A fast calculation method for superconducting coil inductance considering current distribution in the width direction

Abstract

The present invention relates to a method for calculating inductance, specifically a method for rapidly calculating the inductance of a superconducting coil that considers current distribution in the width direction. The method comprises the following steps: S1: Target object confirmation: Establishing a spatial coordinate system for the superconducting coil and determining the path function of the superconducting coil; S2: Current element division: Dividing the current elements based on the geometric dimensions of the strip and coil; S3: Numerical integration: Combining the Neumann formula and the geometric mean distance principle, first calculating the geometric mean distance between the current elements, taking into account the influence of width, then calculating the self-inductance and mutual inductance of each divided current element, and then superimposing and summing the results to obtain the calculated inductance value of the target superconducting coil. Compared with the prior art, the present invention addresses the drawback of the prior art of extremely large computational complexity when considering current distribution in the width direction. This solution simplifies the calculation process of the superconducting coil inductance while ensuring calculation accuracy.

Description

Technical Field

[0001] The present invention relates to an inductance calculation method, and in particular to a method for quickly calculating the inductance of a superconducting coil taking into account the current distribution in the width direction. Background Art

[0002] The calculation of coil inductance is of great significance in electrical engineering, with extensive implications for electrical device design, magnetic field generation, and wireless power transmission. In superconductivity research, superconducting coils are considered one of the most fundamental devices, and their inductance is closely related to power loss, the charge-discharge performance of the magnet, and other characteristic parameters. Superconducting tapes are very thin, and the turns are wound very closely together. Therefore, the calculation of inductance must take into account the influence of current distribution. Numerous methods exist for calculating the inductance of superconducting coils, including the finite element method (FEM), the Newman formula, and the flux accumulation method. The FEM and the Newman formula can calculate the inductance of segmented conductors, while the flux accumulation method can only calculate the inductance of coils with complete circuits. The FEM method allows intuitive construction of two-dimensional or three-dimensional coil models and calculation of inductance with the help of FEM software. However, the modeling process is complex and computationally demanding. Compared to the FEM method, the Newman formula can calculate the inductance of a variety of complex coil shapes with a known path function, making the modeling process simpler. The Newman formula uses numerical integration to calculate inductance, thus involving only the accumulation of numerical sums and requiring less computational resources.

[0003] After searching, it was found that the existing patents and literature on fast methods for calculating inductance of superconducting coils all have the inconveniences mentioned above. The main contents of typical literature are as follows:

[0004] Literature: T.Pingan, F.Yi, L.Chunxia, ​​and G.Yougui. Modeling of mutual inductance for hexagonal coils with horizontal misalignment in wireless powertransfer, 2018. Paper presented at 2018 IEEE Energy Conversion Congress and Exposition (ECCE), 1981-1986 2018.

[0005] The inductance calculation method used in this paper is actually a flux accumulation method, which integrates the induced magnetic flux density of the original coil within the area surrounded by the target coil and divides it by the source current to obtain the mutual inductance. This method can only calculate the mutual inductance or self-inductance of coils with complete loops, but cannot calculate the inductance of irregularly shaped conductors of finite length, which does not meet the requirements of the equivalent circuit model of uninsulated coils. Furthermore, this method treats the current as a current element line with no thickness along the centerline of the conductor, failing to consider the influence of current distribution across the width of the superconducting tape.

[0006] Literature: S.Zhenhua,M.Jun L.and Guangtong,L.Kang,L.Libin,and W.Yiyu.Fastand precise calculation of mutual inductance for electrodynamic suspension:methodology and validation.IEEE Transactions on Industrial Electronics, 69(6):6046–6057,2022.

