Analysis method of eddy current loss on a metal plate excited by parallel circular coils

Abstract

This application discloses a method for analyzing eddy current losses on a metal plate under the excitation of a parallel-placed circular coil, relating to the field of eddy current loss calculation. The method includes solving the vector dynamic potential wave equation in cylindrical coordinates to obtain a vector magnetic potential calculation formula; determining the electromagnetic field expression of the space between the circular coil and the metal plate based on the vector magnetic potential calculation formula; ensuring the circular coil is parallel to the metal plate; obtaining the induced voltage expression on the circular coil based on the electromagnetic field expression of the plane containing the circular coil; determining an approximate formula for eddy current losses on a metal plate under the excitation of a parallel-placed circular coil based on the induced voltage expression on the circular coil; and substituting the state data of the circular coil and the metal plate into the approximate formula for eddy current losses on a metal plate under the excitation of a parallel-placed circular coil to obtain the eddy current losses on the metal plate. This application can quickly determine the eddy current losses generated when a circular coil is placed parallel to a metal plate.

Description

Technical Field

[0001] This application relates to the field of eddy current loss calculation, and in particular to a method for analyzing eddy current loss on a metal plate under the excitation of a parallel-placed circular coil. Background Technology

[0002] The lightweight design of offshore flexible DC converter platforms necessitates a compact layout. This compact layout reduces the distance between different devices / equipment, increasing electromagnetic interactions and potentially affecting their normal operation. One aspect is the magnetic clearance issue caused by eddy current losses in reactors. As an essential electrical component in offshore wind power, the leakage magnetic field of reactors can induce eddy currents in the surrounding space, leading to power loss and temperature rise. Therefore, precise analysis of eddy current losses is crucial. Traditional reactors are cylindrical structures perpendicular to the ground. The coil can be considered a turn within the reactor, and the conductor plate can be seen as the reactor's shielding structure or the metal structure laid on the valve hall floor. For hollow reactors without a metal outer shell, their magnetic field distribution characteristics result in a greater impact on the ground.

[0003] Existing techniques for detailed analysis of eddy current losses rely on a combination of experimental and software calculations. However, experiments are time-consuming and labor-intensive, while software calculations are complex, resulting in low computational efficiency. Summary of the Invention

[0004] The purpose of this application is to provide a method for analyzing eddy current losses on a metal plate under the excitation of a parallel-placed circular coil, which can quickly determine the eddy current losses generated when a circular coil is placed in parallel on a metal plate.

[0005] To achieve the above objectives, this application provides the following solution:

[0006] This application provides a method for analyzing eddy current loss on a metal plate under the excitation of a parallel-placed circular coil, comprising: solving the vector dynamic potential fluctuation equation in a cylindrical coordinate system to obtain a vector magnetic potential calculation formula; determining the electromagnetic field expression of the space between the circular coil and the metal plate based on the vector magnetic potential calculation formula; wherein the circular coil is parallel to the metal plate; obtaining the induced voltage expression on the circular coil based on the electromagnetic field expression of the plane where the circular coil is located; determining an approximate formula for eddy current loss on the metal plate under the excitation of a parallel-placed circular coil based on the induced voltage expression on the circular coil; acquiring the state data of the circular coil and the metal plate; and substituting the state data of the circular coil and the metal plate into the approximate formula for eddy current loss on the metal plate under the excitation of a parallel-placed circular coil to obtain the eddy current loss on the metal plate.

