Superconducting coil inductance rapid calculation method considering current distribution in width direction

Abstract

The invention relates to an inductance calculation method, in particular to a superconducting coil inductance rapid calculation method considering width direction current distribution, comprising the following steps: S1, target object confirmation: establishing a space coordinate system for a superconducting coil, and determining a path function of the superconducting coil; s2, dividing current units: dividing the current units based on the geometric dimensions of the strip and the coil; and S3, numerical integration: by combining a Neumann formula and a geometric mean distance principle, firstly calculating a geometric mean distance considering width influence between the current units, then calculating self-inductance and mutual inductance of each divided current unit, and carrying out superposition and summation to obtain an inductance calculation value of the target superconducting coil. Compared with the prior art, the method has the advantages that the defect that the calculation amount is great when current distribution in the width direction is considered in the prior art is overcome, the calculation process of the inductance of the superconducting coil is simplified, and meanwhile the calculation precision is guaranteed.

Description

Technical Field

[0001] The invention relates to an inductance calculation method, and in particular to a superconducting coil inductance fast calculation method considering current distribution in a width direction. Background Art

[0002] The calculation of coil inductance is of great significance in electrical engineering and is widely related to electrical equipment design, magnetic field generation and wireless power transmission. In superconductivity research, superconducting coils are considered to be one of the most basic devices, and their inductance value is closely related to power loss, charging and discharging performance of magnets and other parameter characteristics. The thickness of superconducting tape is very small, and the turn spacing during winding is very close, so the calculation of inductance should consider the influence of current distribution. There are many methods to calculate the inductance of superconducting coils, including finite element method (FEM), Newman formula and flux accumulation method. The finite element method and Newman formula can calculate the inductance of segmented wires, while the flux accumulation method can only calculate the inductance of coils with complete circuits. Finite element can intuitively construct a two-dimensional or three-dimensional model of the coil and calculate the inductance with the help of finite element software, but its modeling steps are complicated and require high computing resources. Compared with finite element, Newman formula can calculate the inductance of various complex shapes of coils with known path functions, so the modeling process is simpler. Newman formula uses numerical integration to calculate inductance, so it only involves the accumulation of numerical summation and occupies less computing resources.

[0003] After searching, it is found that the existing public patents and documents related to the fast method for calculating the inductance of superconducting coils all have the inconveniences mentioned above. The main contents of typical documents 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 in this document is actually the flux accumulation method, that is, the mutual inductance value is obtained by integrating the induced magnetic induction intensity of the original coil in the area surrounded by the target coil and dividing it by the source current. This method can only calculate the mutual inductance or self-inductance of a coil with a complete loop, and cannot calculate the inductance of an irregularly shaped wire with a finite length, which does not meet the needs of the equivalent circuit model of an uninsulated coil. At the same time, this method regards the current as a current element line without thickness on the center line of the wire, and does not consider the influence of the current distribution in the width direction 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 in this document uses the Neumann formula, which involves the distribution of current in the width direction and focuses on the accurate and fast calculation of the inductance of each part of each turn of the superconducting coil. By treating the entire coil as a single-turn coil, the current is evenly distributed on the cross-section of the wire, with the aim of further accurately calculating the total inductance of the entire coil and the mutual inductance between coils, which is similar to the existing mesh-matrix calculation method. In order to ensure the calculation accuracy, this document divides a large number of grids, and the amount of calculation is very large. Although there are some simplification methods, the most basic grid calculation unit cannot be simplified, so there are great requirements for computing resources.

[0008] Since the conducting cross-section of the superconducting tape has a large aspect ratio, the distribution of current will have a great impact on the inductance. Using the existing calculation method to further divide the current element line along the width direction of the superconducting tape for calculation will increase the amount of calculation, so a method with high accuracy and fast calculation of the inductance of superconducting coils with a large number of 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 to 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 solve the defect of the existing technology that the amount of calculation is extremely large when considering the current distribution in the width direction. This scheme 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 considering 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 the current units considering the influence of width is first calculated, and then the self-inductance and mutual inductance of each divided current unit are calculated, and then the inductance calculation value of the target superconducting coil is obtained by superimposing and summing.

