The Analytical Calculation of the Inductance of Magnetic Shielded Tubular Core Coils Based on the Enhanced Truncated Region Eigenfunction Expansion Method
Yu Dongze1,2, Chen Baichao1,2, Luo Yao1,2, Xiang Yike1,2
1. State Key Laboratory of Power Grid Environmental Protection Wuhan 430072 China; 2. School of Electrical Engineering and Automation Wuhan University Wuhan 430072 China
Abstract：The size of air-core coils does not meet the demands of modern electrical devices, which require both compactness and strong anti-interference capabilities. Additionally, air-core coils require a large amount of material due to their high number of turns, and are often susceptible to external interference, leading to instability. To overcome the defects, the air-cored coil is replaced by a tubular iron-core coil with a magnetic shield, where the tubular iron-core can reduce material cost of an iron core without remarkably affecting the inductance values. However, the complex structure makes it challenging to determine the parameters such as self and mutual- inductance. In previous studies, the inductance problems of iron-core coils were typically solved using boundary value problem (BVP) methods. Recently, a novel approach was provided that can solve problem of coil’s inductance with magnetic core effectively. Building on this approach, this paper proposes formulas for calculating self and mutual-inductance of a tubular iron-core coil with a magnetic shield by the enhanced truncated region eigenfunction expansion (ETREE) method. In Section 1, we firstly address the inductance calculation problem of a tubular iron-core coil with an infinite permeability of the magnetic shield, which consists of three sub-domains in the vertical direction. However, when the permeability of the magnetic shield is not sufficiently large, this assumption may introduce an error. To overcome this limitation, the Section 2 considers the precise permeability and thickness of the magnetic shield. In this case, the coil system has seven sub-domains in vertical direction, requiring more computational steps than in Section 1. By employing the ETREE technique, the resulting equations are simpler and more streamlined than those derived from the traditional TREE method. Matrix operations and the energy method are then applied to efficiently and accurately calculate both self-inductance and mutual inductance. Simulations by COMSOL Multiphysics® are carried out in this paper to verify the accuracy of the proposed formulas. For the simulation verification of self-inductance, the different positions of coils 1 and 2 are verified respectively. The simulation verification of mutual inductance is carried out by moving coil 2 with fixed coil 1. The results show that the analytical solutions by ETREE technology has high computational efficiency and computational accuracy. In addition, the inductance calculated by an infinite magnetic permeability shield shows a small error (<2%) compared to the results obtained from an accurate magnetic permeability model when the ratio γ between permeability of magnetic wall and magnetic core is larger than 30%. In terms of time cost, the method in section 1 consumes around 0.7 seconds whereas the method in section 2 costs averagely 1.2 seconds. For comparison, the corresponding time for the finite elements method is 6~7 seconds. The following conclusions can be drawn: (1) The formulas presented in this paper can be used to calculate the inductance of coil systems with varying geometric parameters, magnetic permeabilities, and coil positions, including those for coils, cores, and shields. (2) The formulas developed in this work exhibit both high accuracy and efficiency. This improvement can be applied to related electrical devices, such as passive filters and iron-core reactors. (3) Assuming the shield has infinite permeability enhances computational efficiency while maintaining accuracy. However, when the difference between the magnetic permeabilities of the iron core and the shield becomes too large, this assumption introduces significant error. In such cases, the method outlined in Section 2 is recommended.
禹东泽, 陈柏超, 罗垚, 向依可. 基于增强型截断域本征函数展开法的磁屏圆筒铁心线圈电感的解析计算[J]. 电工技术学报, 2026, 41(3): 749-759.
Yu Dongze, Chen Baichao, Luo Yao, Xiang Yike. The Analytical Calculation of the Inductance of Magnetic Shielded Tubular Core Coils Based on the Enhanced Truncated Region Eigenfunction Expansion Method. Transactions of China Electrotechnical Society, 2026, 41(3): 749-759.
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