[0007] According to the specific embodiments provided in this application, this application has the following technical effects:

[0008] This application provides a method for analyzing eddy current losses on a metal plate under the excitation of a parallel-placed circular coil. An approximate formula for eddy current losses on a metal plate under the excitation of a parallel-placed circular coil is determined. Using this formula, the eddy current losses on the metal plate can be directly calculated, which improves the calculation efficiency and allows for the rapid determination of the eddy current losses generated when a circular coil is placed in parallel on a metal plate. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 A flowchart illustrating a method for analyzing eddy current losses on a metal plate under the excitation of a parallel-placed circular coil, provided as an embodiment of this application;

[0011] Figure 2 A schematic diagram of an eddy current problem model for a metal plate under circular coil excitation, provided in another embodiment of this application;

[0012] Figure 3 A comparison of the formula solution and finite element simulation results for the eddy current loss on an aluminum plate under the excitation of a parallel-placed circular coil, as provided in Example 1 of this application;

[0013] Figure 4 A comparison of the formula solution and finite element simulation results for the eddy current loss on a copper plate under the excitation of a parallel-placed circular coil, as provided in Example 1 of this application;

[0014] Figure 5 Example 2 of this application provides a steel plate (u) with f = 50Hz, I = 2kA, and a = 0.103m. r =300, σ=6×10 6 A schematic diagram comparing the analytical and approximate solutions under (S / m);

[0015] Figure 6 A comparison diagram of analytical and approximate solutions for the aluminum plate with f = 50Hz, I = 2kA, and a = 0.103m provided in Example 2 of this application;

[0016] Figure 7 The graph shows the variation of the conductor-coil distance b of eddy current loss under aluminum plate, copper plate and steel plate for f=50Hz, I=2kA, a=0.103m, as provided in Example 3 of this application.

[0017] Figure 8 Example 4 of this application shows the variation of eddy current loss on an aluminum plate with plate thickness at f = 50 Hz and I = 2 kA.

[0018] Figure 9 Example 4 of this application shows the variation of eddy current loss on an aluminum plate with plate thickness at f = 100 Hz and I = 2 kA.

[0019] Figure 10 Example 4 of this application shows the variation of eddy current loss on an aluminum plate with plate thickness at f = 500 Hz and I = 2 kA.

[0020] Figure 11 The graph shows the variation of eddy current loss on an aluminum plate with plate thickness at f = 1000 Hz and I = 2 kA, as provided in Example 4 of this application. Detailed Implementation

[0021] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] In one exemplary embodiment, such as Figure 1 As shown, a method for analyzing eddy current losses on a metal plate under excitation by a parallel-placed circular coil is provided, including steps 101 to 106. Wherein:

[0024] Step 101: Solve the vector dynamic potential wave equation in cylindrical coordinates to obtain the vector magnetic potential calculation formula.

[0025] Step 102: Determine the electromagnetic field expression of the space between the circular coil and the metal plate according to the vector magnetic potential calculation formula; the circular coil is parallel to the metal plate.

[0026] Step 103: Based on the electromagnetic field expression of the plane containing the circular coil, obtain the expression for the induced voltage on the circular coil.

[0027] Step 104: Based on the expression for the induced voltage on the circular coil, determine the approximate formula for the eddy current loss on the metal plate under the excitation of the parallel-placed circular coil.

[0028] Step 105: Obtain the status data of the circular coil and the metal plate.

[0029] Step 106: Substitute the state data of the circular coil and the metal plate into the approximate formula for eddy current loss on the metal plate under the excitation of the parallel-placed circular coil to obtain the eddy current loss on the metal plate.

[0030] By implementing steps 101 to 106 above, an approximate formula for eddy current loss on a metal plate under the excitation of a parallel-placed circular coil is determined. This formula can be used to directly calculate the eddy current loss on the metal plate, improving calculation efficiency and enabling rapid determination of the eddy current loss generated when a circular coil is placed parallel on a metal plate.

[0031] This application begins with a single-turn design, simplifying the reactor into a circular coil carrying a harmonic current and an infinitely large metal plate parallel to it. The theoretical model is as follows: Figure 1 As shown, multiple turns can be considered as a superposition of single turns; the superposition formula for multiple turns will be given later.

[0032] This application discloses two schemes for determining approximate formulas for eddy current losses on a metal plate under the excitation of parallel-placed circular coils. The first scheme is based on an exact formula for vector magnetic potential, and the second scheme is based on an approximate formula for vector magnetic potential. The two schemes are described in detail below.