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

[0016] Preferably, the current unit division is performed by determining the current unit length 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 strip of the superconducting coil and the order of magnitude of the wire spacing 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 strip of the superconducting coil and the order of magnitude of the spacing between the wires in the superconducting coil.

[0019] The length of the divided current unit should be the same or smaller than the thickness of the superconducting tape in order to balance the accuracy and speed of the calculation. For specific division rules or methods, please refer to CLV 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 tape.

[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 unit, and wd is the width of the current unit.

[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 magnetic 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 wires 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 wires are divided respectively.

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

[0032] The specific implementation of the present invention is to combine the Neumann formula and the geometric mean distance principle to simplify the calculation process of the superconducting coil inductance and obtain the inductance matrix of the equivalent circuit model. Compared with the finite element method, this fast calculation method occupies less computing resources and the modeling process is not complicated. In addition, the method takes into account the influence of the current distribution of the wire cross section on the inductance, making the calculation result more accurate, indicating that the Neumann formula combined with the geometric mean distance principle can quickly and accurately calculate the inductance. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0034] Figure 2 It is a flowchart of a method for fast calculation of superconducting coil inductance;

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

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

[0037] Figure 5 The results of the fast calculation method of the superconducting coil inductance of the present invention in Example 1 are compared with the calculation method of the prior art. DETAILED DESCRIPTION

[0038] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. The following embodiments are implemented on the premise of the technical solution of the present invention, and detailed implementation methods and specific operation processes are given. It should be pointed out that, for those of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope 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 for calculating complex paths is shown in the figure, and a fast calculation method for the inductance of a superconducting coil considering the current distribution in the width direction is proposed, such as Figure 2 shown.

[0042] Firstly, 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 according to 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 the current units 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 a width of wd and a center distance of 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 setting 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 an order of magnitude smaller than 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 verifies the degree of freedom of the calculation results by dividing the inductance results of each part of the superconducting coil into current 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 will affect the results within a limited range. When the number of divisions is large enough to be of the same order of magnitude as the length Δl of the current unit and the strip thickness th, 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 for calculation comparison, as shown in FIG. Figure 5As shown. When calculating the line segment inductance, the three methods obtain similar results. When calculating the total inductance of the 4-turn and 20-turn coils, that is, adding up the results of each segment, compared with the finite element software, the mesh-matrix and the calculation method proposed by the present invention have a difference of 1.7% and -1.3% in the calculation of the 4-turn coil, and a difference of 1.9% and -0.7% in the calculation of the 20-turn coil.

[0065] Table 3 lists the time consumption of calculating all line segments of 4-turn and 20-turn coils by 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 in 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 the superconducting coil inductance while ensuring the calculation accuracy. Compared with the finite element method, this fast calculation method occupies less computing resources and the modeling process is not complicated. In addition, the method takes into account the influence of current distribution on the wire cross section, making the calculation result more accurate. The results show that the combination of the Neumann formula and the geometric mean distance principle can quickly and accurately calculate the superconducting coil inductance.

[0070] The above description of the embodiments is to facilitate the understanding and use of the invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to these embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments, and 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 fast calculation method for superconducting coil inductance 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 unit 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 considering the influence of width is first calculated, and then the self-inductance and mutual inductance of each divided current unit are calculated, and then the inductance calculation value of the target superconducting coil is obtained by superimposing and summing.

2. A 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 element division divides the superconducting coil into a plurality of straight line segment current units.

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 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.

4. 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 wire spacing 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 4, characterized in that: The current unit division makes the length of the current unit smaller than the thickness of the tape of the superconducting coil and the distance between the wires in the superconducting coil.

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 number of segments of the current unit is not less than Where th is the thickness of the superconducting coil tape.

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: Each turn of the superconducting coil is divided into current units according to the same standard.

8. 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 unit, and wd is the width of the current unit.

9. 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 magnetic 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.

10. 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 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 wires 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 wires are divided respectively.

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