Method for analyzing eddy current loss on metal flat plate under excitation of parallel circular ring coils

Abstract

The invention discloses a method for analyzing eddy-current loss on a metal flat plate under excitation of parallel circular ring coils, and relates to the field of eddy-current loss calculation. The method comprises the following steps: solving a vector dynamic potential wave equation under a cylindrical coordinate system to obtain a vector magnetic potential calculation formula; determining an electromagnetic field expression of a space between the circular ring coil and the metal flat plate according to a vector magnetic potential calculation formula; the circular coil is parallel to the metal plate; obtaining an induced voltage expression on the ring coil according to the electromagnetic field expression of the plane where the ring coil is located; determining an eddy-current loss approximation formula on the metal flat plate under the excitation of the parallel circular ring coils according to an induced voltage expression on the circular ring coils; and substituting the state data of the circular ring coil and the metal flat plate into an eddy-current loss approximation formula on the metal flat plate under the excitation of the parallel circular ring coil to obtain the eddy-current loss on the metal flat plate. The eddy-current loss generated when the circular ring coil is placed on the metal flat plate in parallel can be rapidly determined.

Description

Technical Field

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

[0002] The lightweight design of the offshore flexible direct current commutation platform requires the compact layout of the entire platform. Compact layout means that the distance between different devices / equipment is reduced, which increases the mutual electromagnetic interaction, which may affect the normal operation of each other. One aspect is the magnetic clearance problem caused by the eddy current loss of the reactor. As an indispensable power equipment for offshore wind power, the leakage magnetic field of the reactor may induce eddy currents in the surrounding space, causing power loss and temperature rise, so the eddy current loss needs to be carefully analyzed. The traditional reactor is a cylindrical structure and is vertical to the ground. The coil can be regarded as a turn in the reactor, and the conductor plate can be regarded as the shielding structure of the reactor, or the metal structure laid on the valve hall floor. For this kind of hollow reactor without a metal casing, due to the characteristics of its magnetic field distribution, it has a greater impact on the ground.

[0003] The existing fine analysis technology of eddy current loss is obtained by experiments and software calculations. However, the experiments are time-consuming and laborious, and the software calculations are difficult, resulting in low calculation efficiency. Summary of the invention

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

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

[0006] The present application provides a method for analyzing eddy current losses on a metal plate under the excitation of parallel-placed circular coils, comprising: solving a vector dynamic potential wave equation in a cylindrical coordinate system to obtain a vector magnetic potential calculation formula; determining an electromagnetic field expression in 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; obtaining an induced voltage expression on the circular coil according to the electromagnetic field expression of the plane where the circular coil is located; determining an approximate formula for eddy current losses on the metal plate under the excitation of parallel-placed circular coils according to the induced voltage expression on the circular coil; obtaining 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 losses on the metal plate under the excitation of the parallel-placed circular coils to obtain eddy current losses on the metal plate.

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

[0008] The present application provides a method for analyzing eddy current losses on a metal plate under the excitation of parallel-placed circular coils, determines an approximate formula for eddy current losses on a metal plate under the excitation of parallel-placed circular coils, and uses the formula to directly calculate the eddy current losses on the metal plate, thereby improving the calculation efficiency and quickly determining the eddy current losses generated when parallel-placed circular coils are placed on the metal plate. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0010] Figure 1 A schematic flow chart of a method for analyzing eddy current losses on a metal plate under excitation by parallel-placed circular coils provided in one embodiment of the present application;

[0011] Figure 2 A schematic diagram of a model of eddy current problems of a metal plate under the excitation of a circular coil provided in another embodiment of the present application;

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

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

[0014] Figure 5 f=50Hz,I=2kA,a=0.103m steel plate (u r =300,σ=6×10 6 S / m) under the analytical solution and the approximate solution;

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

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

[0017] Figure 8 f=50Hz, I=2kA, graph of eddy current loss on aluminum plate as a function of plate thickness provided in Example 4 of this application;

[0018] Fig. 9 The graph of f=100 Hz, I=2 kA, and the variation of eddy current loss on the aluminum plate with the plate thickness provided in Example 4 of the present application;

[0019] Fig.10 f=500Hz, I=2kA, graph of eddy current loss on aluminum plate as a function of plate thickness provided in Example 4 of this application;

[0020] Fig.11 Example 4 of this application provides a graph of f=1000 Hz, I=2kA, and eddy current loss on an aluminum plate as a function of plate thickness. DETAILED DESCRIPTION

[0021] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0022] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0023] In an exemplary embodiment, Figure 1 As shown, a method for analyzing eddy current loss on a metal plate under excitation of parallel placed circular coils is provided, comprising the following steps 101 to 106. Among them:

[0024] Step 101: Solve the vector dynamic potential wave equation in a cylindrical coordinate system to obtain a 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: Obtain an induced voltage expression on the circular coil according to the electromagnetic field expression of the plane where the circular coil is located.