[0033] Option 1:

[0034] In another exemplary embodiment of this application, since the vector magnetic potential satisfies the passive wave equation ▽ 2 A+k0 2 If A = 0, then step 101 above can be specifically described as follows: using the method of separation of variables and introducing the Hankel transformation, the vector dynamic potential wave equation is solved in cylindrical coordinates to obtain the precise formula for the vector magnetic potential:

[0035]

[0036] in, Let μ be the vector magnetic potential, μ0 be the free permeability, a be the radius of the circular coil, I be the time-harmonic current passing through the circular coil, λ be the transverse wavenumber, τ0 be the longitudinal wavenumber in the air, J1 be the first-order Bessel function, ρ be the radial distance in cylindrical coordinates, z be the height in cylindrical coordinates, C be the first intermediate parameter, b be the distance from the center of the circular coil to the metal plate, and K be the ratio of the longitudinal wavenumber in the metal plate to the longitudinal wavenumber in the air. r Let t be the relative permeability of the metal plate, t be the thickness of the metal plate, and τ be the longitudinal wavenumber in the metal plate.

[0037]

[0038] K = ττ0;

[0039] μr =μ / μ0;

[0040] C=[(K+μ r ) 2 -(K-μ r ) 2 e -2tτ ] -1 ;

[0041] Where k is the second intermediate parameter, μ is the permeability of the metal plate, σ is the conductivity of the metal plate, j is the imaginary part of the complex frequency domain, ω is the angular frequency, ω=2πf, and f is the time harmonic current frequency on the circular coil.

[0042] For example, such as Figure 1 As shown, c = b + t; c is the farthest distance from the center of the circular coil to the edge of the metal plate.

[0043] In another exemplary embodiment of this application, the electromagnetic field expression for the region between the circular coil and the metal plate can be derived from E = -jωA, B = ▽×A and the basic expression for electromagnetic fields. Therefore, the electromagnetic field expression in step 102 above is:

[0044]

[0045] Among them, E (1) For electromagnetic fields, e φ This represents the electric field intensity component at angle θ in a cylindrical coordinate system. θ is a preset angle in the cylindrical coordinate system.

[0046] In another exemplary embodiment of this application, step 103 described above can be replaced by steps 201 to 202:

[0047] Step 201: Based on the electromagnetic field expression of the plane containing the single-turn circular coil, and using the principle of multiplying the electric field strength of the plane containing the single-turn circular coil by the circumference of the single-turn circular coil to obtain the induced voltage on the single-turn circular coil, the expression for the induced voltage on the single-turn circular coil is obtained as follows:

[0048]

[0049] Where U is the induced voltage on a single-turn circular coil.

[0050] Step 202: Based on the expression for the induced voltage on a single-turn circular coil, and using the superposition principle, the expression for the induced voltage on a multi-turn circular coil is obtained as follows:

[0051]

[0052] Among them, U N The induced voltage on the multi-turn circular coil, a mLet I be the radius of the m-th turn of the circular coil. m Let b be the time-harmonic current passing through the m-th turn of the circular coil. m Let N be the distance from the center of the m-th turn of the circular coil to the metal plate, and N be the number of turns of the circular coil.

[0053] In another exemplary embodiment of this application, step 104 described above can be replaced by steps 301 to 302:

[0054] Step 301: Based on the expression for the induced voltage on a single-turn circular coil, and on the principle that the total complex power equals the induced voltage multiplied by the current in the circular coil and that the eddy current loss on the metal plate is approximately equal to the real part of the total complex power, the approximate formula for the eddy current loss on the metal plate under the excitation of a parallel-placed single-turn circular coil is determined as follows:

[0055]

[0056] Where P is the eddy current loss on the metal plate under the excitation of a parallel single-turn circular coil, and Re is the real part.