[0007] The inductance calculation method described in this paper utilizes the Neumann formula, which involves the distribution of current across the width of the superconducting coil. It focuses on accurately and rapidly calculating the inductance of each individual turn of the superconducting coil. By treating the entire coil as a single turn, the current is evenly distributed across the conductor's cross-section. This allows for more accurate calculations of the total inductance of the entire coil and the mutual inductance between coils, similar to existing mesh-matrix calculation methods. To ensure accuracy, this paper employs a large number of meshes, resulting in a significant computational effort. While some simplifications have been proposed, the most basic mesh calculation units cannot be simplified, placing significant demands on computing resources.

[0008] Because the conducting cross-section of a superconducting tape has a large aspect ratio, the current distribution significantly affects the inductance. Using existing calculation methods, further dividing the current element lines along the width of the superconducting tape increases the computational complexity. Therefore, a highly accurate and fast method for calculating the inductance of superconducting coils with large turns is needed. Summary of the Invention

[0009] The purpose of the present invention is to solve at least one of the above problems and provide a method for quickly calculating the inductance of a superconducting coil taking into account the current distribution in the width direction, so as to overcome the defect of the existing technology that the calculation amount is extremely large when considering the current distribution in the width direction. This solution simplifies the calculation process of the superconducting coil inductance while ensuring the calculation accuracy.

[0010] The purpose of the present invention is achieved through the following technical solutions:

[0011] A method for quickly calculating the inductance of a superconducting coil taking into account the current distribution in the width direction comprises the following steps:

[0012] S1: Target object confirmation: establish a spatial coordinate system for the superconducting coil and determine the path function of the superconducting coil;

[0013] S2: Current element division: divide the current element based on the geometric dimensions of the strip and coil;

[0014] S3: Numerical integration: By combining the Neumann formula and the geometric mean distance principle, the geometric mean distance between current units considering the influence of width is first calculated. Then the self-inductance and mutual inductance of each divided current unit are calculated, and then the sum is added to obtain the calculated inductance value of the target superconducting coil.

[0015] Preferably, the current element division divides the superconducting coil into a number of straight line segment current units.

[0016] Preferably, the current unit length is determined according to the width and thickness of the strip used for the superconducting coil and the size of the superconducting coil.

[0017] Preferably, the current unit division is such that the order of magnitude of the length of the current unit is equal to or smaller than the order of magnitude of the thickness of the tape of the superconducting coil and the order of magnitude of the spacing between the wires in the superconducting coil.

[0018] Preferably, the current unit division is such that the order of magnitude of the length of the current unit is smaller than the order of magnitude of the thickness of the tape of the superconducting coil and the order of magnitude of the distance between the wires in the superconducting coil.

[0019] The length of the current unit should be the same as or smaller than the thickness of the superconducting tape to balance calculation accuracy and speed. For specific division rules or methods, see C.L. Sonntag, Lomonova EA, and Duarte JL, "Implementation of the Neumann formula for calculating the mutual inductance between planar PCB inductors," 2008.

[0020] Preferably, the number of segments of the current unit is not less than Where th is the thickness of the superconducting coil.

[0021] Preferably, each turn of the superconducting coil is divided into current units according to the same standard.

[0022] Preferably, the geometric mean distance g between the two wires in the current unit is line for:

[0023]

[0024] Where R is the center distance between the two wires in the current cell, and wd is the width of the current cell.

[0025] Preferably, the mutual inductance ΔM between the current units considering the current distribution in the width direction is close for:

[0026]

[0027] Where μ0 is the vacuum permeability, R is the center distance between the two wires in the current unit, wd is the width of the current unit, and Δl is the length of the current unit.

[0028] Preferably, the inductance M of the superconducting coil considering the current distribution in the width direction is close for:

[0029]

[0030] Where μ0 is the vacuum magnetic permeability, R is the center distance between the two conductors in the current unit, wd is the width of the current unit, Δl is the length of the current unit; n and m are the number of segments into which the two conductors are divided respectively.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] The present invention combines the Neumann formula and the geometric mean distance principle to simplify the calculation process of superconducting coil inductance and obtain the inductance matrix of the equivalent circuit model. Compared with the finite element method, this rapid calculation method consumes fewer computing resources and has a simpler modeling process. In addition, this method considers the influence of the current distribution in the conductor cross section on the inductance, making the calculation results more accurate, demonstrating that the combination of the Neumann formula and the geometric mean distance principle can quickly and accurately calculate inductance. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 (a) The integration principle for numerically calculating complex paths, and (b) a schematic diagram for calculating the mutual inductance between two current units in a superconducting coil.