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

[0028] Step 105: Acquire status data of the annular coil and the metal plate.

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

[0030] By implementing the above steps 101 to 106, an approximate formula for eddy current loss on a metal plate under excitation by parallel-placed circular coils is determined. The formula can be used to directly calculate the eddy current loss on the metal plate, thereby improving the calculation efficiency and quickly determining the eddy current loss generated when parallel-placed circular coils are placed on the metal plate.

[0031] This application starts with a single turn and simplifies the reactor into a circular coil with a time-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 regarded as the superposition of single turns; the superposition formula for multiple turns will be given later.

[0032] The present application discloses two schemes for determining the approximate formula of eddy current loss on a metal plate under the excitation of a parallel-placed circular coil. The first scheme is determined based on the precise formula of the vector magnetic potential, and the second scheme is determined based on the approximate formula of the vector magnetic potential. The two schemes are introduced in detail below.

[0033] The first option:

[0034] In another exemplary embodiment of the present application, since the vector magnetic potential satisfies the passive wave equation ▽ 2 A+k0 2 A=0, then the above step 101 can be specifically as follows: adopt the separation of variables method and introduce Hankel transformation to solve the vector dynamic potential wave equation in the cylindrical coordinate system, and obtain the precise formula of the vector magnetic potential:

[0035]

[0036] in, is the vector magnetic potential, μ0 is the vacuum permeability, a is the radius of the ring coil, I is the time-harmonic current passing through the ring coil, λ is the transverse wave number, τ0 is the longitudinal wave number in the air, J1 is the first-order Bessel function, ρ is the radial distance in the cylindrical coordinate system, z is the height in the cylindrical coordinate system, C is the first intermediate parameter, b is the distance from the center of the ring coil to the metal plate, K is the ratio of the longitudinal wave number in the metal plate to the longitudinal wave number in the air, μ r is the relative magnetic permeability of the metal plate, t is the thickness of the metal plate, and τ is the longitudinal wave number 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] Wherein, k is the second intermediate parameter, μ is the magnetic permeability of the metal plate, σ is the electrical conductivity of the metal plate, j is the imaginary part in the complex frequency domain, ω is the angular frequency, ω=2πf, and f is the time-harmonic current frequency on the toroidal coil.

[0042] For example, 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 the present application, the electromagnetic field expression of the area between the circular coil and the metal plate can be derived from E=-jωA, B=▽×A and the basic electromagnetic field expression. Then the electromagnetic field expression in the above step 102 is:

[0044]

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

[0046] In another exemplary embodiment of the present application, the above step 103 may be replaced by the following steps 201 to 202:

[0047] Step 201: According to the electromagnetic field expression of the plane where the single-turn circular coil is located, based on the principle that the induced voltage on the single-turn circular coil is obtained by multiplying the electric field strength on the plane where the single-turn circular coil is located by the circumference of the single-turn circular coil, the induced voltage expression on the single-turn circular coil is obtained as follows:

[0048]

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

[0050] Step 202: According to the induced voltage expression on the single-turn toroidal coil, based on the superposition principle, the induced voltage expression on the multi-turn toroidal coil is obtained as follows:

[0051]

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

[0053] In another exemplary embodiment of the present application, the above step 104 may be replaced by the following steps 301 to 302:

[0054] Step 301: According to the expression of the induced voltage on the single-turn toroidal coil, based on the principle that the total complex power is equal to the induced voltage multiplied by the toroidal coil current and 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 the parallel placed single-turn toroidal coil is determined as:

[0055]

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

[0057] Step 302: According to the expression of the induced voltage on the multi-turn toroidal coil, based on the principle that the total complex power is equal to the induced voltage multiplied by the toroidal coil current and 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 the parallel multi-turn toroidal coil is determined as:

[0058]

[0059] Among them, P N Eddy current losses on a metal plate excited by parallel multi-turn toroidal coils.

