Method for Calculating Magnetic Field of Solenoid Coil Accounting for Winding Asymmetry
Xiong Qi1,2, Li Yuanyuan1,3, Cheng Hui2, Wang Lili1,3, Yan Nuo4
1. College of Electrical Engineering & New Energy China Three Gorges University Yichang 443002 China; 2. Guangdong Provincial Key Laboratory of Extreme Conditions Dongguan 523803 China; 3. Hubei Provincial Engineering Research Center of Intelligent Energy Technology China Three Gorges University Yichang 443002 China; 4. Wanzhou Power Supply Branch State Grid Chongqing Electric Power Company Chongqing 404100 China
Abstract：Solenoid coils, made by spirally winding wires, are key components for converting electro-magnetic energy. Due to their advantages of stable structure, simple manufacturing process, and easy reinforcement, they are widely used in electrical equipment such as transformers and motors. In the transient simulation, to reduce modeling complexity and computational time, the coil is modeled as a 2D axisymmetric model with multiple coaxial circular cross-sections. This model achieves high computational accuracy and extremely fast solution times for multi-turn dense-wound coils, but it does not account for axial asymmetry introduced by the winding process. Thus, large simulation errors occur when solenoid coils with high magnetic field intensity, non-dense windings, and large-cross-section wires are used in high-intensity scenarios. Therefore, this paper proposes an improved current filament method that accounts for the winding asymmetry. A numerical solution model is established based on the current filament method and introduces an asymmetric correction coefficient matrix to optimize the current filaments. The optimized current is then imported into the model for magnetic field calculation. The structural asymmetry is equivalent to the excitation-current asymmetry in a symmetric structure, improving solution accuracy without incurring excessive computational load. Taking a single-layer solenoid coil as an example, this paper first subdivides the coil wire into several current filament units, calculates the electromagnetic characteristic parameters between each pair of units, and constructs a numerical solution model. Then, the asymmetry coefficient of the current filament is calculated, and the current is optimized using the asymmetric correction coefficient matrix. Finally, the optimized current is imported into the 2D axisymmetric equivalent model. The results show that the coil magnetic field distribution closely matches the actual situation, verifying the effectiveness and practicability of the proposed method. The conclusions are as follows.（1）This paper proposes an improved current filament method considering the winding asymmetry of the coil, which effectively equates the structural asymmetry of the coil to the asymmetry of the excitation current under a symmetric structure.（2）This method effectively improves the current calculation accuracy, achieving a magnetic field distribution closer to that of the 3D coil. Meanwhile, the calculation time is significantly shortened. The output current accuracy is less than 2%, and the error at the current peak is reduced from 3.814% to 0.132%. The magnetic flux density distribution of the coil is closer to the comparison reference value.（3）It has good effectiveness and stability for different solenoid coils. By studying the current calculation accuracy under different factors such as the number of turns, wire size, discharge capacitance, and coil pitch, it is found that the errors of this method are within 0%~1%. Moreover, for complex calculation models, the advantage in computational efficiency is pronounced.
熊奇, 黎袁袁, 程辉, 王丽丽, 阎诺. 考虑绕制不对称性的螺线管线圈磁场计算方法[J]. 电工技术学报, 2026, 41(16): 5402-5413.
Xiong Qi, Li Yuanyuan, Cheng Hui, Wang Lili, Yan Nuo. Method for Calculating Magnetic Field of Solenoid Coil Accounting for Winding Asymmetry. Transactions of China Electrotechnical Society, 2026, 41(16): 5402-5413.
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2026, Vol. 41 