[0034] Figure 2 This is a flow chart of a method for quickly calculating the inductance of a superconducting coil;

[0035] Figure 3 Schematic diagram of the superconducting coil model in Example 1;

[0036] Figure 4 is the equivalent circuit model of the superconducting coil in Example 1;

[0037] Figure 5 1 is a comparison of the results of the fast calculation method of the superconducting coil inductance of the present invention in Example 1 and the calculation method of the prior art. DETAILED DESCRIPTION

[0038] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operating procedures. It should be noted that those skilled in the art may make several variations and improvements without departing from the scope of the present invention, and these all fall within the scope of protection of the present invention.

[0039] Example 1

[0040] Please also see Figures 1 to 5 .

[0041] This scheme is based on Figure 1 The numerical integration principle of the complex path is shown in the figure, and a fast calculation method for the inductance of superconducting coils considering the current distribution in the width direction is proposed, such as Figure 2 shown.

[0042] First, a suitable three-dimensional coordinate system is established to determine the path function of the target superconducting coil.

[0043] Then, the length of the current unit of the straight line segment that will be used to divide and replace the superconducting coil is determined based on the width and thickness of the tape used for the superconducting coil and the size of the superconducting coil.

[0044] Furthermore, the geometric mean distance principle is combined to calculate the geometric mean distance between current units considering the influence of width, and then the mutual inductance and self-inductance between each current unit are calculated. After superposition, the inductance of each irregular-shaped part of the superconducting coil and the total inductance are obtained.

[0045] The following is a detailed explanation of the calculation process of superconducting coil inductance with a specific case. Figure 3 The coil parameter settings are shown in Table 1.

[0046] Table 1 Main structural parameters of superconducting coil

[0047]

[0048] Neumann formula for calculating inductance is:

[0049]

[0050] Where μ0 is the magnetic permeability of vacuum.

[0051] According to the geometric mean distance principle, the geometric mean distance g between two straight lines with width wd and center distance R is line have:

[0052]

[0053] Therefore, the mutual inductance between the current units on the two conductors considering the current distribution in the width direction is:

[0054]

[0055] The analytical formula for calculating the inductance of the superconducting coil is:

[0056]

[0057]

[0058] Where n and m are the number of segments into which the two wires are cut, respectively; R is the center distance between the two wires in the current unit, wd is the width of the current unit, and Δl is the length of the current unit.

[0059] The settings of n and m should make the current unit length be of the same order of magnitude as the superconducting coil tape thickness and the wire spacing (preferably smaller, so that the current unit length is of the same order of magnitude as the superconducting coil tape thickness and the wire spacing).

[0060] Calculated by the above method Figure 3 The superconducting coil inductance is Figure 4 The equivalent circuit model performs a degree of freedom check on the calculation results of the inductance results of each part of the superconducting coil by dividing the current unit into the number of units, as shown in Table 2.

[0061] Table 2 Inductance changes when the number of divisions changes

[0062]

[0063] It can be seen from Table 2 that the number of divisions affects the results within a limited range. When the number of divisions is large enough to make the length Δl of the current unit and the strip thickness th of the same order of magnitude, the correlation is almost zero.

[0064] In order to confirm the results obtained by the calculation method proposed in the present invention (NeumannFormulaGMD), the finite element software COMSOL (FEM) and the mesh-matrix (Mesh-Matrix) method were used to perform calculations and comparisons, as shown in Figure 2. Figure 5When calculating segment inductance, the three methods yielded similar results. However, when calculating the total inductance of 4-turn and 20-turn coils, which involves summing up the results from each segment, the mesh-matrix and proposed methods showed differences of 1.7% and -1.3%, respectively, for the 4-turn coil, and 1.9% and -0.7%, respectively, for the 20-turn coil, compared to the finite element software.