[0060] Second option:

[0061] In another exemplary embodiment of the present application, the above step 101 may also be specifically as follows: solving the vector dynamic potential wave equation in a cylindrical coordinate system to obtain an approximate formula for the vector magnetic potential:

[0062]

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

[0064]

[0065] μ r =μ / μ0;

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

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

[0068]

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

[0070] In another exemplary embodiment of the present application, the above step 103 may be replaced by the following steps 401 to 402:

[0071] Step 401: According to the electromagnetic field expression of the plane where the single-turn circular coil is located, based on the principle that the induced voltage on the single-turn circular coil is obtained by multiplying the electric field strength on the plane where the single-turn circular coil is located by the circumference of the single-turn circular coil, the induced voltage expression on the single-turn circular coil is obtained as follows:

[0072]

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

[0074] Step 402: According to the induced voltage expression on the single-turn toroidal coil, based on the superposition principle, the induced voltage expression on the multi-turn toroidal coil is obtained as follows:

[0075]

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

[0077] In another exemplary embodiment of the present application, the above step 104 may be replaced by the following steps 501 to 502:

[0078] Step 501: According to the expression of the induced voltage on the single-turn toroidal coil, based on the principle that the total complex power is equal to the induced voltage multiplied by the toroidal coil current and 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 the parallel placed single-turn toroidal coil is determined as:

[0079]

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

[0081] Step 502: According to the expression of the induced voltage on the multi-turn toroidal coil, based on the principle that the total complex power is equal to the induced voltage multiplied by the toroidal coil current and 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 the parallel multi-turn toroidal coil is determined as:

[0082]

[0083] Among them, P N Eddy current losses on a metal plate excited by parallel multi-turn toroidal coils.

[0084] It can be seen from the above two schemes that both involve the determination of the approximate formula for eddy current loss on a metal plate under the excitation of a single-turn toroidal coil and a multi-turn toroidal coil. The following introduces the brief process of eddy current loss calculation, taking a single-turn toroidal coil and a multi-turn toroidal coil as the objects respectively.

[0085] For a single-turn toroidal coil:

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

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

[0088] Among them, the confirmation method of the approximate formula of eddy current loss on the metal plate under the excitation of parallel placed circular coils is:

[0089] Solve the vector dynamic potential wave equation in the cylindrical coordinate system, and then derive the electromagnetic field expression of each region in the space;

[0090] The induced voltage on the current coil can be obtained by multiplying the electric field strength in the plane of the coil by the circumference of the coil;

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

[0092] For a multi-turn toroidal coil:

[0093] In addition to obtaining the data of each single-turn toroidal coil and metal plate, the number of turns of the toroidal coil also needs to be obtained.

[0094] Using the superposition principle, the induced voltage on the multi-turn toroidal coil is obtained;

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

[0096] When the frequency is low, the radiation 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 the present application, the status data of the annular coil and the metal plate in the above step 105 include: the radius of the annular coil, the distance from the center of the annular coil to the metal plate, the magnetic permeability of the metal plate, the dielectric constant of the metal plate, the electrical conductivity of the metal plate, the thickness of the metal plate and the time-harmonic current frequency on the annular coil.

[0098] Four examples are given below to verify the effectiveness of the above-mentioned eddy current loss analysis method on a metal plate under the excitation of parallel placed circular coils.

[0099] Example 1:

[0100] Still see Figure 2 The circular coil and the metal plate are placed in parallel, and the center of the circular coil is used as the origin of the spatial rectangular coordinate system. The coordinate system is established with the xoy plane where the circular coil is located and the straight line between the center of the circular coil and the metal plate as the z axis. The radius of the circular coil is a = 0.103m, and the circular coil is passed with a time-harmonic current of 50Hz and 2kA.

[0101] Figure 3 The aluminum plate (conductivity σ = 3.7 × 10 7 S / m, relative magnetic permeability μ r =1) Eddy current loss changes with the distance b (normalized by a) from the metal plate to the coil; Figure 4 The copper plate (conductivity σ = 5.8 × 10 7 S / m, relative magnetic permeability μ r =1) The eddy current loss changes with the "metal plate-coil" distance b (normalized by a). The formula and finite element simulation results are in good agreement for the two metal plate materials.

[0102] Example 2:

[0103] Still see Figure 2 The circular coil and the metal plate are placed in parallel, and the center of the circular coil is used as the origin of the spatial rectangular coordinate system. The coordinate system is established with the xoy plane where the circular coil is located and the straight line between the center of the circular coil and the metal plate as the z axis. The radius of the circular coil is a = 0.103m, and the circular coil is passed with a time-harmonic current of 50Hz and 2kA.

