Rectangular coil inductance modeling design method based on improved mirror current method

Abstract

The invention discloses a rectangular coil inductance modeling design method based on an improved mirror current method, and the method specifically comprises the following steps: 1, calculating a coil self-inductance value Lcore and a coil mutual inductance value Mcore under the condition of no magnetic core based on a rectangular coil geometric model; 2, calculating a self-inductance value of the coil with the magnetic core; and 3, calculating the mutual inductance value of the coil with the magnetic core. According to the method, the problem of large inductance error caused by a traditional coil modeling method is solved.

Description

Technical Field

[0001] This invention belongs to the field of wireless power transmission technology and relates to a rectangular coil inductance modeling and design method based on an improved mirror current method. Background Technology

[0002] With the rapid development of wireless power transfer technology in electric vehicles, portable electronic devices, medical devices, and implantable electronic devices, the optimization of the coil's structural design, as a key coupling device in wireless power transfer systems, has become an important way to improve system efficiency. Traditionally, designers typically use finite element analysis (FEA) software to model and optimize coils, but this method is computationally intensive and time-consuming, failing to meet the needs of rapid design iteration.

[0003] Currently, the current-image method is a widely used coil modeling method. However, this method assumes an infinitely large core area and fails to effectively account for the magnetic flux leakage problem caused by the finite size of the core in reality, thus introducing significant inductance calculation errors. In particular, rectangular coil structures are widely used in wireless power transmission systems, and their core size is often comparable to or even smaller than the coil size, resulting in a significant magnetic flux leakage effect. Traditional methods are therefore unable to accurately predict the actual coil inductance value. Summary of the Invention

[0004] The purpose of this invention is to provide a rectangular coil inductance modeling and design method based on an improved mirror current method, which solves the problem of large inductance error caused by traditional coil modeling methods.

[0005] The technical solution adopted in this invention is a rectangular coil inductance modeling and design method based on an improved mirror current method, which specifically includes the following steps:

[0006] Step 1: Calculate the coil self-inductance L under coreless conditions based on the geometric model of the rectangular coil. coreless Mutual inductance value M of the coil coreless ;

[0007] Step 2: Calculate the self-inductance of the coil with the magnetic core;

[0008] Step 3: Calculate the mutual inductance of the coil with magnetic core.

[0009] The invention is further characterized by:

[0010] The specific process of step 1 is as follows:

[0011] Step 1.1: Divide the geometric model of the rectangular coil into several basic unit structures. Each basic unit structure includes several parallel wires. The self-inductance L(l,r) of each wire is... c The result is obtained by the following formula (1):

[0012]

[0013] Where, r c Where is the radius of the conductor, l is the length of the conductor, and μ0 is the relative permeability. In each basic unit structure, the mutual inductance M(l, m, d, Δ) between two parallel conductors is calculated by the following formula (2):

[0014]

[0015] Where α = l + m + Δ, β = l + Δ, γ = m + Δ, m and l are the lengths of the two parallel wires respectively, α, β and γ are intermediate variables respectively, Δ is the distance between the two ends of the parallel wires, and d is the distance between the two parallel conductors;

[0016] Step 1.2: Utilizing the property that magnetic fields can be superimposed, sum the contributions of each wire to the coil's self-inductance to obtain the coil's self-inductance value L under coreless conditions. coreless The self-inductance of the coil L coreless It is calculated using the following formula (3):

[0017] L coreless =L 1a +L 1b +L 2a +L 2b +2M 1a1b +2M 2a2b (3)

[0018] Among them, L 1a L 1b L 2a and L 2b These are the self-inductance values ​​of each basic unit of the coil, M. 1a1b and M 2a2b

[0019] It refers to the mutual inductance between coil sub-sections 1a and 1b, and between 2a and 2b; the mutual inductance M of the coil. coreless As shown in formula (4) below:

[0020]

[0021] Where the subscript of M represents the mutual inductance between corresponding sub-parts, and i and j are the coil sub-part number variables, respectively. ia(j+2)b It is represented as the mutual inductance value between sub-parts ia and (j+2)b.

