transformer losses in rectangular Litz wire windings

this paper proposes a fast loss calculation model integrating the proper generalized decomposition (PGD) spatial separation algorithm with an equivalent complex permeability model. Firstly

separate two-dimensional models for the inner and outer core windows are established. To address the complex boundary constraints of the asymmetric core window cross-section

the weighted residual variational form of the PGD spatial separation algorithm under different boundary conditions is derived

enabling dual one-dimensional decoupling of the magnetic field. This method

through alternating direction iteration

reduces the original two-dimensional finite element problem to a series of one-dimensional problems

thereby lowering the computational complexity from the traditional O(N²) to nearly O(N). Under the premise of ensuring robust convergence

a speedup ratio of over 100 times can be achieved

realizing highly efficient magnetic field computation. Secondly

the proximity effect loss is quantified by using the equivalent complex permeability model

and

a complete winding loss calculation model is constructed in combination with an analytical formula for the skin effect. Finally

two high-frequency transformer prototypes employing rectangular Litz wires with different cross-sectional dimensions are fabricated and tested. The computational efficiency and accuracy of the proposed PGD algorithm are compared with those of the two-dimensional finite element method and the mirror method. Results demonstrate that the proposed model maintains high accuracy while improving calculation speed by two orders of magnitude compared to the traditional methods

providing a theoretical foundation for the rapid optimization design and online real-time monitoring of high-frequency transformers.