[0057] Step 302: Based on the expression for the induced voltage on the multi-turn circular coil, and on the principle that the total complex power equals the induced voltage multiplied by the current of the circular coil and that the eddy current loss on the metal plate is approximately equal to the real part of the total complex power, the approximate formula for the eddy current loss on the metal plate under the excitation of a parallel multi-turn circular coil is determined as follows:

[0058]

[0059] Among them, P N This refers to the eddy current loss on a metal plate under the excitation of a multi-turn circular coil placed in parallel.

[0060] The second option:

[0061] In another exemplary embodiment of this application, step 101 above may further be specifically: solving the vector dynamic potential wave equation in cylindrical coordinates to obtain an approximate formula for the vector magnetic potential:

[0062]

[0063] in, Where μ is the vector magnetic potential, μ0 is the free permeability, and μ r Let be the relative permeability of the metal plate, a be the radius of the circular coil, I be the time harmonic current passing through the circular coil, t be the thickness of the metal plate, τ be the longitudinal wavenumber in the metal plate, λ be the transverse wavenumber, τ0 be the longitudinal wavenumber in the air, J1 be the first-order Bessel function, ρ be the radial distance in the cylindrical coordinate system, z be the height in the cylindrical coordinate system, and b be the distance from the center of the circular coil to the metal plate.

[0064]

[0065] μ r =μ / μ0;

[0066] Where k is the first intermediate parameter, μ is the permeability of the metal plate, σ is the conductivity of the metal plate, j is the imaginary part of the complex frequency domain, ω is the angular frequency, ω=2πf, and f is the time harmonic current frequency on the circular coil.

[0067] In another exemplary embodiment of this application, the electromagnetic field expression in step 102 above is:

[0068]

[0069] Among them, E (1) For electromagnetic fields, e φ Let θ be the electric field intensity component at angle θ in the cylindrical coordinate system.

[0070] In another exemplary embodiment of this application, step 103 described above can be replaced by steps 401 to 402:

[0071] Step 401: Based on the electromagnetic field expression of the plane containing the single-turn circular coil, and using the principle of multiplying the electric field strength of the plane containing the single-turn circular coil by the circumference of the single-turn circular coil to obtain the induced voltage on the single-turn circular coil, the expression for the induced voltage on the single-turn circular coil is obtained as follows:

[0072]

[0073] Where U is the induced voltage on a single-turn circular coil.

[0074] Step 402: Based on the expression for the induced voltage on a single-turn circular coil, and using the superposition principle, the expression for the induced voltage on a multi-turn circular coil is obtained as follows:

[0075]

[0076] Among them, U N The induced voltage on the multi-turn circular coil, a m Let I be the radius of the m-th turn of the circular coil. m Let b be the time-harmonic current passing through the m-th turn of the circular coil. m Let N be the distance from the center of the m-th turn of the circular coil to the metal plate, and N be the number of turns of the circular coil.

[0077] In another exemplary embodiment of this application, step 104 described above can be replaced by steps 501 to 502:

[0078] Step 501: Based on the expression for the induced voltage on a single-turn circular coil, and on the principle that the total complex power equals the induced voltage multiplied by the current in the circular coil and that the eddy current loss on the metal plate is approximately equal to the real part of the total complex power, the approximate formula for the eddy current loss on the metal plate under the excitation of a parallel-placed single-turn circular coil is determined as follows:

[0079]

[0080] Where P is the eddy current loss on the metal plate under the excitation of a parallel single-turn circular coil, and Re is the real part.

[0081] Step 502: Based on the expression for the induced voltage on the multi-turn circular coil, and on the principle that the total complex power equals the induced voltage multiplied by the current of the circular coil and that the eddy current loss on the metal plate is approximately equal to the real part of the total complex power, the approximate formula for the eddy current loss on the metal plate under the excitation of a parallel multi-turn circular coil is determined as follows:

[0082]

[0083] Among them, P N This refers to the eddy current loss on a metal plate under the excitation of a multi-turn circular coil placed in parallel.

[0084] As can be seen from the above two schemes, both involve determining the approximate formulas for eddy current losses on a metal plate under excitation by single-turn and multi-turn circular coils. The following section will briefly introduce the calculation process of eddy current losses, taking single-turn and multi-turn circular coils as examples respectively.