[0065] Table 3 lists the time consumption of calculating all line segments of 4-turn and 20-turn coils using three methods. It can be concluded that the calculation method proposed in the present invention has very obvious advantages.

[0066] Table 3 Time consumption of three methods for calculating the total inductance of 4-turn and 20-turn coils

[0067]

[0068]

[0069] In summary, the present invention combines the Neumann formula and the geometric mean distance principle to simplify the calculation process of superconducting coil inductance while ensuring calculation accuracy. Compared with the finite element method, this fast calculation method occupies fewer computing resources and the modeling process is not complicated. In addition, this method takes into account the influence of current distribution on the cross section of the wire, making the calculation results more accurate. The results show that the combination of the Neumann formula and the geometric mean distance principle can quickly and accurately calculate the inductance of superconducting coils.

[0070] The above description of the embodiments is intended to facilitate understanding and use of the invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to these embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above-described embodiments. Improvements and modifications made by those skilled in the art based on the disclosure of the present invention, without departing from the scope of the present invention, should be within the scope of protection of the present invention.

Claims

1. A method for quickly calculating the inductance of a superconducting coil considering the current distribution in the width direction, characterized in that: The steps include: S1: Target object confirmation: establish a spatial coordinate system for the superconducting coil and determine the path function of the superconducting coil; S2: Current element division: divide the current element based on the geometric dimensions of the strip and coil; S3: Numerical integration: By combining the Neumann formula and the geometric mean distance principle, the geometric mean distance between the current units is first calculated, taking into account the influence of the width. Then, the self-inductance and mutual inductance of each divided current unit are calculated, and then the summation is added to obtain the calculated inductance value of the target superconducting coil. The current element division divides the superconducting coil into a number of straight line current units; The number of segments of the current unit is not less than , where th is the thickness of the superconducting coil strip; The inductance M of the superconducting coil considering the current distribution in the width direction close for: ； ； Where μ0 is the vacuum magnetic permeability, R is the center distance between the two conductors in the current unit, wd is the width of the current unit, Δl is the length of the current unit; n and m are the number of segments into which the two conductors are divided respectively.

2. The method for quickly calculating the inductance of a superconducting coil considering the current distribution in the width direction according to claim 1, characterized in that: The current unit division is determined by the width and thickness of the strip used for the superconducting coil and the size of the superconducting coil to determine the current unit length.

3. The method for quickly calculating the inductance of a superconducting coil considering the current distribution in the width direction according to claim 1, characterized in that: The current unit division is such that the order of magnitude of the length of the current unit is equal to or smaller than the order of magnitude of the thickness of the tape of the superconducting coil and the order of magnitude of the distance between the wires in the superconducting coil.

4. The method for quickly calculating the inductance of a superconducting coil considering the current distribution in the width direction according to claim 3, characterized in that: The current unit division makes the length of the current unit smaller than the thickness of the strip of the superconducting coil and the spacing between the wires in the superconducting coil.

5. The method for quickly calculating the inductance of a superconducting coil considering the current distribution in the width direction according to claim 1, characterized in that: Each turn of the superconducting coil is divided into current units according to the same standard.

6. The method for quickly calculating the inductance of a superconducting coil considering the current distribution in the width direction according to claim 1, characterized in that: The geometric mean distance g between the two conductors in the current unit is line for: ； ； Where R is the center distance between the two wires in the current cell, and wd is the width of the current cell.

7. The method for quickly calculating the inductance of a superconducting coil considering the current distribution in the width direction according to claim 1, characterized in that: Mutual inductance ΔM between current cells considering current distribution in width direction close for: ； ； Where μ0 is the vacuum permeability, R is the center distance between the two wires in the current unit, wd is the width of the current unit, and Δl is the length of the current unit.

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