[0022] The specific process of step 2 is as follows:

[0023] The self-inductance L of a coil with a finite area magnetic core can be calculated using the following formula (5). p :

[0024]

[0025] Among them, L p_coreless M represents the self-inductance of the coil without a magnetic core. LpLni Indicates coil L p The mutual inductance between the i-th turn of the wire in the nth mirror coil; g n_i This is the correction factor for the mirror current.

[0026] In step 2, g n_i The value is calculated using the following formulas (6) and (7):

[0027]

[0028] Where, d sp Indicates the turn spacing, I ni I is the current in the i-th segment of the wire in the n-th mirror coil. p N1 represents the primary coil current, and K represents the number of coil turns. n As an intermediate variable, ΔL fe L represents the distance between the edge of the coil and the edge of the magnetic core. yp d represents the coil length. fe_n W represents the distance W between the nth mirror coil and the surface of the magnetic core. xp This indicates the width of the coil.

[0029] In step 2, g n_i The subscript n indicates the nth mirror image, and the value of K is defined as:

[0030]

[0031] Where μ0 is the relative permeability.

[0032] The specific process of step 3 is as follows: The mutual inductance value M between the coils with the offset lower finite area magnetic core is calculated by the following formula (9):

[0033]

[0034] Among them, S lap M is the area where the primary and secondary coils overlap. LsLp2i-2 Defined as the primary-side mirror coil L p2i-2 and secondary coil L s Mutual intuition between them; M LsLp2i-1 Defined as the primary-side mirror coil L p2i-1 and secondary coil L s The mutual intuition between them. W xs L is the width of the secondary coil. ys Δx is the length of the secondary coil, and Δx is the distance the primary and secondary coils are offset in the x-direction.

[0035] In step 3, I p1 I p2i-2 I p2i-1 It corresponds to coil L p1 L p2i-2 L p2i-1 The mirror current satisfies the following equation (10):

[0036]

[0037] Where N1 represents the number of wires.

[0038] In step 3, K 2n-2 K 2n-1 The following formula (11) is satisfied:

[0039]

[0040] In the above equation, d mir_p2n-2_i d mir_p2n-1_i d mir_p1_i The intermediate variable satisfies the following equation (12):

[0041]

[0042] The distance between the coil and the surface of the magnetic core.

[0043] The beneficial effects of this invention are as follows:

[0044] 1. The influence of core size and coil offset on coil self-inductance and mutual inductance is considered, which improves the accuracy of rectangular coil inductance calculation;

[0045] 2. Applicable to rectangular coils of different sizes and offset states, possessing universality;

[0046] 3. Compared with the traditional current mirror method, it significantly reduces the inductance calculation error. Experiments have verified that the self-inductance error is less than 10% and the mutual inductance error is less than 15%.

[0047] 4. The proposed analytical calculation method for coil self-inductance and mutual inductance facilitates rapid iteration and automatic design of coils, which is beneficial for further improving coil design efficiency and coil performance. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the basic unit structure division of the coil in the coil geometric model designed by the improved rectangular coil inductance modeling design method based on the image current method of this invention;

[0049] Figure 2 This is a schematic diagram of two parallel wires in the rectangular coil inductance modeling and design method based on the improved mirror current method of this invention;

[0050] Figure 3 This is a schematic diagram of the coreless primary and secondary coils in the rectangular coil inductor modeling and design method based on the improved mirror current method of the present invention;

[0051] Figure 4 This is a schematic diagram of the coil cross-section in the rectangular coil inductance modeling and design method based on the improved mirror current method of this invention;

[0052] Figure 5 This is a top view of the coil in the rectangular coil inductance modeling and design method based on the improved mirror current method of this invention;

[0053] Figure 6 This is a mirror diagram of the rectangular coil inductor modeling and design method based on the improved mirror current method of this invention;

