Analysis of Short-Circuit Forces and Deformation in Transformer Windings Based on Magnetic Field Gradient Stress Tensors
Yang Fan1, Gao Sance1, Zhao Yi2, Wang Jiawei3, Wang Pengbo1
1. State Key Laboratory of Power Transmission Equipment Technology Chongqing University Chongqing 400044 China; 2. Chongqing Academy of Metrology and Quality Inspection Chongqing 400044 China; 3. State Key Laboratory of Electrical Insulation and Power Equipment Xi'an Jiaotong University Xi'an 710049 China
Abstract：To address the challenges of high modeling complexity and insufficient computational efficiency in conventional methods for calculating electromagnetic forces in transformer windings under three-dimensional multiphysics coupling, this study proposes a novel analytical approach based on magnetic field gradient tensor theory. Through systematic analysis of multiple transformer short-circuit failure cases, it was identified that critical deformation zones in windings consistently occur at locations with maximal magnetic field gradient variations rather than at peak magnetic flux density regions. This observation highlights the intrinsic correlation between magnetic energy density gradients and mechanical strain localization. Building on this principle, a magnetic gradient stress tensor G is formulated to characterize electromagnetic-mechanical energy conversion, and the 3D electromagnetic force density distribution can be directly calculated using G. This framework establishes a mathematical equivalence between magnetic field gradients and force densities, circumventing the need for intricate current density reconstruction in traditional methods by leveraging second-order differential properties of magnetic gradient tensors, thereby transforming volumetric integrals into tensor differential operations. For validation, a 3D model of a 35 kV oil-immersed transformer was developed using magneto-mechanical fully coupled governing equations. Detailed simulations of magnetic fields, deformations, and electromagnetic forces under single-phase short-circuit conditions were performed via Ansys software suite, with preliminary results confirming theoretical predictions. A dedicated experimental platform was constructed, integrating eight Hall-effect magnetic sensors, eight fiber Bragg grating (FBG) stress sensors, and eight FBG strain sensors to synchronously capture magnetic fields, mechanical stresses, and deformations. Standard short-circuit tests demonstrated strong agreement between theoretical and experimental data: axial force exhibited a bimodal distribution along the circumferential direction, with a calculated peak of 188.1 kN showing a 1.8% deviation from the measured 191.5 kN, while the average error in radial forces remained at 2.4%. Cross-validation against conventional methods revealed an 43.9% reduction in computational time (from 9.8 h to 5.5 h) and a 53.8% decrease in memory consumption (from 292 GB to 135 GB) without compromising accuracy. This work establishes a direct theoretical linkage between electromagnetic and structural fields through tensor differential analysis, offering a new paradigm for multiphysics coupling studies in power equipment. The proposed algorithm has been validated via an in-house developed transformer short-circuit withstand design platform and further verified in simulations of critical devices such as ±800 kV converter transformers. These advancements significantly enhance the timeliness and reliability of short-circuit force predictions, providing a robust theoretical foundation for optimizing the mechanical stability and operational safety of large-scale power transformers under fault conditions.
杨帆, 高三策, 赵轶, 王嘉玮, 王鹏博. 基于磁场梯度张量的变压器绕组短路力及形变分析[J]. 电工技术学报, 2026, 41(1): 14-25.
Yang Fan, Gao Sance, Zhao Yi, Wang Jiawei, Wang Pengbo. Analysis of Short-Circuit Forces and Deformation in Transformer Windings Based on Magnetic Field Gradient Stress Tensors. Transactions of China Electrotechnical Society, 2026, 41(1): 14-25.
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