[0085] For a single-turn circular coil:

[0086] Data on a single-turn circular coil and a metal plate are obtained; the data on the single-turn circular coil and the metal plate include: the radius of the circular coil, the distance from the center of the circular coil to the metal plate, the permeability of the metal plate, the dielectric constant of the metal plate, the conductivity of the metal plate, the thickness of the metal plate, and the frequency of the harmonic current on the coil; the circular coil and the metal plate are placed in parallel;

[0087] Substituting the data of the circular coil and the metal plate into the approximate formula for eddy current loss on the metal plate under the excitation of a parallel single-turn circular coil, the eddy current loss on the metal plate is obtained.

[0088] The method for confirming the approximate formula for eddy current loss on a metal plate under the excitation of a parallel-placed circular coil is as follows:

[0089] Solving the vector dynamic potential wave equation in cylindrical coordinates allows us to derive the electromagnetic field expressions for various regions of space.

[0090] The electric field strength of the plane containing the coil multiplied by the circumference of the coil can be used to obtain the induced voltage on the coil.

[0091] When the frequency is low, the radiated power is ignored, and the approximate formula for eddy current loss on the metal plate is obtained from the complex power formula.

[0092] For multi-turn circular coils:

[0093] In addition to obtaining the data for each single-turn circular coil and metal plate, it is also necessary to obtain the number of turns of the circular coil.

[0094] The induced voltage on the multi-turn circular coil is obtained by using the superposition principle;

[0095] The total complex power emitted by a multi-turn circular coil is equal to the induced voltage multiplied by the coil current;

[0096] When the frequency is low, the radiated power is ignored, and the approximate formula for eddy current loss on the metal plate is obtained from the complex power formula.

[0097] In another exemplary embodiment of this application, the state data of the circular coil and the metal plate in step 105 above include: the radius of the circular coil, the distance from the center of the circular coil to the metal plate, the permeability of the metal plate, the dielectric constant of the metal plate, the conductivity of the metal plate, the thickness of the metal plate, and the time harmonic current frequency on the circular coil.

[0098] The following four examples verify the effectiveness of the above-described method for analyzing eddy current losses on a metal plate under the excitation of parallel-placed circular coils.

[0099] Example 1:

[0100] Please see again Figure 2 A circular coil and a metal plate are placed parallel to each other. A coordinate system is established with the center of the circular coil as the origin of a spatial rectangular coordinate system, the xoy plane containing the circular coil, and the straight line connecting the center of the circular coil and the distance to the metal plate as the z-axis. The radius of the circular coil is a = 0.103 m, and a time-harmonic current with a frequency f of 50 Hz and a magnitude I of 2 kA flows through the circular coil.

[0101] Figure 3 The conductivity of the aluminum plate (σ = 3.7 × 10⁻⁶) is given. 7 S / m, relative permeability μ r =1) The variation of eddy current loss with the distance b between the metal plate and the coil (normalized by a); Figure 4 The conductivity of the copper plate (σ = 5.8 × 10⁻⁶) is given. 7 S / m, relative permeability μ r =1) The eddy current loss varies with the distance b (normalized by a) between the metal plate and the coil. The formula and finite element simulation results are consistent and good for both metal plate materials.

[0102] Example 2:

[0103] Please see again Figure 2 A circular coil and a metal plate are placed parallel to each other. A coordinate system is established with the center of the circular coil as the origin of a spatial rectangular coordinate system, the xoy plane containing the circular coil, and the straight line connecting the center of the circular coil and the distance to the metal plate as the z-axis. The radius of the circular coil is a = 0.103 m, and a time-harmonic current with a frequency f of 50 Hz and a magnitude I of 2 kA flows through the circular coil.