[0054] Figure 7 This is a schematic diagram of the coil cross-section in the rectangular coil inductance modeling and design method based on the improved mirror current method of this invention;

[0055] Figure 8(a) is a top view of the offset lower coil in the rectangular coil inductance modeling and design method based on the improved mirror current method of the present invention;

[0056] Figure 8(b) is an offset lower coil side view in the rectangular coil inductance modeling and design method based on the improved mirror current method of the present invention;

[0057] Figure 9 This is a schematic diagram of the coil mirror in the rectangular coil inductance modeling and design method based on the improved mirror current method of this invention;

[0058] Figure 10 This is a comparison chart of the coil length calculation results in the self-inductance simulation and the rectangular coil inductance modeling and design method based on the improved mirror current method of this invention;

[0059] Figure 11 The curves show a comparison between self-inductance simulation and the rectangular coil inductance modeling and design method based on the improved mirror current method of this invention for different coil length parameters.

[0060] Figure 12 This is a comparison chart of the calculation results of offset distance between mutual inductance simulation and the rectangular coil inductance modeling and design method based on the improved mirror current method of this invention;

[0061] Figure 13 This is a comparison chart of the calculation results of coil spacing in mutual inductance simulation and the rectangular coil inductance modeling and design method based on the improved mirror current method of this invention. Detailed Implementation

[0062] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0063] Example 1

[0064] This invention relates to a rectangular coil inductor modeling and design method based on an improved image current method, which specifically includes the following steps:

[0065] Step 1: Calculate the coil self-inductance L under coreless conditions based on the geometric model of the rectangular coil. coreless Mutual inductance value M of the coil coreless ;

[0066] Step 2: Calculate the self-inductance of the coil with magnetic core;

[0067] Step 3: Calculate the mutual inductance of the coil with magnetic core.

[0068] Example 2

[0069] The specific process of step 1 is as follows:

[0070] Step 1.1: Divide the rectangular coil geometric model into several basic unit structures, such as... Figure 1 As shown, it includes four basic unit structures, namely 1a, 1b, 2a, and 2b. Each basic unit structure includes several parallel wires, such as... Figure 1 The wires in the diagram are 1, 2, 3, ..., N1-1, N1, where N1 represents the number of wires, and the self-inductance L(l,r) of each wire is... c The result is obtained by the following formula (1):

[0071]

[0072] Where, r c Where is the radius of the conductor, l is the length of the conductor, and μ0 is the relative permeability. In each basic unit structure, the mutual inductance M(l, m, d, Δ) between two parallel conductors is calculated by the following formula (2):

[0073]

[0074] Where α = l + m + Δ, β = l + Δ, γ = m + Δ, m and l are the lengths of the two parallel wires, α, β and γ are intermediate variables, Δ is the distance between the two ends of the parallel wires, and d is the distance between the two parallel conductors.

[0075] Step 1.2: Utilizing the property that magnetic fields can be superimposed, sum the contributions of each wire to the coil's self-inductance to obtain the coil's self-inductance value L under coreless conditions. coreless The self-inductance of the coil L coreless It is calculated using the following formula (3):

[0076] L coreless =L 1a +L1b +L 2a +L 2b +2M 1a1b +2M 2a2b (3)

[0077] Among them, L 1a L 1b L 2a and L 2b These are the self-inductance values ​​of each basic unit of the coil, M. 1a1b and M 2a2b It refers to the mutual inductance between coil sub-sections 1a and 1b, and between 2a and 2b; the mutual inductance M of the coil. coreless As shown in formula (4) below:

[0078]

[0079] Where the subscript of M represents the mutual inductance between corresponding sub-parts, and i and j are the coil sub-part number variables, respectively. ia(j+2)b The mutual inductance between sub-parts ia and (j+2)b is represented as follows: The mutual inductance between the two coils is as follows: Figure 3 The structure shown is the same as the coil (original coil) located below. Figure 1 The first coil consists of four basic unit structures, namely 1a, 1b, 2a, and 2b; the second coil structure is the same as the first coil structure, but for clarity, the four basic unit structures of the second coil are represented as 3a, 3b, 4a, and 4b.