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

[0105] Example 3:

[0106] Still see Figure 2 The circular coil and the metal plate are placed in parallel, and the center of the circular coil is used as the origin of the spatial rectangular coordinate system. The coordinate system is established with the xoy plane where the circular coil is located and the straight line between the center of the circular coil and the metal plate as the z axis. The radius of the circular coil is a = 0.103m, and the circular coil is passed with a time-harmonic current of 50Hz and 2kA.

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

[0108] Example 4:

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

[0110] Figures 8 to 11 The variation of the aluminum plate with the thickness of the plate when the current of four frequencies of 50Hz, 100Hz, 500Hz and 1000Hz is respectively passed through the toroidal coil is given. It can be seen that when the material is aluminum plate, the eddy current loss reaches a peak value when the thickness increases to 0.15 times the penetration depth, and then decreases to 0.8 times the penetration depth and tends to be stable. At the same time, as the frequency increases, the peak value of the eddy current loss is higher; and the change of frequency has no much effect on the stable point of the eddy current loss.

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

[0112] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, 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 article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting 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: Solve the vector dynamic potential wave equation in the cylindrical coordinate system and obtain the vector magnetic potential calculation formula; According to the vector magnetic potential calculation formula, the electromagnetic field expression of the space between the circular coil and the metal plate is determined; the circular coil is parallel to the metal plate; According to the electromagnetic field expression of the plane where the circular coil is located, the expression of the induced voltage on the circular coil is obtained; Based on the expression of the induced voltage on the circular coil, the approximate formula for the eddy current loss on the metal plate under the excitation of the parallel circular coil is determined; Obtain status data of the toroidal coil and the metal plate; The state data of the circular ring coil and the metal plate are substituted into the approximate formula of eddy current loss on the metal plate under the excitation of the parallel-placed circular ring coils to obtain the eddy current loss on the metal plate.

2. The method for analyzing eddy current losses on a metal plate under excitation of parallel placed circular coils according to claim 1 is characterized in that: Solve the vector dynamic potential wave equation in the cylindrical coordinate system to obtain the vector magnetic potential calculation formula, which includes: By using the separation of variables method and introducing Hankel transformation, the vector dynamic potential wave equation is solved in the cylindrical coordinate system, and the exact formula of the vector magnetic potential is obtained: in, is the vector magnetic potential, μ0 is the vacuum permeability, a is the radius of the ring coil, I is the time-harmonic current passing through the ring coil, λ is the transverse wave number, τ0 is the longitudinal wave number in the air, J1 is the first-order Bessel function, ρ is the radial distance in the cylindrical coordinate system, z is the height in the cylindrical coordinate system, C is the first intermediate parameter, b is the distance from the center of the ring coil to the metal plate, K is the ratio of the longitudinal wave number in the metal plate to the longitudinal wave number in the air, μ r is the relative magnetic permeability of the metal plate, t is the thickness of the metal plate, and τ is the longitudinal wave number in the metal plate; K = ττ0; m r =mm0; C=[(K+μ r ) 2 -(K-m r ) 2 e -2tτ ] -1 ; Wherein, k is the second intermediate parameter, μ is the magnetic permeability of the metal plate, σ is the electrical conductivity of the metal plate, j is the imaginary part in the complex frequency domain, ω is the angular frequency, ω=2πf, and f is the time-harmonic current frequency on the toroidal coil.

3. The method for analyzing eddy current losses on a metal plate under excitation by parallel placed circular coils according to claim 2 is characterized in that: The electromagnetic field expression is: Among them, E (1) is the electromagnetic field, e φ is 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 excitation of parallel placed circular coils according to claim 3 is characterized in that: According to the electromagnetic field expression of the plane where the toroidal coil is located, the expression of the induced voltage on the toroidal coil is obtained, which specifically includes: According to the electromagnetic field expression of the plane where the single-turn circular coil is located, based on the principle that the induced voltage on the single-turn circular coil is obtained by multiplying the electric field intensity on the plane where the single-turn circular coil is located by the circumference of the single-turn circular coil, the induced voltage expression on the single-turn circular coil is obtained as follows: Wherein, U is the induced voltage on the single-turn toroidal coil; According to the induced voltage expression on a single-turn toroidal coil, based on the superposition principle, the induced voltage expression on a multi-turn toroidal coil is obtained as follows: Among them, U N is the induced voltage on the multi-turn toroidal coil, a m is the radius of the m-th toroidal coil, I m is the time-harmonic current passing through the m-th turn of the toroidal coil, b m is the distance from the center of the m-th toroidal coil to the metal plate, and N is the number of turns of the toroidal coil.