[0104] Figure 5 The steel plate (conductivity σ = 6 × 10⁻⁶) is given. 6 S / m, relative permeability μ r =300) Vector magnetic potential ratio (analytical solution / approximate solution) varies with thickness / penetration depth; Figure 6 The conductivity of the aluminum plate (σ = 3.7 × 10⁻⁶) is given. 7 S / m, relative permeability μ r =1) The variation of the vector magnetic potential ratio (analytical solution / approximate solution) with thickness / penetration depth. For both materials, the ratio of the analytical solution to the approximate solution is almost 1, proving that the approximate formula is almost equivalent to the analytical formula, and the calculation is simpler.

[0105] Example 3:

[0106] Please see again Figure 2 A circular coil and a metal plate are placed parallel to each other. A coordinate system is established with the center of the circular coil as the origin of a spatial rectangular coordinate system, the xoy plane containing the circular coil, and the straight line connecting the center of the circular coil and the distance to the metal plate as the z-axis. The radius of the circular coil is a = 0.103 m, and a time-harmonic current with a frequency f of 50 Hz and a magnitude I of 2 kA flows through the circular coil.

[0107] Figure 7 The variation of eddy current loss "conductor plate-coil" distance b (normalized by a) under aluminum, copper, and steel plates is given. It can be seen that the eddy current loss is higher for non-magnetic materials than for magnetic materials, and the rate of decrease of eddy current loss is also slower for non-magnetic materials.

[0108] Example 4:

[0109] Please see again Figure 2 A circular coil and a metal plate are placed parallel to each other. A coordinate system is established with the center of the circular coil as the origin of a spatial rectangular coordinate system, the xoy plane containing the circular coil, and the straight line between the center of the circular coil and the distance to the metal plate as the z-axis. The metal plate is made of aluminum (conductivity σ = 3.7 × 10⁻⁶). 7 S / m, relative permeability μ r =1), the radius of the circular coil is a = 0.103m, the distance from the center of the circular coil to the metal plate is b = 0.0515m, and the magnitude of the time harmonic current I in the circular coil is 2kA.

[0110] Figures 8 to 11 The changes in eddy current loss with plate thickness when currents of four frequencies (50Hz, 100Hz, 500Hz, and 1000Hz) are applied to a circular coil are presented. It can be seen that when the material is aluminum, the eddy current loss first increases with thickness, reaching a peak at 0.15 times the penetration depth, then decreases and tends to stabilize at 0.8 times the penetration depth. Furthermore, the peak value of eddy current loss increases with frequency; and the frequency change has little effect on the stable point of eddy current loss.

[0111] This application performs analytical calculation and characteristic analysis on eddy current loss on a metal plate under the excitation of a parallel-placed circular coil. For the configuration of the circular coil parallel to an infinitely large conductor plate, an integral formula for the total power of eddy current loss in the conductor plate is derived, which can quickly determine the eddy current loss generated when the circular coil is placed parallel to the metal plate.

[0112] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0113] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for analyzing eddy current losses on a metal plate under the excitation of parallel-placed circular coils, characterized in that, include: The vector dynamic potential wave equation is solved in cylindrical coordinates to obtain the vector magnetic potential calculation formula. The electromagnetic field expression of the space between the circular coil and the metal plate is determined according to the vector magnetic potential calculation formula; the circular coil is parallel to the metal plate. Based on the electromagnetic field expression of the plane containing the circular coil, the expression for the induced voltage on the circular coil is obtained; Based on the expression for the induced voltage on the circular coil, determine the approximate formula for the eddy current loss on the metal plate under the excitation of the parallel-placed circular coil; Acquire the state data of the circular coil and the metal plate; Substituting the state data of the circular coil and the metal plate into the approximate formula for eddy current loss on the metal plate under the excitation of the parallel-placed circular coil, the eddy current loss on the metal plate is obtained.

