Mathematical modeling of electromagnetic field propagation in power electronic systems: a tensor-based approach to transformer and inverter design optimization

Abstract

Modern power electronic systems operating at frequencies exceeding 100kHz face fundamental modeling challenges. Traditional scalar and vector approaches inadequately capture the complex multi-dimensional field interactions and anisotropic material properties inherent in high-frequency transformers and inverters, where quasi-static assumptions break down, and conventional Cartesian treatments fail in complex geometries. We develop a covariant tensor formulation using metric tensors on curved manifolds to represent electromagnetic field distributions, naturally accommodating non-uniform geometries and frequency-dependent material responses through differential geometric methods. The framework employs the electromagnetic stress-energy tensor for systematic optimization of core geometry, winding configurations, and switching topologies. Validation combines comparative analysis with commercial finite element packages and experimental measurements on prototype high-frequency transformers operating at 150kHz and three-level neutral-point-clamped inverters.  The tensor-based approach achieves 18.7% improvement in predictive accuracy for magnetic flux density distributions while reducing computational overhead by 42% compared to conventional finite element methods. Root mean square errors remain below 6.3% for field predictions and 4.8% for loss estimations, with excellent agreement between predicted and measured electromagnetic interference characteristics. Conclusion: This methodology provides a mathematically rigorous foundation for next-generation power electronic system design in applications ranging from renewable energy conversion to electric vehicle powertrains, where computational efficiency and accuracy are paramount.