【目的】针对平面变压器因扁平绕组结构加剧邻近效应与趋肤效应导致交流绕组损耗显著升高的问题，提出一种基于变宽度设计的绕组拓扑优化方法，以改善电流分布均匀性并降低损耗。【方法】建立绕组交流效应多物理场耦合模型，通过电磁场理论解析电流密度分布规律；针对圆形绕组提出梯度变宽度参数化模型，验证宽度变化对损耗的调控机制；结合圆形绕组优化经验，构建矩形绕组非线性变宽度设计准则，提出两种差异化宽度调整方案，并采用三维有限元仿真验证方案的电磁性能。【结果】试验数据显示优化后的矩形变宽度绕组在保持相同导电面积条件下，交流欧姆损耗下降7.789%，绕组区域最大磁感应强度降低3.766%，电流密度分布均匀性提升21.6%。优化变宽度绕组的漏感值比等宽度绕组平均高出49.1%，说明变宽度设计通过改变绕组宽度和匝长，间接地提高了漏感。【结论】将圆形绕组变宽度优化设计应用于矩形绕组，通过主动调控导体截面的电磁场边界条件，有效抑制了高频工况下的涡流集聚现象，该成果为平面变压器绕组的多目标协同优化提供了可量化的设计范式。

[Objective] To address the issue of significantly increased AC winding losses in planar transformers caused by the flat winding structure exacerbating proximity and skin effects, this study proposes a topology optimization method for windings based on variable-width design, aiming to improve current distribution uniformity and reduce losses. [Methods] A multi-physics coupling model of winding AC effects was established, and eletromagnetic field theory was employed to analyze current density distribution patterns. A gradient variable-width parametric model was developed for circular windings to validate the regulatory mechanism of width variation on loss reduction. Building on circular winding optimization, nonlinear variable-width design criteria for rectangular windings were formulated, and two differentiated width adjustment schemes were developed. The electromagnetic performance of these schemes was evaluated using 3D finite element simulations. [Results] Experimental data demonstrated that the optimized rectangular variable-width windings achieved a 7.789% reduction in AC Ohmic losses while maintaining equivalent conductive area. Additionally, the maximum magnetic flux density in the winding region decreased by 3.766%, and current density distribution uniformity improved by 21.6%. The leakage inductance of the optimized variable-width winding was, on average, 49.1% higher than that of the equal-width winding. This indicated that the variable-width design indirectly increases the leakage inductance by altering the winding width and the number of turns per unit length. [Conclusion] The optimization design of variable-width circular windings is applied to rectangular windings. By actively controlling the electromagnetic field boundary conditions of the conductor cross-section, the phenomenon of eddy current accumulation under high-frequency conditions is effectively suppressed. This work prorides a quantifiable design paradigm for multi-objective collaborative optimization of planar transformer windings.

国家级(市级)大学生创新训练项目(S202410611114)