2. The method for analyzing eddy current losses on a metal plate under the excitation of a parallel-placed circular coil as described in claim 1, characterized in that, Solving the vector dynamic potential wave equation in cylindrical coordinates yields the formula for calculating vector magnetic potential, which includes: By employing the method of separation of variables and introducing the Hankel transform, the vector dynamic potential wave equation is solved in cylindrical coordinates, yielding the precise formula for the vector magnetic potential: in, Let μ be the vector magnetic potential, μ0 be the free permeability, a be the radius of the circular coil, I be the time-harmonic current passing through the circular coil, λ be the transverse wavenumber, τ0 be the longitudinal wavenumber in the air, J1 be the first-order Bessel function, ρ be the radial distance in cylindrical coordinates, z be the height in cylindrical coordinates, C be the first intermediate parameter, b be the distance from the center of the circular coil to the metal plate, and K be the ratio of the longitudinal wavenumber in the metal plate to the longitudinal wavenumber in the air. r Let t be the relative permeability of the metal plate, t be the thickness of the metal plate, and τ be the longitudinal wavenumber in the metal plate. K = ττ0; m r =mm0; C=[(K+μ r ) 2 -(K-m r ) 2 e -2tτ ] -1 ; Where k is the second intermediate parameter, μ is the permeability of the metal plate, σ is the conductivity of the metal plate, j is the imaginary part of the complex frequency domain, ω is the angular frequency, ω=2πf, and f is the time harmonic current frequency on the circular coil.

3. The method for analyzing eddy current losses on a metal plate under the excitation of a parallel-placed circular coil as described in claim 2, characterized in that, The electromagnetic field expression is: Among them, E (1) For electromagnetic fields, e φ Let θ be the electric field intensity component at angle θ in the cylindrical coordinate system.

4. The method for analyzing eddy current losses on a metal plate under the excitation of a parallel-placed circular coil as described in claim 3, characterized in that, Based on the electromagnetic field expression of the plane containing the circular coil, the expression for the induced voltage on the circular coil is obtained, specifically including: Based on the electromagnetic field expression of the plane containing the single-turn circular coil, and using the principle of multiplying the electric field strength of the plane containing the single-turn circular coil by the circumference of the single-turn circular coil to obtain the induced voltage on the single-turn circular coil, the expression for the induced voltage on the single-turn circular coil is obtained as follows: Where U is the induced voltage on a single-turn circular coil; Based on the expression for the induced voltage on a single-turn circular coil, and using the superposition principle, the expression for the induced voltage on a multi-turn circular coil is obtained as follows: Among them, U N The induced voltage on the multi-turn circular coil, a m Let I be the radius of the m-th turn of the circular coil. m Let b be the time-harmonic current passing through the m-th turn of the circular coil. m Let N be the distance from the center of the m-th turn of the circular coil to the metal plate, and N be the number of turns of the circular coil.

5. The method for analyzing eddy current losses on a metal plate under the excitation of a parallel-placed circular coil as described in claim 4, characterized in that, Based on the expression for the induced voltage on a circular coil, an approximate formula for the eddy current loss on a metal plate under excitation by a parallel-placed circular coil is determined, specifically including: Based on the expression for the induced voltage on a single-turn circular coil, and on the principle that the total complex power equals the induced voltage multiplied by the current in the circular coil and that the eddy current loss on the metal plate is approximately equal to the real part of the total complex power, the approximate formula for the eddy current loss on the metal plate under the excitation of a parallel-placed single-turn circular coil is determined as follows: Where P is the eddy current loss on the metal plate under the excitation of a parallel single-turn circular coil, and Re is the real part; Based on the expression for the induced voltage on a multi-turn circular coil, and on the principle that the total complex power equals the induced voltage multiplied by the current in the circular coil and that the eddy current loss on the metal plate is approximately equal to the real part of the total complex power, the approximate formula for the eddy current loss on the metal plate under the excitation of a parallel multi-turn circular coil is determined as follows: Among them, P N This refers to the eddy current loss on a metal plate under the excitation of a multi-turn circular coil placed in parallel.