5. The method for analyzing eddy current losses on a metal plate under excitation by parallel placed circular coils according to claim 4 is characterized in that: According to the expression of the induced voltage on the toroidal coil, the approximate formula of eddy current loss on the metal plate under the excitation of the parallel toroidal coil is determined, including: According to the expression of the induced voltage on the single-turn toroidal coil, based on the principle that the total complex power is equal to the induced voltage multiplied by the toroidal coil current and 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 the parallel placed single-turn toroidal coil is determined as: Where P is the eddy current loss on the metal plate under the excitation of the parallel placed single-turn toroidal coil, and Re is the real part; According to the expression of the induced voltage on the multi-turn toroidal coil, based on the principle that the total complex power is equal to the induced voltage multiplied by the toroidal coil current and 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 the parallel multi-turn toroidal coil is determined as: Among them, P N Eddy current losses on a metal plate excited by parallel multi-turn toroidal coils.

6. The method for analyzing eddy current losses on a metal plate under the excitation of parallel placed circular coils according to claim 1, characterized in that: Solve the vector dynamic potential wave equation in the cylindrical coordinate system to obtain the vector magnetic potential calculation formula, which includes: Solving the vector dynamic potential wave equation in the cylindrical coordinate system, the approximate formula of the vector magnetic potential is obtained as follows: in, is the vector magnetic potential, μ0 is the vacuum magnetic permeability, μ r is the relative magnetic permeability of the metal plate, a is the radius of the circular coil, I is the time-harmonic current passing through the circular coil, t is the thickness of the metal plate, τ is the longitudinal wave number in the metal plate, λ is the transverse wave number, τ0 is the longitudinal wave number in the air, J1 is the first-order Bessel function, ρ is the radial distance in the cylindrical coordinate system, z is the height in the cylindrical coordinate system, and b is the distance from the center of the circular coil to the metal plate; m r =μ / μ0; Wherein, k is the first intermediate parameter, μ is the magnetic permeability of the metal plate, σ is the electrical conductivity of the metal plate, j is the imaginary part in the complex frequency domain, ω is the angular frequency, ω=2πf, and f is the time-harmonic current frequency on the toroidal 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) is the electromagnetic field, e φ is 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 excitation of parallel placed circular coils according to claim 7, characterized in that: According to the electromagnetic field expression of the plane where the toroidal coil is located, the expression of the induced voltage on the toroidal coil is obtained, which specifically includes: According to the electromagnetic field expression of the plane where the single-turn circular coil is located, based on the principle that the induced voltage on the single-turn circular coil is obtained by multiplying the electric field intensity on the plane where the single-turn circular coil is located by the circumference of the single-turn circular coil, the induced voltage expression on the single-turn circular coil is obtained as follows: Wherein, U is the induced voltage on the single-turn toroidal coil; According to the induced voltage expression on a single-turn toroidal coil, based on the superposition principle, the induced voltage expression on a multi-turn toroidal coil is obtained as follows: Among them, U N is the induced voltage on the multi-turn toroidal coil, a m is the radius of the m-th toroidal coil, I m is the time-harmonic current passing through the m-th turn of the toroidal coil, b m is the distance from the center of the m-th toroidal coil to the metal plate, and N is the number of turns of the toroidal coil.

9. The method for analyzing eddy current losses on a metal plate under excitation by parallel placed circular coils according to claim 8, characterized in that: According to the expression of the induced voltage on the toroidal coil, the approximate formula of eddy current loss on the metal plate under the excitation of the parallel toroidal coil is determined, including: According to the expression of the induced voltage on the single-turn toroidal coil, based on the principle that the total complex power is equal to the induced voltage multiplied by the toroidal coil current and 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 the parallel placed single-turn toroidal coil is determined as: Where P is the eddy current loss on the metal plate under the excitation of the parallel placed single-turn toroidal coil, and Re is the real part; According to the expression of the induced voltage on the multi-turn toroidal coil, based on the principle that the total complex power is equal to the induced voltage multiplied by the toroidal coil current and 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 the parallel multi-turn toroidal coil is determined as: Among them, P N Eddy current losses on a metal plate excited by parallel multi-turn toroidal coils.

10. The method for analyzing eddy current losses on a metal plate under the excitation of parallel placed circular coils according to claim 1, characterized in that: The status data of the toroidal coil and the metal plate include: the radius of the toroidal coil, the distance from the center of the toroidal coil to the metal plate, the magnetic 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 toroidal coil.

Images