[0080] Example 3

[0081] The specific process of step 2 is as follows:

[0082] A correction factor for the image current is further introduced based on the traditional image method. A schematic diagram of the coil with a finite-area magnetic core is shown below. Figure 4 ( Figure 4 In the diagram, dfe represents the distance between the coil wire and the surface of the magnetic core, and N... i In this context, 'i' represents the i-th turn of the conductor. Figure 5 As shown in the diagram. A mirror image is shown when solving for the self-inductance of a coil with a finite area magnetic core. Figure 6 As shown ( Figure 6 In the middle, h fe Represents a mirror image diagram, L P The primary coil and its mirror coil are represented by L. P1 L P2 L P3 , ......, L Pn The self-inductance L of a coil with a finite area magnetic core p Calculated using the following formula (5):

[0083]

[0084] Among them, L p_coreless The self-inductance of the coil without a magnetic core is calculated using formula (3); M LpLni

[0085] Indicates coil L p The mutual inductance between the i-th turn of the wire in the nth mirror coil; g n_i The correction factor for the mirror current is related to the core size (ΔL). fe ), Coil size (coil width W) xp Coil length L yp and the distance d between the coil and the surface of the magnetic core. fe Related to, g n_i The value is obtained by fitting simulation data using the following formulas (6) (n=1) and (7) (n>1), and its value is:

[0086]

[0087] Where, d sp Indicates the turn spacing, I ni I is the current in the i-th segment of the wire in the n-th mirror coil. p N1 represents the primary coil current, and K represents the number of coil turns. n As an intermediate variable, ΔL fe This indicates the distance between the edge of the coil and the edge of the magnetic core, such as... Figure 5 As shown, L yp d represents the coil length. fe_n W represents the distance W between the nth mirror coil and the surface of the magnetic core. xp g represents the width of the coil. n_i The subscript n indicates the nth mirror image, and the value of K is defined as:

[0088]

[0089] Where K represents an intermediate variable, and a is an intermediate variable defined as:

[0090]

[0091] Example 4

[0092] Step 3 is as follows: A schematic diagram of the primary and secondary coils with a finite area magnetic core is shown below. Figure 7 As shown, Figure 8(a) is a top view of the offset coupling mechanism (i.e., when the primary and secondary coils are offset); Figure 8(b) is a side view of the offset coupling mechanism; the mutual inductance M between the coils with finite area magnetic cores under offset is calculated by the following formula (10):

[0093]

[0094] Among them, S lap M is the area where the primary and secondary coils overlap. LsLp2i-2 Defined as the primary-side mirror coil L p2i-2 and secondary coil L s Mutual intuition between them; M LsLp2i-1 Defined as the primary-side mirror coil L p2i-1 and secondary coil L s The mutual intuition between them. W xs L is the width of the secondary coil. ys λ is the length of the secondary coil, Δx is the distance the primary and secondary coils are offset in the x-direction, and λ is the distance λ is the distance Δx ... n M represents an intermediate variable. LsLp2i-2 and M LsLp2i-1 The value of M can be obtained using the method described in steps 1 and 2 above for solving the mutual inductance between coreless coils. LsLp For the primary coil L p and secondary coil L s Mutual intuition between them Figure 9 As shown. M LsLp1 Defined as the primary-side mirror coil L p1 and secondary coil L s The mutual inductance between them. When the primary and secondary coils are not of equal size, the coil with the smaller area is selected for mirroring. A schematic diagram of multiple mirrored coils is shown below. Figure 9 As shown, I p1 I p2i-2 I p2i-1 It corresponds to coil L p1 L p2i-2 L p2i-1 The mirror current satisfies the following equation (11):

[0095]

[0096] In the equation, K 2n-2 K 2n-1 satisfy:

[0097]