6. The method for analyzing eddy current losses on a metal plate under the excitation of a parallel-placed circular coil as described in claim 1, characterized in that, Solving the vector dynamic potential wave equation in cylindrical coordinates yields the formula for calculating vector magnetic potential, which includes: Solving the dynamic potential wave equation in cylindrical coordinates yields an approximate formula for the vector magnetic potential: in, Where μ is the vector magnetic potential, μ0 is the free permeability, and μ r Let be the relative permeability of the metal plate, a be the radius of the circular coil, I be the time harmonic current passing through the circular coil, t be the thickness of the metal plate, τ be the longitudinal wavenumber in the metal plate, λ be the transverse wavenumber, τ0 be the longitudinal wavenumber in the air, J1 be the first-order Bessel function, ρ be the radial distance in the cylindrical coordinate system, z be the height in the cylindrical coordinate system, and b be the distance from the center of the circular coil to the metal plate. m r =μ / μ0; Where k is the first intermediate parameter, μ is the permeability of the metal plate, σ is the conductivity of the metal plate, j is the imaginary part of the complex frequency domain, ω is the angular frequency, ω=2πf, and f is the time harmonic current frequency on the circular coil.

7. The method for analyzing eddy current losses on a metal plate under the excitation of parallel-placed circular coils according to claim 6, characterized in that, The electromagnetic field expression is: Among them, E (1) For electromagnetic fields, e φ Let θ be the electric field intensity component at angle θ in the cylindrical coordinate system.

8. The method for analyzing eddy current losses on a metal plate under the excitation of parallel-placed circular coils according to claim 7, characterized in that, Based on the electromagnetic field expression of the plane containing the circular coil, the expression for the induced voltage on the circular coil is obtained, specifically including: Based on the electromagnetic field expression of the plane containing the single-turn circular coil, and using the principle of multiplying the electric field strength of the plane containing the single-turn circular coil by the circumference of the single-turn circular coil to obtain the induced voltage on the single-turn circular coil, the expression for the induced voltage on the single-turn circular coil is obtained as follows: Where U is the induced voltage on a single-turn circular coil; Based on the expression for the induced voltage on a single-turn circular coil, and using the superposition principle, the expression for the induced voltage on a multi-turn circular coil is obtained as follows: Among them, U N The induced voltage on the multi-turn circular coil, a m Let I be the radius of the m-th turn of the circular coil. m Let b be the time-harmonic current passing through the m-th turn of the circular coil. m Let N be the distance from the center of the m-th turn of the circular coil to the metal plate, and N be the number of turns of the circular coil.

9. The method for analyzing eddy current losses on a metal plate under the excitation of a parallel-placed circular coil as described in claim 8, characterized in that, Based on the expression for the induced voltage on a circular coil, an approximate formula for the eddy current loss on a metal plate under excitation by a parallel-placed circular coil is determined, specifically including: Based on the expression for the induced voltage on a single-turn circular coil, and on the principle that the total complex power equals the induced voltage multiplied by the current in the circular coil and that the eddy current loss on the metal plate is approximately equal to the real part of the total complex power, the approximate formula for the eddy current loss on the metal plate under the excitation of a parallel-placed single-turn circular coil is determined as follows: Where P is the eddy current loss on the metal plate under the excitation of a parallel single-turn circular coil, and Re is the real part; Based on the expression for the induced voltage on a multi-turn circular coil, and on the principle that the total complex power equals the induced voltage multiplied by the current in the circular coil and that the eddy current loss on the metal plate is approximately equal to the real part of the total complex power, the approximate formula for the eddy current loss on the metal plate under the excitation of a parallel multi-turn circular coil is determined as follows: Among them, P N This refers to the eddy current loss on a metal plate under the excitation of a multi-turn circular coil placed in parallel.

10. The method for analyzing eddy current losses on a metal plate under the excitation of a parallel-placed circular coil as described in claim 1, characterized in that, The state data of the circular coil and the metal plate include: the radius of the circular coil, the distance from the center of the circular coil to the metal plate, the permeability of the metal plate, the dielectric constant of the metal plate, the conductivity of the metal plate, the thickness of the metal plate, and the time harmonic current frequency on the circular coil.

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