[0098] In the above equation, d fe_2n-2 d fe_2n-1 d represents the distance d of the nth mirror coil from the surface of the magnetic core. mir_p2n-2_i d mir_p2n-1_i d mir_p1_i The intermediate variable satisfies the following equation (13):

[0099]

[0100] Example 5

[0101] To verify the correctness of the proposed simulation method, simulation and experimental verification were performed. First, simulation verification was conducted, and the comparison between the self-inductance simulation and the theoretical calculation of the method of this invention is shown in the figure below. Figure 10 As shown;

[0102] (a) When the coil width Wxp = 200 mm and the number of coil turns is 5, the comparison curves of self-inductance simulation and theoretical calculation by the method of this invention for different coil length parameters are as follows: Figure 11 As shown;

[0103] (b) When the coil width Wxp = 300 mm and the number of coil turns is 10, the comparison curves of self-inductance simulation and theoretical calculation by the method of the present invention are shown. The error between the self-inductance value calculated by the method of the present invention and the simulation value is within 5%, while the error of the traditional method is greater than 30%, proving that the method of the present invention has high accuracy.

[0104] Example 6

[0105] Comparison and verification between mutual inductance simulation and theoretical calculation of the present invention are as follows: Figure 12 As shown; the primary coil width Wxp = 270mm and the primary coil length L yp =270mm, secondary coil width W xs =220mm and secondary coil length L ys =220mm, with the primary and secondary coil spacing h0 = 50mm, the comparison curves of mutual inductance simulation and theoretical calculation by the method of this invention are shown for different offset distance parameters. The mutual inductance value calculated by the method of this invention has an error of less than 15% compared with the simulation value, while the error of the traditional method is greater than 200%, proving that the method of this invention has high accuracy. Other coil structure parameters involved in the comparison and verification of self-inductance and mutual inductance simulation are shown in Table 1 below:

[0106] Table 1

[0107] symbol value symbol value <![CDATA[u t ]]> 2300 <![CDATA[d sp ]]> 3.3mm <![CDATA[th fe ]]> 5mm <![CDATA[r c ]]> 1.62mm <![CDATA[d fe ]]> 3mm

[0108] To further verify the correctness of the method of this invention, experimental tests were conducted. The coil self-inductance and mutual inductance were both measured using an LCR HIOKI IM3536 bridge instrument. The comparison results of the self-inductance test are shown in Table 2 below:

[0109] Table 2

[0110]

[0111] The table above shows that the error between the self-inductance value theoretically calculated using the method of this invention and the experimentally tested value is within 6%, while the error using the traditional method is greater than 28%, proving that the method of this invention has high accuracy. The comparison results of experimentally tested and theoretically calculated mutual inductance are shown below. Figure 13 The figure shows a comparison curve of the experimentally tested mutual inductance and the theoretically calculated mutual inductance value using the method of this invention at different spacings of the primary and secondary coils. From the above test results, it can be seen that the error between the self-inductance value theoretically calculated using the method of this invention and the experimentally tested value is smaller than that of the traditional method. The mutual inductance calculation error using the method of this invention is within 15%, while the error of the mutual inductance value calculated using the traditional method is over 200%. The coil size and structural parameters involved in the comparison results of the experimentally tested and theoretically calculated mutual inductance are shown in Table 3 below.

[0112] Table 3

[0113]

Claims

1. A rectangular coil inductance modeling and design method based on an improved image current method, characterized in that: Specifically, the steps include the following: Step 1: Calculate the coil self-inductance L under coreless conditions based on the geometric model of the rectangular coil. coreless Mutual inductance value M of the coil coreless ; Step 2: Calculate the self-inductance of the coil with the magnetic core; Step 3: Calculate the mutual inductance of the coil with magnetic core.

2. The rectangular coil inductance modeling and design method based on the improved image current method according to claim 1, characterized in that: The specific process of step 1 is as follows: Step 1.1: Divide the geometric model of the rectangular coil into several basic unit structures. Each basic unit structure includes several parallel wires. The self-inductance L(l,r) of each wire is... c The result is obtained by the following formula (1): Where, r c Where is the radius of the conductor, l is the length of the conductor, and μ0 is the relative permeability. In each basic unit structure, the mutual inductance M(l,m,d,Δ) between two parallel conductors is calculated by the following formula (2): Where α = l + m + Δ, β = l + Δ, γ = m + Δ, m and l are the lengths of the two parallel wires respectively, α, β and γ are intermediate variables respectively, Δ is the distance between the two ends of the parallel wires, and d is the distance between the two parallel conductors; Step 1.2: Utilizing the property that magnetic fields can be superimposed, sum the contributions of each wire to the coil's self-inductance to obtain the coil's self-inductance value L under coreless conditions. coreless The coil's self-inductance value L coreless It is calculated using the following formula (3): L coreless =L 1a +L 1b +L 2a +L 2b +2M 1a1b +2M 2a2b (3) Among them, L 1a L 1b L 2a and L 2b These are the self-inductance values ​​of each basic unit of the coil, M. 1a1b and M 2a2b It refers to the mutual inductance between coil sub-sections 1a and 1b, and between 2a and 2b; the mutual inductance M of the coil. coreless As shown in formula (4) below: Where the subscript of M represents the mutual inductance between corresponding sub-parts, and i and j are the coil sub-part number variables, respectively. ia(j+2)b It is represented as the mutual inductance value between sub-parts ia and (j+2)b.

3. The rectangular coil inductance modeling and design method based on the improved image current method according to claim 2, characterized in that: The specific process of step 2 is as follows: The self-inductance L of a coil with a finite area magnetic core can be calculated using the following formula (5). p : Among them, L p_coreless M represents the self-inductance of the coil without a magnetic core. LpLni Indicates coil L p The mutual inductance between the i-th turn of the wire in the nth mirror coil; g n_i This is the correction factor for the mirror current.

4. The rectangular coil inductance modeling and design method based on the improved image current method according to claim 3, characterized in that: In step 2, g n_i The value is calculated using the following formulas (6) and (7): Where, d sp Indicates the turn spacing, I ni I is the current in the i-th segment of the wire in the n-th mirror coil. p N1 represents the primary coil current, and K represents the number of coil turns. n As an intermediate variable, ΔL fe L represents the distance between the edge of the coil and the edge of the magnetic core. yp d represents the coil length. fe_n W represents the distance W between the nth mirror coil and the surface of the magnetic core. xp This indicates the width of the coil.

5. The rectangular coil inductance modeling and design method based on the improved image current method according to claim 3, characterized in that: In step 2, g n_i The subscript n indicates the nth mirror image, and the value of K is defined as: Where μ0 is the relative permeability.

6. The rectangular coil inductance modeling and design method based on the improved image current method according to claim 3, characterized in that: The specific process of step 3 is as follows: the mutual inductance value M between the coils with the offset lower finite area magnetic core is calculated by the following formula (9): Among them, S lap M is the area where the primary and secondary coils overlap. LsLp2i-2 Defined as the primary-side mirror coil L p2i-2 and secondary coil L s Mutual intuition between them; M LsLp2i-1 Defined as the primary-side mirror coil L p2i-1 and secondary coil L s Mutual intuition between them, W xs L is the width of the secondary coil. ys Δx is the length of the secondary coil, and Δx is the distance the primary and secondary coils are offset in the x-direction.

7. The rectangular coil inductance modeling and design method based on the improved image current method according to claim 6, characterized in that: In step 3, I p1 I p2i-2 I p2i-1 It corresponds to coil L p1 L p2i-2 L p2i-1 The mirror current satisfies the following equation (10): Where N1 represents the number of wires.

8. The rectangular coil inductance modeling and design method based on the improved image current method according to claim 7, characterized in that: In step 3, K 2n-2 K 2n-1 It satisfies the following formula (11): In the above equation, d mir_p2n-2_i d mir_p2n-1_i d mir_p1_i The intermediate variable satisfies the following equation (12): The distance between the coil and the surface of the magnetic core.

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